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Comparison of Three Micrometeorological Methods
to Calculate Evapotranspiration in Owens Valley California1
Lowell F. W. Duell, Jr., and Diane M. Nork2
Abstract.--Using the Bowen ratio/energy-budget, eddycorrelation, and Penman combination methods, 24-hour
evapotranspiration values, in millimeters per day, were
6.1, 6.0, and 21.7 for a salt grass site in May 1984; ].2,
2.0, and 12.3 for a greasewood site in June 1984; and 1.6,
2.2, and 10.4 for a rabbitbrush site in July 1984.
INTRODUCTION
The U. S. Geological Survey, in cooperation
wi th the city of Los Angeles and Inyo County,
has undertaken a ground-water study to quantify
the fluxes of ground water in the aquifer system
of Owens Valley, Calif.
In Owens Valley,
evapotranspiration (ET)--plant transpiration and
evaporation from the soil surface--is one of the
largest fluxes out of the ground-water system and
the least understood.
Because of the valley's
semiarid to arid conditions, more than one method
of calculating ET was required to test the accuracy of results and the applicability of each
method.
The study uses three methods to calculate ET:
Bowen ratio/energy-budget method,
eddy-correlation method, and Penman combination
method.
This paper presents the equations and
selected results for each method.
\ST-JUBA
\
\
STUDY AREA
\
EXPLANATION
Owens Valley is in the eastern part of
central California, bounded by the Sierra Nevada
on the west and the White and Inyo Mountains on
the east. The long, narrow valley comprises 8,500
square kilometers.
The valley floor is about
1,200 meters above sea level, and the mountains
rise more than 4,300 meters above sea level. The
study area (fig. 1) encompasses about 1,300 square
kilometers.
m
,-t
Study area
Watershed bounda ry
CHNAiDIST
Haiwee
Reservoir
Site name and I ocat ion
10
20
30
40
KILOMETERS
1---''-.-1....I.I_..LI'1-.J'
10
20 MILES
Figure l.--Location of study area.
The climate in Owens Valley is semiarid to
arid. Annual precipitation ranges from 100 to 150
millimeters and the phreatophyte growing season is
from March to September.
Soils range from sandy
to loamy and depths to ground water range from
land surface to 5 meters below land surface dependjng on site location.
DESCRIPTION OF METHODS AND SITE LOCATION
Seven locations were selected to calculate
ET rates in Owens Valley.
Three locations are
continuous-record sites that have semipermanent
meteorological instrumentation.
At these sites,
the Bowen ratio/energy-budget method is used for
periods of up to 2 weeks per month during the
growing season.
During plant dormancy and times
when the Bowen ratio/energy-budget is not used,
instrumentation is changed to use the Penman combination method to calculate potential ET.
The
eddy-correlation method also is used at these
sites for comparative and correlative purposes.
The other four locatjons are partial-record sites
Ipaper presented at the North American
Riparian
Conference
[University
of Arizona,
Tucson, AZ, April 16-18, 1985].
2Lowell F. W. Duell, Jr., and Diane M. Nork
are Hydrologists, U. S . Geological Survey, tVRD,
San Diego, CA.
161
where ET is calculated only by the mobile eddycorrelation instruments with data taken 1 to 3
days each month. Additional results of the eddycorrelation method are in Duell (1985).
G is rate of heat storage in the soil or
water, in watts per square meter;
SHF is sensible heat flux, in watts per
square meter;
A is latent heat of vaporization, equal to
2,450 Joules per gram at 20°C; and
E is quantity of water evaporated, in
grams per square meter.
The three continuous-record sites are identified by abbreviations of the codominant phreatophyte species that are within each site (fig. 1).
