Prepared in cooperation with the Bureau of Reclamation

Evapotranspiration from Wetland and Open-Water Sites at

Upper Klamath Lake, Oregon, 2008–2010

U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2013–5014
Cover:

Upper Left: Installing instrumentation at bulrush site near Thomason Creek, April 2008 (photograph taken by Jason Cameron).

Upper Right: Open water in side channel near mixed vegetation site near Crystal Creek, August 2008 (photograph taken by Marshall Gannett).

Lower Left: Bulrush site near Thomason Creek, June 2008 (photograph taken by Jason Cameron).

Lower right: Floating meteorological and water quality platform in Upper Klamath Lake (photograph taken by Marshall Gannett).
Evapotranspiration from Wetland and 

Open-Water Sites at Upper Klamath Lake, 

Oregon, 2008–2010

By David I. Stannard, Marshall W. Gannett, and Danial J. Polette, U.S. Geological 

Survey; Jason M. Cameron, Bureau of Reclamation; M. Scott Waibel, U.S. 

Geological Survey; and J. Mark Spears, Bureau of Reclamation

Prepared in cooperation with the Bureau of Reclamation

Scientific Investigations Report 2013–5014

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2013

For more information on the USGS—the Federal source for science about the Earth, its natural and living 

resources, natural hazards, and the environment, visit http://www.usgs.gov or call 1–888–ASK–USGS.

For an overview of USGS information products, including maps, imagery, and publications, 

visit http://www.usgs.gov/pubprod

To order this and other USGS information products, visit http://store.usgs.gov

Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the 

U.S. Government.

Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials 

as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner.

Suggested citation:

Stannard, D.I., Gannett, M.W., Polette, D.J., Cameron, J.M., Waibel, M.S., and Spears, J.M., 2013, 

Evapotranspiration from marsh and open-water sites at Upper Klamath Lake, Oregon, 2008–2010: 

U.S. Geological Survey Scientific Investigations Report 2013–5014, 66 p.
iii

Contents

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

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

Purpose and Scope ..............................................................................................................................3

Previous Studies ...................................................................................................................................3

Description of Study Area ...................................................................................................................3

Study Sites ....................................................................................................................................5

Bulrush and Mixed Vegetation Sites ...............................................................................5

Open-Water Sites ...............................................................................................................6

Methods of Study...........................................................................................................................................7

Energy Balance of a Vegetated or Open-Water Surface...............................................................7

Eddy-Covariance Measurements of Latent- and Sensible-Heat Flux........................................10

The Energy-Balance Closure Problem...................................................................................11

Eddy-Covariance Sensors and Data Collection....................................................................12

Eddy-Covariance Data Processing.........................................................................................14

Gap-Filling Missing or Bad Eddy-Covariance Data.....................................................15

Meteorological, Energy-Balance, and Biophysical Measurements at 

Eddy-Covariance Sites .........................................................................................................16

Meteorological and Energy-Balance Sensors and Data Collection .................................16

Meteorological and Energy-Balance Data Processing ......................................................17

Biophysical Measurements and Observations.....................................................................18

Bowen-Ratio Energy Balance (BREB) Measurements at Open-Water Sites...........................19

Bowen-Ratio Energy-Balance Method..................................................................................19

Radiation Terms.................................................................................................................20

Net Advected Energy .......................................................................................................21

Energy Transferred to Lakebed ......................................................................................23

Changes in Energy Stored in the Lake ..........................................................................25

Bowen Ratio ......................................................................................................................25

Determination of Reference Evapotranspiration and Crop Coefficients...................................26

Evapotranspiration Results from Bulrush and Mixed Vegetation Sites..............................................26

Site Conditions Affecting Evapotranspiration................................................................................26

Source Areas and Fetch Considerations of Wetland Evapotranspiration Sites ......................30

Energy-Balance Closure and Trends...............................................................................................31

Daily Evapotranspiration and Crop Coefficients............................................................................37

Biweekly Evapotranspiration and Crop Coefficients ....................................................................48

Study-Period and Annual Evapotranspiration ...............................................................................53

Comparison of Wetland Evapotranspiration with Evapotranspiration of Local Crops............55

Comparison of Wetland Evapotranspiration with Previous Studies ..........................................56

Open-Water Evaporation Results..............................................................................................................58

Comparison of Open-Water Evaporation with Previous Studies and With 

Wetland Evapotranspiration................................................................................................60

Summary and Conclusions.........................................................................................................................61

References Cited..........................................................................................................................................63
iv

Figures

1. Map showing Upper Klamath Lake, surrounding area, and data collection 

locations .................................................................................... 4

2. Schematic of the energy balance of a vegetated surface and a water body ...... 8

3. Photograph of eddy-covariance sensors, cup anemometer, and wind vane......... 12

4. Photograph of completed eddy covariance, energy balance, and

meteorological station at bulrush site on June 10, 2008 .............................. 13

5. Photograph showing specialized feet to support energy balance and

meteorological platform and eddy-covariance tripod, on spongy 

wetland surface.............................................................................. 14

6. Chart showing lake stage area and live storage volume curves for Upper

Klamath Lake................................................................................. 22

7. Charts showing Upper Klamath Lake bottom temperatures and fitted sine

function used to parameterize amplitude (A) and phase (c) during 2008, 2009, 

and 2010....................................................................................... 24

8. Charts showing vegetation height, water level, and soil water content at

bulrush site during 2008, 2009, and 2010, and at mixed site during 2008, 2009,

and 2010....................................................................................... 27

9. Charts showing biweekly means of available energy, turbulent flux, and

energy-balance ratio at the bulrush site during the study period ..................... 32

10. Graphs showing daily means of net radiation, sensible-heat flux, and latent-heat

flux at bulrush site during 2008, 2009, and 2010, and at mixed site during 2008,

2009, and 2010 .............................................................................. 34

11. Charts showing daily reference evapotranspiration and measured

evapotranspiration at bulrush site during 2008, 2009, and 2010, and at mixed site

during 2008, 2009, and 2010 ............................................................... 38

12. Charts showing daily crop coefficient at bulrush site during 2008, 2009, and

2010, and at mixed site during 2008, 2009, and 2010, and precipitation measured 

at Klamath Falls AgriMet station ......................................................... 41

13. Charts showing detailed graph of daily crop coefficient during the growing

seasons of all 3 years at the bulrush site, and the mixed site, and piecewise 

linear fits to the means from about June 20 to September 15, and to base values 

outside of this period........................................................................ 45

14. Charts showing comparison of daily evapotranspiration (ET) measured during

the growing season of 2008 through 2010 with ET modeled using the piecewise

linear approach for the bulrush site and mixed site .................................... 46

15. Charts showing biweekly reference evapotranspiration from Agency Lake

AgriMet station and measured evapotranspiration at bulrush and mixed sites

during 2008, 2009, and 2010 ............................................................... 48

16. Charts showing biweekly crop coefficients at bulrush and mixed sites, and

precipitation at Klamath Falls AgriMet station during 2008, 2009, and 2010 ......... 49

17. Charts showing biweekly ensemble average crop coefficients at bulrush and

mixed sites, and fourth-order polynomial fits to the crop coefficients during the

growing season ........................................................................... 51

18. Chart showing comparison of biweekly evapotranspiration (ET) measured

during the entire study period with ET modeled using the ensemble average Kc

approach for the bulrush site and mixed site .......................................... 52

19. Chart showing comparison of biweekly evapotranspiration (ET) measured 

at the bulrush site during the current study with weekly ET measured and 

modeled by Bidlake (2000) at a nearby site during May 28–October 12, 1997 ...... 57
v

20 Charts showing average lake surface temperatures at the midlake (MDL) 

and midlake north (MDN) sites plotted on the left vertical axis and net radiation 

(Qn) plotted on the right vertical axis for the budget periods extending from 

July 2008 to September 2010 ............................................................... 59

21. Charts showing average evaporation rates at the midlake (MDL) and 

midlake north (MDN) sites plotted on the left vertical axis and net radiation 

(Qn) plotted on the right vertical axis for the budget periods from July 2008 to 

September 2010.............................................................................. 60

Tables

1. Meteorological and energy-balance sensors, locations, and data acquisition

characteristics at eddy-covariance sites ................................................ 17

2. Biweekly budget periods used for calculations.......................................... 20

3. Regressions used to gap-fill Williamson River, Wood River, and Seven Mile

Creek temperature records and their associated goodness of fit statistics ......... 22

4. Percentage of time eddy covariance sensors operating (%TimeEC), percentage

of time all energy-balance sensors operating (%TimeALL), energy-balance ratio

(EBR), root-mean-squared error between 30-minute available energy and

adjusted turbulent flux (RMSE), and coefficient of determination (r 2) of

30-minute, daily, and biweekly means of available energy and turbulent flux ...... 33

5. Piecewise linear expressions of crop coefficient (Kc) at both study sites during

the growing season ........................................................................ 44

6. Results of modeling daily evapotranspiration (ET) during the wetland growing

season (May 1–September 30, 2008–2010, n = 457) at both sites using piecewise

linear models of Kc, superseded by setting Kc = 1.5 during days of precipitation

greater than 3 millimeters .................................................................. 44

7. Comparison of environmental variables affecting evapotranspiration from

April 1 to June 30, 2009 and 2010, at both wetland sites. .............................. 47

8. Ensemble mean crop coefficients (Kc) during growing season biweekly periods

and mean non-growing season Kc values at both study sites ........................ 50

9. Results of modeling biweekly evapotranspiration (ET) during the study period 

(n = 63) at both sites using the ensemble-mean Kc approach during the growing

season and the mean Kc approach during the non-growing season.................. 51

10. Coefficients of fourth-order polynomial fits to biweekly growing season

ensemble average Kc values ............................................................ 53

11. Mean evapotranspiration at the study sites and reference evapotranspiration 

at the Agency Lake (AGKO) weather station during the study period (May 1,

2008–September 29, 2010), each year of study, and a full 3-year period 

(January 1, 2008–December 31 2010) ................................................... 53

12. Comparison of 3-year study period averages with 11-year averages of solar

radiation, precipitation, and air temperature .......................................... 55

13. Comparison of mean 2008–2010 growing season, non-growing season, and

annual evapotranspiration (ET) of alfalfa, pasture, and Upper Klamath Lake 

NWR wetland, in meters .................................................................. 56

14. Mean growing season, non-growing season, and annual evapotranspiration

(ET) of Tule Lake NWR fallowed cropland during 2000, and Upper Klamath Lake

NWR wetland during 2008–2010, in meters ............................................. 57

15. Mean surface temperatures (Ts), Bowen ratios (β), net radiation (Rn), net water

advected energy (Qv), energy transferred to lakebed (Qb), net change in energy

stored in the lake (Qx), and energy-budget evaporation rates (Eeb) for biweekly

budget periods in 2008, 2009, and 2010 ................................................... 58
vi

Conversion Factors

Inch/Pound to SI

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

yard (yd) 0.9144 meter (m)

Area

acre 4,047 square meter (m2)

acre 0.4047 hectare (ha)

acre 0.4047 square hectometer (hm2) 

acre 0.004047 square kilometer (km2)

square foot (ft2) 0.09290 square meter (m2)

section (640 acres or 1 square mile) 259.0 square hectometer (hm2) 

square mile (mi2) 259.0 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2) 

Volume

gallon (gal) 0.003785 cubic meter (m3) 

million gallons (Mgal) 3,785 cubic meter (m3)

cubic inch (in3) 16.39 cubic centimeter (cm3) 

cubic foot (ft3) 0.02832 cubic meter (m3) 

cubic yard (yd3) 0.7646 cubic meter (m3) 

acre-foot (acre-ft) 1,233 cubic meter (m3)

Flow rate

acre-foot per day (acre-ft/d) 0.01427 cubic meter per second (m3/s)

acre-foot per year (acre-ft/yr) 1,233 cubic meter per year (m3/yr)

foot per second (ft/s) 0.3048 meter per second (m/s)

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

million gallons per day (Mgal/d) 0.04381 cubic meter per second (m3/s)

inch per day (in/d) 25.4 millimeter per day (mm/d)

inch per year (in/yr) 25.4 millimeter per year (mm/yr)

mile per hour (mi/h) 0.4470 meter per second (m/s)

Mass

ounce, avoirdupois (oz) 28.35 gram (g) 

pound, avoirdupois (lb) 0.4536 kilogram (kg) 

Pressure

atmosphere, standard (atm) 101.3 kilopascal (kPa)

bar 100 kilopascal (kPa) 

inch of mercury at 60 °F (in. Hg) 3.377 kilopascal (kPa) 

pound-force per square inch (lbf/in2) 6.895 kilopascal (kPa)

pound per square foot (lb/ft2) 0.04788 kilopascal (kPa) 

pound per square inch (lb/in2) 6.895 kilopascal (kPa) 

Density

pound per cubic foot (lb/ft3) 16.02 kilogram per cubic meter (kg/m3)

pound per cubic foot (lb/ft3) 0.01602 gram per cubic centimeter (g/cm3)

Energy

kilowatthour (kWh) 3,600,000 joule (J)

calorie (cal) 4.187 joule (J)

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

Vertical coordinate information is referenced to the National Geodetic Vertical Datum of 1929 

(NGVD 29).

Horizontal coordinate information is referenced to the North American Datum of 1927 (NAD 27).

Altitude, as used in this report, refers to distance above the vertical datum.
vii

SI to Inch/Pound

Multiply By To obtain

Length

centimeter (cm) 0.3937 inch (in.)

millimeter (mm) 0.03937 inch (in.)

