An Analysis of the Relationships Between Soil Moisture,
Rainfall, and Boundary Layer Conditions, Based on Direct
Observations from Illinois
by
Kirsten L. Findell
B.S.E., Princeton University (1992)
Submitted to the Department of Civil and Environmental Engineering in
partial fulfillment of the requirements for the degree of
Master of Science in Civil and Environmental Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 1997
© Massachusetts Institute of Technology 1997. All rights reserved.
Signature of Author: ................................... ...................
Department of Civil and Environmental Engineering
SMay 23, 1997
Certified by: ....
Elfatih A. B. Eltahir
Assistant Professor
n Thesis Supervisor
Accepted by: ................................
---
I
Joseph M. Sussman
Chair, Departmental Committee on Graduate Studies
...........
OF- TEC2* *I..
JUN 2 41997
.
Eng.
An Analysis of the Relationships Between Soil Moisture,
Rainfall, and Boundary Layer Conditions, Based on Direct
Observations from Illinois
by
Kirsten L. Findell
B.S.E., Princeton University (1992)
Submitted to the Department of Civil and Environmental Engineering
on May 23, 1997 in partial fulfillment of the
requirements for the degree of
Master of Science in Civil and Environmental Engineering
Abstract
This study of the soil moisture-rainfall feedback uses a dataset beginning in 1981 of biweekly neutron probe measurements of soil moisture at up to 19 stations in Illinois to show that
soil moisture can play a significant role in maintaining drought or flood conditions during the
summer. Results of a linear correlation analysis between initial soil saturation and rainfall in the
subsequent three weeks showed that a positive correlation between these two variables is present
from early June through mid-August. This correlation is more significant than the serial
correlation within precipitation time series, suggesting the likelihood of a physical mechanism
linking soil moisture to subsequent rainfall.
This result prompted further investigation into the nature of such a physical pathway
linking soil moisture to subsequent rainfall. Near-surface hourly observations of pressure, P,
temperature, T, wet-bulb temperature, T., and relative humidity,f, from 13 stations in and close
to Illinois were used in these analyses. From each hourly set of direct observations of P, T, Tw,
andf, wet-bulb depression, Tdpr, temperature of the lifting condensation level (LCL), TLCL,
pressure depth to the LCL, PLCL-P,, mixing ratio, w,potential temperature, 0, virtual potential
temperature, 60, wet-bulb potential temperature, 9, and equivalent potential temperature, OE were
computed. Time series of the spatial average of each of these quantities were then calculated by
averaging data from the 13 stations at each hour.
An analysis of the connections between an average soil saturation time series for the whole
state of Illinois with these state-wide average boundary layer conditions did not yield the
anticipated positive correlation between soil moisture and moist static energy, as quantified by Tw,
0., or OE. It is not clear if this is due to limitations of the data or of the theory. There was
evidence, however, that moisture availability (or lack thereof) at the surface has a very strong
impact on the wet-bulb depression of near-surface air, particularly from mid-May through the end
of August, showing good correspondence to the period of significant soil moisture-rainfall
association.
The final set of analyses performed included an investigation of hourly boundary layer and
rainfall data. Data from the 82 hourly rainfall stations were averaged to compare state-wide
hourly rainfall to state-wide hourly boundary layer conditions. A link between high MSE and high
rainfall was noted for much of the range of MSE during the summer months, and a link between
low Tdpr and high rainfall was evident for all of the months analyzed (April through September).
These analyses, then, suggest that the significant but weak correlation between soil moisture and
rainfall during Illinois summers is due not to soil moisture controls on the boundary layer entropy,
but rather to soil moisture controls on the wet-bulb depression of near-surface air.
Thesis Supervisor: Elfatih A. B. Eltahir
Title: Assistant Professor of Civil and Environmental Engineering
Acknowledgments
There are many individuals who have contributed in countless ways to my academic and
personal growth since I've been at MIT. Thanks are due to my advisor, Elfatih Eltahir, both for
his guidance and feedback on this work, and for his willingness to welcome me into his researchl
group. I am forever grateful to Dennis McLaughlin for his enormous patience with me when I
was blindly searching for the research discipline that was right for me. His advice, support and
understanding are still appreciated more than he can know.
Many people at the Parsons Lab have helped to make this place a warm and welcoming
second home, but a few people deserve special recognition for their companionship and laughter.
Jeremy Pal, for all the soil moisture conversations, for his insights and theories on human nature,
and, of course, for his computer expertise. Sanjay Pahuja for the plants, the stories, the yoga, the
bibliography, and for his ability to find the beauty in everything. Pat Dixon for her warmth and
caring, and for sharing a bit of herself with me. Sheila Frankel for taking care of the lab and for
getting computers in our offices. Cynthia Stewart for making sure that sanity comes before
deadlines. Lynn Reid for her tough big-sisterly love. Tom Ravens, David Senn, Julie Kiang, John
MacFarland, Ida Primus, and Guiling Wang for making me smile every time I see them. And, of
course, Freddi-Jo Eisenberg for being my biographer and soul-mate.
Thanks also go to John Hansman for the runs, swims, and conversations: he has helped
diffuse many headaches and frustrations; to Laura and Hans Indigo for their friendship and
support, and for helping to give me a life outside of MIT; to Miriam Bowling for laughing with
me and helping me keep things in perspective; to my amazing sister Leanne for always believing in
me and knowing just when to tell me so; to my brother Kent and my mother Carol for the open'
doors whenever I need an escape from the city; to my father George for his belief that I can do
anything I want to do; to my house mates Becky Frank and Susan Kaplan for helping to make our
house a home; and especially to my yoga teachers extraordinaire, Gurucharan Singh Khalsa and
Hari Kaur Frank for helping me take care of myself and always encouraging me to keep up!
Steven Hollinger, Randy Peppler, Tami Creech, and Jim Angel of the Illinois State Water
Survey were kind enough to contribute their soil moisture and precipitation data to this study.
Special thanks go to Jim Angel for responding to my last-minute request for digital information on
the Illinois state line.
Much appreciation also goes to the National Science Foundation for supporting me with a
Graduate Student Fellowship.
Table of Contents
Chapter1: Introduction................................................ .......................................................
Chapter2: The Role of Soil Moisture in the Climate System...............................
9
..... 12
A. Background and Theory ......................................................................................
12
B. Previous Data Analyses ........................................................................................ 17
C. GCM Results ............................................................................................................
22
D. Results of Regional Climate Studies ......................................................................
24
Chapter3: The RelationshipsBetween Soil Saturationand Subsequent Rainfall...................28
A. Soil Moisture Data ............................................................................................ .28
B. Daily Precipitation Data .........................................................................................
34
C. Results and Discussion: The Interplay Between Soil Saturation and Subsequent
Precipitation Throughout the Year ................................................. 35
D. Results and Discussion: Focus on Spring and Summer Connections ................ 42
E. Discussion of Results ...................................................
46
Chapter4: The RelationshipsBetween Soil Saturationand Boundary Layer Conditions.......48
A. The NCDC Surface Airways Hourly Dataset................................
..............
48
B. Presentation of Results ............................................................................................ 50
C. Analysis of Initial Soil Saturation Followed by 21-Day Average of Boundary
52
Layer Conditions, Averaged Over All of Illinois ........................................................
D. Analysis of the Linear Correlation Between Soil Saturation and Subsequent
Boundary Layer Conditions Throughout the Year...................................
... 79
E. Discussion of Results ............................................................................................ 87
Chapter5: The RelationshipsBetween Boundary Layer Conditionsand Rainfall................. :90
A. The EarthInfo NCDC Hourly Rainfall Database...................................................90
B. The Diurnal Cycle of Rainfall in Illinois.
............................
90
C. Analysis of Afternoon Storm Events and the Preceding Boundary Layer
Conditions ..........................
.................................................................... 97
D. Discussion of Results ..........................................
Chapter6: Conclusionsand Future Research....................................................................
References .....................................................................
132
136
141........
List of Figures
Figure 3.1: Locations of Illinois State Water Survey (ISWS) soil moisture stations and rainfall
stations. Solid line is the Illinois state boundary ...........................................
.........
29
Figure 3.2: Annual average of soil saturation cycles for each year, 1981-1994. Dashed line is
1988 (extreme drought); solid line is 1993 (extreme flood); all other years are drawn with
dotted lines; thick dotted line is average of all 14 years; a) top 10 cm, b) top 30 cm, c) top
50 cm, d) top 70 cm, e) top 90 cm, f) top 1.1 m. ......................................
..... 32
Figure 3.3: Seasonal average soil saturation profiles: a) December-February (DJF), b) MarchMay (MAM), c) June-August (JJA), d) September-November (SON). Left-most solid line
is 1988 (extreme drought); right-most solid line is 1993 (extreme flood); all other years
are drawn with dotted lines; dashed line is average of all 14 years..............................
34
Figure 3.4: Average total monthly precipitation over Illinois, 1981-1994. Stars indicate means of
the 14 years; lines extend to plus or minus one standard deviation. .............................. 35
Figure 3.5: Linear correlation between initial soil saturation and precipitation in the subsequent
21 days for a) top 10 cm, b) top 50 cm, and c) top 90 cm. Solid line is 21-day moving
average. Level of significance lines refer to the daily values (not the smoothed line).......37
Figure 3.6: Linear correlation between adjacent 21-day precipitation windows; 21-day
smoothing. Solid line is 21-day moving average. Level of significance lines refer to the
daily values (not the smoothed line).................................................
38
Figure 3.7: Linear correlation between 21-day total precipitation and soil saturation at the end of
the 21 days for a) top 10 cm, b) top 50 cm, and c) top 90 cm. Solid line is 21-day moving
average. Level of significance lines refer to the daily values .....................................
40
Figure 3.8: Comparison of smoothed lines of the linear correlation between adjacent precipitation
windows (solid line from Figure 3.6) and of the linear correlation between soil saturation
and subsequent precipitation (dashed lines from Figures 3.5a-c). ................................ 41
Figure 3.9: Linear correlation between initial soil saturation and precipitation in the rest of the
summer (through August 23) for a) top 10 cm, b) top 50 cm, and c) top 90 cm. Solid line
is 21-day moving average. Level of significance lines refer to the daily values (not the
smoothed lines) ......................................................... .............................................. 43
Figure 3.10: Linear correlation between initial soil saturation and precipitation in the rest of the
summer (through September 19) for a) top 10 cm, b) top 30 cm, and c) top 90 cm. Solid
line is 21-day moving average. Level of significance lines refer to the daily values (not the
smoothed lines)....................................................................................................... 44
Figure 3.11: Average Initial soil saturation on June 25 for a given year versus summer (July 1 to
August 23) precipitation for each year. Numbers beside each data point indicate sample
year. Dotted lines are means of the 14 years ± one standard deviation, separating data into
low, normal, and high categories of soil saturation and summer precipitation .............. 45
Figure 4.1: Locations of ISWS soil moisture stations and NCDC Surface Airways Hourly Dataset
stations. Solid line is the Illinois state boundary .......................................
..... 49
Figure 4.2: Soil saturation (SS) and maximum daily temperature (7) for days during July, during
the years 1981 to 1995; a) scatter plot of all data pairs; b) probability density functions
(PDFs) for three subsets of the data based on the degree of soil saturation; c) first
moments of the PDFs in 4.2b; d) cumulative distribution functions (CDFs) for the PDFs in
4.2b ............................................................................................................................ 50
Figure 4.3: First moments and Cumulative Distribution Functions (CDFs) of 21-day mean of
maximum relative humidity (f), given that soil saturation (SS) on the day prior to the
averaging window is low, medium, or high. Note that April, May and September plots are
on one scale, while June, July and August plots are on a different scale: a) April, b) May,
c) June, d) July, e) August, f) September ................................................. 54
Figure 4.4: As in Figure 4.3, but for mixing ratio (w); a) April, b) May, c) June, d) July, e)
August, f) September. .................................................... ........................................... 57
Figure 4.5: As for Figure 4.3 but for air temperature (T); a) April, b) May, c) June, d) July, e)
August, f) September. .................................................... ........................................... 59
Figure 4.6: As for Figure 4.3 but for wet-bulb temperature (Tw); a) April, b) May, c) June, d)
July, e) August, f) September ........................................................ 63
Figure 4.7: As for Figure 4.3 but for wet-bulb depression (Tdp,); a) April, b) May, c) June, d)
July, e) August, f) September ........................................................ 66
Figure 4.8: As for Figure 4.3 but for temperature of the lifting condensation level (TIc 1); a) April,
b) May, c) June, d) July, e) August, f) September ............................................ 69
Figure 4.9: As for Figure 4.3 but for pressure depth to the lifting condensation level (P1,c- P,); a)
April, b) May, c) June, d) July, e) August, f) September ........................................ 72
Figure 4.10: As for Figure 4.3 but for equivalent potential temperature (OE); a) April, b) May, c)
June, d) July, e) August, f) September ................................................................ ......... 75
Figure 4.11: As for Figure 4.3 but for wet-bulb potential temperature (0w); a) April, b) May, c)
June, d) July, e) August, f) September .................................................. 77
Figure 4.12: Linear correlation between initial soil saturation (SS) and average (a) minimum
daily, (b) mean daily, and (c) maximum daily relative humidity (f) in the subsequent 21 '
days, as measured by the coefficient of determination ( 2). Solid line is 21 day moving
average. "LOS" lines are 5 and 10% level of significance lines for the r2 variable (not the
smoothed line). .......................................................... ............................................... 81
Figure 4.13: As for Figure 4.12, but for wet-bulb depression (Tdr). ..........................................
82
Figure 4.14: As for Figure 4.12c but for maximum daily mixing ratio (w).............................. 83
Figure 4.15: As for Figure 4.12c but for maximum daily air temperature (7) ........................... 83
Figure 4.16: As for Figure 4.12c but for maximum daily wet-bulb temperature (Tw). ............... 83
Figure 4.17: As for Figure 4.12c but for maximum daily temperature of the lifting condensation
level (TLCL) .......................................
........................................................................
84
Figure 4.18: As for Figure 4.12c but for maximum daily pressure depth to the lifting condensation
............... 84
level (PL L - Ps) .............................................................................................
Figure 4.19: As for Figure 4.12c but for maximum daily equivalent potential temperature (OE)...85
Figure 4.20: As for Figure 4.12c but for maximum daily wet-bulb potential temperature (w).....85
Figure 4.21: As for Figure 4.12c but for initial soil saturation in the top 50 cm and average
maximum daily wet-bulb depression (Td,,) in the subsequent 21 days ...........................
86
Figure 4.22: As for Figure 4.12c but for initial soil saturation in the top 90 cm and average
maximum daily wet-bulb depression (Td,,) in the subsequent 21 days .........................
86
Figure 5.1: Locations of the NCDC Hourly Rainfall Stations (*) and the NCDC Surface Airways
Stations (o). Solid line is the Illinois state boundary...............................
..... 91
Figure 5.2: The diurnal cycle of rainfall depth, storm duration, and probability of initiation for
April and May; June and July; August and September..................................94
Figure 5.3: Correlations between hourly pressure (P)and rainfall during April and May; June and
July; August and September..........................................................................................
98
Figure 5.4: Correlations between hourly relative humidity (f)and rainfall during April and May;
June and July; August and September ...............................
102
Figure 5.5: Correlations between hourly mixing ratio (w)and subsequent rainfall during April and
May; June and July; August and September .....................................
105
Figure 5.6: Correlations between hourly wet-bulb temperature (Tw) and rainfall during April and
May; June and July; August and September ............................
111
Figure 5.7: Correlations between hourly wet-bulb potential temperature (G0) and subsequent
rainfall during April and May; June and July; August and September ........................ 114
Figure 5.8: Correlations between hourly wet-bulb depression (Tdp,,) and subsequent rainfall
during April and May; June and July; August and September............................
117
Figure 5.9: Correlations between hourly temperature of the lifting condensation level (TLcL) and
subsequent rainfall during April and May; June and July; August and September. ......... 120
Figure 5.10: Correlations between hourly pressure depth to the LCL (P~L - P,) and rainfall
during April and May; June and July; August and September...........................
123
Figure 5.11: Correlations between hourly equivalent potential temperature (OE) and rainfall
during April and May; June and July; August and September............................
126
Figure 5.12: Correlations between hourly air temperature (7) and subsequent rainfall during April
and May; June and July; August and September. ....................................
129
Chapter 1: Introduction
It has long been recognized that soil moisture plays an important role in regional climate
systems through its effect on the partitioning between sensible and latent heat fluxes and on the
albedo of the surface. Early work by Namias (1952, 1960, 1962) showed that spring precipitation
and soil moisture can impact summer precipitation in the interiors of continents. More recently,
many researchers have noted the negative correlation between soil moisture states and mean and
maximum temperatures (Karl, 1986; Georgakakos et al., 1995; Huang et al., 1996), and stressed
the potential increase in surface heating and decrease in local evaporative contributions to
atmospheric humidity that anomalously low soil moisture states can affect (Rind, 1982; Trenberth,
1988; Oglesby, 1991). Recent work by Williams and Renno (1993) and Eltahir and Pal (1996)
suggests a link between rainfall and surface wet bulb temperature during convective rainfall
storms in the tropics. Wet bulb temperature is an indicator of surface conditions, including,
among other variables, soil moisture. Afternoon storms during the summer months in the
Midwestern United States are thought to be of a similar convective nature as tropical storms. As
stated in early work by Carlson and Ludlam (1966), during the summer "the tropical
cumulonimbus convection and its own nearly-neutral stratification tend to advance into higher
latitudes."
Many recent studies involving General Circulation Models (GCMs) have offered support
to Namias' hypothesis, showing that changes in the soil moisture regime at the end of
spring/beginning of summer can significantly impact summer precipitation over continental land
masses (Shukla and Mintz, 1982; Rowntree and Bolton, 1983; Rind, 1982; Yeh et al., 1984;
Oglesby and Erickson, 1989; Oglesby, 1991; Fennessy and Shukla, 1996). These GCMs,
however, have all been rather broad-brush, making global or continental-scale soil moisture
changes. Regional climate studies (Pan et al., 1995; Georgakakos et al., 1995; Huang et al.,
1996; Pal and Eltahir, 1997, for example) have also been used to test this hypothesis regarding the
feedback from soil moisture to the atmosphere. The FIFE experiment in Kansas provided some
short-term real data with which to test the soil moisture-rainfall feedback. Both Betts et al.
(1996) and Eltahir (1997) find a positive feedback relationship between soil moisture and
boundary layer conditions. However, due to a lack of adequate long-term data on soil moisture,
no models have been tested against any directly observed, long-term soil moisture data sets.
This study attempts to fill this gap by analyzing the relationship between precipitation and
soil moisture using the Illinois Climate Network (ICN) data set: a record of soil moisture values
measured bi-weekly at 19 stations across the state of Illinois since 1981 (Hollinger and Isard,
1994). Though this data set is somewhat limited in both temporal and spatial extent, it is the
largest available data set of its kind and its analysis should prove worthwhile. If, as many GCM
and regional studies results suggest, spring soil moisture does indeed affect summer precipitation,
the data should support this hypothesis.
To make this data analysis comparable to modeling studies, the framework for the analysis
is posed as an initial value problem. We are interested in how precipitation responds to an initial
soil moisture condition. In contrast to a computer model, it is difficult to isolate these two
variables when dealing with real data. Nevertheless, the 14 years of data (1981-1994) are more
than has previously been available for this kind of analysis, and could provide some insight into
the coupled land-atmosphere system. Furthermore, this analysis, based on actual observations,
should provide a testing framework for future numerical experiments involving soil water and
precipitation.
After a more detailed discussion of the literature on these processes and on previous data ,
analyses and modeling experiments, this hypothesis will be tested in Chapter 3 by analyzing 14
years of data on soil moisture and subsequent rainfall in Illinois. As predicted by the theory
herein, a positive but weak correlation was found during the summer months. This correlation'
prompted the investigation of the correlations between soil moisture and subsequent boundary
layer conditions in Chapter 4, where we expected to see evidence of increased soil moisture being
followed by increase BLE. This expectation was not met. It is not clear if this is due to
limitations of the data or of the theory. Though this soil moisture-BLE link was not observed,
there was evidence that high soil moisture is likely to be followed by low wet-bulb depression,
Tdpr,
particularly during the summer.
The next phase of analyses, presented in Chapter 5,focused on the link between boundary
layer conditions and rainfall using hourly data. Indeed, a link between high MSE and high rainfall
was noted for much of the range of MSE during the summer months, and a link between low Tdpr
and high rainfall was evident for all of the months analyzed (April through September). These
analyses, then, suggest that the significant but weak correlation between soil moisture and rainfall
during Illinois summers is due not to soil moisture controls on the boundary layer entropy, but
rather to soil moisture controls on the wet-bulb depression of near-surface air.
Chapter 2: The Role of Soil Moisture in the Climate
System
A.
Background and Theory
Atmospheric dynamics over oceans are quite different from those over land. Water has a
much larger heat capacity than soil, and the oceans act as a reservoir for heat and energy. As a
result, the diurnal temperature fluctuations that can be enormous over dry land masses like deserts
are reduced to just a few degrees over oceans. Similarly, seasonal shifts in mean temperature are
much reduced over oceans as compared to lands.
Evaporative processes at the surface of oceans are also quite different from those over
land. Evaporation occurs when three things are available: 1) moisture, 2) energy to convert liquid
water to water vapor, and 3) a transport mechanism to carry saturated air away from the moisture
source. Over open water, moisture is never in short supply, while over land it can often be the
limitation on evaporation. When evaporation is limited, regardless of the controlling mechanism,
incoming energy is dissipated by the less efficient mechanism of sensible heat flux, which leads to
a rise in air temperature. Indeed, it is this difference between the oceanic and land surface ratios
of sensible to latent (evaporative) heat flux which is responsible for the larger temperature
fluctuations over land. Parched ground has no moisture available for evaporation, so all of the
available energy goes to sensible heating of the air, and the air temperature quickly rises. Over a
body of water, on the other extreme, evaporation, E, occurs at the potential rate (a function of the
other two limiting factors, energy and transport mechanisms), and much less energy is available
for sensible heat transfer.
The amount of moisture in the soil controls where the energy balance of the surface lies in
relation to these desert and ocean extremes. This is quantified by the Bowen ratio, P, which is
defined as the ratio of sensible heat flux, H, to latent heat flux, AE, where Ais the latent heat of
vaporization. Both terms have units of energy flux (W/m 2 in S.I. units). Typical values of 3 are
on the order of 0.07 over open oceans, where the sea surface temperature responds little to the
diurnal cycle of solar forcing (Betts et al., 1996), to many hundreds over dry land surfaces, where
all of the energy transfer occurs as sensible heating (e.g. dry lake bed example in Wallace and
Hobbs, 1977, p. 345). During the night over land, both H and AE are very small because the land
responds quite quickly to the disappearance of solar forcing. The sensible heat flux is often
directed downward at night when a temperature inversion is present, so the Bowen ratio may be
negative in sign.
