Seasonal Trends and Variability of Temperature, Precipitation, and Diurnal Temperature
Range in U.S. Climate Divisions
THESIS
Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in
the Graduate School of The Ohio State University
By
Nicholas A. Sakian
Graduate Program in Atmospheric Sciences
The Ohio State University
2015
Master’s Examination Committee
Professor Jay Hobgood, Advisor
Professor Alvaro Montenegro
1
Copyright by
Nicholas A. Sakian
2015
1
Abstract
Seasonal U.S. climate division data (1895-2014) of temperatures and precipitation in
seven chosen divisions are analyzed for trends and patterns of variability and for factors
contributing the most to the variability of temperature in each season and division. The
divisions are chosen to represent regions of the U.S. that conform to particular patterns of
variability of the Palmer Drought Severity Index (PDSI) in summer. Rotated principal
component analysis (RPCA) of atmospheric and oceanic teleconnection indices, annual
atmospheric CO2 concentrations, and time series of cloud cover and divisionallyaveraged precipitation removes intercorrelations between these variables in each region.
The orthogonal factors produced from RPCA are used in stepwise multiple linear
regression (SMLR) to determine the explainable variance in seasonally-averaged daily
maximum and minimum temperatures (Tmax, Tmin) and diurnal temperature range
(DTR). Simple linear regression is used to determine rates of change in divisionallyaveraged DTR, Tmax, and Tmin in each region and season. The major temperature trends
found are accelerated warming of Tmin in most regions and seasons, no decline in spring
DTR nationally, and similarities among the four interior/central regions. These regions
are characterized by statistically significant long-term (1895-2013) and short-term (19602013) decreases in DTR and increases in Tmin, with long-term decreases in annuallyaveraged Tmax and in summer and autumn seasonally-averaged Tmax. The Northwest,
Northeast coastal, and Desert Southwest regions experienced long-term increases in DTR
ii
and significant increases in both Tmax and Tmin. Variance within time series of
seasonally-averaged temperatures is generally greater during warmer periods.
Inconsistency in seasonal precipitation in most regions may be increasing in each
region’s wet season. Cloud cover is the factor explaining the most variability in DTR
overall among all four seasons in Central Ohio (Ohio Valley region), but precipitation is
more important than cloud cover for DTR variability in most other regions. Precipitation
and soil moisture are most commonly the primary predictors for summer DTR and Tmax.
These two predictors combined explain 32% to 56% of variance in summer DTR in most
regions. However, steep warming trends in Tmax and Tmin since 1960 are occurring
nationwide despite increasing precipitation trends in most regions. The accelerated rise in
atmospheric CO2 began in the 1950s, and the CO2 concentration explains 4% to 19% of
variability in temperatures in most cases where it is a significant predictor, at most
36.4%. Teleconnection indices, especially the Arctic Oscillation and the North Atlantic
Oscillation, are more important in winter SMLR analyses. Extreme seasonal temperature
anomalies in summer and winter are usually associated with extremes in precipitation,
cloud cover, or at least one of the teleconnection indices.
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Acknowledgments
Thanks to Dr. Jeffery C. Rogers for providing access to data tables of temperatures,
precipitation, and the Palmer Drought Severity Index in climate divisions; for providing
cloud cover data from selected stations and humidity data from Columbus; and for
editing this thesis and contributing descriptions of parts of the data and methodology
sections. Dr. Rogers was my mentor and advisor until his temporary retirement at the end
of May 2015. Thanks to my parents for financial support and to my sister and friends at
OSU for encouragement.
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Vita
2008................................................................Twinsburg High School
2012 ...............................................................B.S. Chemical and Biomolecular
Engineering, The Ohio State University
Fields of Study
Major Field: Atmospheric Sciences
v
Table of Contents
Abstract ............................................................................................................................... ii
Acknowledgments.............................................................................................................. iv
Vita...................................................................................................................................... v
Table of Contents ............................................................................................................... vi
List of Tables ................................................................................................................... viii
List of Figures .................................................................................................................... xi
Chapter 1 : Introduction ...................................................................................................... 1
Chapter 2 : Literature Review ............................................................................................. 3
Chapter 3 : Data .................................................................................................................. 5
3.1 Spatial and temporal domain of study ....................................................................... 5
3.2 Carbon dioxide, specific humidity, cloud cover, and teleconnection data .............. 10
3.2.1 Atmospheric carbon dioxide............................................................................. 10
3.2.2 Specific humidity and PDSI ............................................................................. 12
3.2.3 Cloud cover....................................................................................................... 13
3.2.4 Atmospheric and oceanic teleconnection indices ............................................. 14
Chapter 4 : Methodology .................................................................................................. 18
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4.1 Analyzing trends ..................................................................................................... 18
4.2 Stepwise multiple linear regression......................................................................... 18
4.3 Rotated principal component analysis..................................................................... 20
4.4 Statistical software and interpretation of output ..................................................... 22
Chapter 5 : Results ............................................................................................................ 27
5.1 General annualized trends and correlations ............................................................ 27
5.1.1 National and regional annual trends in air temperature and DTR .................... 28
5.1.2 Annual precipitation trends .............................................................................. 35
5.1.3 Trends in atmospheric and teleconnection indices ........................................... 39
5.2 Seasonal trends and correlations in DTR, Tmax, Tmin, and precipitation ............. 40
5.2.1 Time series trends in each season ..................................................................... 40
5.2.2 Inter-decadal variability of seasonal temperatures and precipitation ............... 54
5.2.3 Central Ohio summer trends ............................................................................. 69
5.3 Regression analyses on DTR, Tmax, and Tmin ...................................................... 75
5.3.1 Correlations between predictors and predictands among the climate divisions 75
5.3.2. Stepwise Multiple Linear Regression models ................................................. 81
Chapter 6 : Conclusions and Future Work ........................................................................ 96
References ....................................................................................................................... 100
vii
List of Tables
4.1 Rotated component matrix, showing results of transformation of raw time series of
predictor variables (left column) to orthogonalized variables. The square of each
coefficient is the fraction of variance of a raw predictor variable that is contained in an
orthogonalized predictor. ………………………………………………………………..23
4.2 Sample output of the SMLR analysis prepared as in Figure 4.2, showing the list of
significant predictors and the amounts of predictand variability that are explained after
each step of the SMLR model. …………………………………………………………..24
4.3 Sample output showing the standardized coefficients for each predictor in the SMLR
model and the p-value of significance of each step. Inclusion of each predictor requires
p < .050. …………………………………………………………………………………26
5.1 Rates of change of annually-averaged temperatures and total annual precipitation, per
century, with correlation coefficients and statistical significance. Correlations significant
with 95% confidence are in yellow, 99% orange, and 99.9% red……………………….28
5.2 Correlation coefficients between each seasonally-averaged teleconnection index and
time, over the long term (top) and recent shorter terms (bottom), with significance as in
Table 5.1. ………………………………………………………………………………..39
5.3 Rates of change of seasonally-averaged diurnal temperature range, per century, with
correlation coefficients and statistical significance. Correlations significant with 95%
confidence are in yellow, 99% orange, and 99.9% red. …………………………………41
5.4 (a) As in Table 5.1, but seasonally-averaged for winter. (b) Selected short-term trends
in winter temperatures, expressed as rates of change per century, with correlation
coefficients and statistical significance. Period begins with the winter that started in Dec
1959. ……………………………………………………………………………………..43
5.5 As in Table 5.1, but seasonally-averaged for spring. ………………………………..44
5.6 (a) Rates of change of summer seasonally-averaged temperatures, total summer
precipitation, and the seasonally-averaged PDSI, per century, with correlation
coefficients and statistical significance. (b) As in Table 5.4b but for summer…………..45
5.7 As in Table 5.5 but for autumn. ……………………………………………………..46
viii
5.8 Correlation coefficients between each predictor (rows) and each predictand
(columns), and between each predictor and precipitation, in summer from 1895 to 2013
in Central Ohio. The correlation between PDSI and Precip is not emphasized because
precipitation is a major component of the PDSI. Correlations significant with 95%
confidence are highlighted in yellow, 99% orange, 99.9% red, and p < 1×10-6 in purple
with yellow text. …………………………………………………………………………71
5.9 SMLR model results for all four predictands in summer in Central Ohio, as in Tables
4.2 and 4.3, but containing only the important columns. Two columns were added – one
for the predictor variable contained in each significant RPC, and one for the variance
explained by each predictor based on the adjusted R2 after each step. ………………….73
5.10 Correlation coefficients between each predictor (columns) and DTR, Tmax, Tmin,
and precipitation in each of the 7 climate divisions in winter, highlighted for significance
as in Table 5.8. …………………………………………………………………………..76
5.11 As in Table 5.10 but for spring. ……………………………………………………78
5.12 As in Table 5.10 but for summer and including the PDSI. The correlation between
PDSI and Precip is not emphasized because precipitation is a major component of the
PDSI. Note that unlike in the other seasons, significant correlations are not starred. …..79
5.13 As in Table 5.10 but for autumn. …………………………………………………..80
5.14 SMLR results for summer DTR, Tmax, and Tmin in Birmingham with all predictors
but limited by the availability of cloud cover data (left side), and without cloud cover as a
predictor (right side). For each model, the list of significant orthogonalized predictors, the
amounts of predictand variability that are explained in each step of SMLR, the
standardized coefficients (Stand. Coeff.) for each step, and the p-value of significance
(Sig.) of each additional predictor are shown. …………………………………………..82
5.15 As in Table 5.14, but for summer in Phoenix. ……………………………………..83
5.16 As in Table 5.14, but for summer in Des Moines. The highlighted p-values were
rounded to .001 but are less than .001, so these steps explain significantly nonzero
amounts of predictand variance with 99.9% confidence. ……………………………….84
5.17 As in Table 5.16, but for summer in Boston. ………………………………………85
5.18 As in Table 5.14, but for summer in Oklahoma City. ……………………………...86
5.19 As in Table 5.16, but for summer in Portland. ……………………………………..87
5.20 The rankings of the significance of each predictor in explaining the variability of
each predictand in summer in Central Ohio. 1 = most significant, ins = insignificant. …88
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5.21 For each predictand, the rankings of the significance of each predictor in explaining
predictand variability in each of the other 6 climate divisions. …………………………89
5.22 SMLR results for winter DTR, Tmax, and Tmin in (a) Columbus, (b) Birmingham,
(c) Phoenix, (d) Des Moines, (e) Boston, (f) Oklahoma City, and (g) Portland. For each
division, results are from models with all predictors but limited by the availability of
cloud cover data (top), and without cloud cover as a predictor (bottom). For each model,
the list of significant orthogonalized predictors and the amounts of predictand variability
that are explained in each step of SMLR are shown. The coefficients are not included
here, but the sign of each is shown with the predictor variable name. ………………….91
5.23 As in Table 5.22, but for spring and autumn in Columbus. ………………………..95
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List of Figures
3.1 Climate division boundaries in Ohio and Oregon. Ohio climate divisions consist of
entire counties, but in Oregon, climate division boundaries are mostly based on mountain
ranges and valleys, so many counties have parts in two or more climate divisions. Oregon
also has a climate division that consists of a single county. ……………………………...5
3.2 United States Climate Divisions with the highest rotated principal component (RPC)
loadings on each of the first 5 summer PDSI components. After Brewer (2015)…….…..6
3.3 Time series of annual CO2 concentrations estimated from ice core data or linear
regression before 1958 and annually-averaged CO2 concentrations from measurements at
Mauna Loa since 1958. The second series is a copy of the first since 1960, shifted down
by 20 ppm for visual convenience and containing the second-order polynomial trend
curve. …………………………………………………………………………………….12
4.1 Factor Analysis option boxes in SPSS Statistics, showing (a) predictor variables
selected for analysis and one to be added to the selection, and (b) options chosen for
RPCA. …………………………………………………………………………………...22
4.2 Linear regression option box in SPSS, showing the selected predictand and
predictors. The numbered factors are the RPCs extracted from the previous analysis. …24
5.1 Annually averaged DTR (°C) for each climate division and the 344-division CONUS
average, along with the CONUS trend (black line). …………………………………….29
5.2 Running means of annually (Dec-Nov) averaged temperatures (°C) for the 7 climate
divisions and the CONUS (U.S. divisions avg.). Data start in 1925. Note that the Phoenix
Tmax and Tmin series have been shifted down by 10°C and 6°C, respectively, for visual
convenience. ……………………………………………………………………………..32
5.3 As in Fig. 5.2 but for Tavg. Note that the Phoenix series has been shifted down by
8°C. ……………………………………………………………………………………...34
5.4 (a) Annual Dec-Nov precipitation (millimeters) in each climate division, with the
CONUS trend since Dec 1895. (b) Running means of the above data. Note that the
Phoenix series has been shifted up by 1000 mm for visual convenience. ………………36
xi
5.5 Sample standard deviations representing variability of winter seasonally-averaged (a)
DTR and (b) Tmin within moving 30-year periods in each climate division and of winter
CONUS-averaged DTR and Tmin. ……………………………………………………...48
5.6 Running means of seasonally averaged DTR for the 7 climate divisions and the
CONUS in (a) winter, (b) spring, (c) summer, and (d) autumn. ………………………...54
5.7 As in Figure 5.6 but for Tmax. ……………………………………………………...57
5.8 As in Figure 5.6 but for Tmin. ………………………………………………………59
5.9 Running means of seasonal total precipitation in the 7 climate divisions and the
CONUS in (a) winter and (b) spring, and running means of (c) the summer seasonallyaveraged PDSI, (d) summer precipitation, and (e) autumn precipitation. ………………61
5.10 Sample standard deviations representing variability of summer seasonally-averaged
(a) DTR and (b) Tmax within moving 30-year periods in each climate division and of
summer CONUS-averaged DTR and Tmax. ……………………………………………64
5.11 As in Figure 5.10 but for (a) spring DTR and (b) autumn DTR. …………………..66
5.12 Sample standard deviations representing variability of seasonal total precipitation,
within 30-year periods, in the 7 divisions and the CONUS average in (a) winter, (b)
spring, (c) summer, and (d) autumn. …………………………………………………….67
5.13 In the Columbus climate division, (a) seasonal averages of summer Tavg and DTR,
with long-term trendlines of each and the trend in Tavg since 1960, and (b) seasonal
averages of summer Tmax and Tmin, with trendlines of Tmax since 1895 and since 1960
and of Tmin since 1960. …………………………………………………………………70
xii
Chapter 1: Introduction
Climate extremes such as droughts, wet periods, heat waves, and cold spells seem
to be happening more often and more intensely than in the recent past (Cohen et al.,
2014; Peterson et al., 2013). Unusually persistent weather patterns occurring within a
season may be linked to various combinations of natural factors and effects of
anthropogenic global warming, and are almost always associated with anomalous
atmospheric circulation patterns (Francis and Vavrus, 2012; Screen and Simmonds, 2013;
Serreze and Barry, 2011). Changes in average temperatures, diurnal and annual
temperature ranges, and precipitation are affecting crop production, the migration of
invasive plant species and insects, human health, and the threat of environmental hazards
(Jeong et al., 2010; Patz et al., 2005). In western Canada and the northwestern United
States, warmer seasonally-averaged spring temperatures and a lack of winter nights with
lows below -40°C in certain highland areas have led to faster reproduction and greater
survival of pine bark beetles (Kurz et al., 2008; Coops et al., 2012).
Media interests tend to focus on changes in annually averaged air temperatures.
Averages, however, are a combination of individual daily maximum (Tmax) and
minimum temperatures (Tmin), which are in turn often the focus of the extremes that are
taking place in a changing climate over the months and seasons of the year. Record high
Tmax values are of great interest, as are the diminishing number of record low Tmin
(Meehl et al., 2009), and interest especially in record high Tmin values and spells of
1
extremely high Tmin has been increasing (Peterson et al., 2008; Peterson et al., 2013;
DeGaetano and Allen, 2002; Gershunov et al., 2009; Perkins et al., 2013). Diurnal
temperature range (DTR) is a measure of the net difference between Tmax and Tmin and
has been examined on a daily, seasonal, and an annually averaged basis (Dai et al., 1999;
Karl et al., 1991; Karl et al., 1993; Makowski et al., 2008). Impacts of extremely hot or
cold seasons can vary based on whether Tmax or Tmin is more anomalous. For example,
winters with frequent Arctic outbreaks and relatively high DTR may have the most
occurrences of hard freezes that damage crops. In winter and spring, decreases in DTR
due to increasing Tmin may be associated with increases in growing season length and
earlier occurrences of the onset of spring (Leathers et al., 1998; Robeson, 2004). In
summer, decreases in DTR with increasing average temperature may be associated with
increased heat stress on vegetation and humans (Perkins et al., 2012) due to higher
frequencies and longer durations of extremely warm nights. The most intense heat waves
tend to be associated with drought and much lower than normal soil moisture, but drier
soil is also associated with higher DTR (Dai et al., 1999). Many studies have evaluated
DTR on an annual basis (Lauritsen and Rogers, 2012; Dai et al., 1999; Karl et al.; 1991)
and produced consistent findings about the temporal changes in DTR variability. It is
valuable to consider trends in temperatures broken down by season and geographic
regions and by daily maxima (Tmax) and minima (Tmin). It is also useful to consider
whether or not each variable is becoming more inconsistent in each season.
2
Chapter 2: Literature Review
According to the study by Dai, Trenberth, and Karl (1999), the weather element
showing the strongest negative correlation with DTR is cloud cover, followed by soil
moisture, surface specific humidity, and precipitation. Their study focused on the summer
and autumn seasons over an area in Kansas. Their study also used gridded global data and
found a strong negative correlation between cloud cover and DTR in both summer and
winter over the U.S., southern Canada, southern Europe, eastern China and Russia,
southern South America, and South Africa, with a greater magnitude in summer in each
hemisphere. They found that DTR was reduced by 40-50% on cloudy days compared to
clear days. Their study and others use the radiation balance to explain how cloud cover
and humidity affect the diurnal cycle of boundary layer temperatures (Balling, 2003;
Collatz et al., 2000; Durre and Wallace, 2001a; Durre and Wallace, 2001b). Some studies
have suggested that increasing Tmin and decreasing DTR trends are primarily caused by
land use changes and the urban heat island effect (Gallo et al., 1996; Hughes and Balling,
1996) rather than cloud cover or the greenhouse effect. Studies of DTR generally have
not found teleconnections or synoptic patterns to be leading causes of DTR variability.
This study is partly an expansion of Lauritsen and Rogers (2012) to compare
trends in DTR, Tmax, and Tmin between different meteorological seasons. In that study,
which used annual rather than seasonal data, a statistically significant decrease in DTR
occurred over 1901-2002, especially since 1950, in all of five regions of the U.S. except
3
for the Southwest. The study compared raw versus detrended DTR data and gridded
versus station data in finding the relative contributions of factors to DTR variability, but
this thesis will use only climate division data for temperatures. Lauritsen and Rogers
(2012) found statistically significant long-term increases in annual Tmin and cloud cover
in all regions. Trends in Tmax and the Palmer Drought Severity Index (PDSI) varied
widely between different regions. Tmax increased significantly in the Southwest and
decreased significantly in the South Central region. Significant increases in the PDSI
occurred in the Northeast and South Central regions, while insignificant decreases
occurred in the other regions. Cloud cover was found to be the leading cause of DTR
variability in all regions except for the Southwest, where the leading cause of variability
was precipitation. The primary cause of Tmax variability in most regions was soil
moisture. An oceanic temperature teleconnection, the Atlantic Multidecadal Oscillation
(AMO), was the leading cause of both Tmax and Tmin variability in the Northeastern
U.S. Lauritsen and Rogers (2012) extensively compared the contributions of predictor
variables to the variability of DTR, Tmax, and Tmin in each of the five regions.
4
Chapter 3: Data
3.1 Spatial and temporal domain of study
The United States is subdivided into 344 climate divisions, comprising one or
more counties or parts of counties in each state and containing numerous weather
reporting stations over an area of relatively homogeneous climate and uniform terrain and
geography within each state. Fig. 3.1 shows two examples of the partitioning of climate
divisions, the first by county lines only and the second by geographic features with
boundaries within some counties
(http://www.cpc.ncep.noaa.gov/products/analysis_monitoring/regional_monitoring/CLIM
_DIVS/states_counties_climate-divisions.shtml, 6 Feb 2015).
Figure 3.1: Climate division boundaries in Ohio and Oregon. Ohio climate divisions
consist of entire counties, but in Oregon, climate division boundaries are mostly based on
mountain ranges and valleys, so many counties have parts in two or more climate
divisions. Oregon also has a climate division that consists of a single county.
5
The approximate geographic center of each climate division is shown in Fig. 3.2
using a variety of symbols on the map. Fig. 3.2 is from Brewer (2015) and shows the
spatial domains of 5 areas of relatively unique and individual long-term (1895-2012)
temporal variability in the Palmer Drought Severity Index (PDSI) in the climate division
data for summers. The PDSI is a function of temperature and precipitation in the short
term before a given time. It not only measures the severity of drought but is also wellcorrelated with soil moisture in summer (Dai et al. 1999). The figure is a starting basis
for this thesis.
To make the data analysis relatively manageable, it is performed for 7 climate
divisions from around the country and a 344-division average for the entire contiguous
United States (CONUS). The climate divisions for further analysis were chosen based
upon the presence of a weather reporting station that had long records of temperature,
precipitation and cloud cover variability.
