Evapotranspiration From Selected Fallowed

Agricultural Fields on the Tule Lake National

Wildlife Refuge, California, During May to

October 2000

Prepared in cooperation with the

U.S. FISH AND WILDLIFE SERVICE

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 02-4055
U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 02-4055

Evapotranspiration From Selected Fallowed

Agricultural Fields on the Tule Lake 

National Wildlife Refuge, California,

During May to October 2000

Prepared in cooperation with

U.S. FISH and WILDLIFE SERVICE

By William R. Bidlake

Tacoma, Washington

2002
U.S. DEPARTMENT OF THE INTERIOR

GALE A. NORTON, Secretary

U.S. GEOLOGICAL SURVEY

Charles G. Groat, Director

For additional information write to:

District Chief

U.S. Geological Survey

1201 Pacific Avenue – Suite 600

Tacoma, Washington 98402

http://wa.water.usgs.gov

Copies of this report can be purchased

from:

U.S. Geological Survey

Information Services

Building 810

Box 25286, Federal Center

Denver, CO 80225-0286

Any use of trade, product, or firm names in this publication is for descriptive purposes only and does not imply 

endorsement by the U.S. Government.

District Chief

U.S. Geological Survey

1201 Pacific Avenue – Suite 600

Tacoma, Washington 98402

http://wa.water.usgs.gov
Symbols vii

CONVERSION FACTORS, VERTICAL DATUM, SYMBOLS, AND ABBREVIATIONS

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows:

°F= (1.8 °C)+32

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows:

°C= (°F-32)/1.8

Sea level: In this report "sea level" refers to the National Geodetic Vertical Datum of 1929 (NGVD

of 1929)--a geodetic datum derived from a general adjustment of the first-order level nets of both

the United States and Canada, formerly called Sea Level Datum of 1929.

SYMBOLS 

Multiply By To obtain

Length

millimeter (mm) 0.03937 inch

meter (m) 3.281 foot 

kilometer (km) 0.6214 mile 

Area

square meter (m2) 0.0002471 acre

hectare (ha) 2.471 acre

Volume

cubic meter (m3) 35.31 cubic foot 

Mass

gram (g) 0.03527 ounce, avoirdupois

kilogram (kg) 2.205 pound avoirdupois

Energy

joule (J) 0.2388 calorie

9.4787 x 10-4 British thermal unit

Pressure

kilopascal (kPa) 0.01 bar 

0.1450 pound-force per square inch

Power

watt (W) 0.2388 calorie per second

3.412 British thermal unit per hour

Velocity or Rate

meter per second (m/s) 2.2370 miles per hour

millimeter per day (mm/d) 0.03937 inch per day

Symbol Meaning Dimensions

A0 to A6 Coefficients Variable

Am Measured available energy for the surface of interest W/m2

cp Specific heat of air at constant pressure (J/g)/°C

cpd Specific heat of dry air at constant pressure (J/g)/°C

cpv Specific heat of water vapor at constant pressure (J/g)/°C
viii Symbols

cs Specific heat of dry soil (J/kg)/°C

cw Specific heat of water (J/kg)/°C

D Atmospheric water-vapor pressure deficit kPa

d Day of the calendar year days

d0 Zero-plane displacement height m

dp Diameter of soil heat flux plate mm

dr Day of the summer solstice days

dy Number of days per year days

E Evapotranspiration rate (g/m2)/s or mm/d

E0 Reference evapotranspiration rate mm/d

e Water-vapor pressure kPa

es Water-vapor pressure at atmospheric saturation kPa

F Fetch-to-instrument-height ratio for westerly winds Dimensionless

G Soil heat flux at the soil surface W/m2

Gz Soil heat flux at soil depth z W/m2

G′z Uncorrected measured Gz W/m2

H Sensible heat flux W/m2

HBREB Sensible heat flux from the Bowen ratio energy balance technique W/m2

HEC Sensible heat flux from the eddy covariance technique W/m2

hc Height of crop canopy m

kc Empirical crop coefficient Dimensionless

hr Relative humidity Dimensionless

km Thermal conductivity of calibration medium for soil heat flux plate (W/m)/°C

kp Thermal conductivity of soil heat flux plate (W/m)/°C

ks Soil thermal conductivity (W/m)/°C

L Thickness of soil heat flux plate mm

p Atmospheric pressure kPa

R Ratio of available energy at the contaminating surface to that at the surface of interest Dimensionless

Rd Ideal gas constant for dry air (J/g)/K

Rn Net radiation W/m2

s Slope of the relation between water-vapor pressure at atmospheric saturation and temperature kPa/°C

T Air temperature °C

Short-term fluctuation of air temperature from the time-averaged mean °C

Tc Temperature of cavity housing relative humidity sensor °C

Ts Soil temperature °C

Ts Depth-averaged temperature of soil layer °C

Symbol Meaning Dimensions

T′
Symbols ix

t Time s

tUTC Coordinated Universal Time hours

w′ Short-term fluctuation of vertical wind speed from the time-averaged mean m/s

x Fetch m

Z Site altitude m

z Depth in soil m

z0 Roughness length m

zu Height above land surface m

α Coefficient equal to the ratio of λE to λEEQ Dimensionless

β Bowen ratio Dimensionless

βc Bowen ratio for the contaminating surface Dimensionless

βi Actual Bowen ratio for the surface of interest Dimensionless

βm Measured Bowen ratio for the surface of interest Dimensionless

Γ Longitude radians

γ Psychrometer constant kPa/°C

∆ Difference over a vertical interval or vertical displacement Variable

δ Solar declination angle radians

δλE Error in λEm due to the influence of the contaminating surface W/m2

ε Ratio of the mass of a mole of water to the mass of a mole of dry air Dimensionless

η Prescribed minimum for the fetch-to-height ratio Dimensionless

θ Volumetric soil water content Dimensionless

θ* Uncorrected volumetric soil water content Dimensionless

λ Latent heat of vaporization for water J/g

λE Latent heat flux W/m2

λEc Latent heat flux from the contaminating surface W/m2

λEEQ Equilibrium latent heat flux W/m2

λEi Latent heat flux from the surface of interest W/m2

λEm Measured latent heat flux from the surface of interest W/m2

ρ Air density g/m3

ρd Density of dry air g/m3

ρs Soil bulk density kg/m3

ρv Density of atmospheric water vapor g/m3

ρw Density of water kg/m3

τ Period of wave ms

Φ Latitude radians

Symbol Meaning Dimensions
x Symbols and Abbreviations

Φr Latitude of the Tropic of Cancer radians

Ψ Solar elevation angle radians

%EqλE Percentage of equilibration of latent heat flux to the surface of interest Dimensionless

%δλE Percentage error in λEm due to the influence of the contaminating surface Dimensionless

 Overbar representing averaging over time or with distance

Abbreviations Meaning

n Sample size

P Piezometer

PDT Pacific Daylight Time

PT Priestley-Taylor

RMSD Root-mean-square difference

RMSE Root-mean-square error

r Correlation coefficient

sd Standard deviation

BREB Bowen ratio energy balance

NWR National Wildlife Refuge

USFWS U.S. Fish and Wildlife Service

USGS U.S. Geological Survey

Symbol Meaning Dimensions
Contents iii

CONTENTS

Abstract ................................................................................................................................................................ 1

Introduction .......................................................................................................................................................... 2

Acknowledgments....................................................................................................................................... 4

Purpose and Scope ...................................................................................................................................... 4

Climate of the Study Area........................................................................................................................... 4

Study Sites................................................................................................................................................... 4

Evapotranspiration Measurement and Modeling Techniques.............................................................................. 8

Bowen Ratio Energy Balance ..................................................................................................................... 8

Eddy Covariance ......................................................................................................................................... 11

Priestley-Taylor........................................................................................................................................... 11

Reference Evapotranspiration ..................................................................................................................... 12

Applications of Evapotranspiration Measurement and Modeling Techniques .................................................... 13

Net Radiation .............................................................................................................................................. 13

Soil Heat Flux ............................................................................................................................................. 13

Air Temperature and Vapor Pressure.......................................................................................................... 16

Data Screening and Segregation ................................................................................................................. 17

Eddy Covariance and Other Measurements................................................................................................ 18

Estimating Depth to the Water Table.......................................................................................................... 18

Instrumentation Deployments ..................................................................................................................... 19

Vegetation ............................................................................................................................................................ 21

Lot C1B Site................................................................................................................................................ 22

Lot 6 Stubble Site........................................................................................................................................ 23

Lot 6 Cover Crop Site ................................................................................................................................. 24

Meteorological Conditions and Surface Energy Balance .................................................................................... 24

Airstream Equilibration........................................................................................................................................ 30

Comparing Sensible Heat Flux from the Bowen Ratio Energy Balance and Eddy Covariance Techniques ...... 32

Evapotranspiration Modeling............................................................................................................................... 34

Evapotranspiration and Depth to the Water Table............................................................................................... 36

Summary and Conclusions................................................................................................................................... 44

References Cited .................................................................................................................................................. 46
iv Contents

FIGURES

Figure 1. Map showing part of the Upper Klamath Basin, northern California and southern Oregon, 

and the Tule Lake National Wildlife Refuge..................................................................................... 3

Figure 2. Map showing Tule Lake National Wildlife Refuge, lot C1B, and lot 6 ............................................ 6

Figure 3. Graphs showing (A) surface energy balance components net radiation (Rn), energy flux 

into the soil surface (G), and latent (λE) and sensible (H) heat fluxes; (B) wind direction, 

classified as easterly (E), westerly (W), or mixed easterly and westerly (M); (C) Bowen 

ratio (β) and ratio of latent heat flux to equilibrium latent heat flux (α); and (D) wind 

speed (U) and atmospheric water-vapor pressure deficit (D), all as they varied at the 

lot C1B evapotranspiration measurement site during June 14 to 17, 2000 ....................................... 26

Figure 4. Graphs showing (A) surface energy balance components net radiation (Rn), energy flux 

into the soil surface (G), and latent (λE) and sensible (H) heat fluxes; (B) wind direction, 

classified as easterly (E), westerly (W), or mixed easterly and westerly (M); (C) Bowen 

ratio (β) and ratio of latent heat flux to equilibrium latent heat flux (α); and (D) wind 

speed (U) and atmospheric water-vapor pressure deficit (D), all as they varied at the 

lot C1B evapotranspiration measurement site during August 25 to 28, 2000 ................................... 27

Figure 5. Graphs showing comparisons between 30-minute-average sensible heat flux as computed 

by the Bowen ratio energy balance technique and by the eddy covariance technique at the 

lot C1B evapotranspiration measurement site during October 18 and 19, 2000, at the lot 6 

stubble evapotranspiration measurement site during August 29 and 30, 2000, and at the 

lot 6 cover crop evapotranspiration measurement site during August 28 and 29, 2000.................... 33

Figure 6. Graphs showing daily reference evapotranspiration rate at the Intermountain Research 

and Extension Center during May to October 2000, and at the lot C1B evapotranspiration 

measurement site, daily evapotranspiration rate computed by the Bowen ratio energy 

balance (BREB) technique that was supplemented with evapotranspiration rate modeled 

by the Priestley-Taylor (PT) technique, daily evapotranspiration rate modeled by the reference 

evapotranspiration technique, and ratio of latent heat flux to equilibrium latent heat flux 

(α) averaged for 3 to 7 days; (B) daily average volumetric soil water content at a depth of 

0.025 or 0.05 meter, averaged among three locations at the lot C1B evapotranspiration 

measurement site................................................................................................................................ 38

Figure 7. Graphs showing (A) daily reference evapotranspiration rate at the Intermountain Research and 

Extension Center during May to October 2000, and at the lot 6 stubble evapotranspiration 

measurement site, daily evapotranspiration rate computed by the Bowen ratio energy 

balance (BREB) technique that was supplemented with evapotranspiration rate modeled 

by the Priestley-Taylor (PT) technique, daily evapotranspiration rate modeled by the reference 

evapotranspiration technique, and ratio of latent heat flux to equilibrium latent heat flux 

(α) averaged for 3 to 7 days; (B) daily average volumetric soil water content at a depth of 

0.05 meter, averaged among three locations at the lot 6 stubble evapotranspiration 

measurement site................................................................................................................................ 39
Contents v

Figure 8. Graphs showing (A) daily reference evapotranspiration rate at the Intermountain Research and 

Extension Center during May to October 2000, and at the lot 6 cover crop evapotranspiration 

measurement site, daily evapotranspiration rate computed by the Bowen ratio energy 

balance (BREB) technique that was supplemented with evapotranspiration rate modeled 

by the Priestley-Taylor (PT) technique, daily evapotranspiration rate modeled by the reference 

evapotranspiration technique, and ratio of latent heat flux to equilibrium latent heat flux 

(α) averaged for 4 to 8 days; (B) daily average volumetric soil water content at a depth of 

0.05 meter, averaged among three locations at the lot 6 cover crop site ........................................... 40

Figure 9. Graphs showing relation between percentage of site cover by vegetation and (A) the ratio of 

evapotranspiration rate to reference evapotranspiration rate (E/E0); and (B) the ratio of 

latent heat flux to equilibrium latent heat flux (α), all at the lot C1B and lot 6 stubble 

evapotranspiration measurement sites ............................................................................................... 41

Figure 10. Graphs showing depth to the water table below the land surface at lot C1B and at lot 6 

during May to October 2000, as estimated from water level in shallow piezometers....................... 43
vi Contents

TABLES

Table 1. Approximate maximum heights of vegetation or vegetation residues, and heights of air 

and wind sensors ............................................................................................................................... 20

Table 2. Percentage of ground coverage by vegetation and vegetation residues, and percentage of 

exposed soil at the lot C1B and lot 6 stubble evapotranspiration measurement sites, by 

sampling date .................................................................................................................................... 22

Table 3. Daily precipitation measured at the lot C1B and lot 6 cover crop evapotranspiration 

measurement sites, shown for days precipitation was detected at least one site .............................. 25

Table 4. Fetch-to-instrument-height ratio for Bowen ratio energy balance measurements, measured 

and theory-predicted Bowen ratios and energy fluxes, and estimated percentage error and error 

in measured latent heat flux, all for westerly winds during midday (1100 to 1500 hours, 

Pacific Daylight Time) on selected days for the lot 6 stubble and the lot 6 cover crop 

evapotranspiration measurement sites during June to October, 2000 ............................................... 31

Table 5. Monthly average evapotranspiration rate and ratio of evapotranspiration rate to reference 

evapotranspiration rate for the lot C1B, lot 6 stubble, and lot 6 cover crop evapotranspiration 

measurement sites during May to October, 2000 ............................................................................. 36

Table 6. Average of 30-minute-average available energy, latent heat flux, Bowen ratio, and ratio of 

latent heat flux to equilibrium latent heat flux, by wind direction, time of day, and selected 

periods of days, and computed for the lot C1B evapotranspiration measurement site ..................... 50

Table 7. Average of 30-minute-average available energy, latent heat flux, Bowen ratio, and ratio of 

latent heat flux to equilibrium latent heat flux, by wind direction, time of day, and selected 

periods of days, and computed for the lot 6 stubble evapotranspiration measurement site .............. 54

Table 8. Average of 30-minute-average available energy, latent heat flux, Bowen ratio, and ratio of 

latent heat flux to equilibrium latent heat flux, by wind direction, time of day, and selected 

periods of days, and computed for the lot 6 cover crop evapotranspiration measurement site ........ 57
Abstract 1

Evapotranspiration From Selected Fallowed Agricultural 

Fields on the Tule Lake National Wildlife Refuge, 

California, During May to October 2000

By William R. Bidlake

ABSTRACT

An investigation of evapotranspiration, 

vegetation quantity and composition, and depth to 

the water table below the land surface was made at 

three sites in two fallowed agricultural lots on the 

15,800-hectare Tule Lake National Wildlife 

Refuge in northern California during the 2000 

growing season. All three sites had been farmed 

during 1999, but were not irrigated since the 1999 

growing season. Vegetation at the lot C1B and lot 

6 stubble sites included weedy species and small 

grain plants. The lot 6 cover crop site supported a 

crop of cereal rye that had been planted during the 

previous winter. Percentage of coverage by live 

vegetation ranged from 0 to 43.2 percent at the lot 

C1B site, from approximately 0 to 63.2 percent at 

the lot 6 stubble site, and it was estimated to range 

from 0 to greater than 90 percent at the lot 6 cover 

crop site. Evapotranspiration was measured using 

the Bowen ratio energy balance technique and it 

was estimated using a model that was based on the 

Priestley-Taylor equation and a model that was 

based on reference evapotranspiration with grass 

as the reference crop.

Total evapotranspiration during May to 

October varied little among the three 

evapotranspiration measurement sites, although 

the timing of evapotranspiration losses did vary 

among the sites. Total evapotranspiration from the 

lot C1B site was 426 millimeters, total 

evapotranspiration from the lot 6 stubble site was 

444 millimeters, and total evapotranspiration from 

the lot 6 cover crop site was 435 millimeters. The 

months of May to July accounted for 

approximately 78 percent of the total 

evapotranspiration from the lot C1B site, 

approximately 63 percent of the 

evapotranspiration from the lot 6 stubble site, and 

approximately 86 percent of the total 

evapotranspiration from the lot 6 cover crop site. 

Estimated growing season precipitation accounted 

for 16 percent of the growing-season 

evapotranspiration at the lot C1B site and for 

17 percent of the growing-season 

evapotranspiration at the lot 6 stubble and cover 

crop sites. 

The ratio of evapotranspiration rate to the 

reference evapotranspiration rate was strongly 

correlated with percentage of site coverage by 

vegetation at the lot C1B and lot 6 stubble sites 

(correlation coefficient = 0.95, sample size = 6), 

where percentage of site coverage was determined 

from quantitative vegetation surveys. It is 

concluded that evapotranspiration was mediated 

by the vegetation at all three sites, and that the 

differences in seasonal timing of 

evapotranspiration losses were caused by 

differences in timing of vegetation growth and 

development and senescence among the sites. 

Depth to the water table below the land surface at 

lot C1B ranged from 0.67 meters in early July to 

greater than 1.39 meters in late August. Depth to 

the water table at lot 6 ranged from 0.77 meter in 

late May to greater than 1.40 meters in late 

August.
2 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

INTRODUCTION

Management of water resources for water supply 

or conservation typically involves manipulating 

hydrologic balances in space or time, or both. For 

example, a reservoir might be built to detain the waters 

of stream runoff so the waters can be distributed later to 

specified locations. The field of agricultural water 

management is replete with practices intended to alter 

local water balances to achieve conditions favorable to 

plant growth and development. Fallowing, the practice 

of allowing land ordinarily used for crops to lie idle 

during the growing season, can conserve water at a 

given place and time so the water can be used for other 

purposes. Fallowing can reduce evaporative water loss 

by reducing or eliminating water-consuming 

vegetation, thereby allowing some of the soil-moisture 

stores either to be retained for crop growth and 

development during future growing seasons or to drain 

from the soil to recharge an aquifer. Fallowing of 

agricultural lands that are normally irrigated also 

spares water normally diverted for irrigation to be 

conserved and used elsewhere. 

Water conservation through selective fallowing 

of croplands may be an important tool for water 

management in the Upper Klamath River Basin of 

southern Oregon and northern California (fig. 1), where 

there are many demands for scarce water resources. 

The U.S. Fish and Wildlife Service (USFWS) 

administers six National Wildlife Refuges (NWR’s) 

totaling approximately 80,000 hectares (ha) in the 

Klamath River Basin (U.S. Fish and Wildlife Service, 

2001), and is a principal manager of land and water 

resources in the basin. Five of the six Klamath River 

Basin NWR’s are shown in figure 1. The 

15,800-ha Tule Lake NWR contains approximately 

6,900 ha of croplands that have for many years been 

leased to farmers for agricultural production and to 

provide food and habitat for wildlife. Some of the 

water flowing into the Tule Lake NWR maintains 

water levels in its wetlands, some is diverted to irrigate 

croplands, and some is conveyed to the Lower Klamath 

NWR to help maintain wetland habitats in the latter 

refuge. The USFWS is investigating whether or not 

intermittent fallowing with the attendant cessation of 

irrigation on selected Tule Lake NWR croplands will 

conserve water that can then be used to maintain 

wildlife habitats in the basin.

Evapotranspiration often constitutes the greatest 

loss of water from terrestrial sites, and an 

understanding of evapotranspiration from fallowed 

croplands is important for evaluating the effectiveness 

of fallowing as a water conservation practice. Although 

many sources of information exist that can be used for 

estimating evapotranspiration from irrigated, actively 

farmed croplands in the Klamath River Basin (for 

example Doorenbos and Pruitt, 1977; Jensen and 

others, 1990; and Snyder and others, 1987), apparently 

little information is available for estimating 

evapotranspiration from fallowed croplands. 

Additionally, recently fallowed croplands are disturbed 

ecosystems consisting of plants sprouted from seeds of 

previous crops, weedy plants, bare soil, and crop 

residues. For this reason, a strong scientific 

justification probably does not exist for applying 

results of published case studies of evapotranspiration 

from rangelands (Harr and Price, 1972; Duell, 1990; 

Tomlinson, 1996) to estimate evapotranspiration from 

fallowed croplands.

An intensive study was made by the U.S. 

Geological Survey (USGS) with a primary objective of 

estimating evapotranspiration from three agricultural 

fields on the Tule Lake NWR during the 2000 growing 

season. The intent of this objective was to supply 

estimates of fallowed-field evapotranspiration that the 

USFWS can use in conjunction with estimates of 

evapotranspiration from selected crops to estimate 

water savings that would be realized if normally 

farmed fields were to be fallowed. The fields varied 

with respect to cropping histories and drainage 

structures and they were selected by the USFWS to be 

representative of future fallowed fields that might be 

anticipated on the Tule Lake NWR if cropland 

fallowing is applied as a water conservation strategy. 

The second objective of the study was to note and 

report on the field conditions during the growing 

season, including occurrence and relative abundance of 

crop residues and non-crop plants and depth to the 

water table below the soil surface.
Introduction 3

Aspen 

Lake

Chiloquin

Bonanza

Merrill

Dorris Tulelake

Klamath Falls

Keno

Willow Lake 

Reservoir

 Sprague River

Syc an

River

Miller Cre ek

Lost River

Spencer 

C reek

Meiss 

Lake

Clear Lake 

Reservoir

Gerber 

Reservoir

Swan 

Lake

Round 

Lake Alkali 

Lake

Agency 

Lake

Upper 

Klamath 

Lake

North F or k

South Fork

 Williamson River

Wood River

Lower Klamath

National Wildlife 

Refuge

Bear Valley

National Wildlife 

Refuge

Upper Klamath National 

Wildlife Refuge

Hanks Marsh Unit

Clear Lake 

National Wildlife 

Refuge

Upper Klamath 

National Wildlife 

Refuge

CALIFORNIA

 OREGON

Willow Cr.

Klamath

River

Lost River

US

97

US

97

SR

62

SR

140

SR

66

SR

140

SR

70

SR

39

SR

139

SR

161

OREGON

CALIFORNIA

Figure

location

EXPLANATION

State boundary

Roads

Other National Wildlife Refuge

Lava Beds National Monument

Tule Lake National Wildlife Refuge

0 5 10 15 20 25 MILES

0 5 10 15 20 25 KILOMETERS

Base from U.S. Geological Survey digital

data, 1:100,000, 1979-91

Universal Transverse Mercator projection,

Zone 10

Figure 1. Part of the Upper Klamath Basin, northern California and southern Oregon, and the Tule Lake National 

Wildlife Refuge.
4 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

Acknowledgments

Funding for this work was provided by the U.S. 

Fish and Wildlife Service. Dave Stannard, U.S. 

Geological Survey, helped the author to implement the 

former’s theory of airstream equilibration for the 

Bowen ratio energy balance technique. The loan of a 

critical sensor by Guy DeMeo, U.S. Geological Survey, 

to replace one that failed during the study is gratefully 

acknowledged. Tim Mayer and Sam Johnson, U.S. Fish 

and Wildlife Service, each provided technical 

suggestions for improving the report.

Purpose and Scope

This report describes the study area and the study 

sites and approaches, and it presents results relevant to 

the study’s two objectives. The report describes the 

geographic setting and climate of the study area, and 

the size, soils, drainage structures, and vegetation of 

the study sites, and selected features in surrounding 

lands. Descriptions of study approaches include 

descriptions of the theory and application of the Bowen 

ratio energy balance (BREB) technique for estimating 

evapotranspiration and of the eddy covariance 

technique for estimating sensible heat flux, 

descriptions of data collection and estimation 

techniques, and descriptions of the development and 

application of simple models that were used to estimate 

evapotranspiration for periods when the BREB 

technique could not be used for that purpose. 

Techniques for measuring and tabulating relative 

abundance of crop residues and various plants are 

described, as are techniques for monitoring depth to the 

water table below the soil surface. The primary study 

results, the time series of measured and estimated daily 

evapotranspiration at each study site during May to 

October 2000, are presented with descriptions of the 

vegetation, depth to the water table, and other 

environmental variables that may have influenced 

evapotranspiration, as well as with discussions of 

evidence and observations pertaining to the reliability 

of the evapotranspiration estimates.

Climate of the Study Area

Although the Tule Lake NWR is less than 

250 kilometers (km) inland from the Pacific Ocean, the 

influence of air masses from the Pacific Ocean on the 

local climate is reduced by the mountains to the west. 

At the nearby Tulelake meteorological station, which is 

near the town of Tulelake, Calif. (fig. 1), the 30-year 

monthly average precipitation, computed using data 

collected through 1999, averaged 12 millimeters (mm) 

among the three driest months July through September 

(Western Regional Climate Center, 2001). The 30-year 

monthly average precipitation averaged 34 mm for the 

three wettest months: November, January, and March. 