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi)

meter (m) 1.094 yard (yd) 

Area

square meter (m2) 0.0002471 acre 

hectare (ha) 2.471 acre

square hectometer (hm2) 2.471 acre

square kilometer (km2) 247.1 acre

square meter (m2) 10.76 square foot (ft2) 

square hectometer (hm2) 0.003861 section (640 acres or 1 square mile)

hectare (ha) 0.003861 square mile (mi2) 

square kilometer (km2) 0.3861 square mile (mi2)

Volume

cubic meter (m3) 264.2 gallon (gal) 

cubic meter (m3) 0.0002642 million gallons (Mgal) 

cubic centimeter (cm3) 0.06102 cubic inch (in3) 

cubic meter (m3) 35.31 cubic foot (ft3)

cubic meter (m3) 1.308 cubic yard (yd3) 

cubic meter (m3) 0.0008107 acre-foot (acre-ft) 

Flow rate

cubic meter per second (m3/s) 70.07 acre-foot per day (acre-ft/d) 

cubic meter per year (m3/yr) 0.000811 acre-foot per year (acre-ft/yr) 

meter per second (m/s) 3.281 foot per second (ft/s) 

cubic meter per second (m3/s) 35.31 cubic foot per second (ft3/s)

cubic meter per second (m3/s) 22.83 million gallons per day (Mgal/d) 

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

millimeter per year (mm/yr) 0.03937 inch per year (in/yr)

meter per second (m/s) 2.237 mile per hour (mi/h)

Mass

gram (g) 0.03527 ounce, avoirdupois (oz)

kilogram (kg) 2.205 pound avoirdupois (lb)

Pressure

kilopascal (kPa) 0.009869 atmosphere, standard (atm)

kilopascal (kPa) 0.01 bar

kilopascal (kPa) 0.2961 inch of mercury at 60°F (in. Hg)

kilopascal (kPa) 0.1450 pound-force per square inch (lbf/in2)

kilopascal (kPa) 20.88 pound per square foot (lb/ft2)

kilopascal (kPa) 0.1450 pound per square inch (lb/in2)

Density

kilogram per cubic meter (kg/m3) 0.06242 pound per cubic foot (lb/ft3) 

gram per cubic centimeter (g/cm3) 62.4220 pound per cubic foot (lb/ft3) 

Energy

joule (J) 0.000000278 kilowatthour (kWh)

joule (J) 0.2388 calorie (cal)

Power

watt (W) 0.001341 horsepower (hp) 

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

Vertical coordinate information is referenced to the National Geodetic Vertical Datum of 1929 

(NGVD 29).

Horizontal coordinate information is referenced to the North American Datum of 1927 (NAD 27).

Altitude, as used in this report, refers to distance above the vertical datum.
viii

Acknowledgments

This investigation was funded largely by the Science and Technology Program of the Bureau of 

Reclamation Research and Development Office and from the National Research Program of the 

U.S. Geological Survey. Most of the specialized eddy-covariance and meteorological equipment 

was purchased by the Bureau of Reclamation Klamath Basin area office. Thanks are extended to 

the U.S. Fish and Wildlife Service for the reconnaissance efforts of Dave Mauser and Tim Mayer 

and for cooperation in providing access to the Upper Klamath National Wildlife Refuge. Thanks 

are also extended to Amanda Garcia and David Sumner of the U.S. Geological Survey for their 

helpful reviews of the manuscript. Finally, thanks go to Michael Johnson of the U.S. Geological 

Survey for his helpful discussion on specialized supports for deployment of the wetland eddycovariance stations.
Evapotranspiration from Wetland and Open-Water Sites at 

Upper Klamath Lake, Oregon, 2008–2010

By David I. Stannard1, Marshall W. Gannett1, Danial J. Polette1, Jason M. Cameron2, M. Scott Waibel1, 

and J. Mark Spears2

Abstract

Water allocation in the Upper Klamath Basin has become 

difficult in recent years due to the increase in occurrence of 

drought coupled with continued high water demand. Upper 

Klamath Lake is a central component of water distribution, 

supplying water downstream to the Klamath River, supplying 

water for irrigation diversions, and providing habitat for 

various species within the lake and surrounding wetlands. 

Evapotranspiration (ET) is a major component of the 

hydrologic budget of the lake and wetlands, and yet estimates 

of ET have been elusive—quantified only as part of a lumped 

term including other substantial water-budget components. 

To improve understanding of ET losses from the lake and 

wetlands, measurements of ET were made from May 2008 

through September 2010. The eddy-covariance method was 

used to monitor ET at two wetland sites continuously during 

this study period and the Bowen-ratio energy-balance method 

was used to monitor open-water lake evaporation at two sites 

during the warmer months of the 3 study years. Vegetation 

at one wetland site (the bulrush site) consists of a virtual 

monoculture of hardstem bulrush (formerly Scirpus acutus, 

now Schoenoplectus acutus), and at the other site (the mixed 

site) consists of a mix of about 70 percent bulrush, 15 percent 

cattail (Typha latifolia), and 15 percent wocus (Nuphar 

polysepalum). Measured ET at these two sites was very similar 

(means were ±2.5 percent) and mean wetland ET is computed 

as a 70 to 30 percent weighted average of the bulrush 

and mixed sites, respectively, based on community-type 

distribution estimated from satellite imagery.

Biweekly means of wetland ET typically vary from 

maximum values of around 6 to 7 millimeters per day during 

midsummer, to minimum values of less than 1 mm/d during 

midwinter. This strong annual signal primarily reflects 

life-cycle changes in the wetland vegetation, and the annual 

variation of radiative input to the surface and resulting 

temperature. The perennial vegetation begins each growing 

season submerged, emerges from the dead litter mat around 

late May or early June, reaches a maximum height of about 

2.2 meters (m) during summer, senesces in October, and 

subsequently lodges over, contributing to the dead litter mat 

from previous years. Hydroperiods last about 5 to 6 months, 

typically beginning in January or February and ending in July 

or August, and have a minor influence on the annual ET cycle. 

These hydroperiods result from lake levels that typically vary 

about 1.3 m, from around 0.6 to 0.9 m above the wetland 

surface, to around 0.4 to 0.7 m below the wetland surface.

An estimate of 3-year annual wetland ET, made by 

substituting early- and late-season data measured during 

2009 for the missing periods in early 2008 and late 2010, is 

0.938 meter per year (m/yr). Daily values of alfalfa-based 

reference ET (ETr) were retrieved from the Bureau of 

Reclamation AgriMet Web site (http://www.usbr.gov/pn/

agrimet/index.html) and are aggregated into biweekly, annual, 

and 3-year values (for consistency, the 3-year values are also 

computed using substitute data from 2009 for early 2008 

and late 2010). These ETr values are computed from weather 

data measured at the nearby Agency Lake weather station 

(AGKO), and are based on the assumption that the alfalfa crop 

is green and vigorous year-round. The 3-year value of ETr

is 1.145 m/yr, about 22 percent greater than wetland ET. A 

comparison of 2008–2010 alfalfa and pasture growing season 

actual ET with wetland ET is made using data from the more 

distant Klamath Falls AgriMet weather station (KFLO) 

because actual alfalfa and pasture ET are not computed for 

the AGKO site. During the 190-day average alfalfa growing 

season, wetland ET (0.779 m) is about 7 percent less than 

alfalfa ET (0.838 m). During the 195-day average pasture 

growing season, wetland ET (0.789 m) is about 18 percent 

greater than pasture ET (0.671 m). Assuming alfalfa and 

pasture ET are equal to wetland ET during the non-growing 

season, annual estimates become 0.997 m, 0.938 m, and 

0.820 m from alfalfa, wetland, and pasture, respectively.

1

U.S. Geological Survey.

2

Bureau of Reclamation.
2 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

Wetland crop coefficients (Kc=ET/ETr) are computed 

at daily, biweekly, and annual time steps. Approximate 

formulas are given to estimate daily values of growing 

season Kc, thereby allowing computation of daily growing 

season ET using ETr from the AGKO weather station. 

Biweekly values of growing season Kc are computed from 

ensemble average values of ET and ETr during the 3 study 

period growing seasons, and a single, mean Kc is computed 

for the non-growing season. Together, these provide 

relatively accurate estimates of biweekly ET during the 

study (RMSE=0.396 and 0.347 mm/d, r 2=0.962 and 0.971 

at the bulrush and mixed sites, respectively). A fourth-order 

polynomial fit of the biweekly growing season values to day 

of year provides a more automated form of ET computation.

Measured ET at the bulrush wetland site during the 

current study compares very closely with growing-season ET

estimated during a study in 1997 at nearly the same location. 

During the earlier study, ET was measured four times, using 

eddy covariance for 1- to 2-day periods, and was estimated 

between measurement periods using a Penman-Monteith 

model, calibrated to the measurements. Differences between 

time series of ET from the two studies are similar to 

interannual differences within the current study. Compared to 

the 1997 study, the current study measured larger ET rates in 

early summer and smaller rates in late summer, resulting in 

very similar growing-season totals.

A study conducted in 2000 estimated ET from 

nearby fallowed cropland, using the Bowen-ratio energy 

balance method supplemented with Priestley-Taylor 

and crop‐coefficient ET modeling. Seasonal timing of 

ET from three different crop types varied considerably, 

but growing-season totals were remarkably similar, at 

0.435 ± 0.009 m. Wetland ET measured during the current 

study, evaluated over the same growing season was 0.718 m, 

or about 65 percent greater than the fallowed cropland ET.

Open-water evaporation from Upper Klamath Lake 

was measured at two locations during the warmer months 

of 2008–2010 using the Bowen-ratio energy balance 

method. Measured rates were in general agreement with 

those measured in 2003 using the same method. Open-water 

evaporation and wetland ET were nearly equal during late 

June through early August, when wetland vegetation was 

green and abundant. As expected, open-water evaporation 

consistently exceeded wetland ET during late summer, 

as wetland ET responded to vegetation senescence while 

open water evaporation responded to extra available energy 

in the form of heat previously stored in the lake. Overall, 

open-water evaporation was 20 percent greater than wetland 

ET during the same period.

Introduction

Upper Klamath Lake is a primary source of irrigation 

water for the Bureau of Reclamation’s Klamath Reclamation 

Project, which delivers irrigation water to approximately 

210,000 acres of croplands in south-central Oregon and 

northern California. The lake also provides habitat for two 

species of fish listed as endangered under the Endangered 

Species Act, the short-nose sucker (Chasmistes brevirostris) 

and the Lost river sucker (Deltistes luxatus). The outlet of 

Upper Klamath Lake forms the headwaters of the Klamath 

River, the flow of which supports threatened anadromous 

fish populations and is important to tribal communities, 

anglers, and recreationalists. Managing the lake to meet all 

of these demands requires a quantitative understanding of the 

lake’s hydrologic budget. Evapotranspiration from the lake 

and surrounding wetlands is a substantial component of the 

hydrologic budget of the lake.

Although hydrologic budgets have been developed 

for Upper Klamath Lake (Hubbard, 1970; Kann and 

Walker, 1999), estimates of evapotranspiration (ET) from 

the approximately 27,000 hectares (ha) of open water and 

7,000 ha of wetlands surrounding the lake were obtained from 

pan-evaporation measurements and models—and have been 

a major source of uncertainty. Uncertainty in ET from Upper 

Klamath Lake and the surrounding wetlands propagates as 

uncertainty into other components of the budget including 

groundwater inflow; this uncertainty is problematic for lake 

management, water-supply forecasting, and management and 

restoration of drained wetlands.

Year-to-year operation of the Klamath Reclamation 

Project (which includes lake-level management) varies 

depending on statistically based water-supply forecasts made 

by the Natural Resources Conservation Service. One source 

of forecast uncertainty is that the regression equations use net 

inflow to Upper Klamath Lake as the dependent variable. Net 

inflow is a lumped term that includes multiple components 

of the lake budget such as inflow from streams and springs, 

ET, and precipitation. Forecasting equations would likely be 

improved if the dependent variable more directly represented 

the physical response of the watershed to measured conditions 

in the basin (precipitation, snow water content, and so forth) 

as would be the case if ET from the lake and surrounding 

wetlands could be independently determined.

In addition to the 7,000 ha of wetlands still surrounding 

the lake, roughly 12,600 ha of wetlands was separated from 

the lake by levees, drained, and put into cultivation over 

the past several decades. Large tracts of drained wetland 

area were purchased by the Federal Government or private 

conservation organizations between the mid-1990s and 

late 2000s. Understanding the consequences of various 
Introduction 3

management options for these drained wetlands will be 

improved with a better understanding of wetland ET and 

open-water evaporation.

In a review of work to quantify predevelopment water 

budgets in the upper Klamath Basin (Bureau of Reclamation, 

2005), the National Research Council (NRC; 2007) identified 

ET estimates as a major source of uncertainty in hydrologic 

calculations, and improving ET estimates was a specific 

recommendation of the NRC report. The current study was 

conceived to reduce uncertainty in estimates of ET in and 

around Upper Klamath Lake, thereby reducing uncertainty in 

the lake water budget, and improving comparisons between 

ET from different types of land use in the area.

Purpose and Scope

The purposes of this report are to (1) summarize 

measurements of year-round evapotranspiration from the 

dominant vegetative communities in natural wetlands 

surrounding Upper Klamath Lake; (2) summarize 

measurements of open-water evaporation that are more 

comprehensive than measurements made in the past; (3) use 

the resulting measurements to better calibrate standard ET

models for use in water supply planning and water resource 

management in the basin; and (4) compare ET from natural 

wetlands, open water, and various types of agricultural lands 

in the area. This report describes the study area, underlying 

theory, methods of investigation, and results. Measurements of 

wetland ET were made at two sites from May 1, 2008, through 

September 29, 2010, encompassing three growing seasons. 

Measurements of open-water evaporation were made at two 

sites during the warmer months of 2008 through 2010.

Previous Studies

Bidlake (2000) measured ET by the eddy covariance 

method and calculated an energy budget at one location in the 

wetland northwest of the lake for four periods ranging from 

1.2 to 1.9 days in 1997. While the work by Bidlake improved 

understanding of ET from wetlands around Upper Klamath 

Lake, significant improvements in understanding could be 

made by making similar measurements continuously for 

multiple growing seasons in a variety of vegetative settings.

Bidlake (2002) also measured ET by the Bowen-ratio 

energy balance method from three fallowed agricultural fields 

in the Tule Lake National Wildlife Refuge, California, about 

45 kilometers (km) southeast of Klamath Falls, Oregon. These 

sites were selected to typify ET rates that might result from 

water conservation measures applied to formerly irrigated 

agricultural land. Alternative management strategies can be 

evaluated by comparing wetland ET measured in the current 

study to fallowed cropland ET estimated by Bidlake (2002).