Figure 3.2: United States Climate Divisions with the highest rotated principal component
(RPC) loadings on each of the first 5 summer PDSI components. After Brewer (2015).
6
The map symbols represent the centers of climate divisions with the highest
loadings for a particular RPC. Each RPC is represented by a different symbol or shading
to tell them apart. Climate divisions where loadings failed to reach a critical value on any
RPC are represented as small dots. Climate divisions represented with a cross (+) had
loadings in excess of the critical value but they occurred on a lower ranked RPC, 6
through 10. The chosen climate divisions are circled, and they include one each from
regions RPC1 through RPC5 and one each from two relatively large areas outside regions
with one of the top 5 components. These latter two divisions, in the southwestern and
northeastern United States, help round out the representation of geographic climate
variability in the country. The following is the list of the selected climate divisions, the
primary station in each, and the regions represented by each station and division.
0102 Appalachian Alabama (Birmingham), representing the Southeast
0206 South Central Arizona (Phoenix), representing the Southwest
1305 Central Iowa (Des Moines), representing the Northern Plains
1903 Coastal Massachusetts (Boston), representing areas of the Northeast near the coast
3305 Central Ohio (Columbus), representing the Ohio Valley region
3405 Central Oklahoma (Oklahoma City), representing the Southern Plains
3502 Willamette Valley Oregon (Portland), representing the Northwest
Climate division data for maximum (Tmax) and minimum (Tmin) air
temperature, precipitation, and PDSI are available going back to 1895. The analyses of
long-term seasonal trends use data from March 1895 to November 2013, except for
winter and spring temperatures, which include 2014. This period of time consists of
7
shorter periods with distinct, sometimes contradictory trends in temperature and DTR
(Lauritsen and Rogers, 2012).
Data for precipitation (ftp://ftp.ncdc.noaa.gov/pub/data/cirs/climdiv, 8 Feb 2014),
Tmax, Tmin, and PDSI (ftp://ftp.ncdc.noaa.gov/pub/data/cirs/climdiv, 24 June 2014)
were obtained from tables of monthly averages for U.S. climate divisions, in a public
online file directory from NCDC. Each monthly value is the average of Tmax or Tmin for
multiple stations in the climate division over all the days in the month, or the average of
monthly total precipitation for those stations. Monthly PDSI values from NCDC are
calculated based on the water balance of the surface layer of soil (Alley, 1984; Dai et al.,
1998). These calculations include evapotranspiration, which considers temperature data
and soil properties, and monthly precipitation anomalies, generally for the previous 12
months. The PDSI may be an oversimplified representation of soil moisture, as it is
primarily a function of precipitation and inadequately considers snow cover, variability of
soil types within each climate division, and variability of available water capacities
(Alley, 1984; Lauritsen and Rogers, 2012), but PDSI data are conveniently available in
NCDC climate division tables.
The monthly data were grouped by meteorological seasons, and new tables were
created for each season, arranged by climate division number and year. The number of
days in each month was considered to calculate seasonal averages of Tmax and Tmin,
using the following formulas, where the name of each month represents the average
Tmax or Tmin for that month:
𝑊𝑖𝑛𝑡𝑒𝑟 =
31𝐷𝑒𝑐 + 31𝐽𝑎𝑛 + 28.25𝐹𝑒𝑏
90.25
8
𝑆𝑝𝑟𝑖𝑛𝑔 =
31𝑀𝑎𝑟 + 30𝐴𝑝𝑟 + 31𝑀𝑎𝑦
92
𝑆𝑢𝑚𝑚𝑒𝑟 =
30𝐽𝑢𝑛𝑒 + 31𝐽𝑢𝑙𝑦 + 31𝐴𝑢𝑔
92
𝐴𝑢𝑡𝑢𝑚𝑛 =
30𝑆𝑒𝑝 + 31𝑂𝑐𝑡 + 30𝑁𝑜𝑣
91
A uniform number of days in February was used to simplify calculations. In leap
years, which usually occur once every four years, February has 29 days, and winter has
91 instead of 90.
All temperatures were then converted to degrees Celsius, and precipitation
amounts to millimeters. Average temperature was calculated as the average of Tmax and
Tmin, and DTR was calculated as the difference between them. Seasonal precipitation
was calculated simply as the total of the monthly precipitation values within each
meteorological season. Seasonal PDSI was only calculated for summer and was
calculated simply as the average over June, July, and August in each climate division.
The entire contiguous U.S. (CONUS) was represented by averaging the data of all
344 climate divisions for each season for each temperature variable and precipitation.
Annual averages of each temperature variable were calculated based on the number of
days in each season:
𝐴𝑛𝑛𝑢𝑎𝑙 =
90.25 𝑊𝑖𝑛𝑡𝑒𝑟 + 92 𝑆𝑝𝑟𝑖𝑛𝑔 + 92 𝑆𝑢𝑚𝑚𝑒𝑟 + 91 𝐴𝑢𝑡𝑢𝑚𝑛
365.25
Due to the grouping of seasons, full-year averages are not calendar-year averages.
The annual average for each year is the average from December of the previous year to
November of the nominal year. Similarly, annual precipitation was calculated as the sum
9
of seasonal precipitation from winter to autumn, thus from December 1 to November 30.
For 1895 only, the calendar-year averages and totals were calculated, thus December
1895 was included in full-year calculations for both 1895 and 1896.
3.2 Carbon dioxide, specific humidity, cloud cover, and teleconnection data
Four other forms of data are used in the analyses. Data for atmospheric carbon
dioxide are available since 1958, and they can be extrapolated annually back to 1895
based on ice core records. Specific humidity data are only available for summer months
in Columbus over the entire range of years. Cloud cover data go back to 1895 or earlier
for most of the stations chosen, but they are not available after 1996, except at Columbus.
Atmospheric and oceanic teleconnection indices provide measures of atmospheric
circulation strength and ocean temperatures (sea surface temperatures, SST). Data are
available going back to 1895 and earlier for some indices but only to 1900 or 1901 for
others.
3.2.1 Atmospheric carbon dioxide
Data for atmospheric carbon dioxide were obtained from a table containing
monthly concentrations in parts per million (ppm) from measurements at Mauna Loa and
a table containing annual estimates of atmospheric CO2 based on multiple sources of ice
core data (http://scrippsco2.ucsd.edu/data/atmospheric_co2, 16 Mar 2015). The monthly
concentrations at Mauna Loa were reported as having been adjusted to the 15th day of
each month. For years 1958 to 2014, the annual average was calculated as the average of
the mid-month concentrations and seasonally adjusted monthly concentrations within
each calendar year. For simplicity, no adjustments were made for the variation in lengths
10
of months or for missing data in 1958 and 1964. No seasonal averages were calculated.
The Scripps merged ice core data go from the first century CE to 2013 but are missing
many years between 1894 and 1953. Data from individual ice core samples from Law
Dome in Antarctica (Etheridge et al., 1996) were used as a link between data before 1958
and data since 1958 in order to justify the use of the merged ice core data to extend the
Mauna Loa data back to 1895. The correlation between individual ice core data and
Mauna Loa data from 1959 to 1978 was .985. The correlation coefficient of individual ice
core data before 1958 with time was .984, and that of merged ice core data was .975. The
strength of these correlations implies that the three datasets are reasonably similar and
justifies extrapolation of the Mauna Loa data.
Linear regression was used to predict annual CO2 concentrations at Mauna Loa
before 1958 based on the slopes of the three datasets relative to each other. For years
without merged ice core data, the equation used to estimate CO2 in year x was
approximately
𝑦1 = 0.32318𝑥 − 317.406;
𝑥 ≥ 1895
In the equation above, 𝑦1 is the annual atmospheric CO2 concentration at Mauna
Loa, and 𝑥 is the year number. For example, the estimate for CO2 in 1900 using this
equation is 296.64 ppm. Although this estimation method makes the complete time series
almost linear and therefore highly correlated with time, it allows for emphasis of the
period from the 1950s to the 2010s, when the rate of increase of atmospheric CO2
increased with time and when the dependent temperature variables were most likely
affected by this acceleration of atmospheric CO2 concentration. For years with merged
ice core data, concentrations 𝑦2 were adjusted using
11
𝑦1 = 0.99763𝑦2 + 0.843
The resulting dataset of annual atmospheric CO2 concentrations is shown in Fig.
3.3. A second-order polynomial regression of Mauna Loa data since 1960 shows a
remarkably strong correlation that indicates a nearly constant second derivative of the
CO2 concentration with respect to the year.
Figure 3.3: Time series of annual CO2 concentrations estimated from ice core data or
linear regression before 1958 and annually-averaged CO2 concentrations from
measurements at Mauna Loa since 1958. The second series is a copy of the first since
1960, shifted down by 20 ppm for visual convenience and containing the second-order
polynomial trend curve.
3.2.2 Specific humidity and PDSI
For the Central Ohio climate division, a long record of summer season specific
humidity also is available (Rogers et al., 2006), permitting a more detailed analysis there
of the role of humidity on temperature and DTR. Seasonal specific humidity is calculated
using monthly averages of dew points and atmospheric pressure. The monthly data used
12
to create the long-term summer atmospheric pressure, dew point temperature, and
specific humidity record at Columbus are described in Rogers et al. (2006). The
calculation of vapor pressure from monthly mean dew point temperature follows Bolton’s
(1980) empirical relationship, accurate to within 0.3% for temperatures Td between -35°C
and +35°C:
17.67𝑇𝑑
𝑒 = 6.112 exp (
)
𝑇𝑑 + 243.5
Based on the mean vapor pressure, e, and the mean monthly atmospheric pressure, p (in
millibars), the monthly mean specific humidity, q, can be obtained as
𝑞=
. 622𝑒
𝑝 − .378𝑒
3.2.3 Cloud cover
Cloud cover data are available at the 7 stations from 1895-1996. These data are from the
“Historical Sunshine and Cloud Data in the United States” (HSC; 1895-1987) and the
National Climate Data Center (NCDC) Hourly Surface Airways Data (1948-1996). The
HSC data (Steurer and Bodosky 2000) are monthly percentages of United States sky
cover produced by Steurer and Karl (1991) and based on observer estimates of fractional
cloud amount from sunrise to sunset made spanning different observational practices over
these decades. These data are extended to 1996 by incorporating the Surface Airways
Hourly (TD-3280) U.S. cloud reports that were extracted and converted into monthly and
seasonal averages. In these data the reported total sky cover (TSKC), the “amount of the
celestial dome covered by clouds or obscuring phenomena” (Steurer and Bodosky 2000)
13
consists of hourly human observations are changed to tenths from the original
measurements in eighths. After 1996, most first order weather stations switched to
automated observations from which cloud cover data are not available. Missing data in
the HSC were always filled using the long-term (from start of data to 1987) monthly
mean values.
Cloud cover data exhibit long-term trends and decadal variability. Some of the
cloud cover variability with time is due to changes in cloud observation methods over the
20th century (Karl and Steurer 1990) including changes in number of observations in the
1930s and the 1948 change to sky cover observations, that included all obstructions to
visibility such as fog, haze, smoke, and dust. Additionally, increases in U.S. commercial
airplane traffic in the second half of the century, mainly since 1960, led to increasing
numbers of jet contrails that would likely boost sky cover reports. Cloud cover data from
2003 to 2014, are uniquely available for Columbus, Ohio, from the National Weather
Service Wilmington Ohio (http://www.erh.noaa.gov/iln/lcdpage.htm, 26 Mar 2015).
Missing data for summer seasons from 1997 to 2002 at Columbus were filled in using the
seasonal average over the entire period.
3.2.4 Atmospheric and oceanic teleconnection indices
Atmospheric and oceanic teleconnection indices will be used to examine the
effect of atmospheric circulation patterns on temperature and DTR variability. These
include the Atlantic Multidecadal Oscillation (AMO), sea surface temperature (SST)
anomalies in the Niño-3.4 region representing El Niño and the Southern Oscillation
14
(ENSO), the North Atlantic Oscillation (NAO) index, the Arctic Oscillation (AO) index,
the North Pacific Index (NPI), and the Pacific Decadal Oscillation (PDO).
Monthly data for atmospheric circulation and sea surface temperature indices
were obtained from various sources. Extended reconstructed sea surface temperature
(ERSST) data updated in April 2014 from Climate Explorer were used for the AMO and
Niño-3.4 (ENSO) indices. Hurrell (1995) station-based NAO data, updated in April 2014,
are from NCAR/UCAR (https://climatedataguide.ucar.edu/climate-data/hurrell-northatlantic-oscillation-nao-index-station-based). The AO data are from JISAO
(http://jisao.washington.edu/ao/) for the years 1899-2001, and AO data from
NOAA/NCEP
(http://www.cpc.ncep.noaa.gov/products/precip/CWlink/daily_ao_index/monthly.ao.inde
x.b50.current.ascii.table) for 1950-2001 were analyzed by correlation with the JISAO
data to predict the JISAO data values for 2002-2013. This extension of AO data was done
using linear regression for each month separately from 1950-2001 as predictors for the
most recent data values. The NOAA/NCEP monthly data were adjusted with slope
coefficients ranging from .990 to 1.065, and correlation coefficients ranged from .978 to
.992. The strength of these correlations implies that the two datasets are reasonably
similar and justifies extrapolation of the JISAO data. All circulation and SST indices
were ultimately converted to averages in meteorological seasons by simply averaging
three-month periods.
The AMO (Schlesinger and Ramankutty, 1994) is an index of the North Atlantic
sea surface temperature (SST) anomaly. It is obtained from the average of SSTs over
ocean areas within 0°-60°N and 0°-80°W. It is generally cyclical with a period of 60-80
15
years, and it influences terrestrial temperatures in regions around the North Atlantic.
Niño-3.4 is an index of the SST anomaly of a region in the equatorial central Pacific,
from 5°S to 5°N and 170-120°W, that ideally represents the pattern of ENSO. Large
positive Niño-3.4 anomalies are believed to be linked to above-normal winter rainfall in
the southern and southwestern U.S., warmer winter and cooler summer temperatures in
the northern U.S., and more zonal flow in the upper troposphere. Large negative
anomalies are linked to the opposite effects and more frequent atmospheric blocking,
with more Arctic cold outbreaks in winter. ENSO is generally cyclical with a period of 46 years.
The NAO (Serreze et al., 1997) is an index of the anomaly of the sea level
pressure (SLP) difference between the Azores (or coastal Portugal or Gibraltar) and
Iceland, representing the strength of the westerly winds across the Atlantic. The NAO is
considered to be a component of the AO. The AO is derived as the leading mode of
empirical orthogonal function (EOF) analysis of 1000mb height anomalies north of 20°N.
Regression of its time series onto sea level pressure yields a large positive center over the
subtropical Atlantic, like the NAO Azores center, and a large negative anomaly over the
Arctic. The AO is especially influenced by anomalies north of 65°N. The AO and NAO
are generally non-cyclical. Positive values of either index are associated with zonal flow,
and negative values are associated with blocking, a more amplified polar jet stream, and
Arctic cold outbreaks.
The NPI is a monthly index of SLP (Trenberth and Hurrell, 1994) averaged over
the area of the north central Pacific from 30°N to 65°N and 160°E to 140°W. It is
somewhat cyclical and influenced by ENSO, but it has no consistent period. It varies
16
seasonally and is most important in winter, when it represents the strength of the Aleutian
low. Lower NPI values indicate a stronger Aleutian low, which causes greater fluxes of
heat and moisture to the Pacific coast of the U.S. The PDO is an index formed as the time
series of the first EOF of Pacific Ocean SSTs poleward of 20°N. The PDO is mainly
cyclical with periods of 40-60 years. It entered a positive phase around 1977 and has been
mostly negative since 1998, but it may be transitioning in 2015 toward another positive
phase. The positive PDO phase, like negative anomalies of NPI, is associated with
warmer temperatures in the western U.S. and below-normal temperatures in the eastern
and southeastern U.S.
17
Chapter 4: Methodology
4.1 Analyzing trends
Climatological normal temperatures and precipitation, which are often reported in
local news and in climate summaries, use 30-year averages. Normal values in 2015 are
based on Jan 1981 to Dec 2010. For each region or climate division in the study, the
trends of Tmax, Tmin, DTR, precipitation, and summer PDSI will be discussed using 30year averages of the seasonal data, thus representing changes in what is considered
normal. Standard deviations will be used to discuss correlation coefficients of particular
trends and to assess whether each season is experiencing an increase or decrease in
variability of DTR and of precipitation over time. Sample standard deviations for 30-year
periods will be compared in this analysis. The slope and correlation coefficient of the
long-term trend of each variable with time, for each season and division, will be
determined using linear regression.
4.2 Stepwise multiple linear regression
This study will use statistical analyses to assess the contribution of several
meteorological parameters to the variability of Tmax, Tmin, and DTR, similarly to
Lauritsen and Rogers (2012), but expanded into seasons and limited to the chosen climate
divisions. The PDSI will represent soil moisture and will only be used in summer, when
it is most closely related to soil moisture (Dai et al., 2004). Specific humidity will only be
considered in the Central Ohio climate division in summer.
18
Stepwise multiple linear regression analysis (SMLR) will be used to determine
the seasonal relationships between the predictors (precipitation, PDSI in summer,
humidity, cloud cover, and the teleconnection indices) and the predictands (dependent
variables – Tmax, Tmin, and DTR). For each climate division in summer and winter, and
for central Ohio in spring and autumn, the dependent variables will be modeled with
multiple linear regression equations. Summer is of slightly greater interest due to the
public awareness of heat-related health impacts, drought, and severe weather, and due to
the role of soil moisture and humidity. The following equation is the form of a multiple
linear regression model with p independent variables and n sets of values of the
independent variables.
𝑌𝑖 = 𝛽0 + 𝛽1 𝑋𝑖1 + 𝛽2 𝑋𝑖2 + ⋯ + 𝛽𝑝 𝑋𝑖𝑝 + 𝜀𝑖 ,
𝑖 = 1, … , 𝑛
The dependent variable (𝑌𝑖 ) is modeled as a function of a constant term (𝛽0 ), the
independent variables (𝑋𝑖𝑝 ), their corresponding coefficients (𝛽𝑝 ), and an error or
residual term (𝜀𝑖 ). The error term is a random variable, which represents variation in the
dependent variable that is unexplained by the regression equation. The coefficients and
constant are estimated using the least squares method, and the coefficient sign determines
if the independent variable affects the dependent variable positively or negatively.
In SMLR, combinations of orthogonal predictor variables are optimized to explain as
much of the variance of the predictand as possible. First, the predictor explaining the
most predictand variance is chosen, and additional orthogonal predictors are included as
long as each explains more than 2.5% of the remaining predictand variance with 95%
confidence. Regression equation coefficients and r2 are adjusted for each additional
19
predictor. Each additional predictor must also be significant enough to overcome the
adjustment of r2 for reduction of degrees of freedom.
4.3 Rotated principal component analysis
Many of the predictors will be interrelated to one another (e.g. precipitation and
AMO) in complex ways, as represented by their intercorrelations. This intercorrelation
among predictors leads to incorrect interpretation of the individual relation each has with
the predictands and must be removed from the analysis. This multicollinearity problem
among the predictors will be removed using rotated principal component analysis
(RPCA, PCA), as was done in Lauritsen and Rogers (2012). RPCA will produce
orthogonal predictor time series to be used in the SMLR. The orthogonal time series will
then evaluate the contribution of the moisture factors (humidity, PDSI, etc.) and climate
indices to the variation of each dependent variable.
PCA uses matrix operations to determine eigenvectors for a dataset. In this
equation, [A] is the data matrix, which contains variances or correlation coefficients, [X]
is the eigenvector matrix, and λ is an eigenvalue of the eigenvector matrix.
[𝐴] ∙ [𝑋] = 𝜆[𝑋]
Eigenvectors with maximized variance are created, beginning with the one with the
highest eigenvalue (the principal component), and with the constraint that the second and
subsequent eigenvectors are orthogonal to the first, creating a set of empirical orthogonal
functions (EOFs). This is the method by which the AO index time series is created,
formed as the first EOF of hemispheric 1000 hPa heights. In order to show the simple,
unique, and robust patterns of spatial variability, however, the orthogonality constraint is
removed through a procedure known as rotation. The EOFs are subjected to a variance20
maximizing rotation procedure that transforms them from an orthogonal basis to one that
produces unique, compact, patterns showing the spatial regionalization in the data
(Richman 1986; Barnston and Livezey 1987). The rotated principal components may
spatially overlap somewhat, since they are not orthogonal, but their time series retain
their orthogonality and are uncorrelated with one another. This procedure is therefore
used to orthogonalize the predictors before SMLR. Overall RPCA was used to obtain the
unique centers of PDSI in the U.S. (Fig. 3.2) in the study by Brewer (2015).
Loadings, which are the coefficients in eigenvectors, have normalized values
between -1 and +1 and represent the weight each data point has on a particular principal
component pattern. The loadings collectively represent the spatial distribution of the RPC
patterns in the analysis. The loading values can be seen in the rotated component matrix,
and each value |L| ≥ 0.71 indicates an RPC containing at least 50%, or L2, of the variance
of a single predictor variable. For example, if the NAO has L = 0.947 on RPC4, then
RPC4 contains L2 = 89.7% of NAO variance and is assumed to solely represent the NAO
since no other predictor variable can have a large L (L2 < 10.3%) on RPC4. The 𝑖 = 𝑛
predictors (in the SMLR model equation) in each SMLR analysis are collectively
subjected to RPCA with the objective of producing exactly n principal components such
that each predictor variable has its own orthogonalized time series. SMLR then creates a
model containing the most statistically significant of the orthogonal predictors for each
dependent variable.