The 30-year calendar-year average precipitation, which 

was computed as the sum of the 12 monthly averages, 

was 288 mm, and approximately 36 percent of this 

precipitation occurred during the months of May to 

October. Annual precipitation reported by Western 

Regional Climate Center (2001) for Tulelake was 

229 mm in 1999 and 306 mm in 2000. At the time the 

climate data from the Western Regional Climate Center 

were summarized for this report (October 2001), the 

data for year 2000 were provisional (Western Regional 

Climate Center, 2001). Minimum monthly average 

temperature averaged 0 degrees Celsius (oC) for the 

three coldest months, January, February, and 

December, during the 30 years prior to and including 

1999. Maximum monthly average temperature 

averaged 17oC for the three warmest months of June 

through August.

Study Sites

The Tule Lake NWR, which is near the town of 

Tulelake, Calif. (fig. 1), consists of multiple distinct 

tracts with areas of open water, emergent vegetation, 

and croplands (fig. 2). Most of the largest tract of the 

Tule Lake NWR is on nearly flat terrain at an altitude 

of approximately 1,200 meters (m). Surface water 

flows into that tract from the Lost River and watersupply canals. Water on the largest Tule Lake NWR 

tract is regulated by a complex system of water-supply 

canals and ditches, drain canals and ditches, and 

pumps. Many of the water-supply canals deliver water 

to croplands by gravity, so they are elevated above the 

surface of those lands in a network of levees. 
Introduction 5

The drain canals and ditches accumulate water that 

drains from the croplands. Altitudes of water surfaces 

in the drain canals and ditches are generally maintained 

below the altitude of the land surface by pumps that 

remove the water to Tule Lake Sumps 1A and 1B, 

which are shallow water bodies (fig. 2). Several 

thousand hectares of irrigated croplands border the 

Tule Lake NWR to the north and east. Lava Beds 

National Monument lies to the south. Lands 

immediately to the west of the largest Tule Lake NWR 

tract are primarily mountainous rangelands. 

Evapotranspiration and other measurements 

were made at three sites in two agricultural lots on the 

Tule Lake NWR. Lot C1B is approximately 41 ha in 

area (fig. 2, lot C1B). Drainage ditches along the 

northern and southern borders of lot C1B empty into a 

large drain canal that lies on the western border of the 

lot. Beyond the drain canal is an uncultivated buffer 

strip. West of the buffer strip is a levee upon which is a 

road. Immediately west of the levee is a waterway that 

connects Tule Lake Sumps 1A and 1B. A water-supply 

canal and a road are constructed in a levee that lies 

along the east side of lot C1B. The top of the levee is 

approximately 2 m higher than the surface of the lot. 

Irrigation checks, ridges of soil approximately 0.3 m in 

height, spanned almost the entire north-to-south width 

of the field and were spaced approximately 70 m apart. 

The irrigation checks had been constructed to control 

flow of water in the lot during flood-irrigation for the 

crop of the previous year. Lot C1B was not irrigated 

during 2000. Lot C1B was sown to the small grain crop 

barley during the 1999 growing season, and most of the 

eastern half was left unharvested; whereas, most of the 

western half was harvested, leaving stubble that was 

approximately 0.3 m or less in height. The unharvested 

grain was swept by a wildfire prior to late May 2000. 

When this study was begun during May 2000, surface 

coverage in lot C1B consisted of stubble and other crop 

residues, weedy plant species, and small grain plants 

that had sprouted from the seeds from the previous 

crop. During the 2000 growing season, a similarly 

sized lot immediately to the north was sown to a small 

grain crop, and a similarly sized lot immediately to the 

east was sown partly to a small grain crop and partly to 

onions. Land to the south of lot C1B was sown to a 

small grain crop for a estimated distance of several 

hundred meters. Lot C1B was selected for this study 

because it was farmed during 1999, and vegetation 

during 2000 at the lot was thought to be similar to what 

would appear under intermittent fallowing that may be 

practiced to conserve water in the future. An 

evapotranspiration measurement station designed for 

the BREB technique (hereafter, “BREB station”), was 

established in the western half of the lot (fig. 2, lot 

C1B).

Lot 6 is approximately 39 ha (fig. 2, lot 6). A 

drain ditch runs along the northern border of lot 6 and 

empties into a large drain canal that lies on the western 

border of the lot. Two east-west-trending, buried drains 

constructed from perforated pipe traverse most of the 

width of lot 6 and empty to the large drain canal (fig. 2, 

lot 6). Construction plans from 1974 specify a 

minimum depth below the soil surface of 1.2 m for the 

drain pipe. Beyond the drain canal lies a buffer strip. 

West of the buffer strip are the more northern sections 

of the same levee and road that were previously 

described as being to the west of lot C1B. Immediately 

west of the levee is an expanse of Tule Lake Sump 1A 

that is mostly occupied by emergent vegetation. A 

water-supply canal and a road are constructed in a 

levee that lies along the east side of lot 6. The top of the 

levee is approximately 2 m higher than the surface of 

the lot. Irrigation checks similar to those of lot C1B 

were present during this study. Lot 6 was last irrigated 

during 1999, when it was sown to a small grain crop of 

barley. Approximately 4 ha of the 1999 crop was left 

unharvested in parcels that were scattered throughout 

the lot. By early June 2000, the dead standing grain 

plants appeared to have been flattened by the weather. 

Cover crops are commonly sown after harvesting of 

some crops to protect soils from erosion, and part of lot 

6 was tilled and sown to the small grain cereal rye as a 

cover crop during February 2000 to simulate a covercrop that might exist during future fallowing (fig. 2, 

lot 6). Areas that were harvested in 1999 and that were 

not sown to the cover crop were occupied by stubble, 

weedy plants and small grain plants that had sprouted 

from the seeds from the crop of the previous year. A 

similarly sized lot immediately north of lot 6 was 

planted to potatoes during the 2000 growing season, 

and a similarly sized lot immediately to the south was 

sown partly to a small grain crop and partly to onions. 

A lot directly to the east of lot 6 was sown partly to 

onions and partly to a small grain crop during the 2000 

growing season. Lot 6 was selected for this study 

because the presence of buried drains is representative 

of most of the farmed land of the refuge, and it was 

thought that those drains would result in a deeper water 

table than at lot C1B, which did not have the additional 

buried drains. 
6 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000 Lost 

River

0 1 2 3 KILOMETERS

0 1 2 3 MILES

EXPLANATION

Lot division grid

Road

Pump station

Lava Beds National Monument

Emergent vegetation

Fallowed land, planted to cover crop

Tule Lake National Wildlife Refuge

 lands outside of study lots

Open water

Fallowed land, unharvested small grain

 crop or stubble

Base from U.S. Geological Survey digital

data, 1:100,000, 1979-91

Universal Transverse Mercator projection,

Zone 10

Tule Lake

Sump 1B

Intermountain Research

and Extension Center

Tulelake

 SR

139

Tule Lake

Sump 1A

LOT 6

LOT C1B

Figure 2. Tule Lake National Wildlife Refuge, lot C1B, and lot 6.
Introduction 7

250 METERS

0 400 600 800 1000 FEET 200

0 50 100 150 200

Fallowed land, unharvested 

 small grain crop or stubble

Fallowed land, planted to cover crop

Tule Lake National Wildlife Refuge

 lands outside of study lots

EXPLANATION

Open water

Emergent vegetation

Selected drain canal or ditch

Selected water-supply canal or ditch

Road

Buried drain

Mowed path

Bowen ratio energy balance

 station

Piezometer

LOT 6

P2,4

P2,1

P2,3

P2,2

P3,2

P3,1

P3,3

P1,2

P1,4

P1,1

P1,5

P1,3

LOT C1B

?

?

Figure 2. —Continued
8 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

The lot 6 stubble evapotranspiration measurement site 

was established in an area of the lot that had been left 

untreated after farming operations in 1999, and the lot 

6 cover crop site was established in the cover crop. A 

BREB station was installed at each site (fig. 2, lot 6).

The soil mapped throughout lot 6 and lot C1B is 

Tulebasin mucky silty clay loam, a soil in the Tulebasin 

soil series with a land-surface slope gradient ranging 

between zero and one percent (Jahnke, 1994). Soils of 

the Tulebasin series are deep (approximately 1.5 m), 

artificially drained soils that formed in lake bed 

deposits of volcanic ash and diatomite, a material 

resembling chalk that is chiefly derived from skeletal 

remains of a type of algae called diatoms. Jahnke 

(1994) reports the depth to the water table below land 

surface generally ranges from about 0.5 m to about 

0.9 m. Tulebasin-series soils are classified as fine, 

mixed, mesic Andaqueptic Haplaquolls under the 

United States Comprehensive Soil Classification 

System (Soil Survey Staff, 1975). These soils are 

extensively used for crop production. The uppermost 

0.4 m contains between 10 and 15 percent organic 

matter by weight, and the entire soil profile has a 

shrink-swell potential ranking of moderate.

EVAPOTRANSPIRATION MEASUREMENT 

AND MODELING TECHNIQUES

Growing season evapotranspiration was 

evaluated using both measurement and modeling 

techniques. Evapotranspiration measurement 

techniques such as the BREB technique are generally 

technically demanding to apply; however, they can be 

applied at any suitable site without having to rely on 

the site-specific calibration coefficients that are needed 

to apply evapotranspiration modeling techniques. 

Empirically based evapotranspiration modeling 

techniques are advantageous from the standpoint that 

they are generally simpler to apply than are the 

measurement techniques. A weakness of modeling 

techniques is the uncertainty that is introduced into 

modeled evapotranspiration by uncertainty in the 

calibration coefficients where the coefficients have not 

been computed or verified for a particular site. 

Measurement and modeling approaches often can be 

used in a complementary manner to produce a more 

complete and reliable evapotranspiration record for a 

given site than can be obtained by either approach 

alone. An evapotranspiration measurement technique 

can yield a reliable estimate of evapotranspiration with 

which to reliably determine the model coefficients, and 

a model outfitted with those coefficients can then be 

applied to reliably estimate evapotranspiration for 

instances in which the more rigorous environmental or 

data requirements of the measurement technique 

cannot be met.

Bowen Ratio Energy Balance

Evaporation of water into the atmosphere 

constitutes one component of the energy balance of a 

land or water surface. The BREB technique (Tanner, 

1960) is based on the premise that it is easier and more 

accurate to routinely evaluate all major components of 

the surface energy balance and compute 

evapotranspiration using the law of conservation of 

energy than it is to measure the evaporative vapor flux 

directly. An equation for the one-dimensional surface 

energy balance that is applicable for a terrestrial 

surface, such as a bare or vegetated field, can be 

written as

 , (1)

where

where

is net radiation, the energy difference between 

incoming and outgoing short- and longwave radiation, in watts per square meter;

is soil heat flux at the soil surface, in watts per 

square meter;

is the predominantly turbulent sensible heat 

flux, in watts per square meter; and

is the predominantly turbulent latent heat flux, 

in watts per square meter, 

is the latent heat of vaporization for 

water, in joules per gram; and 

is evapotranspiration rate, in grams per 

square meter per second.

Rn – G = H + λE

Rn

G

H

λE

λ

E
Evapotranspiration Measurement and Modeling Techniques 9

The surface energy balance equation is an 

expression of the law of conservation of energy. In the 

sign conventions for equation 1, Rn is positive when the 

total energy of incoming radiation exceeds the total 

energy of outgoing radiation, G is positive when 

energy is flowing into the soil surface, and H and λE

are positive when they are directed upward from the 

surface. Energy exchange from plant respiration and 

photosynthesis and rates of change of energy storage in 

the plant canopy or in the atmosphere below the height 

of measurements were assumed to be negligible in this 

study. The quantity Rn - G is termed “available energy” 

because net radiant energy, less energy stored in soil, is 

usually the primary impetus for the turbulent fluxes H

and λE.

The Bowen ratio (β) (Bowen, 1926), defined as 

H/λE, permits equation 1 to be solved for λE without 

having to know H explicitly. The equation 

 , (2)

can then be rearranged to obtain

 , (3)

where all terms have been defined previously. For 

terrestrial surfaces, β is typically evaluated from 

measurements of temperature and water-vapor pressure 

that are made in the turbulent atmosphere above the 

surface. For instances in which measurements are 

confined to a height of a few meters above a surface, β

can be computed using the equation (Monteith and 

Unsworth, 1990, eq. 14.26)

 , (4)

where

The psychrometer constant can be computed 

(Monteith and Unsworth, 1990, p. 181) as 

 , (5)

where

In computing λE and H by the BREB technique, 

Rn, G, ∆T, and ∆e are measured and averaged for some 

specified period, typically 30 or 60 minutes. 

Measurements and supplementary computations 

needed to apply the BREB technique for this study are 

described in a subsequent section of this report.

The BREB technique described in this report 

relies on some hydrodynamic assumptions about the 

nature of the turbulent atmosphere near the surface 

where the measurements are made. An assumption that 

permits one-dimensional treatment of the turbulent 

fluxes is the equilibration of the surface with the 

airstream in which ∆T and ∆e are determined. For a 

horizontal surface, equilibrium is a state in which the 

horizontal components of momentum, heat, and watervapor fluxes are negligibly small in comparison to the 

respective vertical components. Equilibrium also 

implies the fluxes do not change with height and that 

profiles of wind speed, temperature, and water-vapor 

pressure are horizontally uniform. 

When the wind passes between horizontal 

surfaces that differ with respect to aerodynamic 

roughness, temperature, or aridity, horizontal gradients 

potentially can develop as the air begins exchanging 

momentum, heat, and water vapor with the downwind 

surface. As the air travels downwind from the 

boundary between the surfaces, a locally equilibrated 

air layer develops in which horizontal gradients have 

substantially dissipated and in which fluxes of heat and 

water vapor are constant with height. The distance that 

the wind has traveled from the boundary is the fetch.

is the psychrometer constant, in kilopascals per 

degree Celsius;

is air temperature, in degrees Celsius;

is water-vapor pressure, in kilopascals; and

signifies a difference over a vertical interval 

situated above the surface.

λE

Rn – G

1 + β = ---------------

H β( ) Rn – G

1 + β = ------------------------

β γ∆T

∆e = ------

γ

T

e

∆

is atmospheric pressure, in kilopascals;

is specific heat of air at constant pressure, in 

joules per gram per degree Celsius;

is a ratio (0.622) that is equal to the mass of a 

mole of water divided by the mass of a 

mole of dry air, dimensionless; and

has been defined previously.

γ

pcp

λε = --------

p

cp

ε

λ
10 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

The locally equilibrated air layer grows from the 

downwind surface and increases in thickness with 

distance. Judging the thickness of the locally 

equilibrated air layer is important for determining 

where and at what heights to place the sensors used for 

determining ∆T and ∆e. Maximum sensor height zu is 

commonly computed using a relation similar to

 , (6)

where

Zero-plane displacement height is the effective 

height at which the surface exchanges momentum, 

heat, or water vapor with the atmosphere. For 

agricultural crops, where the vegetation is generally 

uniform and dense, Campbell (1985, p. 138) suggests 

d0 = 0.77hc, where hc is height of the crop canopy, in 

meters. Although d0 might be different for momentum, 

heat, and water vapor, d0 for the latter two quantities 

are generally assumed to equal d0 for momentum; 

empirical relations for heat and water vapor have not 

been formulated. For bare soil or sparse vegetation, d0

can be assumed to be 0 (Brutsaert, 1982, p. 116). 

Values of d0 for vegetation of intermediate densities 

can be expected to range between the values for sparse 

and dense vegetation. An acceptable minimum for the 

fetch-to-instrument-height ratio (η) has often been 

taken to be 100 (Weeks and others, 1987); however, 

results of some investigations with short vegetation 

have shown equilibration to be sufficient for successful 

application of the BREB technique with η as low as 

about 20 (Fritschen and others, 1983; Heilman and 

others, 1989). This lack of consensus in the literature 

regarding η contributes to uncertainty as to whether or 

not the BREB and related techniques are suitable for a 

particular site. 

Stannard (1997) has presented a theory enabling 

one to estimate the degree of equilibration of the 

Bowen ratio and latent heat flux to the surface of 

interest where the airstream has been affected by an 

upwind surface, termed the “contaminating surface.” 

For example, Stannard (1997, eq. 6) gives an equation 

for percentage of equilibration of latent heat flux to the 

surface of interest (%EqλE) as

 , (7)

where

Percentage of equilibration of λE indicates the 

completeness of the transition of λE from its value at 

the contaminating surface (λEc) to its value at the 

surface of interest (λEi). The percentage error in latent 

heat flux due to the influence of the contaminating 

surface (%δλE) follows from equation 2 and is given by 

(D.I. Stannard, U.S. Geological Survey, oral commun., 

May 2001)

 , (8)

where all terms have been defined previously.

In application of the BREB technique, the ideal 

situation is βi = βm, for which%δλE is 0. Divergence of 

βi and βm and error in measured latent heat flux is 

caused by lack of equilibration of the airstream to the 

surface of interest due to the influence of the 

contaminating surface. The airstream equilibration 

theory presented by Stannard (1997) can be used to 

iteratively compute βi from measurements or estimates 

of βm, βc, R, x, d0, heights of the sensors used for 

computing ∆T and ∆e, and the roughness length z0, in 

meters. The roughness length is a characteristic of the 

surface that influences turbulent exchange of 

momentum, heat, or water vapor with the atmosphere. 

Generally, the larger the z0, the more intense is the 

turbulent exchange. Campbell (1985, p. 138) indicates 

z0 for uniform crops can be computed using the 

equation z0 = 0.13hc, where hc is as defined previously.

x is fetch, in meters;

zu is height above land surface, in meters; 

d0 is the zero-plane displacement height, in 

meters; and

η is a prescribed minimum for the fetch-toinstrument-height ratio, dimensionless.

x

zu d0 – --------------- ≥ η is the Bowen ratio for the contaminating surface, 

dimensionless;

is the ratio of available energy at the 

contaminating surface to that at the surface of 

interest, dimensionless;

is the measured Bowen ratio for the surface of 

interest, dimensionless; and 

is the actual Bowen ratio for the surface of 

interest, dimensionless.

%EqλE 100

1 βc R 1 βm ( ) + 1 βi + – ( ) +

1 βc R 1 βi ( ) + 1 βm + – ( ) + = ----------------------------------------------------------------

βc

R

βm

βi

%δλE 100βi βm –

1 βm + = -----------------
Evapotranspiration Measurement and Modeling Techniques 11

Another assumption underpinning the BREB 

technique, that the surface and atmosphere near the 

surface of interest are at steady state, is rarely met 

because of diurnal cycling and other variations of 

meteorological conditions. The transient state of the 

atmosphere can cause BREB-computed fluxes to be 

erroneous, particularly during rapidly changing 

conditions at dawn and dusk. For this study, Rn, G, ∆T, 

and ∆e were initially computed for 15 minutes, and two 

15-minute averages of each quantity were averaged to 

compute β and λE for 30-minute periods, which were 

brief enough that the assumption of steady-state 

conditions was thought to generally be valid. Thus, the 

dynamic, diurnally changing atmosphere was treated as 

though it evolved through a series of steady states. 

Daily and longer term averages or totals of energy 

balance components and other quantities were 

computed by summing or averaging 30-minute 

quantities.

Eddy Covariance

The eddy covariance technique is an alternative 

to the BREB technique for estimating turbulent fluxes 

of energy and mass from a surface. Unlike the BREB 

technique that relies on solution of the surface energy 

balance and measurements of the mean differences ∆T

and ∆e, the eddy covariance technique is based on 

analysis of individually sensed turbulent fluctuations. 

For example, in the equilibrated air above a level 

surface, H can be computed from a simplified, onedimensional equation for turbulent transport (Brutsaert, 

1982, eq. 3.75),

 , (9)

where

The quantity is the covariance between 

vertical wind speed and air temperature. In application 

of the eddy covariance technique, the fluctuations 

and are sampled using fast-response sensors. The 

fluctuations are tallied for a specified period of time to 

compute . An equation similar to equation 9 can 

be applied to measure latent heat flux and 

evapotranspiration, although this was not done in this 

study. Although the BREB and eddy covariance 

techniques share many of the same hydrodynamic 

assumptions, measurement and sampling schemes for 

the two techniques are very different; therefore, the 

eddy covariance technique provides an independent 

means with which to check H computed by the BREB 

technique (equation 3). Because the BREB technique 

relies on specification of all components of the surface 

energy balance to compute H and λE, the independent 

check on H provided by the eddy covariance technique 

indirectly provides an indication of the reliability of the 

BREB estimates of λE. The eddy covariance technique 

was applied intermittently in this study to provide an 

overall check on turbulent fluxes that were computed 

by the BREB technique.

Priestley-Taylor

Models provide a means for estimating λE and E

when and where data needed for more rigorous 

measurement techniques, such the BREB technique, 

are not available or are not sufficiently accurate, but 

where data for environmental variables that govern 

evapotranspiration are available or can be reliably 

estimated. The Priestley-Taylor (PT) equation 

(Priestley and Taylor, 1972) has been the basis for 

empirical models of evapotranspiration from many 

types of land surfaces, including croplands (Steiner and 

others, 1991), semiarid rangelands (Stannard, 1993), 

and forest clearcuts (Adams and others, 1991). The PT 

equation is a simplification of the physically based 

Penman-Monteith equation (Monteith, 1965), where 

the latter explicitly accounts for turbulent transfer with 

an aerodynamic component composed of variables that 

characterize fundamental properties of the surface, the 

atmosphere, and turbulent transfer mechanisms. By 

contrast, the simpler PT equation is 

 , (10)

is air density, in grams per cubic meter;

is short-term fluctuation of vertical wind speed 

from the time-averaged mean, in meters per 

second;

is short-term fluctuation of air temperature from 

the time-averaged mean, in degrees Celsius;

the overbar represents averaging for a 

specified period of time; and

other terms have been defined previously.

H ρc = pw′T′

ρ

w′

T′

w′T′

w′ T′

w′T′

λE αλEEQ =
12 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

where

Equilibrium latent heat flux, the latent heat flux 

that would prevail if the air in contact with the surface 

of interest is saturated with water vapor (Campbell, 

1977, p. 140), is given by 

 , (11)

where

A key to modeling evapotranspiration with the 

PT equation is the evaluation of α, which implicitly 

accounts for the contribution to λE from the 

aforementioned aerodynamic component of the 

Penman-Monteith equation. Priestley and Taylor 

(1972) examined data from several surfaces where 

availability of water was not limiting to 

evapotranspiration, and they concluded that daily 

average α for such surfaces is a constant of 

approximately 1.26 when the evapotranspiration rate is 

not affected by advected energy. Jury and Tanner 

(1975) modified Priestley and Taylor’s (1972) 

approach for surfaces where water availability is not 

limiting by allowing α to vary with variations of 

atmospheric water-vapor pressure deficit, D, in 

kilopascals, where the latter is a composing variable of 

the aerodynamic component of the Penman-Monteith 

equation. Atmospheric water-vapor pressure deficit is 

computed from D = es - e, where es is water-vapor 

pressure at atmospheric saturation, in kilopascals, and e

is as defined previously. 

The PT equation has also been modified and 

applied to surfaces where evapotranspiration is waterlimited, such as a drying soil (Barton, 1979) and waterstressed or senesced vegetation (Williams and others, 

1978; Flint and Childs, 1991). Values reported for α for 

these water-limited situations typically are less than 

1.26 and often are less than 1.0. In some work with 

water-limited surfaces, α as defined by Priestley and 

Taylor has been replaced by the modified variable, α'; 

however, no such distinction is made in this report. The 

PT equation was applied in this study to estimate 

evapotranspiration when estimates by the BREB 

technique were not available or were thought to be 

unreliable, but where the variables in equations 10 and 

11 were measured or could be reliably estimated at a 

particular site.

Reference Evapotranspiration

An evapotranspiration modeling technique that 

is typically applied without measuring any 

environmental variables at the site of interest, which is 

hereafter referred to as the “reference 

evapotranspiration technique,” can be summarized as 

(Jensen and others, 1990, p. 114)

 , (12)

where

Jensen and others (1990, p. 57) define E0 as “... 

the rate at which water, if available, would be removed 

from the soil and plant surface of a specific crop, 

arbitrarily called a reference crop.” The purpose of E0

is to provide an evapotranspiration standard that 

controls for climate effects and with which to compute 

evapotranspiration from surfaces other than the 

reference crop in the same locale or region. A key to 

modeling evapotranspiration with equation 12 is the 

evaluation of kc.

is equilibrium latent heat flux, in watts per 

square meter; and

is a coefficient that is equal to the ratio of 

to , dimensionless.

s is slope of the relation between water-vapor 

pressure at atmospheric saturation and 

temperature, in kilopascals per degree 

Celsius; and 

other terms have been defined previously.

λEEQ

α λE

λEEQ

λEEQ

s R( ) n – G

s + γ = -----------------------

is evapotranspiration rate, in millimeters per 

day;

is an empirical crop coefficient, dimensionless; 

and 

is reference evapotranspiration rate, in 

millimeters per day.

E kcE0 =

E

kc

E0
Applications of Evapotranspiration Measurement and Modeling Techniques 13

APPLICATIONS OF 

EVAPOTRANSPIRATION MEASUREMENT 

AND MODELING TECHNIQUES

Applications of the BREB, eddy covariance, and 

PT techniques to compute or model evapotranspiration 

require numerous field measurements that are made by 

a diverse set of instruments. This report section 

describes measurements, instruments, and 

supplementary computations that were used to evaluate 

terms in the previously presented technique-defining 

equations for the study sites. In addition, this section 

describes techniques and results of supporting work 

conducted to calibrate the type of a soil moisture sensor 

that was used in the field for the Tulebasin mucky silty 

clay loam that was present at the study sites, and to 

estimate bulk density, specific heat, and thermal 

conductivity of that soil.

Net Radiation

Net radiation (Rn) was measured directly at each 

site with a single net radiometer (model Q*7.1 or 

model Q*6.7.1, Radiation and Energy Balance 

Systems, Inc., Bellevue, Wash.) that was suspended at 

a height of approximately 3.5 m above the soil surface. 

