Estimating-Daily-Advective-Contributions-to-Potential-Evapotranspiration.pdf

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advected Ratio dew point depression temperature variable Wind
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advected Ratio dew point depression temperature variable Wind
United States
Department of
Agriculture
Statistical
Reporting
Service
Statistical
Research
Division
May 1982
Esti mati ng
Daily Advective
Contributions
to
Potential
Evapotranspi ration
Richard G. Stuff
Jerry D. Hill
ESTIMATING
DAILY ADVECTIVE
CONTRIBUTIONS
TO POTENTIAL
EVAPCTRANSPlRATlON
Richard G. Stuff
and
Jerry D. Hill
Climate Assessment
Technology,
Inc.
This research was conducted as part of the
AgRISTARS Yield Model Development
Project.
It was developed
in response to task 5 in
major project element number 3 as identified
in the 1981 Yield Model Development
Project
Implementation
Plan.
As an internal project
documeut,
this report is identified
as
shown below.
AgRISTARS
Yield Model Development
Project
YMD-U2-04245
May 1982
Weather Map Information
fOr Estimating Daily
Potential
Evapotranspiration.
By
Richard
Statistical Reporting Service; u.S. Deparbnent
D.C., 20250. SRS Staff Report No. AGES820428.
ABSTRACT
Advective
Contributions
to
G. Stuff and Jerry Hill;
of Agriculture;
Washington
Wind speeds, local and up-wind
temperatures, and dew-point temperatures
extracted from 1200-GMT surface maps were found to explain 37 to 57 percent of
the variance in the ratios of equivalent latent energy (LE) to net radiation
(RN) for "crop stage" subgroups of soybeans at four site-year combinations in
eastern and central
Nebraska.
The
corresponding
linear
regression
relationships were consistent between subgroups. Differences between subgroup
ratios which were not explained by the data may have resulted from differences
in crop maturity, methodology, or insufficient weather information. A similar
analysis applied
to alfalfa at the same sites was less conclusive.
This
possibly was due to underestimation of advective heat by the Bowen Ratio
Energy Balance method used.
Key words: Advection effects, potential evapotranspiration, synoptic weather
applications
*****************************************************************
*
*
*
This paper was prepared for limited distribution to
*
*
the research community outside the Department of
*
*
Agriculture.
The views expressed herein are not
*
*
necessarily those of SRS or USDA.
*
*
*
*****************************************************************
- i -
FOREWORD
Many of the physiologic
crop yield models
now being developed
estimate
moisture
loss through evapotranspiration as a function of solar radiation and
precipitation.
While this may be suitable for humid areas, it is known that
the lateral transfer of heat from other regions does have a material effect on
the potential evapotranspiration in arid and sub-arid regions.
Therefore this
study was sponsored in the interest of determining to what degree the lateral
transfer of heat could be approximated,
even anticipated,
from synoptic
weather maps.
I do particularly want
to express my gratitude
to Dr. Blaine L. Blad,
University of Nebraska, for providing the on-site data required by this study.
Fred B. Warren
Senior Research Statistician
Yield Research Branch
Research Division
Statistical Reporting Service
U. S. Department of Agriculture
- ii -
TABLE OF CONTENTS
SUM¥.AR.Y
• 1
INTRODUCTION
• 2
METHODS
· 3
RESULTS AND DISCUSSION
• 7
CONCLUSIONS
21
REFERENCES
22
APPENDIX
.
24
- iii -
ESTIMATING DAILY ADVECTIVE CONTRIBUTION
TO POTENTIAL EVAPOTRANSPIRATION
SUMMARY
Estimates of daily contributions of advection to potential
evapotranspiration
were
examined
for
possible
relationships
to variables
derived
from
conventional surface weather maps.
Contributions were expressed in
terms of
the ratio of equivalent latent energy
(LE) to net radiation (RN). They were
derived on a total of 105 days from lysimeter measurements
for
soybeans
and
from the Bowen Ratio Energy Balance measurements for alfalfa in four site-year
combinations
in eastern and central Nebraska.
Wind speeds estimated from the
surface pressure gradients, local and up-wind
temperatures,
and
dew-point
temperatures
were
extracted
from I200-GMT surface maps corresponding to the
field observations.
Other weather variables were derived from combinations of
the original variables.
In "crop stage" subgroups of the soybean
data, I200-GMT
temperatures,
dew-point
depressions,
and wind
direction
were
found to explain 37 to 57
percent of the variance
in the LE/RN
ratios.
The corresponding
linear
regression
relationships were consistent between subgroups.
Mean differences
between subgroup ratios which could not be explained by the data may have been
due to crop maturity, methodologies, or insufficient weather information.
The
less conclusive results obtained from the sample of alfalfa data were possibly
due to underestimation of advection by the Bowen Ratio Energy Balance
method.
The
overall
results would
support
further
development
of weather-map
approaches to estimating advection effects.
- 1 -
INTRODUCTION
In many field situations more water will evapotranspire (ET) from a crop
than
would
be indicated
by
the net radiation (RN) supply of energy at the site.
Various micrometeorological
studies
have
documented
that
the
extra
water
consumed
is attributable
to horizontal transfer (advection) of heat and/or
vapor pressure deficits.
This advection results from
the
component
of
the
wind which flows at right angles to a discontinuity or gradient in temperature
or humidity.
The effects of advection on ET are largest in small isolated wet
fields
in dry
areas.
It appears to contribute to £I in about 15 percent of
the spring and summer days where dry conditions prevail and may account for 40
to 50 percent of the total evapotranspiration
(ref. 1 and 2).
In extreme
cases
advection
may
contribute
more
to evapotranspiration
(LE) than net
radiation (LE/RNl2) as often as 1 day in 4.