21
4.4 Statistical software and interpretation of output
In the SPSS Statistics software, choosing Factor Analysis from the Analyze and
Dimension Reduction menus opened a dialog box in which the predictor variables were
selected and analysis options were chosen (Fig. 4.1). Correlation coefficients and
significance levels were enabled in Descriptives. In order to perform RPCA, the
Extraction options were chosen as in Fig. 4.1b, including a fixed number of extracted
(and rotated) factors, equal to the number of predictors. The number of predictors in
Central Ohio summer analyses was 11.
Figure 4.1: Factor Analysis option boxes in SPSS Statistics, showing (a) predictor
variables selected for analysis and one to be added to the selection, and (b) options
chosen for RPCA.
22
The rotation method was Varimax (variance-maximizing), and display of the
rotated solution in the output was enabled, leading to the rotated component matrix
(Table 4.1). The options chosen in Scores were the regression method and that they are
saved as new variables. The following is an example of the output of RPCA, using
predictors for summer in the Central Ohio climate division (Table 4.1).
Table 4.1: Rotated component matrix, showing results of transformation of raw time
series of predictor variables (left column) to orthogonalized variables. The square of each
coefficient is the fraction of variance of a raw predictor variable that is contained in an
orthogonalized predictor.
The highlighted cells contain loadings L > 0.71, indicating that each of the 11
extracted RPCs contains most of the variance of a unique predictor variable. RPC1
represents the PDSI in Central Ohio but also contains 0.4092 = 17% of the variance of
precipitation, as the PDSI is a function of precipitation. However, RPC11 still contains
75.7% of the variance of precipitation, and each of the remaining RPCs contains a single
loading greater than L2 = 75.7%. Therefore, all 11 factors extracted from RPCA are used
as the orthogonalized predictors for SMLR.
23
Choosing Linear from the Analyze and Regression menus opened a dialog box in
which the predictors and predictand were selected and analysis options were chosen (Fig.
4.2). In order to perform SMLR, the factors from RPCA were chosen as the independent
variables, and the method was changed to stepwise. The default settings were used in all
other categories of options. SMLR was repeated for each dependent variable: DTR,
Tmax, Tmin, and Tavg.
Figure 4.2: Linear regression option box in SPSS, showing the selected predictand and
predictors. The numbered factors are the RPCs extracted from the previous analysis.
The first output table lists the factors that were significant in explaining the
variability of the predictand, summer DTR in Central Ohio. The first of these factors, for
example, is RPC8, or cloud cover at Columbus (Table 4.1), explaining 21.8% of the
adjusted total variance in Central Ohio DTR. In the Model Summary table, the adjusted
R2 value equals the cumulative variability of the predictand that is explained by the n
predictors after the nth step of SMLR. R2 is adjusted to account for the loss of one degree
of freedom with each additional term (or step) in the regression equation. Table 4.2 is an
example of these results merged together. The numbers under variables entered are the
RPCs that correspond to particular predictors.
24
a
Model Summary
Variables Entered/Removed
Model
Variables
Entered
Variables
Removed
REGR factor
score 8
REGR factor
2
score 1
REGR factor
3
score 6
REGR factor
4
score 3
REGR factor
5
score 11
REGR factor
6
score 4
a. Dependent Variable: DTROH05
Method
R
1
Stepwise (Criteria:
Probability-of-F-toenter <= .050,
Probability-of-F-toremove >= .100).
R Square
Adjusted
R Square
Std. Error
of the
Estimate
0.473
.224
.218
.878645
0.636
.405
.394
.772935
0.765
.585
.574
.648095
0.821
.675
.663
.576373
0.873
.761
.751
.495891
0.883
.780
.768
.478089
Table 4.2: Sample output of the SMLR analysis prepared as in Figure 4.2, showing the
list of significant predictors and the amounts of predictand variability that are explained
after each step of the SMLR model.
The last output table that contains useful information for this study is the table of model
prediction coefficients. It shows the models for each step of SMLR, but only the model
with all 6 of the final significant predictors (Table 4.3) is important. Except for the
constant 𝛽0, the coefficients used in the model are the standardized coefficients. Table 4.3
is the model for the example shown throughout this section, summer DTR in Central
Ohio.
25
Coefficientsa
Model 6
Unstandardized
Coefficients
B
(Constant)
13.054
Std. Error
Standardized
Coefficients
Beta
t
.044
REGR factor
-.470
.044
score 8
REGR factor
-.422
.044
score 1
REGR factor
-.422
.044
score 6
REGR factor
-.297
.044
score 3
REGR factor
-.292
.044
score 11
REGR factor
.136
.044
score 4
a. Dependent Variable: DTROH05
Sig.
297.860
.000
-.473
-10.685
.000
-.425
-9.591
.000
-.425
-9.585
.000
-.299
-6.756
.000
-.294
-6.642
.000
.137
3.094
.002
Table 4.3: Sample output showing the standardized coefficients for each predictor in the
SMLR model and the p-value of significance of each step. Inclusion of each predictor
requires p < .050.
26
Chapter 5: Results
5.1 General annualized trends and correlations
Table 5.1 organizes the slopes of linear regression of annually-averaged DTR,
temperature, and annual precipitation for the 7 climate divisions and the 344-division
average of the contiguous United States (CONUS) from 1895 to 2013. A statistical t-test
was performed for the correlation coefficients (Pearson r values) between each variable
and time. Highlighted coefficients are significantly nonzero with 95% (yellow), 99%
(orange), or 99.9% confidence (red).
27
Division
Dec-Nov
Slope
3305
Pearson r
Columbus
Since 1960
Slope
CONUS avg. Pearson r
Since 1960
Slope
0102
Pearson r
Birmingham
Since 1960
Slope
0206
Pearson r
Phoenix
Since 1960
Slope
1305 Des
Pearson r
Moines
Since 1960
Slope
1903
Pearson r
Boston
Since 1960
3405
Slope
Oklahoma Pearson r
City
Since 1960
Slope
3502
Pearson r
Portland
Since 1960
DTR
Tmax
Tmin
Tavg
Precip
°C/cent °C/cent °C/cent °C/cent mm/cent
-1.07
-0.15
0.92
0.38
55
-0.6085 -0.0673
0.4118
0.1872
0.1514
-1.23
1.96
3.19
2.58
305
-0.24
0.57
0.81
0.69
70
-0.2604
0.3597
0.5274
0.4622
0.3745
-0.51
2.11
2.61
2.36
124
-1.04
-0.68
0.36
-0.16
211
-0.5958 -0.3516
0.1901 -0.0953
0.3378
-1.73
1.47
3.21
2.34
30
0.39
1.52
1.13
1.33
25
0.2233
0.6761
0.5604
0.6813
0.1005
-1.04
2.32
3.36
2.84
-32
-0.92
-0.08
0.84
0.38
104
-0.4572 -0.0285
0.3390
0.1529
0.2219
-1.24
1.51
2.75
2.13
212
0.22
1.62
1.40
1.51
343
0.2117
0.6621
0.6175
0.6561
0.6134
-0.61
2.85
3.46
3.15
430
-0.66
-0.23
0.42
0.10
115
-0.3099 -0.0949
0.2319
0.0504
0.2120
-0.42
1.63
2.05
1.84
255
0.36
0.93
0.58
0.75
68
0.2690
0.4552
0.3498
0.4348
0.1112
0.00
1.13
1.13
1.13
-67
Table 5.1: Rates of change of annually-averaged temperatures and total annual
precipitation, per century, with correlation coefficients and statistical significance.
Correlations significant with 95% confidence are in yellow, 99% orange, and 99.9% red.
5.1.1 National and regional annual trends in air temperature and DTR
Fig. 5.1 shows the annually averaged DTR for each division and the CONUS. The
CONUS annually-averaged DTR decreased by 0.23 °C per century over the period from
December 1895 to November 2013.
28
Figure 5.1: Annually averaged DTR (°C) for each climate division and the 344-division
CONUS average, along with the CONUS trend (black line).
The black line representing this trend is statistically different from a line of zero
trend with 99% confidence. However, it appears that the downward DTR trend masks the
decadal scale variability showing a slight increase from the 1890s until the 1950s, and the
CONUS DTR trend since 1960 is -0.51 °C per century. The general DTR trend in central
Ohio is similar, except that the decrease since 1960 has been more rapid, -1.23 °C per
century. From Table 5.1, the difference between rates of increase of Tmin, rather than
Tmax, is the main contributor to this difference in the DTR trend. The results in Table 5.1
use data starting in January 1895, while the trendline in Fig. 5.1 uses data starting in
December 1895, leading to slight differences in text slope values between the trendline
and the table.
29
Annually-averaged DTR in the Boston and Phoenix divisions increased over the
long term but decreased at relatively large rates since 1960 (Table 5.1). This
inconsistency is evident in the annual data (Fig. 5.1), where the years with the highest
DTRs in both divisions mainly occurred between 1940 and 1960, and DTR sloped
downward after 1960. For Boston, the long-term positive slope is significant with 95%
confidence, but the negative slope since 1960 is also significant with 95% confidence.
The negative slope since 1960 in the Phoenix division is significant with 99% confidence.
In the Portland division (Fig. 5.1), DTR appears to have peaked in the 1930s,
decreased slightly from then to the 1950s, and neither increased nor decreased since then.
Despite having zero slope since 1960 (Table 5.1), the long-term trend was an increase
with 99% confidence of being significantly different from zero slope. DTR in Des
Moines also peaked in the 1930s but had a noticeable downward slope until about 1980.
The long-term decrease was significant with 99.9% confidence.
The two divisions representing the south central and southeastern U.S. also had
long-term declines in DTR that were significant with 99.9% confidence. In the
Birmingham division, DTR decreased from the 1920s to the 1940s, increased in the
1950s, and decreased nearly continuously since then. However, in Central Oklahoma,
most of the decline occurred before 1950. Another downslope is noticeable from the
1970s to the early 2000s, making the trend since 1960 slightly negative, but Central
Oklahoma was the only chosen division in which the more recent DTR trend was less
negative than the long-term trend. The Columbus and Des Moines divisions are
characterized by highly significant short- and long-term DTR trends with relatively
similar magnitude.
30
Fig. 5.2 summarizes the annually averaged DTR, Tmax, and Tmin as 30-year
running means for each of the eight areas. The 30-year average DTRs (Fig. 5.2a)
noticeably decrease after 1960 in central Ohio and CONUS. Before 1960, both Tmax
(Fig. 5.2b) and Tmin (Fig. 5.2c) appear to have increased slightly in central Ohio and
CONUS, resulting in flat or slightly upward DTR trends. The upward tendency into the
1950s is also apparent for Tmax and DTR in the Boston and Phoenix divisions. In both
divisions, the last 30 years had a higher average DTR than 30-year periods before 1940
and a lower average DTR than periods ending between 1950 and 2000. Boston reached
its peak 30-year average DTR in 1968 (the period from Dec 1938 to Nov 1968) and has
experienced a slow downward DTR trend since then. In the Phoenix division, however,
30-year DTR peaked in 1975 and has decreased more rapidly since then. This peak can
be attributed to increasing Tmax from the 1930s to the 1960s and slightly decreasing
Tmin from the 1940s to the 1970s, followed by a steep increase in Tmin since 1975 with
a more subtle increase in Tmax.
Similarly, the pattern of decreasing DTRs since about 1980 due to Tmin
increasing faster than Tmax is seen in all the remaining chosen divisions except for
Portland. There, 30-year averages of Tmax and Tmin increased at about the same rate,
thus 30-year averages of DTR were nearly steady and actually increased slightly from the
early 1980s to 2013. Central Oklahoma also differed from the pattern somewhat, as the
decrease in 30-year average DTR from 1980 to 1997 was due to decreasing Tmax.
31
(a)
(b)
(c)
Figure 5.2: Running means of annually (Dec-Nov) averaged temperatures (°C) for the 7
climate divisions and the CONUS (U.S. divisions avg.). Data start in 1925. Note that the
Phoenix Tmax and Tmin series have been shifted down by 10°C and 6°C, respectively,
for visual convenience.
32
As different cities and areas have warmed or cooled at different rates, it may be of
interest to indicate cases in which one that was previously cooler than another has
become warmer, or one went from having a larger DTR to a smaller DTR than another. A
few such cases in Tavg are evident in Fig. 5.3, which shows the 30-year running means
of Tavg in the chosen climate divisions. Early in the data record (Fig. 5.2), Oklahoma
City was cooler and had a larger DTR than Birmingham. A steep warming trend in Tmin
in Oklahoma City through the late 1940s led to a temporary reversal of both of these
comparisons. From about 1930 to 1955, 30-year-average DTR was higher in Birmingham
than in Oklahoma City. A downward trend in Tmin in Oklahoma City from the late 1950s
to the 1980s, along with a steep upward Tmin trend in Birmingham since the mid-1980s,
led to the conditions that Oklahoma City has had the larger DTR since the mid-1970s and
that Birmingham has had a smaller DTR than the CONUS average since 2001. Tavg,
based on 30-year means (Fig. 5.3), was slightly higher in Oklahoma City than in
Birmingham from about 1955 to 1992, and since 1993, Birmingham has been slightly
warmer. The difference in rates of increase of Tmin is the main contributor to the faster
upward Tavg trend in Birmingham than in Oklahoma City since about 1990.
Another pair of divisions that switched ranks of 30-year running means of Tavg
was Columbus and Portland. In Fig. 5.3, Columbus was noticeably warmer until about
1960, when a cooling trend began there. A steep downward Tmax trend (Fig. 5.2b) was
the main contributor, as hot individual years from 1930 to 1955 were replaced by years
with cooler Tmax, and Columbus had its lowest 30-year average Tmax in 1985 (Dec
1955 to Nov 1985). The trends and extremes in Central Ohio are discussed at length in
Section 5.2.3. In 3502 (Portland), both Tmax and Tmin decreased only slightly in the
33
1960s and 1970s, and 3502 became warmer than 3305 in 1979. A steep upward Tmin
trend in 3305 since the late 1980s contributed to another reversal, as 3305 has been
slightly warmer since the 30-year average ending in 2010.
Figure 5.3: As in Fig. 5.2 but for Tavg. Note that the Phoenix series has been shifted
down by 8°C.
34
5.1.2 Annual precipitation trends
Fig. 5.4 shows the annual precipitation for each year in each of the 7 climate
divisions and the 344-division average and for 30-year running means. The contiguous
U.S. from Dec 1895 to Nov 2013 has experienced an increase in annual precipitation of
about 68 millimeters per century (Fig. 5.4a). Most of this increase occurred since 1960,
with a rate of 124 mm/century, compared to 23 mm/century from 1896 to 1959. The
driest years in the CONUS were 1963, 1930, 1931, 1904, 1956, 1910, 1936, 1895, 1917,
and 1914. The wettest year was 1973, and 11 of the top 20 wettest years occurred since
1990. The 30-year running mean (Fig. 5.4b) increased fairly steadily from its minimum in
1939 to the late 1990s and was mainly flat since then.
Precipitation has increased over the long term since 1895 in most areas in the
United States. In central Ohio, the long-term increase was insignificant, but the increase
of 305 mm/century since 1960 was significant with 99% confidence. Only in the two
westernmost chosen divisions, Phoenix and Portland, was there no significant increase in
precipitation over either the short term or the long term (Table 5.1). In fact, both divisions
had slight decreasing precipitation trends since 1960. Moving averages of precipitation in
the Phoenix division generally remained close to 250 mm/year throughout the long term
(Fig. 5.4b; Phoenix points are shifted 1000 mm upward). These averages increased when
9 of the 18 wettest years occurred from 1978 to 1995, but a more recent downward trend
resulted as only 5 years from 1996 to 2013 had divisionally-averaged annual precipitation
above 250 mm.
35
(a)
(b)
Figure 5.4: (a) Annual Dec-Nov precipitation (millimeters) in each climate division, with
the CONUS trend since Dec 1895. (b) Running means of the above data. Note that the
Phoenix series has been shifted up by 1000 mm for visual convenience.
Central Ohio was wetter than the Boston division early in the period of record,
based on 30-year averages of annual precipitation. However, a steep increase in Boston
mainly between 1930 and 1960 made this division wetter than Central Ohio since about
1940 and much wetter in more recent 30-year periods. Unusually wet individual years in
36
1933 and 1938 in Boston and extremely dry years in 1930, 1934, and 1941 in Columbus
contributed to this reversal. The gap widened when Boston had three consecutive top-25
wet years from 1953 to 1955, which were contrastingly three of Central Ohio’s 25 driest
years. The 1950s through the 1980s were a relatively dry period in Central Ohio, and the
driest 30-year average occurred over the period ending in 1968. An increasing trend
began in 1989, and the last 30-year average (Dec 1983 to Nov 2013) was the wettest. In
the Boston division, the wettest year was 1972, and 9 of the top 14 wettest years occurred
since 1995. Furthermore, of the seven chosen divisions, Boston had the highest rate of
increase of precipitation both in the long term and since 1960 (Table 5.1).
The wettest two divisions, Birmingham and Portland, were initially similar in 30year averages of annual precipitation, but Birmingham has been much wetter for most of
the long term (Fig. 5.4b). Eleven of the 20 driest individual years in Birmingham
occurred in 1925 or earlier. The gap widened shortly after that, especially in 1929, which
was unusually wet in Birmingham but was the driest year in Portland. A relatively dry
period in Portland continued into the 1940s while a gradual increasing precipitation trend
took place in Birmingham. The decade of the 1950s was especially wet in Portland and
contained 4 of the division’s 25 wettest years, but Birmingham was still wetter in 30-year
running means that included the 1950s. Since 1970, Portland had 11 years with more than
1500 mm of precipitation, while Birmingham had 19 such years.
Another climate division in which precipitation increased steeply in recent
decades was Oklahoma City. Before 1970, 30-year running means of annual precipitation
there remained close to CONUS averages (Fig. 5.4b), except for an extremely dry period
from 1936 to 1939. The decade of the 1970s was unusually dry in Oklahoma City, and
37
1941 and 1945 were two of the division’s 10 wettest years, so 30-year means decreased
and, relative to CONUS, bottomed out in the late 1970s and early 1980s. Then, 14 of the
25 wettest individual years in Oklahoma City occurred after 1980, and this division has
been wetter than the 344-division CONUS average since 1993, based on 30-year means.
CONUS precipitation also clearly peaked in the most recent decades, as its moving
averages rose steadily from a minimum in 1939 until the late 1990s and hovered around
920 mm/year since then. 13 of the 25 wettest years occurred since 1990, and 5 years in
the 1930s were among the 18 driest in CONUS.
Central Iowa has had less precipitation than the CONUS average throughout the
long term (Fig. 5.4b), although it nearly closed the gap after four consecutive wet years
from 2007 to 2010. Like CONUS, Central Iowa had its driest 30-year period ending in
1939. This period included the driest year, 1910, and five years in the 1930s with
divisionally-averaged annual precipitation at or below 700 mm. Like Oklahoma City, the
Des Moines division has had a steep increasing trend since a relative minimum around
1980. The wettest 30-year period, from Dec 1981 to Nov 2011, included 11 years with
precipitation above 1000 mm and contained the wettest year, 1993. Only eight years
before 1982 had divisionally-averaged annual precipitation above 1000 mm.
38
5.1.3 Trends in atmospheric and teleconnection indices
The trend in atmospheric carbon dioxide with time from 1895 to 2013 was
increasing with a correlation of 0.932. Therefore, in most cases, the time trend correlation
between each variable and CO2 is very similar to the correlation between that variable
and the year, and these correlations with CO2 are not shown. Correlation coefficients of
the long-term trends in teleconnection indices are presented seasonally in Table 5.2.
Teleconn. Winter Spring
Summer Autumn
NPI
-0.235
-0.058
-0.142
0.022
AMO
-0.036
-0.048
-0.114
-0.201
NAO
-0.052
-0.035
-0.144
-0.030
AO
0.035
0.114
0.328
0.247
Nino3.4
0.099
0.236
0.245
0.183
PDO
-0.114
0.012
-0.026
-0.148
Since 1960 Winter Spring
Summer Autumn
NPI
-0.030
-0.231
-0.048
0.039
AMO
0.424
0.455
0.388
0.396
NAO
0.216
0.007
-0.158
0.052
AO
0.225
0.144
0.011
0.157
Nino3.4
0.002
0.153
0.136
0.088
PDO
0.142
0.221
0.100
-0.049
AMO ≥1984
0.834
0.652
0.536
0.742
AO ≥1984
-0.197
-0.066
-0.201
0.080
PDO ≥1984
-0.383
-0.525
-0.544
-0.523
Table 5.2: Correlation coefficients between each seasonally-averaged teleconnection
index and time, over the long term (top) and recent shorter terms (bottom), with
significance as in Table 5.1.
Over the long term, the AO had significant increasing trends with time in summer
and autumn, with at least 99% confidence, and had smaller positive correlations with
time in spring and winter. The Niño-3.4 index increased significantly in summer and
spring and also had increasing trends in autumn and winter. The NPI in winter and the
39
AMO in autumn had negative trends that are significant with 95% confidence. However,
from 1960 to 2013, the AMO has increased significantly in every season, having shifted
from the negative phase to the positive phase. In the last 30-year period, the trend of the
AO reversed, mainly in winter and summer, and the PDO in every season except for
winter has had a significant negative trend with 99% confidence.