Because the net radiometers are influenced by wind, 

they were equipped with ventilators that forced air over 

the hemispherical upper and lower windshields of the 

sensor at a constant speed. A wind correction that was 

based on the fixed speed of the forced ventilation and 

that was supplied by the manufacturer was applied to 

the sensed net radiation. The net radiometer was 

monitored by a data logger (model CR10X, Campbell 

Scientific, Inc., Logan, Utah) that also applied the wind 

correction and averaged Rn every 15 minutes.

Soil Heat Flux

The average of soil heat flux at the soil surface 

(G) sampled at three places was used to evaluate the 

energy balance at each evapotranspiration 

measurement site. At each sampling place, G was 

computed by summing soil heat flux that was measured 

at a fixed soil depth (z) and the rate of change of energy 

storage in soil above the fixed depth, where the latter 

rate was estimated calorically from the rate of change 

of depth-averaged soil temperature. An equation for G

is 

 , (13)

where

Soil heat flux at depth z was measured with a 

heat flux plate (model HFT3.1, Radiation and Energy 

Balance Systems, Inc.); z was 0.1 m, except during 

May 19 to June 3 at lot C1B, when z was 0.05 m. The 

soil heat flux plates were monitored by a data logger 

(model CR10X) that averaged soil heat flux every 

15 minutes. Measured soil heat flux was corrected to 

account for errors caused by the mismatch between the 

thermal conductivities of the heat flux plate and the 

soil. The correction equation provided by the 

manufacturer of the heat flux plate and based on Philip 

(1961) is

 , (14)

Gz is soil heat flux, in watts per square meter, at 

soil depth z;

is in meters;

is thickness of the soil layer above depth z, in 

meters;

is depth-averaged temperature of the soil layer, 

in degrees Celsius;

is time, in seconds;

is soil bulk density, in kilograms of dry soil per 

cubic meter;

is specific heat of dry soil, in joules per 

kilogram per degree Celsius;

is volumetric soil water content, in volume of 

water per unit volume of soil, dimensionless;

is density of water, in kilograms per cubic 

meter; and

is specific heat of water, in joules per kilogram 

per degree Celsius. 

G Gz z

dTs

dt

-------- ρscs θρwcw = + ∆ ( ) +

z

∆z

Ts

t

ρs

cs

θ

ρw

cw

Gz G′z

1 1.92L/dp 1 ks/kp – ( ) –

1 1.92L/dp 1 km/kp – ( ) – = ----------------------------------------------------------
14 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

where

The manufacturer of the heat flux plate provided 

values for thickness of the soil heat flux plate (L, 3.91 

mm), diameter of the plate (dp, 38.2 mm), thermal 

conductivity of the plate (kp, 1.22 watts per meter per 

degree Celsius, ((W/m)/oC)), and thermal conductivity 

of the medium that was used to calibrate the plate (km, 

0.906 (W/m)/oC). Thermal conductivity of soil varies 

with water content (Campbell, 1985, p. 32), and 

laboratory experiments were conducted to describe the 

relation between ks and volumetric soil water content 

for the soil at the study sites. A sample from the 

uppermost 0.1 m of soil at lot C1B was used to 

assemble a series of packed soil columns with different 

water contents. The sample was repeatedly packed into 

a 0.1-m-diameter, 0.32-m-long polyvinyl chloride 

cylinder to produce a series of soil columns of varying 

column-average θ. Soil thermal conductivity was 

measured by the line heat source technique (Jackson 

and Taylor, 1986), using a thermal conductivity sensor 

(model TC-18, Thermal Logic Co., Pullman, Wash.) 

that was coupled to a data logger (model 21X, 

Campbell Scientific, Inc.) and inserted into the exposed 

face of each soil column. Two or three replicate 

measurements of ks were made at each water content, 

and measured ks ranged between 0.08 and 0.41 

(W/m)/oC among the replicates and the columns. 

Column-average ρs and θ were determined 

following the thermal conductivity measurements that 

were made in each column. Column-average ρs was 

computed by dividing the mass of the soil, oven-dried 

at 105oC for a minimum of 37 hours, by the volume of 

the cylinder. Column-average θ was computed 

gravimetrically from the change in mass of the soil 

sample resulting from oven-drying and the volume of 

the cylinder. Column-average ρs ranged from 582 to 

614 kilograms per cubic meter (kg/m3) among six 

columns that were prepared, and column-average θ

ranged from oven dry to 0.39. Soil that was oven-dried 

at 105oC contained a small but unknown amount of 

water that was strongly adsorbed to the soil particles or 

was incorporated in the structures of those particles 

(Gardner, 1986). Nonetheless, the numerical value of θ

for oven-dried samples was taken to be 0.

The data for θ and ks that were obtained from the 

soil column experiments were fitted to equation 4.20 of 

Campbell (1985)

 , (15)

where each numerical coefficient, except the exponent 

4, which is suggested by Campbell (1985, p. 34), was 

adjusted using the SOLVER tool of the Microsoft 

Excel program (Microsoft, Inc., Redmond, Wash.) to 

minimize the root-mean-square error (RMSE) of 

predicted ks. The RMSE of ks predicted by equation 15 

was 0.01 (W/m)/oC, and the sample size (n) was 17. 

Equation 15 was used to estimate ks in the soil near the 

heat flux plates at the three evapotranspiration 

measurement sites for the purpose of correcting soil 

heat flux with equation 14. 

Soil temperature Ts, in degrees Celsius, was 

sensed with a soil temperature sensor constructed with 

a 0.077-m-long platinum resistance temperature 

detector that spatially averaged temperature over its 

length (model STP1, Radiation and Energy Balance 

Systems, Inc.). A soil temperature sensor was inserted 

into the 0-to-z-m soil depth interval near each heat flux 

plate at a elevation angle of approximately 60 degrees 

(elevation angle was approximately 45 degrees when z

was 0.05 m), such that the center of the detector was 

approximately z/2 m from the soil surface. The soil 

temperature sensors were monitored with a data logger 

(model CR10X) that averaged Ts and the quantity 

dTs/dt every 15 minutes. Sensed soil temperature was 

assumed to be representative of the depth-averaged 

temperature Ts for the 0-to-z-m soil depth interval, and 

the quantity dTs/dt was assumed to be representative of 

dTs/dt in equation 13.

is uncorrected, measured soil heat flux at soil 

depth z, in watts per square meter;

is thickness of the soil heat flux plate, in 

millimeters;

is diameter of the soil heat flux plate, in 

millimeters;

is thermal conductivity of the soil, in watts per 

meter per degree Celsius;

is thermal conductivity of the soil heat flux 

plate, in watts per meter per degree Celsius; 

and

is thermal conductivity of the medium in 

which the soil heat flux plate was originally 

calibrated, in watts per meter per degree 

Celsius.

G′z

L

dp

ks

kp

km

ks 0.2179 0.4055θ 0.1510

e

( ) 3.4054θ 4 = + – ----------------------
Applications of Evapotranspiration Measurement and Modeling Techniques 15

Soil bulk density (ρs) at the evapotranspiration 

measurement sites was computed from the oven-dried 

mass of soil samples taken from a known volume with 

a hammer-driven core sampler. Multiple samples were 

taken at each site. Bulk density of the uppermost 0.1 m 

of soil averaged 546 kg/m3 at the lot C1B 

evapotranspiration measurement site (standard 

deviation (sd) = 24 kg/m3, n = 12), 554 kg/m3 at the lot 

6 stubble evapotranspiration measurement site (sd = 48 

kg/m3, n = 12), and 494 kg/m3 at the lot 6 cover crop 

evapotranspiration measurement site (sd = 45 kg/m3, 

n = 11).

Specific heat of dry Tulebasin mucky silty clay 

loam soil was estimated using a sample collected from 

the uppermost 0.1 m of soil at lot C1B that was ovendried at 105oC. Specific heat was measured using the 

dual-probe heat-pulse technique of Campbell and 

others (1991). The sample was placed into a 0.054-mdiameter, 0.06-m-long cylinder. A specific-heat sensor 

(Thermal Logic Co.) that was coupled to a data logger 

(model 21X) was inserted in the center of the exposed 

soil face to measure volumetric specific heat of the 

sample, which is a close approximation of ρscs for a 

dry soil. Specific heat of oven-dried soil in the sample 

(cs) was computed by dividing volumetric specific heat 

by the bulk density of the sample (ρs, 561 kg/m3). Two 

replicate cs determinations that were made in the soil 

column were 1,150 and 1,180 joules per kilogram per 

degree Celsius ((J/kg)/oC).

Volumetric soil water content was monitored 

near each heat flux plate using a soil water content 

reflectometer (model CS615, version 8221-07, 

Campbell Scientific, Inc.). The reflectometer senses the 

frequency of electromagnetic waves that are 

propagated along a twin-probe, 0.3-m-long wave guide 

that is inserted into the soil. The frequency of the 

waves, and therefore the period of the waves (τ, in 

milliseconds), vary with the dielectric constant of the 

soil. The dielectric constant of the soil is largely 

controlled by the soil volumetric water content. The 

signal from the reflectometer, τ that ranges from 0.7 to 

1.6 milliseconds, can be applied to compute volumetric 

soil water content using a calibration function that 

relates τ directly to volumetric soil water content. For 

this study, the reflectometer probes were installed 

parallel to the plane of the soil surface and at a soil 

depth of z/2, which was 0.05 m, except during May 19 

to June 3 at lot C1B, when z/2 was 0.025 m. The 

reflectometers were monitored with a data logger 

(model CR10X) that averaged τ every 15 minutes.

A single model CS615 reflectometer similar to 

the nine that were deployed at the evapotranspiration 

measurement sites was used to develop a soil-specific 

calibration model for the sensor in the Tulebasin 

mucky silty clay loam. A sample from the uppermost 

0.1 m of soil at lot C1B was used to assemble a series 

of packed soil columns with different water contents. 

The sample was repeatedly packed into a 0.1-mdiameter, 0.32-m-long polyvinyl chloride cylinder to 

produce a series of soil columns. Column-average ρs

and θ were determined as was discussed previously. 

Average ρs of the soil columns used for the calibration 

ranged from 582 to 614 kg/m3, and column-average θ

ranged from oven dry to 0.39. The reflectometer probes 

were inserted into the exposed face of each soil column 

and τ was read by a data logger (model 21X). The first 

three replicate measurements made at each water 

content were included in the calibration data set, and τ

ranged from 0.79 to 1.54 milliseconds among the 

replicates and columns. Temperature of each column 

was sensed with a chromel-constantan thermocouple 

probe following each set of replicate measurements. 

Temperature of the columns ranged from 18oC to 22oC. 

A temperature-dependent calibration function was then 

developed for the reflectometer. The function is 

 , (16)

where is given by

 , (17)

and other terms are as defined previously.

Equation 16 accounts for the temperature 

dependence of the reflectometer signal and is given by 

the manufacturer. The coefficients of equation 17 were 

computed using the SOLVER tool of the Microsoft 

Excel program to minimize the RMSE of predicted θ. 

The RMSE of θ predicted by the function was 0.01 

(n = 20). The calibration function was applied with 

field measurements of τ and Ts to compute θ for use in 

equations 13 and 15. The use of θ measured at depth 

z/2 for correcting G'z by equations 14 and 15, rather 

than θ at depth z where the soil heat flux plates were 

buried, introduced minimal error into Gz because the 

correction was small in magnitude and was fairly 

insensitive to θ. 

θ θ* Ts = – ( ) – 20

* 0.000346 – 0.019θ* 0.045θ*2

( ) + –

θ

*

θ

* = – 3.1260 + 6.9708τ

4.6487τ

2 – 1.04204τ3

+
16 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

The correction ranged from -9 to -14 percent of 

among the three evapotranspiration measurement sites; 

whereas, θ ranged from 0 to 0.38.

Reliability of the calibration function for the 

Tulebasin mucky silty clay loam for θ greater than was 

measured during development of the function (0.39) is 

not known. However, the range of θ in the calibrations 

was similar to the range measured at the 

evapotranspiration measurement sites. The maximum 

valid τ that was recorded at the evapotranspiration 

measurement sites was 1.3822 milliseconds (Ts= 

13.7oC), which corresponds to a value for θ of 0.38 

according to equations 16 and 17. The minimum, valid 

field-recorded τ was 0.7867 milliseconds (Ts = 19.5oC), 

for which θ computed by equations 16 and 17 is an 

implausible -0.01. This latter result likely was caused 

by variations of soil properties that influenced the 

response of the reflectometer and that are not (and 

likely cannot be) described using a single set of 

calibration coefficients. Negative computed values of θ

were assigned a value of 0.0 for purposes of this study.

The dimensions of soil regions that influenced 

measurements made by the reflectometer were not 

known, and a simple experiment was conducted to 

examine possible effects of the finite volume of the soil 

columns on reflectometer measurements that were 

made to develop the calibration function. The 0.1-mdiameter soil columns were submerged in a water bath 

to approximately 0.02 m below the rim of the cylinder 

to determine whether or not τ was affected by the 

dielectric constant of material outside of the cylinder. 

Submerging a column of oven-dry soil and one with θ

= 0.39 increased τ by 0.6 and 0.7 percent, respectively, 

indicating that the finite columns had only minimal 

effects on the reflectometer measurements. 

Air Temperature and Vapor Pressure

The vertical differences ∆T and ∆e were 

computed from T and e measured at an upper height 

minus T and e measured one m lower. T and e were 

measured at each height by an aspirated air sensor 

(model THP1, Radiation and Energy Balance Systems, 

Inc.). An aspiration fan drew air into a horizontally 

mounted radiation shield attached to each air sensor 

and past a platinum temperature resistance detector that 

sensed the temperature of the airstream. Relative 

humidity of the airstream was sensed with a capacitivetype humidity sensor that was housed in a cavity at the 

end of a shaft that was swept by the airstream. A filter 

across the cavity orifice that protected the humidity 

sensor from contaminants also slowed the movement 

of air in the cavity. The slower movement of air in the 

cavity at times caused the temperature of the cavity to 

differ from that of the airstream. Temperature of the 

cavity (Tc, in degrees Celsius) was sensed with an 

additional platinum temperature resistance detector for 

the sole purpose of obtaining accurate measurements of 

water-vapor pressure (e) of the airstream, which was 

computed from

 , (18)

where

other terms are as defined previously.

The data logger (model CR10X) that monitored 

the air sensors computed es from Tc using the Lowe 

equation (Lowe, 1977; Campbell Scientific, Inc., 

1997). The data logger also computed time-averaged 

∆T and ∆e every 15 minutes. The air sensors were 

mounted to a motor-driven exchange system (model 

AEM, Radiation and Energy Balance Systems, Inc.) 

that exchanged the sensors between the two heights 

every 15 minutes to reduce the effects of individual 

sensor bias on the computed differences ∆T and ∆e. 

Latent heat of vaporization of water (λ) varies 

weakly with temperature and was computed using 

(Jensen and others, 1990, eq. 7.1)

 , (19)

where all terms have been defined previously. 

Atmospheric pressure (p), which is needed to compute 

the psychrometer constant (γ) and density of air (ρ), 

was estimated by the equation (Jensen and others, 

1990, eq. 7.4)

 , (20)

where Z is site altitude, in meters.

Density of air (ρ) was computed as

 , (21)

G′z

is relative humidity, dimensionless; and

e hres =

hr

λ = 2 501 2.361 , – T

p = 101.3 0.01055 – Z

ρ ρd ρv = +
Applications of Evapotranspiration Measurement and Modeling Techniques 17

where

Density of dry air was computed from Brutsaert (1982, 

equation 3.4) as

 , (22)

where

Density of atmospheric water vapor was 

computed using (Brutsaert, 1982, equation 3.5) 

 , (23)

where all terms have been defined previously.

Specific heat of air at constant pressure (cp) was 

computed from the specific heats of dry air and water 

vapor weighted by their mass fractions as

 , (24)

where

The slope of the relation between saturation 

water-vapor pressure of air and temperature was 

computed using a form of the Clausius-Clapeyron 

equation (Brutsaert, 1982, equation 3.22)

 , (25)

where all terms have been defined previously, and 

where es was computed using the previously noted 

Lowe equation (Lowe, 1977), which can be written as

 , (26)

where the coefficients are 

and other terms are as defined previously.

Data Screening and Segregation

Sensible and latent heat fluxes computed by the 

BREB technique were examined to detect and reject 

those computed fluxes that either were physically 

implausible or were suspected to be erroneous. 

Physically implausible fluxes are those for which the 

signs of λE and H computed by the BREB technique 

are not consistent with the signs of ∆e and ∆T and the 

overall surface energy balance. Specifically, BREBcomputed λE and H were rejected when (modified 

from Ohmura, 1982)

 , (27)

where all terms have been defined previously. 

In addition, λE and H from equations 2 and 3 are 

undefined for β = –1, and even relatively small 

measurement or sampling errors in Rn and G can lead 

to large-magnitude errors in computed λE and H when 

β approaches –1. For this reason, λE and H computed 

by the BREB technique were rejected when β was in 

the range of -1.25 to -0.75. 

is density of dry air, in grams per cubic meter; 

and 

is density of atmospheric water vapor, in grams 

per cubic meter.

is the ideal gas constant for dry air, which 

equals 0.28704 joules per gram per kelvin 

(Brutsaert, 1982, p. 38);

273.15 was added to T, in degrees Celsius, to 

convert it to kelvins; and 

other terms are as defined previously.

is specific heat of dry air at constant pressure, 

which is equal to 1.005 joules per gram per 

degree Celsius (Brutsaert, 1982, p. 38);

is specific heat of water vapor at constant 

pressure, which is equal to 1.846 joules per 

gram per degree Celsius (Brutsaert, 1982, 

p. 38); and

other terms are as defined previously.

ρd

ρv

ρd

1 000 , ( ) p e –

Rd( ) T + 273.15 = -------------------------------------

Rd

ρv

1 000 , εe

Rd( ) T + 273.15 = -------------------------------------

cp

cpdρd cpvρv +

ρd ρv + = --------------------------------

cpd

cpv

A0: 6.107799961

A1: 4.436518521 × 10-1

A2: 1.428945805 × 10-2

A3: 2.650648471 × 10-4

A4: 3.031240396 × 10-6

A5: 2.034080948 × 10-8

A6: 6.136820929 × 10-11

s

ελes

Rd( ) T + 273.15 2 = ---------------------------------------

es (A0 T(A1 T(A2 T(A3 T(A4 = ++++

+ T(A5+TA6))))))/10

λε∆e

p ------------ cp + ∆T     • ( ) Rn – G > 0
18 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

Finally, λE and H computed by the BREB technique 

for some 30-minute periods were rejected that were not 

detected by the previous two objective criteria, but that 

clearly appeared to be unreasonable. One example of 

the latter flux estimates was a sudden spike of H near 

the time of sunrise or sunset that was accompanied by 

negative λE.

Nighttime and daytime summaries of surface 

energy balance components and related environmental 

variables were made by discriminating nighttime from 

daytime if the solar elevation angle (Ψ, in radians), was 

less than 0 or greater than 0, respectively. Solar 

elevation angle was computed using (Stull, 1988, eq. 

7.3.1c)

 , (28)

where

 Solar declination angle varies with time of year 

and was computed from (Stull, 1988, equation 7.3.1d)

 , (29)

where

Summaries of surface-energy balance 

components and other environmental variables also 

were made by segregating those data according to a 

simple wind-direction classification scheme. For each 

30-minute period, wind direction was classified as 

westerly if the average wind direction azimuth during 

both composing 15-minute periods was equal to or 

greater than 180 degrees and less than 360 degrees. 

Wind direction for a given 30-minute period was 

classified as easterly if the average wind direction 

azimuth during both composing 15-minute periods was 

equal to or greater than 0 degrees and less than 

180 degrees. Wind direction was classified as mixed if 

the wind direction was westerly during one of the 

15-minute periods and easterly during the other 

15-minute period.

Eddy Covariance and Other 

Measurements

Short-term fluctuations of vertical wind speed 

( ) and air temperature ( ) were sensed with a onedimensional sonic anemometer equipped with an air 

temperature sensor (model CA27, Campbell Scientific, 

Inc.), and the anemometer signals were sampled at a 

nominal frequency of 10 Hz by a data logger (model 

21X) that also computed the covariance every 

15 minutes. Average H was computed using equation 9 

for every 15-minute period, and 30-minute-average H

was computed as the average of two 15-minute 

averages. 

Precipitation at the lot C1B and lot 6 cover crop 

evapotranspiration measurement sites was sensed with 

tipping-bucket rain gages (model 525, Texas 

Electronics, Inc., Dallas, Texas). The rain gages were 

monitored by a data logger (model CR10X) that also 

totaled precipitation every 15 minutes. Horizontal wind 

speed and direction were sensed at each 

evapotranspiration measurement site using a vane-andpropeller-type wind sensor (model 05103-5 or 05305, 

R.M. Young Co., Traverse City, Mich.). The wind 

sensors were monitored with a data logger (model 

CR10X) that also averaged wind speed and direction 

every 15 minutes.

Estimating Depth to the Water Table

Personnel of the USFWS installed piezometers 

at selected locations in lot C1B and lot 6 (fig. 2, lot 

C1B and lot 6) and monitored water levels in those 

piezometers. The piezometers were constructed using a 

0.025-m-diameter polyvinyl chloride casing fitted on 

the bottom with a 0.3-m-long slotted well screen (slot 

size 2.5 × 10-4 m). 

is latitude (positive north), in radians;

is longitude (positive west), in radians;

is solar declination angle, the angle of the sun 

above the equator, in radians; and

is Coordinated Universal Time, computed as 

Pacific Daylight Time plus 7 hours, in hours.

is latitude of the Tropic of Cancer (0.4093 

radians);

is day of the calendar year (for example, 

February 15 is day 46);

is day of the summer solstice (173); and 

is the number of days per year (365.25).

sinΨ sinΦ δ sin Φ δ πtUTC

12 -------------- – Γ     = – cos cos cos

Φ

Γ

δ

tUTC

δ Φr

2π d dr [ ] –

dy

-------------------------     = cos

Φr

d

dr

dy

w′ T′

w′T′
Applications of Evapotranspiration Measurement and Modeling Techniques 19

The casing-and-screen assembly was placed into a hole 

that was made with an auger. Sand was poured into the 

hole around the assembly to imbed the screen. The 

uppermost 0.3 m of the hole was filled with bentonite 

clay. Maximum depth of the piezometers below land 

surface ranged from approximately 1.1 to 1.5 m (Tim 

Mayer, USFWS, written commun., November 2000). 

Water level was measured using a measuring tape with 

a water-contact sensor. 

Instrumentation Deployments

Each BREB station consisted of numerous 

sensors and an enclosure holding the BREB system 

control devices and data logger. The net radiometer and 

the air sensors were mounted on a tripod that was 

approximately 7 m south of a tripod that supported the 

enclosure holding the BREB system control devices 

and data logger. The wind sensor was mounted to a 

metal fence post that was driven into the ground 

approximately 9 m north-northwest of the tripod that 

supported the enclosure. Heights above the land 

surface of the air and wind sensors for each BREB 

station are given in table 1. An ensemble of sensors for 

computing soil heat flux at the soil surface (G) 

consisting of a heat flux plate, a water content 

reflectometer, and a soil temperature sensor, was buried 

at each of three places that were within approximately 

10 m of the data logger enclosure. Burial locations 

were selected to sample G under the range of different 

types of surface cover that existed within the reach of 

the sensor cables. 

The BREB station at the lot C1B 

evapotranspiration measurement site was placed in the 

unburned western part of the lot, and where 

homogeneity of vegetation and stubble cover for 200 m 

in all directions appeared to be greatest. Nonetheless, 

the vegetation and stubble coverage was not fully 

uniform. Patches of stubble with few green plants were 

interspersed with patches of weedy and small grain 

plants within 200 m of the BREB station when it was 

established during mid-May. In addition, an 

approximately 3-m-wide path was mowed to the east of 

the station during late July or early August (fig. 2, lot 

C1B). 

The heterogeneous nature and limited patch size 

of the vegetation and other surface coverage at lot 6 

precluded placing the BREB stations where fetch 

would have been adequate regardless of wind direction. 

During mid-May, vegetation west of the cover crop 

consisted of patches of weedy plants and barley that 

were interspersed with patches and strips of stubble. 

The strips ran in north-south directions and were 

estimated to range from 5 to 20 m in width. 

Approximately 30 percent of lot 6 outside of the cover 

crop was occupied by these “stubble barrens” in midMay. The BREB station at the lot 6 stubble site was 

placed in an area of relatively homogeneous stubble 

near the southeast corner of the lot. Minimum fetch 

over the stubble and the vegetation that later grew 

among and overtopped the stubble was approximately 

120 m during westerly winds. Minimum fetch was 

approximately 50 m during easterly winds, although 

the fetch was broken by a 3-m-wide path that was 

mowed during late July or early August (fig. 2, lot 6). 

Evapotranspiration estimates made by the BREB 

technique for favorable (westerly) wind directions 

were used to calibrate a simple evapotranspiration 

model that was based on the PT equation. The PT 

model was then used to estimate evapotranspiration for 

periods when the wind direction was not westerly or 

the when estimates from the BREB technique were 

otherwise not available or not reliable, but for which 

Rn, G, and average air temperature data were available 

for the stubble site.

Similarly, the BREB station at the lot 6 cover 

crop evapotranspiration measurement site was placed 

near the east edge of the area of the lot that was sown to 

a cover crop of cereal rye during February 2000 (fig. 2, 

lot 6). Fetch over the reasonably uniform cover crop 

was a minimum of approximately 115 m when winds 

were westerly, and fetch was approximately 10 m when 

the wind was directly from the east. Evapotranspiration 

estimates made by the BREB technique for favorable 

(westerly) winds were used to calibrate a simple 

evapotranspiration model that was based on the PT 

equation. The model was then used to estimate 

evapotranspiration for periods when the wind direction 

was not westerly. A data logger programming error 

caused the wind sensor data to be erroneous during 

June 9 to 27, and wind direction during that period was 

estimated using wind direction from the nearby lot 6 

stubble site BREB station.

