-1-
DAILY DIVERGENCE OF
WATER VAPOR TRANSPORT
by
EUGENE BYRON BROCK
B. S.,
Florida State University
(1962)
N4
SUBMITTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
January, 1968
Signature of Author.... .
Department of Meteorology, 15 January 1968
Certified
by.
.......................................
Thesis Supervisor
Accepted by......
X,
qntal Committee
on Graduate Students
ES
DAILY DIVERGENCE
OF WATER VAPOR TRANSPORT
by
-
EUGENE BYRON BROCK
Submitted to the Department of Meteorlogy on 15 January
1968 in partial fulfillment of the requirement for the degree of
Master of Science.
ABSTRACT
The water balance equation for obtaining estimated E-P
(mean evapotranspiration minus precipitation) from measured
< EP>
winds and humidities is written < 5_/jt>+ <'- >
W/Jt is water vapor storage change and V-9 is
where
water vapor flux divergence. In this study, the terms on the
left are obtained from data at 50 mb intervals, vertically integrated from the earth's surface to the 250 mb level. Evaluated
for February 1962 are 28 daily fields of water vapor stream
function for the Northern Hemisphere; and, for the western
, estimated
United States, 24 daily fields of JW/ht , V-(
E-P, and observed precipitation (732 rain gages). Objective
analyses used throughout are an asset. Daily estimated and
observed precipitation are compared for areas of 29x1O5km 2 ,
13 x 105 km 2, and 4x10 5 km 2 (California). Sparseness of observed data prevents a similar thorough test of evapotranspiration estimates. Results indicate that when daily estimates
for areas as large as 29 x10 5 km 2 are averaged over at least
6 days, their mean will agree reasonably well with observed
data. Better results are obtained over longer intervals. At
least a month is required for reasonably reliable estimates
for a 13 x 105 km 2 region and probably at least a season for
areas as small as California. Even so, the monthly total evapotranspiration estimate for California agrees with evaporation
measurements. Thus such E and P estimates play a potentially
important supplementary role in the study of the hydrologic
cycle of mountainous areas.
Thesis Supervisor: Victor P. Starr
Title:
Professor of Meteorology
-3-
TABLE OF CONTENTS
I.
II.
..............
INTRODUCTION.........
IV.
........
of symbols.
14
........................
A.
Explanation
B.
Development of the balance equation...........
C.
Interpretation and usage of the water balance
........
15
18
.. .. .. .. .. .. .. .. .. .. .. .. .....
21
DATA AND PROCEDURES.................................
21
A.
Period of study......................................
B.
Objective analyses,
C.
Precipitation analyses .......................
D.
Analysis of water vapor parameters....................
E.
Evaporation data ...........................
F.
Daily water volume estimates.........................
general ..............
...
.......
.22
.......
.23
.......
REPRESENTATIVENESS OF DATA AND ANALYSES.......
A. Representativeness of water vapor transport
B.
30
30
.32
Representativeness of precipitation data and
36
and analyses.......................................
C.
D.
25
32
data and analyses...................................
V.
14
FORMULATION OF THE BALANCE EQUATION............
equation. . .. .. .. .. .. . ...
III.
8
Representativeness of objective analyses .............. 39
Representativeness of evaporation data and
analyses............................................ 41
DISCUSSION AND RESULTS ............................. 44
A.
B.
Northern Hemispheric water vapor transport........... 44
Observed daily precipitation and estimated
E-P fields .......................................... 47
62 ................
C.
Observed monthly evaporation, Feb.
D.
Precipitation and evapotranspiration volume
estimates for Areas 1,
2 and 3 .......................
.53
54
VI. . CONCLUSIONS AND SUGGESTIONS FOR FURTHER
RESEARCH............................................
A.
B.
67
Conclusions.......................................
67
Suggestions for further research ...................
73
-4-
TABLE OF CONTENTS - cont.
FIGURES.
74
.................................................
BIBLIOGRAPHY.
ACKNOWLEDGEMENTS
........................
..................
96
.............
...
00..0.99
-5-
LIST OF TABLES
Page
Number
Table
Number
37
1.
Distribution of rain gages,
56
2.
Water volumes, Area 1.
57
3.
Water volumes, Area 2.
58
4.
Water volumes, Area 3.
60
5.
Correlations between daily volumes of
observed and estimated precipitation.
61
6.
Correlations between daily volumes of
'observed precipitation and deviations from
2400 of inflow directions.
64
7.
Daily mean precipitation volumes.
66
8.
Daily mean precipitation depth.
-6-
LIST OF FIGURES
Page
Number
Figure
Number
74
1.
Objective analysis region and distribution of aerological stations.
75
2.
Water volume integral areas.
76
3.
Water vapor stream function for North ern
Hemisphere, 8 Feb. 62.
77
4.
Water vapor stream function for North ern
Hemisphere, 9 Feb. 62.
78
5.
Water vapor stream function for North ern
Hemisphere, 10 Feb. 62.
79
6.
Water vapor stream function for North ern
Hemisphere, 11 Feb. 62.
80
7.
Observed precipitation, 8 Feb. 62.
81
8.
Estimated E-P field, 8 Feb. 62.
82
9.
Observed precipitation, 9 Feb. 62.
83
10.
Estimated E-P field, 9 Feb. 62.
84
11.
Observed precipitation, 10 Feb. 62.
85
12.
Estimated E-P field, 10 Feb. 62.
86
13.
Observed precipitation, 11 Feb. 62.
87
14.
Estimated E-P field, 11 Feb. 62.
88
15.
Observed monthly evaporation, Feb. 62.
89
16.
Daily precipitation volumes, Area 1.
90
17.
Daily precipitation volumes, Area 2.
-7-
LIST OF FIGURES - cont.
91
18.
Daily precipitation volumes, Area 3.
92
19.
Inflow-direction deviations from 240 ,
also daily observed precipitation volumes for Area 3.
93
20.
Area-1 daily mean precipitation for
6-day periods.
94
21.
Area-2 daily mean precipitation for
6-day periods.
95
22.
Area-3 daily mean precipitation for
6-day periods.
--8-
I.
INTRODUCTION
Conventionally, hydrologists have predicted evapotranspiration values on a monthly or seasonal basis through the use of empirical formulas. Weekly or even daily estimates are needed, however,
for improving streamflow forecasting and for improving water use
efficiency in irrigation programs.
In addition, the conventional ap-
proach assumes that evapotranspiration is a function of meteorological factors and available soil moisture, necessitating a knowledge
of soil moisture conditions before an estimate of evapotranspiration
can be obtained.
According to Ackerman (1965), there are 15, 000 different
soil types in the United States to study. These soil types vary widely
in physical-chemical characteristics.
Besides such factors as the
nature of the parent material and climatic conditions under which the
soil was formed, he points out that the water relatioships of soils
are further affected by the nature of vegetative cover; the prevalence
of surface mulches; the tillage practices, including compunction, organic supplements, chemical amendments, mechanical adjustments
of surface such as land smoothing and contour listing; the quality of
applied water; the prevalence of frost; and the drainage conditions.
The hydrologic cycle of water on the earth can be thought of as
having two branches - terrestrial and atmospheric. In both, the main
sources and sinks of water on the earth's surface are evapotranspir-
-9-
ation and precipitation.
Since certain areas of the earth are char-
acterized by excesses of evapotranspiration and others by excesses
of precipitation, -continuity of mass dictates that there be a transport
of water to complete the cycle.
In the ground branch, evapotranspiration and precipitation
for a basin are balanced with stream outflow; the storage change of
surface, soil moisture, and groundwater; and the net underground
flow through the vertical boundaries of the basin.
Even if we assume
that the underground flow is very slow and can be neglected when
compared to other terms, we are still restricted in the use of the
terrestrial water balance equation through a lack of knowledge of
soil moisture and evapotranspiration.
The transport of water through the atmosphere can occur as
liquid, vapor, or ice; but the transport in solid and liquid phases appears to be quite small compared to that in the vapor phase
1960; Rasmusson, 1966a).
(Peixoto,
Thus in the atmospheric branch of the
hydrologic cycle, evapotranspiration and precipitation over an area
are balanced with the change in atmospheric storage of water vapor
within the boundaries, and the divergence of water vapor flux through
permeable vertical walls which extend from the earth's surface to
the top of the atmosphere.
The storage and divergence terms are derived from measured values of specific humidity and wind.
Since precipitation is
-10also a measured quantity, evapotranspiration can be determined as a
residual in the atmospheric water balance equation.
In an important
study over a decade ago, Benton and Estoque (1954) pointed out that
evapotranspiration estimates obtained in such a way could be used
with precipitation and river discharge measurements to calculate
changes in ground water storage, thus solving the terrestrial water
balance equation.
Hutchings (1957) used actual winds and moisture data from
the surface and the 950, 900, 850, 800, 750, 650, 550, 450, and
350 mb levels in computing water vapor flux and flux divergence over
southern England for the summer of 1954.
He dealt with a quadran-
gular area formed by the straight lines joining four aerological stations.
Assuming a linear variation of transport between the stations,
he computed the net transport into the area.
Values of precipitation
and evapotranspiration were estimated by independent means.
His
results showed that the net atmospheric transport almost exactly
balanced precipitation minus evapotranspiration.
In one of their many contributions, Starr and Peixoto (1958)
evaluated daily data from some 90 upper air stations to measure the
horizontal divergence of the vertically integrated moisture flux over
the northern hemisphere for the calendar year 1950.
They found cen-
ters of convergence in the general vicinity of the headwaters and
drainage basins of many large rivers.
Several centers of strong di-
-11-
vergence were located over the oceans; these were notably over the
southern Atlantic and the Gulf of Mexico and in the mid-Pacific. The
areas of divergence corresponded to locations where the concentration of oceanic salinity was high.
Divergence centers were also lo-
cated over northern Mexico and the southwestern United States, over
the western Sahara, and over the general region of Arabia, Iraq and
Iran.
Although one would expect to find divergence centers over
deserts, the magnitudes found in their study were surprisingly great.
One of the most comprehensive hydrological studies made yet
by a meteorologist is that of Rasmusson (1966a, 1966b, 1967), who
used twice daily observations of actual winds and humidities to calculate monthly, seasonal, and annual mean values of flux and flux
divergence for North America for the period 1 May 1961 through 30
April 1963.
Through the use of precipitation measurements and wa-
ter vapor flux calculations, he determined evapotranspiration as a
residual.
To test his results, he included available stream flow
measurements and variations of the Great Lakes.
Rasmusson con-
cluded that reliable mean annual, seasonal, and monthly values of
evapotranspiration minus precipitation can usually be obtained for
areas of 20 x 105 km 2 or larger.
In an attempt to define the lower limits in space and time for
which the hydrometeorological approach could prove effective, Fer-
-12-
ruzza (1967) completed another vital step in the quest for knowledge
of the atmosphere's role in the hydrologic cycle. Using both line integral and grid-point divergence methods, he calculated water vapor
flux and flux divergence values for areas of various size and -shape
in the eastern United States for a five-day period in September, 1961.
Although concluding that E-P estimates could be made with accuracy
for periods of two days, even for areas as small as 2. 5 x 10
km2
Ferruzza cautioned against generalizing the results of his study due
to the small sample size.
The primary goal of the present study was to determine the
time and spatial lower limits for which practical use can be made of
the atmospheric water balance equation. Secondly, there was a need
to learn if such methods can produce useful results over the mountainous terrain of the western United States.
To reach these goals,
it was necessary to select a month for study which had enough widespread daily precipitation to provide an independent test of the flux
divergence estimates.
To allow the author sufficient time to process and evaluate
the immense amount of data involved, objective analyses were used.
Of particular interest were the daily fields of hemispheric water
vapor stream function for February 1962, the month of study.
Analyses of estimated E-FP and observed precipitation over
the western U. S. were compared for 4-27 February 1962, as were
-13-
integrated water volumes which were determined from the analyses for three different areas.
Evapotranspiration rates estimated
in a like manner were compared with the few available evaporation
pan measurements and results of other studies.
sents the findings of this investigation.
This report pre-
-14-
II.
A.
FORMULATION OF THE BALANCE EQUATION
Explanation of symbols
=
longitude
=
latitude
=
pressure
= time
't.
=
Q
eastward and northward unit vectors, respectively
=total
vertically integrated horizontal flux of water
vapor above a point on the earth's surface
zonal component of the horizontal flux of water vapor
meridional component of the horizontal flux of water
4> vapor
V
.V
=
=
=
horizontal wind vector at the level p
zonal component of the wind vector
eastward
V
positive
V = meridional component of the wind vector V , posi-
tive northward
= acceleration of gravity
= specific humidity
=
an element of pressure
Ott = an element of time
W
precipitable water contained in a unit column of air
at a given instant, hereafter referred to as the atmospheric storage
= the
--15-
)
U
=
Lt = time mean
f=
individual change in pressure with
respect to time
rate of generation of water vapor in a unit mass of
air
=
mean radius of the earth
the total rate of generation of water vapor in a unit
column of air at a given point over the globe
E
rate
=evapotranspiration
precipitation rate
area
I)oQos$
A A
CL CO
=
spatial mean
/ - precipitation estimate obtained by summing
negatively signed values over a grid
= evapotranspiration estimate obtained by
summing positively signed values over a grid
B.
Development of the balance equation
The formulation of the water balance equation used here is es-
sentially that of Peixoto (1960).
Since we may assume that, to a high degree of accuracy, the
atmosphere is in hydrostatic equilibrium, we shall take the pressure
p as the vertical coordinate in a (
cC,, p, t
) coordinate system.