Janssen (2005) calculated open-water evaporation from 

Upper Klamath Lake for part of summer 2003 using the 

energy-budget method and compared the results with rates 

determined using the modified Penman method (Penman, 

1956). Janssen’s work improved understanding of open-water 

evaporation from the lake and showed that the modified 

Penman method overestimated evaporation, but longer-term 

measurements are needed.

Description of Study Area

The upper Klamath Basin is semiarid but spans a steep 

precipitation gradient extending from the Cascade Range, 

where mean annual precipitation is 1.7 meters (m; Crater Lake 

National Park, Oregon, 1971–2000), to the interior parts of 

the basin where mean annual precipitation can be as low as 

0.291 m (Tulelake, California, 1971–2000); all climate data 

in this section are from Western Regional Climate Center 

(2012). Mean annual precipitation (1971–2000) at Klamath 

Falls at the southern end of Upper Klamath Lake is 0.365 m. 

Of the total annual precipitation at Klamath Falls, 54 percent 

falls (mostly as snow) during the winter season (November 

through February), while only 15 percent falls during summer 

months (June through September). The remaining 31 percent 

falls during the transition months of October and March 

through May. Klamath Falls experiences cold winters with 

average December minimum and maximum temperatures 

of -5.6 degrees Celsius (°C) and 4.2°C, respectively, and 

warm summers with average July minimum and maximum 

temperatures of 10.9°C and 29.7°C, respectively (1971–2000).

Upper Klamath Lake (fig. 1) is the source of the Klamath 

River, and the lake encompasses approximately 270 square 

kilometers (km2) with an average depth of roughly 2.8 m at 

full pool. The lake occupies a fault-bounded structural basin 

immediately east of the Cascade Range volcanic arc. Principal 

tributaries to the lake include the Williamson River, which 

accounts for about half the inflow, the Wood River, Sevenmile 

Canal, and several other smaller canals and streams originating 

from the Cascade Range (Hubbard, 1970). Most of the lake 

is just a few meters deep except for a trench that is as much 

as 15 m deep that runs along the western margin. Although 

Upper Klamath Lake is a natural water body, the stage of 

the lake has been increased and controlled artificially since 

1921 by Link River Dam, a control structure built to facilitate 

management of the lake for irrigation. Total surface inflow to 

the lake is not routinely measured, but the mean annual flow of 

the Williamson River from 1971 to 2000 (measured below its 

confluence with the Sprague River, USGS station 11502500), 

which accounts for roughly half the total inflow, averaged 

about 31 cubic meters per second (m3/s; 1,100 cubic feet per 

second (ft3/s)). Outflow from the lake is principally to the Link 
4 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

tac12-0777_fig01

River

Hawks

Lake

Lost River

lanaC

Sevenmile Canal

Modoc Point Main Canal

Swan

Lake

Round

Lake

Spring

Lake

Lake

Ewauna

Whiteline

Reservoir

Nuss

Lake

John C Boyle

Reservoir

Meadow

Lake

Ball

Bay

Shoalwater Bay

Williamson Upper

Tulana

Goose

Bay

South

Marsh

Hank's 

Marsh

Link

River

Moss

Creek

Pelican

Bay

Klamath

Lake

Aspen

Lake

Howard

Bay

Agency

Lake

Sprague

Nannie Cr

Rock Creek

Cherry Creek

River

Varney

Creek

Clover Creek

Spencer

Trout Creek

Anderson Creek

Lost Creek

A-Canal

Caledonia

Marsh

KLAMATH RIVER

Wocus

Marsh

Creek

Eagle

DAORTNIOP

MODOC

Rattlesnake

Point.

Hagelstein

County Park

Modoc Rim

Ball

Point

97

97

Bare

Island

Buck

Island

140

140

70

62

Klamath

Falls 

Plum Valley

Ridge

Modoc

Point

Link

River 

Dam

MDT

EPT

SET

MDN

MDL

NETRAD

11505800

11505900

11507000

11507500

KFLO

AGKO

Rocky

Point

UPPER 

KLAMATH 

NATIONAL 

WILDLIFE 

REFUGE

122°10' 122° 121°50' 121°40'

42°

30'

42°

20'

42°

10'

Base modified from USGS and other digital sources, various scales. Coordinate 

system is UTM, Zone 10N; North American Datum of 1927.

0246 8 10 MILES

0246 8 10 KILOMETERS

EXPLANATION

Floating meteorological 

and lake temperature station

Eddy covariance station

Lake temperature station

4,110

4,143.3

Lake bottom elevation, in feet above 

 Bureau of Reclamation datum

BUL

MDT

MDL

NETRAD Over-water net radiometer

 station

USGS lake gage

USGS stream gage. A-canal

gaged at diversion near 

Link River Dam.

Stream temperature station.

Link River temperature

measured at gage.

AgriMet meteorological station

OREGON

Study

area

BUL

MIX

Figure 1. Upper Klamath Lake, surrounding area, and data collection locations.
Introduction 5

River (which becomes the Klamath River downstream) and 

to the A Canal which delivers irrigation water to the east and 

south. Link River discharge averaged 38.57 m3/s (1,362 ft3/s) 

from 1971 to 2000 (USGS station 11507500), and annual 

diversions to the A Canal averaged 7.45 m3/s (263 ft3/s) during 

the same period (Jason Cameron, Bureau of Reclamation, 

written commun.). A third component of surface outflow is the 

Keno Canal. Reliable measurements are no longer available 

for this canal, but discharge averaged 5.32 m3/s (188 ft3/s) 

during the period from 1967 through 1983.

Upper Klamath Lake was originally surrounded by 

roughly 196 km2 of wetlands. Between 1889 and 1971 about 

126 km2 was diked off and drained for agricultural use, 

whereas about 70 km2 of natural wetlands remain (Snyder and 

Morace, 1997; Dan Snyder, USGS, written commun., 2011). 

The Upper Klamath Lake National Wildlife Refuge (NWR) 

is the largest natural wetland (58 km2) adjacent to the lake. 

The Nature Conservancy is in the process of restoring about 

28 km2 of previously drained wetlands on the Williamson 

River delta by removing or breaching dikes. Draining 

wetlands around the lake, however, has caused considerable 

oxidation and compaction of the thick peat soils, resulting 

in subsidence of the land surface by as much as 4 m (Snyder 

and Morace, 1997). As a consequence, water depths are too 

deep in most areas for reestablishment of wetland vegetation 

and the areas become open water when previously drained 

wetlands are reflooded. It is not known how much time will be 

required for reestablishment of wetland vegetation.

Upper Klamath Lake has been historically eutrophic 

but is now considered hypereutrophic. For the past several 

decades, the lake has experienced annual blooms of a 

near-monoculture of the blue-green algae Aphanizomenon 

flos‐aquae which results in toxic conditions for fish (Snyder 

and Morace, 1997; Wood and others, 2006). During blooms, 

the algae congregate in the photic zone within a few 

centimeters of the lake surface, possibly affecting the albedo 

(ratio of reflected to incident light) and hence energy budget of 

the lake.

Study Sites

Two ET monitoring sites were chosen within the Upper 

Klamath National Wildlife Refuge (NWR) wetland area and 

two sites were chosen to monitor open-water evaporation 

(fig. 1). At full pool, the ratio of open water to wetland area 

is about 4:1. Despite this partitioning, two wetland sites 

were selected to address questions relating to differences in 

ET from different wetland communities and how these rates 

compare to ET from land historically drained to support 

irrigated agricultural crops, formerly irrigated land allowed to 

go fallow, and land recently returned from crop production to 

wetland status through breaching of dikes.

Bulrush and Mixed Vegetation Sites

The 5,800-ha Upper Klamath NWR is dominated by 

extensive wetlands and forms the northwest margin of Upper 

Klamath Lake, north and south of Pelican Bay (fig. 1), at an 

altitude of about 1,262 m. Lake level is controlled by the Link 

River Dam at the outlet and fluctuates about 1.3 m annually, 

causing large areas of the refuge (including the two study 

sites) to be flooded from about midwinter to midsummer 

of each year. The wetland areas of the NWR are covered in 

dense vegetation, heavily dominated by hard-stem bulrush 

(formerly Scirpus acutus, now Schoenoplectus acutus), 

with smaller amounts of cattail (Typha latifolia) and wocus 

(Nuphar polysepalum), and trace amounts of other vegetation. 

To typify ET from the most common species, one site was 

selected in a stand of almost exclusively bulrush, and another 

site was chosen within a patchwork of about 70 percent 

bulrush, 15 percent cattail, and 15 percent wocus. The sites 

were mapped on a visible light satellite image of the Upper 

Klamath NWR taken on August 28, 2011, and color patterns 

associated with each site were described. The bulrush site 

is located in an extensive, uniform, sepia-colored area, and 

the mixed vegetation site (hereafter called the mixed site) is 

located in a patchwork of sepia, light green, and dark green 

areas. Based on viewing the image of the whole NWR, we 

estimate that the bulrush site is typical of about 70 percent 

of the wetland, and the mixed site is representative of about 

30 percent. Other objectives for site selection were to provide 

adequate fetch (extent of uniform vegetative cover around 

the sensors) for the ET measurements and to minimize the 

effort needed to access the sites during maintenance visits. 

These two objectives were best balanced by navigating along 

existing streams through the refuge far into the wetland, 

then along lateral, open, narrow, channels away from the 

streams, and finally out 30 to 50 m through the vegetation 

perpendicular to the channels. This strategy exploited the 

relatively easy travel along the streams and channels to 

penetrate deep into the wetlands and still kept the effects of the 

streams and channels on the ET measurements negligible. The 

two sites are located near the centers of the two largest lobes 

of wetland in the NWR (fig. 1). The bulrush site location is 

42°30′48.88′′ N., 122°2′4.89′′ W., and the mixed site location 

is 42°28′36.80′′ N., 122°4′ 6.05′′ W. The bulrush and mixed 

site altitudes are 1,261.9 m (4,140.0 feet (ft)) and 1,262.0 m 

(4,140.5 ft) above mean sea level, respectively.
6 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

Bulrush, cattail, and wocus are phreatophytes, meaning 

their roots can remain flooded for extended periods 

without stress or damage caused by anoxia. In contrast, 

non-phreatophytic vegetation requires some degree of 

air penetration in the root zone to supply oxygen for root 

respiration. Consequently, the species at the study sites can 

thrive and transpire during the roughly 6-month period each 

year when lake water floods the local land surface, sometimes 

by as much as about 1 m. Bulrush and cattail are emergent 

vegetation, typically sending stalks and leaves to 2 to 3 m 

above the water surface. Their growth forms are similar, both 

having a central stalk and narrow, elongate leaves, all arranged 

nearly vertically when alive and vigorous. During winter 

dormancy, both plants cease photosynthesis, turn brown and 

brittle, and usually lodge over in response to snow and wind 

loading. At the study sites, the current year’s fallen plants 

merge with the existing dead layers from past years, forming a 

loose network of branching debris, which persists year-round, 

averaging about 0.8 m in depth. Unusually high winds also 

caused patchy areas of live-vegetation blow-down, primarily 

at the mixed site during the 2009 growing season.

Wocus is a pond lily, classified as floating rather than 

emergent vegetation. Its roughly circular leaves are about 

0.2 to 0.3 m in diameter and often rest on the water surface, 

distributed evenly, nearly covering the surface. At the study 

site, the plant sprouts and the leaves surface in the spring 

during the rising water level, remain at the water surface 

through midsummer, and become slightly aerial when water 

level recedes sufficiently in late summer. The leaves senesce 

and become part of the substrate as the water level approaches 

land surface. In early spring, areas occupied by wocus appear 

to be open water until the leaves surface.

Soils at the wetland study sites consist of a mat of roots 

and decaying plant matter from previous years, roughly 

0.3 m thick, underlain by a saturated clay-silt-peat mixture 

sometimes called gyttja (Hansen, 1959; Snyder and Morace, 

1997). The gyttja is basically a high-viscosity fluid just 

beneath the root mat, and it gradually grades into an elastic 

solid with depth. A small (about 5-millimeter (mm)) diameter 

rod pushed into the land surface encounters moderate 

resistance through the root mat and then penetrates easily 

below that point. Sizable impacts delivered to the land surface 

propagate laterally through the root layer as a wave, indicating 

the root layer is a somewhat tough skin, floating on the 

denser, more fluid gyttja below. This lithology posed unique 

challenges for working in the wetland and deploying the 

sensor stations, as discussed in Eddy-Covariance Sensors and 

Data Collection. The soil/root mat surface is hummocky, with 

a relief of about ± 5 centimeters (cm) over small horizontal 

scales (0.5 m), but the mat surface is extremely flat and level 

at horizontal scales larger than about 5 m.

Open-Water Sites

Open-water evaporation was measured using the 

Bowen-ratio energy balance (BREB) method (Anderson, 

1954), with specialized sensors deployed at two open-water 

locations near the middle of Upper Klamath Lake, three 

open-water locations near the deep trench along the western 

margin of the lake, at the mouths of the Williamson and 

Wood Rivers (the two major inlets to the lake), the mouth of 

Sevenmile Canal, and at the beginning of the Link River and 

A Canal (fig. 1). In addition, lake stage was determined using 

existing sensors operated by the USGS located at Rocky Point, 

at Rattlesnake Point, and near the Link River Dam. Surfaceto-air temperature and vapor-pressure differences, and water 

temperatures at various depths were measured at roughly the 

middle of the two largest lobes of the lake, at sites labeled 

MDL and MDN (fig. 1). These are previously established buoy 

locations used in other earlier and ongoing studies (Wood 

and others, 2006), where water depth is about 3 m. Minimum 

fetch to shore at the buoy sites is about 2.4 km, ensuring that 

the temperature and vapor-pressure differences were fully 

equilibrated to the lake surface (Stannard, 1997; Stannard and 

others, 2004).