More
commonly,
advection
may
contribute
for 10 to 90 percent as much energy as net radiation (1.1 - LE/RN
-1.9, ref. 4 & 5).
The most common and extensively studied type of horizontal
heterogeneity
are
boundaries created by different ground covers in adjacent fields.
Part of any
subsequent
advection
is due
to direct
transport
through the edge of the
canopy.
This has been labeled the "clothesline" effect and
considered
local
advection
(ref. 6).
Roughness
effects, buoyancy differences, interactions
between horizontal temperature and moisture gradients, etc. have
prevented
a
useful
analytical
solution to the corresponding differential equations (ref.
1).
Micrometeorological
measurements
and
empirical
relationships
indicate
that
the
edge
effects
extend
40 to 100 times the height of instruments
depending on wind speed, roughness, etc.
A second
type
of
advection
results
from
airflow
above
canopies
which
transports properties from gradients along horizontal transverses extending up
to synoptic
scales.
This
is
called
reiional advection for its origin or
"oasis effect" for its mode of action.
The resulting exchanges
of
heat
and
water
vapor can extend tens of miles across a contrasting surface (ref. 8 and
9). Regional advection accounts for the major part
of
the
total
advective
contributions
to evapotranspiration
in normal size agricultural fields.
In a
small field (2 hectares) of irrigated alfalfa in eastern
Nebraska,
regional
advection
averaged over 90 percent of the total observed advection (ref. 10).
If actual evapotranspiration is less than the potential rate
due
to limited
soil
moisture
or
plant
resistances,
an initial transport of sensible heat
would not appear as advection measured by ET.
It would manifest in terms
of
an increase in temperature of the canopy and adjacent air layers and increased
fluxes of sensible heat to the soil and atmosphere.
The resulting increase in
both
heat and moisture stress on the crop would be detrimental to yields.
In
an adjacent irrigated field the effect is manifest in the extra cost of water
for
the
increased £I.
In such events, it is typical that crop yield is also
increased.
The negative effects of advection are increased during occurrences
of droughts (ref. 4).
In addition to causing increases
in evapotranspiration
rates
in irrigated
fields and immediately after rains, another reason that advection is a problem
- 2 -
is due
to the lack
of applicable
methods of including its effect in PET
estimation models.
Brakke et.al. (ref.
19) found
that micrometeorological
modifications
to the Bowen ratio - energy balance method did not completely
correct the advection related underestimates of LE.
Similar deficiencies have
been found for modifications of the Penman combination
method
(ref.
1).
A
procedure
proposed by Jury and Tanner (ref. 11) for the Priestly-Taylor model
was found to be unsatisfactory by Kanemasu (ref. 12). Alternative
approaches
investigated
particularly
in the USSR (ref. 13) are based on more synoptic
meteorological-climatological
indicators of advection and
PET relationships.
Independent
assessments
of these accuracy and applicability of these methods
are limi ted.
Conceptually, advection can be well defined, but efforts
to quantify
it in
terms
of evapotranspiration have met with limited success.
Its contribution
to PET depends on wind speed,
characteristics
of
the upwind
gradients
of
temperatures
and
vapor
deficits,
and fetch
and roughness features of the
field.
Part of the quantification problem
is due
to the lack of
direct
methods
of measuring
advection;
it must be estimated from a combination of
precision micrometeorological and
lysimetric
measurements
and
controls
of
which few are available (ref. 14).
The purpose
of
this
study
was
to utilize
a set of advection estimates
available from Nebraska to determine the degree to which advection days can be
identified from information provided through regular synoptic weather maps.
METHODS
Data consisting of LE and
RN values
were
provided
to the USDA
by
the
University
of Nebraska.
It covered
four crop-year combinations which are
listed
in table
1.
Fetch
data
and references
that
give
additional
descriptions
of the sites and measurement methods are also given in Table 1.
The Mead and Schuyler sites are in east central Nebraska and the Cozad site is
about 300 kilometers west of Mead in the central part of the state.
A major distinction exists between the methodology used for the soybean versus
the alfalfa data.
The latent energy for soybeans
was
derived
by lysimeter
measurements
of ET while the LE for alfalfa was computed by the Bowen Ratio
Energy Balance (BREB) method.
Surface synoptic weather maps prepared by the National
Weather
Service
for
1200 GMT (6:00A.M.CST) were acquired for each day the field research data were
collected.
These maps were analyzed by NOAA to show the pressure centers and
fronts as well as display the plotted data
for each
reporting
station.
A
sample map is shown in Figure 1.
- 3 -
Table 1
Identification and characteristics of the
Nebraska measurements data used in the study.
NUMBER OF
MIN. FETCH
YEAR
CROP
SITE
OBSERVATIONS
(METERS)
DOCUMENTATION
1969
Soybeans
Mead
37
40
ref. 2
1970
Soybeans
Mead
27
ref. 15
1973
Alfalfa
Schulyer
29
1973
Alfalfa
Cozad
12
125
ref. 16
Further
analyses were performed
to obtain values for variables which
conceivably could represent components or factors related to heat or moisture
advection.
Values were visually interpolated to the approximate locations of
the field sites. They included:
wind speed - estimated using the geostrophic wind relationship based
on isobaric spacing) knots/hour
prevailing wind direction- as above) to the nearest
of 8 cardinal
points
temperature gradient in the upwind direction) deg./mile
dew-point temperature gradient upwind direction) deg./mile
o
dew-point temperature at l200Z) F
dew-point depression at l200Z) of.