If we consider at each point of the earth's surface a unit column of air
which extends from the surface to the top of the atmosphere, the total horizontal flux of water vapor above that point, for a given interval of time
T
,
defines a two dimensional vector field given by
The respective zonal and meridional components in the (X, c), o ,t)
system are represented by
cpAt
I-.L
(2)
and
-
ff a(3)
.
The water vapor stored in a unit column of air at a given instant at
a point on the earth's surface is expressed by
In writing expressions (1) through (4), use has been made of
the hydrostatic equilibrium condition.
The pressure integrations ex-
tend from zero (or in practical use, to that pressure level where q
Expres-
is negligible) to the value of the pressure at the surface.
sion (1) through (4) may be averaged with respect to time over the
interval T
and
,
leading to the corresponding values
\A) ,where
the bar denotes the operator:
t
.(5)
Q
,
X,
-17-
Using the continuity equation, the water vapor balance equation at a given point of the atmosphere for an instant t can be ex-
pressed formally by the general equation of balance, as follows:
/c
V-
=L 0 /4t
LA)/)
~(1r)
(6)
where 6?'(q) represents the rate of generation of water vapor in the
unit mass of atmosphere and W = dp/dt, the individual rate of change
of pressure.
The balance equation (6) may be integrated with respect
to pressure and in the (
A,
4
,
,
t ) system the resulting equation
assumes the form:
since
5
WAf
Cp
is zero for practical purposes.
In
0
equation (7)
(q) represents the total rate of generation of water
vapor in a unit column of the atmosphere at a given point over the
globe.
Since the only sizeable sources and sinks of water vapor in
the atmosphere are those due to evapotranspiration and precipitation
as measured at the earth's surface, we set
E-P
E
(8)
Thus we are led to the water balance equation in the form
/JW/t +
QJJA+ 3/4JO(Q
Cos
<p
=
[-P
(9)
-18-
Applying the "bar" operator (5) to the previous expression gives
because the "bar" and divergence operators are permutable.
If we define a spatial mean operator to be
A
and apply this operator to expression (10)
4 /--
at
+ j/ho (
we get
s}
E
(12)
or in more compact symbology,
+
3~v/t'
C.
V-G'
/it>
=
E-P>
-<VV(13)
Interpretation and usage of the water balance equation
The left side of expression (13) can be conveniently evaluated
from measured quantities by finite difference methods.
Then, through
the use of rain data, the evapotranspiration rate E can be determined
as a residual.
This then is one practical way to make use of the water
balance equation.
We wish to determine if this same equation can be used in such
a way that reasonable estimates of both evapotranspiration and precipi-
-19-
tation can be consistently obtained.
Since the left side of (13) equals
the mean difference between evapotranspiration and precipitation for
any area under consideration, a negative value of the left side indicates that precipitation exceeded evapotranspiration over the area
in the mean.
Also, as we can consider that some evapotranspiration
say X units, occurred, we have E-P = X-P.
Since X-P includes the
contribution of the X units of evapotranspiration but still is of negative sign, we can accept X-P as the lower bound of precipitation
that occurred in the area.
Likewise, if X-P is positive, it is the
lower bound of the evapotranspiration which took place over the area
during the period under study.
To test this approach, the author conducted a preliminary
study of four days (3 summer, lautumn) for a 29 x 10 5 km 2 area in
the eastern United States using reported wind and humidity data from
42 stations. By calculating ( 3v/4'7
+
( V-.7
over a two-degree
grid of latitude and longitude for the area, daily estimates of precipitation and evapotranspiration were obtained. Each local average
of
( N/t'+
< V'
./
was multiplied by the area of its surroun-
ding two-degree quadrangle to give an estimate of precipitation or
evapotranspiration by volume.
These volumes were then summed
according to sign. The sum of the negative values,
.v'-V'
t
was taken as the regional precipitation estimate. The daily evapo-
-20-
transpiration estimate,
analogous way.
(WI/
t
+VQ.
,
was computed in an
Precipitation estimates compared favorably with
actual precipitation (within 20%, on the average).
Evapotranspira-
tion estimates were reasonable and conceivably of the same order
of accuracy, since analogously obtained.
used in this more comprehensive study.
The same approach is
-21-
III.
A.
DATA AND PROCEDURES
Period of study
This is a study of the daily divergence of water vapor trans-
port over the western United States during February 1962.
The
writer's interest in that period was stimulated by the work of
Rasmusson (1966a).
His analysis of monthly mean V Q.
for Feb-
ruary 1962 indicated substantial precipitation over most of the west,
with a convergence center of 36 cm in California.
Remarks in the
Climatological Data, National Summary, were to the effect that
heavy precipitation in February had ended a three year drought in
California and boosted the water supply outlook to normal or above
in most other areas of the far west, except in Washington and Oregon.
Thus Rasmusson was able to depict reasonably well the
monthly precipitation pattern.
But how well can vapor flux divergence fields represent precipitation and evapotranspiration on a daily basis, especially over
rugged terrain?
Only through tests against independent data can
this question be answered.
Due to the sparseness of evaporation
measurements and the dependence of evapotranspiration on soil
moisture as mentioned in the introduction, our main hope for an independent comparison rests with precipitation data.
1962, then, is ideally suited for such tests.
February
-22-
B. Objective analyses, general
Both Rasmusson (1966a) and Ferruzza (1967) have stressed
the need for the use of objective analysis techniques in studies of
this kind, for studies which must rely on hand analyses are seriously
limited by the great amount of time required for plotting, analyzing,
and grid-point reading.
In addition, water volume integrals calcu-
lated by machine offer distinct advantages over graphical methods-not only is there a great saving of time, but the complete consistency
with which the calculations are performed offers less chance for
error.
Objective methods were used almost exclusively to obtain the
Basically,use was made of a main pro-
results of this investigation.
gram which consists of a library of about 95 operators frequently
needed to manipulate fields of observational data.
The program,
developed at Travelers Research Center and adapted by them to the
UNIVAC 1108 computer, is called ANAL68.
element in ANAL68 is a field.
The basic organizational
A field consists of (a) a six-character
name, (b) parameters which define the areal extent of the field, and
(c) a rectangular array of grid point values, which defines the spatial distribution of the field.
In addition to manipulating two-dimensional fields, ANAL68
contains operators which allow the generation of fields from randomly
spaced observational data.
This is the objective analysis process.
-23-
A field is a representation of some physical variable on a regular
convenient grid.
Observational data, on the other hand, are not
regularly spaced-, and usually include values of several physical
variables (phi's) at the observing station.
In ANAL68,
observational
data are organized as an array of stations, each station comprised
of an x coordinate, a y coordinate, and one or four observed values.
If there is only one observed value at each station, as many as 1598
stations cin be handled in the computer.
With four phi's at each
station, as many as 799 stations can be input.
The grid used in ANAL68 is related to that defined by the
Joint Numerical Weather Prediction Unit (JNWP).
JNWP grid points
lie with 1- inch spacing on a polar stereographic map, scale 1:15
million true at 60 0N.
A rectangle of 47 x 51 grid points is defined,
with the lower left point assigned (0, 0), the North Pole assigned
0
(23, 25), and the j-direction of the grid aligned along 80 W.
The
JNWP grid is generalized to suit the particular problem in ANAL6-8.
C.
Precipitation analyses
Some of the pertinent details associated with the objective
analyses of precipitation are included here as an illustration.
analysis region is outlined on the map shown in Figure 1.
sector of the JNWP grid, with zero rotation.
The
It is a
A mesh equal to 1/7
-24-
of the JNWP grid was selected, giving a spacing of from 24-27 nautical miles between neighboring grid points.
Observational data from 732 rain gages distributed over the
eleven westernmost states were read into the computer.
The data
included station location by latitude and longitude, station elevation
in feet, and precipitation amounts in inches.
The February 1962
total precipitation as well as daily values for the period 4-27
February, inclusive, were used.
ANAL68 objective analyses start with an initial guess of the
field to be analyzed.
As an example, there was a requirement for
an analysis of the station elevations; topographical features used as
a first guess came fromScripps Institute of Oceanography data.
The
final analysis -provides major features of topographical relief for
maps on which fields of precipitation and estimated E-P are depicted.
It is emphasized that the topographical features are refined by, and
thus reflect, the actual elevations of the rain gage stations.
ANAL68 operators can handle data by blocks rather than individual stations.
All precipitation data were tabulated by station in-
dex number and mechanically sorted by the unit digit of the index into
ten blocks
prior to being read into the computer for analysis.
One
data block was withheld from the analysis to alloW a meaningful testing of the objective analysis techniques through comparison.
Prior to
-25-
each comparison with the withheld block, the analysis was smoothed
by the operator
+b
where A is the analyzed field and
smoothing parameter.
(14)
(A]
is its space mean; b is a
In general, comparative tests cease and the
final analysis is printed when the error score of the withheld block
reaches a minimum.
D.
Analysis of water vapor parameters
Water vapor storage and flux values for the North American
aerological stations shown in Figure 1 served as the input for estimated E-P (W/
t
+ V7
) analyses.
Thirty of these stations are
located within or along the boundary of the western U. S. region of
study, which is outlined in the figure.
Twice daily observations of
q, u and v taken at 0000 GMT and 1200 GMT in February 1962 were
obtained from magnetic tapes which are part of the MIT General Circulation Library.
Levels used in the vertical integrals were surface
and 50 mb intervals to 250 mb.
In addition to the North American stations, data from the entire Northern Hemisphere were available from the same source, but
only at 0000 GMT.
A discussion of the daily hemispheric analyses of
water vapor stream function is included in Chapter V.
-26-
Two difficult and time
-
consuming phases of the data pro-
cessing involved the unpacking of the February data from five years
of record on the-tapes, and the thousands of vertical integrations required to provide the input for the objective analyses.
Ground rules for vertical integrations were established for
the hemispheric network, as follows:
1) For an integration to be computed for a specific station,
both specific humidity q and wind v had to be available at the surface,
850 mb (unless surface was at a lower pressure), 700 mb and 600
mb levels; and at least v at 500 mb and 400 mb.
2) Interpolation for missing reports between reporting
levels:
(a) linear interpolations were performed between the
nearest reporting levels.
(b) interpolations were performed separately for q,
u, v; ie. qu, qv were not interpolated in the product form.
3) Interpolation for missing levels above highest reporting
level:
(a) estimated values of q, qu, qv were computed up to
250 mb as follows:
1. Since q was required to be available to at
least 600 mb, a linear decrease of q was assumed from its value at
the last reported level to zero at 250 mb.
-27-
2.
at least 400 mb.
Wind components u, v were required to
Once the high-level values of q were estimated,
computations were performed of qu, qv to the highest level at which
wind reports were available.
Above that level, a linear decrease of
qu, qv to zero at 250 mb was assumed.
4)
Finally computed were the atmospheric storage W and
zonal and meridional transports Q,
and Q
, respectively.
These vertical integrations (in expressions (4), (2) and (3) of Chapter II) were performed by a routine coded to solve the equation
4*'A*o
(Xs tXa) (-
o
+
()
+ X I'
'~o
2x2
2.((s-
(15)
where I = the vertically integrated quantity, K = a dimensional constant, X = the quantity to be integrated,
P0
is
= surface pressure and
= pressure of the first even 50 mb level above the surface. Thus
linearly interpolated values of q, qu and qv at 50 mb intervals from
the surface to 250 mb were integrated to give
cm of water) and the flux components Q >
W, Q
and Q
W in gm cm-
and Q
2
(or
in gm(cm sec)~1 .
were initially analyzed each 12 hours for
an area three times the size of, and including, the western U. S.
region.
The grid spacing for this expanded area was approximately
80 nautical miles.
A 60-month mean value of W was used at the boun-
dary and linearly interpolated to the actual data in the smaller region.
-28-
A value of zero for
QN
and Q qwas assumed for the boundary.
At a later step in the analysis process, the 12-hourly field
of
V- Q
was computed and from it a field of velocity potential
was derived.
From the velocity potential an irrotational flow field
was obtained which was considered to represent error.
That flow
was subtracted from the current analyses to give adjusted fields of
Q
and Q
the error.
.
This step was performed three times to minimize
Final analyses of water vapor stream function and velo-
city potential were performed for the large area and interpolated to
give analyses for the western U. S. region.
All final analyses of Q
,
Q
were performed on the
western U. S. area with a grid interval of 24-27 nautical miles.
Q
and
were computed at each grid point.
Q
j
/t
/t
was
obtained by subtracting initial from final 1200 GMT values of I/
while 24-hour average transport values were obtained as in the following example:
Q
o, 5'
+ o. 'o0 Q M+ 0.:5 Q CF)
(16)
where the superscripts refer to initial 1200 GMT (I), mid-time
0000 GMT (M) and final 1200 GMT (F) observations.
The final analysis of
V. Q
was calculated for the smaller
area by using interpolations from the large initial analysis region
with zero divergence on the boundary.
The analysis procedures just discussed gave estimated
E-P fields which compared favorably with hand analyses performed
as an independent check.
Although there are some features which
can possibly be improved upon, the analysis routine produces results which are, in the opinion of the author, at least as good as
can be obtained through the more tedius and time-consuming subjective analyses.
One reason for publishing research results is to apprise
others in the field of findings which could contribute to a better
general understanding of some physical process.
It is quite as
important to afford others the benefit of one's mistakes in order to
prevent needless and possibly costly duplication.
and estimated E-P fields were produced twice.