5.2 Seasonal trends and correlations in DTR, Tmax, Tmin, and precipitation
5.2.1 Time series trends in each season
Table 5.3 compares the trends of annual DTR in each of the 7 climate divisions
with the DTR trends broken down by seasons. The long-term period of data is 1896-2014
for winter, 1895-2014 for spring, and 1895-2013 for summer and autumn. Like Table 5.1,
this table shows the slope of linear regression of DTR with time and the correlation
coefficient of each linear regression. Highlighted coefficients are significantly nonzero
with 95% (yellow), 99% (orange), or 99.9% confidence (red).
40
Division
3305
Columbus
CONUS avg.
0102
Birmingham
0206
Phoenix
1305 Des
Moines
1903
Boston
3405
Oklahoma
City
3502
Portland
DTR by
Winter
Spring Summer Autumn Annual
season °C/100yr °C/100yr °C/100yr °C/100yr °C/100yr
Slope
-0.74
-0.58
-1.61
-1.28
-1.07
Pearson r
-0.3461 -0.2524 -0.5602 -0.3883 -0.6085
Since 1960
-1.52
0.03
-2.30
-0.84
-1.23
Slope
-0.10
0.03
-0.47
-0.37
-0.24
Pearson r
-0.0679
0.0192 -0.3781 -0.1972 -0.2604
Since 1960
-0.57
0.08
-1.07
-0.24
-0.51
Slope
-0.63
-0.71
-1.43
-1.39
-1.04
Pearson r
-0.2936 -0.3327 -0.4773 -0.3765 -0.5958
Since 1960
-0.93
-1.78
-2.41
-1.67
-1.73
Slope
0.36
0.24
0.82
0.17
0.39
Pearson r
0.0888
0.0940
0.3494
0.0529
0.2233
Since 1960
-0.57
-0.92
-1.72
-0.75
-1.04
Slope
-0.78
-0.84
-1.53
-0.44
-0.92
Pearson r
-0.2595 -0.2795 -0.5099 -0.1421 -0.4572
Since 1960
-1.59
-0.44
-2.43
-0.10
-1.24
Slope
0.14
0.25
0.16
0.35
0.22
Pearson r
0.0921
0.1428
0.0819
0.2091
0.2117
Since 1960
-0.24
-0.07
-1.40
-0.63
-0.61
Slope
-0.23
-0.46
-0.64
-1.20
-0.66
Pearson r
-0.0660 -0.1649 -0.2302 -0.3074 -0.3099
Since 1960
-0.02
-0.57
-0.88
0.34
-0.42
Slope
0.84
0.14
-0.25
0.70
0.36
Pearson r
0.4579
0.0535 -0.0812
0.2429
0.2690
Since 1960
0.20
0.24
-0.43
0.00
0.00
Table 5.3: Rates of change of seasonally-averaged diurnal temperature range, per century,
with correlation coefficients and statistical significance. Correlations significant with
95% confidence are in yellow, 99% orange, and 99.9% red.
Summer was the season with the largest decreasing DTR trend in CONUS and
most of the chosen divisions in the long term. These decreasing trends are significant
with 99.9% confidence in the Columbus, Birmingham, and Des Moines divisions and in
the 344-division CONUS average. Columbus had the largest long-term rate of decrease
among the 7 divisions in both summer DTR and annual DTR. Boston and Phoenix had
41
increasing DTR trends in every season in the long term, but the same divisions had
decreasing DTR trends in every season in the short term. In Phoenix, summer was the
season with both the largest long-term increase and the largest short-term decrease in
DTR. The long-term increase was significant with 99.9% confidence, but the short-term
decrease was significant with 99% confidence.
Seasonally-averaged DTR in CONUS decreased over the long term and the short
term in each season except for spring. Columbus and Birmingham had long-term
decreasing DTR trends that were significant with at least 99% confidence in every
season. In Birmingham, the rates of decrease in each season became larger in the short
term, while in Columbus, the trends in spring and autumn DTR were smaller in the short
term than in the long term. Des Moines and Birmingham in summer had the largest shortterm decrease in DTR of all divisions and seasons. In Portland, summer was the only
season with a decreasing DTR trend in either the long term or the short term, and
significant increasing DTR trends occurred in the long term in winter and autumn. In
Oklahoma City, autumn DTR decreased significantly in the long term and at the highest
rate of the four seasons, but autumn DTR had a slight increasing trend since 1960.
The rest of this section will mostly discuss each season separately. The following
tables summarize the trends and time series correlation coefficients for each temperature
variable and precipitation in the 7 chosen divisions. Table 5.4 is for winter, Table 5.5
spring, Table 5.6 summer, and Table 5.7 autumn. The decadal-scale variability and
extremes of DTR, Tmax, Tmin, and precipitation in each season, compared among the 7
divisions, will be discussed in Section 5.2.2, followed by the analysis focused on Central
Ohio summers in Section 5.2.3.
42
(a)
Division
Winter
Slope
3305
Pearson r
Columbus
Since 1960
Slope
CONUS avg. Pearson r
Since 1960
Slope
0102
Pearson r
Birmingham
Since 1960
Slope
0206
Pearson r
Phoenix
Since 1960
Slope
1305 Des
Pearson r
Moines
Since 1960
Slope
1903
Pearson r
Boston
Since 1960
3405
Slope
Oklahoma Pearson r
City
Since 1960
Slope
3502
Pearson r
Portland
Since 1960
(b)
DTR
Tmax
Tmin
Tavg
Precip
°C/100yr °C/cent °C/cent °C/cent mm/cent
-0.74
0.25
0.99
0.62
-9
-0.3461
0.0469
0.1696
0.1133 -0.0547
-1.52
2.93
4.45
3.69
117
-0.10
0.98
1.08
1.03
4
-0.0679
0.2882
0.3030
0.3022
0.0541
-0.57
3.04
3.61
3.33
12
-0.63
-0.31
0.33
0.01
38
-0.2936 -0.0669
0.0667
0.0023
0.1224
-0.93
2.69
3.61
3.15
-22
0.36
1.24
0.88
1.06
23
0.0888
0.3163
0.2594
0.3491
0.1501
-0.57
2.00
2.57
2.29
17
-0.78
0.40
1.18
0.79
-1
-0.2595
0.0656
0.1819
0.1290 -0.0148
-1.59
2.31
3.91
3.11
19
0.14
1.92
1.78
1.85
77
0.0921
0.4189
0.3700
0.3991
0.3731
-0.24
4.29
4.53
4.41
-2
-0.23
0.37
0.59
0.48
29
-0.0660
0.0743
0.1365
0.1114
0.1877
-0.02
3.06
3.08
3.07
70
0.84
1.35
0.51
0.93
-30
0.4579
0.3797
0.1527
0.2797 -0.0692
0.20
0.62
0.42
0.52
-88
Winter
DTR
Tmin
Tavg
1960-2014 °C/cent °C/cent °C/cent
3305
Slope
-1.52
4.45
3.69
Columbus Pearson r
-0.3280
0.3379
0.3032
0102
Slope
-0.93
3.61
3.15
Birmingham Pearson r
-0.1789
0.3489
0.3294
1305 Des Slope
-1.59
3.91
3.11
Moines Pearson r
-0.2239
0.2571
0.2176
1903
Slope
-0.24
4.53
4.41
Boston Pearson r
-0.0658
0.4704
0.4802
Slope
-0.57
3.61
3.33
CONUS avg.
Pearson r
-0.1555
0.4378
0.4228
Division
Table 5.4: (a) As in Table 5.1, but seasonally-averaged for winter. (b) Selected short-term
trends in winter temperatures, expressed as rates of change per century, with correlation
coefficients and statistical significance. Period begins with the winter that started in Dec
1959.
43
Division
Spring
Slope
3305
Pearson r
Columbus
Since 1960
Slope
CONUS avg. Pearson r
Since 1960
Slope
0102
Pearson r
Birmingham
Since 1960
Slope
0206
Pearson r
Phoenix
Since 1960
Slope
1305 Des
Pearson r
Moines
Since 1960
Slope
1903
Pearson r
Boston
Since 1960
3405
Slope
Oklahoma Pearson r
City
Since 1960
Slope
3502
Pearson r
Portland
Since 1960
DTR
Tmax
Tmin
Tavg
Precip
°C/100yr °C/cent °C/cent °C/cent mm/cent
-0.58
0.35
0.93
0.64
13
-0.2524
0.0898
0.2789
0.1864
0.0596
0.03
2.79
2.76
2.78
5
0.03
0.70
0.67
0.68
20
0.0192
0.2646
0.3207
0.3005
0.2343
0.08
2.30
2.22
2.26
27
-0.71
-0.55
0.16
-0.19
44
-0.3327 -0.1839
0.0510 -0.0671
0.1409
-1.78
1.06
2.84
1.95
-99
0.24
1.66
1.43
1.55
2
0.0940
0.3974
0.4311
0.4345
0.0247
-0.92
3.66
4.59
4.13
0
-0.84
-0.01
0.84
0.42
47
-0.2795 -0.0014
0.2316
0.1025
0.1965
-0.44
1.94
2.38
2.16
138
0.25
1.41
1.16
1.28
121
0.1428
0.4028
0.4033
0.4172
0.4914
-0.07
2.72
2.78
2.75
180
-0.46
-0.09
0.38
0.15
29
-0.1649 -0.0231
0.1266
0.0473
0.1120
-0.57
0.89
1.45
1.17
89
0.14
0.49
0.35
0.42
69
0.0535
0.1310
0.1471
0.1472
0.2933
0.24
1.83
1.59
1.71
68
Table 5.5: As in Table 5.1, but seasonally-averaged for spring.
44
(a)
Division
Summer
Slope
3305
Pearson r
Columbus
Since 1960
Slope
CONUS avg. Pearson r
Since 1960
Slope
0102
Pearson r
Birmingham
Since 1960
Slope
0206
Pearson r
Phoenix
Since 1960
Slope
1305 Des
Pearson r
Moines
Since 1960
Slope
1903
Pearson r
Boston
Since 1960
3405
Slope
Oklahoma Pearson r
City
Since 1960
Slope
3502
Pearson r
Portland
Since 1960
(b)
DTR
Tmax
Tmin
Tavg
Precip
PDSI
°C/100yr °C/cent °C/cent °C/cent mm/cent X/cent
-1.61
-0.91
0.71
-0.10
22
0.59
-0.5602 -0.2771
0.2919 -0.0401
0.1039
0.1059
-2.30
0.69
3.00
1.85
82
1.66
-0.47
0.25
0.72
0.48
10
-0.3781
0.1274
0.4708
0.2955
0.1424
-1.07
1.37
2.44
1.91
38
-1.43
-0.99
0.44
-0.27
43
0.33
-0.4773 -0.3025
0.2251 -0.1218
0.1757
0.0605
-2.41
1.16
3.57
2.37
64
-1.07
0.82
1.89
1.07
1.48
-7
-1.67
0.3494
0.7087
0.4362
0.6505 -0.0766 -0.2002
-1.72
1.62
3.34
2.48
2
-4.07
-1.53
-0.84
0.69
-0.07
56
1.60
-0.5099 -0.2111
0.2617 -0.0236
0.1859
0.2259
-2.43
-0.01
2.42
1.21
75
2.27
0.16
1.69
1.53
1.61
76
0.71
0.0819
0.5902
0.6199
0.6467
0.3175
0.1510
-1.40
1.70
3.10
2.40
202
3.56
-0.64
-0.42
0.22
-0.10
27
1.08
-0.2302 -0.0964
0.0891 -0.0312
0.0920
0.1498
-0.88
1.38
2.26
1.82
132
1.21
-0.25
0.74
0.98
0.86
32
0.43
-0.0812
0.2285
0.5269
0.3987
0.2844
0.0831
-0.43
1.18
1.60
1.39
-12
0.82
Summer
DTR
Tmin
Tavg
1960-2013 °C/cent °C/cent °C/cent
3305
Slope
-2.30
3.00
1.85
Columbus Pearson r
-0.4603
0.5736
0.3624
0102
Slope
-2.41
3.57
2.37
Birmingham Pearson r
-0.4038
0.7043
0.4366
0206
Slope
-1.72
3.34
2.48
Phoenix Pearson r
-0.4153
0.5983
0.5304
1903
Slope
-1.40
3.10
2.40
Boston Pearson r
-0.3487
0.6319
0.5369
Slope
-1.07
2.44
1.91
CONUS avg.
Pearson r
-0.4418
0.7176
0.5477
Division
Table 5.6: (a) Rates of change of summer seasonally-averaged temperatures, total
summer precipitation, and the seasonally-averaged PDSI, per century, with correlation
coefficients and statistical significance. (b) As in Table 5.4b but for summer.
45
Division
Autumn
Slope
3305
Pearson r
Columbus
Since 1960
Slope
CONUS avg. Pearson r
Since 1960
Slope
0102
Pearson r
Birmingham
Since 1960
Slope
0206
Pearson r
Phoenix
Since 1960
Slope
1305 Des
Pearson r
Moines
Since 1960
Slope
1903
Pearson r
Boston
Since 1960
3405
Slope
Oklahoma Pearson r
City
Since 1960
Slope
3502
Pearson r
Portland
Since 1960
DTR
Tmax
Tmin
Tavg
Precip
°C/100yr °C/cent °C/cent °C/cent mm/cent
-1.28
-0.48
0.80
0.16
30
-0.3883 -0.1376
0.2642
0.0552
0.1633
-0.84
0.66
1.50
1.08
101
-0.37
0.23
0.60
0.42
36
-0.1972
0.1060
0.3191
0.2287
0.3789
-0.24
1.18
1.42
1.30
47
-1.39
-1.06
0.33
-0.36
83
-0.3765 -0.3011
0.0967 -0.1246
0.2583
-1.67
0.45
2.12
1.28
88
0.17
1.42
1.25
1.34
7
0.0529
0.4087
0.4495
0.4914
0.0689
-0.75
2.35
3.10
2.73
-51
-0.44
-0.14
0.30
0.08
2
-0.1421 -0.0331
0.0887
0.0241
0.0076
-0.10
0.73
0.83
0.78
-19
0.35
1.40
1.05
1.22
67
0.2091
0.4955
0.4032
0.4736
0.2704
-0.63
2.16
2.79
2.48
51
-1.20
-0.97
0.23
-0.37
32
-0.3074 -0.2390
0.0758 -0.1244
0.1131
0.34
0.78
0.44
0.61
-36
0.70
1.18
0.47
0.83
1
0.2429
0.3871
0.2061
0.3631
0.0039
0.00
0.87
0.87
0.87
-35
Table 5.7: As in Table 5.5 but for autumn.
Winter DTR is significantly decreasing in the long term with at least 99%
confidence in the Columbus, Birmingham, and Des Moines divisions, mainly due to
Tmin warming faster than Tmax. In Birmingham, winter Tmax is decreasing while Tmin
is increasing, both insignificantly. In each of these three divisions, winter DTR decreased
at a faster rate in the short term, but only in Columbus was the short-term trend
significant with 95% confidence. The weaker correlation in Des Moines, despite having
the largest rate of decrease in both the short term and the long term, is the result of larger
46
variance in winter DTR in Des Moines than in Birmingham and Columbus. Similarly, the
short-term increase in Tmin was very steep in each of these three divisions but was
significant with 99% confidence only in Birmingham, where variance in winter Tmin was
relatively low recently in the data record. Table 5.4b is an addendum to Table 5.4a
specifying time series correlations and significance levels in divisions with the largest
short-term trends in Tmin and Tavg. Figure 5.5 shows the sample standard deviations of
winter DTR and Tmin over moving 30-year periods in the 7 divisions and CONUS.
The sample standard deviation here represents the amount of variability within
each time series, as datasets that are more scattered have weaker correlations between
variables or with time than datasets that have the same magnitude of trend but are more
consistent or linear. These inconsistencies between magnitudes of trends and significance
of correlations are common in each season, depending on the amount of variability of
each temperature variable or precipitation in different climate divisions.
47
(a)
(b)
Figure 5.5: Sample standard deviations representing variability of winter seasonallyaveraged (a) DTR and (b) Tmin within moving 30-year periods in each climate division
and of winter CONUS-averaged DTR and Tmin.
The Boston division has experienced the largest long-term and short-term trends
in Tmax, Tmin, and Tavg among the 7 divisions in winter, and all of these trends in
Boston are significant with 99.9% confidence. The trend in winter Tmin since 1960,
averaged over the 344 climate divisions of CONUS, is an increase of 3.61°C per century
and is significantly nonzero with 99.9% confidence. Like Boston, Phoenix switched from
48
increasing DTR to decreasing DTR due to greater changes in the rates of increase of
Tmin than those of Tmax, Long-term and short-term increasing trends in Tmin and Tavg
in Phoenix are smaller than those in Boston but are significant with at least 99%
confidence. Portland has had significant increasing trends in winter DTR, Tmax, and
Tavg in the long term but smaller increasing trends since 1960 in each temperature
variable. No significant long-term trends occurred in Oklahoma City winters other than
increasing precipitation, but short-term Tmax, Tmin, and Tavg are each increasing by
slightly over 3°C per century, significantly nonzero with 95% confidence.
Winter precipitation trends in the 7 divisions and CONUS are generally small and
insignificant. The long-term trend in Boston is increasing with 99.9% confidence, but the
short-term trend is near zero. In Central Ohio, the long-term trend is near zero, but the
trend since 1960 is an increase of 117 mm/century and is significant with 99%
confidence. The short-term decreasing trend in Portland is large but not significant, as
precipitation varies widely among winters in that division.
Long-term temperature trends in spring (Table 5.5) in the 7 divisions and CONUS
are highly similar to those in winter. The long-term and short-term warming Tmax, Tmin,
and Tavg trends in CONUS, and in most of the chosen divisions, are smaller in spring
than in winter, but all of these trends in CONUS are significantly nonzero with at least
99% confidence. Phoenix is the climate division with the highest rates of warming in
spring. Of the other 6 divisions, only Columbus has a greater long-term Tavg trend in
spring than in winter, and only Portland has a greater short-term Tavg trend. In Portland,
the short-term increases in Tmin and Tavg, but not Tmax or DTR, are significant with
95% confidence, and none of the long-term temperature trends are significant. Columbus
49
and Portland, along with the CONUS average, had a slight increasing trend in spring
DTR since 1960. In Columbus, the long-term increase in Tmin and short-term increases
in Tmin and Tavg are significant with 99% confidence, and the short-term increase in
Tmax is slightly larger but significant with only 95% confidence. The long-term trend in
spring Tmax is significantly downward in Birmingham with 95% confidence and slightly
decreasing in Oklahoma City and Des Moines. However, upward Tmax trends since 1960
have occurred all three divisions. In Boston, long-term increases in Tmax, Tmin, Tavg,
and precipitation in spring, like those in winter, are significant with 99.9% confidence.
Spring precipitation increased over the long term in all 7 divisions and CONUS,
although the trend in Phoenix was near zero. In CONUS, Des Moines, and Portland,
where no precipitation trends in winter are significant, the increasing trends in spring are
significant with at least 95% confidence. Boston has the largest long-term and short-term
rates of increase, and the short-term increase is significant with 95% confidence. Des
Moines and Oklahoma City also have large short-term trends of increasing spring
precipitation, and Birmingham has a large downward trend, but none of these trends are
significant. The precipitation trend in Columbus is slightly upward and weaker than in the
other divisions except for Phoenix.
The strongest correlations of seasonally-averaged temperatures with time over the
long term were those associated with warming trends or decreasing DTR trends in
summer (Table 5.6a). The rate of increase of summer Tmax in the Phoenix division from
1895 to 2013 was 1.89°C per century, with a correlation coefficient of .7087, the
strongest for any long-term trend in any season. Winter Tmax in Boston (Table 5.4a) is
the only temperature series with a larger long-term rate of increase. Table 5.6b is an
50
addendum to Table 5.6a showing correlation coefficients for short-term trends in
divisions where these trends in DTR, Tmin, and Tavg are significantly nonzero with at
least 99% confidence. The short-term increase in the CONUS average of summer Tmin is
2.44°C per century, with an even higher correlation coefficient, .7176 (Table 5.6b). The
rate is 3.00°C per century or greater in Columbus, Birmingham, Phoenix, and Boston,
and each of these trends has an exceptionally strong correlation coefficient greater than
.57. The long-term warming trends of summer Tmax, Tmin, and Tavg in Boston and
Tavg in Phoenix have similarly high correlation coefficients.
Columbus, Birmingham, Des Moines, and Oklahoma City each have decreasing
trends in summer Tmax and Tavg since 1895, and those in Tmax in Birmingham and
Columbus are significant with at least 99% confidence. However, all of these trends
switched to upward in the short term, except for Tmax in Des Moines. The other three
divisions each had a significant long-term warming trend in summer Tavg, with 99.9%
confidence. Each of the 7 climate divisions has short-term warming trends in summer
Tmax, Tmin, and Tavg greater than 1.11°C (2.00°F) per century, except for Tmax in
Columbus and Des Moines. The short-term trend in Tmax in Des Moines is near zero.