The comparison of land surface and oceanic controls on atmospheric dynamics is an
extreme example of the potential role that soil moisture could play in effecting local weather and
climate. An increase in soil moisture increases the heat capacity and thermal conductivity of the
land surface, thereby increasing its thermal stability (McCorcle, 1988). Furthermore, if water
availability is the limitation on evaporative exchange, then an increase in soil moisture would
allow for an increase in the production of latent heat and a decrease in the production of sensible
heat. This mechanism is important in dry to normal conditions, but above some threshold of
moisture availability, energy input or transport of saturated air away from the moisture source
become the controlling factors on evaporation. Increasing soil moisture beyond this point will not
affect the Bowen ratio. Since this threshold moisture level is variable due to the variability of
winds (the transport mechanism) and incoming solar radiation (the energy source), it generally
appears in data only as decreased sensitivity, rather than a clear cut-off level, of the Bowen ratio
to moisture availability at high moisture contents.
Another important aspect of the influence of soil moisture on land-atmosphere interactions
are the time scales of the many components of the land-atmosphere system. Because the thermal
mass of water is so large, oceans respond slowly-with lags on the order of a season-to changes in
radiative or other forcing, and they only respond to the low frequency variability. Similarly, soil
moisture acts like a reservoir of water which damps out high frequency fluctuations and increases
the memory of the land surface system (Entekhabi et al., 1996). This memory bank is an
important aspect of the feedback loop between the land surface and the atmosphere.
Theories abound on the role that soil moisture plays in the moisture and energy budgets of
the boundary layer (e.g., Betts et al., 1996; Entekhabi et al., 1996; Eltahir, 1997). They all agree
that soil moisture is an important component of the system, but there is disagreement on the
relative strengths of the many different ways which soil moisture can effect the boundary layer.
These differences will be discussed in the next section. In this section, we will simply sketch the
broad outline of the soil moisture-rainfall feedback.
When a stove-top pot is heated from below, energy is added to the lowest levels of the
fluid. This begins to generate turbulence and turbulent heat flux away from the heat source, and
to create an instability where relatively cold, dense, low energy fluids are overlying relatively
warm, less dense, high energy fluids. Turbulence acts to mix these fluids and create uniform
profiles of temperature and energy throughout the range of the turbulent activity. As more heat is
added to the system, the strength of the turbulence grows and the depth of the mixed layer grows
until the whole pot is boiling and well mixed.
Since the atmosphere is largely transparent to solar radiation, the main heat source for
tropospheric air is the land surface. The system acts much like a pot on a stove, with the added
complication of the heat associated with phase changes of water (heat is consumed by evaporation
and released by condensation). During the day, the temperature of the land surface increases in
response to solar forcing, and the corresponding flux of terrestrial radiation increases (this flux is
proportional to the fourth power of ground temperature). Net radiation at the surface, R,, is the
sum of incoming short wave solar radiation, outgoing long wave terrestrial radiation (negative in
sign), and incoming long wave radiation returned to the surface by backscattering off of molecules
in the atmosphere, particularly condensed water in clouds. Some of this net radiation is consumed
as heat flux into the ground, G, (usually on the order of 15% or less, [Betts et al., 1996]). The
remainder, and typically the greater percentage, of R,, is transferred to the air, partly as sensible
heat, and partly as latent heat: R,et - G = H + AE. Both the turbulent sensible and latent heat
fluxes increase the moist static energy (MSE) of the boundary layer (Betts et al., 1996; Carlson
and Ludlam, 1966), and mix the lower levels of troposphere so that quantities like mixing ratio
and potential temperature are nearly constant throughout this mixed layer. MSE is very closely
related to the entropy variable equivalent potential temperature, OE (Emanuel, 1994), and the
terms moist static energy and boundary layer entropy (BLE) are used almost interchangeably.
Temperature, T, is not constant in the mixed layer because the pressure, P, decreases nearly
hydrostatically with increasing height. Potential temperature, 0, accounts for the P dependence of
T: it is defined as the temperature a parcel of air would acquire if it were taken dry adiabatically to
1000 mb. Convection begins when turbulence is strong enough to bring parcels of air from low
levels up past their level of free convection (LFC), where they are neutrally buoyant with respect
to environmental air. Above the LFC, a parcel is positively buoyant and will rise freely until it
reaches the level of neutral buoyancy (LNB), cooling and, after reaching saturation, condensing
out water vapor as it goes. Initial saturation occurs at the lifting condensation level (LCL), which
is often below the LFC. The LCL is usually the cloud base level, while the LNB is approximately
the cloud top. If convection is strong enough, and if enough vapor condenses out, precipitation
occurs. Since the primary energy source for the boundary layer growth described here is surface
fluxes, which are forced by incoming solar radiation, the convective boundary layer is only present
during daylight hours (Wallace and Hobbs, 1977).
Soil moisture plays a role in this process by its effect on the Bowen ratio: i.e., by its effect
on the partitioning of sensible and latent heat fluxes. Sensible heat flux is largely responsible for
the turbulent mixing of near-surface air, so when sensible heat flux increases the boundary layer
grows more rapidly. Since the increase of the moist static energy (MSE) in this mixed layer is
proportional to the sum of the latent and sensible heat fluxes, the contribution of MSE from the
land surface is not dependent on the Bowen ratio. For a given amount of available energy, R,t G, a larger Bowen ratio means more sensible heating of the air, a deeper boundary layer, and
therefore, less MSE per unit depth. Wet soils should lead to a smaller Bowen ratio and, by the
same reasoning, more MSE per unit depth.
An additional level of complexity in this soil moisture-moist static energy relationship is
suggested by Eltahir (1997). Since soil moisture affects the albedo, x,of the surface, for a given
level of incoming solar radiation, wet soils will decrease the surface albedo, thereby increasing the
solar radiation at the surface (R,,,so,,ar = (1-a)Rincoming oar). By decreasing the air temperature,
wet soils decrease the outgoing terrestrial radiation. In addition, wet soils should lead to
increased water vapor content of the air, so more of this terrestrial radiation should be scattered
back towards the surface (greenhouse effect). Each of these three factors, increased Rner, solar,
decreased Rooing terre,,strial, and increased Rincong terrestrial, leads to an increase in net radiation: Ret, =
Rnet, so,ar - Rougoing terrestrial + Rmncoming terrestrial. Wet soils, then, should not only increase the moist
static energy per unit depth of boundary layer by their impact on the boundary layer depth, they
should also increase the contribution of moist static energy from the surface fluxes of sensible and
latent heat by increasing net radiation at the surface.
This basic sketch of the processes leading to convective rainfall suggests that increased
soil moisture should lead to increased moist static energy in the mixed layer, which should then
lead to increased precipitation. However, the style of convection outlined here is not the only
mechanism of rainfall production, particularly in the mid-latitudes. In much of the tropics, local
convection is responsible for the majority of rainfall throughout the year. In mid-latitudes, on the
other hand, synoptic systems play a highly significant part in rainfall production, particularly
during the winter. The convective rainfall discussed here is expected to be important in midlatitude regimes, such as the state of Illinois, only during the summer months. Even in the midlatitude summers, the impact of soil moisture anomalies is reduced when synoptic winds are
strong (Carlson and Ludlam, 1966; Entekhabi et al., 1996).
B.
Previous Data Analyses
The works of Eltahir (1997), Entekhabi et al. (1996), Betts et al. (1996), Betts and Ball
(1995), Williams and Renno (1993), and Carlson and Ludlam (1966), among others, have
contributed greatly to the theoretical understanding of the soil moisture-rainfall feedback. Some
of the details of these studies will be discussed here.
As discussed above, the partitioning of available surface energy has many effects on the
mixed layer. Dry soil leads to increased sensible heating, which leads to increased air
temperatures and greater parcel buoyancy. This increases the depth of the boundary layer, and
parcels must rise higher before reaching saturation at their Lifting Condensation Level (LCL). In
addition, the turbulent energy associated with the parcel is increased, so there is more entrainment
of air from above the mixed layer. This overlying air tends to have lower entropy, so, as pointed
out by Betts et al. (1996), greater turbulence leads to reduction of the rate of entropy increase of
the mixed layer. Carlson and Ludlam (1966) highlight the difference the depth of the mixed layer
has on the wet-bulb potential temperature, 0w, of the layer. The 0, increases during the normal
course of the morning and afternoon through both the increased air temperature from sensible
heating and the increased water vapor content from evaporation of water from the land surface.
When the ground is dry, the available surface energy, Re,t - G, goes into warming and humidifying
a deeper boundary layer. The increase of 08, then, is reduced over dry areas as compared to wet
areas. Over moist areas, 60 in a convective layer about 150 mb deep rises by about 2.5 °C per
day; over arid regions, the convective layer is usually on the order of 400 to 500 mb deep, and the
average daily rise in ,, is on the order of only 0.5 *C per day (Carlson and Ludlam, 1966).
The wet-bulb potential temperature is an important measure which is closely related to
convection and precipitation: it is conserved in pseudo-adiabatic transformations, and it defines
the path of a parcel lifted from the surface after it reaches saturation. The wet-bulb potential
temperature, 06,is defined as the temperature of a parcel taken moist adiabatically from its wet-
bulb temperature, Tw, to a reference pressure of 1000 mb. Tw and ., are very closely related and
are, by definition, on the same pseudo-adiabat. Eltahir and Pal (1996) describe the role of wetbulb temperature in triggering moist convection. The work of Williams and Renno (1993) shows
a linear relationship between wet-bulb potential temperature and the convective available potential
energy (CAPE) of surface air parcels, using surface and upper air data from many tropical
locations. They found a zero-CAPE intercept at approximately 22-23 *C. The results of Eltahir
and Pal (1996) show a similar linear relationship between wet-bulb temperature and the
probability of afternoon rain in the Amazon, with a zero-probability of rainfall intercept at 22 °C.
Ludlam (1980) showed that a 0, of at least 20 OC is required for the buildup of substantial CAPE
in western Europe. Dessens (1995) used daily minimum temperature, which generally occurs in
the early morning, as an approximation of the Ow in following afternoon. He states that there is a
strong correlation between these two variables, and shows that 0, is a good predictor of damage
from severe hail storms in France. Zawadzki and Ro (1978) and Zawadzki et al. (1981) used
vertical soundings from the Toronto area in summer to show that the mean and maximum
precipitation rate are well correlated with parcel convective energy.
Betts et al. (1996) performed much of their analyses in terms of the equivalent potential
temperature, OE, of the boundary layer. This variable is related to the entropy of the layer throtigh
the equation (cpd + r, ct) In OE s + Rd ln Po, where Cpd is the heat capacity of dry air at constant
pressure, ci is the heat capacity of liquid water, r, is the total water mixing ratio, Rd is the gas
constant of dry air, po is a reference pressure of 1000 mb, and s is the specific entropy, or moist
entropy (Emanuel, 1994, p. 120). Both s and OE are conserved in reversible moist adiabatic
processes. During daylight hours, OE increases due to the surface flux of both sensible heat and
latent heat. Betts et al. (1996) stress that "this surface flux of GE is proportional to the sum of the
[sensible heat flux + latent heat flux], and it is not affected by the Bowen ratio" (p. 7214). The
contribution of low GE from above the boundary layer, however, tends to reduce 0E in the layer.
The degree to which this entrainment occurs is closely linked to the sensible heat flux from the
surface and the associated deepening of the boundary layer: "if the surface [Bowen ratio] is large,
although the surface 0E flux may be unchanged, the large [sensible heat] flux drives more
entrainment, produces a deeper [boundary layer], and the diurnal rise of GE is reduced" (p. 7214).
Using data from the FIFE site in Kansas, Betts et al. (1996) showed that, on days during
July and August 1987 which were not substantially affected by precipitation or advection of cold
air, higher soil moisture content was associated with higher mixing ratio, q, throughout the day,
lower mean temperature, lower maximum temperature, and higher maximum GE. They state that
"some of this shift of GE is associated with the sift of the entire diurnal path to higher q with higher
soil moisture, but about half is the result of reduced entrainment of dry low GE into the boundary
layer" (p.7215).
Earlier work by Betts and Ball (1995) focused on subsets of the FIFE data, determined by
rainfall and net radiation. Two of their many analyses are particularly relevant to this study. The
first compared all days from June to September, 1987 to "wet" days and to "dry" days. "Wet"
days were defined to be those with "significant rainfall during the daytime" (p. 25,682), and
constituted 29 days. "Dry" days were "days for which the daytime diurnal cycle was not
disturbed by rain or heavy overcast." (p. 25,682) They defined "overcast" as days with a 3-hour
average near-noontime net radiation below a threshold: 450 W/m2 for June, July, and August, and
400 W/m 2 for September. There were 94 "dry" days in the data set. With these classifications,
they found that increased wetness led to higher maximum OE, higher maximum q, smaller diurnal
range in T, and, as expected from their definition of the classifications, lower Ret. These
classifications, however, are not determined from the soil moisture observations, and are therefore
quite different from the wet, normal, and dry classifications used in this study.
A subsequent analysis in the Betts and Ball work did partition the data by soil moisture,
but they only used the 94 days in the "dry" category described above. This is a critical difference
between their study and this work. Within subcategories of the dry data, they found that the
Bowen ratio and the pressure depth to the Lifting Condensation Level (LCL) were highly
dependent on soil moisture: larger pressure depths and larger Bowen ratios were associated with
drier soils. This was especially true between the two driest categories.
Eltahir (1997) stresses the importance of the control that soil saturation has on the albedo
of the surface, in addition to the aforementioned Bowen ratio controls. Since water absorbs more
solar radiation than dry soil, the albedo of a land surface is negatively correlated with soil
saturation, particularly in the top 10 cm. This effect then propagates into the surface radiation
budget: increased soil moisture should decrease the albedo, which then increases the net solar
radiation at the surface. Eltahir showed that increased soil saturation should also increase the net
terrestrial radiation by increasing the water content of the atmosphere, which will cause more
longwave radiation to be directed back towards the surface, and by decreasing the surface
temperature, which will result in a decreased radiation away from the surface. All else remaining
equal, then, increased soil moisture should lead to an increase in available energy at the surface.
This effect, like that discussed above in connection with the work of Betts et al. (1996), should
lead to a positive relationship between soil saturation and the entropy of the boundary layer, by
increasing the surface flux of the sum of latent and sensible heats. Eltahir (1997) showed that
FIFE data exhibits a positive relationship between soil saturation and wet-bulb temperature.
C.
GCM Results
In addition to theoretical work and small-scale analyses of observations, much insight into
the soil moisture-rainfall feedback has been gained from Global Climate Modeling studies.
Shukla and Mintz (1982), tested two global scenarios: a wet-soil case, where evapotranspiration
is at all times equal to the potential evapotranspiration, and a dry-soil case, where there is no
evapotranspiration. Over almost the entire globe, precipitation in the dry-soil case was much less
than precipitation in the wet-soil case; while surface temperatures in the dry-soil case were much
higher than in the wet-soil case. They concluded that "surface evapotranspiration, which requires
moisture in the soil, is a necessary (though not sufficient) condition for extratropical summer
precipitation" (p. 1500).
The importance of the timing of soil moisture anomalies in their affect on other climatic
variables is stressed by Oglesby's 1991 study of North American droughts. Reduced soil moisture
profiles are introduced into two model runs, one beginning on March 1, and one beginning on
May 1. In the May 1 run, most of the initial soil moisture anomaly is maintained throughout the
summer, except along the east coast of the continent, showing that "through positive feedbacks,
reduced soil moisture can be a self-perpetuating condition" (p. 893). The March 1 run, however,
shows that the anomalous condition can, in fact, correct itself. The anomaly is apparent at 20
days only over the central United States, and at 50 days, virtually all of North America is at a
normal, moist state. He explains these different behaviors by noting that during winter or early
spring, when the March 1 anomaly is introduced, solar insolation is generally less than in late
spring and summer. The two primary direct effects of reduced soil moisture content-reduced
local evaporation and increased surface heating-are, thus, expected to be less important in this
earlier season, and the anomalous condition can be corrected prior to the onset of the new
climatic regime.
Rind (1982) finds similar results in his GCM study of North America. By comparing runs
which have initially reduced soil moisture levels across the entire United States to control runs,
which have normal soil moisture levels on June 1,Rind found significant temperature increases
and precipitation decreases across most of the U.S. The effects were most noticeable in June and
least noticeable in August, and most consistent in the interior of the continent, where the oceans
had the least influence.
Yeh et. al. (1984) conducted a series of numerical experiments which tested, among other
things, the importance of the latitude of soil moisture anomalies. In each of the three latitudinal
bands studied, namely 300N-60°N, 0-30*N, and 15OS-15°N, initial saturation of the soil caused
both an increase in local precipitation and cooling of the surface due to increased evaporation.
Each of the simulations was run during the driest period for the latitudinal band: 1 July to 30
November for the northernmost region, and 1 January to 31 May for the other two.
The studies of Rowntree and Bolton (1983) and Fennessy and Shukla (1996) both found a
positive feedback between soil moisture and precipitation. They determined that the strength of
the impact is dependent on the size of the soil moisture anomaly region. Other important factors
include the solar forcing and the strength of the background winds and regional circulation.
Rowntree and Bolton work in terms of a vertically integrated relative humidity, defined as Q/Qsa,
where Q is the vertically integrated atmospheric water vapor (in g/cm 2 ), and Qsat is the
corresponding saturation vapor content. This quantity is increased by an increase in Q, which can
occur when evapotranspiration exceeds precipitation, and it is decreased by a rise in temperature,
which leads to an increase in Q,.t. They found that an initial soil moisture anomaly over Central
Europe affected the partitioning of turbulent heat fluxes at the ground, which in turn affected the
modeled temperature, humidity and rainfall during the following 50 days. The atmospheric
humidity was found to be much higher in wet soil cases than in dry soil cases, and "the likelihood
of precipitation [was] much increased by the wet surface" (p. 503). Model runs with increased
winds and circulation strength showed less response to the soil moisture anomaly.
Several studies have focused on the causes of the 1988 U.S. summer drought, studying
both sea surface temperatures (SSTs) and soil moisture states. Trenberth et al. (1988) found that
large-scale circulation patterns caused by SSTs in the Pacific were the likely primary cause, but'
that the low soil moisture conditions at the beginning of and throughout the season probably
contributed to the severity and persistence of the drought. Atlas et al. (1993), on the other hand,
found that tropical SST anomalies reduced the precipitation in the Great Plains, but did not
significantly increase the surface temperatures. Simulations with reduced soil moisture levels,
however, both increased surface temperatures and decreased precipitation, accurately
approximating the actual 1988 scenario. Oglesby and Erickson (1989) used the NCAR CCM1
general circulation model to demonstrate that reduced spring soil moisture, like that of 1988, can
"amplify or prolong summertime drought over North America" (p. 1375).
D.
Results of Regional Climate Studies
Perhaps of more relevance to this analysis of data from Illinois are results from regional
scale climate and/or hydrologic models. Pan et al. (1995) focused their study on the flood of
1993 as well as the drought of 1988. They tested the hypothesis that surface moisture availability
provides an additional feedback mechanism, helping to maintain extreme wet or dry conditions.
Models of a portion of the Midwestern U.S. showed that when all other climatic variables were
simulated as observed in each of the two years of interest, extreme changes in the surface
moisture conditions (i.e., 99% of saturation simulated with the temperature, wind, and other
boundary conditions observed in 1988; 1%of saturation with the boundary conditions of 1993)
significantly altered the total summer precipitation.
However, the study of Giorgi et al. (1996) led to the opposite conclusion. They found
that local recycling effects were not important in the development of extreme climatic regimes,
and, contrary to the aforementioned studies, that a dry soil initial condition provides for increased
sensible heat flux, which contributes greater buoyancy to the air, enhancing convective systems
and producing more precipitation. This cycle, then, supports a negative feedback mechanism
between initial soil condition and precipitation.
In their regional modeling study of the 1988 and 1993 events over the Midwestern US, Pal
and Eltahir (1997) found that the sensitivity of the model to soil moisture initialization was
extremely dependent on the convection scheme used in the model. One convection scheme led to
results which were highly dependent on the initial local soil moisture conditions, while a different
scheme led to quick equilibration of soil moisture anomalies and showed little precipitation
difference between wet and dry model runs.
Similar to the Giorgi et al. (1996) study, Georgakakos et al. (1996) found no evidence of
soil water feedback to local precipitation in their study of two 2000 km2 basins in Iowa and
Oklahoma. Using daily precipitation and potential evapotranspiration as input, they were able to
accurately simulate observed daily discharge over a 40 year period in each of the basins. One of
the primary forcings to the river discharge was an estimated soil moisture time series: the
accuracy of their streamflow series (correlation with observations better than 0.8) suggests that
their soil moisture series is good. Though soil moisture was not shown to affect precipitation,
there were significant cross-correlations between upper soil water leading daily maximum
temperature, especially during periods of extreme (high or low) soil water content.
Huang et al. (1996) created a 62 year (1931-1993) time series of monthly soil moisture
data for the entire US using a one-layer soil moisture model. They found that soil moisture is a
better predictor of future monthly temperature than is antecedent precipitation, particularly in the
interior of the continent during summer.
On the smaller end of the spatial and temporal scales, Chang and Wetzel (1991) were able
to model the effects of the spatial variability of vegetation and soil moisture on the development
of individual storm events. Given the absence of real soil data, they estimated soil moisture from
an antecedent precipitation index. The Illinois data set is not of high enough spatial or temporal
resolution to be adequately compared to the results of Chang and Wetzel.
Each of the works mentioned above help to establish and/or substantiate the theory of why
we expect to see a positive feedback between soil saturation and rainfall. The studies mentioned
in Sections C and D highlight many attempts to discern the impact of soil water conditions on
future climate through the use of numerical models. Analyses of small-scale sites such as FIFE
have provided some real-world applications of these theories. In the following three chapters, we
will test the theories presented here by looking at directly observed soil moisture, near-surface air,
and rainfall data from the state of Illinois, and see what these data can tell us about the soil
moisture-rainfall feedback. We begin by analyzing soil moisture and rainfall data in Chapter 3.
Chapters 4 and 5 will include analyses of the relationships between soil moisture and boundary
layer conditions, and boundary layer conditions and rainfall, respectively.
Chapter 3: The Relationships Between Soil Saturation
and Subsequent Rainfall
A.
Soil Moisture Data
Though each of the studies described in the previous chapter provides analyses of the links
between summer rainfall and spring soil moisture, all of them used indirect means to quantify soil
moisture. Since 1981, scientists from the Illinois State Water Survey have been taking direct soil
moisture measurements with a neutron probe at 8 grass-covered sites around their state (Hollinger
and Isard, 1994). Seven additional sites were added in 1982, two more were on-line by 1986, and
by 1992, the total was up to 19. Station locations are shown in Figure 3.1. Bi-weekly
measurements were taken in the top 10 cm, in 20 cm intervals between 10 and 190 cm (10-30 cm,
30-50 cm, etc.), and in the 10 cm interval between 1.9 and 2 meters below the surface.