To estimate advection
of sensible heat or vapor pressure deficits) it was
assumed that the trajectory of the air reaching the target during the next
l2-hour period was represented by the local tangent to the horizontal surface
pressure field pattern.
The temperature and dew-point
temperatures were
estimated along upwind
trajectories for distances equal to 12 time the wind
speed. The magnitude of the temperature or dew-point "advection" was computed
as the product of the gradient and wind speed. Negative values would indicate
that relatively lower temperatures would be advected. A moisture
"advection"
variable was computed as the l200Z dew-point depression plus the temperature
"advection" minus the dew-point temperature "advection". Negative values were
set equal to zero.
- 4 -
SCALE FOR WIND SPEED ESTIMATION
KEY
o
'"
Dish.llce
(N. M;.)
Geo"tr.~iI:.
W,'nJ
(~'l.ts)
ISOBAR
-
-
TANGENT TO PRESSURE PATTERN
ISOTHERM
Figure 1.
Sample map and analysis of weather features for Mead, Nebraska,
July 26, 1970 (sout~ "'1 nd at 30 knots, synopti c type B)
- 5 -
Each day's synoptic weather pattern was placed into one of eight possible
categories.
The categories used were:
A.
h1gh pressure to the north with general N to E circulation
B.
advancing low or front to the west with strong southerly circulation
C.
low pressure or front traversing the area, variable winds
D.
between pressure systems, little or no predominant winds
E.
front to the east, general W or NW circulation
F.
low pressure or trough to the south, E to SE circulation
G.
h1gh pressure dominating, little or nor predominant circulation
H.
h1gh pressure to the east, general SE to SW circulation.
The local temperature at lZOOZ was derived as the sum of the dew-point
temperature and dew-point depression.
Days of the year where numbered
from
March 1 (climatological day).
A listing of the abbreviations used for the
variables is given in the appendix. All data were entered and filed on
the
USDA/Martin Marietta
computer system. The Statistical Analysis System, SAS
(ref. 17) was used for all the computations performed in the study.
The ratio of the latent energy equivalent of the evapotranspiration
to the
daytime
total of net radiation (LE/RN) was used as a relative measure of the
results of advection.
The principal assumptions required for the ratios to be
valid measures are:
- water for evapotranspiration is unrestricted in availability
- sensible heat transfer with the soil and other components of the
energy balance are essentially constant over the period.
Cases where either LE or RN were missing were deleted from the analysis.
- 6 -
RESULTS AND DISCUSSION
The LE/RN ratios were first plotted by dates to examine their
magnitudes
and
seasonal
distribution.
The
plot
for soybeans is presented in Figure 2; it
shows a distinct seasonal pattern which parallels normal
seasonal
trends
of
each component - LE and RN. Seasonal trends in LE are primarily determined by
RN,
crop development stages, and advection.
Forming the dimensionless ratio,
LE/RN, adequately removed the correlation (r:0.68) between the two in that the
correlation between the ratios and RN was 0.09.
Since there was no direct way
for testing for crop maturation effects, the soybean ratios
were
split
into
parts
to study their association with other variables.
Ratios from July 1 to
July 21 were considered group 1 and the others as group 2.
The soybean
ratios
from
1969 and
1970 were
compared
for
between
year
differences
with
a paired-t
test.
A subset of 8 pairs of ratios which had
matching dates of observations in
the
two
years
was
selected.
The
mean
difference
between
the
two years was 0.08 and the paired-t statistic (0.58)
did not reject the null hypothesis of equal means.
With the added
assumption
that
the field
"surroundings"
were
the
same in both years, the data were
pooled then. subdivided into groups 1 and 2 as described previously.
The ratios for alfalfa at Schuyler and Cozad were
distinctly
lower
in
July
than corresponding values in soybeans with a trend upward to similar levels in
August (Figure 2 - Triangles).
This result be itself would indicate there was
less
advection at the Schuyler site in 1973 than observed at Mead in 1969 and
1970.
In terms of crop effects,
alfalfa
normally
has
less
resistance
to
transpiration
fluxes than other crops.
Another possible explanation would be
bias in the BREB method used to derive LE values for
the
Schuyler
alfalfa.
Research at Nebraska has shown that underestimates of 20 to 40% by this method
are
proportional
to amounts of advection (ref. 10 and 15). Other ratios for
alfalfa which are based on lysimeter measurements (ref.
4) were
plotted
in
Figure
3 for comparisons.
The lysimeter based ratios also show higher levels
of advection with a downward trend in late July and August.
- 7 -
1969 0
2.0
0
1970 A
0
0
0
AA
0
A
A
A
0
0
A
A
0
A
1.5
i:!..
i:!.. 0
i:!..
i:!.. A
A
0
A
Q
AbA.
c!-
O
i:!..
A
a
0
A
•.....•
0
Ai:!..
I-
61
~
c:::
0
0
A
i:!..A
00
0
0
:z:
1.0
c:::
0
..•...
0
I.LI
0
-J
0
0
000
0
0
0
0
0
r
I
I
I
I
I
I
I
25
5
15
25
5
15
25
5
JUNE
JULY
AUGUST
SEPT
Figure 2.
Seasonal distributions of advection as indicated by the ratio
of LE to RN for soybeans at Mead,
Nebraska.
- 8 -
3.0
2.5
o
o
If' 3.78
o
o
LYSIMETER
MEASURED
ET, MEAD
1976
0
BREB CALCULATED
ET, SCHUYLER
& COZAD
1973
•
o
o
0 0
2.0
0
0
0
0
0
0
......
~
0 0
c:(
ex:
:z: 1.5
ex:
.....•
I.&.J
...J
1.0
°00
0
0
0
0
0
0
0 0
0 00
0
0
•
°
0
•
•
0•
• •••
•
•
0
• • •
•
• •
•
•
•
•
•
•
••
•
•
• •
•
•••
•
•
•
•
• • • •
•
0.5
Figure 3.