Des Moines has the largest rate of deceasing DTR since 1960, 2.43°C per century, with
99% confidence that it is significantly nonzero. Portland has the smallest short-term
trends in DTR and Tmin. The divisions with the largest short-term rates of increase in
Tmax and Tmin, respectively, are Boston and Birmingham. Summer Tavg since 1960 is
warming at the fastest rate in Phoenix and the slowest in Des Moines.
Short-term rates of increase of summer Tmin in the 7 divisions are generally
much larger than those over the long term, with much greater differences than the
51
changes in Tmax trends. These amplifications of Tmin trends are the main contributor to
the higher magnitude of downward DTR trends over the short term than over the long
term. Summer is the only season in which the short-term DTR trends in all 7 divisions are
more negative than the long-term trends.
The trends of summer precipitation are increasing in the 7 divisions and CONUS,
except for Phoenix over the long term and Portland over the short term. The short-term
decrease in Portland contrasts with the significant long-term increasing trend. Boston has
the largest long- and short-term increasing trends in summer precipitation, and both are
significant with at least 99% confidence. The long- and short-term trends of increasing
PDSI in Des Moines and decreasing PDSI in Phoenix are strong, and both long-term
trends are significant with 95% confidence. Neither is significant in the short term, but
the short-term increase in PDSI in Boston is significant with 95% confidence. The other
divisions except for Birmingham have increasing PDSI trends over the long term and the
short term. The short-term PDSI trend in Birmingham is negative, probably because of
the decreasing trend in spring precipitation in that division since 1960.
Temperature trends in autumn (Table 5.7) in the 7 divisions and CONUS are
fairly similar to those in summer but weaker in most cases. Exceptions include long-term
trends in autumn DTR and Tmax in Oklahoma City and Portland, which are all
significantly nonzero with at least 99% confidence and are larger than those in all the
other seasons except for winter in Portland. However, DTR and Tmax in Oklahoma City
switch from long-term decreasing trends to short-term increasing trends, and short-term
trends in Portland are insignificant. In Portland, short-term trends in autumn temperatures
are similar to those in annual temperatures – rates of increase of Tmax and Tmin are
52
nearly equal. Every division except for Boston and Phoenix has its lowest short-term rate
of increase of Tmin in autumn. The long- and short-term warming trends in Tavg in
CONUS are also the smallest in autumn. Autumn DTR trends in Phoenix and Des
Moines are not significant, and neither are long-term decreases in Tmax in Columbus and
Des Moines.
Autumn is the season with the greatest rate of increase in the CONUS average of
seasonal precipitation, 36 mm/year since 1895, and this trend is significant with 99.9%
confidence. Birmingham and Boston also have increasing precipitation trends that are
significant with 99% confidence. Precipitation in Columbus, Birmingham, and Boston
has also increased greatly in the short term, while the other four divisions have drier
trends.
The climate divisions of Columbus, Birmingham, Des Moines, and Oklahoma
City are generally characterized by significant decreasing trends in DTR, slight
decreasing trends in Tmax, mainly in summer and autumn, and significant increasing
trends in Tmin. Phoenix, Boston, and Portland are generally characterized by significant
increasing trends in Tmax and Tmin in every season and mixed trends in DTR. Long- and
short-term precipitation trends are mostly small and upward, except that long-term
increases in precipitation in Boston are significant in every season with at least 99%
confidence, and short-term upward trends in Boston, Columbus, and Oklahoma City are
strong. Short-term trends in Tmax and Tmin are much more strongly warming in every
season than long-term trends, and most DTR trends are more greatly downward in the
short term, especially in summer. The following section analyzes these trends
graphically.
53
5.2.2 Inter-decadal variability of seasonal temperatures and precipitation
Figure 5.6 summarizes the multidecadal variability of diurnal temperature range
in each of the 7 climate divisions and the 344-division CONUS average, as in Fig. 5.2a
but for each season separately. Seasonally-averaged DTR in CONUS increased early in
the period of record, based on 30-year running means, and the DTR trend in each season
switched to downward or nearly flat at a different time. Some climate divisions in some
seasons have DTR trends much different from this general pattern, such as peaking near
the beginning of the period of record or switching from decreasing to increasing.
(a)
Continued
Figure 5.6: Running means of seasonally averaged DTR for the 7 climate divisions and
the CONUS in (a) winter, (b) spring, (c) summer, and (d) autumn.
54
Figure 5.6 continued
(b)
(c)
(d)
55
Winter DTR in Portland increased nearly continuously for the entire long term,
peaking in the 1980s and in the 30-year period ending in 2012. The long-term upward
DTR trend there is also evident graphically in autumn. Spring DTR peaked from 1923 to
1952 and decreased until about 1980, but a slight increase since 1980 made the long- and
short-term trends positive. Summer DTR in Portland peaked in the 30-year period ending
in 1946 and had a downward trend overall but appears to be increasing since 2000. In
each season in Phoenix, DTR increased steeply between 1940 and 1960, peaked between
1960 and 1980, and had at least a slight downward trend since the late 1970s. In Boston,
like Phoenix, early upward DTR trends that outweigh more recent downward trends are
evident in Fig. 5.6, explaining the switch in every season in Table 5.3.
In Oklahoma City, Birmingham, Des Moines, and Columbus, winter DTR peaked
before 1935. A secondary peak in winter DTR occurred in the late 1970s in Oklahoma
City and Birmingham, but the more recent short-term trend in both divisions was slightly
downward. In these four climate divisions, summer DTR decreased steeply after 1980,
and in Columbus, Birmingham, and Des Moines, 30-year running means ending in 2013
were much lower than at any point before 1990. Most of the decrease in autumn DTR in
Columbus occurred between 1960 and the late 1990s, and that in spring occurred from
the mid-1940s to about 1980, with slight upward trends more recently in both seasons.
The decadal-scale variability of DTR in each climate division and season can be
assessed further in terms of Tmax and Tmin. Fig. 5.7 shows the 30-year running means of
seasonally-averaged Tmax in the 7 divisions and CONUS, while Fig. 5.8 shows those of
Tmin. A common feature of Tmax in most of the divisions and seasons is a relative
minimum in the 1980s or 1990s followed by a sharp increase, explaining long-term
56
downward trends in some divisions and upward trends since 1960. Phoenix, Boston,
Portland, and the CONUS average did not have a downward Tmax trend in any season
over the long term, but short-term rates of increase were generally much larger.
(a)
(b)
Continued
Figure 5.7: As in Figure 5.6 but for Tmax.
57
Figure 5.7 continued
(c)
(d)
From Tables 5.4-5.7, all seasonal Tmin trends since 1895 and since 1960 in the 7
divisions and CONUS are upward. In most of the divisions and seasons, most of the
increase in Tmin occurred since about 1985, making the rates of increase since 1960
much larger than the long-term trends. Tmin trends before 1985 were generally slightly
increasing or nearly flat, and relative minima of 30-year running means occurred in the
1970s and 1980s in many cases, especially in winter and summer. Comparing the timing
58
of these relative minima to the relative minima of Tmax explains the short-term
decreasing trends in DTR. The rapid warming of Tmin began a decade earlier than that of
Tmax, so the difference between Tmax and Tmin, which is DTR, decreased rapidly in the
1980s and 1990s. In some cases, the rate of warming of Tmax caught up to that of Tmin,
thus DTR steadied or increased slightly near the end of the period of record.
(a)
(b)
Continued
Figure 5.8: As in Figure 5.6 but for Tmin.
59
Figure 5.8 continued
(c)
(d)
The possible impacts of climate change on future trends in regional precipitation,
especially seasonal droughts, are of great interest. Fig. 5.9 shows the 30-year running
means of precipitation in each season and the PDSI in summer.
60
(a)
(b)
Continued
Figure 5.9: Running means of seasonal total precipitation in the 7 climate divisions and
the CONUS in (a) winter and (b) spring, and running means of (c) the summer
seasonally-averaged PDSI, (d) summer precipitation, and (e) autumn precipitation.
61
Figure 5.9 continued
(c)
(d)
(e)
62
As discussed with Table 5.6, Birmingham and Phoenix were the only divisions
with decreasing PDSI trends in the short term. In Birmingham, 30-year running means of
annual precipitation decreased sharply after a maximum in 2002. The main seasonal
contribution to this trend was a steep decrease in spring precipitation since 1985. Because
of the influence of spring precipitation on the PDSI in summer, the short-term PDSI trend
in this division was negative despite increasing summer precipitation. The recent rapid
decrease in the PDSI in the Phoenix division is probably due to a combination of large
rates of warming in every season and a lack of unusually wet years since 1996.
Another consideration pertaining to droughts and other seasonal-scale climatic
events is to assess the variability of temperature and precipitation in each season.
Mathematically, variance is the sum of the square of the deviations of temperature or
precipitation in each year from the average value of temperature or precipitation over a
specific period. Standard deviations of temperature or precipitation for each season over
30-year periods, therefore, are greater in periods that contain many individual seasons
that are very anomalous in temperature or precipitation. Comparing these sample
standard deviations between different periods in each season and division would reveal
whether each variable – DTR, Tmax, Tmin, and precipitation – is becoming more erratic
or more consistent in each season. Extremes in winter and summer, spring DTR, and
precipitation in every season are of particular interest for environmental considerations.
Changes in 30-year sample standard deviations of winter DTR and Tmin are shown in
Fig. 5.5, located in the discussion of significant winter trends. Fig. 5.10 shows the
variability of summer DTR and Tmax for each 30-year period in each climate division.
63
(a)
(b)
Figure 5.10: Sample standard deviations representing variability of summer seasonallyaveraged (a) DTR and (b) Tmax within moving 30-year periods in each climate division
and of summer CONUS-averaged DTR and Tmax.
Standard deviations of summer DTR in 30-year periods in Columbus,
Birmingham, Des Moines, and Oklahoma City were greatest before 1960 and after 1990
and smallest in periods ending between 1965 and 1988. In seasons other than winter,
Tmax is more widely spread than Tmin, so the variance of Tmax causes most of the
64
variance of DTR in Fig. 5.10. In both Central Ohio and CONUS, the variance of summer
Tmax was also lowest during the relatively cool period from the early 1960s to about
1985, and it was highest in the late 1930s and near the present. Relatively hot periods,
therefore, had summers that were spread farther from normal, some with extremely high
seasonally-averaged Tmax and others with Tmax much below normal, while periods of
relatively cool summers were more consistent and lacked extremely high Tmax. Summer
DTR was also more consistent during the cool period, mainly earlier in that period, with a
minimum standard deviation in CONUS in 1966.
Unlike the pattern of hotter periods having more dispersed summer seasonallyaveraged temperatures, Portland summers in 30-year periods varied more during the
cooler period. In Phoenix and Boston, trends in the variance in summer Tmax and DTR
are small and seemingly not related to hot or cool periods in these climate divisions. The
only notable trend is that variance of summer DTR in Phoenix is much lower near the end
of the period of record than in all earlier 30-year periods except for those ending in the
1970s. Tmin in summer and spring in CONUS and Columbus, not shown, generally had
minimal standard deviations during the cool period, like the pattern of DTR and Tmax in
summer.
Fig. 5.11 shows the relative amounts of variability in moving periods of spring
and autumn DTR in the 7 climate divisions and CONUS. Spring DTR in CONUS was the
most scattered in 30-year periods ending in the 1930s or the 1990s and the most
consistent around 1970. Near the end of the period of record, standard deviations of
seasonally-averaged spring DTR are decreasing. Trends in moving standard deviations in
Columbus, Birmingham, and Des Moines resemble those in CONUS. Standard deviation
65
of autumn DTR in 30-year periods in CONUS, Columbus, and Des Moines was highest
in the 1970s. Variability of seasonally-averaged autumn DTR increased over the long
term in CONUS and Des Moines but decreased in Columbus.
(a)
(b)
Figure 5.11: As in Figure 5.10 but for (a) spring DTR and (b) autumn DTR.
Large amounts of variability of precipitation between different years within given
periods indicate that frequent droughts or extremely wet years probably occurred in these
66
periods, with relatively few years of near-normal precipitation. Highly inconsistent,
unreliable dispersion of precipitation can cause difficulty and damages in agriculture,
water-related activities, and the availability of drinking water. Fig. 5.12 shows the
sample standard deviations of precipitation in the 7 climate divisions in each season.
(a)
(b)
Continued
Figure 5.12: Sample standard deviations representing variability of seasonal total
precipitation, within 30-year periods, in the 7 divisions and the CONUS average in (a)
winter, (b) spring, (c) summer, and (d) autumn.
67
Figure 5.12 continued
(c)
(d)
68
5.2.3 Central Ohio summer trends
Fig. 5.13 shows seasonally-averaged temperatures for each summer in the
Columbus climate division, with trendlines emphasizing differences in long- and shortterm trends, especially in Tavg and Tmax. Central Ohio experienced a decreasing trend in
summer DTR of 1.61 °C per century from 1895 to 2013 (Fig. 5.13a and Table 5.6a). The
average summer DTR for this period was 13.05°C, and of 22 summers with DTR < 12°C,
20 occurred after 1972. Most of the decrease in DTR seems to have occurred between
1960 and 1990, and the trend since 1990 appears slightly positive. The average DTR for
the last 30 summers, ending in 2013, was 12.19°C, lower than for all other 30-year
periods except for 1977-2006, which averaged 12.18°C. The long-term trend of summer
Tmax is -0.91 °C per century (Fig. 5.13b and Table 5.6a), but the trend since 1960 is an
increase of 0.69 °C per century. Summer Tmin has been warming at a much faster rate
since 1960, 3.00 °C per century, while the long-term trend is 0.71 °C per century, smaller
than the rate of decrease of Tmax.
The long-term trend of seasonal average temperature in the Central Ohio climate
division is a decrease of 0.10 °C per century. However, the trend since 1960 is an
increase of 1.85 °C per century and is statistically significant with 99% confidence. The
average of summer Tavg for the entire period was 22.02°C. Every summer from 1930 to
1944 had Tavg > 22.00°C, including the hottest summer, 1934, which had Tavg =
24.08°C. In contrast, more recently, only five summers from 1960 to 1982 had Tavg >
22.00°C, and none were warmer than 22.41°C. The occurrence of this cooler period after
the extremely hot summers of the 1930s makes the longer-term trend much different from
the recent warming trend.
69
(a)
(b)
Figure 5.13: In the Columbus climate division, (a) seasonal averages of summer Tavg
and DTR, with long-term trendlines of each and the trend in Tavg since 1960, and (b)
seasonal averages of summer Tmax and Tmin, with trendlines of Tmax since 1895 and
since 1960 and of Tmin since 1960.
70
The years with top-10 summer DTR were 1930, 1914, 1913, 1936, 1934, 1932,
1953, 1918, 1933, and 1988. The summers of 1930, 1934, 1953, and 1988 were notorious
for drought, each with seasonally-averaged PDSI below -3. The PDSI for the rest of these
summers, except for 1913, was -1.4 or lower. Summer cloud cover in 1913 was
extremely low, about 29%, compared to the average of about 55%. Cloud cover for the
other summers with top-10 DTR was at least 8 percentage units below average, except
for 1918 and 1934. Table 5.8 shows correlation coefficients between the temperature
variables, which are the predictands in the SMLR analyses that follow below and in
Section 5.3, and the predictors, which include cloud cover and the PDSI. Highlighted
coefficients are significantly nonzero with 95% (yellow), 99% (orange), or 99.9%
confidence (red or purple). Coefficients in yellow text and a dark purple background have
p-values smaller than 1×10-6, making them significant with extremely high confidence.
Summer
DTR
Tmax
Tmin
Tavg
Precip
CO2
-0.582
-0.232
0.378
0.031
0.130
PrecipOH05
-0.575
-0.473
0.045
-0.289
1
PDSIOH05
-0.590
-0.643
-0.167
-0.503
0.675
CloudCover
-0.659
-0.563
0.023
-0.358
0.287
SpecHum
-0.441
0.091
0.647
0.374
0.324
NPI
0.117
0.118
0.021
0.088
-0.065
AMO
0.148
0.298
0.227
0.306
-0.033
NAO
0.235
0.194
-0.018
0.118
-0.108
AO
-0.103
0.098
0.254
0.188
-0.037
Nino3.4
-0.211
-0.143
0.058
-0.065
0.122
PDO
-0.096
-0.019
0.089
0.031
0.262
Table 5.8: Correlation coefficients between each predictor (rows) and each predictand
(columns), and between each predictor and precipitation, in summer from 1895 to 2013
in Central Ohio. The correlation between PDSI and Precip is not emphasized because
precipitation is a major component of the PDSI. Correlations significant with 95%
confidence are highlighted in yellow, 99% orange, 99.9% red, and p < 1×10-6 in purple
with yellow text.
71
From Table 5.8, DTR in Central Ohio in summer is significantly negatively
correlated with cloud cover, PDSI, and specific humidity, each with extremely high
confidence. RPCA and SMLR analysis using all variables from 1895 to 2013 produced a
model with cloud cover, PDSI, CO2, specific humidity, precipitation, and the NAO as the
most important factors (Table 5.9). This list is in order of how much each component
contributed to the variability of DTR. The correlation between DTR and the NAO is
strongly positive. PDSI is also significantly negatively correlated with Tmax and Tavg
and is the most important factor in SMLR for both Tmax and Tavg.
Table 5.9 shows the SMLR model for each predictand in Central Ohio summers.
The models accounted for 76.8%, 66.1%, 60.8%, and 58.2% of the variability from 1895
to 2013 of DTR, Tmax, Tmin, and Tavg, respectively. Because Tavg also had the least
explainable variability in the other divisions and generally had no significant predictors
that were not already significant with Tmax or Tmin, Tavg results in other divisions will
not be discussed at length. Because of the unique availability of recent station-based
cloud cover data in Columbus, these analyses were not repeated without cloud cover data.
Section 5.3 discusses the results of analyses performed in SPSS Statistics for the other 6
climate divisions in summer and winter and for Central Ohio in all seasons.
72
Step in
SMLR
0
1
2
3
4
5
6
Step in
SMLR
0
1
2
3
4
5
6
7
Step in
SMLR
0
1
2
3
4
5
Step in
SMLR
0
1
2
3
4
5
SMLR model for DTROH05
RPC Predictor
Adj. R Variance
factor variable
Square explained
Model constant
0
0
8 CloudCover
0.218
0.218
1 PDSI
0.394
0.177
6 CO2
0.574
0.180
3 SpecHum
0.663
0.089
11 Precip
0.751
0.087
4 NAO
0.768
0.018
SMLR model for TmaxOH05
RPC Predictor
Adj. R Variance
factor variable
Square explained
Model constant
0
0
1 PDSI
0.300
0.300
8 CloudCover
0.500
0.200
11 Precip
0.559
0.059
3 SpecHum
0.599
0.040
5 AMO
0.634
0.035
6 CO2
0.649
0.015
4 NAO
0.661
0.012
SMLR model for TminOH05
RPC Predictor
Adj. R Variance
factor variable
Square explained
Model constant
0
0
3 SpecHum
0.397
0.397
6 CO2
0.504
0.107
1 PDSI
0.559
0.055
5 AMO
0.592
0.033
10 AO
0.608
0.016
SMLR model for TavgOH05
RPC Predictor
Adj. R Variance
factor variable
Square explained
Model constant
0
0
1 PDSI
0.224
0.224
3 SpecHum
0.417
0.193
8 CloudCover
0.516
0.099
5 AMO
0.560
0.044
11 Precip
0.582
0.022
Stand.
Coeff.
13.054
-0.473
-0.425
-0.425
-0.299
-0.294
0.137
Stand.
Coeff.
28.545
-0.553
-0.450
-0.249
0.206
0.193
-0.128
0.120
Stand.
Coeff.
15.491
0.634
0.332
-0.241
0.187
0.138
Stand.
Coeff.
22.018
-0.480
0.444
-0.317
0.218
-0.157
Sig.
0.000
0.000
0.000
0.000
0.000
0.002
Sig.
0.000
0.000
0.000
0.000
0.000
0.018
0.027
Sig.
0.000
0.000
0.000
0.002
0.018
Sig.
0.000
0.000
0.000
0.000
0.010
Table 5.9: SMLR model results for all four predictands in summer in Central Ohio, as in
Tables 4.2 and 4.3, but containing only the important columns. Two columns were added
– one for the predictor variable contained in each significant RPC, and one for the
variance explained by each predictor based on the adjusted R2 after each step.
73
Table 5.9 shows that summer Tmax in Central Ohio is controlled by moisture
variables, especially soil wetness and cloud cover. Tmin is affected primarily by the
specific humidity of the air, the one summer variable that is unique to the Central Ohio
dataset (available for Columbus, Ohio). This result confirms the findings of Dai et al.
(1999) who used specific humidity data gathered in field measurements to show that the
moisture in the air controls summer Tmin. The results also show that Tmin appears to be
strongly related to CO2 concentration. Summer Tavg is affected by soil wetness and
specific humidity, the main controls on Tmax and Tmin. Of the six teleconnections, the
one that explains the most variance in Tmax and Tmin is the AMO, with positive
coefficients. The relatively cool period encompassing the 1960s and 1970s coincided
with a negative phase of the AMO.
The Central Ohio summer DTR is most influenced by cloud cover, a result very
common in most DTR assessment studies. However, PDSI and carbon dioxide
concentration are also important predictors. In the SMLR model for DTR (Table 5.9,
top), CO2 appears to have explained more predictand variance than the PDSI, but the
PDSI is assigned to an earlier step. The reason for this inconsistency is that the predictors
are ranked by significance, and the actual p-values for PDSI and CO2 are 2.91×10-16 and
3.00×10-16, respectively. Slight discrepancies also occur between correlation coefficients
of predictors with a particular predictand and their ranks in the model for that predictand.