Many researchers (Owe and Chang, 1988; Shukla and Mintz, 1982) have noted the
difficulty in obtaining a parameter that represents the soil moisture condition over a whole, large
area. Though this data set is a very extensive collection, both temporally and spatially, we must
consider the relevance of the parameter measured to this study. According to the hypothesis
presented here, the initial soil water condition can provide some positive feedback to the
convective regime during the summer months in Illinois. The parameter of interest, then, is the
amount of soil water available for evapotranspiration. The rate at which soil water can be
removed is a property of the unsaturated hydraulic conductivity of the soil. Eagleson (1978)
Locations of ISWS Soil Moisture Stations (*)and Rainfall Stations (o)
Wisconsin
42
41
-
-
-- I
39
-
38 v
37
F
k..
&entucry
|
-92
-91
nl
....
-90
.
n
-89
-88
-87
Longitude (degrees W)
Figure 3.1: Locations of Illinois State Water Survey (ISWS) soil moisture stations and
rainfall stations. Solid line is the Illinois state boundary.
stresses that in exfiltration processes (interstorm drying of the soil as well as extraction by plant
roots) it is not the moisture content, q, but rather the soil saturation, q/n, where n is porosity, that
is the controlling parameter. Therefore, soil saturation is used as an indicator of the overall soil
water condition at each site. Note that this is used as a qualitative indicator of the soil condition,
not as an exact measure of the mass of water in the soil: the data are by no means complete
enough to offer that level of detail. The soil moisture data, then, were first converted to soil
saturations by dividing by the porosity (measurements were made at each of the 19 sites).
Though the sampling frequency (approximately every two weeks) is much greater than for
most soil moisture field studies, 14 days is significantly longer than a normal wetting and drying
cycle during a Midwestern summer. However, in this study we are not interested in the ability to
predict a storm event or exactly describe the soil water condition at every moment in time.
Rather, we are concerned with the mean climatic behavior over monthly or seasonal time scales
rather than the predictability of erratic weather systems. It is also important to note that the
sampling schedule was not set in response to particular storm or drought events (Hollinger,
personal communication, 1996). The samples obtained, then, are like random realizations of the
ensemble of soil moisture condition at all times throughout the entire state. The assumption
implicit in this analysis is that there are enough observations distributed in time and space to give
an adequate representation of the trends of the mean soil water condition in the state. An ideal
data set for this analysis would have soil moisture sampled multiple times per day at many sites all
over the state. Though this data set is not, by this standard, ideal, it is far more complete than any
other data set known to date, and much useful information can be gleaned from it.
Simple linear interpolation was used to develop a daily time series of soil saturation for
each depth interval at each site. Though each of the site-specific time series may miss important
events, given no better knowledge of the soil conditions between observations, linear interpolation
makes the most of the directly observed information that is available. Furthermore, since it is the
large-scale soil saturation that is of interest-the soil moisture that can contribute to atmospheric
humidity within the region--the state-wide average soil saturation was determined by averaging all
the station-specific values for each day within this 14 year time series. Relative to other data sets
of soil moisture, 19 is a large number of stations.
An important consideration in any study related to soil moisture is the relevant depth of
soil to analyze. The root zone depth is dependent on vegetation type and health, and can be
extremely variable. Estimates for root zone depth usually are in the range of 10 cm to a few
meters. Because the depth of soil from which moisture is available for evaporation is not
constant, the analysis was initially performed for average saturations in all of the available surface
soil layers: 0-10 cm, 0-30 cm, 0-50 cm, 0-70 cm, 0-90 cm, 0-110 cm, 0-130 cm, 0-150 cm, 0-170
cm, 0-190 cm, and the top 2 meters. The average saturation for the layer of interest was
calculated by an appropriately weighted average of saturation within each 10 or 20 cm sample
interval. Figures 3.2a-f show the average soil saturation for each of the 14 years for the top six
surface layers, each highlighting 1988, a substantial drought year, and 1993, a substantial flood
year. Figures 3.3a-d show seasonal average profiles of soil saturation, also highlighting 1988 and
1993. The summertime average (JJA) shows that during both of these extreme conditions, in the
top meter of the profile 1988 is the driest of all the years and 1993 is the wettest of all the years.
The effect of even the well-known drought of 1988 did not reach below this top meter of the soil:
the soil between one and two meters was wetter than average during 1988. This is an indication
that, in Illinois, effects of atmospheric phenomena do not reach below the top meter of the soil.'
This is consistent with the fact that most of the state is covered with crops, which tend to have a
rooting depth of close to one meter.
Average Soil Saturation: Each Year, 1981-94
Jan
100
I
Mar
Feb
1
1
Apr
1
I
g
I
Jul
Jun
May
I
I
'
Sep
Aug
I
Dec
Nov
Oct
11'
80
-
....
.......
c
40
20
0
Top 30 cm
I
I
I
I
i
1
i
I1
I
I
I
I
lI
i
lI
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
100
80
Figure 3.2: Annual average of soil saturation cycles for each year, 1981-1994. Dashed line
is 1988 (extreme drought); solid line is 1993 (extreme flood); all other years are
drawn with dotted lines; thick dotted line is average of all 14 years; a) top 10 cm, b)
top 30 cm, c) top 50 cm.
Average Soil Saturation: Each Year, 1981-94
100
80
60
40
20
0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
100
80
60
40
20
0
100
80
60
40
20
0
Figure 3.2 (cont.): d) top 70 cm, e) top 90 cm, f) top 1.1 m.
MAM Soil Moisture Profile
DJF Soil Moisture Profile
I
0
S.
io
:
150
100
·
15U
• °
.'..
:
..
2.4
.
0
.
200.
)
0.2
0.6
0.4
Soil Saturation
0.
I
0w
0.8
0.2
o
0.
0.
0.4
0.6
0.8
SON Soil Moisture Profile
"'
.
:...
.
. :•
:...... ..
50
S100 ...............
i
..............
100
150
t..
200
0
0.2
.e··
··
I
S........
S150
200
0.
Soil Saturation
JJA Soil Moisture Profile
0
S50
.·
_
°··' c
200
..
"".:.
...
.'.""
..
100
r
•~ ".
50
50
0.6
0.4
Soil Saturation
0.8
1
. .
.
I
0
0.2
I
0.6
0.4
Soil Saturation
0.8
Figure 3.3: Seasonal average soil saturation profiles: a) December-February (DJF), b)
March-May (MAM), c) June-August (JJA), d) September-November (SON). Leftmost solid line is 1988 (extreme drought); right-most solid line is 1993 (extreme
flood); all other years are drawn with dotted lines; dashed line is average of all 14
years.
B.
Daily PrecipitationData
Measures of daily precipitation were available from the Illinois State Water Survey at 129
stations within the state. Their locations are shown in Figure 3.1. In Kunkel et al. (1990), data
from these stations were bulked into 9 crop reporting zones: here, however, we have determined
the state-wide average daily precipitation by averaging daily values at all 129 stations. This time
series of the state-wide average daily rainfall was used in all the analyses discussed below. Figure
3.4 shows the average total monthly rainfall during the 14 years for which we have soil moisture
observations (1981-1994).
Average Total Monthly Precipitation in Illinois Between 1981 and 1994
7-
655-
0.
21
0
2
4
6
8
10
12
Month
Figure 3.4: Average total monthly precipitation over Illinois, 1981-1994. Stars indicate
means of the 14 years; lines extend to plus or minus one standard deviation.
C.
Results and Discussion: The Interplay Between Soil Saturationand
Subsequent PrecipitationThroughout the Year
To relate this data analysis with the modeling discussed in the first chapter, we compared
an initial soil condition to subsequent precipitation, much like a modeler would test for
precipitation sensitivity to soil water. For a given day, say April 1, we looked at the average soil
saturation within the state for each of the available 14 years. We then calculated the total
precipitation in the subsequent 21 days for each of the 14 years, in this case, April 2 through April
23. Twenty-one days is time enough for the system to go through a few wetting and drying soil
cycles, and a few convective storm cycles, so our results will be indicative not of a single weather
event, but of a short climatic period. A linear regression was then performed on these two 14
year series, and the coefficient of determination, r, was recorded as an indicator of the percentage
of rainfall variability that can be explained by the soil water initial condition. This analysis was
performed for all 365 days of the year. The dots in Figure 3.5 show that the ? values reach as
high as 0.7 for the top 10 cm. Even after a 21 day smoothing, more than 40% of the variability in
rainfall can be explained by a simple linear correlation between initial soil saturation and
subsequent rainfall. This correlation was damped at greater depths, but was still significant during
the summer down to a depth of 90 cm.
The level of significance lines of Figure 3.5 are computed using an F-distribution for the
r2. (The 5%level of significance line for an F distribution with 1 and 12 degrees of freedom in the
numerator and denominator, respectively, is 4.75. This yields an r 2 of 0.2836. The 10% line is at
F(1,12) = 3.18, which yields an r2 of 0.2095. See Johnston (1984) for details.) These lines apply
to the daily measurements, not to the smoothed lines. The significance lines for the smoothed
data will be lower since the variability will go down as the inverse of the length of the averaging
window. All Figures 3.5a-c show the daily ? is stronger during the summer than the rest of the
year, though there is also a local peak during April, as well. At the shallower depths, the linear
correlation stays above the 10% level of significance line from the end of May to early August,
and for much of April. During the rest of the year, the correlation between soil moisture and
subsequent precipitation is not significant. We find three possible explanations for these results
showing that there is a significant linear relation between soil saturation and subsequent
precipitation conditions during this
Linear Corrleation Between Soil Day and Subsequent 21-day Rain Window
0.
0.
S0.
0..
0.
0.
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Day Beginning Rain Window
Linear Corrleation Between Soil Day and Subsequent 21-day Rain Window
Dec
Jan
Febb
Mar
Apr
Dec
Jan
Feb
Mar
Apr
4-
0
4-
v
May
June
July
Aug
Sept
Oct
Nov
Day Beginning Rain Window
Linear Corrleation Between Soil Day and Subsequent 21-day Rain Window
0.
0.
'
0.
0.
May
June
July
Aug
Day Beginning Rain Window
Sept
Oct
Nov
Dec
Figure 3.5: Linear correlation between Initial soil saturation and precipitation in the
subsequent 21 days for a) top 10 cm, b) top 50 cm, and c) top 90 cm. Solid line is
21-day moving average. Level of significance lines refer to the daily values (not the
smoothed line).
summer period. First, it is possible that the relationship is due to a persistent large scale
atmospheric forcing that sustains or enhances a persistence in rainfall between adjacent time
periods, and through the correlation between concurrent rainfall and soil saturation, results in the
observed correlation between soil saturation and subsequent rainfall. Second, the correlation
could be a reflection of a feedback process in which initial soil moisture affects rainfall, which then
affects soil moisture, etc. Finally, we must consider a combination of these two mechanisms.
Linear Correlation Between Adjacent 21-day Rain Windows
C)
U
Jan
Feb
Mar
Apr
May
June July Aug
Day Beginning Second Window
Sept
Oct
Nov
Dec
Figure 3.6: Linear correlation between adjacent 21-day precipitation windows; 21-day
smoothing. Solid line is 21-day moving average. Level of significance lines refer to
the daily values (not the smoothed line).
If large-scale atmospheric processes drive the system at hand, persistence in atmospheric
conditions would first be reflected in rainfall persistence, as shown in Figure 3.6. Here,
persistence in rainfall is measured by the correlation between the total precipitation in adjacent 21day windows. Figure 3.7 then shows the correlation between a 21 day rainfall window and soil
saturation at the end of the window. If precipitation forces soil saturation at the end of a given
window (Figure 3.7), and if precipitation is also linearly correlated with precipitation in the next
time window (Figure 3.6), soil saturation may, merely as a direct consequence of this rainfall
forcing, also be significantly correlated with subsequent precipitation (Figure 3.5). In this case,
we would expect the rainfall persistence to be greater than the correlation between soil saturation
and subsequent precipitation.
In a scenario in which soil moisture is a driving force affecting rainfall, we would expect
the state of the soil moisture reservoir to affect rainfall directly. In this case, the correlation
between soil saturation and subsequent rainfall should outweigh the correlation between rainfall in
adjacent windows. Figures 3.8a-c are plots of the smoothed lines of Figures 3.5a-c superimposed
on the smoothed precipitation persistence line of Figure 3.6. From this figure, we can see that for
autumn and winter, the correlation between rainfall and prior soil moisture is comparable to the
correlation between serial precipitation windows. This suggests that persistence due to large- .
scale atmospheric forcing can account for much of the observed linear correlation between soil
moisture and subsequent rainfall during these seasons. Throughout June, July and August, and
for a portion of the spring, however, rainfall is better correlated with prior soil moisture than with
prior rainfall. This suggests that during the summer, feedback from soil moisture is the more
likely physical explanation. At no point, however, can we rule out the possibility that a
combination of the two given explanations is responsible for the observations. These results are
consistent with the GCMs discussed earlier, and with the regional study of Pan et al. (1995).
Linear Correlation Between 21-Day Rain Window Preceeding Soil Day
0.7
0.6
60.5
S0.4
0.3
S0.2
0.1
n
Jan
Feb
Jan
Feb
Jan
Feb
Mar
Apr
Nov
May
June
July
Aug
Sept
Oct
Soil Day (Last Day of Rain Window)
Linear Correlation Between 21-Day Rain Window Preceeding Soil Day
Dec
Mar
Apr
Dec
Mar
Apr
0.7
0.6
1 0.5
0.4
o
0.3
8
.2
0.1
0
May
June
July
Aug
Sept
Oct
Nov
Soil Day (Last Day of Rain Window)
Linear Correlation Between 21-Day Rain Window Preceeding Soil Day
0.
0.
0.
10.
.0 O
0.
0.
May
June
July
Aug
Sept
Soil Day (Last Day of Rain Window)
Oct
Nov
Dec
Figure 3.7: Linear correlation between 21-day total precipitation and soil saturation at the
end of the 21 days for a) top 10 cm, b) top 50 cm, and c) top 90 cm. Solid line is 21day moving average. Level of significance lines refer to the daily values.
Correlation Between Adjacent Windows; Top 10 cm
1&
0.
0.
t"4
"0.
o0.
0.
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Oct
Nov
Dec
Oct
Nov
Dec
Correlation Between Adjacent Windows; Top 50 cm
U.3
0.4
0.3
0.2
0.1
v
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Correlation Between Adjacent Windows; Top 90 cm
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Figure 3.8: Comparison of smoothed lines of the linear correlation between adjacent
precipitation windows (solid line from Figure 3.6) and of the linear correlation
between soil saturation and subsequent precipitation (dashed lines from Figures
3.5a-c).
D.
Results and Discussion: Focus on Spring and Summer Connections
Given the results of the analysis for the entire year, it seems pertinent to focus on the
summer months. An analysis similar to the one described above was performed, comparing the
correlation between an initial soil condition and total precipitation during the rest of the summer.
Assuming that summer is taken to end on August 23, Figure 3.9 shows the ? for every initial
condition day from May 1 to July 31. Similarly, Figure 3.10 shows the results for the case where
summer is taken to end on September 19, with initial condition days moving from May 1 to
August 31.
Again, the linear correlation is significant for much of the summer. Figure 3.9 shows a
maximum of r2 > 0.5 at the end of June, while Figure 3.10, with summer lasting until September
19, reaches this same r2 level in mid-July. Figure 3.11 shows the 14 data points used to obtain
these ? values for the June 25 initial condition and August 23 end of summer. The number beside
each data point denotes the year of the event, and the r2 is given in the upper left corner. Though
the non-extreme years show little pattern, we see that the most extreme years, 1988 and 1993, fit
the expected pattern of a dry (wet) spring being followed by a dry (wet) summer. If the two
variables were completely unrelated, then the probability of both of these events randomly
occurring within one data set would be quite low.
The dashed horizontal and vertical lines in Figure 3.11 divide the data into three spring soil
moisture classes: high, normal, and low, and into three summer rainfall classes: again, high,
normal and low. The lines are calculated by taking the average of the 14 data points ± one
standard deviation. These groupings show that during these 14 years, no abnormally dry spring
was followed by an abnormally wet summer, and vice versa. Though 14 years is not enough data
Linear Correlation Between Initial Soil Saturation and Subsequent Summer Rainfall
0.7
0.6
So.5
~ 0.4
0.3
0.2
0.1
0
May
June
July
Day Beginning Summer; Summer ends on August 23
Linear Correlation Between Initial Soil Saturation and Subsequent Summer Rainfall
0.
0
00
0•
O.
May
June
July
Day Beginning Summer; Summer ends on August 23
Linear Correlation Between Initial Soil Saturation and Subsequent Summer Rainfall
0.7
0.6
Top 90 cm
0o.5
0.4
o 0.3 S5%L.O.S.
u 0.2
_...
10% L.O.S.....
.. . .. .. . ..
--
*
..
.. .. . .. .. . .. .. .
-·
Ol
fl
May
June
Day Beginning Summer; Summer ends on August 23
July
Figure 3.9: Linear correlation between initial soil saturation and precipitation in the rest of
the summer (through August 23) for a) top 10 cm, b) top 50 cm, and c) top 90 cm.
Solid line is 21-day moving average. Level of significance lines refer to the daily
values (not the smoothed lines).
Linear Correlation Between Initial Soil Saturation and Subsequent Summer Rainfall
0.6
Top 10 cm
,0.5
~0.4
Io
0.3
0.2
5%*L.O.S.
...
*
10% L.O.S.
0.1
--""
... .*.
0*
' 60
Ill
May
June
July
Aug
Day Beginning Summer; Summer ends on September 19
Linear Correlation Between Initial Soil Saturation and Subsequent Summer Rainfall
U
0
u
May
June
July
Aug
Day Beginning Summer; Summer ends on September 19
Linear Correlation Between Initial Soil Saturation and Subsequent Summer Rainfall
Top 90 cm
•0.5
0.4
0. 3 S5% L.O.S.
u 0.2
"
..
10% L.O.S.
- •--
S'.
-
._
-.
*
I
..
. ..
II
May
June
July
Day Beginning Summer; Summer ends on September 19
Aug
Figure 3.10: Linear correlation between initial soil saturation and precipitation in the rest
of the summer (through September 19) for a) top 10 cm, b) top 30 cm, and c) top 90
cm. Solid line is 21-day moving average. Level of significance lines refer to the
daily values (not the smoothed lines).
Initial Soil Saturation vs. Summer Precipitation
pin
LU
r"2 = 55%
I
15
-i
093
I
10
087
088------------ 0--91--S9I8
I
, I
30
20
I
rN
- --
Q8L
091
082
- -
- --
-
--
0•
89
I
I
I
50
40
1
i
60
70
80
June 25 Soil Saturation, Top 10 cm
Initial Soil Saturation vs. Summer Precipitation
20
rA2 = 45%
.15
SI
410=_81--
1
S5 - -
-------
0
20
88
-
I
I
I
I
30
40
-
86 090
082
S92
8
Q94 -
3
089
84
- _
_
I
I
50
60
I
093
- - - - - - - - --
I
I
80
70
June 25 Soil Saturation, Top 50 cm
Initial Soil Saturation vs. Summer Precipitation
2u
I
I
C
I
I
rA2 = 32%
.i15
--
* 10
I
I
I
I
_
Q8L -
1097, 087
-------
5
-----------
188
I
0)
I
20
30
I
I
I
-
093
-I
-
8C186 090
O89
R-I 0o4 0
88
I
I
I
I
I
I
-----I1
I
I
40
50
60
June 25 Soil Saturation, Top 90 cm
II
70
Figure 3.11: Average Initial soil saturation on June 25 for a given year versus summer (July
1 to August 23) precipitation for each year. Numbers beside each data point
indicate sample year. Dotted lines are means of the 14 years ± one standard
deviation, separating data Into low, normal, and high categories of soil saturation
and summer precipitation.
80
on which to base final conclusions, it is more data than has ever been collected and analyzed in
this manner to date.
E.
Discussion of Results
This study tests the hypothesis that soil saturation is positively correlated with subsequent
precipitation by analyzing a 14 year soil moisture data set from the state of Illinois. The linear
correlation between an initial soil saturation condition and subsequent rainfall is significant during
the summer months, reaching a peak of r2 > 0.4 in mid-June. This result is consistent with the
hypothesis that knowledge of late spring/early summer soil moisture conditions can aid in the
prediction of drought or flood years, but it does not necessarily prove that feedback from
anomalous soil moisture reservoirs is the cause of anomalous summer conditions. Further
analyses indicate that from early June to mid-August, persistence in rainfall cannot fully account
for the observed correlations, suggesting the likelihood of a physical feedback mechanism linking
early summer soil saturation with subsequent precipitation.
Though these conclusions are striking, they must be accepted with some restraint: the
observed results suggest that though the physical feedback is significant, it is by no means the only
pertinent physical process. Furthermore, the data set is limited in both spatial and temporal
resolution. The 14 years comprising this data set have very few non-normal events from which
we can make inferences regarding the association between soil moisture and subsequent summer
rainfall. Additionally, the aerial coverage is quite small: the entire mid-western United States
would provide a much more comprehensive study region. However, despite these deficiencies,
this data set is by far the largest of its kind that is readily available for analysis.
Observations made here should be useful to those working on the dynamics of droughts
and floods for mid-latitude continental interiors. The results of many GCMs (Shukla and Mintz
(1982); Oglesby (1991); Rind (1982); Trenberth et al. (1988); Atlas et al. (1993); Oglesby and
Erickson (1989)) and Regional studies (Pan et al. (1995); Huang et al.(1996)) are consistent with
those observed in the Illinois data set: extreme soil moisture availability (or lack thereof) acts as
either a feedback mechanism maintaining the wet (or dry) conditions established in the beginning
of each summer, or as a flag indicative of some large-scale process that is affecting both the soil
moisture and the precipitation regime.
Neither these observations nor the modeling studies discussed earlier answer the question
of how these links between soil moisture and precipitation are forged. The subsequent chapters
will address two stages of the physical link between soil water and rain water: Chapter 3 will '
address the relationships between soil saturation and boundary layer conditions, while Chapter 4
will focus on boundary layer conditions and rainfall.
Chapter 4: The Relationships Between Soil Saturation
and Boundary Layer Conditions
The observed relationship between soil saturation and subsequent rainfall, detailed in the
previous chapter, highlights the importance of investigating possible physical mechanisms linking
these two variables. The analyses described in this chapter attempt to address the first of two
intermediary steps between soil and rainfall: the relationship between soil saturation and boundary
layer conditions, as indicated by surface measurements. Chapter 5 will be directed towards the
link between boundary layer conditions and rainfall.
A.
The NCDC Surface Airways Hourly Dataset
Surface meteorological data was obtained from the National Climatic Data Center's
(NCDC's) Surface Airways Hourly Dataset TD-3280. Only eight stations are located within
Illinois. These eight are supplemented by five additional stations: Paducah, Kentucky, just over
the Ohio River at the Southern tip of the state; Milwakee, Wisconsin, approximately 60 km north
of the northeastern corner of Illinois, and three additional stations in western Indiana, 40, 100, and
110 km east of Illinois. See Figure 4.1 for station locations.