Seasonal distribution of advection as indicated by the ratio of
LE to RN for alfalfa at the indicated locations in Nebraska.
- 9 -
If 1973 was not a unusual year, both the level and trends in the ratios could
be due to bias in the BREB method. Therefore the alfalfa data were separated
for individual analysis and tests.
The first factor examined in the soybean data was wind direction.
The mean
LE/RN ratios are plotted in Figure 4. Individual subgroups did not have
enough data to derive reliable means
(n-3) for each direction.
The
June-August
(group 2) cases had predominately south and easterly winds, while
the July (group 1) cases had more occurrences of not and northwest winds which
had higher value of the ratio.
Thus the seasonal distribution
of wind
directions help to explain the higher value of the ratios observed in July.
When both groups were combined, it was found that the ratios increased almost
symmetrically with rotation from a direction slightly south or east (Figure
4). Subsequently, directions were coded in terms of degree deflection from E
SE to form a single linear variable. The simple correlation with ratios
were 0.37 and 0.26 for groups 1 and 2 respectively.
The matrix of Pearson product-movement correlation coefficients was computed
for each group of soybean data - Table 2. Wind speed, dew-point depression,
wind direction, initial temperature, and dew-point depression advection were
the independent variables having the largest correlation with the ratios.
Coefficients - 0.35 are significant at the 95% level of probability.
To statistically search for combinations of variables associated with
the
ratio, R-squared values for all possible regressions with 2 and 3 independent
variables were computed.
The results are given in Table 3.
Initial
temperature-dew-point depression and initial temperature-wind direction were
the pairs of variables which gave the highest R-squares.
The association between the ratios, initial temperature and dew point
depression, was examined by linear regression. It was found that initial
temperature and dew point depression, individually or jointly, explained
significant proportions of the variation in the ratios. The t-test for
equality of slopes (t = 1.185 vs. t(60 0 90) =1.296) did not reject the null
hypothesis
(H :b1 = b2). The regression c6efficients are given in Figures SA
and 5B. The rgsults, particularly
for subgroup 2, generally agree with
results found by investigators in the USSR (ref.13). They frequently used
different combinations of temperature and humidity as criteria for classifying
sukhovei. Failure of minimum daily temperatures to reach the dew point has
also been cited as a sukhovei criterion. The regression for subgroup 2 would
indicate that advection contributions begin when the average 1200Z dew-point
depression is greater that 2.50F.
- 10 -
N
WD = 1050
ALL
SOYBEANS
••
GROUP
1
•
GROUP
2
•
I
I
I
i
1
W
I
\
'
WD
i= 165
0
". \
I
\
.
\
\
\
E
WD = 150
L8 RATIO
1.6
.------
-~-
I
-,
\
\
/
I
I . -. I.-.
I
S
WD = 570
Figure 4.
Distribution
of average LE/RN ratios for Mead soybeans
according to wind directions.
- 11 -
Table 2. Matrix of correlation coefficients for variables in the two
subgroups of soybean data.
WS
TO
TA
G"I
CORRELATION COEFFICIENTS
I ~ - 32
DO
DA
OW
DP
WD
RN
LE
R
TI
Sf!
WS
1.00000 -0.13365 0.17434 -0.24077 -0.32633 0.1380l 0.19748 0.43102 0.15051 0.29191 0.32321 0.22488 0.65097
10
-0.13365 I.OO~JO 0.78721 0.72556 0.58462 0.04397 -0.18254 -0.53877 0.07138 -0.08323 -0.20284 -0.05219 0.05877
Tn
0.17434 0.19721 1.00000 0.48~81 0.53601 0.14893 -0.18087 -0.53627 0.19500 0.06270 -0.12598 0.04389 0.33120
DO
-0.24077 0.72556 0.48281 1.00000 0.94271 -0.20239 0.14269 -0.27755 -0.14589 -0.19814 -0.09516 -0.11166 -0.35007
OA
-0.32633 0.59462 0.53601 0.84271 1.00000 -0.22231 0.13331 -0.38516 -0.01032 -0.14108 -0.20736 -0.13448 -0.47393
O~
0.13902 0.04397 0.14893 -0.20239 -0.22231 1.00000 -0.08516 -0.21875 -0.12121 0.16008 0.36350 0.86446 0.34914
OP
0.19748 -0.18254 ~('.18087 0.14269 0.13331 -0.08516 1.00000 0.15346 0.08815 0.27510 0.35389 0.42726 0.24271
1m
0.43102 -0.53877 -0.53627 -0.27755 -0.39516 -0.21875 0.15346 1.00000 -0.01899 0.08396 0.26823 -0.12107 -0.03770
fiN
0.15051 0.07138 0.19500 -0.14589 -0.01032 -0.12121 0.08815 -0.07899 1.00000 0.82683 0.10167 -0.05552 0.26179
LE