The common plant names, plant genus and species,
and species abbreviations used for site description are as follows:
Use of the Governing Equations
Bowen Ratio/Energy-Budget Method
Salt Grass--DistiahZis striata var. striata(DIST)
Greasewood-- Saraobatus vermiauZatus (SAVE)
Rubber Rabbitbrush--Chrysothamnus nauseosus(CHNA)
Baltic Rush--Junaus baZticus (JUBA)
In determining the components of an energy
budget, net radiation and soil heat storage can
be measured without much difficulty.
Sensible
and latent heat fluxes depend on atmospheric
fluctuations and are somewhat more difficult
to determine.
The Bowen ratio partitions the
energy budget between sensible and latent heat.
Assuming the eddy diffusivities for heat and vapor
transport are equal, rearranging equation (1)
leads to
At the sites, DIST-JUBA, DIST-SAVE, and
CHNA-DIST, ET rates were calculated on Hay 22-23,
June 6-7, and July 14-15, 1984. All results
presented in this paper are from simultaneous use
of all three methods in the same 24-hour period
for each location site.
INSTRUMENTATION
In each of the three methods, the energy
budget is the necessary calculation, however,
instrumentation varies with each method.
The
Bowen ratio/energy-budget instrumentation consists
of a net radiometer, a thermopile-type soil-heatflux plate, a pair of ventilated wet- and dry-bulb
psychrometers, and a micrologger that records data
on cassette tape. The psychrometers--mounted on a
pulley system on a 2-meter tall mast--sense
temperatures and vapor densities at the top of the
plant canopy (1 meter) and 1 meter higher than the
plant canopy.
In order to prevent sensor bias,
the positions of the psychrometers are reversed
every 15 minutes, and data averages are accumulated every 30 minutes.
The mobile eddycorrelation
instrumentation includes a Lymanalpha hygrometer, a sonic anemometer, a fine wire
thermocouple, and a data logger equipped with
covariance software; additional components of the
energy budget are calculated with a net radiometer
and five soil~heat-flux plates. The Penman combination instrumentation consists of net radiometer,
a soil-heat-flux plate, a cup anemometer, a solidstate relative humidity probe, and a data logger.
A more complete description of all instrumentation
is in Simpson and Duell (1984).
radiation,
(3)
B=yb.T//Jpv
(4)
where
Y is psychrometer constant, in grams per
cubic meter per degree Celsius;
T is air temperature in degrees Celsius;
b.T is difference in air temperature at two
heights, in degrees Celsius;
pv is vapor density, in grams per cubic
meter; and
b.pv is difference in vapor density at two
heights, in grams per cubic meter.
The psychrometer constant (y) can be calculated by
y=paCp/>"
(5)
where
pa is air density, equal to
station barometric pressure,~
(6)
1204
in millibars
( sea level barometic pressure,
in millibars
at 20°C in grams per cubic meter;
Cp is heat capacity of air, equal to 1.01
Joules per gram per degree Celsius; and
A is same as defined in equation (1).
Vapor density (pv) can be determined by
pv=pvs-y(T-Tw)
0)
(7)
where
where
is net
meter;
B=SHF/>"E,
AE is latent heat flux, in watts per square
meter; and
B is Bowen ratio, dimensionless (Bowen,
1926).
Other elements are the same as defined in equation
(1).
The Bowen ratio (B) can be determined by
Because ET is a significant component of the
energy budget, theoretically, the ET rate may be
calculated by estimating all of the other elements
in the energy-budget equations.
With photosynthesis, respiration, and heat storage in the crop
canopy neglected, the equation for the energy
budget at the earth's surface can be expressed as
Rn
(2)
where
DEVELOPMENT OF GOVERNING EQUATIONS
Rn-G-SHF-AE=O
>"E=(Rn-G)/(l+SHF/>"E),
pvs is saturated vapor density, in grams per
cubic meter; and
Tw is wet bulb temperature, in degrees Celsius.
in watts per square
162
Other elements are as defined in equation (4).
Saturated vapor density (Pvs) can be calculated by
rH is resistance to heat transport, in seconds per meter; and
Z is instrument height, in meters.