All )W/Jt , V-Q
The first production
run followed a different routine from the one just described; and
the V'G and estimated E-P fields were unsatisfactory due to numerous dipoles in the fields, frequently located in the vicinity of the reporting stations.
The unsatisfactory routine that had been initially
followed involved using the hemispheric stream flow analysis as a
first guess for each analysis over the western United States.
Evi-
dently the disparity between the grid meshes of the initial guess and
final fields caused much of the trouble.
The hemispheric mesh was
twice the JNWP grid, while the western U. S. mesh was 1/7 JNWP.
-30-
E.
Evaporation data
Only a few evaporation pan measurements were listed in the
February 1962 climatological summaries for the eleven westernmost
states; Washington, Utah, Wyoming, Montana and Idaho had none.
The only stations suitable for comparison with vapor flux divergence
calculations were located in California, 20; Arizona, 10; and New
Even though the much more plentiful precipitation data
Mexico, 2.
provide the major test of results, some useful information may be
gained from the evaporation measurements.
F.
Daily water volume estimates
In Section C of Chapter II we discussed the method we would
use to obtain daily estimates of precipitation and evapotranspiration
in this study, i. e., we would sum the negative values of
*I
(tl~..
<OAt7+
over a grid to give the estimate of precipitation
/I
--
+ V,
-
units: km 3 of water) and sum the posi-
tive values to obtain the evapotranspiration rate.
All such calcula-
tions were performed over the western U. S. analysis grid and daily
E and P estimates for three areas were included as part of the computer output.
Area 1 (area 29. 07 x 105 km2 ) includes the eleven westernmost states.
Area 2 (13. 03 x 105 km 2 ) includes California, Nevada,
-31-
and parts of Oregon, Idaho, Utah and Arizona.
km ) approximates the boundaries of California.
Area 3 (4. 05 x 105
These regions are
outlined on the map shown in Figure 2.
Daily volumes of measured precipitation for these areas
were also included as a part of the objective analysis routine.
Total
volumes were computed by adding the individual grid values as determined from the analyzed field.
The consistency with which the
machine computed the volumes of observed and estimated precipitation for comparative purposes is a feature which cannot be overstressed.
-32-
IV.
A.
REPRESENTATIVENESS OF DATA AND ANALYSES
Represencativeness of water vapor transport data and analyses
Primary errors in calculated values of water vapor flux and
storage are due to lag in the humidity element of the radiosonde, inadequate resolution of winds, and sampling.
In an analysis of the
results of his study, Hutchings (1957) found that sampling errors
caused by the averaging of two observations a day made the major
contribution to the vector error.
Rasmusson (1966a,
some detail.
1966b) has discussed these errors in
He found that a 50-mb resolution in the vertical is
adequate for studies of this type, although pronounced diurnal variations in the summer could justify a 25 mb interval through the
lowest 100 mb during that season.
From his study of monthly seasonal and annual mean flux divergence, Rasmusson (1966a) concluded that results over the United
States would probably benefit more by having observations four
times a day from the present station network than by doubling the
number of stations.
Although the present network is adequate for studies of
monthly means, even over the western United States, daily analyses
of estimated E-P for that area often do not represent the true field.
There are several reasons for the unrepresentativeness,
most im-
portant of which are: 1) the lack of "upwind" stations off the west
-33-
coast; 2) the present networkT s inability to reflect the small-scale
irregularities in the field which are caused by mountainous terrain;
and 3) evapotranspiration/precipitation dipole effects.
Let us dis-
cuss these causes in the order given.
1) The void of stations upwind over the Pacific is an inherent problem to west-coastweather forecasters.
In this study, the
most noteworthy example occurred on 9 February.
Though the
monthly peak of precipitation in California was reached on that
date, the estimated E-P field showed an excess of evapotranspiration. , Hand analyses of the water vapor transport fields showed that
divergence of the zonal component
misrepresentation.
Q)
A 3100 gm(cm sec)
played the major role in the
maximum in the
field was located over the California-Arizona border, with values
half that amount along the coast to the west, indicating pronounced
divergence in the southern half of the state.
An examination of sur-
face and 500 mb historical weather maps revealed the following: on
the surface, a N-S oriented occluded front extended through central California; a 500 mb low was located off the California coast,
with the tightest gradient offshore--winds upstream were stronger,
and winds downstream along the flow were lighter, than those along
the California coast.
The abundant observed precipitation and the
500 mb wind flow lead the author to believe that had vertically inte-
-34-
grated moisture transports been available at points off the coast,
flux convergence probably would have been depicted over California.
2) Under conditions of a broad flow of moisture over a region where precipitation is occurring, greater amounts are generally observed on the windward side of mountain slopes.
Thus there
is convergence of water vapor transport due to upslope.
Since the flow diverges as it descends the leeward side of
the mountains, it is there one. would expect an increase of evapotranspiration to occur.
The present network of aerological stations
simply cannot depict all of the irregularities in the E-P field caused
by mountains.
Only 30 stations listed in the taped-data directory
are located within or along the boundary of the objective analysis region (reference the map in Figure 1), and a few of them transmit
only on special occasions.
Vertical integrals from an average of
19 of these 30 stations were used in each 12-hourly analysis for this
study.
For comparison, the author sampled the data received dur-
ing the first 7 days of February of 1967.
No more than 26 stations
were ever received at any one synoptic time, and no fewer than 22
met the vertical integral requirements during the sample period.
3) One should not expect a one-to-one correspondence between observed daily precipitation areas and areas of excess precipitation in the estimated E-P field; while precipitation analyses rep-
-35-
resent daily accumulations of water mass, negative values in the
estimated E-P field represent a 24-hour average of the lower
bound of precipitation.
Often, for example, summer thunder-
storms deposit large volumes of rain over a matter of minutes;then
evapotranspiration exceeds precipitation the remainder of the day.
Also, any time there is a center of one arithmetic sign in the E-P
field, continuity requires that there be one or more centers of the
opposite sign nearby.
When the gradient around such features is
steep, there is a tendency for dipoles to show up in the objective
analysis. Hand analyses of the estimated E-P fields for the 8th, 9th,
10th, and 11th were completed for comparison. It was found that the
dipoles in the objectively analyzed fields were partly due to exaggerations of alternating positive and negative centers found in the hand
analyses. Often, however, they were a result of a lack of data along
the western boundary.
With a steep gradient of negative values as-
sociated with a precipitation center on the coast, the objective analysis routine continued the same gradient going away from the center, eventually reversing the sign of the isopleths and locating an
evapotranspiration center just off the coast.
Note that while the di-
poles in the final analyses appear only near strong centers of action,
the initial run (discussed in Chapter III) produced fields which were
dominated by these doublets.
-36-
B.
Representativeness of precipitation data and analyses
The National Meteorological Center publishes daily analyses
of total precipitation for 24-hour periods ending at 1200 GMT. Such
analyses were used to verify vapor flux estimates of precipitation
for the eastern part of the country in a preliminary study which has
already been discussed.
For consistency, 1200 GMT was also se-
lected as the verification time for all daily calculations performed
in the prdsent work.
Precipitation data were extracted from the Climatological
Data, State Summaries, February 1962.
Although some of the ob-
servations were made at stations manned by Weather Bureau personnel, most were taken by cooperative observers.
As an apparent
consequence; the daily observation time varied from station to station.
By selecting as reasonably representative all stations which
took observations daily at 1200 GMT + 4 hours, the writer was able
to utilize a network of 732 stations in the objective analyses.
The
following table shows the distribution of stations furnishing precipitation data for this study.
On some days, precipitation amounts were not measured at
certain stations but were included in the next daily measurement
with no breakdown by time distribution.
the objective
Such data were handled in
analyses by discarding both the unmeasured and suc-
ceeding daily value.
-37-
Table 1.
Distribution of rain gages
Number
State
26
19
15
92
32
17
16
68
44
66
337
Montana
Nevada
Wyoming
Oregon
Colorado
Idaho
Utah
Washington
New Mexico
Arizona
California
Total:
732
Though precipitation measurements test the accuracy of
vapor flux divergence estimates of precipitation, certain shortcomings must be discussed.
One difficulty lies in the fact that when we
analyze precipitation patterns, we are implying that the field is continuous; this we know is untrue, particularly over mountainous terrain.
It is therefore impossible to have an exact representation of
actual conditions.
In addition, errors in the measurement of precipitation are
not random, but biased towards underestimation,
Younkin, 1963).
son (1966a),
(LaRue and
The errors, discussed in some detail by Rasmus-
are mainly related to the speed of the wind and the
-38-
character of the precipitation.
They are most serious for the
commonly used unshielded rain gage.
by Weiss and Wilson (1958),
In a comprehensive study
most tests showed that the unshielded
gage underestimated the actual rainfall by 5-15% at wind speeds of
4 meters sec~1,
sec~1 .
5-30% at 8 meters sec~1, and 5-50% at 12 meters
General compensation cannot be made for such errors.
Other problems contributing to the underestimation of ac-
tual precipitation are the sparseness of data in mountainous regions and difficulties in measuring snow.
LaRue and Younkin
(1963) are of the opinion that the paucity of data in the mountainous
regions of the United States probably leads to underestimates of a
moderate degree.
Also, Weiss and Wilson (1958) reveal that in
tests of the ground measurement of snow, average underestimates
ranging from 4% to 25% occur with gages having flexible shields.
The underestimation is much larger for unshielded gages and
gages with rigid shields.
Considering the mountainous terrain in the western states
and the fact that much of the February precipitation fell as snow,
underestimates of 10-15% do not seem unreasonable for the present work.
-39-
C.
Representativeness of objective analyses
In a report of his work in the objective analysis field, Eddy
(1967) considers the data evaluation process as separable into
three stages:
a) a physical phenomenon varying in space and time;
b) a data acquisition system comprising sensors
(whose sensing characteristics and whose positions in space and
time are known only to a certain degree of approximation), human
decision making, and encoding, transmission and decoding routines which finally put the data in the analysis device; and
c) the analysis scheme which endeavors to evaluate
the system function of b) and to present the best possible description of the physical phenomenon a).
He has proposed and tested a statistical objective analysis
model for use with scalar data fields which he believes is a first
step along the path to producing a completely objective analysis.
His present model assumes that any patterns or waves are isotropic in the horizontal plane.
Future steps would include the
elimination of this assumption and the taking into account of geographical bias, as well as inclusion of time, data at other levels,
and other parameters.
He states that his present model has eliminated the possibility of forcing uncorrelated data fields to yield "pretty"patterns
-40-
by pre-specification of influence functions.
In his objective anal-
ysis model no "first guess" field is required, though a first guess
may be useful to an analysis.
Also, weight curves used in his in-
terpolation formulae are determined by the data themselves.
Certain features included in Eddy's objective analysis output would be helpful in determining the representativeness of the
present analyses.
1) An estimate of the accuracy of the analysis at each grid
point is effected in an objective manner and presented as a companion map to the final analysis.
2) An estimate of the manner in which the analysis scheme
partitions the variance between the zonal and eddy components is
presented.
The error variance in the original data is estimated.
3) A subjective statement about the possible stochastic nature of the perturbation field is offered with associated implications about possible periodic components.
As was described in Chapter III, the ANAL68 objective
analysis is tested against withheld data blocks until the error
score of the withheld data is at a minimum, thus an optimum analysis of the data is produced.
Even so, the advantages of the model
described by Eddy (1967) are obvious to the research scientist; attempts should be made to incorporate feature
objective analysis schemes.
1), at least, in all
-41-
D.
Representativeness of evaporation data and analyses
It is extremely difficult to measure actual evapotranspira-
tion in practice because of the dependence of this quantity on such
factors as soil type and method of land cultivation, type of plant
cover, and moisture conditions of the soil profile.
Because of
these difficulties, the conventional approach has centered on at'tempts to estimate actual evapotranspiration through the use of
standard surface data.
All such systems embody a means of com-
puting potential evapotranspiration, a means of computing actual
evapotranspiration and soil moisture, and a way of budgeting soil
moisture (Thornthwaite and Hare, 1965).
According to Mather (1961), potential evapotranspiration
is the water loss under conditions of continuously adequate soil
moisture and is controlled solely by available energy.
This quan-
tity is computed by means of an empirical formula based on air
temperature and latitude.
When there is no shortage of water,
actual and potential evaporation are hypothetically the same; when
there is a shortage of moisture in the ground, actual evaporation
will always be less than potential evaporation, according to this
method.
Drinkwater and Jones (1957) have evaluated the relation of
potential evapotranspiration to environment and kind of plant. Fifteen evapotranspirometers
were installed in five units of three
-42--
tanks each to measure potential evapotranspiration (PE) as influenced by surroundings and irrigation of the surroundings.
Mea-
sured PE exceeded evapotranspiration computed by the Thornthwaite empirical formula by 10 to 70 per cent and appeared more
closely associated with the amount of rainfall than with the temperature in summer measurements.
In E. A. Colman's report of a study conducted at the California Forest and Range Experiment Station (Colman, 1945), he expressed surprise that soil measurements indicated evapotranspiration rates were actually higher during the winter rainy season than
any other time of the year.
These measurements, taken in the San
Dimas Forest, showed an average evapotranspiration rate of 0. 07
inch per day.
Colman concluded that the magnitude of evapotrans-
piration was due to the high moisture content during that part of
the year and relatively high temperatures prevailing between
storms.
Another interesting study conducted in the West was that
of van Bavel et al.,
(1963).
A 100 x 100 meter observation area at
the U. S. Water Conservation Laboratory in south-central Arizona
was instrumented with a system of three precision weighing lysimeters for the measurement of evaporative flux.
Four major ex-
periments were carried out during the late spring of 1961.