Each of the orthogonalized predictors, after removal of correlations between the original
predictors, may have a stronger or weaker relationship with the predictand than before.
74
5.3 Regression analyses on DTR, Tmax, and Tmin
Statistical analyses were performed to assess the contribution of teleconnection
indices and moisture parameters to the variability of Tmax, Tmin, and DTR, as in
Lauritsen and Rogers (2012) but expanded into seasons and limited to the chosen climate
divisions.
5.3.1 Correlations between predictors and predictands among the climate divisions
SPSS Statistics was used to generate tables showing correlation coefficients for
every possible pair of variables in each division and season. These tables were rearranged
to remove redundant correlations and to emphasize relationships between the unrotated
predictors and the predictands. The predictors are the moisture variables – cloud cover,
precipitation, and summer PDSI – and the six teleconnection indices and atmospheric
CO2. The predictands are DTR, Tmax, and Tmin.
In the seasonal correlation tables, precipitation is grouped with the predictands in
order to show relationships between each teleconnection index and precipitation.
However, precipitation is not a predictand in any of the SMLR analyses. The names of
the predictands in each table include climate division numbers rather than names of cities,
but they are grouped by division in this order: Columbus, Birmingham, Phoenix, Des
Moines, Boston, Oklahoma City, and Portland. Table 5.10 shows the correlation
coefficients between predictors and predictands in winter. Highlighted coefficients are
significant with 95% (yellow), 99% (orange), 99.9% (red), or extremely high confidence
(p < 1×10-6, purple with yellow text). Coefficients are also labeled with stars if significant
with 95% (*) or at least 99% confidence (**).
75
Winter
CO2
Precip
Cloud
NPI
AMO
NAO
AO
Nino3.4 PDO
.079
-.012
.050
.111
DTROH05
-.378**
-.647 **
.275 **
-.380 **
-.256 **
.054
.074
-.090
TmaxOH05
.309 **
.252 **
.247 **
.429**
.474**
-.246 **
*
**
**
*
**
**
.126
.059
-.128
TminOH05
.188
.250
.293
.228
.370
.388
.007
1
.013
.116
Precip
.496 **
.234*
.256**
-.218*
-.347 **
.040
-.032
.025
.017
-.054
DTRAL02
-.275**
-.367 **
-.589 **
-.276 **
**
**
*
**
**
-.036
.103
TmaxAL02
.256
.431
.224
.523
.512
-.398 **
-.369 **
.088
TminAL02
.400 **
.343 **
.383 **
.222 *
.475**
.468**
-.248 **
-.319 **
.067
1
.062
.078
.100
-.089
Precip
.405 **
.266 **
-.241 **
**
**
*
.033
-.059
.052
-.079
-.130
DTRAZ06
-.809
-.479
-.221
-.239 **
**
**
**
-.107
-.014
.039
-.081
-.092
-.019
TmaxAZ06
.309
-.463
-.304
**
**
**
**
-.079
.141
.066
.164
TminAZ06
.319
.453
.453
-.280
.270**
**
**
.151
1
-.004
-.054
-.026
.063
.150
Precip
.555
.279
.174
-.039
.030
.029
-.116
DTRIA05
-.284**
-.451 **
-.544 **
-.328 **
.071
-.089
.160
.074
.052
TmaxIA05
-.199 *
-.211 *
.362**
.341**
*
**
**
*
.021
.050
-.166
.170
.103
TminIA05
.198
.331
.311
.223
*
.023
1
.114
.049
.037
.038
.106
-.045
Precip
.224
**
**
*
*
.035
-.080
-.053
-.044
-.058
DTRMA03
-.252
.301
.212
-.228
**
*
*
**
**
*
.105
.066
.037
TmaxMA03
.419
.223
.208
.273
.287
-.229
**
*
*
*
*
.180
.080
.164
.108
TminMA03
.388
.238
.212
.206
-.200
**
*
*
1
-.109
-.067
-.149
-.167
.001
Precip
.304
.232
.204
**
**
**
*
-.020
.162
-.062
.063
.049
DTROK05
-.653
-.683
-.449
-.236
*
**
*
**
**
**
.103
.090
-.172
TmaxOK05
-.186
-.308
.218
.351
.253
-.284
.132
-.027
.037
-.006
TminOK05
.312 **
.199 *
.298 **
.349**
.248**
*
**
*
1
-.057
-.012
.093
.158
.116
Precip
.197
.350
.198
**
**
**
**
*
-.142
.035
.008
.113
DTROR03
.389
-.566
-.334
-.274
.195
.044
.144
-.066
-.078
-.100
TmaxOR03
.349 **
-.660 **
.397**
.264**
.158
.008
-.102
-.111
TminOR03
.358 **
.327 **
-.552 **
.315**
.219*
**
-.092
1
.057
.018
-.013
.058
-.128
Precip
.392
-.182*
Table 5.10: Correlation coefficients between each predictor (columns) and DTR, Tmax,
Tmin, and precipitation in each of the 7 climate divisions in winter, highlighted for
significance as in Table 5.8.
In Columbus, Birmingham, Des Moines, and Oklahoma City, the NAO and AO
have stronger correlations with winter temperatures than cloud cover and precipitation.
Correlations between the PDO and winter temperatures in the eastern climate divisions –
Columbus, Birmingham, and Boston – are all negative and much more significant than
correlations between the AMO and temperatures in the two westernmost climate
divisions. The Niño-3.4 index has significant negative correlations with DTR and
76
temperatures in Birmingham and Oklahoma City and significant positive correlations
with DTR and temperatures in Portland. The correlation between cloud cover and DTR in
every division except for Boston is highly negative and significantly nonzero with at least
99.9% confidence. The most significant correlation of all in winter is -.809, between
precipitation and DTR in Phoenix. Winter precipitation in Central Ohio is significantly
correlated with each of the teleconnection indices except for the AMO with at least 95%
confidence.
The following correlation tables organize the relationships between predictors and
predictands in spring (Table 5.11), summer (Table 5.12), and autumn (Table 5.13), like
the correlation table for winter (Table 5.10). Correlation coefficients are highlighted if
significant, and those in seasons other than summer are also marked with stars.
77
Spring
CO2
Precip
Cloud
NPI
AMO
NAO
AO
Nino3.4 PDO
.009
.123
.122
.087
-.096
-.004
DTROH05
-.237**
-.470 **
-.463 **
*
**
*
**
.150
-.049
.119
-.059
-.159
TmaxOH05
-.231
.247
.229
.320
.065
.053
-.002
TminOH05
.339 **
.268 **
.281 **
.182*
.313**
-.182*
.049
1
-.008
.103
-.132
Precip
.204 *
.198 *
.268**
-.180*
**
**
**
**
-.077
-.017
.010
-.075
.044
DTRAL02
-.361
-.545
-.597
-.267
-.110
-.162
-.120
TmaxAL02
.291 **
.185 *
.237**
.309**
-.320 **
-.189*
.139
-.121
TminAL02
.215 *
.272 **
.325 **
.185 *
.217*
.341**
-.207*
.096
1
.146
-.143
-.062
.036
-.039
-.152
Precip
.423 **
**
**
.018
.026
.162
.124
.061
.068
DTRAZ06
-.750
-.434
-.307 **
**
**
**
*
.183
-.104
.054
-.156
.028
TmaxAZ06
.421
-.484
.241
.185
**
*
**
**
*
-.038
-.027
.137
TminAZ06
.519
.226
-.258
.260
.183
.273**
*
**
.015
1
.066
-.127
-.064
-.137
Precip
-.230
.389
.273**
**
**
**
**
.020
.088
.122
.125
.010
DTRIA05
-.259
-.657
-.457
-.261
**
**
*
**
.044
.087
.068
-.096
.050
TmaxIA05
-.334
-.332
.205
.272
**
**
.095
-.062
.101
.020
.177
.088
.060
TminIA05
.277
.267
**
**
*
1
.123
-.020
.128
.110
.058
Precip
.258
.355
-.201
**
**
**
**
.100
.078
.023
-.003
-.125
DTRMA03
-.347
-.362
.247
.269
**
.014
.043
.060
.104
.109
.163
.078
-.074
TmaxMA03
.399
**
*
**
.026
.113
-.019
.034
.097
-.013
TminMA03
.425
.229
.314
**
**
**
1
-.031
-.010
-.090
.073
.126
Precip
.464
.573
.261
**
**
**
-.096
.170
-.028
.103
-.009
-.139
DTROK05
-.597
-.691
-.300
.045
.118
TmaxOK05
-.370 **
-.460 **
.258 **
.260**
.270**
-.358 **
-.205*
.147
.094
.092
.166
.176
-.171
-.128
TminOK05
.232*
.350**
**
.103
1
.036
-.108
.052
.169
.167
.034
Precip
.437
**
*
.019
-.163
.053
.051
-.002
.177
.118
DTROR03
-.682
-.247
.128
-.176
-.001
.044
-.036
TmaxOR03
-.421 **
-.507 **
.401**
.471**
.086
-.005
-.059
.014
-.055
TminOR03
.180 *
-.618 **
.437**
.611**
**
**
1
-.087
.042
-.074
-.024
.034
.005
Precip
.297
.294
Table 5.11: As in Table 5.10 but for spring.
In Columbus and Birmingham, the AO is significantly correlated with spring
Tmax and Tmin with 99.9% confidence. These correlations are positive and stronger than
those between the AO and cloud cover or precipitation, like in winter. Phoenix, Des
Moines, and Oklahoma City also have significant correlations between the NAO and AO
and spring temperatures. Negative correlations between precipitation and DTR are
significant with extremely high confidence in every division except for Boston and with
99.9% confidence in Boston.
78
Summer
CO2
Precip
PDSI
Cloud
NPI
AMO
NAO
AO
Nino3.4 PDO
DTROH05
-0.582
-0.575
-0.590
-0.659
0.117
0.148
0.235
-0.103
-0.211
-0.096
TmaxOH05
-0.232
-0.473
-0.643
-0.563
0.118
0.298
0.194
0.098
-0.143
-0.019
TminOH05
0.378
0.045
-0.167
0.023
0.021
0.227
-0.018
0.254
0.058
0.089
TavgOH05
0.031
-0.289
-0.503
-0.358
0.088
0.306
0.118
0.188
-0.065
0.031
Precip
0.130
1
0.675
0.287
-0.065
-0.033
-0.108
-0.037
0.122
0.262
DTRAL02
-0.516
-0.731
-0.678
-0.595
0.119
0.046
0.069
-0.277
-0.114
0.004
TmaxAL02
-0.248
-0.654
-0.758
-0.638
0.160
0.216
0.017
-0.234
-0.057
0.086
TminAL02
0.374
0.028
-0.226
-0.223
0.084
0.289
-0.077
0.033
0.079
0.136
Precip
0.169
1
0.619
0.467
-0.097
0.138
0.025
0.186
-0.053
-0.027
DTRAZ06
0.157
-0.442
0.098
-0.257
-0.025
-0.054
-0.111
0.149
0.089
0.058
TmaxAZ06
0.638
-0.433
-0.293
-0.065
0.038
0.003
-0.046
0.269
0.091
0.002
TminAZ06
0.544
-0.047
-0.413
0.220
0.065
0.055
0.056
0.149
0.014
-0.053
Precip
-0.081
1
0.260
0.308
0.034
0.033
0.128
0.020
-0.160
-0.109
DTRIA05
-0.521
-0.657
-0.696
-0.572
0.093
0.233
0.225
0.055
-0.275
-0.036
TmaxIA05
-0.202
-0.462
-0.569
-0.621
0.100
0.266
0.254
0.213
-0.193
0.044
TminIA05
0.288
0.053
-0.063
-0.343
0.045
0.133
0.125
0.256
0.022
0.106
Precip
0.187
1
0.669
0.461
-0.067
-0.116
-0.086
-0.167
0.194
0.189
DTRMA03
-0.071
-0.587
-0.639
-0.211
-0.104
-0.041
0.092
0.082
0.139
0.120
TmaxMA03
0.521
-0.142
-0.253
0.050
-0.005
0.185
0.022
0.418
0.070
-0.136
TminMA03
0.660
0.298
0.211
0.252
0.076
0.246
-0.047
0.420
-0.029
-0.253
Precip
0.340
1
0.746
0.468
0.121
0.091
0.082
0.194
-0.126
-0.142
DTROK05
-0.204
-0.753
-0.755
-0.606
0.145
0.040
0.099
-0.012
-0.065
-0.039
TmaxOK05
-0.064
-0.719
-0.730
-0.547
0.206
0.154
0.131
-0.018
-0.071
-0.058
TminOK05
0.117
-0.429
-0.446
-0.288
0.203
0.229
0.121
-0.019
-0.052
-0.059
Precip
0.129
1
0.648
0.347
-0.057
0.110
-0.118
-0.021
-0.020
0.048
DTROR03
-0.082
-0.676
-0.601
-0.669
0.143
0.125
0.219
0.055
-0.013
-0.147
TmaxOR03
0.230
-0.462
-0.496
-0.523
-0.076
0.084
0.126
0.078
0.168
0.043
TminOR03
0.531
0.298
0.119
0.256
-0.363
-0.057
-0.137
0.046
0.311
0.312
Precip
0.193
1
0.613
0.607
-0.246
-0.114
-0.148
0.054
0.049
0.201
Table 5.12: As in Table 5.10 but for summer and including the PDSI. The correlation
between PDSI and Precip is not emphasized because precipitation is a major component
of the PDSI. Note that unlike in the other seasons, significant correlations are not starred.
In summer, DTR and temperatures are much more significantly correlated with
the moisture variables and CO2 than with any of the teleconnections. Every coefficient
between the moisture variables and DTR in Columbus, Birmingham, Des Moines,
Oklahoma City, and Portland is larger than -.50. Negative correlations between
precipitation and DTR are significant with extremely high confidence in every division.
Correlations between the PDSI and DTR are negative and significant with extremely high
79
confidence in every division except for Phoenix. Negative correlations between
precipitation and Tmax are significant with extremely high confidence in every division
except for Boston and insignificant in Boston. The largest correlation coefficient in
summer is -.758, between PDSI and Tmax in Birmingham. Correlations between the AO
and Tmax are significant in Columbus, Birmingham, Phoenix, and Des Moines, but the
coefficient in Birmingham is negative. Correlations between the AMO and Tmax are
significant and positive in the three eastern divisions and Des Moines.
Autumn
CO2
Precip
Cloud
NPI
AMO
NAO
AO
Nino3.4 PDO
**
**
**
**
.017
.141
.023
DTROH05
-.362
-.674
-.809
.241
-.287 **
-.207*
**
**
*
*
-.092
.174
.012
.101
TmaxOH05
-.250
-.501
.208
-.218
-.249 **
**
**
**
*
-.061
-.142
.092
.060
-.065
TminOH05
.289
.445
.298
.225
*
**
**
1
.168
-.109
.010
.091
.066
Precip
.211
.524
-.236
**
**
**
*
**
.020
.150
-.031
DTRAL02
-.358
-.722
-.728
.198
-.336
-.182*
*
**
**
*
*
**
-.045
-.047
-.118
TmaxAL02
-.230
-.480
-.501
.222
.208
-.243
**
*
*
*
.150
.001
-.016
.113
.076
TminAL02
.286
.241
.207
-.209
**
**
*
1
-.061
-.158
-.084
.032
.133
Precip
.240
.555
.228
-.049
-.028
.164
.165
-.001
DTRAZ06
-.703 **
-.530 **
-.407 **
-.290 **
-.132
.173
.063
.091
TmaxAZ06
.373 **
-.565 **
-.326 **
-.194*
-.310 **
.097
-.133
.029
-.110
.114
-.056
TminAZ06
.522 **
.269 **
.221*
**
*
**
.014
1
.091
-.060
Precip
.623
-.232
-.253
.309**
.208*
**
**
**
*
-.158
-.061
.036
.070
DTRIA05
-.626
-.765
.358
-.219
-.350 **
-.023
.090
.097
.149
TmaxIA05
-.191 *
-.497 **
.263 **
-.223*
-.348 **
**
.116
.085
.163
-.007
.085
.117
-.071
-.102
TminIA05
.336
**
**
.007
1
.139
-.095
-.050
.019
.092
Precip
.490
.245
**
**
*
.072
-.125
-.047
-.097
-.088
-.028
DTRMA03
-.368
-.350
.212
**
**
**
-.011
.084
.100
.083
-.015
-.060
TmaxMA03
.445
.280
-.298
**
*
**
*
**
.120
.046
.168
-.009
TminMA03
.436
.223
.344
.188
-.305
**
**
1
.047
-.012
.088
.145
.056
-.112
Precip
.262
.333
**
**
**
**
**
.002
.135
.003
.006
DTROK05
-.242
-.746
-.798
-.245
-.263
**
**
**
**
-.180
.106
-.030
.034
TmaxOK05
-.531
-.596
.271
-.282
-.319 **
.071
.142
-.044
.038
-.063
-.090
TminOK05
.250 **
.225 *
.191 *
**
.085
1
-.041
-.102
-.009
-.044
.091
Precip
.548
.228*
*
**
**
-.033
.002
.129
.061
.091
.109
DTROR03
.183
-.600
-.632
-.003
.162
.035
TmaxOR03
.331 **
-.366 **
-.368 **
-.285 **
.185*
.183*
-.006
.052
-.031
.131
.105
TminOR03
.207 *
.271 **
.314 **
-.335 **
**
.004
1
.127
-.028
-.170
-.105
Precip
.526
-.211*
-.214*
Table 5.13: As in Table 5.10 but for autumn.
80
Negative correlations between cloud cover and autumn DTR are significant with
extremely high confidence in every division except for Boston and with 99.9%
confidence in Boston. The correlation coefficient between cloud cover and autumn DTR
in Columbus is -.809, which is larger than all other coefficients in every season except for
the largest one in winter, -.809 between precipitation and DTR in Phoenix. El Niño and
the PDO are fairly important in autumn. Correlations between Niño-3.4 and DTR and
Tmax are significant and negative in Columbus, Birmingham, Phoenix, Des Moines, and
Oklahoma City. Correlations between the PDO and Tmax are significant in every
division except for Birmingham and negative in every division except for Portland.
5.3.2. Stepwise Multiple Linear Regression models
SMLR analyses were performed for summer in the 6 climate divisions other than
Central Ohio, and models were generated as in Tables 4.2, 4.3, and 5.9. The predictors in
these models are the time series of the RPCs for each climate division, not the actual
values of the moisture variables and teleconnection indices. The following six tables
show these models for summer DTR, Tmax, and Tmin in Birmingham (Table 5.14),
Phoenix (Table 5.15), Des Moines (Table 5.16), Boston (Table 5.17), Oklahoma City
(Table 5.18), and Portland (Table 5.19). Due to the lack of cloud cover data after 1996,
two sets of models were created in each division. The first, shown on the left side of each
table, excludes these years without cloud cover data, while the second set, on the right
side, neglects cloud cover as a predictor but covers the entire long term from 1895 to
2013.
81
Birmingham
Step in
SMLR
0
1
2
3
4
5
6
Step in
SMLR
0
1
2
3
4
5
6
7
Step in
SMLR
0
1
2
3
SMLR model for DTRAL02 1895-1996
Predictor
Adj. R Variance Stand.
variable
Square explained Coeff.
Constant
0
0
12.912
Precip
0.250
0.250
-0.508
PDSI
0.464
0.214
-0.466
CloudCover
0.636
0.172
-0.415
CO2
0.737
0.101
-0.317
AO
0.776
0.039
-0.200
AMO
0.785
0.009
0.101
SMLR model for TmaxAL02 1895-1996
Predictor
Adj. R Variance Stand.
variable
Square explained Coeff.
Constant
0
0
31.623
PDSI
0.268
0.268
-0.524
CloudCover
0.465
0.197
-0.448
Precip
0.616
0.151
-0.390
AMO
0.673
0.057
0.242
CO2
0.722
0.049
-0.223
AO
0.753
0.031
-0.177
PDO
0.760
0.007
0.098
SMLR model for TminAL02 1895-1996
Predictor
Adj. R Variance Stand.
variable
Square explained Coeff.
Constant
0
0
18.711
AMO
0.069
0.069
0.279
PDO
0.134
0.065
0.270
PDSI
0.174
0.040
-0.218
Sig.
0.000
0.000
0.000
0.000
0.000
0.031
Sig.
0.000
0.000
0.000
0.000
0.000
0.000
0.047
Sig.
0.003
0.004
0.018
Step in
SMLR
0
1
2
3
4
Step in
SMLR
0
1
2
3
4
5
6
Step in
SMLR
0
1
2
3
4
DTRAL02 1895-2013 without CloudCover
Predictor Adj. R Variance Stand.
variable Square explained Coeff.
Constant
0
0
12.751
Precip
0.289
0.289
-0.543
PDSI
0.558
0.269
-0.520
CO2
0.747
0.189
-0.433
AO
0.778
0.031
-0.180
TmaxAL02 1895-2013 without CloudCover
Predictor Adj. R Variance Stand.
variable Square explained Coeff.