Given the paucity of data within the approximately 300 km by 650 km control volume of
Illinois, the inclusion of this supplemental information was deemed beneficial to the statistical
validity of the analysis. The Kentucky station is only nominally outside of Illinois, and the other
four are in the predominately downwind direction of Illinois, and can therefore be an indicator of
Locations of ISWS Soil Moisture Stations (*)and NCDC Surface Airways Stations (o)
43
I
I
I
I
I
I
Wisconsin
I
S
42
41
-
Indiana
40
F
120
39
F
38
Fh
37
F-
*ir
ALI.,VALMuLZJ
·
-92
-91
-89
-88
-90
Longitude (degrees W)
-87
-86
Figure 4.1: Locations of ISWS soil moisture stations and NCDC Surface Airways Hourly
Dataset stations. Solid line is the Illinois state boundary.
the influence of soil saturation on boundary layer air as it is advected out of our study area. The
averaging of data both within and downwind of the soil moisture study area is intended to address
two of the difficulties of working with real data: the complications of advection, and the
limitations of data collection and availability.
Surface parameters obtained from the NCDC hourly dataset include temperature, T, wetbulb temperature, Tw, pressure, P, and relative humidity, f. From these quantities, wet-bulb
depression, Tdpr = T- Tw, potential temperature, 0, virtual potential temperature, 60, equivalent
potential temperature, OE, wet-bulb potential temperature, 86, temperature of the lifting
condensation level (LCL), TLCL, pressure depth to the LCL, PLCL - P,, and mixing ratio, w were
calculated at each station for each hour. The hourly values of each of these variables were then
averaged all 13 stations. The daily minimum, mean, and maximum of each of these twelve
variables was then determined, and these 36 quantities were then used in an analysis with the daily
soil saturation time series described in the previous chapter.
July: Soil Saturation vs. Maximum Temperature (Same day)
1
40
~35
I
-I
-
530-
A
.55
I
1
920151
0.1
0.7
0.5
0.6
0.4
Soil Saturation
PDFs of Maximum Daily Temperature in Each of Three Soil Saturation (SS) Groups
0.3
0.2
U.4
0.3
S0.2
0.1
0
15
20
25
30
Average Daily Maximum Temperature
35
40
Figure 4.2: Soil saturation (SS) and maximum daily temperature (T) for days during July,
during the years 1981 to 1995; a) scatter plot of all data pairs; b) probability
density functions (PDFs) for three subsets of the data based on the degree of soil
saturation.
B.
Presentationof Results
Figures 4.2a-d show the same data in four different ways. Figure 4.2a shows, for the
month of July in each of the years for which both soil saturation data and NCDC surface
Mean Daily Maximum Temperature on Days With High, Medium, or Low Soil Saturation in July
30.5
30-
,
,
,
0
.0 29.5
_, 29
S28.5
0.25
+
0.3
0.35
0.4
0.45
0.5
0.55
Average Daily Soil Saturation in Each of Three Soil Saturation Categories
CDFs of Daily Maximum Temperature in Each of Three Soil Saturation (SS) Groups
0,
0.
U 0.
0.
Daily Maximum Temperature
Figure 4.2 (cont.): c) first moments of the PDFs in 4.2b; d) cumulative distribution functions
(CDFs) for the PDFs in 4.2b.
observations are available (1981-1995), the state-wide average soil saturation (top 10 cm) on a
given day and the state-wide average maximum temperature on the same day. Since soil
saturation is only one of many factors which could potentially impact temperature, a strong trend
is not indicated by this raw data. Other factors, particularly incident solar radiation at the surface,
are responsible for the majority of temperature fluctuations. However, the role of soil moisture
c*an be important for days on which the incident solar radiation is equal. Since daily observations
of this quantity were not obtained for Illinois, we are unable to factor out this dependence.
Instead, we split the data into three different categories of soil saturation and compared the
behavior of surface variables given that soil saturation was high, medium, or low. The 465 data
points (15 years, 31 days in July) in Figure 4.2a were split into three groups: the 155 points with
the lowest soil saturation, the 155 points with the highest soil saturation, and the 155 points in the
middle. Figure 4.2b shows probability density functions (PDFs) of temperature for each of these
three soil saturation groups.
The PDFs show a fair amount of overlap, due to the dominance of factors other than soil
saturation, but Figure 4.2c shows that the means of these distributions indicate that, on average,
drier soil conditions lead to warmer daily maximum temperatures. The cumulative distribution
functions (CDFs) for these distributions are shown in Figure 4.2d. This figure is potentially more
revealing than the PDFs: we can see that the CDF of the high soil saturation category increases
more rapidly than the other two, indicating that more of the mass of the distribution is at lower
temperatures. This effect can also be seen in the PDFs, but the overlap of the lines makes PDFs
of these data sometimes difficult to interpret. Results from subsequent analyses with other
variable combinations will only be presented in the manner of Figures 4.2c and 4.2d.
C.
Analysis of Initial Soil Saturation Followed by 21-Day Average of
Boundary Layer Conditions, Averaged Over All of Illinois
The previous section compared daily soil saturation to air temperature on the same day of
the soil saturation observation. This approach does not appropriately address the issue of how
land surface conditions might impact the boundary layer, because it is not clear if, for example,
low soil saturation is the result or the cause of a high air temperature. To address this causeeffect issue, the following analyses were performed with soil saturation on a given day and
average boundary layer conditions in the subsequent 21 days. Same-day analyses were also
performed for all of the variables presented in this section, and the results were not significantly
different. A twenty-one day window was chosen to be consistent with the soil moisture-rainfall
analyses presented in Chapter 3. As discussed in that chapter, this approach is meant to mimic the
control a person running a climate model has in setting the initial soil saturation condition in their
simulation domain.
The analyses show that when a trend between a given boundary layer variable and soil
saturation is strong, this trend is consistent in the minimum, mean and maximum daily value. For
most variables, with the exception of relative humidity, the maximum daily values show equal or
slightly greater dependence on soil saturation than the mean or minimum. When a trend with s6il
saturation is not strong, the maximum, mean, and minimum still almost always show consistent
relative positions: if the intermediate soil category shows the highest average of daily maximums
of the variable in question, followed by the lowest soil category and then the highest, the daily
minimum and mean of the variable show this same pattern. To avoid redundancy, only the results
with maximum values will be presented here.
Daily maximum relative humidity shows a strong dependence on soil saturation in each of
the months May through September, as seen in Figure 4.3. April does not show a distinct
dependence on soil saturation. As stated above, relative humidity is the one variable where the
minimum and mean show stronger patterns than the maximum. The maximum shows a weaker.
effect because of the possibility of reaching complete saturation: once this threshold is reached,
the measure can go no higher. This makes the range of the maximum relative humidity smaller
than that of the minimum and mean, so the slope of the lines connecting the first moments in
Figure 4.3 is smaller than that shown by minimum and mean relative humidity plots.
Nevertheless, the trend is consistent: wetter soil on an initial day implies that the air in the
following 21 days will be closer to saturation. Mixing ratio, however, only shows this
dependence during July. June and August both have the highest w associated with the wettest
21-day Mean of Maximum Relative Humidity Following Soil Saturation (SS) on 1 day in April
_·
0.8
0
Gf
0.6
·
/
4
0.4
0 Low SS
........ :.... m....
..
. 0:
. . . .. . . . .
0.2
4L
*;I/ /
,
+High
SS
High SS
+ -M(
-I-
n
75
80
85
90
0.4
0.6
0.8
1
21-day Mean Daily Maximum f (%)
Daily Soil Saturation
21-day Mean of Maximum Relative Humidity Following Soil Saturation (SS) on 1 day in May
0
0.2
20
0
4-
86
.0
E
o•
82
'
UO
I
0
0.2
I
I
I
0.4
0.6
0.8
Daily Soil Saturation
1
21-day Mean Daily Maximum f (%)
21-day Mean of Maximum Relative Humidity Following Soil Saturation (SS) on 1 day in June
,,
Qa
92
C
'
B
86
E-
0
U
XI4
0
0.2
0.6
0.8
0.4
Daily Soil Saturation
1
21-day Mean Daily Maximum f (%)
Figure 4.3: First moments and cumulative distribution functions (CDFs) of 21-day mean of
maximum relative humidity (f), given that soil saturation (SS) on the day prior to
the averaging window is low, medium, or high. Note that April, May and
September plots are on one scale, while June, July and August plots are on a
different scale: a) April, b) May, c) June.
21-day Mean of Maximum Relative Humidity Following Soil Saturation (SS) on 1 day in July
I Ill p i I Ill I
III
II I
i
I
C 0.
90 I88 ·-
·
·
00.
·
86 ........................................
-
--
--
--
0
0.2
0.4
0.6
0.8
1
21-day Mean Daily Maximum f (%)
Daily Soil Saturation
21-day Mean of Maximum Relative Humidity Following Soil Saturation (SS) on 1 day in August
I
1
..
.............
92
-
-m
00
0.8
B
+
o 0.8
L.5
o
.:. . . .
88
d
0.6
/
-I
/1
S0.4
................':
I)
86
0.2 I
it
_
__
_
0
0.8
0.6
0.4
0.2
Iln
__
1
m•
m
&t•
At
-
-
--A
90
92
88
86
84
21-day Mean Daily Maximum f (%)
Daily Soil Saturation
21-day Mean of Maximum Relative Humidity Following Soil Saturation (SS) on 1 day in Sept
,
.
88 · · · ·86
,,
.
t·· · 0-I
·-
,
.
,
.
*
·
'
84
82
. ...............
..
...
0
0.2
0.8
0.4
0.6
Daily Soil Saturation
21-day Mean Daily Maximum f (%)
Figure 4.3 (cont.): As above, for d) July, e) August, and f) September.
soils, but the normal and dry soils do not fit this pattern. April and September show a negative
correlation with soil moisture, as does May, though the normal soils have a slightly higher mean w
than the driest soils. Though wetter soil seems to imply that the air is closer to saturation, it does
not necessarily imply higher mixing ratio.
Mixing ratio was calculated from temperature, pressure and relative humidity at each
station, for each hour of observations, using the following equations from Rogers and Yau (1989)
and Bolton (1980). Relative humidity is defined asf = w/Wsat, so w = fwsat. The saturation mixing
ratio, wat, is determined from the relation:
- esat)
Wsat = (p esat
(4.1)
where e = mJm = 0.622 and the saturation vapor pressure is given by:
esat (T) = 6.112 exp T +.2435)
(4.2)
The maximum daily temperature dependence on soil moisture demonstrated for the month
of July in the above Section B is mimicked by the months of April, May and September (see
Figure 4.5). During June and August, however, the pattern is not as strong: the drop in average
temperature from the lowest soil saturation category to the intermediate soil saturation category is
followed by an increase, rather than a drop, in average temperature between the intermediate and
high soil saturation groups. This behavior was also seen in the same-day analysis of temperature
and soil saturation, so it is not thought to be a result of the 21-day averaging masking the
influence of the initial condition.
As mentioned above, soil saturation exhibits an important influence on air temperature, but
it is by no means the dominant influence. We would expect higher soil moisture to mean that
21-day Mean of Maximum Mixing Ratio Followin
I
0
11
..
.
. .
. .
. . . . . ....
..
. . . . . .
:.
.
.
.
.
.
.
=0
0.0
s,
U
i
0
I
0.2
,
I
I
0.4
0.6
0.8
Daily Soil Saturation
1
10
21 -day Mean Daily Maximum w (g/kg)
21-day Mean of Maximum Mixing Ratio Following Soil Saturation (SS) on 1 day in May
·
·
·
0
11 ··
.
............. ...........
..... . .. . . .. . .. . .
,0.
10 ·-
0
....... .. . .. .. . .. .
Q 0.
I
0
0.2
I
I
l
0.4
0.6
0.8
Daily Soil Saturation
1
21-day Mean Daily Maximum w (g/kg)
21-day Mean of Maximum Mixing Ratio Following Soil Saturation (SS) on 1 day in June
16.5
'
=
.
I
'
16
p 15.5
S
7
a
..
..
.............................
a0
15
··-
4.5
a 0.0.
'
.•
.........
S14
..............
0.
I·
13.5
U
I
0
0.2
I
I
E)
l
0.4
0.6
0.8
Daily Soil Saturation
1
10
12
14
16
21-day Mean Daily Maximum w (g/kg)
Figure 4.4: As in Figure 4.3, but for mixing ratio (w); a) April, b) May, c) June.
21-day Mean of Maximum Mixing Ratio Following Soil Saturation (SS) on 1 day in July
16.5
2
16
C)
M
15.5
-
-
-
15
.
. .
. .
. ."..o. .
. .
. . .
. .
. .
. .
.......
. .
o..
. .
. .
. .
. .
. .
.2
...
-
.0
U,
14.5
-
14
13.5
.
. . . .. . . .
.°
. . .
i:: ,::: :::::
13
0
I
0.2
I
I
I
0.4
0.6
0.8
Daily Soil Saturation
1
21-day Mean Daily Maximum w (g/kg)
21-day Mean of Maximum Mixing Ratio Following Soil Saturation (SS) on I day in August
16.5
o
16
.. . .
15.5
S0.
15
00
14.5
..............
- w
14
.0
13.5
U
13
0
I
0.2
I
I
!
0.4
0.6
0.8
Daily Soil Saturation
21-day Mean of Maximum Mixing
12I
I
11
.. ·
10
··
·
·
·
21-day Mean Daily Maximum w (g/kg)
o Following Soil Saturation (SS) on 1 day in Sept
0
0
=0
·
.. ... .* .. . . . .
00
E
l
0
0.2
~I ~
0.4
0.6
Daily Soil Saturation
21-day Mean Daily Maximum w (g/kg)
Figure 4.4 (cont.): As above, for d) July, e) August, and f) September.
21-day Mean of Maximum Temperature Following Soil Saturation (SS) on 1 day in April
24
..
...............
22
·
20
··
.0*
· · ·
|
0
1
1
0.2
0.4
0.6
0.8
1
15
20
25
Daily Soil Saturation
21-day Mean Daily Maximum T (C)
21-day Mean of Maximum Temperature Following Soil Saturation (SS)on 1 day in May
I
0
24 . . . . . . . .. . . . . . . ... . . ..+. . . . . . . . . . . . . . . . .
.............
22
0e• 0.
so,0
.•
Uo
U0.
Ui
I
I
I
I
0.2
0.4
0.6
0.8
1
15
20
25
30
Daily Soil Saturation
21-day Mean Daily Maximum T (C)
21-day Mean of Maximum Temperature Following Soil Saturation (SS) on 1 day in June
0
·
_·
·
·
0
29
E. .
28
· -·
27
·
26
~····
U0
Q0
.0
CO
E"
I
0
0.2
i
I
I
0.4
0.6
0.8
Daily Soil Saturation
1
21-day Mean Daily Maximum T (C)
Figure 4.5: As for Figure 4.3 but for air temperature (T); a) April, b) May, c) June.
21-day Mean of Maximum Temperature Following Soil Saturation (SS) on 1 day in July
·
0
·
O
29
E -: -
:........
.....
:·..
1
0.8
....
+
28
1
I
0.6
.........
0.4
26
0
ic
0.2
E
0O Low SS
.+High SS
E- High SS
Il
0
0.2
0.4
0.6
0.8
Daily Soil Saturation
1
°
-
26
28
30
32
21-day Mean Daily Maximum T (C)
21-day Mean of Maximum Temperature Following Soil Saturation (SS) on 1 day in August
4
I
..
. . ..
29
.
.
i
.
I
I.
•
-'0
--
-F"IF
:0
28
·
0.
26
OO Low SS
-High SS
0.
· · · · · ·
**m
High SS
I
0
0.2
i
i
I
0.4
0.6
0.8
Daily Soil Saturation
1
30
32
21-day Mean Daily Maximum T (C)
21-day Mean of Maximum Temperature Following Soil Saturation (SS) on 1 day in Sept
--
26
0.
24
22
E-4
......
...............
K
S0'
0•
I
0
0.2
I
I
I
0.4
0.6
0.8
Daily Soil Saturation
1
15
20
25
21-day Mean Daily Maximum T (C)
Figure 4.5 (cont.): As above, for d) July, e) August, and f) September.
_-M
• N
Ir
more of the available energy is used to evaporate water than in a drier soil moisture scenario.
This makes less energy available for sensible heating of the air, so we would expect higher soil
moisture to lead to a lower Bowen ratio (13 = ratio of sensible heat flux to latent heat flux) and a
lower air temperature, given equivalent incident solar radiation at the surface. This qualifier is an
important one that cannot always be assumed to be a given. Differences in incident solar radiation
may be a significant factor in the ambiguity of the soil moisture-temperature relationship during
June and August. In the FIFE data analysis of Betts and Ball (1995), their study of the effects of
soil moisture on the boundary layer only takes into account days with net radiation above a given
threshold, thereby acknowledging the potential significance of this forcing mechanism.
Another important factor which may be influencing the temperature behavior is the
threshold dependence of evapotranspiration on soil moisture, as discussed in Chapter 2, and as
pointed out by Betts and Ball (1995): "Above some soil moisture threshold, evapotranspiration
depends primarily on atmospheric parameters, rather than soil moisture controls on vegetative
conductance (p. 25,686)." Clearly, this cannot explain the mean temperature increase from the
normal to the wettest soil category, but it can partially account for the non-negative trend.
Minimum, mean and maximum daily pressure are all entirely independent of both soil
saturation and month (April through September). Each of the three quantities remain essentially
constant over the combinations of months and soil saturations studied, with means of
approximately 990 mb, 995 mb, and 998 mb.
Potential temperature, 0,is given by
T1000.~02854(1-0.28x10- 3w)
P)
TK
(4.3)
where p is pressure, w is mixing ratio in g/kg, and TK is temperature in degrees Kelvin (Bolton,
1980). Since w is usually on the order of 10-25 g/kg, its influence on 0 is very small. Given that
pressure is independent of soil saturation, we expect that the observed patterns in potential
temperature should be very similar to those seen in the normal air temperature. The results were,
indeed, nearly identical to those seen with normal air temperature and are not shown here.
The virtual temperature, T,, accounts for the fact that moist air is lighter than dry air at the
same pressure and temperature. It is approximately given by Tv = T(1+0.608x10' 3w), where w is
again in g/kg, and is generally very close to T (Emanuel, 1994). The virtual potential temperature,
0~, is the potential temperature associated with Tv. The behavior of these variables is negligibly
different from that of temperature. These results are not shown here.
The wet-bulb temperature, Tw, is a function of both the air temperature and the water
vapor content of the air. It is defined as the temperature to which air may be cooled by
evaporating water into it at a constant pressure, until saturation is reached (Rogers and Yau,
1989). The dew point temperature, Tdw, is defined as the temperature at which saturation is
reached by cooling a parcel with pressure and mixing ratio held constant (Rogers and Yau,
1989). The Tw is, by definition, between the Tdw and the T since it includes evaporating water
into the parcel: this leads to an increase in mixing ratio and a decrease in temperature due to the
latent heat consumed by evaporation. Hot, dry air, then, will have a lower Tw than hot, moist air,
since more evaporation and more evaporative cooling is needed to reach saturation. Given
constant solar radiation, soil moisture increases are expected to lead to increased mixing ratio and
decreased temperature. These changes do not independently affect Tw, but in general, increased
mixing ratio would tend to increase the wet-bulb temperature, while decreased temperature would
21-day Mean of Maximum Wet-bulb Temperature Following Soil Saturation (SS) on 1 day in April
C
0
U
o
16
· · ·-
·
0
14
· · · · · · · ·
U
L4
oO
'E
vl.
°.,
II
0
0.2
I
|
|
0.4
0.6
0.8
Daily Soil Saturation
10
15
20
21-day Mean Daily Maximum Tw (C)
1
21-day Mean of Maximum Wet-bulb Temperature Followiing Soil Saturation (SS) on 1 day in May
)K .......
.......;.......:. ........ ........
0.8
0.6
0.4
/00
Low SS
0.2
S•
I
0
0.2
|
1
-* High SS
|
0.4
0.6
0.8
Daily Soil Saturation
1
10
15
20
21-day Mean Daily Maximum Tw (C)
21-day Mean of Maximum Wet-bulb Temperature Following Soil Saturation (SS) on 1 day in June
C
0
U
'5
=0.
0
O
21
o 0.
'=
E
00.
20
·
E
U
0
0.2
0.4
0.6
0.8
Daily Soil Saturation
1
18
20
22
24
21-day Mean Daily Maximum Tw (C)
Figure 4.6: As for Figure 4.3 but for wet-bulb temperature (T,); a) April, b) May, c) June.
A
21-day Mean of Maximum Wet-bulb Temperature Following Soil Saturation (SS) on 1 day in July
23
-·
·
·
O0
-22
0
521
I.......
20
0
U
I
0
I
0.2
I
I
0.4
0.6
0.8
Daily Soil Saturation
1
18
20
22
24
21-day Mean Daily Maximum Tw (C)
21-day Mean of Maximum Wet-bulb Temperature Following Soil Saturation (SS) on 1 day in August
23
0O
22
..
. . .
. ...
.
. .
. .
. ...
.
. .
. .
..
[-(
0
.......
....
21
...
.
. .
. ..
.
.O
..
.
..
. .
. .
..
. . ...
. .
. .....
. .
..
..
r
0 '
5 0G
U
0
0.2
--
--
0.4
0.6
0.8
Daily Soil Saturation
1
18
20
22
24
21-day Mean Daily Maximum Tw (C)
21-day Mean of Maximum Wet-bulb Temperature Following Soil Saturation (SS) on 1 day in Sept
.0.
16
E
14
. . . . . . .. . . . . . . . . .
12
'
I 1
I
0
0.2
--
I
--
0.4
0.6
0.8
Daily Soil Saturation
1
21-day Mean Daily Maximum Tw (C)
Figure 4.6 (cont.): As above, for d) July, e) August, and f) September.
tend to decrease Tw. The non-linearity of the relationship between these variables and wet-bulb
temperature, and the uncertainty about the extent of the effect of soil moisture changes on
temperature and mixing ratio makes it makes it difficult to anticipate the role of soil saturation on
Tw. The data (Figure 4.6) show that for the months of June and August, days with wet soils are
followed by days with a wet-bulb temperature that is approximately 0.5 *C greater than days with
dry soils, and 1-1.5 *C greater than days in the intermediate soil saturation category. During July,
the driest soil has the lowest, and the wettest soil has the highest, subsequent mean daily
maximum wet-bulb temperature. The difference between the two means is less than 0.5 °C: much
smaller than the 1.5-2 'C ranges we see in the opposite trends in April and May, both of which
have the highest wet-bulb temperatures after days with the driest soils. September also shows this
negative trend, but the range is less than 0.5 oC.
The wet-bulb depression, Td,r = T - Tw, shows the strongest and most consistent trend of
any of the variables studied (Figure 4.7). Whether the mean, minimum or maximum wet-bulb
depression was analyzed, wetter soils were consistently followed by 21 days with a lower mean
wet-bulb depression. The difference in daily maximum, mean, and minimum Tdpr between the
wettest and driest soils was between 2 and 3 *C, 1 and 1.5 *C, and 0.3 to 0.7 *C, respectively, in
each of the months April through September.