The four components of net radiation were measured 

at a shallow open-water location near the shore at the mouth 

of the Williamson River (fig. 1). A four-component net 

radiometer was deployed at this site to investigate the effects 

of the high concentration of suspended algae on reflected solar 

(short-wave) radiation from the lake. In many lake evaporation 

studies, incoming radiation is measured on shore, and reflected 

solar radiation is modeled, assuming optical properties of 

clear water (Koberg, 1964; Sturrock and others, 1992). The 

known proliferation of algal blooms in Upper Klamath Lake 

suggested that a separate measurement of reflected solar 

radiation was warranted. The net radiometer site was chosen to 

typify the optical properties of water in the deeper parts of the 

lake but still provide water depths shallow enough to deploy 

a tripod on the lake bottom to support the sensor. Deployment 

from a raft was undesirable due to the inability to level the 

sensor reliably. Water depth at the site generally ranged from 

several centimeters to about 1 m, which was sufficient to 

behave optically like deeper midlake water during the bulk of 

the algal bloom periods.

Computation of open-water evaporation using the BREB 

method requires measurement or estimation of heat advected 

to or from the water body caused by inflows and outflows of 

surface water and groundwater. Therefore, water temperature 

and stage were measured at the two major surface-water 

inflows (the mouths of the Williamson and Wood Rivers) and 

at the Link River and A Canal outflows (fig. 1). Other surface 

water inputs were much smaller and were, therefore, not 

instrumented. The net heat exchange with groundwater also 

was considered to be minor (Janssen, 2005), and no attempt 

was made to measure it.
Methods of Study 7

Methods of Study

Evapotranspiration (ET) of water is an important 

component of the hydrologic cycle. Globally, ET is 

equal to precipitation (P), and over land, ET is about 

62 percent of P (Brutsaert, 1982, table 1.1), larger 

than any other terrestrial hydrologic component. 

The importance of ET is underscored by recognizing 

that once water evaporates into the atmosphere, it is 

no longer available for human consumption until it 

returns to the surface as P, which led to the adoption 

of the term consumptive use as a synonym for ET. 

Although the ratio ET:P decreases in humid climates 

(generally reducing the importance of ET there), 

ET:P approaches unity as aridity increases, making 

ET extremely important in semiarid and arid parts of 

the world.

The word evapotranspiration was coined in the 

1930s to combine the processes of evaporation and 

transpiration into a single term (Brutsaert, 1982). 

Whereas evaporation is the phase change of liquid 

water to water vapor, transpiration is evaporation that 

specifically occurs within the substomatal cavities of 

vegetation. Plants withdraw soil water and nutrients 

from the root zone and transport them up through the 

plant stems to the leaves, where the nutrients are used 

by plant tissues and the water evaporates through 

microscopic holes in the leaves called stomata. 

Current usage of ET refers to the sum of evaporation 

from open water, wet plant and mineral surfaces 

(such as shortly after rainfall), sublimation from snow 

and ice, and transpiration. In this report, ET refers 

to water loss from vegetated sites to the atmosphere, 

and evaporation (E) is reserved for water loss from 

extensive open-water sites to the atmosphere. Both 

ET and E can be expressed in a variety of units. In 

this report, daily and biweekly totals are expressed 

in millimeters per day (where millimeters is depth of 

liquid water per unit area of land surface); these basic 

units are aggregated into meters per year to describe 

annual evaporative losses.

Evaporation of water consumes a relatively 

large amount of energy, known as the latent heat 

of vaporization of water, L. Consequently, ET is a 

substantial component of the energy balance of the 

Earth’s surface, as well as the hydrologic balance. As 

liquid water vaporizes at the surface, it carries energy 

into the atmosphere, which is released at some later 

time when the vapor re-condenses into liquid. 

The rate of energy used to sustain a given ET rate is known as the 

latent-heat flux (LE) and is equal to:

2 3

W mm 1 d 1 m kg J

m m d 86400 s 1000 mm kg

where

is the density of water,

is the latent heat of vaporization, and

W is joule per second.

w

w

LE ET L

L

          

= × × ×ρ ×                      

ρ

(1a)

Both ρw and L are very weak functions of temperature, and they are 

roughly constant over the range of temperatures encountered in this 

study. Therefore equation 1a can be rewritten approximately as:

2

mm W 0.0351

d m ET LE    = ×       (1b)

Energy Balance of a Vegetated or Open-Water Surface

Virtually all of the energy arriving at the Earth’s surface 

originates from the sun (Kiehl and Trenberth, 1997). On a global, 

annual average basis, solar (short-wave) radiation arriving at the 

top of the atmosphere is 342 watts per square meter (W m-2), and is 

reduced to 198 W m-2 at the Earth’s surface. On average, 168 W m-2of 

the solar radiation arriving at the surface is absorbed, and 30 W m-2 is 

reflected, giving an average reflectivity (a, also known as albedo) of 

0.15. Some of the solar radiation arriving at the top of the atmosphere 

is reflected to space (77 W m-2) or absorbed by the atmosphere 

(67 W m-2). Atmospheric absorption occurs primarily by clouds, water 

vapor, dust, trace gases, and aerosols. The absorbed energy heats the 

atmosphere, which in turn emits long-wave (infrared) radiation, some 

of which arrives at the surface. The surface either reflects or absorbs 

this long-wave radiation, and also emits its own long-wave radiation. 

The processes of reflection, absorption, emission, and transmission of 

long-wave radiation between the surface and atmosphere are complex, 

but on average, the net long-wave exchange is 66 W m-2 from the 

surface upward to the atmosphere.

At the Earth’s surface, the algebraic sum of incoming solar 

radiation (positive), reflected solar radiation (negative), incoming 

long-wave radiation (positive), and outgoing long-wave radiation 

(negative) constitutes net radiation, Rn. On average, Rn is (198 minus 

66, or) 102 W m-2 (Kiehl and Trenberth, 1997) and drives all of the 

other (nonradiative) energy exchanges at the surface. A schematic 

of the typical daytime energy balance of a vegetated surface is 

shown in fig. 2A. The surface typically warms during the day in 

response to the input of energy from Rn. Some of that energy moves 

into the subsurface by conduction, known as the soil heat flux, G. 
8 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

tac12-0777_fig02a

G

Soil-heat

flux 

H

Sensibleheat flux 

LE

Latentheat flux 

Rn

Net

radiation

Qc

Canopy

storage

Qp

Heat of 

precipitation

A. Vegetated surface

Qp

Heat of 

precipitation

H

Sensibleheat flux 

LE

Latentheat flux 

Rn

Net

radiation

B. Water body

Qv

Advectedheat flux

Lake bottom

heat flux

Qb

Water body

heat storage

Qx

Qe

Heat of

evaporating

water 

Figure 2. Energy balance of A, a vegetated surface and B, a water body.
Methods of Study 9

The portion that warms the vegetation biomass is canopy 

storage, Qc. On most days, absorbed radiation warms the 

vegetation and soil surfaces above the temperature of the 

overlying air, giving rise to turbulent transfer of heat into the 

air, known as sensible-heat flux, H. Water evaporating from 

the surface carries with it the latent-heat flux, LE, another 

turbulent flux from the surface to the air. Global annual 

average values of H and LE are 24 and 78 W m-2, respectively. 

Finally, the excess heat content of precipitation above the 

surface temperature produces a typically small flux, the heat 

of precipitation, Qp. Adopting the sign convention shown 

in figure 2A, the surface energy-balance equation can be 

written as:

R G Q Q H LE n cp −− + = + (2)

The left side of equation 2 is called the available energy (AE), 

and the right side is the turbulent flux (TF). In many settings, 

Qc and Qp are minor terms, leaving Rn, G, H and LE as the 

four main components of the energy balance. In this study, Qc

and Qpwere determined to be negligible and are not included 

in the calculations.

At night, solar radiation terms become zero and outgoing 

long-wave radiation typically exceeds incoming radiation, 

causing Rn to become negative. Usually, the surface cools 

faster than the overlying air due to this long-wave emission, 

creating a temperature inversion in the air, leading to a 

sign change in H and a downward flux of sensible heat. 

Typically, the surface is also cooler than the subsurface soils, 

and G similarly changes sign. Outgoing night-time G is 

comparable to incoming daytime G, and long-term values of 

G approach zero. Most plants close stomata at night, shutting 

off transpiration, and due to the lack of available energy and 

colder temperatures, evaporation from soil also approaches 

zero, resulting in a surface LE that approaches zero at night. If 

the surface cools below the dew-point, water vapor in the air 

deposits as dew (or frost when the surface is below freezing) 

and LE becomes slightly negative.

The dynamic changes in the major fluxes between 

day and night result in typical 24-hour time series of flux 

resembling sinusoidal waves, with maxima near solar noon 

and minima near midnight. Daily average amplitudes and 

means are greatest in summer and least in winter. In addition, 

substantial variability about the average patterns occurs, 

caused by changes in the amount of cloud cover, green 

vegetation, water availability, wind speed, and atmospheric 

properties.

The surface energy balance shown in figure 2A is a 

one‐dimensional, vertical model, written for a specific, 

uniform surface of interest. Energy balances can vary 

substantially from one surface type to another. Because the 

turbulent fluxes are measured at some height above the plant 

canopy, the assumption is made that they are equal to the 

values at the surface, corrected for any change in heat or vapor 

storage between the canopy and the sensor. This assumption is 

valid if the horizontal extent of the uniform surface of interest 

in the upwind direction (the fetch) is sufficiently large that 

the air passing by the turbulent flux sensors has equilibrated 

to the surface of interest. Consequently, turbulent flux sensors 

typically are deployed in the midst of a large expanse of 

a uniform surface type. Tests are available to evaluate the 

adequacy of the fetch (Schuepp and others, 1990; Stannard, 

1997) and are used in this study.

Compared to the energy balance of a land surface, 

the balance of an open-water surface is complicated by 

the subsurface transfer of heat in three dimensions as 

the bulk liquid water mixes in response to wind, density 

gradients, inflows, and outflows. In addition, solar radiation 

typically penetrates the water column to some depth, further 

complicating the subsurface energy exchange. To avoid the 

problems of measuring the near subsurface energy input, the 

entire water body is taken as a control volume, and energy 

fluxes into and out of that volume (rather than a surface) are 

conceptualized and measured (fig. 2B). The fluxes of Rn, 

H, LE, and Qp are analogous to those occurring over land. 

The flux of heat energy exchanged between the surface 

and subsurface (the equivalent of G on land) is recast as a 

change in heat stored in the water body, Qx, measured by 

changes in temperature profiles through the water column 

(Anderson, 1954; Sturrock and others, 1992). If the water 

body is relatively shallow, heat exchange also may occur 

between the water and the lake bottom sediments, designated 

as Qb. Water bodies also are often connected to streams and 

groundwater, which can add or remove heat to or from the 

water body through advection, designated as Qv. Finally, 

heat can be added or removed to or from the water body 

by the evaporating water, depending on whether that water 

is cooler or warmer, respectively, than the mean waterbody temperature. Designated as Qe, this small flux also 

occurs over land but is seldom evaluated there because the 

temperature of the evaporating water usually is not known. 

The resulting energy balance of a water body can be written as 

(Anderson, 1954):

R Q Q Q Q Q H LE nxbve p − − + − + =+ (3)
10 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

The diurnal behavior of energy-balance fluxes is quite 

different over water than over land, primarily because 

(1) solar radiation partially penetrates the surface, (2) the 

thermal inertia of water is much greater than that of land, 

and (3) water availability at the water surface is always 

100 percent. These factors combine to create a daytime 

balance where heating of the water surface from Rn occurs 

more slowly than heating of the land (or vegetation) surface, 

moderating surface temperature compared to temperature 

over land. Usually the overlying air heats more quickly than 

the water surface, resulting in a temperature inversion and 

a downward (negative) H during the day. Rather than being 

partially converted into a positive H as over land, Rn (aided 

by a downward H) drives a large value of Qx by storing 

heat at depth in the water column, and the residual energy 

is partitioned into LE. At night, the air cools faster than the 

water surface, and H becomes positive. Even though Rn is 

negative, heat comes back out of storage from the water 

column (Qx > -Rn), driving both a positive LE and a positive 

H. Daytime Qx over water is a large fraction of Rn, whereas 

G + Qc usually is a small fraction of Rn over a densely 

vegetated canopy on land. The 24-hour wave-like behavior of 

H over water is about 12 hours out of phase with H over land, 

and magnitudes are much smaller. The 24-hour behavior of LE

over water is less wave-like, tending toward a more constant 

(positive) value fluctuating about the 24-hour mean.

The two wetland sites of the current study exhibit 

energy-balance characteristics of both the vegetated land 

surface and the water body described in the previous several 

paragraphs. Between midsummer and midwinter, standing 

water is not present at the sites, and the surface behaves purely 

as a vegetated land surface. From midwinter to midsummer, 

water depth at the sites typically increases to as much as about 

0.8 m, is maintained at that level for about 2 months, and then 

recedes back to zero. During this period, diurnal energy flux 

patterns are intermediate between those of a vegetated land 

surface and an open-water body, depending on vegetation 

status and water depth. The energy balance of a wetland 

surface with standing water contains elements of equations 2 

and 3, and can be written:

R Q G H LE n x − −= + (4)

At times when standing water is present, the dense vegetation 

canopy effectively inhibits significant lateral exchange of 

energy in the water column, and therefore Qv is assumed to be 

zero. At times when standing water is not present, Qx and Qv

are both zero.

Eddy-Covariance Measurements of Latent- and 

Sensible-Heat Flux

Turbulent exchange of energy and mass in the lowest 

layer of the atmosphere, the atmospheric boundary layer 

(ABL), occurs through eddy diffusion (Brutsaert, 1982, 

p. 52–56). Above a flat, level surface, the mean air movement 

is commonly recognized as being horizontal and is quantified 

as wind speed. However, superimposed on the mean wind 

are random turbulent upward and downward motions, 

resulting in instantaneous wind vectors with non-zero vertical 

components. The interplay between air viscosity, geostrophic 

wind (wind at upper levels of the atmosphere caused by 

regional pressure differences), surface heating, and surface 

roughness creates an ABL where air motions tend to aggregate 

into blobs or eddies which span a wide range of sizes, from 

centimeters to kilometers. Within an eddy, movements are 

highly correlated and can be quite distinct from those in 

nearby eddies. Similarly, concentrations of admixtures (for 

example, the heat, water vapor, or carbon dioxide content) 

may vary from eddy to eddy. Vertical transport of eddy 

admixtures results from the vertical components of eddy 

motions, a process similar to molecular diffusion but on a 

much larger scale. As an eddy moves upward or downward, 

it carries the admixtures along with it, giving rise to vertical 

turbulent flux. Above an extensive uniform surface, the net 

vertical transport of an admixture is equal to the algebraic sum 

of the transport contributions from all eddies (or a statistically 

significant sample thereof) passing over the surface. Thus, 

over an evaporating surface, upward-moving eddies contain, 

on average, more water vapor than downward-moving eddies. 