Other elements are the same as defined in
equa tions (1), (4), and (7).
The slope of the
saturated vapor density (S) can be calculated
by the results of a cubic regression on data
presented in Campbell (1977) which gives the
following equation
(8)
where
Tw is the same as defined in equation (7).
S =0.337569+0.02067T+0.00427T 2 +O.000011T 3
Eddy-Correlation Method
Swinbank (1951) proposed an eddy-correlation
method to calculate the vertical flux of heat and
water vapor that is transported by fluctuations,
or eddies, in the atmosphere.
For the eddycorrelation method, sensible and latent heat
fluxes are calculated independent of other energy
budget components.
Sensible heat flux is calculated from the covariance of wind and temperature
flux, and latent heat flux is directly calculated
by the covariance of vapor and wind flux.
These
two components, theoretically, should equal the
energy budget; however, in field conditions the
components failure to do so results in the need
to calculate the difference, or closure, between
the fluxes and the energy budget.
The percent
closure of the energy budget is calculated by
Energy-budget closure= (AE+SHF) 100
Rn - G
where
T is the same as defined in equation (4).
The resistance to heat transport (rH) can be calculated by
h
is (average crop height) x (vegetation
percent cover), in meters;
d is 0.979 log h-0.154, in meters (Stanhill,
1969);
Zm is 0.13 h, in meters;
Zh is 0.2 Zm, in meters; and
k is von Karman's constant equal to 0.4,
dimensionless; and
u is mean wind speed at height Z, in meters
per second.
Other elements are the same as defined in equation
(9)
(11) .
RESULTS AND DISCUSSION
Selected results from the three methods for
each site are given in table 1.
In order to
minimize the error associated with each component
of the energy budget--in particular the change in
energy storage above the point measurement of soil
heat flux--all components used for the calculation
of values (presented in table 1) are mean weighted
totals for each t or I-hour period of measurement
integrated during 24 hours.
(10)
Combination Method
Calculations of Bowen ratio values varied
considerably throughout a 24-hour period, particularly during sunrise and sunset. Fuchs and Tanner
(1970), Black and McNaughton (1971), Grant (1975),
and Gay (1980) have recognized such discrepancies,
and current data usually include only the daylight
hours. In general, data collected from sunset to
sunrise may be considered unimportant because
there is little energy available to cause evaporation, and the energy that is available produces
sensible heat loss.
Bowen ratio fluctuations
throughout the day may be attributed to errors in
temperature and vapor-density measurements or instrumentation malfunction.
Nany equations are available for estimating
potential ET from climatic data, and of these, the
Penman combination equation is used for this
study.
The original Penman equation (Penman,
1956) for calculating potential ET is based on
the assumptions that water is in plentiful supply,
the plant is of uniform height, and canopy resistance to heat and vapor transfer to the atmosphere
are equal.
Based on field conditions, the original equation was altered to meet conditions in
Owens Valley.
The equation used for the Penman
combination method (Campbell, 1977) is
AEp=
S
S+y
(Rn-G)+ y (A/rH) (pvs-pv)
S+y
(13)
where
Elements are defined in equation (1).
Pel~an
In (Z - d + 2h) In (Z - d + Zm)
Zh
Zm
rH
The elements are the same as defined in equation
(1). The energy-budget residual is more accurate
than measurements of direct vapor flux based on
regression analysis of the energy-budget closure,
calibration problems associated with the directvapor flux instrument, manufacturers' recommendations, and field tests.
Therefore, the latent
heat flux is calculated as a residual of the other
energy-budget components by the following equation
AE=Rn-G-SHF
(12)
(11)
The eddy-correlation method allows for the
direct determination of sensible and latent heat
fluxes independent of the energy budget. In this
study, the latent heat flux also is calculated as
a residual of the other energy-budget components.