In the
first a small wetted surface was observed, in the second a small
-43-
ponded surface, in the third a large ponded area, and in the fourth
a large wetted area.
The soil was bare in all cases.
Data were
collected every 15 minutes by telemetry, including wind conditions,
for the experiments in March, April, and May 1961.
Evaporation
ranged from 0. 2 to 0. 8 cm (0. 08 to 0. 31 inch) per day with the
rates decreasing with increasing dryness of the soil.
Curves of eva-
poration rate were irregular during daylight hours with maximum
rates from 1200 to 1600 local time.
The studies just described demonstrate the difficulties in
measuring evapotranspiration directly, and the need for a more satisfactory way of obtaining this quantity.
Certainly the 32 evapora-
tion pan measurements (read daily at 1200 GMT + 4 hours) used in
the present study cannot be entirely representative of the rate of
evapotranspiration from the variety of soils and vegetation. Evaporation analyses, considering the paucity of data, would be unrepresentative of the evapotranspiration throughout the region even if
vegetation and soil conditions played no part.
-44-
V.
A.
DISCUSSION AND RESULTS
Northern Hemispheric water vapor transport
Benton, Blackburn and Snead (1950) stressed in their pio-
neering study of the atmosphere's role in the hydrologic cycle,
that although tremendous quantities of water vapor move across
the continents from the oceans, only about 20% is ever precipitated.
Thus, while the extreme mobility of the atmosphere may
provide a necessary supply of water vapor for excessive precipitation, a large moisture flux is not a sufficient condition for
such precipitation to occur.
The sufficiency criterion
is depen-
dent upon the degree of flux convergence.
In this chapter we begin with a look at the "big picture,"
the daily water vapor transport for the Northern Hemisphere. A
summary of the major points noted in the analyses of water vapor
stream function for each day during the period 1-28 February 1962
will be presented.
Particular emphasis will be given the flow of
moisture into the United States from the Pacific.
From this
frame of reference we will go on to compare the daily analyses of
observed precipitation and estimated E-P over the western United
States for the period 4-27 February.
Finally we will compare esti-
mated and observed precipitation volumes in an effort to learn the
capabilities of the hydrometeorological approach under the conditions of this study.
-45-
Although February 1962 was characterized by abundant precipitation in California and widespread lighter precipitation over the
remainder of the area of study, the first few days were for the most
part dry.
Precipitation during the first two days was generally re-
stricted to Washington and Oregon, spreading to Montana-and Wyoming by the 4th,and to the rest of the area about the 6th.
It is interesting to compare this precipitation with the hemispheric flow of moisture.
Because the cost of printing is prohibi-
tive, only the analyses which bracket the peak of precipitation are
included in this report.
These analyses, for the 8th through the
11th, are shown as Figures 3-6.
The numbers on the analyses
are for shading, but their values do increase towards anticyclonic
centers and decrease towards centers of cyclonic circulation.
With one's back to the flow, the ascending numbers are on the
right and descending are on the left.
The gradient is an indication
of the amount of vertically integrated moisture being transported
horizontally over a given point on the earth's surface at 0000 GMT.
The units are 1000 gm-grid interval (cm sec)
between any two
adjacent shaded bands, with the flow parallel to the bands.
The major points of interest on the 28 daily water vapor
stream function analyses can be summarized in a few brief words.
During the first two days of the month both the Pacific high and
-46-
Aleutian low were very weak and thus the transport of water vapor
toward the U. S. west coast was at .a low ebb.
Both of these sys-
tems continued-to build over the next few days, and the Aleutian
low moved eastward and began to affect the western region.
The
circumpolar vortex became more organized with time, with a peak
zonal flow around the hemisphere being reached on the 9th and 10th
(see Figures 4 and 5).
There was a general coalescence of the
circump6lar vortex on the 9th, with the Aleutian low as the main
center.
The flow of moisture on these two days was approximately
normal to the Sierra Nevadas of California, thus orography played
an important part in determining the precipitation which occurred.
The circumpolar flow of moisture was abruptly interrupted
on the 11th through the blocking action of the Azores high at 45 N.
From that date until the 17th, the blocking action continued.
Al-
though the zonal flow into the west coast was reduced somewhat,
the Aleutian trough retained a strong influence on the weather of
the western states during that period.
After the 17th there was only one minor block by a small
high over Iceland, and the weather over the western region was
characterized by a train of moving waves in the westerlies.
The
stronger westerlies remained to the south, giving occasionally
high moisture contents near San Diego or over Mexico, while less
-47-
steep gradients predominated farther to the north,
Whenever the
moisture flow increased along the west coast during the last few
days of the month, there was a tendency for it to be from the northwest,parallel to the mountain barriers in California.
B.
Observed daily precipitation and estimated E-P fields.
Daily precipitation analyses for the period 8-11 February
1962 are shown in the odd numbered Figures 7, 9, 11 and 13.
ease in making comparisons, estimated E-P (
W/Jt
For
+
)
fields for the same time are shown in the even numbered Figures
8, 10, 12 and 14.
Although the patterns can be compared directly,
with negative values of E-P corresponding to estimated precipitation, the units are not the same.
The E-P values are in mm of
water per day, while the precipitation is in inches.
Positive val-
ues of E-P indicate areas where evapotranspiration exceeded precipitation over the daily mean. Elevation contour units: 103 feet.
In an attempt to maintain day-to-day continuity throughout
this discussion, the observed precipitation charts will be discussed
first.
Each analysis is of 24-hour measurements taken at 732 sta-
tions within the eleven westernmost states at 1200 GMT (± 4hours)
daily.
Practically the entire region of study received precipitation on 8 February (Figure 7), with the Continental Divide serving
-48-
as the eastern boundary.
Most of Montana, Wyoming, southern
New Mexico and southern Arizona were dry.
Substantial amounts
of rainfall were received over southern California, with other precipitation maxima occuring over the northern California coastal
ranges and the Sierra Nevadas.
Minima in the field were analyzed
over the Great Nevada Basin and just west of Great Salt Lake.
A
0. 7 inch maximum was analyzed over the western Rockies, while
the eastern slopes were predominantly dry.
No precipitation
occurred in the desert area of southeastern California.
A cross-
check of the data reveals good agreement with the analysis.
Although the pattern of precipitation on 9 February (Figure
9) is not quite as widespread as on the preceding day, it still covers over half the area.
A significant increase is shown in the
central valley of California; where amounts of a few tenths of an
inch per day had been reported previously, now reports of 1 to 2
inches are common.
When added to the substantial amounts still
observed over the coast and higher terrain, we see that a tremendous volume of water was received in California on this date,
Of
the 337 California stations used in this study, 191 reported one
inch or more precipitation on the 9th, with 3 reporting over 4 inches.
The predominant feature of the 10 February analysis (Figure 11) is the widespread precipitation of 0. 5 inch or greater
-49-
which now covers much of the west coast, almost all of California,
the Great Nevada Basin and the slopes northwest of Great Salt Lake.
The southern California coastal ranges and the Sierras received 3
to 4 inches of precipitation in spots, and amounts of an inch were
again common; but the southeast deserts were still dry.
The great-
est daily volume of precipitation for the area as a whole was received on 10 February, while the volume for California was only
slightly exceeded on the previous day.
Several California stations
had over 4 inches of precipitation, while Challenge Ranger Station
(3929 N
12114 W) recorded a total of 7. 13 inches for the day.
The
analysis shows about 4. 5 inches in the vicinity of Challenge.
A significant decrease in the areal extent of precipitation on
11 February (Figure 13),
quite noticeable.
as opposed to that of the previous day, is
Heavy precipitation is confined to the southern
California coastal ranges and the Sierras, with several dry spots
in northern California.
Precipitation in Washington and Oregon is
light and found mostly over the western slopes of the Cascades. A
center of 1. 5 inches is shown in the southwestern end of the Great
Nevada Basin.
General precipitation in the range 0. 1 to 0. 2 inch
extends southeastward to about the middle of Utah, where it had
reached Colorado on the day before.
Although we have included only the analyses for the peak
-50-
precipitation period, by necessity, the rest of the analyses also
showed the dramatic effects of orography on the precipitation field.
Day after day, more precipitation fell on the coastal ranges, the
Sierras and the Rockies of southern Colorado than on the rest of
the area.
We will now evaluate the daily fields of estimated E-P, to
see how well the twice-daily observations of upper winds and humidities for the existing network of aerological stations can depict
the true field.
We make this judgment through comparison with
the observed precipitation.
It is well to mention first, however, that though separate
VI
/
,
,
and estimated E-P (the sum &
J +V9)
fields were evaluated, only the latter are included as figures in this
report.
In most of the 24 daily cases which were studied, the di-
vergence term made the greater contribution to the sum.
The
maximum magnitudes of divergence/convergence were on the average 3 to 4 times greater than the maximum changes of water vapor
storage.
During the peak precipitation period of 8-11 February, the
extreme values of \-Q
responding values of
check, daily values of
averaged 7-8 times greater than the cor-
I/t
JT/It
.
As a further order of magnitude
and
V Q.
576 (see Figure 1) were read from the analyses.
at stations 493 and
When averaged
-51-
Q
over all days, \-
TI/Jt
greater than
576,
-
Wit
was one order of magnitude
at station 493
and of the same sign (negative); at station
was just over half an order of magnitude greater
,
than
again with both means having a negative sign.
When comparing fields of observed precipitation and estimated E-P, one should remember that the analyses of precipitation
extend beyond the dashed boundary line of the eleven-state region
and are unreliable except within the boundary.
The broad-scale features of the 8 February estimated
E-P field (Figure 8) agree quite well with the basic pattern of precipitation depeicted in Figure 7.
Notice how the evapotranspira-
tion center over the Great Nevada Basin agrees with two'dry patches in the precipitation field.
The E-P field indicates that preci-
pitation exceeded evapotranspiration over all of California except
just south of the Mojave Desert.
The E-P field of 9 February (Figure 10) does a poor job of
depicting the observed precipitation.
According to the analysis,
evapotranspiration exceeded precipitation over much of the area
where precipitation occurred (reference Figure 9).
Especially im-
portant is the strong evapotranspiration over southern California,
with center of 55 mm over the coast.
As discussed in Chapter IV,
surface and 500 mb charts for that date indicate that had aerological stations been available upstream over the Pacific, a more rep-
-52-
resentative E-P field perhaps could have been obtained. In addition,
the moisture inflow as determined previously from the stream function analysis (Figure 4) was directly perpendicular to the Sierra
Nevada Range.
This was a pronounced orographic effect which the
present aerological network could not describe.
Although the estimated E-P field for 10 February (Figure 12)
does show an excess of precipitation over the Sierra Nevadas, the
pattern is broader and amounts are less than the observed.
Again
there is an excess of evapotranspiration along the coast and over
Southern California which does not agree with the observed precipitation depicted in Figure 11.
The precipitation patterns described by the estimated E-P
field for 11 February (Figure 14) agree closely with the broadscale
shape and extent of observed precipitation as shown in Figure 13.
The estimated precipitation over California runs roughly parallel to
the mountains but is much smoother and of lighter intensity than the
field of observed data.
The estimated precipitation is displaced to
the east of the observed.
Comparisons have been made between objective analyses of
observed precipitation and estimated E-P fields on a daily basis for
February 1962, 4 days of which have been discussed at some length.
Although there was often good agreement between areas of estimated
and observed precipitation, on the one hand, and between areas of
-53-
evapotranspiration and no precipitation, on the other, the correspondence was far from perfect.
a one-to-one
In Chapter IV we pointed out that
correspondence should not be expected as a rule,
since the divergence of water vapor flux represents a mean condition which is derived from 12-hourly observations of wind and humidity data.
In addition,we have stressed that the aerological net-
work cannot depict the true field near the boundary of the data and
over mountainous terrain.
The final test of the worth of precipita-
tion and evapotranspiration estimates, however, will be determined
by comparing observed and estimated precipitation volumes for regions of various size during the period of study. Before proceeding
to a discussion of the volume results, we examine one last field-the observed monthly evaporation.
C.
Monthly evaporation, February 1962
Daily evaporation-pan measurements from the limited net-
work of stations ranged from low readings of zero to a maximum
of 0. 46 inch (1. 2 cm).
Subjective analyses of daily evaporation
data were completed but are not included in this report. One problem in attempting to analyze the fields of evaporation was that no
readings could be taken under freezing conditions, thus data at
some stations were frequently missing.
The analysis for February 1962 is shown in Figure 15.
A
-54-
maximum evaporation rate of about 6. 0 inches per month is found
over northwestern Arizona, with over 3. 0 inches in most of Arizona
and the Mojave Desert of California.
Low readings of less than 1. 0
inch are found near Sacramento, within a region of less than 2. 0
inches of evaporation overlying the San Joaquin Valley.
These
monthly totals give a daily average of 0. 05 inch over the northern
two-thirds of California and 0. 12 inch for the southern third.
It is
interesting to reflect that the daily estimated E-P fields often
showed strong centers of evapotranspiration across southern California in support of the monthly evaporation picture.
D.
Precipitation and evapotranspiration volume estimates for
Areas 1, 2 and 3
Daily volumes of precipitation and evapotranspiration were
estimated for the 24 days ending 27 February 1962 by the method
described in Chapter II.
Water volumes were computed for three
5
separate regions, shown in Figure 2 as Area 1 (29. 07 x 10 km 2
2
Area 2 (13. 03 x 105 km 2 ) and Area 3 (4.05 x 10 5 km ).
Area 3
approximates the boundaries of California.