Finally, a mobile eddy covariance station was 

operated to compute sensible heat flux during at least 

one diurnal cycle at each evapotranspiration 

measurement site. 
20 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

Table 1. Approximate maximum heights of vegetation or vegetation residues, and heights of air and wind sensors—Continued

Date

Approximate maximum vegetation or vegetation residue height (meters) Sensor height 

(meters)

Near air 

sensors

Northeast 

quadrant

Southeast 

quadrant

Southwest 

quadrant

Northwest 

quadrant Air Wind

Lot C1B evapotranspiration measurement site

05-20-00 <0.5 0.5 to 0.59 0.5 to 0.59 0.2 to 0.29 0.3 to 0.39 1.5 2

06-02-00 0.8 – – – – 1.9 2

06-11-00 0.9 – – – – 1.9 2

07-07-00 1.4 – – – – 1.9 2

07-12-00 1.3 – – – – 2.1 2

07-20-00 1.2 1.1 to 1.19 1.1 to 1.19 0.9 to 0.99 1.0 to 1.09 2.3 2

08-04-00 1.1 – – – – 2.2 2

08-11-00 1.1 – – – – 2.3 2

08-24-00 1.1 – – – – 2.3 2

08-29-00 1.4 1.0 to 1.09 0.9 to 0.99 >1.0 to 1.09 >1.0 to 1.09 2.3 2

08-30-00 – – – – – 2.5

09-08-00 1.2 – – – – 2.5 2

09-15-00 1.2 – – – – 2.5 2

09-22-00 1.2 – – – – 2.5 2

09-29-00 1.2 – – – – 2.5 2

10-18-00 1.4 – – – – 2.5 2

Lot 6 stubble evapotranspiration measurement site

06-10-00 – – – – – 1.4 1.5

06-11-00 0.2 0.3 to 0.39 0.4 to 0.49 0.3 to 0.39 0.5 to 0.59 1.4 1.5

06-28-00 0.3 – – – – 1.4 1.5

07-07-00 0.8 – – – – 1.3 1.5

07-12-00 0.9 – – – – 1.9 1.5

07-18-00 – 0.8 to 0.89 0.8 to 0.89 0.9 to 0.99 0.9 to 0.99 1.9 1.5

07-19-00 1.1 – – – – 2.2 2

07-21-00 – – – – – 2.4 2

08-04-00 1.1 – – – – 2.4 2

08-11-00 1.2 – – – – 2.4 2

08-16-00 -- – – – – 2.3 2

08-24-00 1.2 – – – – 2.3 2

08-27-00 -- 1.0 to 1.09 >1.0 to 1.09 1.1 to 1.19 >1.1 to 1.19 2.3 2

08-28-00 1.3 – – – – 2.5 2

09-08-00 1.3 – – – – 2.5 2

09-15-00 1.3 – – – – 2.5 2

09-22-00 1.2 – – – – 2.5 2

09-29-00 1.2 – – – – 2.5 2

10-18-00 1.3 – – – – 2.5 2

Table 1. Approximate maximum heights of vegetation or vegetation residues, and heights of air and wind sensors 

[Approximate maximum vegetation or vegetation residue height: Height above the land surface of vegetation or vegetation residues near the air sensors 

was estimated average maximum height within a distance of approximately 15 meters from the sensors; maximum height of vegetation or vegetation residues 

for the quadrants was the tallest height class that was tallied in each quadrant during a vegetation survey. Height of vegetation or vegetation residues that were 

on the irrigation checks was estimated as the height of those materials above the land surface adjacent to those checks. Air sensor height: Height of air sensors 

is height of the midpoint between the upper and lower air sensors above the land surface; –, not measured; <, less than; >, greater than]
Vegetation 21

The sonic anemometer and data logger were mounted 

on a tripod that was approximately 12 to 15 m north or 

north-northeast of the BREB data logger enclosure at 

each site. The sonic anemometer was oriented to the 

west at each site and was at a height approximately 

equal to the current average height of the air sensors of 

the nearby BREB station.

VEGETATION

Vegetation was described by using observations 

of general vegetation condition, such as whether 

particular types of plants appeared to be vigorous or 

senesced, judged by color or by changes of color with 

time, by estimates of vegetation height, and 

systematically by an objective survey technique. The 

survey technique was modified from the step-point 

technique (Interagency Technical Team, 1996). A pole 

approximately 1.3 m long was fixed with a sight 

consisting of an approximately 0.002-m-diameter 

metal shaft. The pole was placed and held vertically at 

a point on a temporary survey transect, and the operator 

sighted down the length of the pole to find the first 

object that intercepted the line of sight established by 

the operator's eye and the end of the shaft. The object 

was tallied as one of the known plants, as an unknown 

plant, as vegetation residue, or as the bare soil surface. 

Vegetation residue is defined as any nonliving 

vegetative matter. The height of the tallied object above 

the soil surface was classified in 0.1-m increments by 

comparing its height against height increments marked 

on the pole. Specimens of particular plants that were 

not tallied but that were observed as being present were 

so noted.

Transects at lot C1B were run in northeast, 

southeast, southwest, and northwest directions for 

distances of approximately 200 m from the BREB 

station. At the lot 6 stubble site, the survey transects 

were run in northeast and southeast directions from the 

BREB station to the edge of the lot, in southwest and 

northwest directions to the edge of the cover crop or to 

the mowed path along the southern edge of the lot, 

westerly to the edge of the cover crop, and on a bearing 

of 300 degrees to the edge of the cover crop. 

Lot 6 cover crop evapotranspiration measurement site

06-03-00 0.4 – – – – 1.5 2

06-11-00 0.5 – – – – 1.6 2

07-07-00 1.4 – – – – 2.1 2

07-12-00 1.3 – – – – 2.1 2

07-19-00 1.4 – – – – 2.5 2

08-04-00 0.9 – – – – 2.5 2

08-11-00 0.9 – – – – 2.5 2

08-16-00 – – – – – 2.2 2

08-24-00 0.9 – – – – 1.8 2

08-28-00 1.0 – – – – 2 2

09-08-00 0.8 – – – – 2 2

09-15-00 0.7 – – – – 2 2

09-18-00 – – – – – 1.5 2

09-22-00 0.6 – – – – 1.5 2

09-29-00 0.5 – – – – 1.5 2

10-18-00 0.5 – – – – 1.3 2

Table 1. Approximate maximum heights of vegetation or vegetation residues, and heights of air and wind sensors—Continued

Date

Approximate maximum vegetation or vegetation residue height (meters) Sensor height 

(meters)

Near air 

sensors

Northeast 

quadrant

Southeast 

quadrant

Southwest 

quadrant

Northwest 

quadrant Air Wind
22 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

Transects were established anew for each survey by 

pacing distances between points. Percentage of land 

coverage by each type of object was computed as the 

number of points where the object type was identified 

divided by the total number of points in the survey. 

Each vegetation survey consisted of between 595 and 

722 points. Percentage of site coverage by vegetation at 

the lot 6 cover crop site was estimated by cursory 

observations, rather than by the objective survey 

technique. The stand of cereal rye at the cover crop site 

was dense and essentially a monoculture, and the 

estimates were considered to be sufficiently accurate to 

meet the study objectives. 

Lot C1B Site

Vegetation at the lot C1B evapotranspiration 

measurement site was in a state of early growing–

season growth and development when the site was 

established during late May 2000. On May 20, 

33 percent of the surface was covered by vegetation, 

chiefly small grain plants and mustard plants, that had 

recently emerged from the soil surface or from beneath 

residues of the previous crop (table 2). Approximately 

half of the surface was covered by vegetation residues, 

chiefly standing stubble and matted straw from the 

previous crop, and 15.9 percent of the soil surface was 

exposed. 

Table 2. Percentage of ground coverage by vegetation and vegetation residues, and percentage of exposed soil at the lot C1B 

and lot 6 stubble evapotranspiration measurement sites, by sampling date

[n, number of sampling points; P, plant was noted as present but was not tallied; –, plant was not tallied or noted as present; Because of rounding, percentages 

in each column might not total 100]

Common plant name, 

vegetation residues, or 

exposed soil

Lot C1B site, 

05-20-00, 

n = 603

Lot C1B site, 

07-20-00, 

n = 595

Lot C1B site, 

08-29-00, 

n = 683

Lot 6 stubble 

site, 06-11-00, 

n = 722

Lot 6 stubble 

site, 07-18-00, 

n = 649

Lot 6 stubble 

site, 08-27-00, 

n = 653

Tansymustard1 8.8 2.0 – P – –

Brown mustard1 P 0.3 P P – 0.2

Common tumblemustard1 3.8 3.9 – – – --

Prickly lettuce1 1.7 6.9 2.8 1.8 13.4 4.9

Common lambsquarters1 0.8 5.2 3.8 0.3 3.5 2.3

Wild oat1 – 4.2 – – 23.1 5.2

Kochia1 0.2 0.7 2.6 0.6 1.7 17.5

Small grains1 17.7 19.7 -- 6.9 15.3 0.3

Perennial pepperweed – P – – – –

Curly dock – P P – – P

Unknown broadleaf plant(s) P 0.3 P P 1.9 0.3

Unknown grass(es) – – – – 4.3 –

All vegetation 33.0 43.2 9.2 9.6 63.2 30.7

Vegetation residues 51.1 55.0 81.1 79.6 35.1 67.4

Exposed soil 15.9 1.8 9.7 10.8 1.7 2.0

1Annual or biennial.
Vegetation 23

The stubble was generally less than 0.3 m in height and 

the vegetation was generally were less than 0.5 m in 

height. Vegetation to a distance of 200 m in easterly 

directions from the BREB station appeared to be 

slightly more dense than was the vegetation in westerly 

directions from the station. By June 11, the vegetation 

had become dense and reasonably uniform in all 

directions from the BREB station, except for areas on 

the irrigation checks, which remained stubble-covered. 

Composition, density, and height of vegetation that 

grew in the burned eastern part of the lot was similar to 

that of vegetation in the remainder of the lot. 

Approximate maximum height of the vegetation 

canopy in the vicinity of the air sensors was 0.9 m 

(table 1). The tallest individual plants were mustards, 

some of which had begun to flower by June 11. By the 

time of the second survey at lot C1B, on July 20, the 

total percentage of coverage by vegetation was 

43.2 percent (table 2). The total percentage of coverage 

by mustard plants had decreased since the previous 

survey, and percentage of coverage by prickly lettuce, 

common lambsquarters, wild oat, and small grain 

plants had increased. The percentage of coverage by 

vegetation residues (55 percent) was almost the same 

as it was on May 20 (51.1 percent); however, more of 

the residues at the later date consisted of stems and 

leaves of erect plants that had senesced and died since 

June 11. The vegetative canopy in the vicinity of the air 

sensors was of a maximum height of approximately 

1.2 m. Many of the plants had turned yellowish-green 

in color, suggesting the period of peak vegetation 

growth and physiological activity or physiologically 

mediated activity, including transpiration and carbon 

uptake, almost certainly had been completed prior to 

July 20. By the time of the final vegetation survey at lot 

C1B, on August 29, percentage of coverage by live 

vegetation was only 9.2 percent, and the only living 

plants that were tallied during the survey were prickly 

lettuce, common lambsquarters, and kochia. The small 

grain plants and mustards had all gone to seed and died. 

Total percentage of coverage by vegetation residues 

was 81.1 percent. No live plants were noted during the 

final site visit of October 19, indicating the growing 

season had come to an end at the C1B 

evapotranspiration measurement site before that time. 

Almost all of the plants identified at lot C1B are 

annuals, meaning they complete their life cycle during 

a single year, or biennials, meaning they require 2 years 

to complete their life cycle. 

Lot 6 Stubble Site

The lot 6 stubble evapotranspiration 

measurement site was almost completely devoid of 

vegetation when the BREB station was installed there 

during June 10 and 11, 2000. What little vegetation that 

was present consisted chiefly of juvenile small grain 

plants. Overall, percentage of coverage by vegetation 

was 9.6 percent (table 2). Percentage of coverage by 

residues was 79.6 percent, and the residues consisted 

mostly of stubble and matted straw from the small 

grain crop that was harvested during the previous year. 

Maximum heights of stubble and vegetation near the 

air sensors was 0.2 m (table 1). By July 18, the time of 

the second vegetation survey, the site had become 

occupied by dense, dark-green vegetation. Total 

percentage of site coverage by vegetation was 

63.2 percent, and the most common plants were prickly 

lettuce, wild oat, and small grain plants. Although the 

vegetation at the lot C1B evapotranspiration 

measurement site had likely passed its peak of growth 

and physiological activity by mid- to late July, the 

vegetation at the lot 6 stubble site clearly was near its 

seasonal peak. Maximum height of vegetation near the 

air sensors was estimated to be 1.1 m on July 19. Most 

of the vegetation at the lot 6 stubble site had senesced 

or had begun to senesce by August 27. Total percentage 

of site coverage by vegetation was 30.7 percent, and 

kochia was the most common plant. Percentage of 

coverage by vegetation residues, which by August 27 

included many dead standing plants, had almost 

doubled since July 18. Maximum height of vegetation 

near the air sensors was estimated to be 1.3 m on 

August 28. By October 18, the only living plants 

observed at the site were small, scattered grass plants 

that were probably small grain plants that had recently 

sprouted in the mowed paths. Desiccated residues of 

vegetation that grew during 2000 stood erect at the site, 

except for a few patches that formerly were small grain 

plants that had collapsed. Almost all of the plants 

identified at the lot 6 stubble site are annuals or 

biennials.

Causes of the differences between the lot C1B 

and lot 6 stubble sites with respect to vegetation 

composition and percent cover are not known; 

however, the causes could have been related to 

differences in farming practices at the two lots prior to 

1999. 
24 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

For example, differences in past uses of herbicides at 

the two lots, such as the types of herbicides used, the 

number of years herbicides were applied, and the 

seasonal timing of herbicide applications, might have 

suppressed particular weedy plant species at one of the 

lots by more than they were suppressed at the other lot. 

Part of the reason that vegetation cover developed 

more rapidly at the lot C1B site than at the lot 6 stubble 

site was that the lot C1B site supported many more 

mustard plants than did the lot 6 stubble site; the 

mustards tend to grow and develop earlier in the 

growing season than do most of the other species that 

grew at the two sites (Sam Johnson, USFWS, oral 

commun., August 2001). In addition, crop residues 

tend to cause spring soils to be cooler than they would 

be without such residues (Bidlake and others, 1992), 

and the cooler soils can delay germination, growth, and 

development of vegetation. Differences in the quantity 

(thickness and bulk density) of residues, although not 

measured in this study, could have been partly 

responsible for the observed temporal differences in 

vegetation growth and development at the lot C1B and 

lot 6 stubble sites. 

Lot 6 Cover Crop Site

The cover crop of cereal rye was planted at lot 6 

during February 2000. By June 3, 2000, the dark-green 

crop was fairly uniform, except for areas on the 

irrigation checks and a few areas a few meters in width 

where the crop was sparse. Overall, vegetation 

coverage at the site appeared to be greater than 

80 percent. Maximum height of the crop near the air 

sensors was approximately 0.4 m (table 1). The 

extensive stubble barren of the lot 6 stubble site was 

immediately to the east of the cover crop (fig. 2, lot 6), 

and the mixture of growing vegetation and smaller 

stubble barrens described previously extended from the 

west edge of the cover crop to the west edge of the lot. 

On July 19, maximum crop height near the air sensors 

was approximately 1.4 m. Seed kernels had developed. 

The obviously senescing, light yellowish green cereal 

rye plants contrasted with the dark-green vegetation 

that had by that time occupied the former stubble 

barrens. Coverage by the crop appeared to be greater 

than 90 percent. By August 28, the plants had turned 

light brown in color and appeared to be dead above 

ground. The desiccated standing crop residues had 

begun to collapse, and the average height of the crop 

residue canopy was approximately 1.0 m. By 

October 18, the crop residue canopy had collapsed to a 

height of approximately 0.5 m. 

METEOROLOGICAL CONDITIONS AND 

SURFACE ENERGY BALANCE

Fair weather dominated the period of field 

measurements for this study. Total precipitation 

measured at lot C1B during May 20 to October 18 was 

42.8 mm, and 69 percent of the precipitation fell during 

the rainy period of September 1 to 4 (table 3). 

Precipitation was measured at lot 6 from June 4 to 

October 18, although data for June 28 to July 18 were 

lost due to a data retrieval anomaly. Total precipitation 

measured at lot 6 was 36.9 mm. If precipitation data for 

lot C1B are substituted for the missing data, total 

estimated precipitation at lot 6 for May 20 to October 

18 is 43.0 mm. Precipitation at the Tulelake 

meteorological station near Tulelake during May 

through October totaled 97 mm (Western Regional 

Climate Center, 2001). Precipitation at lot C1B during 

May and October was estimated by multiplying 

precipitation at the Tulelake meteorological station for 

each of those months by the ratio of total precipitation 

at lot C1B during June through September to total 

precipitation at the Tulelake meteorological station 

during those same months. The ratio was 0.70, and 

estimated precipitation at lot C1B for the complete 

months of May and October was 14 and 17 mm, 

respectively. Estimated total growing-season 

precipitation at lot C1B, which was computed by 

summing measured precipitation at the lot for June 

through September with estimated precipitation for 

May and October, was 68 mm. Estimated total 

growing-season precipitation at lot 6, which was 

computed using the approach that was used for lot 

C1B, was 75 mm.

Analysis and interpretation of surface energy 

balance and related data were first conducted for the lot 

C1B evapotranspiration measurement site where 

vegetation was thought to be generally extensive and 

homogeneous enough to enable valid BREB 

measurements to be made regardless of wind direction. 

An exception to the vegetation homogeneity occurred 

during May 20 and June 11, before the developing 

vegetation had become dense and uniform. 
Meteorological Conditions and Surface Energy Balance 25

Selected environmental variables that influenced or 

were related to variations of evaporative loss from lot 

C1B are depicted for selected days in figures 3 and 4. 

During the fair weather of June 14 to 17, Rn was 

negative at night and became positive shortly after 

sunrise (fig. 3). Net radiation reached a maximum of 

approximately 700 W/m2 during 1300 to 1400 Pacific 

Daylight Time (PDT), and it then decreased and 

became negative roughly half an hour before sunset. 

Under the time notation used in this report, a day 

begins at 0000 PDT and ends at 2400 PDT. Noon is 

1200 PDT, and 3:30 p.m. is 1530 PDT. Net radiation at 

lot C1B followed a similar pattern of diurnal variation 

during the fair weather of August 25 to 28, when the 

vegetation was largely senesced, except that maximum 

Rn was approximately 550 W/m2 (fig. 4). 

Soil heat flux at the soil surface (G) was negative 

at night, indicating energy was being discharged to the 

atmosphere, and G became positive in the mornings at 

approximately the same time as or shortly after Rn

became positive (figs. 3 and 4). During mid-June, 

daytime G increased to a maximum of approximately 

100 W/m2 during 1000 to 1100 PDT, roughly 2 hours 

before Rn reached its daily maximum. During late 

August, daytime G reached a maximum of 

approximately 90 W/m2. Average daytime G was 

equivalent to 7 percent of average daytime Rn during 

June 14 to 17, and average daytime G was equivalent to 

10 percent of average daytime Rn during August 25 to 

28. Average G during sunrise to 1200 PDT was 

equivalent to 13 percent of average Rn during June 14 

to 17, and average G during sunrise to 1200 PDT was 

equivalent to 14 percent of average Rn during 

August 25 to 28.

Latent and sensible heat fluxes computed by the 

BREB technique varied diurnally in a manner similar 

to diurnal variations of Rn (figs. 3 and 4). Latent heat 

flux was very nearly zero at night, became positive 

after sunrise, and reached its daily maximum at the 

same time as or shortly after the Rn maximum. Daily 

maximum λE was approximately 450 W/m2 during 

June 14 to 17, and daily maximum λE was 

approximately 100 W/m2 during August 25 to 28. 

Sensible heat flux generally was negative at night, 

became positive after sunrise, and reached its daily 

maximum within an hour of the maximum Rn. The 

gaps in the time series of λE and H in figures 3 and 4

resulted from those data being rejected during the 

screening procedure that was described previously. 

The partitioning of available energy (Rn - G) 

between latent and sensible heat fluxes during midJune differed markedly from the partitioning during 

late August. During mid-June, when the vegetation at 

lot C1B was likely near its seasonal peak of growth and 

physiological activity, available energy was partitioned 

strongly to λE at the expense of H. The roles were 

reversed by late August, when the vegetation was 

mostly dead or senesced, and available energy was 

partitioned strongly to H. Latent heat flux during late 

August was substantially diminished as compared to 

λE during mid-June.

The Bowen ratio (β) is strongly influenced by 

the aridity of the surface where energy and water are 

exchanged with the atmosphere. As a result, some 

tentative inferences about the aridity of a surface can 

be made by examining β (Campbell, 1977; Lafleur and 

Rouse, 1988). For terrestrial surfaces where water to 

meet evaporative demand is scarce, available energy is 

partitioned strongly to H at the expense of λE, and 

midday β for such sites tends to be greater than 1.0. On 

the other hand, where the soil surface is moist or where 

the land is occupied by actively transpiring vegetation, 

β tends to be smaller than 1.0. Campbell (1977, p. 136) 

indicates β = 0.2 is typical for well-watered short grass 

or wet soil. 

Table 3. Daily precipitation measured at the lot C1B and lot 

6 cover crop evapotranspiration measurement sites, shown 

for days precipitation was detected at least one site

[Lot C1B: Period of record is May 20 to October 18, 2000. Lot 6 cover 

crop: Period of record is June 4 to June 27 and July 19 to October 18, 2000. 

Precipitation is in millimeters; -– no data]

Date

Evapotranspiration

measurement site

Lot C1B Lot 6 cover crop

06-08-00 1.8 0

07-05-00 5.3 –

07-06-00 0.3 –

07-10-00 0.5 –

09-01-00 16.8 22.4

09-02-00 5.3 4.6

09-03-00 2.8 0.5

09-04-00 4.6 3.0

09-05-00 0 0.3

10-09-00 4.3 4.3

10-10-00 0.8 1.0

10-11-00 0.3 0.5

10-12-00 0 0.3
26 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

U

D

Rn

G H

E

0

100

200

300

400

500

600

700

800

900

-4

-2

0

2

4

6

8

10

0

2

4

6

8

10

-5

-4

-3

-2

-1

0

1

2

3

4

5

0

1

2

3

4

-100

E

W

M

2400 1200 1200 2400 2400 1200 1200 2400 2400

JUNE 14 JUNE 15 JUNE 16 JUNE 17

WIND SPEED (

U), 

IN METERS PER SECOND

WIND 

DIRECTION

ENERGY FLUX,

IN WATTS PER SQUARE METER

VAPOR-PRESSURE 

DEFICIT (

D),

IN KILOPASCALS

A

B

C

D

2000

RATIO OF LATENT 

HEAT FLUX TO EQUILIBRIUM

LATENT HEAT FLUX ( )

BOWEN RATIO ( )

Figure 3. (A) Surface energy balance components net radiation (Rn), energy flux into the soil surface (G), 

and latent (λE) and sensible (H) heat fluxes; (B) wind direction, classified as easterly (E), westerly (W), or 

mixed easterly and westerly (M); (C) Bowen ratio (β) and ratio of latent heat flux to equilibrium latent heat flux 

(α); and (D) wind speed (U) and atmospheric water-vapor pressure deficit (D), all as they varied at the lot C1B 

evapotranspiration measurement site during June 14 to 17, 2000.
Meteorological Conditions and Surface Energy Balance 27

Rn

G H

E

U

D

0

100

200

300

400

500

600

700

800

900

-4

-2

0

2

4

6

8

10

0

2

4

6

8

10

-5

-4

-3

-2

-1

0

1

2

3

4

5

0

1

2

3

4

-100

E

W

M

2400 1200 1200 2400 2400 1200 1200 2400 2400

AUGUST 25 AUGUST 26 AUGUST 27 AUGUST 28

WIND 

DIRECTION

ENERGY FLUX,

IN WATTS PER SQUARE METER

A

B

C

D

VAPOR-PRESSURE 

DEFICIT (

D),

WIND SPEED (

IN KILOPASCALS

U), 

IN METERS PER SECOND

2000

RATIO OF LATENT 

HEAT FLUX TO EQUILIBRIUM

LATENT HEAT FLUX ( )

BOWEN RATIO ( )

Figure 4. (A) Surface energy balance components net radiation (Rn), energy flux into the soil surface (G), 

and latent (λE) and sensible (H) heat fluxes; (B) wind direction, classified as easterly (E), westerly (W), or 

mixed easterly and westerly (M); (C) Bowen ratio (β) and ratio of latent heat flux to equilibrium latent heat flux 

(α); and (D) wind speed (U) and atmospheric water-vapor pressure deficit (D), all as they varied at the lot C1B 

evapotranspiration measurement site during August 25 to 28, 2000.
28 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

During June 14 to 17 at lot C1B, midday average β, 

computed using data from 1100 to 1500 PDT, ranged 

from 0.39 to 0.56 and averaged 0.48. During August 25 

to 28, midday average β ranged from 4.08 to 4.66 and 

averaged 4.27. 

The Bowen ratio also varied diurnally. Most 

typically, β increased from sunrise until about 

1300 PDT, and it then decreased for the remainder of 

the daytime (fig. 3). The Bowen ratio often varied 

erratically during dusk, dawn, and at night, however, 

because the air-temperature and water-vapor pressure 

gradients were generally small in magnitude during 

those times, and even small measurement errors in ∆T

and ∆e could have caused large absolute errors in β. 