Calculating latent heat flux as an energy-budget
where
AEp is potential latent heat flux, in watts
per square meters;
S is slope of the saturated vapor density,
in grams per cubic meter per degree
Celsius;
163
Table 1.--Comparison of evapotranspiration rates and site and micrometeoro10gica1
characteristics between sites.
[Site characteristics: Vegetation cover from City of Los Angeles, Department of
Water and Power (written commun., 1984); Average plant height from D. C. Warren,
Inyo County (oral commun., 1984)]
DIST-JUBA
DIST-SAVE
CHNA-DIST
6.1
1.2
1.6
6.0
4.0
21.7
2.0
.6
12.3
2.2
.3
10.4
70.0
.25
22.0
.4
50.0
.5
122.0
88.0
148.0
2.5
2.8
15.2
75.0
65.0
133.0
6.5
2.6
20.8
Evapotranspiration rate
Bowen ratio/energy-budget method~------mm/d-­
Eddy-correlation method
Residua1---------------------------mm/d-Direct measurement-----------------mm/d-Penman combination method--------------mm/d-Site characteristics
Vegetation cover--------------------percent-Average plant height-,--------------------m-Micrometeoro10gica1 characteristics
Average sensible heat flux
Bowen ratio/energy-budget method-----W/m 2 -Eddy-correlation method--------------W/m 2 -Average net radiation------------------W/m 2 -Average soil heat f1ux-----------------W/m 2-Average wind speed----------------------m/s-Average vapor density deficit----------g/m 3-residual
(equation
10)
eliminates
some
of
the error associated with the direct deterMination of latent heat flux by the eddycorrelation instrumentation.
At the DIST-SAVE
and CHNA-DIST sites, ET rates calculated by
the eddy-correlation method are larger than
the
ET
rates
calculated
by
the
Bowen
ratio/energy-budget
method.
In
these
two
cases, large ET rates are probably due to
sensib1e-heat-f1ux values
being
too low as
determined
by
the
eddy-correlation
method
which indicates that some error can be attributed to this measurement.
Thus, the residual
ET values indicate an upper limit to the
flux values rather than the absolute value.
The error is small for the DIST-JUBA site
because total sensible heat flux was small.
At the other sites, sensible heat flux was
dominant so even a small percentage error in
sensib1e-heat-f1ux
calculations
can
produce
a percentage error in 1atent-heat-f1ux calculations (E. P. Weeks, U.S. Geological Survey,
written commun., 1985).
This study indicates
that errors associated with the calculation
of sensible heat flux by the eddy-correlation
instrumentation are less than those associated
with the direct 1atent-heat-f1ux determination,
thus indicating that ET rates resulted from
energy-budget residual 1atent-heat-f1ux values
may be more accurate than t.hose resulting from
1atent-heat-f1ux values determined directly by
the
eddy-correlation
instrumentation.
The
residual 1atent-heat-f1ux values (maximum rate)
12.0
3.0
200.0
27.2
4.8
22.0
and the determined 1atent-heat-f1ux values (minimum rate) are in table 1.
Large potential ET rates using the Penman
combination method at the DIST-JUBA site may
be due to wind speeds that ranged from 2.5 to
8.7 meters per second.
Error associated with
vapor-density-deficit
calculation
also' could
be responsible for the large potential ET values;
however, variance analysis of the vapor-density
deficit determined with the relative humidity
probe, versus that calculated from psychrometric
data, indicated no significant difference between
the two means of data collection.
This study
indicated that is was necessary to adjust the
Penman equation for resistance to heat transfer
(equation 13) in order to account for the lack
of complete vegetation cover at the sites. Thus,
altering resistance to heat transport and the
elements of the wind function in the Penman
combination method had a Significant effect on
the calculated potential ET rates.
It also
seems likely that in the semiarid to arid
environment of Owens Valley, incomplete cover
and the nature of the vegetation combine to
make the resistance to vapor transport from
the canopy to the air considerably greater than
resistance to heat transport (E. P. Weeks,
U.S. Geological Survey, written commun., 1985).