The strength of the negative correlation between soil moisture and wet-bulb depression can be
explained by considering the anticipated effects of soil moisture on temperature and mixing ratio:
the variables which ultimately affect Tdpr. As stated above in the discussion of wet-bulb
temperature, we expect increased soil moisture to lead to increased mixing ratio and decreased
temperature. This would have the effect of closing the gap between Tdc and T: at saturation,
21-day Mean of Maximum Wet-bulb Depression Following Soil Saturation (SS) on 1 day in April
8
7.5
...
....
..
.....
.:
. . 0 . ....
7
..
. .
. .
. .
. .
. .
. .
...
. .
. . O ...
.
. .
. .
. ...
.
. .
. .
.
6.5
..+
6
-
5.5
--
0
0.2
0.4
0.6
0.8
Daily Soil Saturation
uA4, %W
U
1
6
8
10
21-day Mean Daily Maximum Tdpr (C)
21-day Mean of Maximum Wet-bulb Depression Following Soil Saturation (SS) on 1 day in May
8.5
0
8
7.5
0
"0
7
r)
6.5
vSS
6
5.5
hSS
U
I
0
0.2
l
I
0.4
0.6
0.8
Daily Soil Saturation
10
21-day Mean Daily Maximum Tdpr (C)
1
21-day Mean of Maximum Wet-bulb Depression Following Soil Saturation (SS) on 1 day in June
8.5
o
8
0
o
7.5
7 . . . . . . . . . . . . . . . .. . ... . . . . . . . . . . . . . .. . . .
0
0
-•0
6.5
6
5.5
0
0.2
0.4
0.6
0.8
Daily Soil Saturation
1
21-day Mean Daily Maximum Tdpr (C)
Figure 4.7: As for Figure 4.3 but for wet-bulb depression (Tdp,); a) April, b) May, c) June.
21-day Mean of Maximum Wet-bulb Depression Follb
8.5
... ..
.-..
.
... .:
. . . . . . . .•. . . . . . .. .. . . . . . . . . . . . . . . . . . . . . . .
I
I
I
IX ···
......................................
.......................................
00
0.8
0.6
0.4
0.6
0.8
1
Daily Soil Saturation
21-day Mean Daily Maximum Tdpr (C)
21-day Mean of Maximum Wet-bulb Depression Following Soil Saturation (SS) on 1 day in August
0.2
0.2
0.4
1
........
+.......
........
.....
..
.......
a 0.8
0
= 0.6
Uo
0.4
O Low SS
o.•
.
I.
.
.i
. .
. .
X
. .
. .
.
····
= V.,•
.
.
/
+.
.•
O .2t.e 0
0
0.2
0.4
0.6
0.8
Daily Soil Saturation
1
:
-t--t
.0
High SS
,
4
6
8
10
21-day Mean Daily Maximum Tdpr (C)
21-day Mean of Maximum Wet-bulb Depression Following Soil Saturation (SS) on 1 day in Sept
1
k
= 0.8
0
" 0.6
.4
Q 0.4
. .)
6
5
. . . . . . . . . .
/ /
70.2
.
0
5
0
0.2
0.4
0.6
0.8
Daily Soil Saturation
.
-
,
O Low SS
+-+
**i High SS
4
21-day Mean Daily Maximum Tdpr (C)
Figure 4.7 (cont.): As above, for d) July, e) August, and f) September.
Taw = Tw = T. Since, by definition, whenever the air is unsaturated Tw lies between the dew-point
and the air temperature, an increase in soil moisture which should lead to a decrease in T - Tkew
will also lead to a decrease in T - T,. The wet-bulb depression, in a sense, amplifies the impacts
that soil moisture has on the temperature and humidity of the air. Weak correlations between
these other two variables lead to stronger correlations with wet-bulb depression.
It is interesting to note that in five of the six months (September being the exception), the
difference between the mean wet-bulb depressions associated with dry and normal soils is greater
than the difference between the mean wet-bulb depressions associated with normal and wet soils.
This is probably due to the moisture threshold controls on evapotranspiration previously discussed
in regard to the results of the temperature analyses.
The temperature at the lifting condensation level, TLCL, is calculated from the formula of
Bolton, (1980):
1
TLCL = 5 5 +
1
ln(f / 100)
TK - 55
2840
(4.4)
During June, July and August, the TLCL is highest, by up to 2 K, after days with wet soils
(Figure 4.8). In July, this temperature is lowest after days with dry soils, making for a consistent
dependence on soil saturation: as soil saturation increases, the TLCL also increases, indicating
lower cloud base heights. This is consistent with the earlier results regarding relative humidity
and wet-bulb depression: as more water is available in the soil, the air is closer to saturation, and a
parcel lifted from the surface reaches saturation at a lower altitude (higher pressure, higher
temperature). During August, however, the lowest soil saturation category shows mean TLCL's
that are approximately 1 K higher than that in the intermediate soil saturation category, and in
21--day Mean of Maximum Temperature of the LCL F4
286
0
I=
o
284
.°
.0
U
282 ........,
2SO
278
1'u
U
E
ro
·· · · · · · ·
I
0
0.2
I
i
I
0.4
0.6
0.8
Daily Soil Saturation
1
280
285
290
21-day Mean Daily Maximum Tlcl (K)
21--day Mean of Maximum Temperature of the LCL Following Soil Saturation (SS) on 1 day in May
0
286
0
.. ..............
284
0
......... .......
80
0
282
1.
.4
:I
280
278
0
I
0.2
0.4
0.6
0.8
Daily Soil Saturation
1
280
285
290
21-day Mean Daily Maximum Tlcl (K)
21-day Mean of Maximum Temperature of the LCL Following Soil Saturation (SS) on 1 day in June
293
0
r-
292
0
............
E 291
.....
.
00
5 290
E
6m
289
0
0.2
0.4
0.6
0.8
Daily Soil Saturation
1
21-day Mean Daily Maximum Tlcl (K)
Figure 4.8: As for Figure 4.3 but for temperature of the lifting condensation level (Tkl); a)
April, b) May, c) June.
66
21-day Mean of Maximum Temperature of the LCL Following Soil Saturation (SS) on 1 day in July
293
0o
292
3
..
..
..
.....
.......... ..
+.
°N
291
c·E
W
790
289
U
0
0.2
0.4
0.6
0.8
Daily Soil Saturation
1
6
21-day Mean Daily Maximum Tlcl (K)
21-day Mean of Maximum Temperature of the LCL Following Soil Saturation (SS) on 1 day in August
293
292
0
E 291
Im0.
0
O
E 290
289
U0
+
I
0
0.2
I
I
I
0.4
0.6
0.8
Daily Soil Saturation
6
1
21-day Mean Daily Maximum Tlcl (K)
21-day Mean of Maximum Temperature of the LCL Following Soil Saturation (SS) on 1 day in Sept
0
q
&II %J
0
|
0.2
+
|
II
|
0.4
0.6
0.8
Daily Soil Saturation
1
280
285
290
21-day Mean Daily Maximum Tlcl (K)
Figure 4.8 (cont.): As above, for d) July, e) August, and f) September.
June the dry and intermediate soils yield equivalent TLCL's. In April and September, the lowest
TLCL
is associated with the wettest soils, and the highest TLCL with the driest soils. The May
pattern is closest to these two, but the intermediate soils have a slightly higher maximum TLCL than
the driest soils.
The temperature of the LCL is an indication of the subcloud layer depth, but it includes no
information about the condition of the LCL relative to the surface. A more appropriate quantity
to describe the cloud base height is the pressure depth of this layer, i.e., the pressure at the surface
minus the pressure at the LCL: PLCL - P,. PLCL is approximated from surface measurements by
calculating the saturation pressure of a surface air parcel. We know from Equation 4.1 that
esat
Wsat
P = esat + esat
(4.5)
where wat is calculated from the surface observations of P and T, but eat is calculated using TLCL.
The work of Betts and Ball (1995) and Betts et al. (1996) supports the theory that dry soil
conditions lead to increased sensible heat flux and increased parcel buoyancy. This leads to a
deeper and drier mixed layer, which suggests a larger pressure depth to the LCL. Indeed, Figure
4.9 shows that, in each of the months, the deepest boundary layers are associated with the driest
soils. Similarly, in April, May, July, and September, the shallowest boundary layers are associated
with the wettest soils. This is not true in June and August, however. This pattern is quite
consistent with the temperature results shown in Figure 4.5. Since the depth to the LCL is closely
related to parcel buoyancy, this correspondence is internally consistent.
The equivalent potential temperature, eE, is often used as a measure of entropy in the
boundary layer. It is defined as the temperature that a parcel of air would have if all the moisture
21-day Mean of Maximum Pressure Depth to LCL Following Soil Saturation (SS) on 1 day in April
22
• 20
0
/
S18
...
.
. . .
. .
-16
.•.
. .
. .
. .
. .
/'0
0.
a 14
...
.......
E 12
...
.........
...)K
10
0
0.2
0.8
0.6
0.4
Daily Soil Saturation
O) Low SS
4-High
High SS
25
20
15
10
21-day Mean Daily Maximum (Plcl - Ps) (mb)
1
21-day Mean of Maximum Pressure Depth to LCL Following Soil Saturation (SS) on 1 day in May
22
I
20
+
= 0.8
18
0
- 0.6
/c
16
I.
a0.4
14
.. . . . .
..
12
.
.
:5 0.2
.
"O
/0p
10
0
0.2
0.8
0.6
0.4
Daily Soil Saturation
OLow SS
+-+
High SS
25
20
15
10
21-day Mean Daily Maximum (Plcl - Ps) (mb)
1
21-day Mean of Maximum Pressure Depth to LCL Following Soil Saturation (SS) on 1 day in June
30
0
28
.•0
26
00
24
=0
QC0
O
22
750
20
18
0
--
E
0~ 0.
0.2
.
.
0.
0.6
0.8
0.4
Daily Soil Saturation
1
21-day Mean Daily Maximum (Plcl - Ps) (mb)
Figure 4.9: As for Figure 4.3 but for pressure depth to the lifting condensation level (Pkl Ps); a) April, b) May, c) June.
21-day Mean of Maximum Pressure Depth to LCL Fc
E
:0
.0
I
o
E
ci
0
2
:
0
0.2
.......................
0.4
0.6
0.8
Daily Soil Saturation
15
20
25
3U
21-day Mean Daily Maximum (Plcl - Ps) (mb)
1
21-day Mean of Maximum Pressure Depth to LCL Following Soil Saturation (SS) on 1 day in August
I
30
"
=
9
7~"-t"rl~iCim~~,
-. 28
0.8
026
U,
. . . . . . . ..
CV
E
. . . . . . . . .. .. .. .. .. .. .. ..
0.6
-
24
E
0.4
+:
22
-
Low SS
E
0.2
0.2
0.4
0.6
0.8
Daily Soil Saturation
et+.,
"
01 3= %W
Y----*-15
20
25
30
21-day Mean Daily Maximum (Plcl - Ps) (mb)
I
0
J:U C!
7-JK1•11 o9
1
21-day Mean of Maximum Pressure Depth to LCL Following Soil Saturation (SS) on 1 day in Sept
0.
................. · ·
20
0.)
0.
. . . . . . . . ... . . . . . . ... . . . . . .
18
16
"==
0.
E0.
*
U
14
*20
2
U
"0.
12
I
0
0.2
I
I
I
0.4
0.6
0.8
Daily Soil Saturation
1
5
21--day Mean Daily Maximum (Plcl - Ps) (mb)
Figure 4.10 (cont.): As above, for d) July, e) August, and f) September.
were condensed out pseudoadiabatically, and then the sample was taken dry adiabatically to a
pressure of 1000 mb (Rogers and Yau, 1989). It is calculated following Bolton (1980):
1000
E
w)
0.2854(-0
exp[(
3.376
37 6
0.00254w(1+ 0.81x10-3 w)
(4.6)
The behavior shown in Figure 4.10 closely mimics that of the wet-bulb temperature shown
in Figure 4.6, but the temperature differences are amplified on the OE scale. The results of the
analysis between the wet-bulb potential temperature, 0,, (which is calculated by substituting Tw
for T in Equation 4.2) and soil moisture also mimics the patterns of Tw and OE, as expected by the
one-to-one relationship between 0w and both of these other variables. Figure 4.11 shows these
results. This correspondence between OE, Ow, and Tw is consistent with the discussion in Chapter
2: all three variables are measures of the boundary layer entropy, or the moist static energy in the
boundary layer.
21-day Mean of Maximum Equivalent Potential Temperature Following Soil Saturation (SS) on 1 day in April
330
325
320
315
........
....
............
........
.......
310
l
0
I
0.2
I
I
1
0.4
0.6
0.8
Daily Soil Saturation
1
300
310
320
330
3'40
21-day Mean Daily Maximum ThetaE (K)
21-day Mean of Maximum Equivalent Potential Temperature Following Soil Saturation (SS) on 1 day in May
330
-··
· ·
325
· · ·
·
+
:··
............
320
E
.........:.
.......
315
310
I ,
I
I
0
0.2
I
0.4
0.6
0.8
Daily Soil Saturation
1
0
21-day Mean Daily Maximum ThetaE (K)
21-day Mean of Maximum Equivalent Potential Temperature Following Soil Saturation (SS) on 1 day in June
355
S350
.345
0:
340
335
330
. .
. .
I
0
0.2
. .
I
I
I
0.4
0.6
0.8
Daily Soil Saturation
1
21-day Mean Daily Maximum ThetaE (K)
Figure 4.10: As for Figure 4.3 but for equivalent potential temperature (OE); a) April, b)
May, c) June.
0
^"
21-day Mean of Marimum Equivalent Potential Temperature Following Soil Saturation (SS) on 1 day in July
355
0
.....
... .... .... ...
350
,I
Z 345
I
E=
:t.. ..
340
.
i=
0
. ............
......
..
S335
ro
2U
22a~
0
21-day
0.2
0.4
0.6
0.8
Daily Soil Saturation
of
Mean
Maximum
Equivalent
0
1
21-day Mean Daily Maximum ThetaE (K)
Temperature
Potential
355
S0.
0
-350
0.
w 345
0
340
- -- - --o
:
:· · · · ·:··
~ 0.
--
335
o
rJ
211n
JJv
360
350
340
330
0.8
1
0.4
0.6
21-day Mean Daily Maximum ThetaE (K)
Daily Soil Saturation
21-day Mean of Maximum Equivalent Potential Temperature Following Soil Saturation (SS) on 1 day in Sept
0
0.2
0o
330
325
E
+-
320
0
315
310
0.
E
•°
U
0
0.2
0.4
0.6
0.8
Daily Soil Saturation
1
;0
21-day Mean Daily Maximum ThetaE (K)
Figure 4.10 (cont.): As above, for d) July, e) August, and f) September.
21-day Mean of Maximum Potential Wet-bulb Temperature Following Soil Saturation (SS) on 1day in April
·
I
·
·
292
291
290
289
288
287
..........
286
•
X
285
0
0.2
0.4
0.6
0.8
Daily Soil Saturation
1
285
290
295
21-day Mean Daily Maximum ThetaW (K)
21-day Mean of Maximum Potential Wet-bulb Temperature Following Soil Saturation (SS) on 1 day in May
·
·
·
·
1
o
292
' 0.8
,,291
-a
~290
• 0.6
E 289
.0
S288
S0.4
287
S0.2
C
286
'
) Qr
i
|
0
I
4."0 Low SS
!
0.4
0.6
0.8
1
21-day Mean Daily Maximum ThetaW (K)
Daily Soil Saturation
21-day Mean of Maximum Potential Wet-bulb Temperature Following Soil Saturation (SS) on 1 day in June
L
0.2
·
/
·
I
o
o
296
F
295
· ·
0
0
·
·
"I
6 00
294
0
E
293r
m
0
0.2
m
m
m
0.4
0.6
0.8
Daily Soil Saturation
21-day Mean Daily Maximum ThetaW (K)
Figure 4.11: As for Figure 4.3 but for wet-bulb potential temperature (0.); a) April, b)
May, c) June.
,,
21-day Mean of Maximum Potential Wet-bulb Temperature Following Soil Saturation (SS) on 1 day in July
2
C
0
, 296
o
C.)
2 95
. ..
-
i
i
!
S0.
7nU, 0.
.0.•
294
293
0.
" 0.
U
0
0.2
0.4
0.6
0.8
Daily Soil Saturation
1
21-day Mean Daily Maximum ThetaW (K)
21-day Mean of Maximum Potential Wet-bulb Temperature I
·
·
·
297
c
0
C .
• 296
n0.
0.
o
- 295
n0.
0o
E
E
9294 E · ·- ·
293i
0
+•
0.2
U0
•0.
m=0.
Ej
0.4
0.6
0.8
Daily Soil Saturation
1
292
294
296
298
21-day Mean Daily Maximum ThetaW (K)
21-day Mean of Maximum Potential Wet-bulb Temperature Following Soil Saturation (SS) on 1 day in Sept
0o
292
S0.
291
- .......
....
..+.,..
~ 290
"
0.
9 289
Q 0.
:
...................................
288
287
0.
·· ·
286
285
--
vv
U
I
0
0.2
I
I
i
0.6
0.8
0.4
Daily Soil Saturation
1
295
285
290
21-day Mean Daily Maximum ThetaW (K)
Figure 4.11 (cont.): As above, for d) July, e) August, and 1)September.
D.
Analysis of the Linear Correlation Between Soil Saturation and
Subsequent Boundary Layer Conditions Throughout the Year
To test the annual cycle of any linear correlation which might be present between soil
saturation and any of the boundary layer variables considered, time series of the correlation
coefficients between soil saturation and the minimum, mean, and maximum daily values of each of
the 12 variables were generated for the full year. This procedure was similar to that described in
Chapter 3: for each day of the year, the linear correlation between the 15 years of data pairs (soil
saturation on that day, and the mean of the variable in question over the following 21 days) was
quantified by the coefficient of determination ( 2). (The procedure described in Chapter 3 tested
pairs which consisted of soil saturation on a given day and the subsequent 21-day total rainfall,
rather than the mean daily rainfall.) The results for relative humidity and wet-bulb depression are
shown in Figures 4.12 and 4.13, respectively, for the minimum (top plot), mean (middle plot), and
maximum (bottom plot). Figures 4.14 through 4.20 show the results of only the maximum of
each of the other variables: the minimum and mean for each variable show very similar results.
Each of these plots is calculated using soil saturation in the top 10 cm. The level of significance
lines are computed by relating the r2 to an F-distribution with 1 and 15 degrees of freedom, as
described in Chapter 3. The 5% level of significance yields an ? of 0.2643, while the 10% level
of significance yields an r2 of 0.1945.
Only relative humidity (Figure 4.12) and wet-bulb depression (Figure 4.13) show a
significant linear correlation with soil saturation in all of the daily minimum, mean, and maximum.
These correlations are strongest from mid-May through mid-September, but mid-April, early
October, and late November all show local peaks with significant correlations. As stressed in
Chapter 3, the level of significance lines on these correlation time-series figures are calculated for
the individual data points. The solid line, representing a 21-day moving average, is significant at
lower r2, due to the averaging process.
A few other variables have brief periods of significance. The minimum, mean, and
maximum temperature of the lifting condensation level (Figure 4.17) are all significant for a week
or two at the end of June, and again at the end of November. The maximum daily temperature
(Figure 4.15), and the maximum pressure depth to the LCL (Figure 4.18) pass above the 10%
level of significance line for a few weeks at the beginning of May, and again at the end of August,
lasting past the middle of September.
It should be stressed that these figures show only the degree of linear correlation between
soil saturation and each of the boundary layer quantities: non-linear relationships, such as
threshold behavior, will not be captured by this analysis. The negative correlation between soil
moisture and measures of parcel buoyancy (T, 0, Tv, PLcL-Ps) seen during the spring and fall in the
previous section is captured in the linear correlation analysis presented here, but the possible
threshold dependence of evapotranspiration on soil moisture cannot be captured by the linear
correlation coefficient. This accounts for the June-August drop in the r2 in the daily maximums of
these variables.
The negative correlations seen in Section C between the measures of boundary layer
entropy (OE in Figure 4.10, Ow in Figure 4.11, and Tw in Figure 4.6) and soil moisture during the
spring and fall were not strong enough to show up in the linear correlation analysis of this section.
Nevertheless, it is revealing to see that wet-bulb depression and relative humidity have such a
strong summertime relationships with soil saturation.
Correlation Between Soil Saturation and 21-day Mean of Daily Minimum Relative Humidity
1
O-0.8
0.6
0.4
0.2
n
Nov
Deýc
Oct
Sept
Aug
June
July
May
Apr
Day Beginning Minimum Relative Humidity Window
Correlation Between Soil Saturation and 21-day Mean of Daily Mean Relative Humidity
Feb
Mar
Jan
Feb
Mar
Jan
Feb
Mar
Jan
1
0.8
• 0.6
0.4
U
0.2
A
Apr
May
June
July
Aug
Sept
Oct
Nov
D
Day Beginning Mean Relative Humidity Window
Correlation Between Soil Saturation and 21-day Mean of Daily Maximum Relative Humidity
Xc
1
0.8
0.6
S0.4
0.2
n
Apr
May
June
July
Aug
Sept
Oct
Day Beginning Maximum Relative Humidity Window
Nov
D Xc
Figure 4.12: Linear correlation between initial soil saturation (SS) and average (a)
minimum daily, (b) mean daily, and (c) maximum daily relative humidity (f)in the
subsequent 21 days, as measured by the coefficient of determination (r). Solid line
is 21 day moving average. "LOS" lines are 5 and 10% level of significance lines for
the r? variable (not the smoothed line).
All of Illinois: Soil Day Preceeds 21 Day Min WBD Window; 21 day smoothing
0.
0.
0.
0.
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Day Beginning Min WBD Window
All of Illinois: Soil Day Preceeds 21 Day Mean WBD Window; 21 day smoothing
Dec
Jan
Feb
Mar
Apr
Oct
Nov
July
Aug
Sept
May
June
Day Beginning Mean WBD Window
All of Illinois: Soil Day Preceeds 21 Day Max WBD Window; 21 day smoothing
Dec
Jan
Feb
Mar
Apr
L..
'4
0
'44.
0
U
1
0.8
S0.6
S-0.
4
0.2
0
Sept
June
July
Aug
May
Day Beginning Max WBD Window
Figure 4.13: As for Figure 4.12, but for wet-bulb depression (T4,).
Oct
Nov
Dec
Correlation Between Soil Saturation and 21-day Mean of Daily Maximum Mixing Ratio
I
1K
t
.
I
*
..
...
.'tl
Jan
Feb
Mar
. -
S
/
s
L
Apr
May
June
July
Aug
Sept
Day Beginning Maximum Mixing Ratio Window
Oct
Nov
Dec
Figure 4.14: As for Figure 4.12c but for maximum daily mixing ratio (w).