0.29191 -0.08323 0.06270 -0.19914 -0.14108 0.16008 0.27510 0.08396 0.82693 1.00000 0.63025 0.28405 0.37747
~
0.3~321 -0.20284 -0.12599 -0.09516 -0.20736 0.36350 0.35389 0.Z6823 0.10167 0.63025 1.00000 0.50840 0.30231
TI
0.22488 -0.05219 0.04389 -0.11166 -0.13448 0.86446 0.42726 -0.12107 -0.06552 0.28406 0.50840 1.00000 0.43835
SA
0.65091 0.05977 0.33120 -0.35007 -0.47393 0.34814 0.24271 -0.03770 0.26179 0.37747 0.30231 0.43836
1.00000
W6
TO
TA
G-2
CORRELATION COEFFICIENTS
IN-
32
DG
OA
OW
DP
WD
RN
LE
R
TI
SA
1015
1.')0000 0.26056 0.41147 0.19653 0.19408 -0.00458 0.39077 0.46580 0.18447 0.34618 0.32111 0.24100 0.59638
lG
0.26056 1.00000 0.85742 0.82315 0.75255 0.22573 -0.05617 -0.11802 0.03455 -0.04958 -0.13098 0.19914 0.06066
TA
C.47147 0.85742 1.00000 0.71'1)"160.80913 0.23333 0.05989 -0.21106 0.06114 0.03611 -0.03724 0.28531 0.24847
DG
0.19563 0.82315 0.711076 1.000,") 0.90009 -0.04964 0.09458 -0.02346 0.11599 0.00235 -0.09396 0.00793 -0.18403
1"1
l'.19408 0.75255 0.80913 0.90009 1.00000 -0.07671 0.08934 -0.21415 0.02796 -0.09145 -0.15406 -0.02349 -0.18129
OW
-0.00459 0.22573 0.23333 -0.04964 -0.07671 1.00000 -0.36309 -0.20298 -0.17454 0.09111 0.288S0 0.81031 0.09587
OP
0.39u77 -0.05617 0.06989 0.09458 0.08934 -0.36309 1.00000 0.39464 0.22622 0.45386 0.51499 0.25179 0.69565
W!I
0.4E~80 -0.11802 -U.21106 -0.02346 -0.21415 -0.20298 0.39464 1.00000 0.19160 0.33495 0.35791 0.03f36
0.29482
RM
0.184~7 0.03455 0.06114 0.11589 0.02796 -0.11454 0.22622 0.19160 1.00000 0.77749 0.13865 -0.03901 0.20195
L~
0.34618 -0.04958 0.03611 0.00235 -0.09145 0.09111 0.45396 0.334!!5 0.77749 1.00000 0.72103 0.38007 0.~7719
R
0.32111 -0.13098 -0.03/24 -0.09386 -1).15406 0.2ae90 0.51499 0.35791 0.13865 0.72103 1.00000 0.52395 0.50971
'1
0.~·11(J00.19914 0.28631 0.0')793-,).02349 0.91031 0.::SI79 0.03736 -0.03901 0.39007 0.62395 1.00000 0.53708
SA
v.:J!J6380.061)65
0.24917 -O.1!l4':>J
-0.18129 0.08587 0.69565 0.29482 ~.20195 u.47719 0.50971 0.53708
1.00000
NOTE: SI)S INST1l1J1E,6ns C:~CLE, BOX 81l'-"1,
CA!lYNC 27511
~'.I\DY
- 12 -
Table 3. Maximum R-square values from all possible regressions of
ratios on combinations of 2 and 3 independent variables.
REGRESSION MODELS FOR DEPENDENT VARIABLE R
NUMBEh' IN
MODEL
r~-SQUARE
VARIABLES IN MODEL
2
O.280~ul]9
~
0.28131828
2
0.28863705
~
O.301121~1
2
0.36884389
1(\
rI
DP
r 1
TLl TI
WS TI
~-JD T I
:3
O. ~37005800
TA
l·JD Tl
:3
u.3727088::5
DG
~'JD T1
3
0.37302922
I:JS
ItJD TI
3
0.37181213
DP
L·JD rl
3
0.37568088
l-JD
f 1 SA
32
REGRESSION MODELS FOR DEPENDENT VARIABLE H
NUMBER IN
MODEL
2
2
..,-
2
2
R-SQUARE
0.13215585
0.11<1008305
0.4571'1186
U.501<12'161
0.52806616
VARIABLES IN MODEL
TI SA
fA
r I
TG TI
l·JD T I
DP TI
3
0.51951380
TG WD TI
3
0.~=72S3'15
DA OP 11
3
u.58786'126
DP
\tJD II
3
0.5/'163685
1G DP
rI
3
0.576'111081
TA DP TI
- 13 -
Since the contributions to the ratio from a degree increase in temperature
or
dew-point depression were nearly the same, these two variable were combined to
simplify
the
examination
of further multiple variable
relationships.
Coefficients for the linear regression of temperature and dew-point depression
sums and other statistics for the subgroups are given in Table 4. The between
group differences in any of the other variables
except
the temperature
"advection" could potentially
explain the mean difference in ratios between
groups.
Table 4
Regression equation for the temperature-plus-dew-point depression
variable and mean values of other variables for soybean subgroups.
TA
Group
Regression Equation
WS
Means
WD
SA
1
2
R = 0.61 + 0.013(TI+DP)
R = -0.48 + 0.022(TI+DP)
0.28
.52
17.7
15.7
63
40
-.13
1.56
8.5
6.7
The negative relationship between temperature "advection" values and ratios
were
found both between and within subgroups. To examine this unexpected
result, the values were examined by wind direction groups.
Scatter diagrams
containing all the soybean data in any given wind direction are plotted in
Figure 6. The negative relationship is indicated most strongly in the north
and northwest groups. Multiple linear regressions were run with the N and NW
data points removed, but the slopes and partial correlations
for the
temperature "advection" variable
remained negative
in all cases where any
other statistically significant variable was in the equation.
- 14 -
Z.O
p
GROUP 1
A
II
1.9
A
•.• £
A
A
"
:.,
1.6
I.'
0
H
f-< 1.4
<~
Z 1.3
l}:;
A
..••...