Constant
0
0
31.577
PDSI
0.375
0.375
-0.617
Precip
0.588
0.213
-0.463
AMO
0.630
0.042
0.211
AO
0.662
0.032
-0.186
CO2
0.684
0.022
-0.154
NPI
0.698
0.014
0.126
TminAL02 1895-2013 without CloudCover
Predictor Adj. R Variance Stand.
variable Square explained Coeff.
Constant
0
0
18.826
CO2
0.156
0.156
0.404
AMO
0.237
0.081
0.294
PDSI
0.285
0.048
-0.232
PDO
0.305
0.020
0.158
Sig.
0.000
0.000
0.000
0.000
Sig.
0.000
0.000
0.000
0.000
0.003
0.014
Sig.
0.000
0.000
0.003
0.041
Table 5.14: SMLR results for summer DTR, Tmax, and Tmin in Birmingham with all
predictors but limited by the availability of cloud cover data (left side), and without cloud
cover as a predictor (right side). For each model, the list of significant orthogonalized
predictors, the amounts of predictand variability that are explained in each step of SMLR,
the standardized coefficients (Stand. Coeff.) for each step, and the p-value of significance
(Sig.) of each additional predictor are shown.
In the Birmingham climate division, precipitation is the main factor controlling
summer DTR, and Tmax is primarily affected by soil wetness. These results correspond
to the largest correlation coefficients between the predictors and predictands in
Birmingham (Table 5.12). The models for DTR and Tmax accounted for much more
predictand variability than the Tmin models. Increasing CO2 concentration is a factor
explaining decreasing DTR and warming Tmin, but it appears to be associated with
82
cooling Tmax in the long term. In the Tmin model without cloud cover, CO2 explains
15.6% of the variability of Tmin and is the most significant predictor, but it does not
significantly explain Tmin variability in the model including cloud cover. The AO has a
significant negative effect on summer DTR and Tmax in Birmingham, as in Table 5.12.
The AMO is the most significant of the teleconnections in explaining variability of
summer Tmin and Tmax, with positive coefficients.
Phoenix
Step in
SMLR
0
1
2
3
Step in
SMLR
0
1
2
3
Step in
SMLR
0
1
2
3
4
SMLR model for DTRAZ06 1895-1996
Predictor
Adj. R Variance Stand.
variable
Square explained Coeff.
Constant
0
0
15.800
Precip
0.174
0.174
-0.427
CO2
0.343
0.169
0.416
CloudCover
0.379
0.036
-0.205
SMLR model for TmaxAZ06 1895-1996
Predictor
Adj. R Variance Stand.
variable
Square explained Coeff.
Constant
0
0
38.009
CO2
0.332
0.332
0.582
Precip
0.500
0.168
-0.414
PDSI
0.521
0.021
-0.158
SMLR model for TminAZ06 1895-1996
Predictor
Adj. R Variance Stand.
variable
Square explained Coeff.
Constant
0
0
22.209
PDSI
0.118
0.118
-0.355
CO2
0.158
0.040
0.219
NAO
0.196
0.038
0.212
CloudCover
0.220
0.024
0.177
Sig.
0.000
0.000
0.010
Sig.
0.000
0.000
0.024
Sig.
0.000
0.014
0.018
0.047
Step in
SMLR
0
1
2
3
Step in
SMLR
0
1
2
3
4
Step in
SMLR
0
1
2
DTRAZ06 1895-2013 without CloudCover
Predictor Adj. R Variance Stand.
variable Square explained Coeff.
Constant
0
0
15.772
Precip
0.204
0.204
-0.459
AO
0.233
0.029
0.188
PDSI
0.261
0.028
0.184
TmaxAZ06 1895-2013 without CloudCover
Predictor Adj. R Variance Stand.
variable Square explained Coeff.
Constant
0
0
38.162
CO2
0.364
0.364
0.608
Precip
0.518
0.154
-0.396
PDSI
0.552
0.034
-0.193
AO
0.580
0.028
0.176
TminAZ06 1895-2013 without CloudCover
Predictor Adj. R Variance Stand.
variable Square explained Coeff.
Constant
0
0
22.39
CO2
0.295
0.295
0.549
PDSI
0.442
0.147
-0.387
Sig.
0.000
0.019
0.022
Sig.
0.000
0.000
0.002
0.004
Sig.
0.000
0.000
Table 5.15: As in Table 5.14, but for summer in Phoenix.
Precipitation is also the leading cause of DTR variability in Phoenix in summer.
Remarkably, unlike in the other 6 divisions, summer DTR in Phoenix is positively
correlated with CO2 and the PDSI. The PDSI has a stronger effect on Tmin than on
Tmax, both with negative coefficients (Table 5.15), and has been trending downward,
83
especially since 1960, along with a steep downward DTR trend (Table 5.6). Despite the
recent decline in DTR, the long-term DTR trend is positive, justifying the positive
correlation between CO2 and DTR. CO2 explains more than 30% of the variance in
Tmax, with or without considering cloud cover, and nearly 30% of the variance in the
Tmin model without cloud cover. Increasing seasonally-averaged cloud cover decreases
DTR and increases Tmin. In models without cloud cover, DTR and Tmax increase with
the AO.
Des Moines
Step in
SMLR
0
1
2
3
4
5
6
7
Step in
SMLR
0
1
2
3
4
5
Step in
SMLR
0
1
SMLR model for DTRIA05 1895-1996
Predictor
Adj. R Variance Stand.
variable
Square explained Coeff.
Constant
0
0
12.988
PDSI
0.285
0.285
-0.54
Precip
0.447
0.162
-0.408
CloudCover
0.611
0.164
-0.406
CO2
0.689
0.078
-0.28
AMO
0.715
0.026
0.167
NAO
0.731
0.016
0.135
Nino3.4
0.746
0.015
-0.128
SMLR model for TmaxIA05 1895-1996
Predictor
Adj. R Variance Stand.
variable
Square explained Coeff.
Constant
0
0
28.494
CloudCover
0.242
0.242
-0.500
PDSI
0.438
0.196
-0.447
Precip
0.493
0.055
-0.242
AMO
0.527
0.034
0.196
NAO
0.560
0.033
0.189
SMLR model for TminIA05 1895-1996
Predictor
Adj. R Variance Stand.
variable
Square explained Coeff.
Constant
0
0
15.507
CloudCover
0.105
0.105
0.337
Sig.
0.000
0.000
0.000
0.000
0.001
0.009
0.012
Sig.
0.000
0.000
0.000
0.004
0.005
Sig.
Step in
SMLR
0
1
2
3
4
5
6
Step in
SMLR
0
1
2
3
4
Step in
SMLR
0
1
2
DTRIA05 1895-2013 without CloudCover
Predictor Adj. R Variance Stand.
variable Square explained Coeff.
Constant
0
0
12.823
PDSI
0.242
0.242
-0.499
Precip
0.456
0.214
-0.466
CO2
0.625
0.169
-0.411
NAO
0.645
0.020
0.15
Nino3.4
0.664
0.019
-0.147
AMO
0.683
0.019
0.145
TmaxIA05 1895-2013 without CloudCover
Predictor Adj. R Variance Stand.
variable Square explained Coeff.
Constant
0
0
28.424
PDSI
0.201
0.201
-0.456
Precip
0.282
0.081
-0.294
AMO
0.314
0.032
0.193
NAO
0.345
0.031
0.189
TminIA05 1895-2013 without CloudCover
Predictor Adj. R Variance Stand.
variable Square explained Coeff.
Constant
0
0
15.601
CO2
0.081
0.081
0.298
AO
0.109
0.028
0.189
Sig.
0.000
0.000
0.000
0.005
0.005
0.006
Sig.
0.000
0.000
0.011
0.013
Sig.
0.001
0.031
0.001
Table 5.16: As in Table 5.14, but for summer in Des Moines. The highlighted p-values
were rounded to .001 but are less than .001, so these steps explain significantly nonzero
amounts of predictand variance with 99.9% confidence.
84
In the Des Moines division, the PDSI is the predictor explaining the most variance
of summer DTR, followed by precipitation, cloud cover, and CO2 concentration (Table
5.16). The model including cloud cover accounts for 74.6% of the variance of DTR.
Cloud cover is the main factor controlling variability of Tmax, with a negative
coefficient, and of Tmin, with a positive coefficient in the model despite having a
negative correlation (Table 5.12). The AMO is the most significant of the teleconnections
in explaining variability of summer DTR and Tmax in Des Moines, with a positive
coefficient in each model.
Boston
Step in
SMLR
0
1
2
3
Step in
SMLR
0
1
2
3
4
5
Step in
SMLR
0
1
2
3
4
5
SMLR model for DTRMA03 1895-1996
Predictor
Adj. R Variance Stand.
variable
Square explained Coeff.
Constant
0
0
10.519
PDSI
0.259
0.259
-0.516
Precip
0.365
0.106
-0.334
CO2
0.422
0.057
0.249
SMLR model for TmaxMA03 1895-1996
Predictor
Adj. R Variance Stand.
variable
Square explained Coeff.
Constant
0
0
25.159
CO2
0.257
0.257
0.514
AO
0.371
0.114
0.345
PDSI
0.473
0.102
-0.324
Precip
0.512
0.039
-0.207
AMO
0.546
0.034
0.193
SMLR model for TminMA03 1895-1996
Predictor
Adj. R Variance Stand.
variable
Square explained Coeff.
Constant
0
0
14.640
CO2
0.185
0.185
0.440
AO
0.338
0.153
0.398
AMO
0.375
0.037
0.206
PDO
0.403
0.028
-0.180
CloudCover
0.420
0.017
0.151
Sig.
0.000
0.000
0.001
Sig.
0.000
0.000
0.000
0.003
0.005
Sig.
0.000
0.000
0.008
0.020
0.049
DTRMA03 1895-2013 without CloudCover
Predictor Adj. R Variance Stand.
variable Square explained Coeff.
Constant
0
0
10.465
PDSI
0.377
0.377
-0.618
Precip
0.444
0.067
-0.268
TmaxMA03 1895-2013 without CloudCover
Step in Predictor Adj. R Variance Stand.
SMLR variable Square explained Coeff.
0
Constant
0
0
25.286
1
CO2
0.293
0.293
0.546
2
AO
0.422
0.129
0.365
3
PDSI
0.511
0.089
-0.303
4
AMO
0.541
0.030
0.182
5
Precip
0.557
0.016
-0.139
6
PDO
0.571
0.014
-0.128
TminMA03 1895-2013 without CloudCover
Step in Predictor Adj. R Variance Stand.
SMLR variable Square explained Coeff.
0
Constant
0
0
14.821
1
CO2
0.376
0.376
0.618
2
AO
0.482
0.106
0.33
3
AMO
0.533
0.051
0.233
4
PDO
0.573
0.040
-0.206
5
PDSI
0.588
0.015
0.136
Step in
SMLR
0
1
2
Table 5.17: As in Table 5.16, but for summer in Boston.
85
Sig.
0.000
0.000
Sig.
0.000
0.000
0.000
0.003
0.023
0.036
Sig.
0.000
0.000
0.000
0.001
0.023
Summer DTR in the Boston division is most influenced by soil wetness and
precipitation (Table 5.17). Increasing the PDSI decreases DTR and Tmax. The most
important factors controlling Tmax and Tmin are CO2 and the AO. Cloud cover is
unimportant except that it explains about 2% of variability of Tmin, and the models
without cloud cover explain more predictand variability than those with cloud cover. The
AMO is another teleconnection that controls Tmax and Tmin. The AO and the AMO
have positive coefficients in each model. The PDO is less important but explains some
variability of Tmin and Tmax, with negative coefficients.
Oklahoma City
SMLR model for DTROK05 1895-1996
Step in Predictor
Adj. R Variance Stand.
SMLR
variable
Square explained Coeff.
0
Constant
0
0
13.105
1
Precip
0.266
0.266
-0.523
2
PDSI
0.524
0.258
-0.510
3
CloudCover
0.729
0.205
-0.451
4
CO2
0.746
0.017
-0.141
SMLR model for TmaxOK05 1895-1996
Step in Predictor
Adj. R Variance Stand.
SMLR
variable
Square explained Coeff.
0
Constant
0
0
33.446
1
Precip
0.307
0.307
-0.561
2
PDSI
0.558
0.251
-0.503
3
CloudCover
0.685
0.127
-0.356
4
AMO
0.704
0.019
0.146
5
NPI
0.714
0.010
0.112
SMLR model for TminOK05 1895-1996
Step in Predictor
Adj. R Variance Stand.
SMLR
variable
Square explained Coeff.
0
Constant
0
0
20.342
1
Precip
0.159
0.159
-0.409
2
PDSI
0.254
0.095
-0.319
3
AMO
0.323
0.069
0.272
4
NPI
0.343
0.020
0.160
Sig.
0.000
0.000
0.000
0.006
Sig.
0.000
0.000
0.000
0.007
0.038
Sig.
0.000
0.000
0.001
0.05
Step in
SMLR
0
1
2
3
Step in
SMLR
0
1
2
3
4
Step in
SMLR
0
1
2
3
4
5
DTROK05 1895-2013 without CloudCover
Predictor Adj. R Variance Stand.
variable Square explained Coeff.
Constant
0
0
13.062
Precip
0.342
0.342
-0.590
PDSI
0.676
0.334
-0.578
CO2
0.689
0.013
-0.124
TmaxOK05 1895-2013 without CloudCover
Predictor Adj. R Variance Stand.
variable Square explained Coeff.
Constant
0
0
33.467
Precip
0.330
0.330
-0.579
PDSI
0.633
0.303
-0.551
AMO
0.655
0.022
0.157
NPI
0.677
0.022
0.156
TminOK05 1895-2013 without CloudCover
Predictor Adj. R Variance Stand.
variable Square explained Coeff.
Constant
0
0
20.405
Precip
0.125
0.125
-0.364
PDSI
0.227
0.102
-0.328
AMO
0.278
0.051
0.236
CO2
0.321
0.043
0.220
NPI
0.346
0.025
0.173
Table 5.18: As in Table 5.14, but for summer in Oklahoma City.
86
Sig.
0.000
0.000
0.018
Sig.
0.000
0.000
0.003
0.004
Sig.
0.000
0.000
0.002
0.004
0.022
Precipitation and soil moisture combined explain more than 50% of the variance
in summer DTR and Tmax in Oklahoma City (Table 5.18). All three predictands are
primarily affected by precipitation and second-most by soil wetness, regardless of the
inclusion of cloud cover in the models. Cloud cover is the third most significant factor
affecting DTR and Tmax. The model for DTR that includes cloud cover accounts for
74.6% of the predictand variance, and the models without cloud cover for DTR and Tmax
explain at least 67% of the predictand variance. The AMO and the NPI control Tmin and
Tmax with positive coefficients.
Portland
Step in
SMLR
0
1
2
3
4
5
6
Step in
SMLR
0
1
2
3
4
5
Step in
SMLR
0
1
2
3
SMLR model for DTROR03 1895-1996
Predictor
Adj. R Variance Stand.
variable
Square explained Coeff.
Constant
0
0
14.261
CloudCover
0.319
0.319
-0.570
PDSI
0.545
0.226
-0.479
Precip
0.646
0.101
-0.319
PDO
0.665
0.019
-0.150
NAO
0.681
0.016
0.136
CO2
0.691
0.010
0.110
SMLR model for TmaxOR03 1895-1996
Predictor
Adj. R Variance Stand.
variable
Square explained Coeff.
Constant
0
0
24.134
CloudCover
0.246
0.246
-0.503
PDSI
0.412
0.166
-0.413
CO2
0.507
0.095
0.312
Precip
0.542
0.035
-0.197
NAO
0.558
0.016
0.140
SMLR model for TminOR03 1895-1996
Predictor
Adj. R Variance Stand.
variable
Square explained Coeff.
Constant
0
0
9.873
CO2
0.130
0.130
0.372
NPI
0.209
0.079
-0.295
PDO
0.277
0.068
0.271
Sig.
0.000
0.000
0.000
0.008
0.016
0.049
Sig.
0.000
0.000
0.000
0.004
0.037
Sig.
Step in
SMLR
0
1
2
3
Step in
SMLR
0
1
2
3
Step in
SMLR
0
1
2
3
4
5
DTROR03 1895-2013 without CloudCover
Predictor Adj. R Variance Stand.
variable Square explained Coeff.
Constant
0
0
14.257
Precip
0.288
0.288
-0.542
PDSI
0.480
0.192
-0.442
NAO
0.500
0.020
0.153
TmaxOR03 1895-2013 without CloudCover
Predictor Adj. R Variance Stand.
variable Square explained Coeff.
Constant
0
0
24.229
Precip
0.150
0.150
-0.397
PDSI
0.301
0.151
-0.394
CO2
0.374
0.073
0.278
TminOR03 1895-2013 without CloudCover
Predictor Adj. R Variance Stand.
variable Square explained Coeff.
Constant
0
0
9.972
CO2
0.237
0.237
0.493
NPI
0.308
0.071
-0.276
PDO
0.371
0.063
0.260
Precip
0.404
0.033
0.192
Nino3.4
0.425
0.021
0.158
0.000
0.001
0.001
Table 5.19: As in Table 5.16, but for summer in Portland.
87
Sig.
0.000
0.000
0.020
Sig.
0.000
0.000
0.000
Sig.
0.000
0.000
0.000
0.007
0.026
Summer DTR and Tmax in Portland are primarily controlled by cloud cover. In
the models with cloud cover, soil wetness explains more predictand variability than
precipitation, but in those without cloud cover, precipitation is the leading predictor for
DTR and Tmax. DTR increases with the NAO, while increasing the PDO decreases DTR
and increases Tmin. Tmin is more significantly influenced by the NPI, with a negative
coefficient. As in most of the other climate divisions, a higher percentage of the variance
of DTR than that of Tmax and Tmin was accounted for in the SMLR models.
The following tables summarize the significant factors in summer SMLR analyses
in the Columbus climate division (Table 5.20) and in the other chosen divisions (Table
5.21). For each predictand and division, in columns, the step number for each significant
predictor in SMLR is shown and highlighted. Predictors with smaller numbers are
therefore more significant.
Columbus DTR
Spec.Hum.
4
CloudCover
1
Precip
5
PDSI
2
CO2
3
NAO
6
AMO
ins
NPI
ins
PDO
ins
Nino
ins
AO
ins
Tmax Tmin Tavg
4
1
2
2
ins
3
3
ins
5
1
3
1
6
2
ins
7
ins
ins
5
4
4
ins
ins
ins
ins
ins
ins
ins
ins
ins
ins
5
ins
Table 5.20: The rankings of the significance of each predictor in explaining the
variability of each predictand in summer in Central Ohio. 1 = most significant, ins =
insignificant.
88
Most important factors explaining DTR variability
Division
AL02 AZ06 IA05 MA03 OK05 OR03
CloudCover
3
3
3
ins
3
1
Precip
1
1
2
2
1
3
PDSI
2
ins
1
1
2
2
CO2
4
2
4
3
4
6
NAO
ins ins
6
ins ins
5
AMO
6
ins
5
ins ins ins
NPI
ins ins ins ins ins ins
PDO
ins ins ins ins ins
4
Nino
ins ins
7
ins ins ins
AO
5
ins ins ins ins ins
WithoutCC
Precip
1
1
2
2
1
1
PDSI
2
3
1
1
2
2
CO2
3
ins
3
ins
3
ins
NAO
ins ins
4
ins ins
3
AMO
ins ins
6
ins ins ins
NPI
ins ins ins ins ins ins
PDO
ins ins ins ins ins ins
Nino
ins ins
5
ins ins ins
AO
4
2
ins ins ins ins
Most important factors explaining Tmax variability
Division
AL02 AZ06 IA05 MA03 OK05 OR03
CloudCover
2
ins
1
ins
3
1
Precip
3
2
3
4
1
4
PDSI
1
3
2
3
2
2
CO2
5
1
ins
1
ins
3
NAO
ins ins
5
ins
ins
5
AMO
4
ins
4
5
4
ins
NPI
ins ins ins ins
5
ins
PDO
7
ins ins ins
ins ins
Nino
ins ins ins ins
ins ins
AO
6
ins ins
2
ins ins
WithoutCC
Precip
2
2
2
5
1
1
PDSI
1
3
1
3
2
2
CO2
5
1
ins
1
ins
3
NAO
ins ins
4
ins
ins ins
AMO
3
ins
3
4
3
ins
NPI
6
ins ins ins
4
ins
PDO
ins ins ins
6
ins ins
Nino
ins ins ins ins
ins ins
AO
4
4
ins
2
ins ins
Most important factors explaining Tmin variability
Division
AL02 AZ06 IA05 MA03 OK05 OR03
CloudCover ins
4
1
5
ins ins
Precip
ins ins ins ins
1
4
PDSI
3
1
ins ins
2
ins
CO2
ins
2
ins
1
ins
1
NAO
ins
3
ins ins ins ins
AMO
1
ins ins
3
3
ins
NPI
ins ins ins ins
4
2
PDO
2
ins ins
4
ins
3
Nino
ins ins ins ins ins ins
AO
ins ins ins
2
ins ins
WithoutCC
Precip
ins ins ins ins
1
4
PDSI
3
2
ins
5
2
ins
CO2
1
1
1
1
4
1
NAO
ins ins ins ins ins ins
AMO
2
ins ins
3
3
ins
NPI
ins ins ins ins
5
2
PDO
4
ins ins
4
ins
3
Nino
ins ins ins ins ins
5
AO
ins ins
2
2
ins ins
Most important factors explaining Tavg variability
Division
AL02 AZ06 IA05 MA03 OK05 OR03
CloudCover
2
ins
1
ins
3
2
Precip
4
3
ins ins
1
ins
PDSI
1
2
2
4
2
3
CO2
ins
1
ins
1
ins
1
NAO
ins ins
3
ins
6
ins
AMO
3
ins
4
3
4
ins
NPI
ins
4
ins ins
5
4
PDO
5
ins ins
5
ins ins
Nino
ins ins ins ins
ins ins
AO
ins ins ins
2
ins ins
WithoutCC
Precip
2
3
ins ins
1
3
PDSI
1
2
1
ins
2
2
CO2
ins
1
ins
1
ins
1
NAO
ins ins
4
ins
ins ins
AMO
3
ins
2
3
3
ins
NPI
5
ins ins ins
4
4
PDO
ins ins ins
4
ins
5
Nino
ins ins ins ins
ins
6
AO
4
ins
3
2
ins ins
Table 5.21: For each predictand, the rankings of the significance of each predictor in
explaining predictand variability in each of the other 6 climate divisions.