If certain criteria are met, the flux of an admixture can be 

measured through a high-speed bookkeeping of vertical 

eddy motion and admixture concentration, known as eddy 

covariance (EC). In the case of water vapor, the EC equation 

takes the form (Dyer, 1961):

86.4

where

is measured evapotranspiration, in millimeters

per day;

is vertical component of wind speed, in meters

per second (upward is positive);

is vapor density, in grams per cubic meter;

= ⋅ρ′ ′

ρ

m v

m

v

ET w

ET

w

primes denote deviations from mean values;

overbar denotes mean value; and the factor

86.4 converts grams per square meter per

second into millimeters per day.

(5)
Methods of Study 11

The quantity w′ ′ ρv is the covariance of w and ρv. Similarly, the 

equation for sensible heat is:

where

is measured sensible heat flux, in watts per

square meter;

is air density, in kilograms per cubic meter;

is specific heat of air at constant pressure, in

joules per kilogram per de

m ap a

m

a

p

H c wT

H

c

=ρ × ′ ′

ρ

gree Celsius; and

is air temperature, in degrees Celsius. Ta

(6)

Typically, means are computed over 20 to 60-minute periods, 

and deviations from means are measured 5 to 20 times 

per second.

In addition to turbulent flux of heat and mass between 

the surface and atmosphere, a turbulent flux of horizontal 

momentum also occurs from the atmosphere to the surface. 

Horizontal wind speed is zero at the surface and increases with 

height above the surface—a wind-speed profile that indicates 

greater momentum at height, decreasing to zero momentum 

at the surface. This gradient implies a flux of horizontal 

momentum from the upper atmosphere downward to the 

surface, also recognized as a drag force exerted on the surface 

by the air. The transfer of momentum downward occurs 

through eddy diffusion and can be expressed as:

where

is measured momentum flux or drag per unit

 area of land surface, in kilograms per meter

 per second squared; and

is horizontal wind speed, in meters per second.

m a

m

w u

u

τ = −ρ × ′ ′

τ

(7)

Usually, τm is measured concurrently with ETm and Hm

because it is needed to calculate corrections to those fluxes.

The Energy-Balance Closure Problem

The surface energy balance illustrated in figure 2A and 

quantified in equation 2 accounts for all significant energy 

fluxes to and from a surface that are currently recognized 

(Wilson and others, 2002). Commercially available 

instrumentation provides measurements of each term in 

equation 2 separately. If all measurements are accurate and 

all significant fluxes appear in equation 2, then the left side 

of the equation, the available energy (AE), should be equal 

to the right side, the turbulent flux (TF), within the limits 

of measurement accuracy. This concept is commonly called 

energy-balance closure. Graphical and statistical comparison 

of AE with TF frequently is used to identify problems 

associated with sensor inaccuracies and malfunctions, 

sensor deployment, insufficient fetch, or complex terrain. 

Due to random components of some errors, measurement 

accuracy usually increases as the accumulated time interval of 

continuous measurements increases. In addition, some errors 

may be systematically linked to time of day or year, but are 

largely self-compensating when the measurement interval is 

a full day, a number of full days, or a full year. Consequently, 

energy-balance closure usually is evaluated over longer time 

periods, preferably a year or multiple years.

Comparisons of long-term AE with TF from many 

studies display a chronic mismatch between the two. The 

ratio of TF to AE generally ranges from about 0.6 to 1.0, 

it most frequently is around 0.7 to 0.8 (Twine and others, 

2000; Wilson and others, 2002; Foken, 2008). In the past, 

undermeasurement of TF (Dugas and others, 1991; Twine and 

others, 2000; Gash and Dolman, 2003) or overmeasurement 

of Rn (Campbell, 1980; Halldin and Lindroth, 1992; Bossong 

and others, 2003), both presumably caused by instrumental 

performance or deployment, have been suggested as reasons 

for the mismatch. Soil-heat flux and storage terms are not 

suspect because long-term measured values approach zero, 

consistent with principles of environmental physics. Recently, 

Foken (2008) argued that current instrumentation and field 

practices are now sufficiently accurate that they can no longer 

account for the lack of closure. Rather, Foken proposed that 

land-surface scales of heterogeneity on the order of 1 to 10 km 

may generate large-scale eddies that contribute to turbulent 

flux in a fashion that is unlikely or impossible to be fully 

measured using the EC method. Foken argues that the time 

of passage of these very large eddies may be too long for 

typical averaging periods (which are 30 minutes to 1 hour; 

longer averaging periods violate the stationarity principle) to 

capture. Further, he suggests that the large eddies cluster near 

substantial changes in land-surface type (the very locations 

that are avoided as measurement sites if the goal is to obtain 

a clear, unambiguous flux signal from a surface of interest), 

inducing undetected horizontal flux advection over the central 

areas of homogenous land-surface patches, where sensors 

typically are deployed. Large-scale (~5 km) scintillometer 

measurements of turbulent flux and large eddy simulation 

modeling results support these ideas, both indicating adequate 

energy-balance closure when applied to horizontal scales of 

several kilometers encompassing changes in land-surface 

type (Foken, 2008). Although a proven remedy for ordinary 

EC data collection is not offered, Foken suggests as a first 

guess closing the energy balance by adjusting both H and LE, 

maintaining the ratio between them (H/LE=β, the Bowen 

ratio). This method has also been used commonly in the past 

(Barr and others, 1998; Blanken and others, 1998; Twine 

and others, 2000) when energy-balance closure was not 

obtained. Although Foken’s (2008) ideas are promising, the 

scientific community is still undecided on the answer to the 

energy-balance closure problem.
12 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

In this report, measured H and LE are corrected using 

the energy-balance closure principle. A single value of the 

energy-balance ratio is computed as:

where

is the mean energy-balance ratio (unitless)

during the study period (May 1, 2008 to

September 29, 2010);

indicates the sum of all measured values

during the study period, us

+ = − −

∑

∑ ∑

∑∑∑

m m

n x

H LE

EBR

R QG

EBR

ing only 

30-minute periods when all energybalance sensors were operating correctly; 

and

 and refer to the measured values of and ,

uncorrected for energy-balance closure.

H LE m m H LE

(8)

First, gap-filling and standard corrections (described in 

Eddy-Covariance Data Processing) are applied to the 

30-minute H and LE data. Then the resulting Hm and 

LEm values are divided by EBR to obtain final 30-minute 

values that produce long-term energy-balance closure. The 

use of a single, mean value of EBR, rather than multiple 

values calculated over shorter periods, is discussed in 

Energy-Balance Closure and Trends. The EBR values at 

both EC sites are reported in Energy-Balance Closure and 

Trends, allowing the reader to compute Hm and LEm (or ETm) 

if desired. Applying this EBR correction to the measured 

wetland EC fluxes facilitates direct comparison with measured 

open-water evaporation, which is based on the concept of full 

energy-balance closure.

Eddy-Covariance Sensors and Data Collection

The EC method requires fast-response sensors to 

adequately measure the rapid fluctuations in wind-speed 

components, air temperature, and vapor density caused 

by movement of the smallest eddies that contribute to 

the turbulent flux of momentum, heat, and water vapor. 

Two specialized sensors developed for eddy-covariance 

measurements by Campbell Scientific were used in the present 

study. A 3-axis sonic anemometer (Model CSAT3) measured 

wind vectors along three measurement paths, all at 60 degrees 

(°) from vertical, and at 120° from each other in the horizontal 

plane (fig. 3). The sensor was leveled in the field by means 

of a sensitive bubble level. Software in the CSAT3 converted 

the measured vectors into 3 orthogonal vectors aligned with 

KH20 krypton

hygrometer

CSAT3 sonic

anemometer 

Cup anemometer

and wind vane

Figure 3. Eddy-covariance sensors, cup anemometer, and wind vane.
Methods of Study 13

the sensor’s major axes (one vertical and two horizontal). 

The CSAT3 measured the wind vectors by sending ultrasonic 

signals between transducer pairs (fig. 3), measuring the travel 

time, and using the Doppler effect to compute the wind speed. 

The two orthogonal horizontal vectors were used to compute 

the resultant horizontal vector (u) appearing in equation 7. 

The CSAT3 also measured sonic air temperature, Ts, using the 

dependence of the speed of sound on temperature. This sonic 

air temperature is slightly different than true air temperature, 

Ta, and requires a small correction

to obtain the ′ ′ w Ta covariance (eq. 6), described in 

Eddy-Covariance Data Processing. A krypton hygrometer 

(Model KH20) was deployed adjacent to the CSAT3 to sense 

vapor density fluctuations (fig. 3). The source tube emits a 

krypton radiation signal through a window, along the short 

(1 cm) measurement path, and through another window to 

the receiver tube. Because the radiation is absorbed by water 

vapor, the signal strength received is inversely proportional 

to the vapor density in the measurement path, providing a 

virtually instantaneous measure of ρ′

v .

The EC sensors were deployed from a galvanized steel 

tripod and were oriented to minimize interference upwind 

of the measuring paths during wind flow from the prevailing 

directions. The tripod was installed immediately adjacent to a 

platform structure that supported all of the other sensors and 

hardware and provided a working surface during installation 

and site visits (fig. 4). Isolation of the tripod from the platform 

prevented disturbing the EC sensors while researchers were 

moving about on the platform during site visits. The platform 

and tripod required special modifications to obtain adequate 

support from the spongy peat soil underlain by gyttja. Slow 

settling of the structures into the peat could affect sensor 

levels unacceptably, and penetration into the semiliquid 

gyttja below could topple the entire station. Large wooden 

feet made from 2 by 10-inch treated lumber were attached to 

the bottom of the tripod legs—and to the platform legs with 

additional sections of leg protruding below the feet to puncture 

the peat layer and anchor the platform (fig. 5). This design 

was sufficient to prevent any noticeable differential settling 

of the structures, thereby maintaining sensors level within 

acceptable limits between site visits. The EC sensors were 

set at heights of 3.61 m and 3.76 m above land surface at the 

bulrush and mixed sites, respectively. At both sites, the KH20 

measurement path was located 10 cm from the midpoint of the 

CSAT3 measurement paths (fig. 3).

Figure 4. Completed eddy covariance, energy balance, and meteorological station at 

bulrush site on June 10, 2008. Photo courtesy of Brian Wagner, U.S. Geological Survey.
14 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

The response times of the CSAT3 and KH20 sensors 

are nearly instantaneous, ensuring that rapid sampling of 

their outputs accurately tracks the random variations in wind, 

temperature, and vapor density. All 5 EC variables (three 

orthogonal wind vectors, sonic air temperature, and vapor 

density) were sampled at 10 hertz (Hz), using a Campbell 

Scientific CR1000 data logger. The 10 Hz data were 

temporarily stored in the data logger during each 30-minute 

period. These data were then used by the logger to compute 

means and standard deviations of each variable and all (10) 

of the possible covariances between variables (using block 

averaging) at the end of each period. In addition, a time 

stamp (year, month, day of month, hour, minute), preliminary 

flux values, wind direction, data-logger temperature, system 

battery voltage, and sensor diagnostics were recorded at 

the end of each period. Data were sent automatically via 

cell phone modem to the USGS Water Science Center in 

Portland, Oreg., daily. At each site, power was supplied from 

a single 40 W solar panel, with storage initially provided 

by a 100 ampere‐hour deep cycle flooded battery (fig. 4). 

Subsequently a second battery was added at each site after 

night-time low-power problems occurred at the mixed site.

Eddy-Covariance Data Processing

Although the EC method is the most direct measurement 

of turbulent fluxes between the surface and atmosphere 

currently available, the apparent simplicity of equations 

5 through 7 is slightly complicated by the need for minor 

corrections arising from limitations of the method and sensors. 

The following commonly used corrections were applied to EC 

data in the present study.

First, the use of w′ in equations 5 through 7 is predicated 

on the assumption that mean wind flow past the sensors 

is horizontal (that is, w =0). Over surfaces with uneven 

topography, vegetation, or heating, 30-minute mean wind 

vectors may not be horizontal, and the 30-minute mean 

vertical component may change depending on wind speed, 

wind direction, and solar heating. Although land surface at 

both EC sites was very flat and level, disturbances to the 

vegetation occurred from station installation and from wind 

gusts that lodged patches of bulrush and cattail, creating 

depressions in the canopy in the vicinity of the stations. 

Coordinate rotation was, therefore, performed to correct 

the three covariances in equations 5 through 7 (Tanner 

and Thurtell, 1969). This correction requires computing 

tac12-0777_fig05

A B

Specialized feet

Specialized feet

Energy-balance and 

meteorological

platform

Eddy-covariance

tripod 

Figure 5. Specialized feet to support A, energy balance and meteorological platform and B, eddy-covariance tripod, on spongy 

wetland surface. Platform shown just before installation into wetland surface.
Methods of Study 15

second-order moments and may increase or decrease the 

calculated flux, depending on the vertical direction of the 

rotation. Rotations were made based on the 30-minute mean 

wind vector, rather than using the long-term planar fit method 

(Paw U and others, 2000), which is more appropriate when the 

land surface or the sonic anemometer is not level.

Second, above even a flat, level surface, a more subtle 

effect contributes to a nonzero w when H ≠ 0, caused by the 

inverse relation between air temperature (Ta) and density 

(ρa) at constant pressure. For example, if H > 0, rising 

eddies are warmer and, therefore, less dense than sinking 

eddies. Because the vertical flux of dry air over a horizontal 

surface is zero, a small (upward) w > 0 occurs to maintain 

conservation of mass (Webb and others, 1980), and the 

converse occurs (w < 0) when H < 0. A correction to the 

measured w′ ′ ρv (eq. 5) was made to remove the effect of 

w ≠ 0 following Webb and others (1980). This correction 

increases ET when H > 0 (usually daytime) and decreases ET

when H < 0 (usually nighttime), generally producing a net 

increase in daily ET.