Correlation Between Soil Saturation and 21-day Mean of Daily Maximum Temperature
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Day Beginning Maximum Temperature Window
Oct
Nov
Dec
Figure 4.15: As for Figure 4.12c but for maximum daily air temperature (T).
Correlation Between Soil Saturation and 21-day Mean of Daily Maximum Wet-bulb Temperature
I
0.8 -
I
I
I
'
I
I I
I
I
II
I
'
I
I
I
I
Soil Saturation in Top 10 cm
0.6
0.4
5% L.O.S.
0.2
0
..,•-.----
-----
10% L.O.S..-
Jan
Ja Feb
Feb
Ma
Mar
p
Apr
s
ýb~L
-~I 7 I~ICL~
·
~JYIi
V1~
a
May
Jn
June
- ----
-
IC~
rC
etOtN
uyAg
July
-- ,•..
•-,--~r-/-,-
Aug
Sept
Oct
Day Beginning Maximum Wet-bulb Temperature Window
N(ov
Figure 4.16: As for Figure 4.12c but for maximum daily wet-bulb temperature (T,).
Dec
Correlation Between Soil Saturation and 21-day Mean of Daily Maximum Temperature of the LCL
I'
0.8
I
I
'
I
I
I
I
I
I
I
I
I
I
Soil Saturation in Top 10 cm
0.6
0.4
5%L.O.S.
0.2 10% L.O.S.
•
-
- --- - - ---i-
o
•
o
0
Jan
Feb
•
:
----- -
.
. -.-
0
Mar
Apr
May
June
July
Aug
Sept
Oct
Day Beginning Maximum Temperature of the LCL Window
Nov
Dec
Figure 4.17: As for Figure 4.12c but for maximum daily temperature of the lifting
condensation level (TLCL).
Correlation Between Soil Saturation and 21-day Mean of Daily Maximum Pressure Depth to LCL
1
0.8
0.6
o
U
0•.4
0.2
0
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Day Beginning Maximum Pressure Depth to LCL Window
Nov
Figure 4.18: As for Figure 4.12c but for maximum daily pressure depth to the lifting
condensation level (PLCL - P,).
Dec
Correlation Between Soil Saturation and 21-day Mean of Daily Maximum Equivalent Potential Temperature
1
0.8
I
'
'I
I
I '
I
I
I
'
I
I
I
I
I
I
I
'
'
Soil Saturation in Top 10 cm
0.6
0.4
5%L.O.S.
L.O.S.
P10%.-.-..-.---.
4b
*
--
...
Feb
--
• -
.*
-i"i
- "l.
- ""
..
:
Jan
"---- •
0
9.
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Day Beginning Maximum Equivalent Potential Temperature Window
Dec
Figure 4.19: As for Figure 4.12c but for maximum daily equivalent potential temperature
(oE)*
Correlation Between Soil Saturation and 21-day Mean of Daily Maximum Wet-bulb Potential Temperature
I
SI
I ' I I I ' I
II I I
I
I
I
I I
0.8
Soil Saturation in Top 10 cm
0.6
0.4
5%L.O.S.
:
10% L.O.S.
.
. ..
Jan
Feb
,-" +
*
..-.
A
I
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Day Beginning Maximum Wet-bulb Potential Temperature Window
Figure 4.20: As for Figure 4.12c but for maximum daily wet-bulb potential temperature
(OW).
-
Dec
Figures 4.21 and 4.22 show the correlation between wet-bulb depression and soil
saturation averaged over deeper depths: the top 50 cm in Figure 4.21, and the top 90 cm in Figure
4.22. The summertime significance of this correlation is seen in both plots, but it is damped with
depth.
Correlation Between Soil Saturation and 21-day Mean of Daily Maximum Wet-bulb Depression
1
0.8
0-k
0.6
0.4
0.2
A
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Day Beginning Maximum Wet-bulb Depression Window
Nov
Dec
Figure 4.21: As for Figure 4.12c but for initial soil saturation in the top 50 cm and average
maximum daily wet-bulb depression (T,,) in the subsequent 21 days.
Correlation Between Soil Saturation and 21-day Mean of Daily Maximum Wet-bulb Depression
I
0.8
0.6
4-
0.4
U
0.2
A
Jan
Feb
Mar
Oct
July
Aug
Sept
Apr
May
June
Day Beginning Maximum Wet-bulb Depression Window
Nov
Dec
Figure 4.22: As for Figure 4.12c but for initial soil saturation in the top 90 cm and average
maximum daily wet-bulb depression (To,,) In the subsequent 21 days.
E.
Discussion of Results
This chapter focused on the relationships between soil moisture conditions and subsequent
boundary layer conditions, as described by observations of near-surface air. There were three
main classifications of variables analyzed:
1) Measures which are functions of both the temperature and the degree of saturation:
* relative humidity,f, and
* wet-bulb depression, Tdpr;
2) Measures of buoyancy:
* temperature, T,
* potential temperature, 0,
* virtual potential temperature, a0, and
* pressure depth to the Lifting Condensation Level, PLCL - P,; and
3) Measures of moist static energy:
* wet-bulb temperature, Tw,
* wet-bulb potential temperature, 0,, and
* equivalent potential temperature, OE.
Additional variables included in the analysis were mixing ratio, q, which is a measure of
the water content, but contains no information about the air temperature (or, therefore, about the
relative humidity), and the temperature of the Lifting Condensation Level, TLCL, which is related
to the depth of the boundary layer, but contains no information about the pressure at the LCL, or
the pressure or temperature of the surface relative to the LCL.
The first category of variables, measures of temperature and saturation, showed a strong
and clear dependence on initial soil saturation. The results show that days with wetter soil
moisture conditions tend to be followed by days with surface air closer to saturation.
Neither the buoyancy nor the energy variables show such a clear relationship to initial soil
moisture conditions. Days with dry soils are, on average, followed by periods of greater
buoyancy than either the normal or wet soil days, but the wet soil days tend to be followed by
periods of greater buoyancy than the normal soil days. This is potentially due to the fact that lack
of moisture at the surface can be the limitation for evaporation when soils are dry, but once the
soil is wetter than some threshold, the moisture source is no longer the controlling factor on
evaporation.
The energy variables show less of the expected trends than the buoyancy variables. As'
discussed in Chapter 2, previous studies have shown a positive association between soil moisture
and moist static energy in the boundary layer (e.g., Betts and Ball, 1995: higher soil moisture
leads to higher OE). The results presented here, however, show a negative correlation between
soil moisture and the energy variables during the spring and fall, a very slight positive correlation
in July, and mixed results in June and August.
Though these results are quite illustrative of the strong impact the soil conditions can have
on the wet-bulb depression of near-surface air, further analyses are needed to more accurately
determine the relationships between the land surface and the whole boundary layer. It is not clear
if surface observations are appropriate indicators of the conditions throughout the boundary layer;
further analyses should include upper air data. Nor is it clear that the limitations of the soil
moisture dataset discussed in Chapter 3 and/or the limited number of hourly surface observations
stations are not dampening the strength of the theoretical relationships between soil moisture and
moist static energy of the boundary layer discussed in the Chapter 2.
Despite these data limitations, the analyses in this chapter clearly show that soil moisture
has a positive impact on the wet-bulb depression of near-surface air during the summer months.
This correlation become significant in mid-May, and persists through mid-September, almost
perfectly matching the time period of significance of the soil moisture-rainfall correlation
discussed in Chapter 3.
The soil moisture-wet-bulb depression correlation is strongest with the daily maximum
Tdpr,
rather than the minimum or mean. The maximum Tdp, usually occurs a few hours after the
noontime peak of solar forcing, corresponding to the usual time of occurrence of local convective
storms. The next chapter will discuss this temporal dependence of the mechanisms initiating
rainfall, and will then investigate the question of what boundary layer conditions are most
favorable for convective rainfall during the summer.
Chapter 5: The Relationships Between
Boundary Layer Conditions and Rainfall
A.
The EarthInfo NCDC Hourly Rainfall Database
The hourly rainfall data used in this analysis was obtained through EarthInfo, Inc. This
dataset is a subset of the National Climatic Data Center's (NCDC's) TD-3240 file, with hourly
precipitation records for many stations throughout the United States beginning in 1948. Within
Illinois, there were 82 stations with consistent hourly rainfall records. The locations of these
stations are shown in Figure 5.1. Also shown in this figure are the locations of the Surface
Airways Stations discussed in Chapter 4. These data will again be used to quantify the hourly
conditions of the boundary layer.
B.
The Diurnal Cycle of Rainfall in Illinois
There are three main mechanisms of initiating rainfall in Illinois: the Low Level Jet, which
brings air north from the Gulf of Mexico during the night when the boundary layer over the Great
Plains has collapsed (Carlson and Ludlam, 1966; Bonner, 1968; McCorcle, 1988), synoptic
systems associated with the Jet Stream from the north and west, and locally triggered small-scale
convective storms. It is this third type of storm that is the focus of this study on the effects of soil
moisture on rainfall in Illinois; however, it is very difficult to isolate these events from the synoptic
scale events.
Small-scale convective storms generally are due to local instabilities in the vertical
distribution of temperature and humidity. Eltahir and Pal (1996) present a detailed discussion of
the triggering mechanisms leading to the release of energy associated with convective rainfall
events.
Locations of NCDC Surface Airways Stations (o)and Rainfall Stations (*)
J•
43
42
41
Z
40
39
38
37
-92
-91
-90
-89
-88
-87
-86
Longitude (degrees W)
Figure 5.1: Locations of the NCDC Hourly Rainfall Stations (*)and the NCDC Surface
Airways Stations (o). Solid line is the Illinois state boundary.
Figure 5.2 shows the diurnal cycle of rainfall during the years of this analysis, 1981 to
1995, for each of the months between April and September. It is clear from the left-most column
that there is very little evidence of a diurnal cycle in the average depth of rainfall per hour. In
tropical climates, most of the rainfall occurs during afternoon thundershowers, and the average
depth of rain during the afternoon hours can be many times that of nighttime hours (see, for
example, Eltahir and Pal, 1996). In Illinois, however, the largest range for any month shows the
maximum average hourly rainfall rate is at most only two times the minimum rate (0.01 to 0.02
cm per hour), and the minimum comes at mid-day, rather than during the night, as in the tropical
case. During August and September, there is virtually no dependence on time of day. Clearly, the
situation in Illinois is quite different from that of the tropics, even during the summer.
The plots in the middle column of Figure 5.2 show, for each month, the average duration
of storms initiated during each hour of the day. Similarly, the right-most plots show the
probability of storm initiation for each hour of the day. In general, the average storm duration
peaks in the early morning hours, while the probability of storm initiation peaks in the afternoon.
These two plots combine to explain the lack of a diurnal cycle in the depth of rainfall: early
morning (after midnight) storms are long but fairly rare, while late afternoon storms are short but
more frequent. April, May, June and July show a minimum in rainfall depth near mid-day, when
neither the storm duration nor the probability of initiation is peaked. August and September show
less of a diurnal cycle in storm duration or likelihood of initiation than the earlier months. This is
reflected in the near-constant average rainfall depth throughout the day.
The long early morning storms are likely the result of large-scale forcing by the Low Level Jet,
which originates over the Gulf of Mexico, and carries warm, moist air onto the continent when
the boundary layer is not present (Carlson and Ludlam, 1966; Bonner, 1968; McCorcle, 1988).
The late afternoon storms are likely the convective storms we wish to investigate. The analyses
presented in this chapter will focus on boundary layer conditions, as described by surface
observations, between 2 and 6 PM, and rainfall in the hour following each surface observation,
i.e., 3 to 7 PM. We focus on rainfall in the hour after a given surface observation to avoid
contamination of boundary layer data by rainfall events. Since convective rainfall is a threshold
process, where energy is stored until some factor lifts the air past an energy barrier, we discard
any data observed while rainfall was occurring. This allows us to focus on role that the boundary
layer plays in triggering rainfall events.
Also removed from the analysis are hours preceding large-scale events, defined by
continuous rainfall for more than five hours. This is an attempt to remove the synoptic influence
from the data. The five hour threshold was varied between three and eight hours, with little to no
change in the results. This is consistent with the above analysis of the diurnal cycle of rainstorm
duration: very few large-scale storms occur during the afternoon.
April: The Diurnal Cycle of Rainfall Depth, Storm Duration, and Storm Initiation
Diurnal Cycle of Rainfall Depth
Hourly Average Storm Duration Probability of Rain Beginning in a Given Hour
·
U.UL
·
·
U.J
0
i
U.4
0.015
0.3
S0.01
0.005
0.2
F
ra
U. I
F
n
5
10
15
20
0
5
10
15
20
Hour in Day
For Storms Initiated During Given Hour
Hour of Initiation
May: The Diurnal Cycle of Rainfall Depth, Storm Duration, and Storm Initiation
Diurnal Cycle of Rainfall Depth
Hourly Average Storm Duration Probability of Rain Beginning in a Given Hour
,,
0C
0.02
U.f
ES0.015
0o
I
cA
s
r
0.3
0
0.01
S0.2
0.005
U.I
0
I
0
5
I
I
10
15
Hour in Day
I
l
0
5
10
15
20
For Storms Initiated During Given Hour
0
5
l
l
I
10
15
20
Hour of Initiation
June: The Diurnal Cycle of Rainfall Depth, Storm Duration, and Storm Initiation
Hourly Average Storm Duration Probability of Rain Beginning in a Given Hour
: iurnal Cycle of Rainfall Depth
0.02
0.3
10
·
I
em
0.015
I.-S
S0.01
0 0.3
0.2
U'
~ 0.2
or
p
C-
o 0.005
!
st
em3
0I
3
.
.
,
n
n· ·
J
20
15
10
5
0
20
15
10
5
0
15 20
10
Hour of Initiation
For Storms Initiated During Given Hour
Hour in Day
July: The Diurnal Cycle of Rainfall Depth, Storm Duration, and Storm Initiation
Hourly Average Storm Duration Probability of Rain Beginning in a Given Hour
Diurnal Cycle of Rainfall Depth
5
0.02
0
o
'-4
4-
0.01
an
o 0.005
0
0.10
w
5
20
15
10
Hour in Day
15
20
0
5
10
For Storms Initiated During Given Hour
0
-J
I
•
V.
1u
13
zu
3
Hour of Initiation
August: The Diurnal Cycle of Rainfall Depth, Storm Duration, and Storm Initiation
Diurnal Cycle of Rainfall Depth
Hourly Average Storm Duration Probability of Rain Beginning in a Given Hour
0.02
af
u'
re
1
-
1
_
·
S0.015
S0.01
S0.005
a
r2
0
n
10
15 20
0
5
10
15
20
0
5
10
15
20
Hour in Day
For Storms Initiated During Given Hour
Hour of Initiation
September: The Diurnal Cycle of Rainfall Depth, Storm Duration, and Storm Initiation
of Rain Beginning in a Given Hour
Hourly Average Storm Duration Probability
Diurnal Cycle of Rainfall Depth
,,
I
0.02
I
I
I
0
5
I
*
1
·
U.,3
,,
U.4
S0.01
L
',
'aBo
a.,
0.3
~A~-JAVAA\
0.01
,a
0.2
g0.005
ni
LU. r
I
II
0
5
I
I
10
15 20
Hour in Day
0
5
10 15 20
For Storms Initiated During Given Hour
5
10
15
20
Hour of Initiation
C.
Analysis of Afternoon Storm Events and the Preceding Boundary
Layer Conditions
The pressure at the ground surface is often a good indicator of the synoptic setting of the
region: low pressure centers are associated with cyclonic flow, which causes convergence, lifting,
and, quite often, rainfall. Figure 5.3 shows that the afternoon hours of 2 to 6 PM are not free of
this dependence. The right-most columns show the probability of the initiation of rainfall after an
hour with pressure in a given bin, centered around each astrix. The raw data, shown in the leftmost columns of Figure 5.3, are grouped such that each of ten bins has an equal number of data
points. Ten bins was chosen arbitrarily, but was used consistently in all the subsequent analyses to
minimize the bias that can be introduced by the bining process. After removal of the abovementioned data points, still remaining were between 1190 and 1640 valid observations each
month. The number of data points in each bin ranged from 119 in April to 164 in September.
The raw data are presented in all subsequent analyses so that the effects of bining are clear.
However, many of the data points have zero rainfall and are overlain on the raw data plots.
The middle columns in Figure 5.3 show the average depth of rain per hour, given that
rainfall did indeed occur, associated with the ten bins in the probability of initiation plots. Little
association between pressure and average depth of rain in the subsequent hour is observed. The
probability of initiation plots, however, show that, during each month, rainfall is more likely to
begin after hours with a low pressure than after hours with a relatively high pressure. This
suggests that though other boundary layer conditions may be associated with occurrence of
rainfall, as the results presented herein will demonstrate, the synoptic influence may assist in
triggering rainfall events and cannot be neglected. This will be discussed in greater detail in the
next section.
April: Rain Initiated in the Hour After Pressure Observed Between 1400 and 1800; Storms < 5 hrs
•e
ul
9:
ta
11
o
0.12
0.1
0.025
0.08
0.02
ii
ga
0.06
,
0.04
-
0.02
N
)K
to
L
-9mC~C
980
,q
0.06
E
aI
0.04
0.02
-
o
O
O90
0
0.005
0.10
*
*
0.05
0
N
0.03
0.025
1
·I
1010
0.2
r2 = 5.5%
rA2=49%
0.15
-
< 0.02
-
0
" *a
o0.1
0.015
*
)K
*
0.01
0
N
980
990
1000
Hourly P
00
)Km
0.05
0
0.005
sj~eX
n
970
4-o
10
-
-
0.15
N
~Y
0.1
me
rA2 = 32%
10
990
1000
970
980
990
1000 1010
970
980
990
1000
Hourly P
Average Hourly P
Average Hourly P
May: Rain Initiated in the Hour After Pressure Observed Between 1400 and 1800; Storms < 5 hrs
0.12
0.08
r^2 = 7.2%
0.01
r
970
0.015
0.2
*
oo
II
v
0
04
*
000
tf
0.03
·
1010
1
970
n
980
990
1000
Average Hourly P
1010
97(0
I
I
I
980
990
1000
Average Hourly P
1010
June: Rain Initiated in the Hour After Pressure Observed Between 1400 and 1800; Storms < 5 hrs
0.03
0.025
U5
0
0.15
u.4
-r^2 = 5.3%
0.3
14
)KE
0.02
O
o1
X A
A
0.05
0.015
X)
bo
N
I
9710
980
00.2
O
0.01
)K
*
L
0
0
0.005
N
L
o0.1
O
0~4
n
**
970
970
980
990
1000
980
990
1000 1010
990
1000 1010
970
Average Hourly P
Average Hourly P
Hourly P
July: Rain Initiated in the Hour After Pressure Observed Between 1400 and 1800; Storms < 5 hrs
1010
UUJ
0035
.U03
0
0.03 r^2 = 10%
0.15
0.025
)K
*
0.05
N
-
97'0
-
0.015
0.01
0.005
990
1000
Hourly P
1010
-D
00.
00
,
970
0.1.
O0O
o
-
N L
980
* X )K
0
0.02
X
*
A
X
*lIE
*m *
L
rA2 = 30%
*
X
n
***
980
990
1000
Average Hourly P
05-
*X
1010
970
980
990
1000
Average Hourly P
1010
August: Rain Initiated in the Hour After Pressure Observed Between 1400 and 1800; Storms < 5 hrs
0.03
0.5
r2 = 0.27%
0.025
.0.4
r"2 = 69%
*39
)
0.15
0.02
S0.3
0
0
cP0
.i.=
0.015
00.2
0.005
1010
n 2_
970
*
)K
*K )
0.1
)KN
oa
O0
0
0.05
)
n
980
0cU
o
0
,a 0.01
a0.1
O
*
*
1
n
...
1
.980
990 1000
)10
970
970
980
990
1000
990
1000 1010
Average
Hourly P
Average Hourly P
Hourly P
Sept: Rain Initiated in the Hour After Pressure Observed Between 1400 and 1800; Storms < 5 hrs
1010
0.(
03
0.12
a
0.025
0.1
0r^2 = 26%
rA2 = 50%
0.15
S0.08
00
0o
0.02
o
**
0.06
0.015
2 0.04
0.01
0.02
0.005
0
970
*
X)
)K
0 O
0.05
OOO000
n
n
980
990
Hourly P
1000
1010
970
)K
980
990
1000
Average Hourly P
1010
97(0
980
990
1000
Average Hourly P
1010
Please note in all Figures 5.3 through 5.13 that the axes scaling are variable. The spring
and fall months (April, May, and September) have the same x-axis scaling for each variable, as do
the summer months (June, July, and August). The two groups often have different x-axis ranges.
The y-axes are scaled according to the results, so careful attention should be paid to these limits.
Relative humidity is shown in Figure 5.4 to have a strong association with the initiation of
rainfall in the subsequent hour during all of the six months studied. The linear correlation
between relative humidity and the probability of initiation of rainfall is strongest during the
summer months of June, July and August, when the r 2's are all between 79 and 83%. The
average depth of rain in the hour following an observation shows almost no association with
relative humidity.
Figure 5.5 shows that mixing ratio displays a similarly close association with the likelihood
of rainfall as relative humidity, but it tends to be a better predictor of rainfall depth in the
subsequent hour. The r2 s of the probability of occurrence are quite high in June and August,
lower during spring and fall, and quite low in July. The month of July exhibits some interesting
behavior at both extremes of low and high mixing ratio. Between about 10 and 16 g/kg, there is a
strong positive correlation between w and the probability of initiation of rain, with probabilities
changing from approximately 0.07 to 0.17. The two bins beyond 16 g/kg, however, show that
rainfall is less likely to begin in these very wet circumstances. The highest w bin, centered near 20
g/kg, has dropped down to a probability of about 0.08: as low as the bin centered near 11 g/kg.
The August data also show this drop in probability for the highest w group, but the transition is
much less extreme: from about 0.18 to 0.17.
101
April: Rain Initiated in the Hour After Relative Humidity Observed Between 1400 and 1800; Storms < 5 hrs
0.03
0.12
U
U
0.1
0.08
0.06
0.025
i
0.2
r^2 = 19%
rA2 = 67%
0.15
I
0.02
)K
0.04
XR *
0.02
HE
0.015
0
)K
0O
0.01
0.005
*~
S0.1F
O
I-
M
. 0.05
) *
HKE
0
O
0
(9
O
)K
|
100
50
100
50
Average Hourly RH
Average Hourly RH
Hourly RH
May: Rain Initiated in the Hour After Relative Humidity Observed Between 1400 and 1800; Storms < 5 hrs
r
0.12
100
0.03
U
0.1
0.025
0.08
0.02
r^2 = 0.15%
r^2=55%
**
K
0.15
.8
0.015
0.06
0.04
1o
C.)
0.02
E
K
)K
0.1
mm
0.01
O0 o
0.005
o ood
0.05
o
)1S
HE
XEH
**
)
E
50
Hourly RH
100
50
Average Hourly RH
100
50
Average Hourly RH
100
June: Rain Initiated in the Hour After Relative Humidity Observed Between 1400 and 1800; Storms < 5 hrs
0.03
rA2 = 79%
rA2 = 5%
.0
U
'.