~
...:l 1.2
1.1
"
I
I
I
I
I
I
I
I
I
,
I
I
I
I
I
I
I
I
I
I
I
I
'2
'3
'4
'5
56 57 58 58 60 61 62 63 64 65 6S 67 68 68 70 71 72 73 74 75 76 77 78 78 80 8:
82
TI
II
GROUP 2
I••
I.'
1.4
1.2
l.2
01•1
H
f-<< 1.0
l}:;
Z 0.9
~
..••...
~ 0.8
...:l
0.7
II
0.6
A
A
A
R· -.57 + O.025(TI)
I
I
~h' ••,
~;.:::~3
~0:1
1:: •.•
56
':7
";1../
59
61,,'
6:
"'_
:3
S4 65 Bb E(.' 6E' 62 7L)
II
t
,_
73 7~
-...
7£ 77 78 7~ St, ~!
Figure SA.
Plots and simple linear regression relationships
between LE/RN
ratios and initial temperatures
(TI in OF) for soybean subgroups.
- 15 -
LEGEND:
,: ; ! 095. ~ ;
.2 ClBS. ETC •
GROUP 1
Z.o
A
A
A
1.S
A
1.8
A
:.7
1.44 + O.022(OP)
A
0
~
H 1.5
E-<
<i;
~
1.5
Z
A
~
A
........
W
1.4
A
.....:l
B
A
A
A
A
1.3
A
I.Z
A
1.1
A
I
I
2
3
5
8
10
II
..
'"
14
..
DP
1.6
GROUP 2
A
1.5
A
A
A
1.4
A
---------
1.3
A
A
A
I.Z
A
0
1.1
r,
H
E-<
<i;~
!.o
Z 0.2
"
~
A
A
........
~
A
.....:l O.B
(.'.7
A
0.6
" ,
0
e
Il
II
..
~3
DP
Figure 5B.
Plots and simple linear regression
relationships
between
ratios
and dew-point
depressions
(OP in OF) for soybean subgroups.
- 16 -
•
N
NE
•
•
•
•
•
•
•
•
NW
•
0.5
2.0 r : .
o 1.5
I-
<C
0::
~ 1.0
.....•.
W
....J
E
•••
2.0
•
•
SW
• •
S
• •
0 1.5
••
-
•
l-
•
~
• •
•
:z: 1.0
•
• •
0::
.•.•.•.
•
I.IJ
...J
•
0.5
•
I
I
I
I
I
I
I
,
-10
-5
0
5
-10
-5
0
5
10
-5
MAP ESTIMATED
TEMPERATURE
ADVECTION,
of/DAY
•
• ••
•
•
•
•
C
0
5
SE
•
I
I
10
15
•
•
Figure 6. Scatter diagrams of weather map d~rived temperature "advection" and ratios of lE to RH.
-
~
-----------------
--
The negative relationship between Rand
TA was
probably
a "time
of dayn
phenomena
corresponding
to the
1200Z maps.
Source
region
conditions
associated with larger advective effects or daytime ET are usually
associated
with
lower minimum
temperatures
in
the early
morning.
Thus,
cool air
advection (negative TA) in the morning
would
probably
switch
to warm
air
advection
later
in the day.
Since the LE/RN ratios are an integrated result
of advection over a day, map estimates of heat and moisture advection based on
more than one observation time should give more useful variables.
Except for wind direction, none of the other variables were found
to give
a
significant
additional reduction in R-squares after the temperature-dew point
depression
variable
entered
a regression
in stepwise
procedures.
The
resulting equations with wind direction included were:
Group 1, Ratio = 0.51 + 0.013(TI + DP) + 0.0014(WD)
with R2 = 0.37
Group 2,
Ratio =-0.43 + 0.021(T1 + DP) + 0.0012(WD)
with R2 = 0.57
Wind
direction
in this
case may
be a substitute
for heat and moisture
advection
variables
by appearing
more
significant
statistically
due
to
weaknesses
in
the latter as described above.
If it were possible to replace
wind direction with advection variables, a more universal relationship
should
be obtained.
After
accounting for regression the ratios were still 0.3 to 0.5 units higher
in group 1 than in group 2 over the range of temperatures and wind
directions
encountered.
Thus it is possible that the lower ratios early and late in the
season are due in part to soybean development or maturity effects.
Ratios
of
irrigated soybean ET to pan evaporation display similar seasonal distributions
(ref. 19).
The only
synoptic weather pattern associated with a distinct LE/RN ratio for
soybeans was the "E" category; it was always larger than one with
a relative
small
standard
deviation.
Large variances in ratios within the other seven
categories suggested that the classification by itself was of little value
in
estimating advection.
The alfalfa data were separated by sites since the ratios for Cozad (all dates
after
August
20, see Figure 2) had a higher mean level than Schuyler -- 1.34
vs 1.07. THe higher ratios at Cozad could
be due
to physical
differences
between
sites
and
time
periods
or a bias in the BREB method as discussed
previously.
In attempts to fit the variables found to be statistically significant in
the
soybean data in all possible regressions, none were found to be significant (F
S 0.1) with
the
Schuyler
alfalfa.
However,
with
the small sample (12
observations) of Cozad alfalfa, relationships similar
to those
in soybeans
were found.
The multiple regression result was:
Ratio = 0.37 + 0.011(T1 + DP)
0.0020(WD)
with R2 = 0.70
- 18 -
The coefficients
for the Pearson product-moment correlations are given in
Table 5.
An additional test on the Schuyler
data was performed
by comparing
the
observed ratios with
those predicted
by the three regression equations
containing TI + DP and WD derived from the other data subgroups.
There were
no correlations
between
the observed
and ratios
predicted by any of the
equations (maximum r= -0.04). Also the time trend which
was significant
in
the BREB derived ratio did not occur in the predictions.