To evaluate the accuracy of the precipitation estimates,
daily volumes of observed precipitation were computed for the
same areas.
Water volume estimates of precipitation ( CP W/
), evapotranspiration
([*/
4
t
+
V-
+
), and
their algebraic sum (E-P)are shown in tabulated form along with the
-55-
computed volumes of observed precipitation.
Units are km3
Results for Arca 1 are shown in Table 2.
Totals for the
24-day period ending 27 February are also included.
Note that
although the precipitation was greatly underestimated on the 9th
and 10th, the total estimated and observed volumes are very
nearly equal.
Comparative curves displayed in Figure 16 show
that on some days the estimated precipitation exceeded the observed to average out these errors over the month.
The results for Areas 2 and 3 are shown in Tables 3 and
4, respectively.
The precipitation is greatly underestimated on
the 9th and 10th for these areas just as it was for Area 1.
Com-
parative curves of daily estimated and observed precipitation are
shown in Figure 17 for Area 2, and Figure 18 for Area 3.
As has been previously discussed, hand analyses for the
8th, 9th, 10th and 11th compared favorably with objective analyses for the same days.
Water volume estimates computed from
the hand analyses were graphed for comparison with the machine
results.
Although the hand computed volumes were of larger am-
plitude, their curves dipped on the 9th and 10th exactly as the objectively derived ones did.
Tables 2, 3 and 4 are shown on next three pages.
-56-
Table 2.
Water volumes for Area 1.
Feb.
1962
-Estimated P
(CESI/n -tV'%neq
Vt
-6.
-2.
-2.
-7.
-12.
-7.
-6.
-13.
-14.
-9.
-8.
-8.
-11.
-6.
-1.
-4,
-7.
-5.
-3.
-5.
-4.
-3.
-3.
-3.
Total: - 163. 14
Observed
Precipitation
Units:
3
Estimated E
C'S/4+-C
0.55
0.27
1.74
7.31
13.77
18.15
18.57
11.23
9.26
12.58
9.26
10.29
9.34
6.29
3.70
6.15
5.41
2.57
1.76
3.75
2.90
3.47
3.86
2.49
164.67
Km
Estimated
E-P
-5.
-1.
1.
-2.
-9.
-3.
-3.
-12.
-11.
-5.
-4.
-7.
-10.
-5.
1.
-4.
-6.
-4.
-0.
-4.
-4.
-1.
-3.
-2.
51.04
-112. 10
-57-
Table 3.
Water volumes for Area 2.
Feb.
1962
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Total:
-Estimated P
-2.
-0.
-1.
-4.
-8.
-2.
-4.
-10.
-9.
-5.
-4.
-3,
-8.
-3.
-0,
-2.
-5.
-3.
-1.
-1.
-2.
-2.
-1.
-2.
-91. 21
Observed
Precipitation
Units: Km
Estimated E
_./Ye.'
Estimated
E-P
-1.
0.
2.
-1.
-6.
1.
-2.
-9.
-8.
-3.
-1.
-2.
-6.
-2.
1.
-2.
-5.
-3.
-1.
-0.
-2.
-2.
-1.
-1.
0.
0.
1.
5.
10.
15.
16.
10.
6.
9.
5.
9.
7.
2.
1.
5.
4.
1.
0.
0.
1.
2.
2.
1.
124. 05
3
28. 26
-62. 95
~58-
Table 4.
Water volumes for Area 3.
Feb.
1962
-Estimated P
(U)J//C
Total:
+9
Observed
Precipitation
Units: Kin3
Estimated E
I/ltt+-7N
Estimated
E-P
-0. 59
-0.18
-0.19
-2. 67
-4.38
-1.41
-2.18
-5.25
-4.27
-1.10
-2.36
-1.98
-1.91
-0. 79
-0.59
-1.50
-3.23
-0.78
-0.75
-0.57
-0. 68
-0.47
-0.54
-0.48
0.00
0.01
0.94
4.70
6. 88
10.72
10.39
6.45
3.18
6.32
3.78
7.47
4.78
1.48
1.24
4.00
1. 68
0. 79
0.09
0.14
0. 79
0.64
0.70
0.12
0.31
0.29
2.53
1.28
0.48
2.12
0. 65
0.02
0.10
1.54
1.48
1.13
1.08
0.38
1.06
0.47
0.18
0.28
0.08
0.48
0.32
0.08
0.18
0.32
-0.28
0.11
2.44
-1. 39
-3.90
0. 71
-1.53
-5.23
-4.17
0.44
-0.88
-0.85
-0.83
-0.41
0.47
-1.03
-3.05
-0.50
-0. 67
-0.09
-0.36
-0.39
-0.36
-0. 16
-38. 75
77.29
16.84
-21. 91
-59-
Under ideal conditions where continuous perfect measuremnents of wind, humidity, precipitation and evapotranspiration are
taken over a large smooth area, the water balance equation must
be very nearly exact (<.
/at'7 -
d~if'7 ). As the num-
ber of reporting stations and frequency of upper-air observations
decreases, the positive correlation between the left and right sides
of the equation should decrease.
Imperfection in the observation
and analysis of the parameters involved also contributes to the inexactness of the results.
To test the hypothesis that, despite such
limitations, reasonably reliable daily estimates of precipitation
can be obtained for large areas over the western part of the United
States using the water balance equation, correlation coefficients
were calculated for the 24-day period in February 1962.
If we let x = observed precipitation volume (km 3 ) on a
given day and y = the estimated precipitation volume (km 3 ) for the
same day, then the variance in x is indicated by x
2,
the covariance
between x and y is x'y', and their correlation coefficient is r(x, y).
The statistics for 24 days are shown in Table 5.
pected, there is a significant positive correlation.
the correlations for Areas 2 and 3 are equal.
As was ex-
Surprisingly,
-60-
Table 5.
Correlations between daily
volumes of observed and estimated precipitation
X'I
:
X'
Y(1,3)
Area 1
Area 2
Area 3
26.0698
12.3849
10.8602
+0.60
21. 1660
7.0919
6.5036
+0.53
10.5691
1.9740
2.4309
+0.53
Since the monthly precipitation' peak occurred in California, pronounced orographic effects in that state should be reflected in the
curves of observed precipitation for all three areas. To gain some
quantitative estimate of these effects, the average direction of the
California water vapor inflow between 300 and 400 North Latitude
was measured by protractor from the daily hemispheric analyses
of stream function.
The Sierra Nevada Range is approximately
oriented in a 3300 - 1500 direction; an inflow of moisture from 240
would be perpendicular to the Sierras. Because water vapor transport cores are usually found at levels far below the tops of these
mountains, there should be a pronounced orographic effect which
is at a maximum when the deviation of the flow from 240
minimum.
is at a
This then is a second hypothesis which can be tested.
A graph of the daily deviations from 2400 of the inflow direction was plotted for comparison with California's observed pre-
-61-
cipitation; both curves are shown in Figure 19. The inflow curves
are not moisture weighted; they reflect the variability of the flow
direction only.
Notice that the direction curve is inverted, such
that the 00 deviation is at the top (flow perpendicular to the mountains) and 900 is at the bottom (flow parallel to the mountains).
The direction curve shows a peak of orographic effect on 9 February, coinciding with the maximum of observed precipitation.
Correlations which were computed are shown in Table 6.
Notation is the same as previously used, except 7
inflow deviation (in degrees of arc).
refers to the
The correlations are signi-
ficantly negative, demonstrating the powerful effects of orography.
Table 6.
Correlations between daily
volumes of observed precipitation and
deviations from 2400 of inflow directions
Area 1
Area 2
Area 3
X
26.0698
="
676.3889
21. 1660
676.3889
10.5691
676.3889
-85. 2899
-0. 71
-62. 3321
-0. 74
X''P
-91. 2782
YNE -0. 69
It has now been shown that there is a positive correlation between observed and estimated daily precipitation, with the highest
correlation occurring for the area largest in size.
It has also
been shown that an even more significant negative correlation
-62-
existed for February 1962 between observed precipitation and the
deviation of the inflow direction from a perpendicular to the Sierra
Nevada Mountains.
This effect is greatest in California, naturally,
but we reiterate that the abundance of precipitation which fell there
affected all three areas under study.
At this point it is reasonable to ask if there was a general
tendency for underestimation of precipitation in all three areas on
the 9th and 10th or if all the underestimation can be attributed to
California alone.
In an attempt to shed some light on this question,
Area 3 estimated volumes for the 8th-11th period were subtracted
from those of Area 1 and compared with corresponding differences
in the observed precipitation.
Thus volumes for that portion of
Area 1 which excluded California were considered.
The precipita-
tion for this reduced area was underestimated by about 50% on the
9th and 10th, where the Area 1 (includes California) estimate was
approximately 65% too low.
Thus we conclude that though the Cali-
fornia underestimate played a significant part in the overall results,
there was a general tendency throughout the region for such an underestimation.
To demonstrate the degree to which precipitation estimates
improve with area and time, daily means were- computed for Areas
1, 2 and 3 for periods of 3, 4, 5, 6 and 24 days.
These results,
63-
for estimated and observed precipitation, are shown in Table 7.
There was an obvious dampening with time of the day-to-day differences between the observed and estimated values.
The Area 1
daily mean estimate for the 5 days including the 9th and 10th (6-10
February) differed from the mean observed value by but 39%.
For four consecutive 6-day periods, the Area 1 daily mean
estimates agreed with the observed precipitation within 6, 14, 14
and 32%.
A comparison is shown in Figure 20.
Estimates of
daily mean precipitation for Areas 2 and 3 also improved when
longer intervals were considered, with Area 2 showing just slightly
better results than Area 3 for 6-day periods.
shown in Figures 21 and 22.
These results are
Daily mean estimates computed from
the total 24 days of the study were much better, with differences
between means of observed and estimated volumes of 1% for Area
1, 26% for Area 2 and 50% for Area 3.
As the accuracy of the mean estimates was greatest when
long time-intervals were considered, daily mean precipitation
depths were computed from 24-day totals and are shown in Table
8 for each area.
Units are inches per day.
Included in the table
are daily mean evapotranspiration estimates.
The evapotranspiration estimates are higher than February
normal potential evapotranspiration (PE) computed by the Thornth-
Period
Feb.62
4-6
7-9
10-12
13-15
16-18
19-21
22-24
25-27
Area 1
Observed
Estimated
4.04
0.85
13.08
9.08
13.02
11. 63
10.71
8.87
6.44
6.70
4.71
6.02
2.80
4.51
3.52
3.27
Area 2
Estimated
1.32
Observed
0.45
4.86
7.93
4.55
10.63
3. 89
3. 83
2.02
2.01
4.12
11.07-
8.06
3.97
1.02
2.03
Area 3
Observed
Estimate d
0.32
0.29
7.43
2.82
6.67
3.90
5.86
1. 81
2.50
1.10
2.16
1.84
0.34
0. 67
0.49
0. 50
4-7
8-11
12-15
16-19
20-23
24-27
4.90
9.96
10.36
6.27
5.41
3.89
2.47
15.43
10.35
6.37
3.37
3.18
2.08
6.11
5. 80
3.59
3.12
2.10
1.74
13.18
7. 72
4.51
1.91
1.94
0.88
3.30
2.43
1.20
1.33
0.54
1.41
8..61
5. 19
2.88
0.68
0.56
6-10
11-15
16-20
21-25
7.23
11.03
6.45
4.51
11.91
10.52
6.18
2.89
3.99
6.67
3.98
2.33
9.86
8.26
4.49
1.47
2.15
2.99
1. 60
0. 65
6.73
5.44
2. 64
0.49
4-9
10-15
16-21
22-27
6.56
10.25
6.36
4.02
6.96
11.86
5.58
3.04
3.09
6.24
3.86
2.01
5.54
9.56
4.05
1.53
1.57
2.86
1.47
0. 58
3.88
6.26
2.33
0.41
4-27
6.80
6.86
3.80
5.17
1.61
3.22
Table 7.
Daily mean precipitation volumes.
Units: Km3 day~ .
-65-
waite method (Thornthwaite et al.,
1964) but in California agree
amazingly well with evaporation pan measurements depicted in
Figure 15.
The estimated daily rate of 0. 07 inch per day was used
to compute a monthly total of 1. 96 inches for California.
The area-
average of evaporation pan measurements is about 2 inches, as
can be seen from the chart.
Tabulated normal values of potential
evapotranspiration (Thornthwaite et al.,
1964) show a July maxi-
mum and winter minimum for each of the 11 western states.
The
February daily mean PE for California was 0. 03 inch day, less
than half the estimate achieved in these results.
-66-
Table 8.
Daily mean precipitation depth.
Units: inches day~
Area 1.
Evapotranspiration
0.03
Estimated
Pre cipitation
0.09
Estimated
0.09
Observed
Area 2.
Evapotranspiration
0.04
Estimated
Precipitation
0. 11
Estimated
0.16
Observed
Area 3.
Precipitation
0. 16
Estimated
0.31
Observed
Evapotranspiration
0.07
Estimated
-67
VI.
CONCLUSIONS AND SUGGESTIONS
FOR FURTHER RESEARCH
A. Conclusions
The time saved by using objective analysis procedures during this study were a definite asset, allowing the author to evaluate
far more information than would otherwise have been possible, including daily fields of Northern Hemispheric water vapor stream
flow; and for the western United States, daily fields of water vapor
storage change ( aV/It ), flux divergence ( V7Q), their sum(es#IV
timated E-P), and observed precipitation.
The analyses of precipitation data, using an approximately
25-mile grid mesh and 732 reporting stations, gave both reasonable
and useful results.