0.02
0.3
0
I.
U
• 0.015
U
I.
O
O0000
5 0.01 i
'4.
0.2
O
0
m
X
X
X
O
0.1
00
0.005
)
<
10
0
1
I
100
100
Average Hourly RH
Hourly RH
July: Rain Initiated in the Hour After Relative Humidity Observed Between 1400 and 1800; Storms < 5 hrs
Average Hourly RH
Y ~I\CI
U.U0
0.025
."
0.4
rA2 = 79%
rA2 = 0.15%
0.02
r 0.(15
'
0.3
L
.4z
'.
0
). 1
*
*K
*9
)K-
05
I
0
)K
0.2
C.)
0.01
m
0.
o0
0.015
00.1
_]
*)
0.005
|
m
50
Hourly RH
----
100
100
Average Hourly RH
50
Average Hourly RH
100
August: Rain Initiated in the Hour After Relative Humidity Observed Between 1400 and 1800; Storms < 5 hrs
0.5
0.05
W
3,0.4
rA2 = 83%
5 0.04
0.3
0.03
0.2
0.02
10.3
o4-
r 0.2
O
o
0
0.1
S0.01
- 0.11
X
I
_
)
S0
50
100
C1
1C
)0
50
Hourly RH
Average Hourly RH
Average Hourly RH
Sept: Rain Initiated in the Hour After Relative Humidity Observed Between 1400 and 1800; Storms < 5 hrs
•
1
- -
0.12
·:
0.1
|
100
0.03
rA2 = 62%
rA2 = 5.1%
0.025
F
0.15
0.08
0.02
C.
0.06
0.015
0.04
0.02
O
0
0.01
A X
)K
0.05
0.005
)K
o
00
Oo
*m
)K0)
at
0
-,-,,.....--1
50
Hourly RH
100
50
Average Hourly RH
100
0
50
Average Hourly RH
100
April: Rain Initiated in the Hour After Mixing Ratio Observed Between 1400 and 1800; Storms < 5 hrs
0.12
0.03
50.1
0.025
rA2 = 68%
r2 = 61%
0.15
0.02
, 0.08
00.06
A
0.015
0.1
0
E
2 0.04
0.01
K
~ 0.02
aLN
A
0
\
*
1
K
X
m~iD-f~'j
)KW)K
)K
X
)K
cOOO
0.005
)K
,
5
0.05
00
0
)K
I
i
I
•
5
10
15
15
20
0
5
10
15
20
10
Average Hourly w
Average Hourly w
Hourly w
May: Rain Initiated in the Hour After Mixing Ratio Observed Between 1400 and 1800; Storms < 5 hrs
^
0.2
0.03
r"2 = 70%
0.025
" 0.15
0.02
o
0.015
0.01
O
0 O
0.005
I
0
Hourly w
o 0.1
O
I
-0.05
I
5
10
15
Average Hourly w
I
20
5
10
15
Average Hourly w
June: Rain Initiated in the Hour After Mixing Ratio Observed Between 1400 and 1800; Storms < 5 hrs
A
0.03
__
rA2 = 27%
0.025
0.15
F
0.3
X
0.02
O
0.1
0.05
0.01
KX*
00O
000
0.005
**
0
S0.2
O0
0.1
n
*~r;* mommommme0
5
10
15
20
0
5
10
15
20
10
15
20
Hourly w
Average Hourly w
Average Hourly w
July: Rain Initiated in the Hour After Mixing Ratio Observed Between 1400 and 1800; Storms < 5 hrs
II
I
5
O
0.015
)K
I
•
U.4
|
|
|
0.03
0.2
rA2 = 3.1%
O
0.025
s 0.15
r2 = 23%
K
)K
0.15
0.02
0.1
00
0.015
)K
0.05
K
**m
*
K*
0.1
0
O
0.01
0.05 F
0.005
0
I
0
5
10
15
Hourly w
20
0
5
10
15
20
Average Hourly w
0
5
I
|
|
10
15
20
Average Hourly w
August: Rain Initiated in the Hour After Mixing Ratio Observed Between 1400 and 1800; Storms < 5 hrs
0.03
0.5
.2
0.4
O
r2 = 37%
0.025
K
O
W0.3
0.015
OO
0.01
0.1
0.005
t
0
5
0.1
O
0.2
U.1
**
0.15
0.02
0
r^2 =89%
0.05
OO
i
IK
15
20
10
5
0
20
15
5
10
0
15
20
10
Average Hourly w
Average Hourly w
Hourly w
Sept: Rain Initiated in the Hour After Mixing Ratio Observed Between 1400 and 1800; Storms < 5 hrs
^A
0.03
0.2
0.025
S
X
rA2 = 43%
re2 = 19%
U
0.15
0.02
*
0.1
0.015
" 0.0
0.01
4.0
'a0.0
)K
00
0.05
m,
0.005
0
Hourly w
15
10
5
Average Hourly w
20
0
*K
m
15
10
5
Average Hourly w
At the low end of the observations of mixing ratio, the positive linear trend is also broken
in June and August, as well as in July. Below w's of approximately 8 g/kg, the probability of
rainfall initiation is nearly constant. Both of these deviations from linearity are seen in other
variables presented in this chapter. Possible causes will be discussed in the next section.
The studies of Williams and Renno (1993) and Eltahir and Pal (1996) showed a
dependence between rainfall and wet-bulb potential temperature, O, and wet-bulb temperature,
Tw, respectively. Both focused on tropical regions, but, as Carlson and Ludlam (1966) point out,
during the summer the mid-latitudes often acquire much of the behavior of the tropics. Figure 5.6
shows that there is, indeed, a strong relationship between Tw and subsequent rainfall during June
and August. Between approximately 15 and 25 *C there is a strong positive linear trend in the
probability of storm initiation. July shows a similar trend (but with much more scatter) in this
range, but the lowest probability of rainfall is associted with the largest Tw of approximately 26
*C. Below 15 *C, the probability is nearly constant in June. The fall and spring months show
very little pattern in the probability of initiation, but some positive dependence on Tw is evident in
the average depth of rain per hour in these months, as well as in June and August.
As stated in Chapter 4, the equivalent potential temperature, OE, is a measure of the moist
static energy of the boundary layer, and is conserved in dry and moist adiabatic transformations.
It is closely related to the development of cumulus and cumulonimbus convection, and is often
used as an indicator of boundary layer depth and growth (Betts and Ball, 1995). There is a oneto-one relationship between GE and 0., and the results for GE in Figure 5.7 and for GE in Figure 5.8
are very similar. As with T., both OE and A show particularly good correlations with probability
of rainfall occurrence during June and August, while during July the one anomalous highest bin
108
throws off a scattered but positive linear trend. April, May and September also have similar
rainfall initiation patterns in 0, and OE as in Tw. The average depth of rain after surface
observations of OE or 0, shows weak positive association in all months except July. This is also
consistent with wet-bulb temperature results.
Figure 5.9 shows that wet-bulb depression is good at predicting storm occurrence in all
months, with r2's between 45 and 83%, but especially in May (83%), June (76%), and July (77%).
Given the results of Chapter 4 showing the strong connection between soil moisture and
subsequent wet-bulb depression, this is an important result for the determination of a physical
pathway connecting soil moisture and rainfall. This will be discussed in greater detail in the next
section. Though wet-bulb depression is a good predictor of rainfall occurrence, it is not,
however, as robust a predictor of subsequent rainfall depth.
Another good predictor of storm occurrence is the temperature of the Lifting
Condensation Level (LCL) (see Figure 5.10). A positive linear correlation explains between 70
and 85% of the variability in storm initiation during April, May, June, and August, and 47 and
42% in July and September, respectively. It is also a fairly robust indicator of average rainfall
depth in the next hour in April, May, June, and August. The correlation shows that rainfall is
more likely to occur when the LCL is at higher temperatures than at lower temperatures. July
exhibits the same anomalous behavior at the highest TLCL's that was noted in the highest q, T,, and
0, bins. Threshold behavior is demonstrated by the near-constant initiation probabilities at TLczs
less than about 280 K in the summertime.
Peppler and Lamb (1989) analyzed the correlation between rainfall and what they called
SSITPs: Static Stability Indicies and Related Thermodynamic Parameters. They determined that
109
the variables which were most closely related to tropospheric static stability over central North
America were not typical buoyancy parameters, but were related to the pressure of the LCL. The
results with TLCL found here show a similarly high correlation: a high LCL temperature implies a
lower LCL pressure and a lower cloud base height.
Interestingly, this strong association between TLCL and rainfall does not carry over to the
pressure depth of the LCL. Figure 5.11 shows June, August and September (except for the
lowest bin) with a scattered positive trend between PLCL - P, and probability of rainfall. July,
however, shows a negative trend. April and May do not show clear trends in the probability of
initiation, but show much stronger correlation with average hourly rainfall depth than the other
months.
As discussed in Chapter 4, the pressure depth to the LCL is, in a sense, a measure of
buoyancy. The soil moisture-boundary layer analyses results showed that this variable responded
to soil moisture in a very similar manner as temperature, potential temperature, and virtual
potential temperature. This correspondence between these four variables is also seen in their
relationship to rainfall in the following hour. Figure 5.12 shows the results for temperature, but
results for potential temperature and virtual potential temperature are not shown. The patterns in
Figure 5.12 are very similar to those in Figure 5.11 for the pressure depth to the LCL. Of note is
July's even stronger negative correlation between probability of initiation of rain T (r2 = 68%).
110
April: Rain Initiated in the Hour After Wet-bulb Temperature Observed Between 1400 and 1800; Storms < 5 hrs
0.2
-0.03
U.12
0.025 r"2 = 37%
0.1
0.08
r^2 = 19%
0.15
mX m
m
0.02
m
)K
0.06
t.
X
O
0.04
0.015t
S0
0.02
i.
i
II
I
r~
i.
0
~9Yllp
0
0 OO
)K
0.05
1
DO
)K
10
20
Average Hourly WBT
May: Rain Initiated in the Hour After Wet-bulb Temperature Observed Between 1400 and 1800; Storms < 5 hrs
0
10
20
Hourly WBT
0.12
-
0.1 I
0
0
10
20
Average Hourly WBT
0.2
0.03
> 0.025
.4 0.08 I.
0.02
S0.06 I.
0.015
rA2 = 62%
r^2 = 26%
15
0.
4-
O0.04 i
X )K
0.02
0
0.1
0.01
O
*
0
00
OO
- 4
oI
0.
05
0.005
0
10
20
Hourly WBT
S
0
0
10
20
Average Hourly WBT
0
10
20
Average Hourly WBT
June: Rain Initiated in the Hour After Wet-bulb Temperature Observed Between 1400 and 1800; Storms < 5 hrs
Sb
> 0.025
0.15
1.
0.4
0.03
0.2
*)K
-
0.02
0
0.015
r^2 = 30%
r"2 = 64%
0(3 Z
0.3
00
I
A
O
X
AX
0.05
0.01
C4
O
O
00O
U. 1
0.005
lIOK
K
*
as
O
i
i
0
I
t
*
*
I
l
I
25
15
20
10
25
20
15
10
30
20
25
15
Average Hourly WBT
Average Hourly WBT
Hourly WBT
July: Rain Initiated in the Hour After Wet-bulb Temperature Observed Between 1400 and 1800; Storms < 5 hrs
a'
0
10
0.03
0.2
5'
0.025
E
r^2 = 0.4%
rA2 = 2.6%
0.15
0.15
X
o0
0.02
0
= 0.1
O
O
0.015
)
OO
U
X
X
0.01
E
X
A*K X
00
**
40.05
0.1
O O
O
0O
X*)K
0.05
0.005
i
i
i0
I
10
15
20
25
Hourly WBT
30
10
25
20
15
Average Hourly WBT
10
I
I
I
25
20
15
Average Hourly WBT
August: Rain Initiated in the Hour After Wet-bulb Temperature Observed Between 1400 and 1800; Storms < 5 hrs
,,
0.5
E-0.03
X
~0.4
r2 = 91%
rA2 = 42%
1 0.025
0.02
- 0.3
0
UQ U'
ED!
Pr..
Cr
0.01
g 0.1 I
0
15
3
I
0
10
0.2
0.03
A
a 0.025 r 2= 16%
0.1f
r2= 21%
0.15
F
0.06
0.02
i
i
II
0l
20
0.12
0.04
0
i••
, 0.05
25
20
15
10
25
20
15
WBT
Hourly
Average
Average Hourly WBT
Hourly WBT
Temperature Observed Between 1400 and 1800; Storms < 5 hrs
Wet-bulb
After
Hour
in
the
Initiated
Rain
Sept:
10
L<
0.08
0
0.005
*d
I
00Oo
hi
0.2
0.15
0.1
0.015
cD
f
0
**
)K
0.02
i
0.015
I
0.1
0 0.015F
0 0
0.05
0.005 I
10
Hourly WBT
0
0
20
10
Average Hourly WBT
0
10
20
Average Hourly WBT
April: Rain Initiated in the Hour After Wet-bulb Potential Temperature Observed Between 1400 and 1800; Storms < 5 hrs
0.12
5 0.03
0.1
e 0.025
sr
X.
0.06
0.015
0.04
S0.01 F.
0.02
S0.005
= 49%
rA2 =
22%
NE K
;Iada&-~
I
X mm
I
0.1
O
O
O
)K
NENENE
NENE
0.05
0
SoOoo0
I.
X
)K
)
lDOO
Kr 6>
0
280
290
300
270
280
290
300
270
280
290
300
Hourly ThetaW
Average Hourly ThetaW
Average Hourly ThetaW
May: Rain Initiated in the Hour After Wet-bulb Potential Temperature Observed Between 1400 and 1800; Storms < 5 hrs
"i
270
W
A
J
,
dA
I
I
l
I
0.03
U.12
CS
r2
0.15
9
1cr
U0.
0.02 i.
0.08
I
,,
.1
r2 = 25%
E 0.025
0.15
0.08
5
0.06
So 0.015
0.0
)4
* *K
0.02
0.1
N l
NE
0.01
m3
0.05
0.0
r2
c 0.005
A
270
280
290
Hourly ThetaW
>
300 .e
0
0
270
280
290
Average Hourly ThetaW
300
270
280
290
300
Average Hourly ThetaW
June: Rain Initiated in the Hour After Wet-bulb Potential Temperature Observed Between 1400 and 1800; Storms < 5 hrs
^^
g
t
U.2
0.4
0.03
0.3
w0.15
C,
0.02 I
a
O
OO
5 0.015
0.1
·
·
rA2 = 82%
rA2 = 35%
S0.025
ta
·
I
5 0.2
NE
nMX
)
I
I
SF.(
40.05
0
280
r-
0
O
OO
I
X
0.1
o 0
e
*NmN
X
0
I
n
I
I
|
1
280 285 290 295 300
. 0.005 80 285 290 295 300
290 295 300
Average Hourly ThetaW
Average Hourly ThetaW
Hourly ThetaW
July: Rain Initiated in the Hour After Wet-bulb Potential Temperature Observed Between 1400 and 1800; Storms < 5 hrs
285
0.03
= 0.025
g
r2 = 6.4%
rA2 = 0.069%
Oi
NE
X XX
0.15
0.02
I
0
O
O
0.015
m X
0.1
XE
•
0
0.01
M
0
X
0.05
= 0.005
Ca
0~
2 80 285
I
Hourly ThetaW
I
I
I
290 295 300
Average Hourly ThetaW
n
280
I
I
I
285 290 295 300
Average Hourly ThetaW
August: Rain Initiated in the Hour After Wet-bulb Potential Temperature Observed Between 1400 and 1800; Storms < 5 hrs
1
·
·
*
0.4
,,
0.03
0.025
Uo
O
r^2 = 40%
0.02
0.3
o
0.015
0.2
0.005
A
0 0
0o
0.01
0.1
0
GO
0
O
n
|I
280 285 290 295 300
290 295 300
280 285 290 295 300
Hourly ThetaW
Average Hourly ThetaW
Average Hourly ThetaW
Sept: Rain Initiated in the Hour After Wet-bulb Potential Temperature Observed Between 1400 and 1800; Storms < 5 hrs
280
285
0.12
0.(
03
0..1
0.025
.8 0.08
0.02
80.06
0.015
. 0.04
0.01
0.02
0.005
U.2
r^2 = 20%
rA2 = 20%
0.15
0
000
OO
0.1
*
0.05
00
0
Hourly ThetaW
300
290
280
270
Average Hourly ThetaW
270
280
290
300
Average Hourly ThetaW
April: Rain Initiated in the Hour After Wet-bulb Depression Observed Between 1400 and 1800; Storms < 5 hrs
0.12
0.2
0.03
15U
0.1
A·
0.025
E
I.
0.15
'-4
0.08
0.02
U
X
00.06
44-
0 0.1 I
0.015
0o
'-
0.04
*m
-~
X
0
X
Xm
X 3r9K
S0.02
X
0.01
0
0.005
C.)
_
rA2 = 5.1%
e2 = 61%
|
I
--- C"Y~·
10
5
15
0
0
5
10
5
10
1
Average Hourly WBD
Average Hourly WBD
Hourly WBD
May: Rain Initiated in the Hour After Wet-bulb Depression Observed Between 1400 and 1800; Storms < 5 hrs
0.2
0.03
0.12
1.1%
c-
0.025
-i
. 0.08
U
'-4
0.15
I.
0.02
4.'
S0.04
*3K
1
h1
0.02 I
0.01
0.05
0.005
n
rA2 = 83%
)K
-
C!
3K6
v
0.015
S0.06
5
10
Hourly WBD
15
0
5
10
Aver -ageHourly WBD
v
15
0
5
10
Average Hourly WBD
15
June: Rain Initiated in the Hour After Wet-bulb Depression Observed Between 1400 and 1800; Storms < 5 hrs
QI0.03
0.2
M
U
0
0.15
X
I
0.4
*
·
0.025
0.3
E
0.02
0.015
X
X
MA&
X*
0.1
*
X li
Oo
K
W
-i
*
I.
0,
**
0.01
0.05
0
v
15
0.1
0
0.005
D
o 0.2 )
O
*
o0
rA2= 76%
rA2 = 1.4%
X
5
10
0
15
10
5
Average Hourly WBD
Average Hourly WBD
July: Rain Initiated in the Hour After Wet-bulb Depression Observed Between 1400 and 1800; Storms < 5 hrs
5
10
Hourly WBD
0
0.4
0.03
0.2
0.15
*1
0
0.025
C3
U
0.02
e
O
0.015
X
X
0.1
0.3
0
o
A
0o0
d'-
0.01
X X
0.05
0.2
S=*%
0.1
O
XX )K
4-i
0.005
rA2 = 77%
rA2 = 2.7%
s
I
5
10
Hourly WBD
__
15
0
10
5
Average Hourly WBD
15
0
m
10
5
Average Hourly WBD
15
August: Rain Initiated in the Hour After Wet-bulb Depression Observed Between 1400 and 1800; Storms < 5 hrs
J,•
0.5
0.2
E0.04
X
S0.4
0.15
0.03
; 0.3
0.1
0
o
1 0.02
0.2
O
0
0•.
e•
0
0o
0.01
)
0.05
rA2 = 64%
rA2 = 0.0029%
0
--
.A
5
10
15
0
5
10
0
10
5
Average Hourly WBD
Average Hourly WBD
Hourly WBD
Sept: Rain Initiated in the Hour After Wet-bulb Depression Observed Between 1400 and 1800; Storms < 5 hrs
U.I/.r
. IL
-c~~
0.03
U.2
0.025
0.1
E
0.15
O 0.02
I
0.08
0
U
0.015
0.06
0.04
0.02
'-a
l
*
X
0.1
S
0.05
0.01
X
O
0 O0
O2 = 4.4%
0.005
rA2 = 4.4%
15
5
10
Hourly WBD
4
nEl
0
5
10
Average Hourly WBD
15
0
10
5
Average Hourly WBD
15
April: Rain Initiated in the Hour After LCL Temperature Observed Between 1400 and 1800; Storms < 5 hrs
0.12
U 0.03
·
F
0 0.025 I
0.08 F
0.02 t
0.1
0.2
r^2 = 60%
rA2 = 83%
0.15
0.06
0.04
0.02
0
I
II'
0
*
m
0.1
0
*et
0.01
00
be
0.005
:1
0
I
260
4 0
l
0.05
E
%R0~
I
l
I
I
I
I
I
I
270 280 290
300o
260 270 280 290 300
260 270
280 290
Hourly TLCL
Average Hourly TLCL
Average Hourly TLCL
May: Rain Initiated in the Hour After LCL Temperature Observed Between 1400 and 1800; Storms < 5 hrs
300
0.2
O 0.03
U.1Z
o
0.015
U
m 4
)
U.2
rA2 = 46%
0.1
1 0.025 i
0.08
0.02 )
rA2 = 70%
*
15
.
)
E.
-9
0.06
O
0.015
2.
0.1
m
XE
N
NE*
I-
S0.04
U;
0.05
0.005
C,
0
0
oo*
0
OO
*o
a
260
270 280 290
Hourly TLCL
N
0.01
0
.0.02
X
300W
260 270 280
290
Average Hourly TLCL
300
*
260 270 280 290 300
Average Hourly TLCL
June: Rain Initiated in the Hour After LCL Temperature Observed Between 1400 and 1800; Storms < 5 hrs
$.-0.03
0.2
r^2 = 44%
0.025
0.15
0.3
)K
I_
r02 = 85%
0.02
Ui
0.015
)K
X *
**
40.05
NE
0.01
0 00
A
0
0
0o
0.2
0
*
0.1
X
0.005
c"'-7 -~280
270
n
ýM
n
0
n
I
mA
KNE
)K~e
W
•
290
300
280
300
270
280
290
270
290
Average Hourly TLCL
Average Hourly TLCL
Hourly TLCL
July: Rain Initiated in the Hour After LCL Temperature Observed Between 1400 and 1800; Storms < 5 hrs
"
ý4
"
300
.*=04
,"1
, 0.025
0.2
I
r2 = 47%
rA2 = 270
N
0.15
0.02 I
0
So0.015 I
0.01
0
0
0.1
0
F
0.05
0
*a0.005
% )K
A NE
0
1
}
0
Hourly TLCL
270
A
L
1
•
1
280
290
Average Hourly TLCL
300
270
290
280
Average Hourly TLCL
300
August: Rain Initiated in the Hour After LCL Temperature Observed Between 1400 and 1800; Storms < 5 hrs
I
1
,,
U 0.035
U.2
0.03 .r2 = 24%
0.4
0.15
0.025
0.3
0.02
.d
0.2
0.01
30
0.1
n
0.1
0
0.015
L
0.005
Co
--
~L
0.05
0
0
n
n
270
280
290
280
290
300
280
270
290
Hourly TLCL
Average Hourly TLCL
Average Hourly TLCL
Sept: Rain Initiated in the Hour After LCL Temperature Observed Between 1400 and 1800; Storms < 5 hrs
270
0.12
0.03
0.1
0.025
S0.o08
S0.02
00.06
0.015
300
0.2
rA2 = 7.2%
r2 = 42%
)K
0.15
0.1
O
I-
)K
S0.02
me"
0.2
)K*A
m "".~au
~L~ax·
260
270 280 290
Hourly TLCL
A
0.01
0.05
9
CO
0.005
i
3006
O
3K
OOO
260 270 280 290
Average Hourly TLCL
300
260 270 280 290
Average Hourly TLCL
300
April: Rain Initiated in the Hour After Pressure depth to the LCL Observed Between 1400 and 1800; Storms < 5 hrs
En,,
U.I
0.12
.