Third, a small correction to the measured w′ ′ ρv

covariance in equation 5 is needed because the krypton 

radiation emitted by the KH20 source tube is slightly 

attenuated by oxygen, and oxygen density is proportional 

to total air density. At constant pressure, warmer eddies are 

less dense, creating a small error in the measured w′ ′ ρv when 

H ≠ 0. Following Tanner and Greene (1989), a correction 

proportional to H was made to the measured w′ ′ ρv , to remove 

this artifact.

Fourth, the sonic air temperature, Ts, is slightly different 

than true air temperature, Ta, because Ts is affected by the 

water vapor content of the air. Following Schotanus and others 

(1983), a small correction proportional to LE was made to

convert ′ ′ w Ts to ′ ′ w Ta . Because the second, third, and fourth 

corrections are interdependent, these corrections were iterated 

until convergence was obtained.

Fifth, frequency response corrections (Massman, 2000) 

were made to compensate for the inability of the EC method to 

record flux contributions from the largest and smallest eddies 

under certain conditions. The largest eddies contributing to 

flux may require longer than 30 min to pass by the sensors 

in low wind speeds (less than about 0.5 m/s). However, 

averaging periods longer than 30 min begin to violate the 

stationarity principle and are generally not used. At the other 

extreme, contributions to flux from the smallest eddies (about 

10 cm) may not be fully recorded due to sensor geometry 

such as path-length averaging and sensor separation. These 

corrections apply to H, LE, and τ and the corrections to each 

flux depend on the magnitudes of the other fluxes, so these 

corrections also were iterated until convergence was obtained.

The calibration factor of the KH20 varies slightly with 

ambient vapor density, ρv. The manufacturer supplies the 

calibration curve data points, and the slopes of least squares 

linear regression fits to the data in the high and low ρv ranges. 

The manufacturer suggests using one or the other slope as the 

calibration factor, depending on ambient ρv. This approach 

creates unnecessary discontinuities at the transition and small 

errors in computed ET. We improved upon the piecewise 

linear approach by fitting a cubic polynomial to the calibration 

data (r 2 > 0.999) and using a more exact calibration factor for 

each 30-minute period, equal to the slope of the cubic curve (a 

quadratic function of ρv).

Fully processed 30-minute ET and related data are 

aggregated into longer period averages and totals for 

presentation, seasonal analysis, comparison with other work, 

and computation of crop coefficients. Depending on the 

application, periods of 1 day, 2 weeks, a growing season, or 

1 year are used as averaging periods.

Gap-Filling Missing or Bad Eddy-Covariance Data

The EC sensors can malfunction when their measurement 

paths or surfaces are obstructed by water droplets, water 

films, snow, ice, particulates, leaves, insects, webs, avian 

fecal matter, or other solids or liquids that interfere with the 

transmission or reception of the sensor signals. By far, the 

most common interference during this study occurred from 

precipitation, and it affected primarily the KH20 hygrometer. 

The CSAT3 sonic anemometer also was affected at times by 

the presence of liquid or solid water, but much less frequently 

than the KH20 hygrometer. Once the measurement paths 

and surfaces of either sensor are sufficiently free of water 

and other foreign matter, correct sensor operation and data 

collection resume.

Periods of invalid data were identified by graphing the 

four energy-balance fluxes, precipitation, air temperature, 

vapor density, the KH20 voltage signal, horizontal wind speed, 

and momentum flux for periods of a week and searching for 

anomalous patterns in H, LE, and τ. Anomalous patterns in 

H and LE (extended periods of zero flux, spikes, noise) were 

identified based on energy-balance principles. Periods of 

suspect data were then graphed on an expanded time scale 

(1 or 2 days per graph) to identify invalid data by 30-minute 

intervals. In almost all cases, reasons for invalid flux data were 

identified by inspection of the auxiliary data from the same 

period. For example, recorded precipitation, a sudden decrease 

in the KH20 voltage signal without a corresponding increase 

in vapor density, and relative humidity near 100 percent, 

were commonly noted during invalid flux data collection 

and strongly suggested that water interfered with one or both 

EC sensors.
16 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

Based on the close inspection of flux and auxiliary 

data, flags were added to data records to indicate: (1) invalid 

data, (2) which fluxes were affected, and (3) the appropriate 

gap-filling method to use. By inspection, it was found that 

the status of H and τ (operational or invalid) were identical, 

requiring only a single flag to indicate the status of both fluxes. 

Gap-filling was accomplished through linear interpolation 

or through energy-balance modeling. Linear interpolation 

was used when the gap was sufficiently short (≤2 hours) 

or the auxiliary data suggested that the missing flux varied 

approximately linearly between the last valid data point before 

the gap and the first valid data point after recovery. During the 

growing season, this second condition typically was restricted 

to periods of 8 hours or less because the diurnal cycle typically 

imposes a curvature in energy-balance fluxes during longer 

periods. During winter, periods as long as 18 hours were 

interpolated if the data indicated low sunlight (overcast), 

cold temperature, and precipitation—a winter storm. This 

practice is reasonable because with little diurnal variation in 

available energy, little resulting diurnal variation in turbulent 

flux occurs, creating extended periods when H and LE are 

small and relatively constant. Energy-balance modeling was 

required to gap-fill LE data only, because all gaps in H and τ 

were sufficiently short to gap-fill using linear interpolation. 

Energy‐balance gap-filling of LE incorporated the concepts 

embodied in equations 4 and 8, and took the form:

= −− − ( ) LE EBR R G Q H m n xm (9)

This method estimates LE using the energy-balance closure 

principle (eq. 4), modified by the observation that the 

long‐term ratio of measured turbulent flux to available energy 

(that is, the EBR) usually is less than one (eq. 8).

Periods of missing data occurred at the mixed 

vegetation site, caused by inadequate battery storage during 

June 14–25, 2008, and by cell-phone malfunction during 

July 30–August 12, 2009. The first incident was a series of 

13 night-time gaps, separated by daytime periods of successful 

data collection when adequate power was supplied directly 

from the solar panel. The second gap was a 13.1-day period 

of no data collection. During the low battery power gaps, both 

EC and meteorological data were missing, whereas during the 

cell-phone gap, only EC data were missing. Because the two 

EC sites are of similar land cover and are separated by only 

5.8 km, energy fluxes and most weather conditions are very 

highly correlated at the two locations. Periods of missing data 

at the mixed site were, therefore, gap-filled using simple linear 

regression against the equivalent data collected at the bulrush 

site. The linear relations were established using periods 

immediately before and after each gap, when data collection at 

both sites was successful. The periods before and after the gap 

were each about one-half the length of the gap, or longer. In 

the case of the recurring night-time gaps, round-the-clock data 

collected before the first occurrence of low power and after the 

problem was remedied were used to create robust regressions 

(exploiting the full diurnal range in flux), even though only 

night-time periods were gap-filled.

Meteorological, Energy-Balance, 

and Biophysical Measurements at 

Eddy-Covariance Sites

Meteorological and Energy-Balance Sensors 

and Data Collection

In addition to basic EC data collection, sensors were 

deployed at both EC sites to measure meteorological and 

energy-balance variables: (1) to help identify times when 

EC sensors were inoperative due to environmental moisture 

(rain, snow, ice) or other interference; (2) to gap-fill 

compromised EC data during these times; (3) to evaluate the 

degree of energy-balance closure; (4) to associate ET and 

energy-balance results with environmental conditions; and 

(5) to evaluate the fetch at the EC sites. Variables measured 

were net radiation, soil-heat flux, wind speed, wind direction, 

soil water content, rainfall, air temperature, relative humidity, 

and water temperature at various depths (when standing water 

was present). Sensor make and model, measurement height, 

scan interval, and summary statistics are presented in table 1.

The summary interval for all sensors except the 

water-temperature sensors was 30 min. The summary 

interval for the water temperature sensors was 15 min. The 

CNR1 net radiometer consisted of four separate sensors to 

measure incoming solar, reflected solar, incoming long-wave 

and outgoing long-wave radiation. The rainfall gage was a 

nonheated tipping bucket and, therefore, did not accurately 

record snowfall. Small snowfall amounts were recorded upon 

melting, but they were diminished slightly by any sublimation 

in the interim. Large snowfall amounts could overtop the 

gage and be substantially undermeasured. Because the 

rainfall data were used primarily to determine times when 

the EC sensors were affected by water, these limitations in 

the snowfall record were relatively unimportant. The Vaisalla 

HMP45C temperature-humidity probe and the RM Young 

03001 wind speed and direction sensors were deployed to 

measure wind, temperature, and humidity data even though 

the EC sensors (CSAT3 and KH20) nominally measure these 

variables because: (1) gaps exist in the EC data record caused 

by precipitation or other interference; and (2) the KH20 

hygrometer accurately senses rapid deviations from mean ρv

only—it does not accurately sense mean ρv. The standard, 

non-EC sensors provided a continuous and accurate record 

used in troubleshooting and computing small corrections 

to EC data.
Methods of Study 17

Table 1. Meteorological and energy-balance sensors, locations, and data acquisition characteristics at eddy-covariance sites.

[Abbreviations: Bul, bulrush site; m, meters; Mix, mixed site; m3, cubic meters; m-3, per cubic meter; mm, millimeters; m s-1; meters per second; W m-2, 

watts per square meter; °, degrees; °C, degrees Celsius]

Variable 

measured 

and units

Sensor make 

and model

Sensor height

above land surface 

(m)

Scan

interval

(s)

Summary

statistic(s)

Net radiation (Rn), W m-2 Kipp and Zonen CNR1 Bul: 3.05; Mix: 3.28 1 Mean

Soil heat flux (G), W m-2 Radiation and Energy 

Balance Systems HFT3

Bul: -0.02; Mix: -0.02 1 Mean

Wind speed (Ucup), m s-1 RM Young 03011 Bul: 3.81; Mix: 3.91 1 Mean

Wind direction (WD), ° RM Young 03011 Bul: 3.81; Mix: 3.91 1 Mean, standard deviation

Soil water content (θ), 

m3 water m-3 soil

Campbell Scientific 

CS616

Bul: 0 to -0.3 integrated

Mix: 0 to -0.3 integrated

1,800 Sample

Rainfall (R), (mm) Texas Electronics 525MM Bul: 3.22; Mix: 3.56 1 Total

Air temperature (Ta), °C Vaisalla HMP45C Bul: 3.73; Mix: 3.91 0.1 Mean

Relative humidity (RH), percent Vaisalla HMP45C Bul: 3.73; Mix: 3.91 0.1 Mean

Water temperature (Tw), °C Onset Tidbit v2 Bul: 0.01, 0.27, 0.52, 

water surface

Mix: 0.01, 0.27, 

0.52, water surface

4 Mean

Meteorological and Energy-Balance 

Data Processing

Saturated vapor pressure (es, kPa) was computed 

from measured air temperature (Ta) using the algorithm 

of Lowe (1977). This is the maximum amount of water 

vapor the air can hold, and it increases with increasing 

temperature. Actual vapor pressure (e, kPa) was computed 

from es and measured relative humidity (RH, percent) as: 

0.01 s e e RH = ×× . Vapor density (ρv, g/m3) is the mass of 

water vapor per unit volume of air and was computed from 

e using the ideal gas law: /( ) ρ= × × vw k M e RT where Mw is 

the molar weight of water (18.0153 g/mol), R is the universal 

gas constant (0.0083145 kPa (m3/mol)/K), and Tk is air 

temperature in kelvin.

Mean atmospheric pressure (P, kPa) was 

calculated using the atmospheric scale height equation: 

0 PP z =× − exp( / 8434.4) where P0 is mean atmospheric 

pressure at sea level (101.33 kPa), z is site altitude (m), 

and 8434.4 is the scale height of the atmosphere (m). Air 

density (ρa, g/m3) was calculated as the sum of dry air 

density (ρd, g/m3) and vapor density (ρv): ρ =ρ +ρ a dv where 

( )/( ) ρ= × − × d d M P e RTk and Md is the molar weight of 

dry air (28.97 g/mol). Specific humidity (q, g H2O/g air) 

is the mass of water vapor per unit mass of air, and was 

calculated as =ρ ρ/ v a q . Specific heat of air at constant 

pressure, cp (in joules per kilogram per degree Celsius), 

was calculated as the weighted average of the specific heats 

of dry air (cpd) and water vapor (cpv) at constant pressure: 

(1 ) p pd pv c q c qc = − × +× (Brutsaert, 1982, p. 43). Quadratic 

expressions were fit to tabulated data given for cpd and cpv

(Garratt, 1992, p. 285; Engineering Toolbox, 2011), which 

vary slightly as a function of temperature.

Wind speed measured with a cup anemometer and wind 

direction measured with a vane at 1 Hz were processed using 

data-logger software to compute mean wind speed (Ucup) and 

mean wind direction (WD) each half hour. Each 1-second 

Ucup and WD were combined to produce a wind vector, and 

the 1-second wind vectors were added in vector fashion to 

compute the resulting half-hour summaries.
18 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

Soil-heat flux, G, was measured directly using a soil-heat 

flux plate (HFT3, table 1) buried at about 2 cm beneath the 

soil surface. Any change in energy storage in the soil above 

the plate was assumed to be negligible. The plates were 

not buried at the beginning of the study due to the depth 

of standing water at that time. Scheduled site visits did not 

correspond to the cessation of standing water, so the plates 

were buried during the next visit after cessation. This late 

installation created a period of about 25 days in mid-2008 

when G was unmeasured. Later data indicated that when 

water depth exceeded about 20 cm, G ≈ 0. A model of G

was created to fill in the missing data during 2008 when 

water depth was less than 20 cm. G was modeled as a linear 

combination of current and past Rn and Ta, using data from 

times of similar water depth during 2009 when the plate was 

operational. Candidate past values of Rn and Ta included 

30-minute data from the previous 7 half-hours, and the mean 

from the past 24 hours. Multiple linear stepwise regression 

was used to select the subset of variables at each site that were 

significantly related to G. Root-mean-squared errors (RMSE) 

of the two models were 8.7 and 2.1 W/m2 at the bulrush and 

mixed sites, respectively. Coefficients of determination (r 2) 

were 0.78 and 0.94, respectively.