The analyses depicted rather well the observed
conditions, including orographic effects.
Though the objectively analyzed E-P fields compared favorably with hand analyses for a 4-day sample of 8-11 February 1962,
results indicate that neither method is able to produce consistently
reliable estimates of E-P on a daily basis over the western states,
even for areas as large as 29 x 105 km 2 .
In all, 24 objective
analyses of estimated E-P and observed precipitation were compared, covering the period 4-27 February 1962.
The main factors which contributed to the unreliability of
daily estimated E-P are as follows:
-68-
1) The lack of data off the Pacific coast, which caused
unrepresentative fields of divergence along the western boundary.
2) The strong orographic effects prevalent throughout
the region and especially in California.
The aerological network
simply cannot depict the many irregularities in the E-P field which
are caused by mountains.
3) Sampling errors caused by the averaging of 12hourly observations to depict conditions for an entire day.
Contributing factors are the limited number of stations in
the present network, and dipole effects which occurred in the objective analyses near strong centers of evapotranspiration or precipitation along the coast.
The latter factor is related to the lack
of data upwind over the ocean.
The atmospheric water balance equation for obtaining spatial and time mean estimates of E-P is
(
+(.7*Q
=
E-P> The left side of the equation is evaluated from measured
winds and humidities.
In this study the estimated E-P value at
each grid point on an approximately 25 mile mesh was multiplied
by its surrounding grid area and summed according to sign, giving
total volumes of minus and plus E-P.
The total minus-volume
within a given region was accepted as the lower bound of the estimated precipitation; similarly, the total plus-volume was used as
the evapotranspiration estimate.
-69-
With the limited evapotranspiration data available, it is impossible to have good independent tests of evapotranspiration estimates.
With widespread precipitation and with measurements from
732 stations available however, it is possible to evaluate the precipitation estimates.
The assumption is that since both types of esti-
mate are made from the same data and analysis, they have the same
degree of accuracy.
Following the described procedures, estimated and observed
precipitation volumes for three different sized areas were compared for each day during the period 4-27 February 1962.
The
largest area (Area 1) was 29 x 10 5 km 2 and included the eleven
westernmost states.
Area 2 (13 x 105 km 2 ) included California,
Nevada, and- parts of Oregon, Idaho, Utah and Arizona.
Area 3
(4 x 105 km 2) bounded California.
Although precipitation estimates correlated significantly
positively with observed precipitation (+0. 60 for Area 1, +0. 53 for
Areas 2 and 3), more highly correlated with observed precipitation
was the direction of water vapor inflow.
A flow of moisture from
2400 is approximately perpendicular to the Sierra Nevada Range
in California; thus if orographic enhancement of precipitation is important, any deviation from 2400 of the inflow direction will be
negatively correlated with precipitation amounts.
Correlations de-
-70-
ter aI ed from this limited 24-day sample were -0. 74 for Area 3,
-0. 7 1 for Area 2, and -0. 69 for Area 1 (correlations becoming
less significant with distance inland). Thus the tremendous effect
of orographic uplift is clearly shown.
The results of this study agree with Rasmusson's finding
(1966a) that the accuracy of E-P estimates is best for large areas
and long intervals of time.
The daily estimates we calculated for
the western states were not consistently reliable when compared
with daily observed precipitation.
On the other hand, when the
daily volumes were added and averaged over longer periods, errors
in the estimated field compensated each other; and we obtained decidely useful results.
Following such a procedure for the 29 x 105
km 2 area gave reasonable results for periods as short as 6 days
(difference between observed and estimated daily mean precipitation averaged 14%, max. 32%).
The daily mean precipitation for
24 days was within 1% of the observed.
The evapotranspiration es-
timate of 0. 03 inch per day was probably just as accurate.
The 24-day precipitation volume was underestimated by
26% for the 13 x 10 5 km 2 area and by 50% for California.
The re-
sults suggest that reasonably reliable mean estimates of both precipitation and evapotranspiration can probably be obtained for the
13 x 105 km2 area if periods of a month are considered, while
areas as small as California would require at least a season to ob-
-71-
tain reliable daily mean estimates from flux divergence fields.
The California mean estimate of evapotranspiration for
February 1962 agreed closely with evaporation pan readings.
The
daily mean estimate of 0. 07 inch (average of 24 values) was higher
than the potential evapotranspiration normal for February, of 0. 03
inch per day.
The potential rate, heavily weighted by temperature,
reaches a maximum in July; however, the studies of Colman (1945),
Drinkwater and Jones (1957),
and others have suggested that evapo-
transpiration is more closely related to the amount of rainfall than
with temperature.
Thus, we conclude that even though the daily
mean estimate of evapotranspiration for California is probably off
as much as 50%, it is as representative of the true rate as are estimates obtained through conventional techniques.
Daily mean esti-
mates taken over intervals longer than 24 days do considerably
better.
Comparisons have been made between estimated and observed values.
It is well to remember that just because the monthly
estimate of precipitation for Area 1 was within 1% of the observed,
does not mean to imply that the estimated and true precipitation
values agreed that well.
The observed values themselves are
thought to underestimate the actual precipitation by 10 - 15%.
Another objection which could be raised concerns the reli-
-72-
ability of flux-divergence methods when evapotranspiration is
much more significant, say over the eastern United States in summer.
In a pilot study already mentioned, a 29 x 105 km 2 of the
eastern United States was considered for June 1967.
For the 3-
day period ending on the 23rd, the estimated E-P field gave daily
estimates of precipitation which were larger than the observed
by an average of 22% (the worst daily difference was 32%).
If we
accept that precipitation measurements are moderate underestimates themselves, the daily results obtained under summer conditions are quite reasonable.
In summary, evaluation of the limited 24-day sample in
this study indicates that when daily water vapor flux-divergence
estimates of. evapotranspiration or precipitation are averaged over
periods of at least 6 days, they give reasonably reliable results
for areas as large as 29 x 105 km 2 over the western United States.
Even better results are obtained with longer intervals of time. At
least a month is required for reasonably reliable daily mean estimates for a 13 x 105 km 2 region, and probably a season for areas
as small as California (4 x 10 5 km 2 ).
Even so, the evapotranspir-
ation estimates taken over a month agree with evaporation-pan
measurements for California.
Thus the hydrometeorological ap-
proach to estimating evapotranspiration and precipitation for large
areas over the mountainous western states can play an important
-73-
supplementary role in the study of the hydrologic cycle.
B.
Suggestions for further research
Since the methods used in this study received their sever-
est test in the western region and yet still produced useful information, it is suggested that a similar study be conducted over the
eastern states where the terrain is smoother.
In particular, close
cooperation between a hydrologist and meteorologist in the form
of a joint study would be highly beneficial.
In this way, a compre-
hensive study of all phases of the hydrologic cycle could be studied
for regions of various size, as small as river basins.
Methods developed in this study could be applied on a hemispheric basis, adding up daily estimates of precipitation and evapotranspiration to give more accurate longer-term values.
Such
values could then be used to increase the knowledge of the energetics of the general circulation of the earth's atmosphere.
-74-
Figure 1.
Objective analysis region and distribution of aerological
stations.
-75-
Figure 2.
Water volume integral areas.
L\1
C+
0
0
CD2
C-.
co
SCO
CD
0i
Cd
zs
4-40
0
4-4
Cdc
C)
Co
OI
o
a)
p) I
0
P) C1
0
C.)
a)
r4
C)
SOLIDUT :sIlunI -961 Sxenqf
a'-
0T- 0-TCIT0-Ta0-TaTa.
0T- o-
~~~a
a
-a
1.-T.TT.-T0--0aa
a.
..
8 'UOTj-ejTdTZO;jd PaAJasqoJ
T0- 0T-0!a'
0
0.
.'.. a.
0T0.
TOTrIa'
0.
.
T1
.
0TT. .
a-
-L aJfl2L!
0TT.
1.
0.
0
a- -4-a
iITT
ITT T T U?
YNTTIITITTITTO;Ia'
TTTTTT
ITTIT IT TIII
-E-oTTTTTITTTTTTIIITTTTT tITITTTTtTITII
*
*
-
0
-
a*-
a*- 0-
'-
a'
IT
a- a.. . .
.
ITTITT
..-
~
nan 3N
-o
0.
T~~~TjT~lTTTTTTT
O~27
a..
TIT
ITTTTY
TT
TTTTTTIIT
IITTTaTTTI~aTTTTT
ltTTITTTaTIITTIITTa
ITTTITTTTITT
"ITT IllTTITTTTTITTTTTITT
1. 0.
TTTUU
IT?
T UTMI'll
TTUTT
TITITTTTITT
TTTT
i
T"T
.TITI1aa
V,
".11
ta.
TI
TTTTTTTTTTTTTTTTTTTTTITTIITTTTTTTTTTTTTTITTT
TTTTTTTUTT
0a
a
0.a.
a.-
O
T 0'
'lI-
a'-
T.-
0.
a. TITI
- a
t
-
I
M001a.
a
aAcI '
~
I
a Itj TT
TIIITl I TIII I;TT
---lt~SIT:m ITiTIT I
10 .
a
--
-
1'' .
.
1111 I
I
.
1.
6
1V
IT
. .
.
.
.
Il
i TTITT
iiTTTTTTITITTTTiITTITTTTTTITTTTTaaII TIITTITITRTIT
iI IITTTTTI
TITT aa
I~TTTITaI aIT
I I TIT TTTTIIITTTTYITTIT
a
I~
hI
a
a~ P
T
1 1111TINN
-08-
-81-
Figure 8.
Estimated E-P field, 8 February 1962.
Units: mm day
1
0
C.- 0.-
0.-
0.-
*Z96T S-renaqaA 6
0.-
C.-0.-
a-
0
aT
S-ep SaLI;DUT :SjTufj
UOT
p
.j-ejTd-paad aAlasqo
0.-
0.-
v
1-
0..
0.
0.
0.
0.
0.
0.
0.
0
6 ain.2-ij
a-
0.
0.
1.
1.1.
D.
0.
0.
a1.
0.
0.
0.
0.
1.
0. 1. 0. a- 1. 0 0.
1.
-0. 0
0
0.- 0.
0.-0.-
ad_0.-a.- 1.
1.
0'
.TttlTttTTTT'
I.
I
tTTTTtITTTT
1.
0.-o
0
a-,
a-
0
0.
0."0
0.
0.
0'
1.
a'
0'
1
0.-
1.
1.
T
1
1.
0
1.
1.
0.
1. gm a,
a-
V
I.
V,
0.
1*- 0
T'
a.
0.
jP) 0!
1
v
ITI ITTTIT
Till
vViviv
."IT
!11. 1. 1.
I
a
8.\a-
TtTTITT1
ITI ITITTT
TTTTIt
Till
JITTT
!, T I IIT
t
TTTTTTT
TITTiTTTli
*
'hITT
'TTTTTTYTtt
IT
I
1;it-IT
1IT;ILTI
Tlkti
L
'311TIll
_ITTiTvl
-I tTkTiniTTytitTTT"
r
itii;TTj;TTiITitTTITtT
I- 1- 0. 1- a- 0. 0. a
TTTtTTTTTTTITTTTTTITTTTT
"TVITTVITTITTTI-I
I. I.
.
G. 0. D.
1
0.
0.-0.
0
IT!TTTITTtTTT
0.- 0.-a
01
0.01 a- 0. a- a
0,
1..
4a.-0.- C.-
TTTITTTITTTTTT"T
TtVTTTT
I
0'
D-MP11
1.
0. G.
cn
o
0' 0 0.
C. 0.0- -0--0
TITT
o,
M
TIT TTTVITTTTTTY
C.-0. 0.-84
4,
C.-0.- 0'
-//a
. .....
Akc)OJ
t,
a-
0.1* - 1, 0'.
- 1; 0.
IV
0.-a.IT -I will
if
I
7?ppb
ttl*
*I'I 'I
'Till'Tit
9N;_.
'E itNiTlti
Till I TTTTTTTI
T!I ITT!ILTT
I,
MIN
vv T_IT_
_Till
_TTTt
if
I
T' 0- 0
IT,if ITS
'I Till
If TITTTITTTITTTITTITTITITTITT
TITIT
TLH!TTTT IT
----ITTITTTTTTTTTtITTVITTItTt
IT
Till
Till
liffiiiAii4iiiiiiiiiiiiiN
Tiii"iii
...i?
,
iiikmf
-iiiiiiiMiTiiiii
TV
I 17
0
Tillm
TIT!ITIT!Tlt
ggTiiTIT
1
11
0.0 , a-
0..0.-C.-
o,
0.-G--
1.
MIT
Till
III I
TIT
I
;ai
ITTITTITIT"
I
i;TT;i4TITT
ITjj4T!!TTrt;li;MI
TTTTT
Till
ITTITTTTTIT
MITI
IT
It
TITAII I I"
ITT
o
0.A.A.Aj.
0
0
T! IT TITTITTTTTIT
II
Vviiiii
..............
I
I1.
o
-1
------- vy
ITTITIT
ITT
IT
If
VVITY
Till
T-T6-
g'
-fig--if
Willi.
if-!Tfgv
-Tivim-ti
t
1
g-
2- C* g' 0
VITITITITTlift
IT
"T"T
..........
......
if
I
9.
IlTR
--tvT
1. 1. a-
........
if
Till
t
ttlttTTTTtTZ
TTTVITTtiTTTTiTTITiTTTTi'TT
ITT;bITjiTTITTh;jiTTTT
if
--- -------
!.