U.U3
0.1
• 0.025
0.08
b 0.02
r^2 = 58%
rA2 = 2%
0.15
*
0.06
*
0
O
0.01
*
*K )K
.~81~- )K
dc~uY4-s
)K
0.02
S0.005
04
0
)K I
)Ker
)K
*
O
0.05
00 0 0cb0
0
10
20
*
m*
*m
0.1
S0.015
0.04
X
I
30
i
i
i
10
30
20
30
10
20
0
Hourly Plcl-Ps
Average Hourly Plcl-Ps
Average Hourly Plcl-Ps
May: Rain Initiated in the Hour After Pressure depth to the LCL Observed Between 1400 and 1800; Storms < 5 hrs
•
U
0.12
0.03
E 0.1
a 0.025
0.08
S0.02
0.2
r^2 = 52%
rA2 = 22%
0.15
.
80.06
0
0.01
S0.04
)3K
K*
4-1
0.015
0
0O
o 0.1
)K~l
*
X
1 0.05
)
0.02
Hourly Plcl-Ps
.>0
0.005
>•
o
<
0
10
20
30
Average Hourly Plcl-Ps
0
10
20
30
Average Hourly Plcl-Ps
June: Rain Initiated in the Hour After Pressure depth to the LCL Observed Between 1400 and 1800; Storms < 5 hrs
1
o
15
0.4
I 0.03
0.025
0.3
*
S0.02
*
o 0.2
0.015
0.1
*)K
*
*
0.05
0.01
*
0.1
. 0.005
0
0
10
20
30
40
10
20
30
40
20
30
40
Average Hourly Plcl-Ps
Hourly Plcl-Ps
Average Hourly Plcl-Ps
July: Rain Initiated in the Hour After Pressure depth to the LCL Observed Between 1400 and 1800; Storms < 5 hrs
10
i
0.2
0.03
rA2 = 24%
0.025
.0.15
S0.02
)K X
**
K
K
0
o0.015
*
*
0.01
0.05
. 0.005
co
>
10
20
30
Hourly Plcl-Ps
.
0
0
10
20
30
40
Average Hourly Plcl-Ps
10
20
30
40
Average Hourly Plcl-Ps
August: Rain Initiated in the Hour After Pressure depth to the LCL Observed Between 1400 and 1800; Storms < 5 hrs
0.2
U.2
0
0.04
*
S0.4
0.3
,,
--
0.5
rA2 = 52%
2 = 9.7%
2 0.15
I
0.03 )
I
0.1I
0.02
Oc
)
a 0.01
0.1
X W
S0
t
)K
0.05
0
*as
3KY
0
40
10
20
30
40
40
30
20
10
Average
Hourly
Plcl-Ps
Hourly Plcl-Ps
Sept: Rain Initiated in the Hour After Pressure depth to the LCL Observed Between 1400 and 1800; Storms < 5 hrs
10
20
30
Average Hourly Plcl-Ps
U,
0.12
_
0.2
U.Uj
E 0.1
0.025
S0.08
0.02
0 0.06
5 0.015
r"2 = 13%
.20.15
o 0.1
0
0.01
" 0.04
•
'C
10.02
0
-
S0.005
11:
>
0
10
20
Hourly Plcl-Ps
30
0
O 000
O
O
0.05
0
0
30
20
10
0
Average Hourly Plcl-Ps
30
20
10
0
Average Hourly Plcl-Ps
April: Rain Initiated in the Hour After Equivalent Potential Temperature Observed Between 1400 and 1800; Storms < 5 hrs
0.12
0.1
0.08
0.06
0.04
U
0.03
·
rA2 = 53%
o 0.025
I
E
0.2
·
r2 = 34%
0.15
r
0.015
0.1I
O
*
0.01
S0.0
oO nOo
*3K
0.02 E
I
0.02 i
)K
A5~
0.005
*t
ME
0
0
280
300 320 340 360
280 300 320 340 360
280 300 320 340 360
Hourly ThetaE
Average Hourly ThetaE
Average Hourly ThetaE
May: Rain Initiated in the Hour After Equivalent Potential Temperature Observed Between 1400 and 1800; Storms < 5 hrs
0.12
0.03
S0.025
0.1
E
0.2
rA2 = 72%
*
r^2 = 23%
)K
0.15
.0
0.02 i.
0.08
S0.06
0 0.015
a 0.04
3lSKm
40.02
0
~pq~il
280
X3K
P lk
K*
f.
o 0.1
O
0.01 I.
00
300 320 340 360
Hourly ThetaE
O
0%0
0.005
WIL.-
*
0 280
300 320 340 360
Average Hourly ThetaE
E0.05
280 300 320 340 360
Average Hourly ThetaE
June: Rain Initiated in the Hour After Equivalent Potential Temperature Observed Between 1400 and 1800; Storms < 5 hrs
0.2
ua
Sa
El
r2 = 91%
r2 = 41%
0.025
0.15
-1 ·
0.4
0.03
_·
-
0.3
,m
0.02
A Al g
.001
0.1
no
0.05
0
*
ne
X
L
r
0 0.2
j
OO
0.01
OO
)
0.1
0.005
..
A
0
30 0
)K
0
I
I
i
•
X)K
*
)K
X
0K E
301N
A
'
320 340 360 380
Average Hourly ThetaE
Average Hourly ThetaE
Hourly ThetaE
July: Rain Initiated in the Hour After Equivalent Potential Temperature Observed Between 1400 and 1800; Storms < 5 hrs
320
340
360
380
300
0.2
0.2
360
380
300
0.2
0.03
rA2
rA2 = 0.12%
0 0.025
i. 0.
340
320
1.8%
0.15
1
S0.02
0.1 .
0.
K
*K
0.01
05
. 0.005
Co
0
0
L____
300
-
320
340
300
Hourly ThetaE
30U
>
0
3
O
O
00.015
0
*
mNN
NE *
I
I
I
I
320
340
360
380
S0.1
cb o
o
i
t0.05
)
A
1
O0
320
340
360
380
Average Hourly ThetaE
300
Average Hourly ThetaE
August: Rain Initiated in the Hour After Equivalent Potential Temperature Observed Between 1400 and 1800; Storms < 5 hrs
1ý
0
o0.025 r"2 = 44%
rA2 = 73%
0.4
0
0.02
Ml
0.3
I
O
0.3
>
W
C
f
o 0.015
0.2
"•o
I
m
0.2
OoO
o
, 0.01 I
*
0.1
S00
0.1
. 0.005
0
E
A,-·~g~i~·~ka~$,
-
-
>
n
00
*)K
mX
A
E
-
<J1 00 320
340
360 380
300 320 340 360 380
320 340 360 380
Average Hourly ThetaE
Average Hourly ThetaE
Hourly ThetaE
Sept: Rain Initiated in the Hour After Equivalent Potential Temperature Observed Between 1400 and 1800; Storms < 5 hrs
30
3O(0
^
0.03
^
0 0.025
8 0.02
<
rA2 = 7.5%
rA2 = 34%
AA( *
i
*
O
0.015
*
0.1
O
0.01
0.005
280
300 320 340
Hourly ThetaE
360
0
OO
0O 0
0
280 300 320 340 360
Average Hourly ThetaE
0.05
K *K*
K
280
300 320 340 360
Average Hourly ThetaE
April: Rain Initiated in the Hour After Temperature Observed Between 1400 and 1800; Storms < 5 hrs
0.12
0.03
0.1
0.025
r"2 = 52%
r^2 = 0.59%
E
0.15
0.08
0.02
X
0.06
0.015
0.1
4m
*K A m
m* *
*m
O
0.04
O
0.01
XK
0.02
X
?
0.005
0
~~,.jK)K
0
)K
0000
10
20
0
10
20
30
0
10
20
30
Hourly T
Average Hourly T
Average Hourly T
May: Rain Initiated in the Hour After Temperature Observed Between 1400 and 1800; Storms < 5 hrs
0.12
0.03
I
0.025
r^2 = 64%
rA2 = 12%
0.15
0.08
0.02
0.06
0.015
0.04
0.02
*
ram~a
0
0.1
0.05
00
K
)KV
W
L
0
0
0.01
o6b
O00O
0.005
10
20
Hourly T
30
0
10
20
30
Average Hourly T
A
A
)K
*
*m
A)K
0.1
*ze
0.05
0
10
20
30
Average Hourly T
June: Rain Initiated in the Hour After Temperature Observed Between 1400 and 1800; Storms < 5 hrs
0.2
, 0.03
r^2 = 24%
0.025
, 0.15
)K
)K
0
0.02
0%
E
*
r
X
0o
0.01
X)K
A
O
0.05
)KE
)K
15
E
0.005
15 20 25 30 35
15 20 25 30 35
25 30 35
Average Hourly T
Average Hourly T
Hourly T
1800;
Storms < 5 hrs
1400
and
Between
Observed
Temperature
Hour
After
July: Rain Initiated in the
20
-
0.03
rA2 = 68%
r2 = 13%
• 0.025
0.15
A
0.1
0.015
0.1
40.05
"a
rA2 = 29%
O
0.15
E
E
0.02 I.
o
: 0.015
K I
O
l K
I
0
*
)K
*
)KW
0.01 I.
m
0.05
O
mT
0.05
E
E
r 0.005 I
15 20 25 30 35
Hourly T
15
20 25 30 35
Average Hourly T
15
20 25 30 35
Average Hourly T
August: Rain Initiated in the Hour After Temperature Observed Between 1400 and 1800; Storms < 5 hrs
0.5
- 0.035
0
0.03 r,2 = 14%
*
~0.4
0.025
0.3
0.02
E
0.015
0.2
E
0.01
0.1
.0
0
15
0
0
0
0
0.005
E
0
15 20 25 30 35
15 20 25 30 35
25 30 35
Average Hourly T
Average Hourly T
Hourly T
Sept: Rain Initiated in the Hour After Temperature Observed Between 1400 and 1800; Storms < 5 hrs
20
0.12
E-. 0.03
E 0.1
0.025
.00.08
0.02
0.2
r^2= 11%
r2 = 13%
0.15
0.1
o.
0.015
00.06
m
K
E
0.01
0.04
0.0
00
OOOOO
K W*:
0.02
0
0.05 I
0.005
meýLrm J
0
fill
0
10
20
Hourly T
30
0
10
20
30
Average Hourly T
0
30
20
10
Average Hourly T
D.
Discussion of Results
This chapter focused on the relationship between hourly observations of boundary layer
conditions, as measured by hourly observations at 13 stations in the NCDC Surface Airways
Hourly Database, and rainfall in the subsequent hour. Variables used to describe boundary layer
conditions are the same as those used in Chapter 4. Hourly rainfall data at 82 stations within
Illinois was obtained through EarthInfo, Inc., and is a subset of the NCDC Hourly Rainfall
Database TD-3240. The analyses were performed on hourly state-wide averages of each of the
boundary layer variables and of rainfall in the subsequent hour.
Wet-bulb depression, Tdp, relative humidity, f, mixing ratio, w, and the temperature of the
lifting condensation level (LCL), TLCL, consistently showed strong correlations with the
probability of initiation of a rainfall event. TLCL showed some correlation with average depth of
rainfall in the hour after the surface observation, given that rainfall occurs, but the others showed
weak to no correlation with this quantity.
The strong negative correlation between wet-bulb depression and rainfall initiation (low
wet-bulb depression is associated with higher probability of a storm beginning) is an important
result, in light of the results of the soil moisture-boundary layer study of Chapter 4. The analyses
of Chapter 4 revealed a negative correlation between soil moisture and subsequent wet-bulb
depression, particularly during summer. These two results combined, then, suggest that wet-bulb
depression may act as the carrier of information from the soil to rainfall. This will be discussed
more thoroughly in the conclusions.
Wet-bulb depression and the other three variables mentioned above (f,w, and TLCL)
showed strong association with initiation of rainfall in all months between May and September,
132
but practical experience of Illinois weather indicates that climatic behavior is different during the
summer months than during the spring and fall. We expect the data to reflect this difference. The
positive linear trends seen in June, July, and August (strong association in June and August,
weaker in July) between rainfall and the moist static energy of the boundary layer over a large
portion of its range (between approximately 15 and 25 *C for Tw,288 and 298 K for ,,,and 320
and 362 K for OE) are perhaps a manifestation of this difference. They are indicative of the landsurface controls on convection which we expect to be important during the summer in midlatitudes, as discussed in Chapter 2. More moist static energy in the lower levels of the boundary
layer should be associated with a higher likelihood of overturning and initiation of convection.
This is consistent with the results of Eltahir and Pal (1996), Williams and Renno (1993), and Betts
et al. (1996). At low levels of moist static energy, the probability of initiation of rainfall is nearly
constant, suggesting the likelihood of a threshold moist static energy necessary for convection.
This, too, is consistent with many previous studies (e.g., Carlson and Ludlam, 1966; Williams and
Renno, 1993; Eltahir and Pal, 1996) and is a reasonable result, given that convective rainfall
results from the release of energy temporarily locked in a conditionally unstable vertical profile of
temperature and humidity. The drop in both rainfall depth and occurrence at high T,
,,,, and OE,
on the other hand, is not an easily explained phenomenon.
Buoyancy variables (T, 6, 6,, and PLcL - P,) showed inconsistent connections with
subsequent rainfall. In June, August and September (except for at low values of each variable in
September), there was a scattered positive trend between buoyancy and the probability of rainfall
occurrence. In July, however, there was a weak negative trend, and in April and May there was
only scatter. These spring months were the only ones to show any association between buoyancy
and average rainfall depth in the next hour.
133
This lack of association between surface buoyancy measures and rainfall may be an
indication of the complexity of the interactions between boundary layer growth and triggering of
moist convection. As discussed in Chapter 2, increased sensible heating of the air (associated
with higher temperatures) increases the depth of the boundary layer, such that the contribution of
moist static energy (MSE) from the ground, which is proportional to the sum of sensible and
latent heat fluxes, is spread over a greater depth. The increase of MSE per unit depth, then, is
smaller in high temperature conditions than in low temperature conditions. According to our
previously mentioned theory and to results connecting higher MSE to higher likelihood of rainfall
(except at very high MSE), this suggests that, given similar early-morning MSE, days with higher
temperature should have a lower afternoon MSE and therefore a lower likelihood of rainfall than
days with lower temperature. This is complicated by the fact that a necessary condition for the
triggering of convection is a lifting agent to pull low level air up beyond its level of free
convection (LFC). Turbulence generated by sensible heat flux often is this mechanism. Higher
temperatures lead to greater boundary layer growth and a higher likelihood of the boundary layer
breaking through the LFC associated with surface air. These competing factors may explain the
lack of a consistent relationship between buoyancy of near-surface air and subsequent
precipitation.
In summary, the results in this chapter indicate that there are connections between nearsurface measurements of atmospheric quantities and subsequent rainfall in the state of Illinois.
Wet-bulb depression is a good indicator of the likelihood of the initiation of afternoon rain storms
in all of the months analyzed (April through September). Boundary layer entropy, or moist static
energy, as quantified by Tw, ,,, and OE, shows a positive linear association with rainfall occurrence
through a limited range of observations. Below this range of moist static energy, the probability
134
of rainfall is nearly constant and very small, while above this range, the probability drops back
down to a low level. Buoyancy, as measured by T, 0, 0v, and PLCL - Ps, on the other hand, shows
little clear association with subsequent rainfall.
135
Chapter 6: Conclusions and Future Research
This study of the soil moisture-rainfall feedback was focused on the state of Illinois, an
area of approximately 300 by 650 km centered around 40°N and 890W. The Illinois State Water
Survey's (ISWS's) extensive dataset of bi-weekly neutron probe measurements of soil moisture at
up to 19 stations, beginning in 1981, motivated the study. Most previous investigations of this
feedback mechanism have used inferred or modeled soil moisture time series, rather than directly
observed data. Though these data are not of ideal spatial or temporal resolution, this is the largest
long-term record of directly observed soil moisture currently available, and can provide muchneeded validation of modeling results which often use simulated or non-realistic soil moisture
conditions.
Results of a linear correlation analysis between initial soil moisture and rainfall in the
subsequent three weeks showed that a positive correlation between these two variables is present
from early June through mid-August. This correlation is more significant than the serial
correlation within precipitation time series, suggesting the likelihood of a physical mechanism
linking soil moisture to subsequent rainfall.
This result prompted further investigation into the nature of such a physical pathway
linking soil moisture to subsequent rainfall. Theory and previous studies indicated the likelihood
of a positive impact of soil moisture on the moist static energy (MSE) of the boundary layer, and
a positive impact of MSE on rainfall. To explore these possibilities, hourly data of surface air
136
conditions and precipitation since 1981 (corresponding to the soil moisture dataset) were obtained
for 13 and 82 stations, respectively. Near-surface hourly observations of pressure, P,
temperature, T, wet-bulb temperature, Tw, and relative humidity,f, were obtained from the
National Climatic Data Center (NCDC) Surface Airways Hourly Dataset TD-3280. Data from 13
such stations in and close to Illinois were used in the analyses. From each hourly set of direct
observations of P, T, Tw, andf, many other variables were calculated and used in the analyses.
These included wet-bulb depression, Tdpr, temperature of the lifting condensation level (LCL),
TLCL, pressure depth to the LCL, PLCL-PS, mixing ratio, w, potential temperature, 0, virtual
potential temperature, 06,wet-bulb potential temperature, 0,, and equivalent potential
temperature, OE. Time series of the spatial average of each of these quantities were then
calculated by averaging data from the 13 stations at each hour. These time series were used as a
representation of the average near-surface conditions over the whole state of Illinois. These
conditions were assumed to be an indication of conditions in the whole boundary layer. This
assumption could be relaxed by including data from soundings in subsequent analyses.
An analysis of the connections between an average soil saturation time series for the whole
state of Illinois with these state-wide average boundary layer conditions did not yield the expected
result of a positive correlation between soil moisture and moist static energy, as quantified by T,,
0,, or OE. This result is at odds with previous research on this topic (Betts and Ball, 1995). It is
not clear if this is due to limitations of the data or of the theory. The impact of variable incoming
solar radiation was not accounted for in these analyses, and may be relevant to this result, but two
other possible factors may also be playing a role; the observations from the surface may not truly
be representative of conditions in the boundary layer, or data used in this study may not robust
enough to describe either the surface air conditions or the soil conditions over the entire state of
137
Illinois at a daily time scale. Though one of the important aspects of this study is the use of
directly observed soil moisture data, these data are still quite limited in both space and time and
may not accurately represent conditions in the state as a whole. When more extensive datasets
are available, particularly data on incoming solar radiation, it may be instructive to revisit this
analysis.
Though the anticipated soil moisture-boundary layer entropy link was not observed, there
was evidence that moisture availability (or lack thereof) at the surface has a very strong impact on
the wet-bulb depression of near-surface air, particularly from mid-May through the end of August,
showing good correspondence to the period of significant soil moisture-rainfall association.
The final set of analyses performed included an investigation of the hourly boundary layer
and rainfall data. The latter dataset was also NCDC hourly data, purchased through EarthInfo,
Inc. Data from the 82 hourly rainfall stations were averaged to compare state-wide hourly rainfall
to state-wide hourly boundary layer conditions. A link between high MSE and high rainfall was
noted for much of the range of MSE during the summer months, and a link between low Tdpr and
high rainfall was evident for all of the months analyzed (April through September). These
analyses, then, suggest that the significant but weak correlation between soil moisture and rainfall
during Illinois summers is due not to soil moisture controls on the boundary layer entropy, but
rather to soil moisture controls on the wet-bulb depression of near-surface air.
In addition to the complete pathway by wet-bulb depression between soil moisture and
subsequent rainfall, some other interesting results were seen in the two phases of this interaction.
In the first phase of this physical connection, i.e., the interaction between the soil and the mixed
layer of the atmosphere, a negative feedback on buoyancy of near surface air was seen at low to
138
normal soil moisture conditions. In July, this effect of lower soil moisture leading to higher
buoyancy is also seen in the jump from normal to wet soils, though this is not seen in June and
August. One possible reason that this effect is not present between normal and wet soils during
the other summer months is the decreased sensitivity of evapotranspiration to soil moisture in wet
or very wet conditions. This is due to that fact that above a certain level of soil moisture, water
availability is no longer the limiting factor on the rate of evapotranspiration (Betts and Ball,
1995). This behavior could be investigated in more detail by accounting for differences in
incoming radiation. As discussed by Eltahir (1997), the role of soil moisture on atmospheric
processes is not as significant as other factors such as incoming solar radiation. On days with
equivalent inputs of solar energy, different soil moisture conditions may account for differences in
boundary layer conditions. We see some evidence of the role of soil moisture in affecting the
boundary layer, but research which accounts for the solar conditions should be performed.
The second phase of the link between soil conditions and rainfall is between the boundary
layer and rainfall. Results of this work show that the saturation of near surface air is positively
associated with rainfall in the subsequent hour. The buoyancy measures T, 0, and 0, however,
show poor association with rainfall. This may be due to the competing factors of increased soil
moisture leading to increased moist static energy in the boundary layer-which is expected to lead
to more convective rainfall, and decreased sensible heat flux-which decreases the likelihood of
boundary layer growth overtaking the level of free convection and initiating convection.
As mentioned above, measures of the moist static energy (MSE) of the boundary layer did
show reasonable connections with rainfall during the summer months. Over most of the range of
MSE observations, there was a strong positive correlation with rainfall. At the very top of the
139
MSE range, however, the likelihood and the depth of rainfall dropped well below that in the nextto-highest MSE bin. At the bottom of the range, there is a nearly constant probability of initiation
of rainfall until the MSE surpasses some threshold. This is understandable, given the threshold
nature of convection in general, but the suppression of rain at high MSE is not as easily explained.
The spatial and temporal limitations of the soil moisture dataset, the spatial limitations of
the surface conditions dataset, and the lack of both radiation data and vertical profiles of
temperature and humidity throughout the boundary layer restrict the potential for more detailed
investigations of the energetics of the different environments corresponding to dry, normal, and
wet soil moisture conditions. Despite these limitations, these analyses show that during the
summer in Illiois, soil moisture significantly impacts subsequent rainfall through its impact on the
wet-bulb depression of the boundary layer. Future work intended to refine our understanding of
the role of soil moisture in the energy balance of the mixed layer will include vertical soundings
and radiation data.
140
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