When standing water was present, change in energy 

stored in the water column, Qx, was calculated from 

temperatures measured at various depths in the water column. 

Temperature sensors were located at nominal heights of 0.01, 

0.27, and 0.52 m above the soil surface, and (floating) at 

the water surface (table 1). These sensors divided the water 

column into layers and the change in heat content of each 

layer was computed. The value of Qx was computed as the 

sum of the change in heat stored in each of the layers:

1 1

11 1 1

2

6

3

where

is in watts per square meter;

is the volumetric specific heat of water

(4.187 10 joules per cubic meter

per degree Celsius (J/m / C));

is the thic

n tt t t

x i i

i

x

C Q TH T TH T TH T TP

Q

C

TH

− −

=

  = × − × + ×∆    

×

°

∑

kness of each layer, in meters;

is the mean temperature of each layer, in

degrees Celsius;

is the change in temperature from the

 previous time period for layers 2

through , in degrees Celsius;

is the

T

T

n

TP

∆

 length of time period between

temperature measurements, in seconds;

refers to the present time period;

1 refers to the previous time period;

1 refers to the first layer;

refers to the th layer; and

is 

t

t

i i

n

−

the number of layers, where layers are

numbered from the top down.

(10)

Each layer is bounded by temperature sensors at the top and 

bottom of the layer, and the mean temperature of the layer 

is set equal to the mean of the upper and lower sensors. This 

formula accounts for a change in thickness of the top layer 

caused by a change in lake level during the time period and 

assumes lower layers are constant thickness. As water level 

varied and fixed sensors became exposed or submerged, the 

value of n changed accordingly. This formula was applied to 

time periods of 30 min.

Gaps in the Qx record occurred for two reasons: (1) the 

sensors were not deployed early enough each year to record 

the onset of inundation by the rising water; and (2) at times 

the floating sensor would become entangled in vegetation as 

the water level receded, causing the sensor to be suspended 

in air, invalidating the measurement. Models of each of the 

four water temperatures were devised for gap-filling, using 

data from periods when measurements were valid. These 

models are linear combinations of lagged air temperature, 

sensor depth, and vegetation height above water surface. 

Air temperature was lagged using a recursive filter, whose 

coefficients also depended on sensor depth. Because of small 

variations from year to year in actual sensor height above land 

surface and vegetation shading patterns, a separate model was 

calibrated for each sensor-year combination. The RMSE of the 

temperature models ranges from 0.47 to 1.47°C, averaging 

1.00°C, and the adjusted r 2 ranges from 0.872 to 0.984, 

averaging 0.938. Due to the extreme sensitivity of Qx to small 

changes in temperature, coupled with the random intermittent 

heating of the sensors from the solar beam penetrating gaps 

in the vegetation canopy, both computed and modeled Qx

were quite noisy on a 30-minute time step, but they displayed 

reasonable daily patterns. Therefore a seven-point running 

mean was used as the final best estimate of both measured 

and modeled Qx. The RMSE of the Qx models varies from 

45.1 to 100.1 W/m2, averaging 74.6 W/m2, and the r 2 ranges 

from 0.580 to 0.826, averaging 0.739. Although these RMSE

values appear to be large at first glance, Qx typically ranged 

from about -300 W/m2 at night to about 400 W/m2 in late 

morning in summer—a range of about 700 W/m2, or about 

10 times the mean RMSE. The main purpose of measuring 

and modeling Qx on a 30-minute basis (since long-term Qx

approaches zero by definition) is for estimating missing 

or bad LE data using the energy-balance equation (eq. 9). 

The Qx models used here are considered to be adequate for 

this purpose.

Biophysical Measurements and Observations

During site visits, various measurements and observations 

were made to characterize slowly changing variables. Mean 

canopy height, mean height of the dead vegetation stalk layer, 

and mean water depth were measured at 6 to 10 locations at 
Methods of Study 19

each site. Vegetation height between site visits was estimated 

using linear interpolation. Observations of greenness (whether 

the canopy was live or dormant) were made to determine 

the potential for transpiration to occur. Many photographs 

were taken during each visit to substantiate the observations 

and measurements.

Lake stage is measured daily by the USGS at the Rocky 

Point station (11505800; fig. 1) and was used to determine 

daily water depth at each site. The land surface altitude at each 

site was calculated by subtracting the observed mean water 

depth from the lake stage during each of the nine site visits 

when standing water was present. Each depth observation was 

the mean of six to eight measurements near the platform. Site 

altitudes were determined to be 1,261.88 m (4,140.02 ft) and 

1,262.03 m (4,140.52 ft), with standard deviations of 3.3 cm 

and 4.6 cm (n=9) at the bulrush and mixed sites, respectively.

Bowen-Ratio Energy Balance (BREB) 

Measurements at Open-Water Sites

Evaporation is one of the largest components of the 

budget of Upper Klamath Lake (Hubbard, 1970). Past efforts 

to determine the evaporative flux have largely relied on 

evaporation pan data (Hubbard, 1970; Kann and Walker, 1999) 

or modeling approaches based on meteorological inputs (for 

example, Hostetler, 2009). Prior to the current study, the only 

effort to measure evaporation from Upper Klamath Lake is the 

work of Janssen (2005), who used an energy-budget approach 

similar to that employed in this study. The energy budget 

method provides an indirect measurement of evaporation as 

represented by the latent-heat flux. The energy budget method 

is based on the conservation of energy and the ability to 

measure or calculate all major energy inflows to and outflows 

from the lake except for the latent- and sensible-heat fluxes. 

By then measuring the ratio of sensible- to latent-heat flux 

(the Bowen ratio), the latent-heat flux and evaporation rate can 

be computed.

Bowen-Ratio Energy-Balance Method

The Bowen-ratio energy balance (BREB) method 

described by Anderson (1954) was used to calculate 

evaporation from Upper Klamath Lake for biweekly budget 

periods May through October, 2008 through 2010 (table 2). 

Full-year measurements were not possible because the floating 

instrumentation platforms were removed from the lake during 

winter months. The instrumentation platforms in the lake 

were deployed for water quality and hydrodynamic studies 

(Wood and others, 2006; Wood and Gartner, 2010). The two 

floating platforms are referred to as the midlake (MDL) site 

near the middle of the lake and the midlake north (MDN) site 

near the middle of the northern section of the lake (fig. 1). 

Meteorological instrumentation at the EC stations, described 

in Meteorological and Energy-Balance Sensors and Data 

Collection, was used for supplementary data collection and 

gap-filling. Data used for this study collected at the MDL 

and MDN sites include water temperature at the surface, 

1 m below the surface, and 1 m above the lake bottom; and 

air temperature and relative humidity at approximately 2 m 

above the water surface. Because no relative humidity data 

were available at the MDN site during 2008, evaporation rates 

were only calculated at the MDL site that year. However, 

evaporation rates at the MDL and MDN sites were both 

calculated in 2009 and 2010.

The energy-budget evaporation rate is determined using 

the following equation (from Winter and others, 2003) which 

can be derived from equation 3 and describes the evaporation 

rate as a function of components of the lake energy budget that 

can be measured or calculated:

( )

2

2

1

where

is the energy-budget evaporation rate (m/s),

is incoming solar radiation (W/m ),

is reflected solar radiation (W/m ),

is incoming long-wave atm

s sr a ar bs v b x

eb

w w s

eb

s

sr

a

RR RR R QQQ E

c T

E

R

R

R

− −− − +−− = ρ λ +β +    

2

2

2

2

ospheric

radiation (W/m ),

is long-wave atmospheric radiation reflected

from the water body (W/m ),

is long-wave radiation emitted from the water

body (W/m ),

is net advected energy (W/m ),

is ener

ar

bs

v

b

R

R

Q

Q 2

2

3

gy transferred to lakebed (W/m ),

is the net change in energy stored in water

body (W/m ),

is the density of water (1,000 kg/m ),

is the latent heat of vaporization of water (J/kg),

is the Bowen rat

x

w

v

Q

ρ

λ

β io (dimensionless),

is the specific heat of water (4,184 J/kg/ C), and

is the temperature of the water surface ( C)

w

s

c

T

°

°

(11)

Discussions of equation 11 can be found in Anderson 

(1954), Sturrock and other (1992), Winter and others (2003), 

and Janssen (2005). Outgoing long-wave radiation is the sum 

of Rar and Rbs. The first five terms in the numerator of equation 

11 constitute net radiation, Rn. Other than Eeb, all terms of 

equation 11 are known, or can be measured or calculated. 

Measurements and calculations involving radiation terms, 

advected energy, energy transferred to lakebed, and Bowen 

ratios are described in the following sections.
20 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

Radiation Terms

Energy budget studies commonly employ upward facing 

radiometers to measure incoming long- and short-wave 

radiation, and calculate reflected and emitted radiation 

(Winter and others, 2003). This study employed a net 

radiometer deployed over water to measure both incoming 

and reflected short- and long-wave radiation. For stability, 

the net radiometer was anchored to the lake bottom using 

a tripod near the lake margin. The site was selected with 

southern exposure to the lake to ensure reflected radiation 

was from the water surface only. Conditions at the site are 

considered reasonably representative of the whole lake. The 

instrument was operational July through October in 2008 

and 2009 (instruments were removed from the lake during 

winter due to ice), hence there are substantial gaps in the 

measurement record.

Date Budget period

05-01-08 0:00

05-15-08 0:00

1

05-15-08 0:00

05-29-08 0:00

2

05-29-08 0:00

06-12-08 0:00

3

06-12-08 0:00

06-26-08 0:00

4

06-26-08 0:00

07-10-08 0:00

5

07-10-08 0:00

07-24-08 0:00

6

07-24-08 0:00

08-07-08 0:00

7

08-07-08 0:00

08-21-08 0:00

8

08-21-08 0:00

09-04-08 0:00

9

09-04-08 0:00

09-18-08 0:00

10

09-18-08 0:00

10-02-08 0:00

11

10-02-08 0:00

10-16-08 0:00

12

10-16-08 0:00

05-15-09 0:00

13

Date Budget period

05-01-09 0:00 14

05-15-09 0:00

05-29-09 0:00

15

05-29-09 0:00

06-12-09 0:00

16

06-12-09 0:00

06-26-09 0:00

17

06-26-09 0:00

07-10-09 0:00

18

07-10-09 0:00

07-24-09 0:00

19

07-24-09 0:00

08-07-09 0:00

20

08-07-09 0:00

08-21-09 0:00

21

08-21-09 0:00

09-04-09 0:00

22

09-04-09 0:00

09-18-09 0:00

23

09-18-09 0:00

10-02-09 0:00

24

10-02-09 0:00

10-16-09 0:00

25

10-16-09 0:00 26

Date Budget period

05-01-10 0:00

05-15-10 0:00

27

05-15-10 0:00

05-29-10 0:00

28

05-29-10 0:00

06-12-10 0:00

29

06-12-10 0:00

06-26-10 0:00

30

06-26-10 0:00

07-10-10 0:00

31

07-10-10 0:00

07-24-10 0:00

32

07-24-10 0:00

08-07-10 0:00

33

08-07-10 0:00

08-21-10 0:00

34

08-21-10 0:00

09-04-10 0:00

35

09-04-10 0:00

09-18-10 0:00

36

09-18-10 0:00

10-02-10 0:00

37

10-02-10 0:00

10-16-10 0:00

38

10-16-10 0:00 39

Table 2. Biweekly budget periods used for calculations.

[For any given budget period, the first date and time (24-hour clock) is the beginning of the period and the second is the end. Calculations 

were not made for shaded periods due to incomplete data]
Methods of Study 21

During periods when data from the over-water net 

radiometer were not available, incoming radiation data 

from the two radiometers deployed on the eddy-covariance 

platforms were used. Although incoming radiation is 

comparable at all the sites, the reflected radiation is 

considerably different because the eddy-covariance sites 

were over a vegetated landscape. Because of this, calculated 

values of reflected solar radiation were used during periods 

of missing record. Reflected shortwave solar radiation Rsr is 

calculated as:

R Ra sr s = (12)

where a is the albedo (reflectivity) of water dependent upon 

the solar zenith angle (φ) at the approximate center of the lake 

(Janssen, 2005; Oke, 1987; Lee, 1980). Solar zenith angles are 

estimated by equations which were adapted from a publicly 

accessible National Oceanic and Atmospheric Administration 

spreadsheet. The equation for the albedo of a smooth water 

surface as presented in Janssen (2005) is:

0

b

a a ce φ = + (13)

where a0, c, and b are constants. These constants were 

determined by nonlinear regression using estimated albedos,

calculated as sr

s

Q

Q , from the 2008 and 2009 incoming and

reflected solar radiation data at the over-water net radiation 

site as the regressor and corresponding solar zenith angles 

at the approximate center of the lake, as the regressand. 

Substituting albedos calculated from equation 13 into 

equation 12 results in half-hour reflected shortwave radiation 

values for open water.

Reflected long-wave radiation, Rar, is calculated as 

3 percent of the measured incoming long-wave radiation 

(Anderson, 1954; Sturrock and others, 1992; Janssen, 2005). 

Long-wave radiation emitted from the water body, Rbs, is 

calculated using the Stefan-Boltzmann Law for gray-body 

radiation (Jannsen, 2005; Dingman, 2002):

4

8 24

where

is the temperature of the water surface,

averaged from MDL and MDN sites

when possible,

is the Stefan-Boltzman constant 

[5.671 10 Wm K ], and

is the emissivity of the wa

in

t

 kelvin,

er 

bs

s

s

T

R T

− −−

= εσ

σ

×

ε surface

[dimensionless] taken to be 0.97

(Anderson, 1954).

(14)

Net Advected Energy

Net advected energy, Qv, for a budget period is calculated 

as the total energy exiting the lake through streamflow out 

of the lake subtracted from the total energy entering the 

lake through streamflow into the lake, precipitation, and 

groundwater flow into the lake (Anderson, 1954):

 

 

is the area of the lake surface, in square 

meters,

and are the flows entering and exiting the lake, 

in cubic meters per second, and

and are water te

( )

where

w w v in q in out q out

L

L

in out

q in q out

c Q qT q T A

A

q q

T T

ρ = ∑ −

mperatures of the incoming

and outgoing water flows, in degrees

Celsius.