The BREB technique remains tenable for computing 

daily evapotranspiration because all of the surface 

energy balance components tended to be small in 

magnitude, and thus relatively unimportant for 

computing daily values, when the gradients ∆T and ∆e

were small. 

The coefficient α is related to β through

 , (30)

where all terms have been defined previously, and thus 

α is also strongly influenced by aridity of the surface of 

interest. Average midday (1100 to 1500 PDT) α at lot 

C1B during June 14 to 17 ranged from 0.87 to 0.93 and 

averaged 0.90 (fig. 3). During August 25 to 29, average 

midday α ranged from 0.23 to 0.26 and averaged 0.25 

(fig. 4). The late August α values at lot C1B were 

similar to the minimum daily values reported by 

Williams and others (1978) for dry rangeland in British 

Columbia, Canada, and are indicative of 

evapotranspiration under strongly water-limited 

conditions.

The coefficient α also varied diurnally. During 

the daytime, α generally was largest in the morning, 

decreased to a minimum approximately at 1300 PDT, 

and increased late in the afternoon (figs. 3 and 4). 

De Bruin (1983) simulated a similar “U-shaped” 

daytime variation of α using a model of heat and 

moisture exchanges between the land surface and the 

lower atmosphere for a clear summer day in the 

Netherlands. At night at the lot C1B site, α could be 

negative or positive, depending on whether or not β

was greater than -1, as is indicated by equation 30, 

because the quantity (s + γ)/s is always positive. As 

was the case for β, the particular numerical values of α

during nighttime were relatively unimportant for 

computing total daily evapotranspiration because all of 

the components of the surface energy balance tended to 

be small in magnitude at night.

 Wind direction and speed and atmospheric 

water-vapor pressure deficit also exhibited 

characteristic diurnal variations (figs. 3 and 4). The 

most typical pattern of diurnal variation was for wind 

direction to be westerly from about midday until after 

midnight, when wind direction changed to easterly. 

Wind direction generally remained easterly until midto late morning, when it shifted back to westerly. The 

most common wind direction was westerly, followed 

by easterly, and then by mixed wind directions. Wind 

speed at night generally averaged less than 2 meters per 

second (m/s). Wind speed generally increased during 

mid-morning and it generally decreased to less than 2 

m/s before midnight. Because of the previously 

described diurnal variations of wind direction and 

speed, wind speed tended to be largest when wind 

direction was westerly (figs. 3 and 4). An exception to 

this typical diurnal variation occurred at lot C1B on 

June 16, when wind direction was easterly or mixed 

during most of the day.

Diurnal cycling of the atmospheric water-vapor 

pressure deficit is chiefly due to cycling of air 

temperature, because water-vapor pressure at 

atmospheric saturation (es) varies strongly with 

temperature, as is predicted by equation 26. At lot C1B 

during mid-June and late August, daily maximum 

atmospheric water-vapor pressure deficits generally 

occurred during mid-afternoon, when wind direction 

was generally westerly (figs. 3 and 4). Daily maximum 

D ranged from 2.22 to 3.16 kilopascals (kPa) during 

June 14 to 17, and it ranged from 3.15 to 3.54 kPa 

during August 25 to 28. The daily minimum 

atmospheric water-vapor pressure deficit generally 

approached zero shortly before sunrise, indicating the 

atmosphere near the surface was saturated or almost 

saturated with water vapor at those times.

Variations of selected surface energy balance 

components, β, and α for the lot C1B 

evapotranspiration measurement site that are depicted 

in the long-term, tabular summary (table 6, at back of 

report) exhibited many of the same features that were 

previously described for the short-term, graphical 

summaries. The tabular summary was made from the 

complete data record for the lot C1B BREB station by 

averaging available energy, λE, β, and α for all 30-

minute periods when λE and H computed by the BREB 

were valid. 

α

s + γ

s ---------- 1

1 + β = • ------------
Meteorological Conditions and Surface Energy Balance 29

This excluded all data from periods when λE and H

were rejected as a result of the screening procedures 

that were described previously, and other periods for 

which λE and H were not available due to such factors 

as a shutdown of the BREB station or to known system 

malfunctions. Most notable among the malfunctions 

was the bird-wrought destruction of the net radiometer 

that occurred sometime between October 7 and 

October 18. The selected energy balance components, 

β, and α were averaged by wind direction, by selected 

intervals of time of day, and for periods that nominally 

were 7 days, but that ranged 2 to 7 days. Duration of 

multi-day averaging periods was varied to capture 

shorter-term variations of the components that were 

associated with precipitation or because of breaks in 

data continuity. Finally, multi-day average β and α

were computed from multi-day-average available 

energy, λE and λEEQ, rather than as the averages of β

and α from each 30-minute period. 

Among the similarities between the long- and 

short-term summaries are the overall predominance of 

westerly winds, the tendency for easterly winds to 

occur at night or in the morning, and the relative 

scarcity of periods of mixed easterly-and-westerly 

winds. Easterly winds during sunrise to 1100 PDT 

tended to occur earlier during that period than did 

westerly winds, as is evidenced by the generally 

smaller average available energy for easterly winds 

(table 6). Also, average nighttime available energy and 

λE were negligibly small during the entire period of the 

summarized data for the lot C1B evapotranspiration 

measurement site. 

Long-term variations of β and α at the lot C1B 

evapotranspiration measurement site reflected 

variations of surface energy balance partitioning that 

likely were caused by variations of surface aridity. For 

westerly winds, average midday (1100 to 1500 PDT) β

decreased from 0.90 during May 19 to May 25 to a 

minimum of 0.55 during June 9 to 15, when 65 percent 

of the available energy was partitioned to λE (table 6). 

After June 9 to 15, β began to increase until, by 

October 4 to 7, average midday β during westerly 

winds was 7.89. The trend of increasing β was 

interrupted by the rainy spells of early July and early 

September. For example, average midday β for 

westerly winds decreased from 1.32 during June 30 to 

July 4, immediately before the rain, to 0.39 during July 

5 to July 7 (table 6). The rainfall during July 5 and 6 

wetted the plants and the soil, and the decreased aridity 

of the surface caused a shift in available energy 

partitioning to favor λE at the expense of H. Long-term 

variations of α and the responses of α to precipitation 

substantially mirrored those of β. 

The long-term summaries of selected energy 

balance components, β, and α for the lot 6 stubble and 

cover crop evapotranspiration measurement sites 

(tables 7 and 8, at back of report) exhibited features 

that were similar to those depicted in the summary for 

lot C1B. The similarities included the predominance of 

westerly winds, the tendency for any easterly winds to 

occur at night or during the morning, relatively 

infrequent periods of mixed-direction winds, and 

negligibly small nighttime λE. As was discussed 

previously, the fetch-to-instrument-height ratios at the 

lot 6 sites for all but westerly winds likely were too 

small to obtain reliable estimates of λE and H by the 

BREB technique. Summaries of λE, β, and α computed 

by the BREB technique for easterly and mixeddirection winds, although they are presented in tables 7

and 8 (at back of report), were not used to compute 

daily or growing-season evapotranspiration.

 Surface energy balance partitioning at the lot 6 

stubble evapotranspiration measurement site trended 

differently from the partitioning at the lot C1B site, 

suggesting that trends of surface aridity were dissimilar 

for the two sites. At the lot 6 stubble site, average 

midday β during westerly winds decreased from 2.97 

during June 11 to 15 to a minimum of 0.19 during 

July 29 to August 4, when 84 percent of the available 

energy was partitioned to λE (table 7, at back of 

report). After July 29 to August 4, average midday β

began an increasing trend, a trend that was interrupted 

by the rainy spell of early September, but that 

culminated with a value of 7.30 for westerly winds 

during October 4 to 7. Thus, excluding the rainy period 

of early July, the growing-season minimum of midday 

β during westerly winds at the lot 6 stubble site 

occurred approximately six weeks after the minimum 

occurred at the lot C1B evapotranspiration 

measurement site. Excluding the rainy period of early 

July, the maximum percentage of midday available 

energy partitioned to λE during westerly winds was 

84 percent at the lot 6 stubble site and 65 percent at the 

lot C1B site. Peak availability of moisture to meet 

evaporative demand was greater at the lot 6 stubble site 

than at the lot C1B site.
30 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

Although part of the June and most of the July 

data from the BREB station at the lot 6 cover crop site 

were lost or were unreliable due to a data retrieval 

anomaly and to equipment malfunctions, the available 

data suggest energy balance partitioning trends at the 

lot 6 cover crop site differed from the trends at the lot 

C1B and lot 6 stubble sites. Average midday β during 

westerly winds at the cover crop site decreased slightly 

from 0.48 during June 3 to 8 to a minimum of 0.40 

during June 23 to 27, when 71 percent of the available 

energy was partitioned to λE (table 8, at back of 

report). Following the data gap, average midday β

during westerly winds increased from 1.29 during July 

21 to 28 to a maximum of 9.69 during October 4 to 7, 

when 9 percent of available energy was partitioned to 

λE. The trend of increasing β was interrupted by the 

rain that fell during early September, as were the trends 

of increasing β at the lot C1B and lot 6 stubble sites. 

The growing-season minimum of β is not known for 

the lot 6 cover crop site because it could have occurred 

during the period for which the data were lost or 

unreliable. 

AIRSTREAM EQUILIBRATION

The previously discussed airstream equilibration 

theory (Stannard, 1997) was used to explore possible 

effects of the limited fetch on λE measured by the 

BREB technique (λEm) at the lot 6 stubble and cover 

crop evapotranspiration measurement sites during 

westerly winds. The theory was applied using fetch 

computed from wind direction and figure 2, using 

measured or estimated vegetation height, using d0 and 

z0 estimated as was described previously, and using 

measured heights of the air sensors for the BREB 

stations. Because many of the data needed to apply the 

theory were by necessity estimated, and because of a 

simplifying assumption in the theory, which is 

discussed later in this report, errors in λEm computed 

using the theory are not considered to be accurate in an 

absolute sense. Instead, the computed errors are used to 

identify periods when accuracy of λEm was most likely 

reduced by the limited fetch, and to provide rough 

estimates of the errors attributable to the limited fetch.

 The cover crop was the contaminating surface 

for the stubble site during westerly winds (fig. 2, lot 6). 

The theory indicated that a lack of equilibrium of the 

airstream with the stubble site generally could have 

caused actual λE (λEi) to be underestimated by less 

than 10 percent during midday (1100 to 1500 PST) 

(table 4). However, during the first two weeks of 

measurements at the stubble site, the theory indicated 

λEi was overestimated by λEm by as much as 

60 percent. The cover crop was actively growing 

during June, and available energy was partitioned 

preferentially to λE at the expense of H, as was 

indicated by daytime β being less than 1.0 during that 

month (table 8). Vegetation at the stubble site probably 

remained sparse until late June and available energy at 

that site was strongly partitioned to H, as was indicated 

by a relatively large β (table 7). The airstream 

equilibration theory predicted that this sharp contrast in 

β between the two sites caused βm to overestimate the 

actual Bowen ratio (βi) at the lot 6 stubble BREB 

station due to the influence of heat and water vapor that 

arose from the cover crop and traveled in on the wind. 

Measured β for the two sites converged during late 

June, when vegetation at the stubble site likely grew 

rapidly. As a result of the reduced contrast of β that 

occurred by June 27, the theory predicted that airstream 

equilibration during westerly winds was almost 

complete by the time the air reached the stubble site 

BREB station, such that error in λEm was less than 

5 percent of λEi (table 4).

The predicted error in midday λEm for the 

stubble site was relatively small (-3.3 percent) on 

August 16, despite the fact that βm for the stubble and 

cover crop sites differed by almost an order of 

magnitude (table 4). A key difference between the 

Bowen ratio contrast of August 16 compared to those 

of June 12 and 19 (when contrasting Bowen ratios 

yielded large theory-predicted percentage errors) was a 

larger β at the cover crop site on August 16 than at the 

stubble site. Thus, although the theory predicted that 

percentage errors in λEm were relatively large under 

limited-fetch conditions when the wind transited from 

a moist to a dry surface, the same was not true for a 

dry-to-moist surface transit. In fact, the previously 

cited examples from the literature of successful 

applications of the BREB technique with fetch-toinstrument-height ratios as small as about 20 (Fritschen 

and others, 1983; Heilman and others, 1989) were 

applications of the technique that were made under 

dry-to-moist surface wind transitions. 
Airstream Equilibration 31

Table 4. Fetch-to-instrument-height ratio for Bowen ratio energy balance measurements, measured and theory-predicted 

Bowen ratios and energy fluxes, and estimated percentage error and error in measured latent heat flux, all for westerly winds 

during midday (1100 to 1500 hours, Pacific Daylight Time) on selected days for the lot 6 stubble and the lot 6 cover crop 

evapotranspiration measurement sites during June to October, 2000

[F, fetch-to-instrument-height ratio for westerly winds; dimensionless; βm, Measured Bowen ratio for surface of interest, dimensionless; βc, Bowen ratio for 

the contaminating surface; dimensionless; βi, Actual Bowen ratio for the surface of interest, dimensionless; Am, measured available energy for the surface of 

interest, in watts per square meter; R, ratio of available energy at the contaminating surface to that at the surface of interest, dimensionless; λEm, measured 

latent heat flux from the surface of interest, in watts per square meter; %δλE, percentage error in λEm due to the influence of the contaminating surface; δλE, 

error in λEm due to the influence of the contaminating surface, in watts per square meter]

Date F βm βc βi Am R λEm %δλE δλE

Surface of interest: Lot 6 stubble site Contaminating surface: Lot 6 cover crop site

June 12 76 2.62 0.21 4.79 187 1.12 52 60 19

June 19 85 2.14 0.58 2.82 520 1.19 166 22 29

June 27 98 0.94 0.41 1.03 561 1.09 289 4.7 13

July 21 69 0.13 0.53 0.10 608 0.92 539 -2.4 -13

Aug. 4 68 0.23 1.92 0.17 572 0.85 464 -5.2 -25

Aug. 16 132 0.91 7.31 0.85 526 0.90 276 -3.3 -9

Aug. 28 151 2.18 10.36 2.08 457 0.98 144 -3.2 -5

Sept. 8 62 2.47 3.67 2.38 411 1.03 118 -2.7 -3

Sept. 21 89 3.07 5.96 2.90 413 1.17 101 -4.3 -5

Oct. 6 60 7.93 10.41 7.71 330 0.92 37 -2.4 -1

Surface of interest: Lot 6 cover crop site Contaminating surface: Lot 6 stubble site1

June 12 70 0.21 4.79 0.12 209 0.89 172 -8.1 -15

June 19 98 0.58 2.82 0.53 619 0.84 392 -2.8 -11

June 27 111 0.41 1.03 0.40 610 0.92 432 -0.5 -2

July 21 92 0.53 0.10 0.58 559 1.09 366 3.5 12

Aug. 4 64 1.92 0.17 3.06 489 1.17 167 39 47

Aug. 16 94 7.31 0.85 14.25 472 1.11 57 84 26

Aug. 28 107 10.37 2.08 12.51 449 1.02 39 19 6

Sept. 8 64 3.68 2.38 3.91 422 0.97 90 5.1 4

Sept. 21 90 5.81 2.89 6.15 479 0.86 70 5.1 3

Oct. 6 87 10.42 7.71 10.70 305 1.08 27 2.5 1

1Lot 6 stubble site was used as a surrogate for the contaminating surface that was upwind of the cover crop site during westerly

winds.
32 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

Depiction of airstream equilibration and 

potential errors in λEm for the cover crop site required 

the additional assumption that βc and R computed 

using measurements made at the stubble site, which 

actually was downwind of the cover crop site during 

westerly winds, accurately represented βc and available 

energy for the contaminating surface for the cover crop 

during westerly winds. As was discussed previously, 

vegetation was less sparse west of the cover crop than 

east of the crop when measurements began at the 

stubble site during June, and use of the stubble site as a 

surrogate for the contaminating surface for the cover 

crop site is probably least tenable for theory predictions 

made for June. In addition, because βm for the stubble 

site was influenced by the cover crop, theory-predicted 

βi for the stubble site crop was used as βc when the 

airstream equilibration theory was applied to predict 

potential errors in λEm for the cover crop site. The 

theory indicated that the largest percentage errors in 

λEm at the cover crop site during westerly winds 

occurred during moist-to-dry surface wind transitions 

during August. Measured β for the cover crop was 

consistent with the vegetation being either water 

stressed or in an advanced state of senescence (table 8). 

Conversely, β at the stubble site indicated that moisture 

availability was greater at the stubble site than at the 

cover crop site (table 7).

The airstream equilibration theory indicated that 

the greatest potential for fetch-related errors in λE

computed by the BREB technique for westerly winds 

occurred in June for the lot 6 stubble site and in August 

for the lot 6 cover crop site. Errors computed using the 

theory are subject to numerous uncertainties, including 

errors in estimates of data that were supplied in 

implementing the theory, as well as a simplifying 

assumption in the theory. For example, degree of 

equilibration predicted by the theory is sensitive to the 

particular values used for the roughness parameters d0

and z0, and those parameters were computed for the 

theory computations using empirical relations intended 

for uniform crops. The lack of uniform vegetation 

height at the lot 6 stubble site imparts substantial 

uncertainty into the estimates of the roughness 

parameters for that site. Consequently, the accuracy of 

theory-predicted errors in λEm for the lot 6 stubble site 

is uncertain.

 Finally, the airstream equilibration theory does 

not account for variations of atmospheric stability 

(Stannard, 1997). Atmospheric turbulence is generated 

both by mechanical forces and vertically directed 

buoyant forces, and the state of atmospheric stability 

reflects the role buoyant forces play in enhancing or 

suppressing turbulence (Campbell, 1977, p. 40). 

Turbulent transport is enhanced in an unstable 

atmosphere, a state readily achieved when a relatively 

dry surface is heated by the sun. The enhanced 

turbulent transport of an unstable atmosphere would 

lead to more complete airstream equilibration than 

would occur in a neutral atmosphere, where buoyant 

forces sum to 0. The airstream equilibration theory 

assumes a neutral atmosphere. Moderately unstable 

conditions tended to prevail at the surface of interest 

when moist-to-dry wind transitions occurred; therefore, 

the airstream equilibration theory likely 

underestimated the degree of airstream equilibration 

and overestimated errors in λEm during June 12 and 19 

at the lot 6 stubble site and during August 4, 16, and 28 

at the lot 6 cover crop site (table 4).

COMPARING SENSIBLE HEAT FLUX 

FROM THE BOWEN RATIO ENERGY

BALANCE AND EDDY COVARIANCE 

TECHNIQUES

One technique for examining reliability of 

turbulent fluxes that are computed by the BREB 

technique is to measure one or more of those fluxes 

independently from the surface energy balance. In this 

study, sensible heat flux computed intermittently by the 

eddy covariance technique (HEC) was compared with 

sensible heat flux computed by the BREB technique 

(HBREB). The comparisons between HBREB and HEC

did not provide direct evidence concerning reliability 

of λE that was computed by the BREB technique, but 

the comparisons did provide a sense of how well the 

surface energy balance was understood and 

characterized by measurements during selected days.

Sensible heat flux computed by eddy covariance 

at the lot C1B evapotranspiration measurement site 

during October 18 and 19 generally agreed closely with 

HBREB (fig. 5). Overall, 30-minute-average HEC

averaged 3 W/m2, or 5 percent, smaller than HBREB

(root-mean-squared difference (RMSD)= 15 W/m2, 

n = 35). The close overall agreement is consistent with 

the notion that H computed by the two techniques 

approached the scientific true value of H. It is possible, 

but unlikely, that the agreement of HEC and HBREB was 

the result of compensating errors. 
Comparing Sensible Heat Flux from the Bowen Ratio Energy Balance and Eddy Covariance Techniques 33

-100

0

100

200

300

400

500

-100

0

100

200

300

400

500

-100

0

100

200

300

400

500

-100 0 100 200 300 400 500

SENSIBLE HEAT FLUX FROM BOWEN RATIO ENERGY BALANCE,

IN WATTS PER SQUARE METER

SENSIBLE HEAT FLUX FROM EDDY COVARIANCE,

IN WATTS PER SQUARE METER

EXPLANATION

Mixed wind direction

Westerly wind

Easterly wind

line of equality

line of equality

line of equality

LOT C1B SITE

LOT 6 STUBBLE SITE

LOT 6 COVER CROP SITE

Figure 5. Comparisons between 30-minute-average sensible heat flux as computed by the Bowen ratio 

energy balance technique and by the eddy covariance technique at the lot C1B evapotranspiration 

measurement site during October 18 and 19, 2000, at the lot 6 stubble evapotranspiration measurement site 

during August 29 and 30, 2000, and at the lot 6 cover crop evapotranspiration measurement site during 

August 28 and 29, 2000.
34 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

The degree of agreement also did not appear to vary 

significantly with direction of the wind. An implication 

of this apparently negligible effect of wind direction is 

that available energy and partitioning of available 

energy to H and λE were probably spatially uniform 

and were accurately measured at the lot C1B site, at 

least during mid-October. Spatial uniformity of 

available energy and turbulent fluxes could have varied 

at lot C1B earlier during the growing season in 

response to vegetation heterogeneity; however, 

measurements of HEC were not made at lot C1B to 

confirm this. Also, the comparisons between HBREB

and HEC were made under the relatively dry surface 

conditions of mid-October, when the average midday β

computed by the BREB technique was approximately 

5.1, and agreement between HBREB and HEC might 

have not been as strong had the comparisons been 

made earlier in the growing season when, β was 

smaller. 

Eddy covariance measurements of sensible heat 

flux were made at both lot 6 evapotranspiration 

measurement sites during August 28 to 30. Agreement 

between HEC and HBREB was generally close at the lot 

6 stubble evapotranspiration measurement site during 

August 29 and 30 (fig. 5). Overall, 30-minute-average 

HEC averaged 8 W/m2, or 12 percent, less than HBREB

(RMSD = 19 W/m2, n = 47). The degree of agreement 

also did not appear to vary significantly with direction 

of the wind, despite the relatively small fetch during 

easterly winds. As was the case for the lot C1B site, the 

close agreement of sensible heat flux computed by the 

BREB and eddy covariance techniques is consistent 

with the notion that available energy and the turbulent 

fluxes H and λE were spatially uniform and the surface 

energy balance was accurately characterized at the lot 6 

stubble site during August 29 and 30. The agreement 

during periods when wind direction was thought to be 

unfavorable (easterly) also suggests (but does not 

prove) that the air stream at the heights of the BREB air 

sensors and the eddy correlation sensors was 

substantially in equilibrium with the stubble site 

surface. Average midday β at the lot 6 stubble site 

during westerly winds on August 29 and 30 was 

approximately 2.2.

Agreement between HBREB and HEC was 

generally poor at the lot 6 cover crop 

evapotranspiration measurement site during August 28 

and 29 (fig. 5). Overall, 30-minute average HEC

averaged 26 W/m2, or 23 percent, smaller than HBREB

(RMSD = 40 W/m2, n = 49), and the degree of 

agreement did not appear to vary with wind direction. 

The causes of the disagreement between HBREB and 

HEC are not known. The previously discussed theory 

predictions of airstream equilibration for the cover crop 

site indicated the BREB technique would have 

overestimated λE during on August 28 (table 4). If λE

had been overestimated by the BREB technique, H

would have been underestimated; therefore, error in 

HBREB due to the incomplete equilibration of the 

airstream to the cover crop does not help explain the 

observed differences between HBREB and HEC at that 

site. Average midday β at the lot 6 cover crop site 

during westerly winds was approximately 9.9 on 

August 28 and it was approximately 6.8 on August 29. 

Malfunction of the eddy covariance instrumentation or 

improper field procedures were unlikely to have caused 

the disagreement because HEC at the cover crop site 

was computed using the same equipment and 

procedures that later agreed closely with HBREB at the 

lot 6 stubble and C1B sites. Finally, a check of the eddy 

covariance instrumentation that was performed by the 

manufacturer following the field measurements 

revealed no significant deficiencies. Nonetheless, the 

generally poor agreement between HBREB and HEC at 

the cover crop site during August 28 and 29 indicates 

the surface energy balance was not well understood and 

characterized by measurements at that time. 

EVAPOTRANSPIRATION MODELING

Both PT and reference-evapotranspiration 

modeling techniques were used to estimate λE and 

evapotranspiration during periods when it could not be 

reliably computed by the BREB technique. Sitespecific PT models were developed and applied to 

augment the daily records of 30-minute λE for periods 

when λE computed by the BREB was not available or 

not reliable, but for which data were available to 

compute or estimate λEEQ. Examples of periods when 

λE was estimated by a PT model include those when 

λE computed by the BREB technique was rejected as a 

result of the previously described screening 

procedures, and for the lot 6 sites, when wind direction 

was not westerly. Equilibrium latent heat flux for a 

given site, if it could not be computed using the data 

from the BREB station at the site, was estimated for 

30-minute periods totaling up to two daytime hours 

during any day. 
Evapotranspiration Modeling 35

If gaps in 30-minute λEEQ at a site totaled more than 

2 hours during any given day, average λE for the entire 

day was computed using the reference 

evapotranspiration technique as is described 

subsequently in this report. Missing λEEQ was 

estimated as the product of the ratio of λEEQ for the 

station of interest to λEEQ for another BREB station, 

computed using data from immediately before and 

after the data gap, and λEEQ for the other BREB 

station. Daily average λE for each evapotranspiration 

measurement site was computed for each day that a 

complete record of measured or estimated 30-minuteaverage λE could be assembled by using the BREB 

technique and the site-specific PT model. Daily 

average λE, in W/m2, was multiplied by the conversion 

factor 0.0351 to compute daily evapotranspiration rate, 

in millimeters per day (mm/d). The conversion factor 

was based on values of λ and ρw at a temperature of 

15oC, which are 2,466 J/g (Brutsaert, 1982; table 3. 4), 

and 998.98 kg/m3 (Campbell, 1977; ρw was computed 

by interpolating between temperatures of 10oC and 

20oC in table A2), respectively.