In this case, then, resistance to vapor transport
is not equal to resistance to heat transport,
which indicates that another I:lethod may be more
suitable for estimating potential ET.
164
CONCLUSIONS
Bowen, I. S.
1926.
The ratio of heat losses
by conduction and by evaporation from any
water surface. Phys. Rev., v. 27, p. 779-787.
In Owens Valley, ET accounts for the removal
of a significant quantity of ground water.
The
valley's phreatophyte communities differ largely
in species composition and percent cover, therefore, ET rates were monitored at a variety of
sites.
The valley's semiarid to arid conditions
require the use of more than one method to calculate ET rates in order to test the applicability
of each method.
Campbell, G. S. 1977. An introduction to environmental biophysics.
Springer-Verlag, New
York, 159 p.
Duell, L. F. W., Jr.
1985.
Evapotranspiration
rates from rangeland phreatophytes by the
eddy-correlation method in Owens Valley, California.
17th Conference on Agricultural and
Fores t Meteorology.
[Phoenix, AZ, May 1985]
American
Meteorological
Society
Bulletin,
Paper A&F3.2, p. 44-47
Results from the Bowen ratio/energy-budget
method for calculating ET rates can be both consistent and satisfactory, as well as fluctuating.
Despite the fluctuating data, which needs to
be adju.sted to account for the sunset to sunrise hours in a 24-hour period, the Bowen
ratio/energy-budget method is suitable for calculating actual ET .rates in Owens Valley. ET rates
calculated by the eddy-correlation method are
generally larger than ET rates calculated by the
Bowen ratio/energy-budget method.
This difference in ET rates may indicate an upper limit to
latent-heat-flux values as calculated by the
eddy-correlation method; however, the results of
the two methods generally agree. The eddycorrelation method presents usable results with
the advantage of instrument mobility. The Penman
combination meth9d needs to be adjusted to
account for physical and biological variables
indigenous to Owens Valley, and does not seem to
be reliable in calculating potential ET in Owens
Valley at this time.
Fuchs, M. R. and C. B. Tanner.
1970.
Error
analysis of Bowen ratios measured by differential psychrometry.
Ag. Heteorology, v. 7,
p. 329-334.
Gay, L. W.
1980. Energy budget measurements of
evaporation from bare ground and evapotranspiration from salt cedar groves in the Pecos
Ri ver flood plain, New Nexico.
Report to
U.S. Geological Survey, WRD, Grant No. 14-08001-G-617, 46 p.
Grant, D. R. 1975.
Comparison of evaporation
measurements using different methods.
Quart.
J. R. Met. Soc., v. 101, p. 543-550.
Penman, H. L.
1956.
Trans. Am. Geophys.
Estimating evaporation.
Union, v. 37, p. 43-50.
Simpson, M. R. and L. F. H. Duell, Jr. 1984.
Design and implementation of evapotranspiration
measuring equipment for Owens Valley, California.
Ground Water Moni toring Review, Fall,
p. 155-163.
For calculating actual ET rates, results from
the Bowen ratio/energy-budget and eddy-correlation
methods are satisfactory and indicate the methods'
suitability for continued use in the ongoing Owens
Valley studies.
The methods presented in this
report can have applicability to similar areas in
the semiarid to arid Western United States.
REFERENCES
Stanhill, G. A.
1969. A simple instrument for
the field measurement of turbulent diffusion
flux.
Journal of Applied Meteorology, v. 8,
p. 509-513.
Black, T. A. and K. G. McNaughton.
1971.
Psychrometric apparatus for Bowen ratio determinations over forests.
Boundary-layer Meteorology, v. 2, p. 246-254.
Swinbank, W. C. 1951. The measurement of vertical
transfer of heat and water vapor by eddies in
the lower atmosphere. J. Meteorology, v. 8,
p. 135-145.
165