C,
TTTITTITTTT
I
'I
a,
a-
9
I
I TIM I I
ITTTTTTItTTTT
TtTTiTITTiTTtITITTTI
--- -----------------
TTTTT
MIT
T"T I Ill
IT
11TITIT
TtlITTITTV
9;,,
gttTVTTTTT'
IT
0.1L.
.1
c
g.v*
c I PT
t-
g.
g.
TTTTTTT
"
t-
I
tTVTTTITT
TtiTITTi
Win-
.88!.
I
p'VTT
1 B-T
8=
.!
II
TX1
1 11
1.
I
a
g.
I TTTtTTv
I
0.
-----------------
it'
M IT I
.....
-------
iiiTTTTITTTTTTTtTNiNijTTj
TtTtt iiiii-itiv-uiiiiiiii
I
iii
*
T'ImilmTT
_T!
I !TTtVTTTlTTIIT;TT
TVITTTTTTTT
I
i;Tiii
MT
1:
-- TT;'TTT
C.-0.-0.-
o".
-10-
0
0.-
TITTITIT11TIT
TrIttil
I
TTITI
TIT
I
TillI I IT TITIT
ITT1!1!!
Tltttt.tt
-!I
IV TITITVVVTITTTI
"TIVIII
I
if?
!--v
I
A.
I'
C; i*
,
0.
igI!'
------ - -V V-V!-VI ifIMIT" !fill TV
i-TiitTTITT;iTTTTT'
iitlii
iiiii
ItIT
tit
I
1.-0.-0-
"Rij-
iialiftit
TvTi1hHkTIIjagTTT
it
0.-
a,
0.- 0.-0.-0.-0.-
IT IT TITTITTITT
Tlfj -
TA C. 0.
Tw
ITT
tITIT
ITT
TTTTTTTTt
I If
ceecce 199M
A*c;W r
I ITITITVITTTT
IT
ITTITtl
1TTt__ _TTTT!TT__
_TTITTTTT!TT
T!TTTTI
fut q
a
c
ITTTITI
Me
TiVITTi
TTTM
0
ITITTITInt!
TTITTTT
TITTIt
TITT
TV-TITIT
ITT H
1
I
rl IM
;1
11
I
-
1*
-----------rivi
! 'fit
tV2
iiiiii
HAI!iiViTTV
D.-
amar
q-T
Tim
TIT
ITT T!TT
I I IITT
TITTITt
fit
0
TITMIT
0.- VINT
0.-ej-
--
1.,
t
0
C.-0.
0.-
I
0.
0.
&
a.-0.
0.
0.
a-
0.
a
0. 0.
1.
0.
a
0.
Q.-0.-a'
0.
7
ITT,
U
O-T I.
R.88aftega
iiiii
Till
tITIITT
ITT
c
9*12
1a
I-_
t
6
0.__o-___i
-- - - ------W"Miii If~ TITITt.i
Tillt TITITTITITT
0.
0
1. 1.
..........
Tit 11mvVTTI
ITTITTT
t4- I,
aggamaggame
;"T"C'T
1w9m.
argaggaam
I
--Cc
Tywyll
TV
I
1.
-0
___9
I'
1'
6-
ITT
TTTTTT
t' Ir
1.
MITT TTITTT
IT
IT,
ITITTITT
0'
g.
TTTTTTITVTtTIT'T
TTTtTTItTTTTITT
I I T,1
Till
9. IngTI.tIt I I
9
TV!t
TItT
TTTt!TtTTI
S
*2 - 1
0.
IIIIIIIIIT"T"Ill,
Im"'INTiming",
1. 1. 1. 1. 1.
ItTIMITTITYTTTIMITTV
TTTTTTTTTTITITTITTTTTTI
.
1. 1.
1. C.
TV, ,
I'll
IITTTIIIT
S!TTTTII
ITIIIIIIIIII
..
...
/ II..
1.
II
VI'MVITTY
ITT
I!% .
! I TITTTTTTITTTT
.
1.
I
V!TTTI
TitT!TttTT!TTTT!ITIT!TTTVT!TTTtt!lM
1
1. 0. 0. dDt7
1
V!TTTt!l#
111'1 TTIIITITT
TITTTIIIIIIIIIIIIITMITTll
Iff" TITTTTT
TTTT
TI
TillTTTITTTTTTTI
ITTTTITTITITY
IT TITTTTT
II IT
ITITTTTTT
I,.I ....
I.. IT,
IV-
0.I
N
1-
0-10'
-
S.TII,1!ITITTITI1T
C-tI'T
am
saaarm
2
mnanze
9't1 3 9-11
I.
TITIT
0
gag"ZUZ
I
V 1 237'."
*-1 1 1ammag 190299anaural
"M,
"NaHm!"ag.
G' Z' ?-I1
It
I
It
1.
'a,
anagal
MITI?- I
IT It
C.
t.Ito
C. C. a, 1.I II'll
Till MIT TITTY
I ITTItTlITTTTTTTITTTTTTTTTITTTT
ITill
111" 0
TTTTTTTT
ITT
ITTTTT
II
itI
I MITT
I I TTITTIT
I 1. 0.
TTTTTTITTTTTTTTTTTTTTTTITTTTTTTTTTTTTTTTTTI
ITTillI ITTITTITT
Tit
TTTtTT
I
TTTIT
TITTTY17ITTT
0
0
C.__
-2
TTW
TIMMYT
M411
I
IT
....
I'
It ITTITTY
ITTTTTTTTTTTT
IT
ITI.11 I1111ITIMIll........
""IT'
Rlll'TTT
11 _. ..
T. 0.
1.
1. 1.
1
1. 1.,
-_
9- 9- L' L'
ITTITITTTTTTTTT
TillL' IL' I'
ITTTTIVIT
it IllttTTTTtt
TTtTTTITT
SIT
T7TTTTTTTTTTTITTTTTt'TTITITIT
9.TTSNIT
S-TT
2.-1. ITT
... ITTIT
I
I
I.
II"
13TTIVIIII Ift"11,111T,
TTTTTTITTITTTTTTtTTIITTTITITTTTTVITTTI
TTVITTTVIITTTTTI
ITT
TITIT
ITTT I 12]3tTIT
TITT;TIT
R
Till T
fit
0.
0.
NITT
I
I
IT ;114ITTIT
I..
ITTITT
TIVITIMI
I
I.
1.
1111TTTTITTIT
ITT
IT
Till .1
TTTTTITTTTTTTTI
.?I
MITTIVITT --ItTUTT III
itTITTTTITTTTTT
0.
D-M
ir-
fec
1
0.
t
VITT
I
T
0.
I
VMT
4.
11
0.
a-
9-T
covegfggfefw
M
1 2an 6
....
iINTil
ITTjVj
TTl!!!!;FT!!!1!!!;T1
IT
I ITT
0.-0.-a*-0'
I
0.
0-
0
0'
Till M
0'
=
-
0-16 1
9.1
c
ATTITiTNdITTTITTTIIZTITTVITTTT,,, if
AW Assvi*")
... II.... MIT
-------r.
---------Niiiiiiiiiijfiiiiii
iiii
ii !y4w
olazip
-
0.
;iiiia
0.- 0.-0.- 0.-0
0.
0.
0.
ITTI
IT t ITT
nITITTtITTITT
T1.
0'
cc
cm
rum
1 9-8*-1 G-T_
t-t0-1
tem'suct
zalm
- -----
9-T4
gam
jTTTTTTT'TjT!TTT!tTT
TTT!TIT
-------------
10. a. k. a.or"IT
0.-a-
1.
9
fill
I.0.
- , 0.-a.- 0.-
1 I-T
tITtTTTTTtii
__:7
iii-M
?_
2,MI
_T4
MITI,-TTTVITTTTITTItTiii'
i
iiiiiiiiiiRkiTt
II
I?
0.
a- -0.
I.
I
0. 0. 0.
?ITTTTrTTTf
TTTTTtT
I
-No g .
0.
ttITTTTTTT
-Ttv"T
ITT
m
0.
0. 0. T'
1!
0. 0
0.
T;
ITTITI'M
T111MIT1.11
TTITttTTTTTITTTTTTTTTI
TIM
.
- __1
-,I,
TitjTjjtjTTttTTTTTITTITtTTITT
ITTTTTTIITT
ITT
TTTTTITT
TITM TITTITTTITIIII
I
0'
a-
a-
IT
0
0.
0. -0.
-83-
Figure 10.
Estimated E-P field, 9 February 1962.
Units: mm day~1.
.
-
--
--
:Z961 Sieaa
- -- -- -- - -- ---11
0.-
D.- __o-- o--
a .4
o-18--
o
a-
-A-- 0.-
saqz3UI :Sl.Tua
01 'Uo-r-eTdT~ad pa~aq
*
-Sp
o.
o--
o--
Q.
o-
ci
D.
a
a.
a
o-
o-
0'
.
o.
I.
0'
o.
G'
.1.
o.
o.
0'
0'
a
D
0'
0'
8-
D.
0'
.
.
1..
Sa~
a.0
a-
0'
0--
a-a--
~
a. D. a o.
0a-- .--
aC.-
0
a-a.0
a. aC..
0
1-- o
1-
-
o
D. Q.
'a-8-/o o
o-o--a-o--
P. a--a
.
~ ~~~ ~ ~
_~00 -
7bS ,
~
~- ~
~
:z
o
-
e-
a0-
a
a-
0'
0
a--
-
-
-
a
G-MD(;11
D.
o.
D.
00001
o.
o
D.
o
a-
0.
-a
a a a
-a
a,
-NW-.
'i
oloano--10100a1000001
~ ~ ~
~~~~
aa0aooaoooa
fIl00l
Iaoaoaafoo0a~OOO~OaO-'M1
-a
a
- 0000
100t
00-0-aOOOO
aaaTa01001
IT00000-a0---aOa~a
"T
-,0I1000
ITT!TT!"T
a-.
. . aa1aI
. . . a~ll .
.
ITo-alloo
_______
a Ia
a0
oao
9a 9a0--0aoaa
ByaaTI
aa
coa
at
-
.I
a-
a
.
- a'
-
.
9
.
ay 07 a
0.-a D.$0.
--
0.- , F----
a-- a -
.
.
.
-Jobaoaaooooooaaaooooaao
Pao
u
ITa.;
.
.
.
;Q
.
000
.
.
.
.
.
A7o.
I 8
A~
"at
ta
~
al
.
.
T
-
.
a
a
000
m
a
0
ccm
TaT~
faitlyaaa
000
a
0000.ta
-
6.
a-
01
89a
~
zaaa
mooA.:
.N
010.00
10
'lOT9
~~~
01
?101100000001000?0010000
V 00000010
a
D'
o.
0-a
-a
0--
~
a--T a-Ta
a
-
a
a
-
0
D, o* c, a- a- c
0. a-
~
~
a a
.-
aa
oaaoooaooaoaaaafoaoaaaoaoaao
~
~
A Iiaaoaaaaaoaa
jaaaaooaaoaaaaaaaoaoaa0aoIaaoaaaaooaoaaoaayfT~r"!ttlTtTTTtTa-~~~~~~~~
iti
I-- ---------
~
0a
a-aaT--aaaaI --
D'
o.
o o. o. 1. o.T D. 1.
I.- D.-I1.
o.- a- o- o.o.o.-c.-
*a-
0.
0.-.
/
~
D. D. D. a- o- o
a- o- o- o G. o- o- a,
a. D. o. o. o. o. o. Q
--o-1
a
a.Bo
a.
0-
0.
.aja
0a-
~
a-1
a-
a
a-a
~
.-0.a0. a- a a a
a
-10-000110
4oaooaoooaaaoaoaaaaoooaoaaooaoaaaonaooaraaaaoaoaaao
6
a-
~
.
-oo-ooon-o
0. -;aa
0
0
4-- a-Ia-T
A
.1I1 ;Jfl2!RIf
- - a, 91a, ,
A
I
IA
I
D-
I.- o.
o - o-A, *- e- e
ot
a- .-0 a-CAa-apaFa---
I
--
-
-a
*
0 a
I
0 a-
~
a
Neff179o.- a-/-L-.-A--.
-4 a- -
o.11 01.
~~~~
000~
001
.
910000
tL
000
.a.
.
.
.
01001000100
0110010001
0111IT
IT
-000001
0--I-
1
0111,0 I
TV10
001
O0100001000a1001.
a
;a
Ta.NT;TT
aT
010
tTt0T
9
PJa
,11.
a
..
Ma?..
0.
0 0*---00
I
-85-
Figure 12.
Estimated E-P field, 10 February 1962.
Units: mm day .
0
0
a--0.-0r-0.1- D. 0.
.- 0-
.
*Z96T iSxenjqqa
-
00-
0.-
-0 0.-
W_ C' 1
Xep
S~qZpui :Sjiufl
11 'uoA-elTdioaad paA.I9sqQ
0-
0
.
0
0
1
1.
1
.
a
.
0.
0.
0
1.-
0.
-
0.-
-0 ./
0.
0.
a.-0
0,
6.
.-.
0.
0
0.-
.
~
1*0-
0.
0~ 00
0 a
~
~
VIA
I~
0
-e
0.
anIT
a-
0.
0-
1~ - 1,
0.
0
0
-
--
---- -~ --
---
1
0-0
04
4.
0
0
-
-
~
0
0
-
-0-
~
0
~
'*
~
-0
0 .0
0(.1
l
MI01III
-
ti011001lI000010010100100000
. IT
CI
~
*
.
-'--
0
~
I-
~~~~
*0-0- 0-0
ei
I00I*0I-0I.