Differences among the PT models developed for 

the three sites were confined to the site-specific 

schemes for assigning α. The value assigned to α for a 

particular 30-minute period for each lot 6 

evapotranspiration measurement site was taken directly 

from the “westerly winds” column for table 7 or 8, and 

for the appropriate multi-day period and time of day. 

For the lot C1B evapotranspiration measurement site, 

α was computed in a manner similar to that for the lot 6 

sites, except α was averaged among all wind 

directions. This assignment scheme was intended to 

account for the previously discussed variations of α

among the sites, during the growing season, and with 

the time of day.

Variations of α with wind direction can have 

implications for the reliability of evapotranspiration 

estimates that are made using PT models. Fluxes of 

heat and moisture that are directed into the atmosphere 

from distant surfaces upwind of the surface of interest 

can influence air temperature and water-vapor pressure 

to heights of several tens of meters or more above the 

locally equilibrated air layer that was described 

previously. This atmospheric conditioning can affect 

turbulent fluxes and parameters, such as β and α, that 

are properly determined from measurements made in a 

locally equilibrated air stream (Weeks and others, 

1987; Lafleur and Rouse, 1988; and Souch and others, 

1996). In general, development and application of a 

PT-type model where α is computed or assigned 

independently of wind direction, as was necessarily the 

case in this study (owing to insufficient fetch at the lot 

6 sites), strictly should be supported by evidence that 

upwind conditioning is similar enough among all wind 

directions so that α does not vary with wind direction.

Analysis of the surface energy balance for lot 

C1B, the only site in this study where fetch was large 

enough to confidently compute λE, H, and α for all 

wind directions using the BREB technique, indicated 

that α generally did not vary substantially with wind 

direction. Excluding the data from before 1100 and 

after 1500 PDT, for which interactions between diurnal 

variations of α and wind direction make it impossible 

to isolate effects of wind direction alone, evidence for 

negligibly small daytime wind-direction effects in α

can be seen in both the short- and long-term energy 

balance summaries for lot C1B. Firstly, on June 16, 

when the midday (1100 to 1500 PDT) wind direction 

was predominantly and uncharacteristically easterly, 

midday average α was 0.87 (fig. 3); whereas, midday 

average α during predominantly westerly winds on 

June 14, 15, and 17 averaged 0.91, a difference equal to 

5 percent of the June 16 value. Secondly, midday α

averaged for periods of several days generally did not 

vary significantly among easterly, westerly, and mixed 

wind directions (table 6). The most substantial 

exceptions to this uniformity of α were for periods that 

encompassed rainy spells (July 5 to 7 and September 1 

to 5), and for periods when only 30 minutes of data 

were available for one or more wind directions (August 

19 to 25, September 13 to 19, and September 27 to 

October 3). The wind direction-related variations of α

that were associated with rainy spells were chiefly the 

result of the particular timing of precipitation and the 

unsteadiness of even midday conditions during the 

cloudy, rainy weather. Because of the general 

insensitivity of α to wind direction at lot C1B, and 

given that upwind surfaces at lot C1B and at lot 6 were 

generally similar in terms of moisture availability 

(irrigated agriculture, wetlands, or water), it was 

assumed that α was insensitive to wind direction at the 

lot 6 sites as well. Therefore, it was assumed that the 

PT models developed for the lot 6 sites with α

computed during the favorable westerly winds could be 

used to reliably estimate λE at the lot 6 

evapotranspiration measurement sites regardless of 

wind direction.
36 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

The reference-evapotranspiration modeling 

technique (eq. 12) was used to estimate daily 

evapotranspiration rate at an evapotranspiration 

measurement site for each day that a complete daily 

record of 30-minute λE could not be assembled by 

applying the BREB measurement and PT modeling 

techniques. Daily E0 for a grass reference crop 

obtained from the nearby University of California 

Intermountain Research and Extension Center 

(University of California, 2000; fig. 2) was used to 

develop and apply the reference-evapotranspiration 

models for the three evapotranspiration measurement 

sites. Daily kc for a given site was computed as the 

ratio of E0 to daily evapotranspiration rate computed 

by the combined BREB and PT techniques. The value 

of kc during May 1 to the first full day of successful 

operation of a given BREB station was assumed to 

equal the value on the first full day of operation. 

Similarly, the value of kc from the last full day of 

successful station operation until the end of October 

was assumed to equal kc on the last full day of 

successful station operation. The value of kc during 

gaps in the record of daily evapotranspiration rate 

computed by the combined BREB and PT techniques 

was computed by assuming kc changed linearly with 

time from the beginning to the end of the gap. Finally, 

for days precipitation fell and when evapotranspiration 

rate could not be reliably computed by the BREB and 

PT techniques, daily evapotranspiration rate was 

assumed to equal the greater of the evapotranspiration 

rate computed by equation 12 and a precipitationmodified rate. The precipitation-modified 

evapotranspiration rate was computed as the lesser of 

the daily precipitation rate and E0.

EVAPOTRANSPIRATION AND DEPTH TO 

THE WATER TABLE

Total evapotranspiration during May to October 

did not differ significantly among the three 

evapotranspiration measurement sites; however, the 

seasonal distribution of evapotranspiration did vary 

among the sites. Total evapotranspiration for the 184 

days was 426 mm for the lot C1B evapotranspiration 

measurement site, 444 mm for the lot 6 stubble site, 

and 435 mm for the lot 6 cover crop site. The 

maximum monthly average evapotranspiration rate 

occurred in June for the lot C1B and the lot 6 cover 

crop evapotranspiration measurement sites, and it 

occurred in July for the lot 6 stubble site (table 5). The 

months of May to July accounted for approximately 

78 percent of the total evapotranspiration from the lot 

C1B site and approximately 86 percent of the total 

evapotranspiration from the lot 6 cover crop site 

(table 5). These same three months accounted for 

approximately 63 percent of the evapotranspiration 

from the lot 6 stubble site (table 5). 

Table 5. Monthly average evapotranspiration rate and ratio of evapotranspiration rate to reference 

evapotranspiration rate for the lot C1B, lot 6 stubble, and lot 6 cover crop evapotranspiration measurement 

sites during May to October, 2000

[E, evapotranspiration rate, in millimeters per day (averaged for the month); E/E0, ratio of evapotranspiration rate to reference evapotranspiration 

rate, dimensionless]

Evapotranspiration measurement site

Lot C1B Lot 6 stubble Lot 6 cover crop

Month E E/E0 E E/E0 E E/E0

May 3.15 0.68 1.44 0.31 3.51 0.75

June 4.64 0.76 2.37 0.39 5.21 0.85

July 3.06 0.54 5.27 0.92 3.50 0.61

August 1.64 0.30 3.75 0.67 0.85 0.15

September 1.13 0.33 1.22 0.35 0.89 0.26

October 0.32 0.17 0.39 0.21 0.28 0.15

Overall average1 2.32 0.51 2.41 0.53 2.36 0.52

1Overall averages were computed by summing daily E and E/E0 and thus do not necessarily equal the average of the monthly average 

rates or ratios.
Evapotranspiration and Depth to the Water Table 37

Variations of evapotranspiration rate among the 

sites and with time at each site were linked to 

vegetation quantity and condition, indicating that 

evapotranspiration was mediated by the vegetation. As 

was indicated previously, the parameter α is of 

diagnostic value for describing the availability of water 

from a given surface to meet evaporative demand. 

Variations of α at each site can largely be explained by 

variations of vegetation quantity and condition. At the 

lot C1B evapotranspiration measurement site, the 

developing vegetation initially was sparse when 

measurements began during late May, and 

correspondingly, α was smaller than 1.0 (fig. 6), 

indicating that surface aridity was limiting evaporative 

loss from the site. Once the vegetation canopy at the lot 

C1B site had become dense during early June, α

exceeded 1.0. Dense vegetation cover developed last at 

the lot 6 stubble evapotranspiration measurement site, 

and α did not exceed 1.0 there until early July (fig. 7). 

At the lot 6 cover crop site, the rapidly growing cereal 

rye plants had substantially occupied the site when 

energy balance measurements began there in early 

June, and correspondingly, α was greater than 1.1 

(fig. 8). Furthermore, when the lot C1B and lot 6 cover 

crop sites were visited during late July, vegetation at 

both sites clearly had begun to senesce, and α was less 

than 0.8, indicating that aridity was limiting 

evaporative loss from both sites. Vegetation at the lot 6 

stubble site was still green and probably 

physiologically active during late July, and α was 

greater than 1.2 during most of that month, indicating 

that evaporative loss was controlled principally by 

evaporative demand. Vegetation at the lot C1B and lot 

6 cover crop sites was all or mostly dead by late 

August, and α was less than 0.3, indicating 

evapotranspiration was strongly controlled by surface 

aridity.

The increase of α at each site during the rainy 

spell of early September likely was caused by wetting 

of the near-surface soils and the vegetation and 

vegetation residues (figs. 6 to 8). Most of the plants that 

were alive during early to mid-September were 

senesced and likely acquired and transpired little of the 

newly added soil water, as can be seen in the return of a 

strongly water-limited evapotranspiration regime (α < 

0.5) at each site by mid-September. Measured soil 

water content at the 0.05-m depth at each site during 

mid-September was larger than it had been at any time 

prior to the early September rainy spell (figs. 6 to 8). 

Had the sites been occupied by actively transpiring 

vegetation that had access to the ample soil water, α

during mid-September likely would have approached 

or surpassed its maximum observed value for each site. 

Instead, evaporative losses during and after the early 

September rainy spell likely were dominated by direct 

evaporation from the soil surface and by evaporation 

from surfaces of wetted vegetation and vegetation 

residues. When the soil, vegetation, and vegetationresidue surfaces dried out, evapotranspiration became 

strongly water limited.

Additional evidence for the role of the vegetation 

in mediating evapotranspiration can been seen in the 

ratio of evapotranspiration rate to the reference 

evapotranspiration rate (E/E0) and α. Both E/E0 and α

were positively correlated with percentage of site 

coverage by vegetation that was determined by the 

objective vegetation surveys at the lot C1B and lot 6 

stubble sites (fig. 9). Assuming that E0 and λEEQ each 

either is a measure of evaporative demand or is 

correlated with evaporative demand, the strong positive 

correlations of E/E0 and α with percentage of site 

coverage by vegetation is consistent with the 

vegetation exerting control on evaporative loss from 

the lot C1B and lot 6 stubble sites. A similar correlation 

analysis was not made for the lot 6 cover crop site 

because percentage of site coverage was estimated 

from cursory observations, rather than by the objective 

survey technique, and the estimated site coverage at 

that site was not considered to be accurate enough to 

warrant statistical analysis and interpretation.

The role of vegetation residues in controlling 

evaporative loss at the study sites is less certain than 

the role of the vegetation. Vegetation residues can 

reduce evaporation from an underlying moist soil 

surface by altering the microclimate at the soil surface 

to reduce evaporative demand, such as by shielding the 

surface from solar radiation (Hillel, 1980, p. 141). In 

fact, percentage of coverage by vegetation residues at 

the lot C1B and lot 6 stubble sites was strongly and 

negatively correlated with E/E0 (r = -0.98; n = 6) and α

(r = -0.99; n = 6). However, most of the area of each of 

the study sites at any time was covered either by 

vegetation or by vegetation residues (table 2), and 

increases or decreases of percentage of coverage by the 

residues were largely accounted for by opposing 

changes in percentage of coverage by vegetation. 
38 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000 

0123456789

10

0

0.10.20.30.40.5

MAY JUNE JULY AUGUST SEPTEMBER O

SOIL WATER

CONTENT

AB

Reference evapotranspiration rate

BREB technique supplemented with Reference evapotranspiration mode

EVAPOTRANSPIRATION RATE

2000

RATE OF EVAPOTRANSPIRATION

OR REFERENCE EVAPOTRANSPIRATION, 

IN MILLIMETERS PER DAY

Figure 6. Daily reference evapotranspiration rate at the Intermountain Research and Extension Center during May to October 2000, a

evapotranspiration measurement site, daily evapotranspiration rate computed by the Bowen ratio energy balance (BREB) technique thaevapotranspiration rate modeled by the Priestley-Taylor (PT) technique, daily evapotranspiration rate modeled by the reference evapotr

and ratio of latent heat flux to equilibrium latent heat flux (

α) averaged for 3 to 7 days; (B) daily average volumetric soil water content at 

0.05 meter, averaged among three locations at the lot C1B evapotranspiration measurement site. 
Evapotranspiration and Depth to the Water Table 39

0123456789

10

0

0.10.20.30.40.5

MAY JUNE JULY AUGUST SEPTEMBER O

SOIL WATER

CONTENT

AB

RATE OF EVAPOTRANSPIRATION

OR REFERENCE EVAPOTRANSPIRATION, 

IN MILLIMETERS PER DAY

EVAPOTRANSPIRATION RATE

Reference evapotranspiration rate

BREB technique supplemented with PT modelReference evapotranspiration model

2000

Figure 7. (A) Daily reference evapotranspiration rate at the Intermountain Research and Extension Center during May to October 200

evapotranspiration measurement site, daily evapotranspiration rate computed by the Bowen ratio energy balance (BREB) technique thaevapotranspiration rate modeled by the Priestley-Taylor (PT) technique, daily evapotranspiration rate modeled by the reference evapotr

and ratio of latent heat flux to equilibrium latent heat flux (

α) averaged for 3 to 7 days; (B) daily average volumetric soil water content at 

averaged among three locations at the lot 6 stubble evapotranspiration measurement site.
40 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000 EVAPOTRANSPIRATION RATE Reference evapotranspiration rate BREB technique supplemented with PT model Reference evapotranspiration model

MAY JUNE JULY AUGUST SEPTEMBER O

0123456789

10

0

0.10.20.30.40.5

SOIL WATER

CONTENT

AB

RATE OF EVAPOTRANSPIRATION

OR REFERENCE EVAPOTRANSPIRATION, 

IN MILLIMETERS PER DAY

2000

Figure 8. (A) Daily reference evapotranspiration rate at the Intermountain Research and Extension Center during May to October 200

crop evapotranspiration measurement site, daily evapotranspiration rate computed by the Bowen ratio energy balance (BREB) techniquwith evapotranspiration rate modeled by the Priestley-Taylor (PT) technique, daily evapotranspiration rate modeled by the reference eva

technique, and ratio of latent heat flux to equilibrium latent heat flux (

α) averaged for 4 to 8 days; (B) daily average volumetric soil water c

meter, averaged among three locations at the lot 6 cover crop site.
Evapotranspiration and Depth to the Water Table 41

0 20 40 60 80

PERCENTAGE OF COVERAGE BY VEGETATION

0

0.2

0.4

0.6

0.8

1.0

1.2

0

0.2

0.4

0.6

0.8

1.0

1.2

A

B

Y = 0.0138 X + 0.091

 r = 0.95 n = 6

Y = 0.0142 X + 0.218

 r = 0.96 n = 6

LOT C1B SITE LOT C1B SITE - CONSECUTIVE 

 MEASUREMENT

LOT C1B SITE

LOT 6 STUBBLE SITE

RATIO OF LATENT HEAT FLUX TO 

EQUILIBRIUM LATENT HEAT FLUX

( )

RATIO OF EVAPOTRANSPIRATION RATE TO 

REFERENCE EVAPOTRANSPIRATION RATE

(E/E0)

Figure 9. Relation between percentage of site cover by vegetation and (A) the ratio of evapotranspiration rate 

to reference evapotranspiration rate (E/E0); and (B) the ratio of latent heat flux to equilibrium latent heat flux (α), 

all at the lot C1B and lot 6 stubble evapotranspiration measurement sites.

Both members of each abscissa-and-ordinate data pair were determined from data collected on the same day, 

except the pairs indicated with open symbols, for which E/E0 and α were computed using data collected one day 

after percentage of site coverage was measured. Each plotted line represents the indicated equation.
42 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

Thus, although E/E0 and α were statistically related to 

percentage of coverage by vegetation residues, they 

likely responded to variations of transpiration from 

vegetation that either replaced or was replaced by the 

vegetation residues. Evidence for the role of the 

residues in controlling evaporative loss could be 

developed in the future by comparing losses from 

residue-covered and bare fields where living vegetation 

is eliminated. Finally, the vegetation residues might 

have indirectly affected evapotranspiration rates and 

seasonal timing of evapotranspiration at the lot C1B 

and lot 6 stubble sites by slowing spring warming of 

the soils and thereby slowing germination, growth, and 

development of the vegetation at those sites. Additional 

study of vegetation residues as they relate to soil 

temperature and vegetation germination, growth, and 

development would be required to ascertain this 

possible indirect effect of vegetation residues on 

evapotranspiration rates.

 Although the observed range of variation of 

depth to the water table was truncated beginning in late 

July, when some of the piezometers became dry, the 

overall trend of increasing depth to the water table at 

lot C1B and lot 6 with time mirrored the overall trend 

of decreasing soil water content at the two lots 

(fig. 10). The overall trend of increasing depth to the 

water table at the two lots was broken by decreases in 

depth around the times of the previously discussed 

rainy spells of early July and early September. These 

decreases of depth to the water table were partly caused 

by recharge from precipitation to the shallow groundwater systems and to the overlying unsaturated soils at 

lot C1B and at lot 6.

During May to mid-July and before piezometers 

began to go dry, depth to the water table did not vary 

substantially within each lot at any given time. Depth 

to the water table at lot C1B during that period varied 

by less than 0.3 m among the piezometers that were 

measured, except piezometer P1,3, where depth to the 

water table varied by 0.35 m (fig. 10). Overall, depth to 

the water table at lot C1B ranged from 0.67 m in early 

July to greater than 1.39 m in late August. Depth to the 

water table at lot 6 varied by less than 0.3 m among the 

measurement locations during May to mid-July and 

before piezometers in that lot began to go dry. Overall, 

depth to the water table at lot 6 ranged from 0.77 m in 

late May to greater than 1.40 m in late August.

Depth to the water table also did not vary 

substantially between lot C1B and lot 6. On June 27, 

depth to the water table at P1,1, the piezometer closest 

to the BREB station at the lot C1B evapotranspiration 

measurement site (fig. 2, lot C1B), was 0.07 m less 

than depth to the water table at P3,1, the piezometer 

closest to the BREB station at the lot 6 cover crop 

evapotranspiration measurement site (fig. 2, lot 6). 

Depth to the water table at P1,1 averaged 0.13 m less 

than depth to the water table at P3,1 during July (n=3). 

Piezometer P3,1 was dry on August 4, indicating depth 

to the water table was greater than 1.30 m; whereas, 

depth to the water table at P1,1 was 1.11 m on that date. 

Depth to the water table at P1,1 increased to 1.30 m by 

August 18, and the piezometer became dry by August 

25, indicating depth to the water table was greater than 

1.39 m at that time. During September, depth to the 

water table at P1,1 averaged 0.18 m less than depth to 

the water table at P3,1 (n=3).

Whether or not depth to the water table affected 

the evapotranspiration rate at any of the sites is 

generally not known. Soil physics theory indicates that 

the steady-state evaporation rate from a bare soil 

surface above a shallow water table, where water flows 

upward from the water table in response to a soil waterpotential gradient, is controlled by evaporative demand 

as long as the soil profile can transmit water from the 

water table to the soil surface at rates sufficient to 

replace water lost by evaporation (Hillel, 1980, p. 114-

119). Ability of the soil profile to transmit water at 

sufficient rates to meet a given evaporative demand 

decreases with increasing depth to the water table and 

is generally greater for medium-textured soils (for 

example, a silt loam) than for coarse-textured soils (for 

example, a sandy loam). As the water table recedes, a 

water-table depth can be reached at which the soil 

cannot transmit water at rates sufficient to meet 

evaporative demand, the soil begins to dry, and the 

evaporation rate falls below the rate that is specified by 

the evaporative demand. Prediction of maximum soilwater transmission rates in the field is almost always 

complicated by uncertainties concerning soil hydraulic 

properties. 
E

vapotranspirationandDepthtotheWaterTable43

MAY JUNE JULY AUGUST SEPTEMBER 

0.60.81.01.21.41.60.60.81.01.21.41.6

DEPTH TO WATER TABLE,

IN METERS

2000

P2,1P2,2P2,3P2,4

P3,1P3,2P3,3

Piezometers of Lot 6

P1,1

P1,2P1,3P1,4P1,5

Piezometers of Lot C1B

Figure 10. Depth to the water table below the land surface at lot C1B and at lot 6 during May to October 2000, as estimated from wate

piezometers. 

Open symbol indicates piezometer was dry, thus, depth to the water table was greater than plotted. Water levels in piezometers P2,2 a

estimated.
44 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

Evaluation of evaporative demand at the soil surface is 

often made difficult by the presence of vegetation 

residues, which can reduce evaporative demand at the 

soil surface as was described previously. Soil physics 

theory nonetheless provides a framework for 

understanding evaporative losses from a soil without 

plants that lies above a shallow water table. 

Assessing possible effects of depth to the water 

table on evaporative losses from vegetated sites is 

much more difficult than for sites without plants. 

Actively transpiring, rooted plants can take up and 

transpire soil water from throughout their depth of 

rooting and thereby enhance total evaporative loss as 

compared to a soil without plants. The magnitude of 

vegetation enhancement of total evaporative loss from 

a site with a shallow water table is controlled in part by 

complex biological and biophysical processes, 

including growth, development and senescence of 

plants, biophysical processes of plant water relations 

and gas exchange, and the physical processes of soil 

water flow and uptake by plant roots. The detailed 

treatment of these processes that would be needed to 

predict effects of depth to the water table on 

evaporative loss from vegetated sites, although 

possible, was beyond the scope of this study. However, 

the available data do show how vegetation can 

confound the role of water-table depth in controlling 

evaporative loss. For example, the average 

evapotranspiration rate at the lot 6 cover crop site 

during June was roughly twice as great as it was at the 

nearby lot 6 stubble site (table 5), although measured 

depth to the water table at lot 6 varied by less than 

0.2 m during that month (fig. 10). A likely qualitative 

explanation for the observed evapotranspiration 

difference is that the dense, actively growing 

vegetation at the cover crop site during June was taking 

up and transpiring soil water at much greater areaaverage rates than was the initially sparse and 

developing vegetation at the lot 6 stubble site. In fact, 

evapotranspiration at the latter site during mid-June 

might have been dominated by evaporation from the 

soil surface, rather than by transpiration by the 

vegetation, although additional study would be needed 

to ascertain this. 

Finally, growing-season evapotranspiration from 

each study site was greater than the precipitation, 

indicating that water other than precipitation that fell 

during the growing season was entrained in the 

evaporative fluxes. Estimated growing season 

precipitation accounted for 16 percent of the growingseason evapotranspiration at the lot C1B site and 

17 percent of the growing-season evapotranspiration at 

the lot 6 stubble and cover crop sites. The remaining 

water that composed the evaporative losses from each 

site was water from precipitation or irrigation that 

occurred before the start of the 2000 growing season 

and was stored in the soils or the shallow ground-water 

systems at the sites, or water from ground-water 

inflows to the shallow ground-water systems at the 

sites.

SUMMARY AND CONCLUSIONS

A study of evapotranspiration, vegetation 

composition, and depth to the water table below the 

land surface was made at three sites in two fallowed 

agricultural lots on the 15,800-ha Tule Lake National 

Wildlife Refuge in northern California during the 2000 

May-to-October growing season. The study area 

receives approximately 288 mm of precipitation 

annually. The lot C1B evapotranspiration measurement 

site was near the center of a 41-ha lot that had been 

farmed during 1999. The lot 6 stubble and lot 6 cover 

crop evapotranspiration measurement sites were in a 

39-ha lot that had been farmed in 1999. The lot 6 

stubble site was in an area of the lot that had been left 

untreated following harvesting operations of the 

previous year, and the lot 6 cover crop site was in an 

area of the lot that had been planted to a cover crop of 

cereal rye during February 2000. The soil at both lots 

was Tulebasin mucky silty clay loam.

Evapotranspiration and components of the 

surface energy balance were measured or computed 

using the Bowen ratio energy balance (BREB) 

technique. Evapotranspiration also was computed by 

using locally calibrated evapotranspiration models that 

were based either on the Priestley-Taylor equation or 

on the reference evapotranspiration rate. Modeled 

evapotranspiration was used to estimate 

evapotranspiration when it could not be reliably 

computed by the BREB technique.
Summary and Conclusions 45

Application of the BREB technique involved 

directly measuring net radiation (Rn) with a net 

radiometer, and making measurements to compute the 

Bowen ratio (β) and soil heat flux at the soil surface 

(G). The Bowen ratio was computed from the 

difference of air temperature and water-vapor pressure 

measured with temperature and relative humidity 

sensors at two heights above the surface of each site. 

Soil heat flux at the soil surface was computed from the 

energy balance of the soil to a depth of 0.05 m or 0.1 m. 

The soil energy balance was evaluated from the 

calorically computed rate of change of energy storage 

in the soil layer and the heat flux at the bottom of the 

layer that was measured with soil heat flux plates. 

Measured specific heat of dry soil from a sample of 

Tulebasin mucky silty clay loam from lot C1B 

averaged 1,170 (J/kg)/ oC. Soil thermal conductivity 

was measured to allow for corrections to heat flux that 

were needed due to the mismatch between the thermal 

conductivities of the soil and material composing the 

soil heat flux plates. Thermal conductivity of soil 

samples packed to bulk densities that ranged from 582 

to 614 kg/m3 varied from 0.08 to 0.41 (W/m)/ oC for a 

range of soil volumetric water content of oven dry to 

0.39. 