However, both the
observed and predicted
values
in the Schuyler data subset has smaller
variances
than other
subsets and this reduces
the strength of the test
results.
This consistency
and level of statistical
significance
obtained
for
relationships
between map derived weather variables and relative advection
provide positive support for the approach of using synoptic map information '
estimate advection.
The use of additional site and crop information Wit:,{h.
weather maps should allow development of empirical models that are phys'
sound and universal.
Surface maps 1 or more other times during the d? .
ld
allow integration
of the diurnal
temperatures
before projection
.
the
transport.
Additional
dependent
data as well as the crop and weat~.......•..
' data
described above is available for Nebraska and other locations.
::\
•
I
'il,;
'';"""~
.•..._,,,,,,
- 19 -
Table 5. Matrix of correlation coefficients for variables in the two
subgroups of alfalfa data (1= Schuyler, 2=Cozad).
WS
TG
TA
DG
G:1
CORRELATION
COEFFICIENTS
I
DA
DW
DP
N : 29
WD
RN
LE
TI
SA
~s
1.00000 0.09626
0.21655
0.03947
0.15831
0.04029
0.07600
0.43797
0.07125 -0.09058 -0.18950
0.09289
0.15592
:~
0.09625
1.00000 0.82803
0.888B5
0.76323
0.12320 -0.12230 -0.57961 -0.09306 -0.04228
0.10381
0.01578 -0.00467
1A
0.21655
0.82803
1.00000
0.79106
0.93542
0.06768
0.00290 -0.45310 -0.07040 -0.10100 -0.04303
0.06168
0.11671
D~
0.03947
0.88885
0.78106
1.00000
0.87596 -0.05863 -0.02131 -0.48848
0.04108
0.OB082
0.12B18 -0.06765 -0.12828
P"
0.15831 .0.76323
0.93542
0.B7596
1.00000 -0.06161
0.04985 -0.38480
0.02504
0.00983
0.01220 -0.01645 -0.01646
V'·,
0.04029
0.12320
0.06768 -0.05863 -0.06161
1.00000 -0.25912 -0.09296
0.36288
0.317B6 -0.21040
0.68293 -0.06512
DP
0.0/600 -0.12230
0.00290 -0.02131
0.04985 -0.25912
1.00000 0.29178 -0.01221
0.01754
0.08229
0.52858
0.87209
\olD
0.43797 -0.57961 -0.45310 -0.48848 -0.3B480 -0.09296
0.29178
1.00000
0.06065
0.01130 -0.01817
0.13897
0.16837
R'
0.07125 -0.09306 -0.07040
0.04108
0.02504
0.36288 -0.01221
0.06065
1.00000
0.87690 -0.30721
0.30970 -0.14289
L~
-0.09058 -0.04228 -0.10100
0.OB082
0.00983
0.31786
0.01754
0.01130
0.87690
1.00000 0.14256
0.29263 -0.13675
Ii
-0.18950
0.10381 -0.04303
0.12818
0.01220 -0.21040
0.06229 -0.01817 -0.30721
0.14256
1.00000 -0.12268
0.00088
11
0.09289
0.01578
0.06158 -0.06765 -0.01645
0.68293
0.52858
0.13897
0.30970
0.29263 -0.12268
1.00000
0.60235
s~
0.15592 -0.00467
0.11671 -0.12928 -0.01646 -0.06512
0.87209
0.16837 -0.14289 -0.13675
0.00088
0.60235
1.00000
liS
TG
TA
DO
G:2
CORRELATION
COEFFICIENTS
I
DA
OW
DP
N : 12
\olD
RN
LE
TI
SA
If
R
II
S:'
1.000"0 -0.01263
0.00315 -0.25725 -0.25142
-0.01263
1.00000 0.96337
0.45616
0.43034
0.0031)
0.96337
1.00000 0.43519
0.44738
-0.25725
0.45616
0.43519
1.00000 0.96379
-0.26142
0.43034
0.44738
0.96379
1.00000
0.45167
0.~3373
0.37273
0.40227
0.31123
0.39055 -0.65114 -0.56832 -0.59738 -0.49494 -0.37047
0.25224
1.00000
0.09248
0.49662
0.55841 -0.10880
0.10997
-fJ.23286 0.05748
0.05999 -0.53396 -e.60983 -0.38321
0.09211
0.09248
1.00000
0.60581
0.00630 -0.23575
0.47391
0.3i9!! -0.13512 -0.15854 -0.85811 -0.85520 -0.09055
0.54341
0.49662
0.60581
1.00000 0.79887
0.32506
0.75450
0.6~982
-'J.21851
-0.24721 -0.67595 -0.61399
0.16808
0.60539
0.55841
0.00630
0.79987
1.00000 0.57480
0.58312
(i. If. 76(11) O.~J~5~;S 0.28n25
0.01J352 -0.01653
0.69077
0.62172 -0.10880 -0.23575
0.32506
0.57480
1.00000
0.53770
0.25308
0.295!!! 0.31911 -0.59065 -0.56586 -0.04563
0.78606
0.10997
0.47391
0.75450
0.58312
0.53770
1.01'<)I)U
Nc'E: SAS INSTITUTE, SAS CIR~LE. BOX 8000. ~ARY NC 27511
- 20 -
CONCLUSIONS
This study is considered a preliminary survey of agroclimatic
relationships
between advection and potential evapotranspiration; it involved small samples
of two methods
of measuring PET for two crops and only one weather map per
day. Specific findings which were important
relative
to the more
general
conclusion are:
variables which are "statistically" related to relative advection
can be obtained
from standard weather maps.