~
eh
~
-0-0
0.
0
~
~~~
0.-0.
0.- 0.- 0.
a-
-0.-
0.- a'-0.-I-a
-0'-0.-
0.-
-
0.0
0~~~~~~~~~~
a--/
OTji?!40
0
0. 00 0 0~.o~o*01.0 0.- 01-a
t00001100001001TT
ItiOOf
1
91
00
0-
91
TUITTIT
G.
IT
TTTTTTTTTTT
Mill
T'll"T
""If
I
I I
IT
TV
0-1
-1
!TTTiiiijrIiiiiiiiiiiiiijifiTlift-Tit
IT
Rk TiiiiiiiiiiK
101!00110j000o0_Y00001To0im1 __
0,
o+{
0
0.
0
0.-
00.10000~~~~~
-
v
-o~
dlb90fooT;l..o0000010
I 0A
-
-
.
.
gam0
~ ~~~~~.
00000~
o0
O.
-
.
-
10001
oI o -
.
I
100101
0000000000
0
00
oooooooooooooooooooi
-_01
0
0
A*0j~~
fit I 0T10.1
0.
IT
-0000
-------00.100
evi
a0
00
-.
1.
0
----
/~~~
I
~
~
-0
0.10
0.
0.10~oo~Aoooo
00010001
1'T 0
0
0
I
0
ITT
. ..
. .
.
.1.. .
100 0001011001010001
Tm
001
.
.
1001010101
1
0
.
___
00
V00
-
0f
It
-
-
-
; 10,47MMIT
0000000000010101100
t-:1i ---------------------------------------tITTTTTITIT
IT T-iii
TITT!!TTtit
IT
4 tTiT,
0. 0.b
o.-
0.
...
C
0~0~
0.'10.
0.
a.-
I.
It
'
- ITT
N JT!TtTliFttl'tTTtt;TTYTiITTTiJT;&YT!T!
TJ!T!iTTy1i
!_I tTiTTTfiTTITfStTTT%!!TiTIT
__JTTTT'tTI;TTTTT
I.
Ik
ir.
-0~-0-0.0
0
0a
a-
0'
.0
0-i.0-01~0i
0.- 0C .
0.
0.
a-
0
0
0
'
0
'
0.000
'
0.
0.
0
0.01
0'
0.
0
'
0
0-
.
.
....
.
00
00
~ ~~ ~ ~ ~~
~ ~
0.
w
-01-
.
I
'M
.
0.
0.
0.
~ ~ ~~
'0'0'
0
i
a-M
0.
0.-
0
~
~
0
1
0'
01
.
G'
a~
0
~
~
00'
'T..
0
1
.
'
0
0'. 0'T0
I.
-0-
0
11
~
~
0
1.
I
0
1.
it
TTTITtTT
TTTTtTTITTTTTTT"TT
I
I
TTjTTTTTT..
IrTTTIIT@l
I
p4TS
TIT",
0. 1.
0.
0. 0
0
W
IT
o
101100100
1-
.
-1
'T'0
0/
IT
I?
fi
0
~
~
00
-'--.
.
I
1 WTT
0 .
0
0
~
~
0
0--
' .
00
0
'
I'__
~
~
0.
0
0.
T'
IIITIT
0."
-
o I
0.
0.
.
.
.
.
.
00
.
.
.
.
0'
0
'0
00 0. 0.
a
01P
0.
'
ii
P'
~
0!
l
-
0
'0'0
I-
~*
I.o
Of 01.10
0
?IT 0'
I-
0'
0
0
I-.
T' 0P
~~ ~
~
0
0
0
01
0
0 . I
!I
T
I'
a'
-98-
-87-
-?-59
.2
-1.
-1.3
1.9
l'1-19. 117-1-6
--
-.
1..
-14
1.5-1
-1.7
-1.7
-1.5
-6
-~
e
.2-
1..16
1.7-1.9
-17
1.
e3
1.1
.2-1.n
-.
-.
-1.
2
1-7-1.
-16
-. 0-2.2
-1
1 -~g
1.
I
-.
15
5
.
-12-.
8 -1-9-1.6-. 7
-'.7-16-1.-1.5
-1.8
-1.9
-1.5-,
-20-.
--.
..
:
.7
**"18-2.0
-2.2
-2.2
-2.*I
- 2 -2-3
-2.2
-2.3
-2.9
-3.5
-9.-2.2e5-2.0
-3
-9.5
-2.6
-5
-2.6
-9-3
3.-.
-
0
*6-2.2
-2.6
-2.8
*72.5
-
-271
-9
-2.7
-3.1
-3.4
-3.2
-2-5
-2.7
-19*.
.0 -2.8
Ja .5
00
1a'-.
-3.1
-3.-2.9
-27
1.-.
0
0 0
0
-3.3
-3.4
-3-1
-2e5
- .4-1.9
-1.2
-1 .7
00
0 -3.o-3.6-
.1-2-3
-2.2
-17
-
.
.9-3.1
-2.2
-2.4
-2-1
-1.2
-2.
3
0
03
0 0
,3-2.9
-3..
-3.8 -
00
00
-300
-2..
-3.1 -3., -2-9 -2.9
8
.7-2.-2.
Do
00
0 000
-2.7
-1.7
-2--2*9-2.
0
0
-
M
Figure 14.
-
.
-
Estimated E-P field, 11 February 1962.
Units: mm day~ 1 .
-88-
1.91
2.02
1.72 .97M
1.95 -0.89
1,87'1
1.66
3
3
2,49
4 5
,1.64
1.66
2
1.86
5 4
3
. 1.92
-5.94
2
2.12
3.60.2.61
3.24 ' :
3.85
2.05
3,.17
*5Q
4.55
3
\4
3
OBSERVED
UNITS:
EVAPORATION
inches
FEBRUARY
Figure 15.
3
4
month-
1962
Observed monthly eva oration, February 1962.
Units: inches month .
PRECIPITATION
VOLUMES ,
AREA
KM 3
I
(LaW/t +
V.Q neg)
2018
1614-
1210-
864 -'
01
4
7
I
15
FEBRUARY
Figure 16.
19
23
1962
Daily precipitation volumes, Area 1.
27
KM3
t
- Ineg)
niiW/-
2018161412
0
10
8-
I
I't
6
I
\
'
I
4-I
2-e
4
Figure 17.
7
I1
15
FEBRUARY
19
23
1962
Daily precipitation volumes, Area 2.
27
PRECIPITATION
VOLUMES . AREA
3
KM 3
20
18
16
14
12
10
8
6
4
2
0
4
7
Figure 18.
I
15
FEBRUARY
19
1962
23
Daily precipitation volumes, Area 3.
27
KM3
Degs.
20-
,
0
lB
16
-10
14-
-20
12 -
-30
Co
10-
-40
8
-50
6 -
-60
4
-70
2-
-80
0
4
Figure 19.
7
I
15
FEBRUARY
19
23
27
1962
Inflow-direction deviations from 2400. Also shown are
daily observed precipitation volumes for Area 3.
90
A
AR
EA
I .FA
1
DAILY
ME
AN
MEAN
.AILY
PRECIPITATION
FOR
6-DAY
PERIODS
Observed
Estimated
KM
3
2018161412I O-
FEBRUARY
Figure 20.
1962
Area-1 daily mean precipitation for 6-day periods.
AREA
2.
DAILY
MEAN
PRECIPITATION
FOR
6- DAY
PERIODS.
Observed
Estimated
3
KM
20F-
16 14
-
FEBRUARY
Figure 21.
1962
Area-2 daily mean precipitation for 6-day periods.
3.
AREA
DAILY
MEAN
PRECIPITATION
FOR
6- DAY PERIODS.
KM3
2018161412-
Co
1086
4-
0
4
to
16
FEBRUARY
22
27
1962
Figure 22. Area-3 daily mean precipitation for 6-day periods.
-96-
BIBLIOGRAPHY
Ackerman, William C., 1965: Committee on status and needs in
hydrology: a look at data and instrumentation. Trans. AGU,
46, 700-715.
Benton, G. S., R. T. Blackburn, and V. 0. Snead, 1950: The role
of the atmosphere in the hydrologic cycle. Trans. AGU, 31,
61-73.
Benton, G. S., and M. A. Estoque, 1954: Water vapor transfer
over the North American Continent. J. Meteor., 11, 462-477.
Bock, P., H. M, Frazier and J. G. Welsh, 1967: Moisture flux
over North America, II, 99 pp. Final report 7477-244,
Contract Cwb-11313, The Travelers Research Center,
Inc., Hartford, Conn.
Colman, E. A., 1945: Report of the committee on evaporation and
transpiration, 1944-1945. Trans. AGU, 26, 451-455.
Drinkwater, W. 0., and B. E. Jones, 1957: Relation of potential
evapotranspiration to environment and kind of plant. Trans.
AGU, 38, 524-528.
Eddy, Amos, 1967: The statistical objective analysis of scalar data
fields. J. Appl. Meteor., 6, 597-609.
Ferruzza, D., 1967: Analysis of synoptic scale water vapor transport. S. M. Thesis, M. I. T., 100 pp.
Hastenrath, S. L.,1 1966: The flux of atmospheric water vapor over
the Caribbean Sea and the Gulf of Mexico. J. Appl. Meteor.,
5, 778-788.
Hutchings, J. W., 1957: Water vapor flux and flux divergence over
southern England: summer 1954. Quart. J. R. Meteor. Soc.,
83, 30-48.
LaRue, J. A., and R. J. Younkin, 1963: Large-scale precipitation
volumes, gradients, and distribution. Mon. Wea. Rev., 91,
393-401.
-97-
Linsley, Ray K., 1951: The hydrologic cycle and its relation to
meteorology-river forecasting. Compendium of Meteorology, American Meteorological Society, 1048-1050.
Mather, J. R., -1961: The climatic water balance. Pubs. in Climatology, 14, 251-264. C. W. Thornthwaite Associates Labor, ,ory of Climatology, Centerton, N. J.
Munn, R. E., and D. Storr, 1967: Meteorological studies in the
Marmot Creek Watershed, Alberta, Canada, in August
1965. Water Resources Res., 3, 713-722.
Patric, J. H., 1967: Evaporation and transpiration. Trans. AGU,
48, 701-707.
Peixoto, J.P., 1960: On the global water vapour balance and the
hydrological cycle. Trop. Meteor. in Africa, Munitalp
Foundation, Nairobi, 232-243.
Rasmusson, E. M., 1966a: Atmospheric water vapor transport
and the hydrology of North America. Report No. Al, M. I. T.
Dept. of Meteor., Planetary Circulations Proj., 169 pp.
Rasmusson, E. M., 1966b: Diurnal variations in the summer water
vapor transport over North America. Water Resources Res.,
2, 469-477.
Rasmusson, E. M., 1967: Atmospheric water vapor transport and
the water balance of North America: Part I. Characteristics of the water vapor flux field. Mon Wea. Rev., 95, 403426.
Roberts, W. J. , 1963: Evaporation and transpiration. Trans. AGU,
44, 556-558.
Starr, V. P., and J. P. Peixoto, 1958: On the global balance of
water vapor and the hydrology of deserts. Tellus, 10, 188-194.
Thornthwaite, C. W., et al., 1964: Average climatic water balance
data of the continents, part VII, United States. Pubs. in
Climatology, 17, 615 pp. C. W. Thornthwaite Associates
Laboratory of Climatology, Centerton, N. J.
98--
Thornthwaite, C. W., and F. Kenneth Hare, 1965: The loss of
water to the air. Met:cor, Monographs, 6, 163-180. Am.
Meteor. Soc., Boston, Mass.
U. S. Department of Commerce - Weather Bureau:
Climatological
Data - State Monthly Summaries, February 1962.
van Bavel, C. H. M., et al., 1963: Surface energy balance in arid
lands agriculture 1960-61. Prod. Res. Rept. No. 76, Agricultural Research Service, U. S. Dept. of Agriculture, 46 pp.
Water Resources Committee, 1966: In committee reports, soil
characteristics in the hydrologic continuum. Soil Sci. Soc.
Am. Proc., 30, 418-421.
Weiss, L. L. and W. T. Wilson, 1958: Precipitation gage shields.
Trans. Int. Assn. Sci. Hydrology, 1, 462-484.
White, R. M., 1950: The meridional eddy flux of energy. Quart.
J. R. Meteor. Soc., 77, 188-199.
-99-
ACKNOWLEDGEMENTS
I am most grateful to the United States Air Force for making
my residence at the Massachusetts Institute of Technology possible.
The atmosphere created through the efforts of dedicated MIT professors and students alike has been most conducive to learning.
Especially noteworthy have been the advice, encouragement
and continued support of Professors V. P. Starr, J. P. Peixoto,
E. N. Loi-enz, and J. M. Austin.
I also wish to thank Capt. David
Ferruzza, who stimulated the interest which led to the study just
concluded.
The tremendous data processing job was conducted through
support of the National Science Foundation and performed by the
Travelers Research Center (TRC), Hartford, Conn.
The coordin-
ator at TRC was Mr. Howard Frazier; vertical integral programs
were by Mr. Edward Sweeton, and the intricate objective analysis
routines for all fields were written by Mr. James G. Welsh.
Pre-
cipitation data were furnished by Mr. W. M. McMurray of the
National Weather Records Center and punched on cards at MIT.
Many hours preparing the data for punching were spent by the author's wife, Eloise.
Drafting of the figures was done by Miss Isabelle Kole, and
the manuscript was typed by Mrs. Cynthia Webster.
tiring efforts I am most grateful.
For their un-