Fetch at the two lot 6 evapotranspiration 

measurement sites was smaller than what would have 

been ideal for the BREB technique. The BREB stations 

at those sites were placed to maximize the amount of 

fetch during westerly winds (azimuth equal to or 

greater than 180 degrees and less than 360 degrees), 

which were more common than easterly winds 

(azimuth equal to or greater than 0 degrees and less 

than 180 degrees). Latent heat flux and selected 

environmental variables that were measured during 

westerly winds were used to calibrate site-specific 

evapotranspiration models that were used to estimate 

latent heat flux when winds were not westerly. 

Minimum fetch during westerly winds was 

approximately 120 m at the lot 6 stubble site and 

approximately 115 m at the lot 6 cover crop site. 

Vegetation was described by using cursory 

observations of general vegetation condition, by 

estimates of vegetation height, and systematically by 

an objective survey technique. Composition of 

vegetation and timing of vegetation growth and 

development varied among the three 

evapotranspiration measurement sites. Vegetation at 

the lot C1B evapotranspiration measurement site 

consisted chiefly of mustard plants, prickly lettuce, and 

small grain plants. Percentage of site coverage by 

vegetation varied from 33.0 percent on May 20, to 

43.2 percent on July 20, to 9.2 percent on August 29. 

Vegetation at the lot 6 stubble site included wild oat, 

small grain plants, and prickly lettuce. Percentage of 

coverage by vegetation varied from 9.6 percent on 

June 11, to 63.2 percent on July 18, and to 30.7 percent 

on August 27. The cereal rye of the lot 6 cover crop site 

was planted during February 2000. Percentage of site 

coverage by the plants was estimated to be greater than 

80 percent on June 3 and greater than 90 percent by 

July 20. By July 20, vegetation at the lot C1B and lot 6 

cover crop sites had begun to senesce. Vegetation 

senescence was first noted at the lot 6 stubble site on 

August 27. All vegetation appeared to be dead by late 

August at the lot 6 cover crop site and by mid-October 

at the lot C1B site. The only living vegetation 

remaining at the lot 6 stubble site by mid-October were 

scattered, small grass plants that were probably small 

grain plants.

Partitioning of available energy (Rn - G) to λE

and sensible heat flux (H) varied among the three 

evapotranspiration measurement sites and with time. 

Average midday (1100 to 1500, Pacific Standard Time) 

β during westerly winds at the lot C1B site ranged from 

0.39 during July 5 to 7 to 7.89 during October 4 to 7. 

At the lot 6 stubble site, average midday β during 

westerly winds ranged from 0.19 during July 29 to 

August 4 to 7.30 during October 4 to 7. Average 

midday β during westerly winds at the lot 6 cover crop 

site ranged from 0.40 during June 23 to 27 to 9.69 

during October 4 to 7.

An airstream equilibration theory was used to 

examine possible errors in measured latent heat flux 

that might have been caused by the influence of the 

surface that was upwind of the lot 6 stubble and cover 

crop sites. The upwind “contaminating” surface was 

thought to cause errors in measured λE at each of the 

lot 6 sites because the fetch-to-instrument-height ratio 

at those sites often was smaller than the ideal minimum 

of 100. Midday, minimum fetch-to-instrument-height 

ratios for westerly winds during the days selected for 

analysis with the theory were as small as 60 at the lot 6 

stubble site and as small as 64 at the lot 6 cover crop 

site. The theory predicted that actual midday λE at the 

stubble site would have been overestimated by as much 

as 60 percent during mid-June and that actual midday 

λE at the cover crop site would have been 

overestimated by as much as 84 percent during midAugust. 
46 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

Predicted errors in midday λE ranged from -25 to 29 

W/m2 at the lot 6 stubble site and from -15 to 47 W/m2

at the lot 6 cover crop site. Because of uncertainties in 

key data needed to apply the theory and because the 

theory did not account for the increased degree of 

airstream equilibration that likely occurred due to 

atmospheric instability, the predicted errors in λE were 

not considered to be accurate in an absolute sense. 

Instead, the theory identified periods of time when 

fetch-related errors likely were most significant. 

Sensible heat flux, one of the energy balance 

components computed by the BREB technique, was 

cross-checked against sensible heat flux that was 

computed by the eddy covariance technique. Eddy 

covariance measurements were made for 24 hours or 

more at each evapotranspiration measurement site. 

Sensible heat flux computed by the eddy covariance 

technique at the lot C1B site during October 18 and 19 

averaged 5 percent smaller than sensible heat flux that 

was computed by the BREB technique. Sensible heat 

flux computed by the eddy covariance technique at the 

lot 6 stubble site during August 29 and 30 averaged 

12 percent smaller than sensible heat flux that was 

computed by the BREB technique. Sensible heat flux 

computed by the eddy covariance technique at the lot 6 

cover crop site during August 28 and 29 averaged 

23 percent smaller than sensible heat flux computed by 

the BREB technique.

Total evapotranspiration during May to October 

varied little among the three evapotranspiration 

measurement sites, although the timing of 

evapotranspiration losses did vary among the sites. 

Total evapotranspiration from the lot C1B site was 

426 mm, total evapotranspiration from the lot 6 stubble 

site was 444 mm, and total evapotranspiration from the 

lot 6 cover crop site was 435 mm. The months of May 

to July accounted for approximately 78 percent of the 

total evapotranspiration from the lot C1B site, 

approximately 63 percent of the total 

evapotranspiration from the lot 6 stubble site, and 

approximately 86 percent of the total 

evapotranspiration from the lot 6 cover crop site. 

Estimated growing season precipitation accounted for 

16 percent of the growing-season evapotranspiration at 

the lot C1B site and 17 percent of the growing-season 

evapotranspiration at the lot 6 stubble and cover crop 

sites.

Variations of evapotranspiration rate among the 

sites and with time at each site were linked to quantity 

and condition of the vegetation, indicating that 

evapotranspiration was mediated by the vegetation. 

The ratio of latent heat flux to equilibrium latent heat 

flux (α) tended to be larger than 1.0 at each site when 

the site was densely occupied by actively growing 

vegetation, and α was less than 1.0 when the site was 

sparsely occupied or occupied by vegetation that 

appeared to have senesced. Furthermore, the ratio of 

evapotranspiration rate to the reference 

evapotranspiration rate and α were each statistically 

correlated with the percentage of site coverage by 

vegetation. 

Depth to the water table below the land surface 

was estimated from water-level measurements that 

were made in shallow piezometers. Measured depth to 

the water table at any given time prior to late July, 

when some piezometers in each field became dry, 

varied by 0.35 or less within each lot and between the 

lots. Depth to the water table at lot C1B ranged from 

0.67 m in early July to greater than 1.39 m in late 

August. Depth to the water table at lot 6 ranged from 

0.77 m in late May to greater than 1.40 m in late 

August. Depth to the water table was not 

unambiguously related to evapotranspiration rate, and 

it is concluded that any effect that depth to the water 

table had on evapotranspiration rate was obscured by 

variations of soil water uptake and transpiration by 

vegetation that was associated with growth, 

development, and senescence of the vegetation. 

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Hillel, D., 1980, Applications of soil physics: San Diego, 

Calif., Academic Press, 385 p.

Interagency Technical Team, 1996, Sampling vegetation 

attributes: Denver, Colo., Bureau of Land Management 

– National Business Center, Technical Reference 

1734-4, 163 p.

Jackson, R.D., and Taylor, S.A., 1986, Thermal conductivity 

and diffusivity, in Klute, A. ed., Methods of soil 

analysis part 1, physical and mineralogical methods 

(2d ed.), Agronomy Monograph No. 9: Madison, Wisc., 

American Society of Agronomy, Inc., and Soil Science 

Society of America, Inc., p. 945-956.

Jahnke, J.J., 1994, Soil survey of Butte Valley-Tule Lake 

Area, California, parts of Siskiyou and Modoc 

Counties: Washington, D.C., U.S. Department of 

Agriculture, Soil Conservation Service, 284 p., 

25 sheets.

Jensen, M.E., Burman, R.D., and Allen, R.G., eds., 1990, 

Evapotranspiration and irrigation water requirements: 

New York, American Society of Civil Engineers, 322 p.

Jury, W.A., and Tanner, C.B., 1975, Advection modification 

of the Priestley and Taylor evapotranspiration formula: 

Agronomy Journal, v. 67, p. 840-842.

Lafleur, P.M., and Rouse, W.R., 1988, The influence of 

surface cover and climate on energy partitioning and 

evaporation in a subarctic wetland: Boundary-Layer 

Meteorology, v. 44, p. 327-247.

Lowe, P.R., 1977, An approximating polynomial for the 

computation of saturation vapor pressure: Journal of 

Applied Meteorology, v. 16, p. 100-103.

Monteith, J.L., 1965, Evaporation and environment, in The

state and movement of water in living organisms, 

symposium of the Society for Experimental Biology: 

San Diego, Calif., Academic Press, v. 19, p. 205-234.

Monteith, J.L., and Unsworth, M.H., 1990, Principles of 

environmental physics: New York, Edward Arnold, 

291 p.

Ohmura, A., 1982, Objective criteria for rejecting data for 

Bowen ratio flux calculations: Journal of Applied 

Meteorology, v. 21, p. 595-598.

Priestley, C.H.B. and Taylor, R.J., 1972, On the assessment 

of surface heat flux and evaporation using large-scale 

parameters: Monthly Weather Review, v. 100, p. 81-92.

Philip, J.R., 1961, The theory of heat flux meters: Journal of 

Geophysical Research, v. 66, p. 571-579.

Snyder, R.L., Lanini, B.J., Shaw, D.A., and Pruitt, W.O., 

1987, Using reference evapotranspiration (ETo) and 

crop coefficients to estimate crop evapotranspiration 

(ETc) for agronomic crops, grasses, and vegetable 

crops: Davis, Calif., Cooperative Extension, University 

of California, Division of Agricultural and Natural 

Resources Leaflet 21427, 11 p., [revised 1989].

Soil Survey Staff, 1975, Soil taxonomy: Washington, D.C., 

U.S. Department of Agriculture Handbook No. 436, 

754 p.
48 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

Souch, C., Wolfe, C.P., and Grimmond, S.B., 1996, Wetland 

evaporation and energy partitioning- Indiana Dunes 

National Lakeshore: Journal of Hydrology, v. 84, 

p. 189-208.

Stannard, D.I., 1993, Comparison of Penman-Monteith, 

Shuttleworth-Wallace, and modified Priestley-Taylor 

evapotranspiration models for wildland vegetation in 

semiarid rangeland: Water Resources Research, v. 29, 

p. 1379-1392.

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Bowen-ratio fetch requirements: Boundary-Layer 

Meteorology, v. 83, p. 375-406.

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evapotranspiration models for grain sorghum: 

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meteorology: Boston, Mass., Kluwer Academic 

Publishers, 666 p.

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evapotranspiration from crops: Soil Science Society of 

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sites in Benton, Spokane, and Yakima Counties, 

Washington, May 1990 to September 1992: U.S. 

Geological Survey Water-Resources Investigations 

Report 96-4002, 84 p.

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report, TULELK2.A: Davis, Calif., University of 

California, California Weather Databases, data accessed 

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B.D., 1987, Water use by saltcedar and by replacement 

vegetation in the Pecos River Floodplain between 

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Survey Professional Paper 491-G, 33 p.

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summaries for Tulelake, California, National Climatic 

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Tables 6, 7, and 8 49

Tables 6, 7, and 8
50 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

Table 6. Average of 30-minute-average available energy, latent heat flux, Bowen ratio, and ratio of latent heat flux to 

equilibrium latent heat flux, by wind direction, time of day, and selected periods of days, and computed for the lot C1B 

evapotranspiration measurement site—Continued

Easterly winds Westerly winds Mixed wind directions

Rn-G λE β α Hours Rn-G λE β α Hours Rn-G λE β α Hours

May 19 to May 25, 2000

Nighttime -11 -4 1.77 0.65 10.0 -41 3 -14.34 -0.11 41.5 -17 -3 4.43 0.30 9.0

Sunrise to 1100 104 63 0.64 0.94 13.0 315 187 0.69 0.87 14.0 169 106 0.59 0.92 4.0

1100 to 1500 –- –- –- –- –- 595 314 0.90 0.71 25.0 602 364 0.65 0.84 0.5

1500 to sunset –- –- –- –- –- 280 177 0.58 0.84 34.0 –- –- –- –- –-

May 26 to June 1, 2000

Nighttime -10 -1 10.03 0.17 8.0 -37 LE <-100 0.00 38.5 -18 -3 5.44 0.29 3.5

Sunrise to 1100 141 152 -0.07 1.59 4.0 235 117 1.01 0.83 22.0 97 43 1.27 0.73 4.0

1100 to 1500 –- –- –- –- –- 593 317 0.87 0.80 24.0 –- –- –- –- –-

1500 to sunset –- –- –- –- –- 288 172 0.68 0.87 26.5 –- –- –- –- –-

June 2 to June 8, 2000

Nighttime -10 -2 5.61 0.27 10.5 -30 3 -12.06 -0.14 35.5 -19 1 -19.88 -0.09 7.0

Sunrise to 1100 144 94 0.52 1.03 8.5 226 154 0.46 1.00 14.5 269 165 0.62 0.92 5.5

1100 to 1500 –- –- –- –- –- 541 339 0.60 0.85 24.5 537 333 0.61 0.83 1.5

1500 to sunset –- –- –- –- –- 250 210 0.19 1.15 31.5 –- –- –- –- –-

June 9 to June 15, 2000

Nighttime -10 -3 2.33 0.56 9.5 -31 LE >100 0.02 36.0 -16 -2 5.45 0.27 6.5

Sunrise to 1100 190 105 0.80 0.92 8.0 243 153 0.58 0.97 18.5 268 157 0.71 0.91 3.5

1100 to 1500 314 190 0.65 0.95 1.0 489 316 0.55 0.91 25.5 399 223 0.79 0.90 1.5

1500 to sunset 185 136 0.36 1.09 0.5 239 196 0.22 1.13 34.0 –- –- –- –- –-

June 16 to June 22, 2000

Nighttime -16 -3 3.87 0.36 12.5 -39 2 -17.51 -0.09 40.0 -19 -2 7.21 0.20 10.0

Sunrise to 1100 153 105 0.45 1.03 14.5 351 227 0.55 0.93 15.0 230 149 0.55 0.97 5.0

1100 to 1500 622 406 0.53 0.88 5.0 613 384 0.60 0.83 19.5 618 392 0.58 0.85 3.5

1500 to sunset 304 254 0.20 1.11 5.5 282 234 0.21 1.08 28.0 490 372 0.32 0.95 1.0

June 23 to June 29, 2000

Nighttime -8 -3 1.88 0.59 22.0 -39 8 -6.05 -0.28 29.5 -16 LE >100 0.00 7.0

Sunrise to 1100 152 102 0.49 0.99 13.5 368 219 0.68 0.83 12.5 307 197 0.56 0.89 6.0

1100 to 1500 589 347 0.70 0.75 5.0 591 332 0.78 0.73 16.5 600 349 0.72 0.74 6.0

1500 to sunset 414 278 0.49 0.84 5.0 243 208 0.17 1.08 24.5 376 265 0.42 0.88 3.5

Table 6. Average of 30-minute-average available energy, latent heat flux, Bowen ratio, and ratio of latent heat flux to 

equilibrium latent heat flux, by wind direction, time of day, and selected periods of days, and computed for the lot C1B 

evapotranspiration measurement site

[Rn-G, available energy, in watts per square meter; λE, latent heat flux, in watts per square meter. Because of rounding, tabulated λE might not equal 

(Rn-G)/(1+β), as indicated by equation 2. β, Bowen ratio, dimensionless; α, ratio of latent heat flux to equilibrium latent heat flux, dimensionless; Hours, 

number of hours of summarized data; –, no data. LE, absolute value less than 0.5 watts per square meter; <, less than; >, greater than]
Tables 6, 7, and 8 51

June 30 to July 4, 2000

Nighttime -8 -2 2.83 0.48 9.0 -28 3 -9.23 -0.20 30.0 -12 -3 3.50 0.40 4.0

Sunrise to 1100 207 101 1.04 0.74 8.5 280 122 1.30 0.68 10.0 271 141 0.93 0.76 4.0

1100 to 1500 559 269 1.08 0.66 1.5 534 230 1.32 0.60 16.0 551 249 1.21 0.62 2.5

1500 to sunset –- –- –- –- –- 232 141 0.64 0.84 23.0 –- –- –- –- –-

July 5 to July 7, 2000

Nighttime -8 -3 1.62 0.72 3.5 -17 LE <-100 -0.01 9.5 -10 -2 3.30 0.42 3.5

Sunrise to 1100 196 91 1.15 0.76 9.0 227 140 0.62 1.04 1.5 312 177 0.76 0.93 1.5

1100 to 1500 461 218 1.12 0.68 3.0 139 100 0.39 1.07 3.5 279 153 0.82 0.80 4.5

1500 to sunset –- –- –- –- –- 145 97 0.49 0.98 14.5 465 200 1.33 0.58 1.0

July 8 to July 14, 2000

Nighttime -7 -1 4.23 0.31 15.0 -28 LE 73.45 0.02 32.5 -14 -2 6.51 0.21 8.0

Sunrise to 1100 190 94 1.01 0.74 17.0 378 162 1.33 0.61 8.5 289 123 1.36 0.61 5.0

1100 to 1500 578 260 1.22 0.58 5.0 562 240 1.34 0.56 16.0 570 247 1.31 0.58 7.0

1500 to sunset 191 131 0.46 0.89 2.5 271 152 0.79 0.72 29.5 329 171 0.93 0.67 3.0

July 15 to July 21, 2000

Nighttime -6 -1 2.91 0.43 15.5 -29 2 -18.15 -0.08 39.0 -8 -2 3.95 0.32 4.0

Sunrise to 1100 182 89 1.04 0.70 18.0 350 145 1.41 0.57 6.0 249 108 1.32 0.61 6.5

1100 to 1500 521 231 1.26 0.58 5.0 541 242 1.24 0.58 16.5 562 265 1.12 0.60 4.0

1500 to sunset 196 141 0.39 0.92 6.5 250 157 0.59 0.80 21.0 369 197 0.87 0.68 5.5

July 22 to July 28, 2000

Nighttime -5 -2 1.38 0.73 14.0 -36 2 -18.57 -0.08 39.0 -19 -4 3.68 0.33 3.5

Sunrise to 1100 168 66 1.54 0.58 16.0 348 134 1.59 0.54 10.0 281 110 1.56 0.55 3.5

1100 to 1500 560 258 1.17 0.58 2.5 544 220 1.48 0.53 21.5 574 245 1.35 0.55 2.5

1500 to sunset 255 156 0.63 0.77 5.0 283 154 0.84 0.69 23.5 296 166 0.78 0.71 5.0

July 29 to August 4, 2000

Nighttime -8 -3 1.77 0.58 20.5 -30 5 -7.53 -0.21 35.0 -11 -1 8.48 0.15 10.0

Sunrise to 1100 152 72 1.11 0.64 20.5 318 129 1.46 0.54 9.5 165 76 1.17 0.63 3.0

1100 to 1500 436 208 1.09 0.60 2.0 498 214 1.32 0.54 22.0 456 227 1.01 0.62 4.0

1500 to sunset 191 150 0.27 0.96 6.0 288 160 0.80 0.68 22.0 225 155 0.45 0.85 3.5

Table 6. Average of 30-minute-average available energy, latent heat flux, Bowen ratio, and ratio of latent heat flux to 

equilibrium latent heat flux, by wind direction, time of day, and selected periods of days, and computed for the lot C1B 

evapotranspiration measurement site—Continued

Easterly winds Westerly winds Mixed wind directions

Rn-G λE β α Hours Rn-G λE β α Hours Rn-G λE β α Hours
52 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

August 5 to August 11, 2000

Nighttime -9 -2 2.92 0.42 18.0 -34 3 -13.27 -0.12 34.5 -14 -2 5.62 0.23 10.0

Sunrise to 1100 154 61 1.51 0.57 17.5 358 115 2.12 0.43 7.5 194 76 1.56 0.54 4.0

1100 to 1500 –- –- –- –- –- 501 165 2.04 0.42 26.5 502 191 1.63 0.48 1.5

1500 to sunset –- –- –- –- –- 233 109 1.14 0.59 26.5 279 142 0.96 0.63 2.5

August 12 to August 18, 2000

Nighttime -6 -2 1.75 0.67 18.0 -39 -1 46.12 0.03 39.0 -11 -2 4.26 0.31 8.5

Sunrise to 1100 118 36 2.27 0.49 9.0 334 77 3.32 0.33 13.5 182 51 2.60 0.41 3.5

1100 to 1500 500 109 3.61 0.28 0.5 494 119 3.17 0.32 24.5 489 111 3.40 0.30 3.0

1500 to sunset –- –- –- –- –- 258 79 2.27 0.39 27.5 251 78 2.23 0.40 2.5

August 19 to August 25, 2000

Nighttime -7 -2 2.61 0.49 17.5 -34 -1 23.16 0.06 34.0 -11 -3 3.19 0.41 16.0

Sunrise to 1100 98 24 3.07 0.40 10.0 305 63 3.85 0.30 14.0 161 26 5.30 0.23 3.0

1100 to 1500 431 128 2.38 0.36 0.5 468 93 4.02 0.26 23.0 496 96 4.16 0.26 3.0

1500 to sunset 326 73 3.50 0.30 0.5 213 60 2.53 0.36 28.5 227 35 5.59 0.19 0.5

August 26 to August 31, 2000

Nighttime -6 -2 2.06 0.57 19.5 -33 -1 44.66 0.03 30.5 -15 -3 3.18 0.38 6.5

Sunrise to 1100 142 34 3.19 0.36 13.0 312 59 4.29 0.27 6.5 165 30 4.44 0.27 2.5

1100 to 1500 392 74 4.30 0.24 1.5 422 80 4.27 0.25 20.0 477 95 4.01 0.26 1.0

1500 to sunset –- –- –- –- –- 186 43 3.31 0.30 21.5 293 67 3.39 0.29 2.5

September 1 to September 5, 2000

Nighttime -3 -1 1.33 0.83 2.0 -12 -1 14.41 0.12 14.0 -7 1 -14.66 -0.13 3.5

Sunrise to 1100 101 61 0.67 1.09 7.0 149 93 0.60 1.09 8.0 168 138 0.22 1.46 1.5

1100 to 1500 221 154 0.44 1.19 5.5 269 139 0.93 0.85 13.0 273 116 1.36 0.68 1.5

1500 to sunset 110 97 0.13 1.49 5.5 133 69 0.93 0.82 11.5 33 29 0.12 1.55 1.0

September 6 to September 12, 2000

Nighttime -4 -1 2.12 0.56 6.5 -14 LE -77.71 -0.02 20.0 -10 -1 8.18 0.18 4.5

Sunrise to 1100 172 71 1.42 0.69 10.0 286 91 2.14 0.51 7.0 273 86 2.17 0.48 4.0

1100 to 1500 374 109 2.42 0.40 0.5 426 114 2.74 0.37 24.5 342 98 2.49 0.41 2.0

1500 to sunset 122 80 0.53 0.89 3.0 241 73 2.29 0.41 19.0 261 88 1.98 0.45 3.0

Table 6. Average of 30-minute-average available energy, latent heat flux, Bowen ratio, and ratio of latent heat flux to 

equilibrium latent heat flux, by wind direction, time of day, and selected periods of days, and computed for the lot C1B 

evapotranspiration measurement site—Continued

Easterly winds Westerly winds Mixed wind directions

Rn-G λE β α Hours Rn-G λE β α Hours Rn-G λE β α Hours
Tables 6, 7, and 8 53

September 13 to September 19, 2000

Nighttime -7 -3 1.63 0.62 6.5 -16 -2 5.52 0.23 21.0 -11 -2 4.56 0.27 8.5

Sunrise to 1100 141 66 1.15 0.73 9.0 255 80 2.19 0.45 9.0 195 75 1.59 0.56 2.5

1100 to 1500 441 124 2.56 0.39 1.0 393 93 3.25 0.31 26.5 126 53 1.39 0.60 0.5

1500 to sunset 99 57 0.73 0.78 1.0 196 51 2.82 0.34 21.0 39 32 0.19 1.20 1.0

September 20 to September 26, 2000

Nighttime -15 -1 9.65 0.18 13.0 -24 LE -53.83 -0.03 16.0 -19 -1 14.62 0.12 6.0

Sunrise to 1100 123 42 1.91 0.64 6.0 247 48 4.19 0.32 11.5 149 44 2.36 0.49 3.5

1100 to 1500 370 53 6.05 0.20 4.0 375 59 5.34 0.23 21.0 366 58 5.34 0.25 3.0

1500 to sunset 254 28 8.07 0.15 3.5 170 30 4.63 0.25 18.5 240 30 7.13 0.17 1.0

September 27 to October 3, 2000

Nighttime -3 -1 1.79 0.68 4.0 -24 -2 10.56 0.13 27.5 -10 -2 3.29 0.39 4.5

Sunrise to 1100 118 40 1.96 0.58 9.0 250 46 4.45 0.28 7.0 184 42 3.39 0.36 4.5

1100 to 1500 320 21 14.03 0.09 0.5 353 47 6.57 0.19 26.5 361 44 7.28 0.17 1.0

1500 to sunset –- –- –- –- –- 185 18 9.13 0.13 19.5 –- –- –- –- –-

October 4 to October 7, 2000

Nighttime -1 LE 2.18 0.65 1.5 -33 LE <-100 0.00 4.0 –- –- –- –- –-

Sunrise to 1100 114 29 2.98 0.44 5.0 227 34 5.58 0.25 4.0 149 32 3.64 0.37 3.0

1100 to 1500 –- –- –- –- –- 328 37 7.89 0.16 15.5 280 27 9.23 0.14 0.5

1500 to sunset –- –- –- –- –- 152 10 14.64 0.09 11.5 –- –- –- –- –-

October 18 to October 19, 2000

Nighttime -4 -2 1.68 0.75 3.0 -17 -2 6.95 0.20 1.5 -7 -2 2.21 0.59 3.5

Sunrise to 1100 159 47 2.37 0.51 2.5 175 38 3.65 0.37 0.5 207 42 3.89 0.34 0.5

1100 to 1500 234 38 5.15 0.26 1.0 205 33 5.23 0.24 3.5 146 28 4.29 0.28 0.5

1500 to sunset -4 LE 17.00 0.08 0.5 82 20 3.00 0.37 1.5 55 18 2.09 0.47 1.0

Table 6. Average of 30-minute-average available energy, latent heat flux, Bowen ratio, and ratio of latent heat flux to 

equilibrium latent heat flux, by wind direction, time of day, and selected periods of days, and computed for the lot C1B 

evapotranspiration measurement site—Continued

Easterly winds Westerly winds Mixed wind directions

Rn-G λE β α Hours Rn-G λE β α Hours Rn-G λE β α Hours
54 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