Variables from the
1200Z map which contain information on advection in eastern Nebraska
are temperature, dew point depression, wind direction,
wind
speed,
and an estimate of moisture "advection".
Linear combinations of morning temperature, dew-point depression,
and wind
direction explained from 37 to 57 percent of the variance
of relative advection in cases where PET was measured by lysimeter.
Information
available
for alfalfa where PET was estimated by the
Bowen Ratio Energy Balance method was insufficient to explain
the
mixed results.
Some general observations which were indicated through the study are:
1.
There are no practical micrometeorological models available to
directly or indirectly
provide
estimates
of advection
fro crop
moisture assessments; model estimates of PET are of limited value as
components in variables representing advection.
2.
Weaknesses
in assumptions
regarding
crop effects, boundary,
roughness effects, and other energy balance components restrict
the
availability
and usefulness
of field measurements for quantifying
advection effects on PET.
3. Standard weather data and analysis
contain useful
information
for
estimating
the contribution
of advections;
the weather
information combined with area moisture
indices and agricultural
data provide
feasible
bases for developing statistical models of
advection if the dependent data are available.
- 21 -
REFERENCES
1. Absel-Aziz,
M.H.,
S.A.Taylor
and G.L. AShcroft,
1964,
Influence
of
advective eneray on transpiration.
Agron, J. 56:139-142
2. Rosenberg, N.J. 1972, Freauencv of
Central
Great
Plans.
J. Irrig.
2:204-206.
potential
evapotransDiration
in
and Drain Div. Am. Soc. Civil Bug.
the
IR
3. Lemon, E.R., A.B. Glaser and L.E. Satterwhite, 1957. Some aspects of soil.
plant
and meteorological
factors
to eva~otranspiration
by
irfiiated
alfalfa:
a consequence
of the 1976 midwestern drou2ht.
J. Appl. Meteor.
17:934-941.
4. Evans, G.N.
1971,
EvaDoration
from Rice at Griffith,
N.S.W.
Agric.
Meteorl. 8:117-127.
5. Rosenberg, N.J. 1974, Microclimate:
The Bioloaical
Environment.
New York.
315p.
Wiley,
6. Munn, R.E. 1966,
DescriDtive micrometeoroloay.
Advances
in GeoDhvsics,
Supplement 1. Academic Press, New York,245p.
7. Lemon, E.R., A.H. Glaser and L.E. Satterwhite, 1975, Some AsDects of Soil.
plant
and meteorological
factors
to evapotr~nsDiration, Proc. Soil Sci.
Soc. Am 21:4b4~8.
8. Rider, N.E. and J.R.Phi1ip, 1960, Advection and Evaporation, Alsoc.
Int.
Hydro1, Sci. 53:421-427
9. Brakke, T.W., S.B. Verma and N.J.
Rosenberg,
1978,
Local and
Reaional
Components of Sensible Heat Advection.
J. App1. Meteoro1.
17:955-963.
- 22 -
10. Jury, W.A. and C.B. Tanner, 1975, Advection Modification of the Priest
and Taylor Evapotranspiration Formula, Agron. J. 67:840-842
11. Kanemasu, E.T., L.R. Stone
and W.L.
Powers,
1976,
Evapotranspirati<
Model Tested for Soybean and Sor2hum, Agron. J. 68:569-572.
12. Dzerdzeevskii, B.L. ed, 1957, Sukhoveis and Drou2ht Control,
Academy
(
Sciences
of the USSR, Moscow.
Translated by Israel Program for Scientifi
Translations, 1963. U.S. Department of Commerce, Washington.
13. Penman, H.L., D.E. Angus and C.H.M. vanBavel, 1967, Microclimate
Factor
Affectin2 Evaporation and Transpiration, Chap. 26 in Hagen, et. al editors
Irrigation
of Agricultural
Lands.
Monograph N.11. American Soc. Agron
Madison, Wis. pp 483-505
14. Blad, B.L. and N.J. Rosenberg, 1974, Lysimetric calibration of the Bowe
·ratio-ener2V balance
method
for
evapotranspiration
estimation
in
th
central Great Plains.
J.Appl. Meteor. 13:227-235.
15. Rosenberg, N.J., 1975.
Various reports.
"Nebraska Water Resources
Res
Inst.,
Agricultural meteorology program reports".
University of Nebraska
Lincoln, Nebraska.
16. Statistical Analysis System, SAS user's guide, 1979 edition.
Cary, North Carolina, 494p.
SAS
Inst.
17. Rosenberg,
N.J.,
1969.
Seasonal
patterns
irri2ated alfalfa in the central Great Plains.
in evapotranspiration
Agron. J. 61:879-886.
18. Haddock,
D.,
1981.
Pan
evaporation:
2uide
to
estimatin2
watel
requirements
of soybeans and peanuts.
Weekly Weather and Crop Bulletin 6f
(No. 30):6-8.
- 23 -
APPENDIX
Abbreviations
used for variables.
TI - l200Z temperature
TG - temperature gradient 1n the "upwind" direction
TA - Estimated temperature "aJvection" based on the l200Z temp. gradient
DW - l200Z dew-point temperature
DP - dew-point temperature depression
DC - dew-point temperature gradient in the "upwind" direction
DA - estimated dew-point "advection"
SA - estimated dew-point depression, "moisture advection"
WS - wind speed
WD - coded wind direction
LE - latent energy equivalent of evapotranspiration
IN - net radiation
R - Ratio of LE to aN, dependent measure of advection
CD - climatological
day of the year
TIDP - sum of the values of TI and DP.
':,u.S. GOVERNMENT PRINTING OFFICE:
1982- 360-932:
SRS-1099
- 24 -