89
Precipitation and the PDSI are more important than cloud cover as influences on
summer DTR, except for in Columbus and Portland. The largest contributions to
predictand variance by a single predictor were found in models without cloud cover.
These contributions were the PDSI explaining 37.7% of DTR variance in Boston, CO2
explaining 37.6% of Tmin variance in Boston, and the PDSI explaining 37.5% of Tmax
variance in Birmingham. Models with cloud cover generally explain more total
predictand variance than those without cloud cover. The moisture variables generally
explain much larger percentages of predictand variance than any of the teleconnections,
for most predictands and climate divisions. This result confirms the findings of Lauritsen
and Rogers (2012) and other studies that showed the relative unimportance of the
teleconnections compared to the moisture variables. However, this result is only for
summer, and this study will show that the teleconnections are more important in winter,
as in Table 5.10.
The NPI does not significantly explain the variability of summer DTR in any of
the 7 climate divisions, but it influences Tmin in Oklahoma City and Portland. El Niño
also has very little influence on summer temperatures in general. CO2 is most commonly
the primary factor influencing Tmax, Tmin, and Tavg in Phoenix, Boston, and Portland.
In the other four climate divisions, the primary factor for each predictand is one of the
moisture variables, except that Tmin in Birmingham is most influenced by the AMO.
The next part of this discussion will turn toward the contributions of the
teleconnections, cloud cover, precipitation, and CO2 to the variability of DTR, Tmax, and
Tmin in other seasons. Table 5.22 combines the winter SMLR results for each predictand
90
and climate division. For each predictand, the model without cloud cover is shown
directly below the one with cloud cover. Unlike in the tables of summer models, the
model coefficients and p-values are not shown, but the signs of coefficients are indicated
with the predictor variable names.
(a)
OH05
DTROH05 1896-1996
Tmax 1896-1996
Tmin 1896-1996
Step in Predic- Adj. Var. Predic- Adj. Var. Predic- Adj. Var.
SMLR
tor
R^2 Exp.
tor
R^2 Exp.
tor
R^2 Exp.
1
CloudC. - 0.388 0.388 AO +
0.116 0.116 AO +
0.094 0.094
2
Nino3.4 - 0.444 0.055 NAO +
0.203 0.086 NAO +
0.179 0.085
3
PDO 0.474 0.030 AMO +
0.276 0.073 CloudC. + 0.259 0.080
4
Precip +
0.321 0.045 AMO +
0.318 0.058
5
PDO 0.343 0.023 Precip +
0.348 0.030
Without CloudCover, Winter 1896-2013
Step in Predic- Adj. Var. Predic- Adj. Var. Predic- Adj. Var.
SMLR
tor
R^2 Exp.
tor
R^2 Exp.
tor
R^2 Exp.
1
CO2 0.143 0.143 AO +
0.118 0.118 NAO +
0.079 0.079
2
Nino3.4 - 0.249 0.105 NAO +
0.212 0.094 AO +
0.151 0.072
3
PDO 0.283 0.034 AMO +
0.285 0.073 AMO +
0.217 0.066
4
Precip +
0.318 0.033 CO2 +
0.254 0.037
5
PDO 0.344 0.026 Precip +
0.278 0.024
6
Nino3.4 + 0.298 0.020
Continued
Table 5.22: SMLR results for winter DTR, Tmax, and Tmin in (a) Columbus, (b)
Birmingham, (c) Phoenix, (d) Des Moines, (e) Boston, (f) Oklahoma City, and (g)
Portland. For each division, results are from models with all predictors but limited by the
availability of cloud cover data (top), and without cloud cover as a predictor (bottom).
For each model, the list of significant orthogonalized predictors and the amounts of
predictand variability that are explained in each step of SMLR are shown. The
coefficients are not included here, but the sign of each is shown with the predictor
variable name.
91
Table 5.22 continued
(b)
AL02
DTR 1896-1996
Tmax 1896-1996
Tmin 1896-1996
Step in Predic- Adj. Var. Predic- Adj. Var. Predic- Adj. Var.
SMLR
tor
R^2 Exp.
tor
R^2 Exp.
tor
R^2 Exp.
1
CloudC. - 0.309 0.309 NAO +
0.120 0.120 NAO +
0.121 0.121
2
CO2 0.377 0.069 AO +
0.207 0.087 AO +
0.203 0.082
3
Precip 0.429 0.051 Nino3.4 - 0.271 0.064 Precip +
0.272 0.070
4
Nino3.4 - 0.469 0.040 PDO 0.320 0.049 AMO +
0.317 0.045
5
NPI +
0.365 0.045 CloudC. + 0.362 0.045
6
AMO +
0.400 0.035 NPI +
0.403 0.041
7
Precip +
0.433 0.033 PDO 0.428 0.024
8
Nino3.4 - 0.447 0.019
Without CloudCover, Winter 1896-2013
Step in Predic- Adj. Var. Predic- Adj. Var. Predic- Adj. Var.
SMLR
tor
R^2 Exp.
tor
R^2 Exp.
tor
R^2 Exp.
1
Precip 0.130 0.130 NAO +
0.152 0.152 NAO +
0.128 0.128
2
Nino3.4 - 0.207 0.077 AO +
0.255 0.103 Precip +
0.232 0.103
3
CO2 0.271 0.065 Nino3.4 - 0.317 0.062 AO +
0.312 0.080
4
PDO 0.367 0.050 AMO +
0.363 0.051
5
AMO +
0.416 0.048 NPI +
0.405 0.042
6
NPI +
0.456 0.041 PDO 0.436 0.031
7
Precip +
0.485 0.029
(c)
AZ06
DTR 1896-1996
Tmax 1896-1996
Tmin 1896-1996
Step in Predic- Adj. Var. Predic- Adj. Var. Predic- Adj. Var.
SMLR
tor
R^2 Exp.
tor
R^2 Exp.
tor
R^2 Exp.
1
Precip 0.501 0.501 Precip 0.191 0.191 CloudC. + 0.127 0.127
2
CloudC. - 0.609 0.107 NPI 0.313 0.123 Precip +
0.244 0.117
3
PDO 0.655 0.046 CO2 +
0.372 0.059 NPI 0.314 0.070
4
AO 0.677 0.022
PDO +
0.359 0.045
5
CO2 +
0.690 0.013
NAO +
0.387 0.028
Without CloudCover, Winter 1896-2013
Step in Predic- Adj. Var. Predic- Adj. Var. Predic- Adj. Var.
SMLR
tor
R^2 Exp.
tor
R^2 Exp.
tor
R^2 Exp.
1
Precip 0.628 0.628 Precip 0.212 0.212 Precip +
0.179 0.179
2
PDO 0.666 0.038 NPI 0.307 0.095 CO2 +
0.236 0.057
3
Nino3.4 - 0.675 0.008 CO2 +
0.391 0.083 NPI 0.293 0.057
4
PDO +
0.328 0.035
5
NAO +
0.357 0.029
Continued
92
Table 5.22 continued
(d)
IA05
DTR 1896-1996
Tmax 1896-1996
Tmin 1896-1996
Step in Predic- Adj. Var. Predic- Adj. Var. Predic- Adj. Var.
SMLR
tor
R^2 Exp.
tor
R^2 Exp.
tor
R^2 Exp.
1
CloudC. - 0.245 0.245 NAO +
0.070 0.070 NAO +
0.075 0.075
2
Precip 0.383 0.138 AO +
0.127 0.057 AO +
0.140 0.066
3
Nino3.4 - 0.442 0.059
Nino3.4 + 0.190 0.050
4
CO2 0.467 0.026
AMO +
0.220 0.029
Without CloudCover, Winter 1896-2013
Step in Predic- Adj. Var. Predic- Adj. Var. Predic- Adj. Var.
SMLR
tor
R^2 Exp.
tor
R^2 Exp.
tor
R^2 Exp.
1
Precip 0.184 0.184 NAO +
0.095 0.095 NAO +
0.085 0.085
2
CO2 0.264 0.079 AO +
0.169 0.074 AO +
0.147 0.061
3
Nino3.4 - 0.336 0.072 Precip 0.209 0.040 Nino3.4 + 0.202 0.055
4
AMO +
0.246 0.037 AMO +
0.246 0.044
5
CO2 +
0.286 0.040
(e)
MA03
DTR 1896-1996
Tmax 1896-1996
Tmin 1896-1996
Step in Predic- Adj. Var. Predic- Adj. Var. Predic- Adj. Var.
SMLR
tor
R^2 Exp.
tor
R^2 Exp.
tor
R^2 Exp.
1
NAO +
0.051 0.051 CO2 +
0.084 0.084 AMO +
0.047 0.047
2
NPI 0.096 0.045 NAO +
0.134 0.050 CO2 +
0.085 0.038
3
CO2 +
0.136 0.040 AMO +
0.183 0.049 Nino3.4 + 0.118 0.033
4
Precip 0.171 0.035 PDO 0.211 0.028
5
Nino3.4 - 0.199 0.028
Without CloudCover, Winter 1896-2013
Step in Predic- Adj. Var. Predic- Adj. Var. Predic- Adj. Var.
SMLR
tor
R^2 Exp.
tor
R^2 Exp.
tor
R^2 Exp.
1
NAO +
0.065 0.065 CO2 +
0.160 0.160 CO2 +
0.133 0.133
2
Nino3.4 - 0.111 0.047 AMO +
0.213 0.054 AMO +
0.192 0.059
3
Precip 0.157 0.045 NAO +
0.265 0.052 Nino3.4 + 0.220 0.028
4
NPI 0.188 0.031 PDO 0.306 0.040 PDO 0.249 0.029
5
AO +
0.335 0.029
Continued
93
Table 5.22 continued
(f)
OK05
DTR 1896-1996
Tmax 1896-1996
Tmin 1896-1996
Step in Predic- Adj. Var. Predic- Adj. Var. Predic- Adj. Var.
SMLR
tor
R^2 Exp.
tor
R^2 Exp.
tor
R^2 Exp.
1
CloudC. - 0.336 0.336 NAO +
0.071 0.071 NAO +
0.089 0.089
2
Precip 0.615 0.279 CloudC. - 0.139 0.068 AMO +
0.171 0.081
3
Nino3.4 - 0.707 0.092 AMO +
0.168 0.028 Precip +
0.230 0.060
4
AMO 0.717 0.010
Without CloudCover, Winter 1896-2013
Step in Predic- Adj. Var. Predic- Adj. Var. Predic- Adj. Var.
SMLR
tor
R^2 Exp.
tor
R^2 Exp.
tor
R^2 Exp.
1
Precip 0.387 0.387 NAO +
0.097 0.097 NAO +
0.105 0.105
2
Nino3.4 - 0.536 0.149 AMO +
0.135 0.038 AMO +
0.205 0.099
3
PDO 0.550 0.014 Nino3.4 - 0.173 0.037 Precip +
0.275 0.070
4
Precip 0.207 0.035
(g)
OR02
DTR 1896-1996
Tmax 1896-1996
Tmin 1896-1996
Step in Predic- Adj. Var. Predic- Adj. Var. Predic- Adj. Var.
SMLR
tor
R^2 Exp.
tor
R^2 Exp.
tor
R^2 Exp.
1
Precip 0.245 0.245 NPI 0.389 0.389 NPI 0.270 0.270
2
CO2 +
0.406 0.161 Nino3.4 + 0.457 0.068 Precip +
0.406 0.136
3
CloudC. - 0.476 0.070 CO2 +
0.498 0.041 CloudC. + 0.481 0.076
4
NPI 0.536 0.059
Nino3.4 + 0.530 0.048
Without CloudCover, Winter 1896-2013
Step in Predic- Adj. Var. Predic- Adj. Var. Predic- Adj. Var.
SMLR
tor
R^2 Exp.
tor
R^2 Exp.
tor
R^2 Exp.
1
Precip 0.291 0.291 NPI 0.350 0.350 NPI 0.244 0.244
2
CO2 +
0.408 0.117 CO2 +
0.441 0.091 Precip +
0.394 0.149
3
NPI 0.464 0.056 Nino3.4 + 0.510 0.069 Nino3.4 + 0.445 0.051
4
AMO 0.478 0.013
CO2 +
0.459 0.015
Winter DTR is primarily controlled by cloud cover in Columbus, Birmingham,
Des Moines, and Oklahoma City, and by precipitation in Phoenix and Portland. Boston
uniquely has a teleconnection, the NAO, as the main influence on DTR, with a positive
coefficient. In Birmingham, Des Moines, and Oklahoma City, the NAO is the most
significant predictor for Tmax and Tmin, in every model with or without cloud cover.
94
Tmax and Tmin in Columbus in winter are primarily controlled by the AO. Table 5.23
shows the SMLR results for spring and autumn in Central Ohio. The NPI is much more
significant in these seasons than in winter or summer.
Spring
DTROH05 1895-1996
TmaxOH05
Step in Predic- Adj. Var. Predic- Adj.
SMLR
tor
R^2 Exp.
tor
R^2
1
Precip 0.182 0.182 AO +
0.055
2
CloudC. - 0.322 0.140 CloudC. - 0.109
3
NPI +
0.155
4
Without CloudCover, Spring 1895-2013
Step in Predic- Adj. Var. Predic- Adj.
SMLR
tor
R^2 Exp.
tor
R^2
1
Precip 0.244 0.244 AO +
0.073
2
CO2 0.295 0.051 NPI +
0.113
3
AO +
0.318 0.023 AMO +
0.136
4
TminOH05
Var. Predic- Adj.
Exp.
tor
R^2
0.055 NPI +
0.067
0.054 Precip +
0.112
0.046 AO +
0.142
CO2 +
0.168
Var.
Exp.
0.067
0.045
0.030
0.026
Var. PredicExp.
tor
0.073 CO2 +
0.040 NPI +
0.023 Precip +
AO +
Adj.
R^2
0.109
0.159
0.199
0.240
Var.
Exp.
0.109
0.050
0.041
0.040
Autumn
DTROH05 1895-1996
TmaxOH05
Step in Predic- Adj. Var. Predic- Adj.
SMLR
tor
R^2 Exp.
tor
R^2
1
CloudC. - 0.402 0.402 CloudC. - 0.178
2
Precip 0.669 0.266 NPI +
0.215
3
CO2 0.719 0.051
4
PDO 0.733 0.014
Without CloudCover, Autumn 1895-2013
Step in Predic- Adj. Var. Predic- Adj.
SMLR
tor
R^2 Exp.
tor
R^2
1
Precip 0.402 0.402 Precip 0.056
2
CO2 0.481 0.079 NPI +
0.083
3
Nino3.4 - 0.514 0.032
4
AMO +
0.534 0.020
5
PDO 0.551 0.017
TminOH05
Var. Predic- Adj.
Exp.
tor
R^2
0.178 Precip +
0.125
0.036 NPI +
0.179
CloudC. + 0.208
Var.
Exp.
0.125
0.054
0.030
Var. PredicExp.
tor
0.056 Precip +
0.027 CO2 +
NPI +
Var.
Exp.
0.155
0.048
0.024
Adj.
R^2
0.155
0.203
0.227
Table 5.23: As in Table 5.22, but for spring and autumn in Columbus.
95
Chapter 6: Conclusions and Future Work
The purpose of this study was to expand the study of Lauritsen and Rogers (2012)
into seasons, emphasizing summer and winter, in terms of long- and short-term trends of
DTR, Tmax, and Tmin and the factors that explain the most long-term variability of
temperatures. Trends in annually- and seasonally-averaged temperatures in the
contiguous United States from 1895 to 2014 mostly include significant decreases in DTR
and significant increases in Tmax and Tmin. Rates of change in DTR are smallest in
spring and most negative in summer. Rates of warming are largest in winter and smallest
in autumn. Each of these trends is magnified in the short term since 1960. The climate
divisions of Columbus, Birmingham, and Des Moines are characterized by significant
decreases in DTR, at higher rates in the short term than in the long term, mainly due to
greater upward changes in rates of increase of Tmin than in those of Tmax. The
predictors used in SMLR account for 32% to 79% of DTR variance in most of the
analyses and lower portions of variance of Tmax and Tmin individually.
The atmospheric CO2 concentration as a predictor in SMLR explains higher
percentages of predictand variance in models without cloud cover than those ending in
1996. Overall, it explains 4% to 19% of variability in temperatures in most cases where it
is a significant predictor, at most 36.4%. The analyses without cloud cover include more
years in the period of accelerating CO2 that would have influenced climate, from the late
1950s to the present. For trends since 1960, in general, it is unclear whether increasing
96
CO2 or the cycle of the AMO, if either, is causing large rates of warming and changes in
DTR, especially the accelerated warming of summer Tmin. However, the findings that
increasing CO2 is significant in explaining the increasing trend in Tmin agree with those
in other studies including the one by Jeong et al. (2010). SMLR results indicate that cloud
cover, soil moisture, and precipitation are the predictors that most commonly explain the
greatest amounts of variance of summer temperatures and DTR over the long term. This
general result is in agreement with the findings of Lauritsen and Rogers (2012) using
annualized DTR data.
Many models with cloud cover explain a greater percentage of predictand
variance than those without cloud cover for the same predictand, but they do not include
predictand variability from 1997 to 2013. Similarly, the models without cloud cover show
the relative effects of the other predictors on each predictand over the entire long term,
but it is unclear how much more variance could be explained if cloud cover from 1895 to
2013 could be used as a predictor. Correlations and SMLR model coefficients between
cloud cover and some predictands from 1895 to 2013 may be much different from those
based on cloud cover from 1895 to 1996. Future work could include analysis of the
contributions of the predictors used in this study to the variability of DTR, Tmax, and
Tmin in different regions, not limited to those chosen for this study, from about 1900 to
2014. This future study could also include SMLR analyses over the short term from 1960
to 2014 and compare the results to those of the long-term analyses. One would need a
complete, reliable dataset of cloud cover for each region to be analyzed, perhaps in
gridded form rather than station-based.
97
Precipitation, PDSI, and cloud cover are the most important factors in explaining
DTR variability in summer, but the NAO/AO and other teleconnections are more
important in winter. Teleconnections are the leading causes of winter Tmax and Tmin
variability in all of the chosen climate divisions except for Phoenix. The AO is very
significantly positively correlated with temperatures in the north central and eastern
United States. Winters are more likely to have frequent Arctic outbreaks in these regions
when the AO and NAO indices are highly negative. The trend in the AO since 1984,
although not statistically significant, has been strongly negative in winter, and this trend
may have made the recent “polar vortex” events and other recent record cold or record
snowfall events more likely. Steady warming trends in the two westernmost divisions,
along with decreasing winter precipitation in Portland and decreasing PDSI in Phoenix,
may indicate that the West will become more vulnerable to droughts and invasive
species. Summer precipitation in the two climate divisions representing the Great Plains
was much more inconsistent over the last 30 years (1984-2013) than in periods ending
before 1990, based on 30-year sample standard deviations. Winter precipitation in the
Northwest was also more inconsistent in recent decades than in 30-year periods ending
before 1977. The combination of warming, precipitation trends, and more unreliable
amounts of wet-season precipitation may increase climate-related stresses and damages
on agricultural lands in the near future.
However, this study shows that trends in climatological variables are temporary
and sometimes cyclical. In some regions and seasons, trends that were statistically
significant in the long term in which climate division data are available reversed,
flattened, or decreased in magnitude at various points in time. The media and studies that
98
produce model projections of future climate change tend to assume that trends will be
mostly continuous. Global warming is not continuous; there are short-term periods with
slight cooling trends and others with rapid warming. Average temperatures and diurnal
temperature ranges are regionally influenced by a combination of climate cycles with
long periods, others with short periods, weather events at much smaller spatial and
temporal scales, and human activity. Correlations between the predictors and the
predictands may be much different in the near future from the results of this study. The
summer of 2011 was extremely hot and extremely wet in Central Ohio. Summers in years
with high precipitation in spring and June have large positive values of the PDSI, usually
causing below normal Tmax and Tavg. Other factors, such as unusually persistent
meridional advection of moisture and warm air and upper-atmosphere wave patterns not
well represented by teleconnection indices, may be reasons for much wetter and much
warmer than normal seasons. Based on findings in this study that warmer periods have
greater variance in temperatures between different years within each period, future
warming may increase the likelihood of extremely anomalous seasons, especially of
extremely hot summers, in terms of seasonally-averaged temperature.
99
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