Table 7. Average of 30-minute-average available energy, latent heat flux, Bowen ratio, and ratio of latent heat flux to 

equilibrium latent heat flux, by wind direction, time of day, and selected periods of days, and computed for the lot 6 stubble 

evapotranspiration measurement site—Continued

Easterly winds Westerly winds Mixed wind directions

Rn-G λE β α Hours Rn-G λE β α Hours Rn-G λE β α Hours

June 11 to June 15, 2000

Nighttime -13 -6 1.28 0.81 9.5 -26 -4 5.68 0.23 27.0 -17 -6 1.81 -13 -6

Sunrise to 1100 205 74 1.76 0.56 9.5 237 71 2.35 0.43 9.0 172 63 1.72 205 74

1100 to 1500 317 62 4.09 0.31 0.5 395 99 2.97 0.34 17.0 429 100 3.29 317 62

1500 to sunset 230 48 3.75 0.31 1.0 210 61 2.42 0.39 26.5 253 49 4.15 230 48

June 16 to June 22, 2000

Nighttime -19 -3 4.65 0.31 16.5 -32 -3 8.36 0.16 38.0 -20 -5 3.27 0.39 8.0

Sunrise to 1100 162 66 1.45 0.62 16.5 288 106 1.71 0.53 13.5 256 95 1.69 0.54 5.5

1100 to 1500 526 158 2.34 0.40 7.5 523 172 2.03 0.44 16.0 514 190 1.70 0.48 4.5

1500 to sunset 240 88 1.71 0.49 5.5 246 107 1.31 0.56 30.0 486 195 1.49 0.50 1.0

June 23 to June 29, 2000

Nighttime -12 -5 1.29 0.75 24.0 -29 LE 74.43 0.02 29.0 -16 -4 3.05 0.40 9.5

Sunrise to 1100 125 78 0.59 0.94 13.5 372 190 0.96 0.71 12.5 235 130 0.81 0.78 8.0

1100 to 1500 546 308 0.77 0.72 3.5 547 263 1.08 0.62 20.0 556 270 1.06 0.63 4.5

1500 to sunset 476 278 0.71 0.73 1.0 235 160 0.47 0.86 30.0 419 255 0.65 0.76 4.0

June 30 to July 4, 2000

Nighttime -15 -6 1.37 0.75 11.5 -30 -1 40.22 0.04 27.0 -21 -5 3.21 0.42 5.5

Sunrise to 1100 201 117 0.72 0.88 9.0 253 129 0.96 0.79 9.5 278 148 0.88 0.82 5.5

1100 to 1500 532 283 0.88 0.73 4.0 571 289 0.97 0.70 13.0 434 206 1.11 0.69 3.0

1500 to sunset – – – – – 240 155 0.55 0.89 24.0 – – – – –

July 5 to July 7, 2000

Nighttime -12 -5 1.41 0.76 9.5 -20 LE -58.23 -0.03 8.0 -15 -4 2.73 0.47 3.0

Sunrise to 1100 168 111 0.51 1.08 12.5 324 154 1.11 0.81 0.5 322 212 0.52 1.05 1.5

1100 to 1500 414 267 0.55 0.94 7.0 105 87 0.20 1.38 1.5 220 161 0.37 1.07 3.5

1500 to sunset 224 161 0.39 1.01 2.0 137 122 0.12 1.31 11.5 216 170 0.28 1.11 2.0

July 8 to July 14, 2000

Nighttime -17 -8 1.22 0.80 22.5 -36 LE >100 0.01 28.0 -27 -4 6.25 0.22 9.5

Sunrise to 1100 236 166 0.42 1.04 21.5 347 238 0.46 0.98 4.0 337 216 0.56 0.94 5.5

1100 to 1500 605 416 0.46 0.92 11.5 595 411 0.45 0.92 9.5 587 391 0.50 0.90 6.5

1500 to sunset 298 265 0.13 1.14 1.5 270 246 0.10 1.19 30.0 379 310 0.22 1.06 4.0

Table 7. Average of 30-minute-average available energy, latent heat flux, Bowen ratio, and ratio of latent heat flux to 

equilibrium latent heat flux, by wind direction, time of day, and selected periods of days, and computed for the lot 6 stubble 

evapotranspiration measurement site

[Rn-G, available energy, in watts per square meter; λE, latent heat flux, in watts per square meter. Because of rounding, tabulated λE might not equal 

(Rn-G)/(1+β), as indicated by equation 2. β, Bowen ratio, dimensionless; α, ratio of latent heat flux to equilibrium latent heat flux, dimensionless; Hours, 

number of hours of summarized data; –, no data. LE, absolute value less than 0.5 watts per square meter; <, less than; >, greater than]
Tables 6, 7, and 8 55

July 15 to July 21, 2000

Nighttime -14 -5 1.62 0.64 25.0 -37 4 -10.95 -0.14 32.5 -16 -4 2.59 0.44 7.0

Sunrise to 1100 208 148 0.40 1.02 24.0 297 217 0.37 1.05 5.0 220 159 0.38 1.02 5.5

1100 to 1500 581 420 0.38 0.95 9.5 589 445 0.33 0.99 9.5 605 446 0.36 0.96 8.5

1500 to sunset 300 287 0.05 1.23 5.0 271 286 -0.05 1.36 20.0 294 284 0.03 1.25 5.5

July 22 to July 28, 2000

Nighttime -15 -6 1.53 0.68 21.5 -36 2 -19.57 -0.08 38.0 -24 -3 6.61 0.20 6.0

Sunrise to 1100 223 150 0.49 0.99 26.0 365 246 0.48 0.96 2.0 358 244 0.47 0.97 4.5

1100 to 1500 596 436 0.37 0.96 13.5 599 433 0.38 0.96 9.0 575 395 0.46 0.93 5.5

1500 to sunset 406 377 0.08 1.18 5.5 286 295 -0.03 1.34 22.5 396 356 0.12 1.15 4.0

July 29 to August 4, 2000

Nighttime -15 -4 3.23 0.38 24.5 -34 15 -3.31 -0.59 30.5 -19 1 -21.49 -0.07 11.0

Sunrise to 1100 221 166 0.33 1.03 25.5 320 237 0.35 1.01 4.0 247 176 0.40 0.96 2.5

1100 to 1500 498 406 0.23 1.04 7.5 552 462 0.19 1.05 17.5 485 391 0.24 1.04 3.0

1500 to sunset 343 345 -0.01 1.25 10.5 253 292 -0.13 1.44 15.5 262 282 -0.07 1.34 5.5

August 5 to August 11, 2000

Nighttime -15 -2 5.88 0.24 26.5 -34 11 -4.10 -0.46 26.0 -15 LE -56.24 -0.03 14.0

Sunrise to 1100 233 161 0.44 0.99 19.0 392 273 0.43 0.95 2.5 272 174 0.57 0.92 7.5

1100 to 1500 556 374 0.49 0.87 9.5 536 375 0.43 0.90 9.5 544 396 0.37 0.94 8.5

1500 to sunset 320 244 0.31 0.97 1.5 256 262 -0.02 1.30 23.5 284 272 0.04 1.20 2.5

August 12 to August 18, 2000

Nighttime -12 -4 1.73 0.67 24.0 -38 5 -8.27 -0.21 36.0 -15 -4 2.66 0.47 8.5

Sunrise to 1100 201 107 0.88 0.81 18.0 359 170 1.12 0.69 3.5 339 170 1.00 0.73 6.0

1100 to 1500 516 292 0.77 0.75 4.5 522 282 0.85 0.72 18.0 517 281 0.84 0.72 5.5

1500 to sunset 494 332 0.49 0.85 0.5 283 222 0.28 1.02 20.5 352 258 0.37 0.94 6.0

August 19 to August 25, 2000

Nighttime -9 -2 3.76 0.38 27.5 -33 2 -16.10 -0.10 32.0 -12 -2 6.47 0.22 11.0

Sunrise to 1100 124 57 1.17 0.74 16.5 338 128 1.64 0.55 8.0 293 108 1.70 0.54 4.5

1100 to 1500 481 177 1.72 0.50 2.0 475 199 1.39 0.55 20.5 476 187 1.54 0.52 5.0

1500 to sunset 338 160 1.12 0.60 0.5 227 146 0.56 0.83 21.5 349 185 0.89 0.69 5.0

August 26 to August 31, 2000

Nighttime -13 -4 2.49 0.50 28.5 -29 LE <-100 -0.01 26.5 -16 -2 5.44 0.25 8.0

Sunrise to 1100 155 59 1.63 0.58 15.5 313 103 2.04 0.47 4.0 256 81 2.17 0.46 3.0

1100 to 1500 438 136 2.22 0.41 8.5 425 149 1.86 0.46 7.5 387 132 1.94 0.45 7.0

1500 to sunset 290 132 1.20 0.58 2.5 127 79 0.60 0.81 18.5 331 144 1.29 0.56 5.5

Table 7. Average of 30-minute-average available energy, latent heat flux, Bowen ratio, and ratio of latent heat flux to 

equilibrium latent heat flux, by wind direction, time of day, and selected periods of days, and computed for the lot 6 stubble 

evapotranspiration measurement site—Continued

Easterly winds Westerly winds Mixed wind directions

Rn-G λE β α Hours Rn-G λE β α Hours Rn-G λE β α Hours
56 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

September 1 to September 5, 2000

Nighttime -8 -2 2.84 0.50 2.5 -9 -1 8.41 0.20 18.5 -5 -1 5.47 0.29 4.5

Sunrise to 1100 132 78 0.70 1.07 6.5 134 83 0.62 1.07 8.5 134 97 0.38 1.31 1.5

1100 to 1500 228 143 0.59 1.06 6.5 246 137 0.80 0.93 10.5 306 167 0.83 0.89 3.0

1500 to sunset 82 83 -0.01 1.77 4.5 124 79 0.58 1.02 11.5 172 91 0.90 0.84 4.0

September 6 to September 12, 2000

Nighttime -7 -2 2.99 0.45 24.5 -18 -1 18.61 0.08 19.5 -10 -2 5.12 0.29 12.0

Sunrise to 1100 141 74 0.91 0.90 8.5 304 94 2.24 0.47 7.0 286 93 2.06 0.52 4.5

1100 to 1500 409 101 3.06 0.37 1.0 417 118 2.53 0.39 23.0 401 114 2.52 0.39 4.0

1500 to sunset 128 58 1.19 0.62 9.5 231 85 1.72 0.49 13.0 262 101 1.60 0.51 5.0

September 13 to September 19, 2000

Nighttime -11 -3 2.86 0.42 24.5 -21 -4 4.21 0.29 23.0 -14 -3 3.21 0.38 11.5

Sunrise to 1100 162 74 1.19 0.69 9.5 248 93 1.66 0.55 7.0 167 76 1.20 0.67 7.5

1100 to 1500 418 118 2.53 0.39 2.0 392 117 2.36 0.39 23.0 395 112 2.54 0.39 2.5

1500 to sunset 62 61 0.02 1.28 6.0 215 79 1.71 0.48 17.0 109 59 0.83 0.73 1.5

September 20 to September 26, 2000

Nighttime -14 -1 16.14 0.11 32.5 -27 -2 12.96 0.12 20.0 -16 -1 10.40 0.17 16.5

Sunrise to 1100 142 48 1.93 0.62 9.5 249 68 2.67 0.44 8.0 208 58 2.60 0.46 4.5

1100 to 1500 373 60 5.22 0.24 6.5 393 76 4.16 0.28 19.5 414 86 3.83 0.32 2.0

1500 to sunset 127 23 4.60 0.24 2.5 181 47 2.85 0.36 17.5 121 36 2.31 0.40 4.0

September 27 to October 3, 2000

Nighttime -6 -2 2.11 0.61 28.5 -27 -4 6.71 0.20 24.0 -7 -2 2.40 0.50 8.0

Sunrise to 1100 136 52 1.61 0.67 7.5 225 55 3.12 0.37 9.5 180 56 2.24 0.49 4.5

1100 to 1500 353 57 5.23 0.23 2.5 359 49 6.38 0.19 19.5 361 55 5.57 0.21 6.0

1500 to sunset 294 38 6.72 0.17 0.5 131 23 4.57 0.24 21.5 178 32 4.56 0.25 1.0

October 4 to October 7, 2000

Nighttime -4 -1 3.22 0.49 14.5 -12 -1 8.24 0.18 6.0 -12 -1 8.96 0.17 5.5

Sunrise to 1100 142 40 2.56 0.49 7.0 163 46 2.56 0.51 0.5 232 41 4.68 0.29 4.5

1100 to 1500 339 40 7.40 0.16 2.0 337 41 7.30 0.17 11.0 344 48 6.18 0.20 2.5

1500 to sunset 217 21 9.44 0.12 0.5 128 15 7.76 0.15 9.0 147 20 6.23 0.19 2.5

Table 7. Average of 30-minute-average available energy, latent heat flux, Bowen ratio, and ratio of latent heat flux to 

equilibrium latent heat flux, by wind direction, time of day, and selected periods of days, and computed for the lot 6 stubble 

evapotranspiration measurement site—Continued

Easterly winds Westerly winds Mixed wind directions

Rn-G λE β α Hours Rn-G λE β α Hours Rn-G λE β α Hours
Tables 6, 7, and 8 57

Table 8. Average of 30-minute-average available energy, latent heat flux, Bowen ratio, and ratio of latent heat flux to 

equilibrium latent heat flux, by wind direction, time of day, and selected periods of days, and computed for the lot 6 cover crop 

evapotranspiration measurement site—Continued

Easterly winds Westerly winds Mixed wind directions

Rn-G λE β α Hours Rn-G λE β α Hours Rn-G λE β α Hours

June 3 to June 8, 2000

Nighttime -19 -5 2.56 0.52 11.0 -35 4 -9.09 -0.20 30.0 -28 LE -69.82 -0.02 7.5

Sunrise to 1100 176 130 0.36 1.11 6.5 231 161 0.44 1.04 15.0 160 116 0.38 1.13 2.5

1100 to 1500 532 404 0.32 0.98 0.5 490 332 0.48 0.93 21.0 586 402 0.46 0.92 2.5

1500 to sunset 300 274 0.10 1.17 2.0 198 177 0.12 1.23 26.5 256 239 0.07 1.20 1.5

June 9 to June 15, 2000

Nighttime -16 -7 1.35 0.79 11.5 -31 2 -18.54 -0.09 35.0 -20 -6 2.36 0.52 9.5

Sunrise to 1100 197 119 0.66 0.98 10.5 237 169 0.41 1.09 15.0 296 190 0.55 0.98 5.0

1100 to 1500 378 227 0.67 0.96 0.5 462 328 0.41 0.99 23.5 491 317 0.55 0.97 4.0

1500 to sunset 256 194 0.32 1.11 1.0 224 206 0.09 1.25 31.5 -- -- -- -- --

June 16 to June 22, 2000

Nighttime -24 -5 3.50 0.39 16.0 -43 1 -34.27 -0.05 37.0 -30 -7 3.60 0.37 8.0

Sunrise to 1100 173 128 0.35 1.12 13.0 332 238 0.39 1.03 15.0 334 242 0.38 1.06 6.0

1100 to 1500 612 392 0.56 0.86 6.5 610 434 0.41 0.95 18.5 607 460 0.32 0.99 3.0

1500 to sunset 281 218 0.28 1.03 5.0 273 263 0.04 1.25 30.5 -- -- -- -- --

June 23 to June 27, 2000

Nighttime -16 -7 1.26 0.78 13.0 -40 3 -12.47 -0.13 19.0 -24 -5 4.14 0.32 6.0

Sunrise to 1100 157 110 0.42 1.06 6.5 377 268 0.41 1.00 11.0 304 212 0.43 0.99 4.0

1100 to 1500 587 448 0.31 0.99 1.5 608 434 0.40 0.93 17.0 625 434 0.44 0.92 1.0

1500 to sunset -- -- -- -- -- 264 263 0.00 1.27 24.5 546 440 0.24 1.02 1.0

July 21 to July 28, 2000

Nighttime -14 -6 1.42 0.71 17.5 -40 3 -13.51 -0.12 42.5 -24 -4 4.71 0.27 5.0

Sunrise to 1100 212 91 1.33 0.63 18.5 381 150 1.54 0.55 6.5 392 157 1.50 0.57 3.5

1100 to 1500 546 244 1.23 0.58 8.5 544 238 1.29 0.57 13.0 530 222 1.38 0.55 9.5

1500 to sunset 347 199 0.74 0.72 4.0 226 143 0.58 0.81 32.5 329 158 1.08 0.61 3.0

July 29 to August 4, 2000

Nighttime -14 -4 2.14 0.51 21.5 -38 5 -8.04 -0.19 31.5 -20 -1 20.06 0.07 12.5

Sunrise to 1100 181 75 1.42 0.57 23.0 318 108 1.95 0.46 6.0 194 78 1.48 0.55 2.5

1100 to 1500 392 157 1.50 0.51 5.0 477 172 1.78 0.45 21.0 367 142 1.60 0.49 2.0

1500 to sunset 299 123 1.43 0.50 5.5 181 90 1.00 0.62 23.5 203 97 1.10 0.59 5.5

Table 8. Average of 30-minute-average available energy, latent heat flux, Bowen ratio, and ratio of latent heat flux to 

equilibrium latent heat flux, by wind direction, time of day, and selected periods of days, and computed for the lot 6 cover crop 

evapotranspiration measurement site

[Rn-G, available energy, in watts per square meter; λE, latent heat flux, in watts per square meter. Because of rounding, tabulated λE might not equal 

(Rn-G)/(1+β), as indicated by equation 2. β, Bowen ratio, dimensionless; α, ratio of latent heat flux to equilibrium latent heat flux, dimensionless; Hours, 

number of hours of summarized data; –, no data. LE, absolute value less than 0.5 watts per square meter; <, less than; >, greater than]
58 Evapotranspiration, Tule Lake National Wildlife Refuge, California, May to October 2000

August 5 to August 11, 2000

Nighttime -15 -3 4.07 0.32 24.0 -38 LE <-100 -0.01 26.0 -19 -2 8.22 0.16 15.5

Sunrise to 1100 170 51 2.34 0.43 17.0 321 56 4.69 0.24 5.5 234 49 3.76 0.29 4.5

1100 to 1500 471 94 4.00 0.26 4.5 463 83 4.60 0.23 18.0 464 89 4.23 0.25 5.5

1500 to sunset 213 42 4.05 0.25 1.0 172 43 2.99 0.31 28.5 374 51 6.28 0.17 1.5

August 12 to August 18, 2000

Nighttime -12 -4 1.74 0.66 19.5 -44 -4 10.62 0.13 36.5 -15 -5 2.28 0.52 8.5

Sunrise to 1100 126 33 2.87 0.41 12.5 327 43 6.59 0.19 9.0 295 40 6.35 0.20 4.5

1100 to 1500 432 50 7.64 0.15 0.5 463 62 6.49 0.18 21.5 448 55 7.17 0.16 6.0

1500 to sunset 402 67 4.97 0.21 0.5 184 24 6.56 0.17 30.5 358 46 6.78 0.16 1.5

August 19 to August 25, 2000

Nighttime -9 -2 3.13 0.42 27.0 -38 -4 7.57 0.17 33.0 -14 -3 4.10 0.32 9.5

Sunrise to 1100 111 27 3.10 0.39 10.5 310 38 7.25 0.18 9.5 188 24 6.73 0.19 6.0

1100 to 1500 451 62 6.33 0.17 0.5 433 50 7.73 0.15 22.0 447 58 6.72 0.17 5.5

1500 to sunset -- -- -- -- -- 181 20 8.13 0.14 27.0 292 13 20.78 0.06 2.0

August 26 to August 31, 2000

Nighttime -12 -4 1.73 0.64 26.5 -32 -5 6.19 0.21 27.0 -14 -4 2.80 0.42 9.5

Sunrise to 1100 132 24 4.53 0.28 11.0 297 36 7.15 0.17 6.0 149 23 5.58 0.22 4.0

1100 to 1500 399 41 8.75 0.13 4.5 386 41 8.31 0.14 12.0 411 47 7.76 0.15 7.5

1500 to sunset 278 22 11.46 0.10 1.5 117 5 23.32 0.05 18.0 296 26 10.33 0.11 5.0

September 1 to September 5, 2000

Nighttime -4 -2 1.22 0.88 4.0 -11 -1 16.01 0.11 29.5 -7 1 -9.85 -0.21 3.0

Sunrise to 1100 129 79 0.64 1.11 6.5 129 74 0.73 1.00 8.0 186 137 0.36 1.31 2.0

1100 to 1500 241 158 0.52 1.10 7.0 242 126 0.93 0.87 11.0 323 129 1.51 0.64 2.0

1500 to sunset 71 65 0.10 1.58 4.5 124 62 1.00 0.80 12.0 141 75 0.88 0.86 3.0

September 6 to September 12, 2000

Nighttime -10 -2 4.75 0.30 24.0 -21 -1 19.79 0.08 25.0 -11 -2 5.56 0.26 15.0

Sunrise to 1100 195 75 1.60 0.63 10.5 332 92 2.61 0.43 6.0 258 78 2.30 0.48 5.5

1100 to 1500 425 72 4.93 0.24 1.0 438 83 4.27 0.26 24.0 365 62 4.87 0.24 3.0

1500 to sunset 91 37 1.44 0.56 7.5 214 47 3.55 0.29 16.5 286 63 3.54 0.29 3.0

September 13 to September 19, 2000

Nighttime -11 -3 2.64 0.44 18.5 -25 -5 3.95 0.31 22.5 -9 -2 3.57 0.34 13.5

Sunrise to 1100 158 64 1.46 0.62 8.5 264 73 2.60 0.40 8.5 196 71 1.78 0.53 6.0

1100 to 1500 462 88 4.26 0.26 1.5 435 68 5.44 0.21 24.0 415 67 5.24 0.22 2.0

1500 to sunset 57 36 0.60 0.83 4.0 226 44 4.11 0.25 19.5 91 32 1.83 0.46 2.0

Table 8. Average of 30-minute-average available energy, latent heat flux, Bowen ratio, and ratio of latent heat flux to 

equilibrium latent heat flux, by wind direction, time of day, and selected periods of days, and computed for the lot 6 cover crop 

evapotranspiration measurement site—Continued

Easterly winds Westerly winds Mixed wind directions

Rn-G λE β α Hours Rn-G λE β α Hours Rn-G λE β α Hours
Tables 6, 7, and 8 59

September 20 to September 26, 2000

Nighttime -18 -2 6.71 0.24 14.5 -31 -3 8.96 0.17 22.5 -22 -2 7.72 0.21 7.0

Sunrise to 1100 104 26 3.07 0.43 11.5 273 49 4.62 0.28 10.0 125 42 1.98 0.57 3.0

1100 to 1500 351 42 7.29 0.18 5.0 450 55 7.12 0.17 21.0 388 47 7.32 0.18 2.0

1500 to sunset 319 31 9.29 0.13 1.0 224 37 5.11 0.23 16.0 208 30 5.85 0.19 3.0

September 27 to October 3, 2000

Nighttime -10 -4 1.63 0.81 19.0 -31 -5 5.47 0.25 23.0 -15 -5 2.00 0.67 7.5

Sunrise to 1100 64 18 2.54 0.48 6.5 180 33 4.43 0.28 9.0 141 32 3.42 0.36 9.0

1100 to 1500 396 46 7.68 0.16 1.5 365 40 8.10 0.15 21.5 380 48 6.91 0.18 5.0

1500 to sunset -- -- -- -- -- 164 23 6.15 0.19 16.5 217 26 7.42 0.16 1.5

October 4 to October 7, 2000

Nighttime -10 -3 1.97 0.76 21.0 -27 -4 5.24 0.27 8.5 -12 -3 3.43 0.45 8.5

Sunrise to 1100 45 10 3.58 0.37 6.0 247 34 6.20 0.22 1.5 135 20 5.66 0.24 5.0

1100 to 1500 328 32 9.29 0.13 1.5 328 31 9.69 0.13 11.0 324 36 8.01 0.16 3.0

1500 to sunset -- -- -- -- -- 129 16 7.13 0.16 11.0 134 21 5.40 0.21 1.0

Table 8. Average of 30-minute-average available energy, latent heat flux, Bowen ratio, and ratio of latent heat flux to 

equilibrium latent heat flux, by wind direction, time of day, and selected periods of days, and computed for the lot 6 cover crop 

evapotranspiration measurement site—Continued

Easterly winds Westerly winds Mixed wind directions

Rn-G λE β α Hours Rn-G λE β α Hours Rn-G λE β α Hours
USGS-WRIR 02-4055 W.R. Bidlake

Printedonrecycledpaper

EVAPOTRANSPIRATION FROM SELECTED FALLOWED AGRICULTURAL FIELDS ON THE TULE LAKE

NATIONAL WILDLIFE REFUGE, CALIFORNIA, DURING MAY TO OCTOBER 2000