(15)

The area of the lake is determined in the same manner as 

Janssen (2005) using the Bureau of Reclamation 1974 Upper 

Klamath Lake stage-area curve (fig. 6). Areas were determined 

from this curve using stage data from U.S. Geological Survey 

lake stage gage 11507001. Stage at this station is calculated as 

a daily weighted mean of lake elevations from three gages in 

order to offset seiche effects (Janssen, 2005). Daily mean lake 

stage data for Upper Klamath Lake are reported to the nearest 

0.01 ft while the stage-area curve is incremented by 0.1 ft. 

Hence, interpolation was used to determine areas for stages 

falling between points on the curve, to reduce rounding errors.

Sources of uncertainty in calculating advected energy 

entering the lake are the lack of flow and temperature data 

for many of the smaller streams feeding the lake. The rate 

and temperature of groundwater discharge to the lake is also 

poorly quantified. During this study, the only measured inflow 

to the lake was that of the Williamson River, which accounts 

for about half the total inflow.

Temperature data were collected for the Williamson and 

Wood Rivers, and Sevenmile Canal near their outlets into 

the lake. During low flow conditions, temperature probes 

periodically were exposed to air resulting in several gaps in 

the records. Regression techniques, using these same streams 

as regressors (independent or explanatory variables) and 

regressands (dependent or response variables) in turn, were 

used to gap-fill missing portions of records (table 3). This 

was possible since the majority of time the probes of the three 

streams were not out of the water at the same time. Linear 

interpolation was used to gap-fill the few parts of records in 

which regressions could not be used.
22 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

tac12-0777_fig06

0

100

200

300

400

500

600

700

0

50

100

150

200

250

300

350

400

1260.5 1261 1261.5 1262 1262.5 1263

Lake area, in millions of square meters

Lake stage, in meters above MSL

Active storage. in millions of cubic meters

EXPLANATION

Lake surface area

Active lake storage

Figure 6. Lake stage area and live storage volume curves for Upper Klamath Lake. Active 

storage refers to the portion of the lake above the outlet control. There is also a dead storage 

volume below this elevation. Total storage in the lake is the sum of active and dead storage. 

MSL, mean sea level above Bureau of Reclamation datum.

Table 3. Regressions used to gap-fill Williamson River, Wood 

River, and Seven Mile Creek temperature records and their 

associated goodness of fit statistics. 

[Regressions only involve these three streams and ‘vs all’ indicates the 

use of two regressors. Original temperature measurements were in degrees 

Fahrenheit. Abbreviations: n, number of observations; σ ^ , standard error of 

regression, r 2, coefficient of determination]

Regression n 

σ r 2

Williamson vs all 290 1.5 0.93

Wood vs all 290 1.3 0.92

Seven vs all 290 3 0.85

Seven vs Wood 379 3.4 0.82

Williamson vs Wood 311 1.7 0.93
Methods of Study 23

To account for the ungaged flow into the lake, an 

approach was developed which centered on a simple 

mathematical model of the lake’s water budget. For this 

approach, we subtract the gaged inflow from estimates of the 

total outflow considering estimated evaporation and measured 

changes in lake volume to estimate the ungaged inflow for 

budget periods as shown in equation 16:

, ,

,

is estimated average

whe

ev

re

is the average outflow exiting the lake over a

budget period,

is the 

aporation lost to the

atmosphere from the la

average gaged i

ke surfa

nflo

ce,

out in g in un

out

in g

Q E VQ Q

Q

E

Q

+ +∆ − =

,

w entering the lake, 

 and

is the resulting estimation of average ungaged

inflow over a budget period.

Qin un

(16)

For this equation, the Jensen-Haise method described in 

Rosenberry and others (2007, table 1) is used to estimate 

evaporative rates, and these rates multiplied by lake surface 

area from the stage-area curve produce volumetric estimates 

of evaporation for a budget period. Changes in lake volume 

for a budget period are derived directly from the Bureau of 

Reclamation stage-volume curve.

With the ungaged inflow now estimated for budget 

periods, equation 15 requires a means to partition these 

flows to the various ungaged components that contribute 

to the lake. This is accomplished using the detailed water 

budget of Hubbard (1970) which includes measurements of 

inflow from all significant sources during a 3-year period 

from 1995 through 1997. Using Hubbard’s monthly values, 

mean monthly coefficients were calculated for the discharge 

of ungaged components to the lake. Coefficients for budget 

periods were then determined using weighted averages of 

mean monthly coefficients and the number of days of a 

particular month in a time period. Finally, the ungaged inflow 

of a budget period was multiplied by a stream’s budget period 

coefficient to yield that portion of the flow contributed to 

the lake by the stream. Sevenmile Creek temperatures were 

assigned to all ungaged components except groundwater, 

which was estimated at a constant temperature of 10°C for all 

budget periods.

Energy entering the lake by precipitation was based on 

Bureau of Reclamation precipitation gages and air temperature 

sensors at the AGKO and KFLO AgriMet sites, just to the 

north and south of the lake respectively. As with a previous 

study of the lake, the temperatures of precipitation at the two 

stations were assumed equal to the air temperatures at the 

AgriMet sites (Janssen, 2005). Temperatures and precipitation 

from the two stations were averaged in an attempt to represent 

mean conditions across the lake.

Advected energy exiting the lake is calculated based on 

the discharge of Link River, diversions through the A-Canal, 

and the temperature recorded at the Link River gage. The 

temperature of water diverted into the A-Canal is assumed 

equal to that of Link River.

Energy Transferred to Lakebed

Daily Qb is calculated by parameterization of heat flow 

and temperatures of water overlying the lakebed (Janssen, 

2005; Pearce and Gold, 1959):

 

2 2 sin

4

where

is the period of temperature variation 

 [365 days],

is the thermal diffusivity of the lakebed 

sediments, which is assumed equal to the 

value of gyttja soils presented 

b

t Q KA c

p p

p

π ππ   =   + +

α  

α

2 1

2

-1 -1

by Wetzel 

 and Likens (1991) [1.728 10 m d ,

is the thermal conductivity of the lakebed

sediment [0.75 Wm C ] as estimated 

by Sass and Sammel (1976),

is the amplitude of the water temperature

varia

K

A

− − ×

°

tion overlying the lakebed, in degrees

Celsius,

is the time, in days, beginning June 1st for a 

year of interest, and

is the phase offset, in radians, of the observed

temperature wave.

t

c

(17)

Amplitude (A) and phase (c) are estimated by means of a 

four-parameter sine wave of the form:

0

0

2 ( ) sin 365

where

( ) is the lake bottom temperat

is 

ure at time , a

the mean-annual lake bottom temperatu

n

r

d

e.

t Tb t Tb A c

Tb t t

Tb

  π

=+ +    

(18)

This is fitted by means of sinusoidal regression to the 

lake bottom temperature (fig. 7), based on the average of 

the temperatures measured 1 m above the lake bottom at 

water-quality stations MDN, EPT, SET, and MDT (fig. 1; 

T.M. Wood, U.S. Geological Survey, unpub. data). Janssen 

(2005) found no statistical difference between daily 

lake bottom temperatures and corresponding Link River 

temperatures. Therefore, if no records were available from any 

of the water-quality stations for a day or period of days, daily 

mean temperatures at the Link River were used.
24 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

tac12-0777_fig07

EXPLANATION

Lake bottom temperature

Fitted sine function

Temperature, in degrees Celsius Temperature, in degrees Celsius

0

5

10

15

20

25

0

5

10

15

20

25

A

B

Temperature, in degrees Celsius

0

5

10

15

20

25

May June July Aug.

2010

Sept. Oct. Nov. Dec. Jan. Feb. Mar.

2011

Apr.

May June July Aug.

2009

Sept. Oct. Nov. Dec. Jan. Feb. Mar.

2010

Apr.

May June July Aug.

2008

Sept. Oct. Nov. Dec. Jan. Feb. Mar.

2009

Apr.

C

Figure 7. Upper Klamath Lake bottom temperatures and fitted sine function used to parameterize 

amplitude (A) and phase (c) during A, 2008, B, 2009, and C, 2010.
Methods of Study 25

Changes in Energy Stored in the Lake

Changes in energy stored in the Upper Klamath Lake 

were estimated using the same well-mixed lake assumption 

that Janssen (2005) used for his study. This assumption 

is based on the findings of Wood and others (2006), who 

demonstrated that Upper Klamath Lake does not develop a 

strong thermocline due to its shallow depth. When thermal 

stability does develop, it typically disappears in less than a day 

(Wood and others, 2006). The following equation is used to 

estimate the changes in stored energy:

( )

where

is the total time of the budget period, in

seconds,

is the average temperature of the water

column, in degrees Celsius,

is the volume, in cubic meters, of the lake,

and

and ind

w w x ii f f

L

c Q TV T V A t

t

T

V

i f

ρ = −

icate the initial and final value of a budget

period, respectively.

(19)

Temperature data collected at the five temperature 

stations on the lake (fig. 1) 1 m below the water surface and 

1 m above the lake bottom were used to calculate an average 

water column temperature at that location. Average water 

column temperatures for a particular day were then averaged 

to estimate the mean temperature of the lake. Lake stage data 

from USGS gage 11507001 and storage volume, interpolated 

to nearest 0.01 ft (fig. 1), were used for calculations in 

equation 19. Dead storage of 2.61×108 m3 (211,300 acre-ft; 

from the station description for the above referenced 

gage) was added to the active storage term to yield total 

lake volume.

Bowen Ratio

The Bowen ratio (β in the denominator of equation 11) is 

the ratio of sensible heat to latent heat. It is calculated (Bowen, 

1926; Sturrock and others, 1992) as:

where

are the water surface and air 

temperatures respectively, in degrees 

C

 and 

 and are vapor pressures at the water surface

and air, respectively, in kilopascals, 

a

elsius

d

,

n

s a

s a

s

s a

T T

e e

T T

e e

  − β=γ     −

γ is the psychometric constant, in 

kilopascals per degree Celsius.

(20)

The psychometric constant is a function of the specific 

heat of air ca [1.00416 J kg-1 °C], atmospheric pressure 

P [kPa] and the latent heat of vaporization λv (Janssen, 2005; 

Dingman, 2002):

0.622

a

v

c P

γ = λ

(21)

The latent heat of vaporization [J kg-1] is a function of 

surface temperature and can be approximated by (Janssen, 

2005; Dingman, 2002):

6 3 2.49 10 2.36 10 λ= × − × v s T (22)

Atmospheric pressure was estimated by (Janssen, 2005; 

Shuttleworth, 1993):

5.256

where

is lake stage altitude, in meters (US

293 0.0065 101.3

GS station

stat

3

i

293

on 11507001).

z P

z

  − =     (23)

Vapor pressure of the air is estimated as:

17.3

237.3 ×0.611

a

a

T

T

ae RH e + = (24)

where RH is the relative humidity [dimensionless] and the rest 

of the right-hand side is the saturated vapor pressure of the air 

[kPa] which is a function of air temperature (Janssen, 2005; 

Dingman, 2002). Similarly, the vapor pressure at the water 

surface can be calculated as:

17.3

237.3 0.611

s

s

T

s

T

e e + = (25)

As can be seen from equations 24 and 25, the vapor 

pressure at the surface is saturated and a function of water 

surface temperature.

One Bowen-ratio value was calculated for each 2-week 

energy budget period using air and water surface temperatures 

and vapor pressures (eq. 20) averaged over the period.
26 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

Determination of Reference Evapotranspiration 

and Crop Coefficients

Potential evapotranspiration (ETp) is the ET that occurs 

from an extensive land or water surface under a given set of 

meteorological conditions when the surface is well supplied 

with water. In the most general interpretation, the concept 

applies to a wide range of land-surface types, from dense 

rainforests to bare soil. Because vegetation type, density, 

and vigor have a strong effect on the resulting ETp, the 

need gradually arose for a more specific quantity—one that 

assumes a standard vegetation type and density, growing 

vigorously, and therefore depends only on weather conditions. 

Penman (1948) suggested dense grass cover as the reference 

vegetation, although other crops (and open water) have been 

suggested over the years. Computation of ETp for a specific 

reference crop led to the adoption of the notation ETr to refer 

to potential ET from a reference crop. During the late 20th 

century, the Food and Agricultural Organization (FAO) of the 

United Nations took the lead in standardizing the computation 

of ETr

, most recently through the work of Allen and others 

(1998), who presented the Penman-Monteith equation 

in a user-friendly form, for use with a 12-cm tall, dense 

grass reference crop. Using this methodology, ET for other 

well-watered crops is computed as the product of ETr and a 

crop coefficient, Kc, which varies based on growth stage of 

the crop:

ET K ET = ×c r (26)

Subsequently, the American Society of Civil Engineers 

modified the FAO equation to also accommodate alfalfa as 

a reference crop (Allen and others, 2005). The Bureau of 

Reclamation maintains a network of weather stations in the 

Pacific Northwest region states that can be used to calculate 

ET and crop ET using the Allen and others (2005) alfalfa (tall 

crop) equation. Daily values of ET and crop ET are posted on 

the Bureau of Reclamation Web site (http://www.usbr.gov/pn/

agrimet/h2ouse.html) in near real time, for use by irrigators 

and others.

In the current study, we divide measured values of ET

from the two wetland sites by posted values of tall crop ETr 

calculated from nearby weather station data to compute daily 

and biweekly values of Kc. Daily values of ETr are obtained 

from the Agency Lake (AGKO) weather station, located 

about 7.1 km northeast of the bulrush site. When daily values 

of ETr are equal to 0, Kc is infinite, and we arbitrarily set Kc

to a value of 6. Daily values of ET and ETr are aggregated 

into biweekly values to compute biweekly values of Kc. To 

investigate relations between Kc and precipitation, daily 

values of precipitation were retrieved from the Klamath Falls 

(KFLO) weather station, located about 44 km southeast of the 

bulrush site, in Klamath Falls, Oregon. This station deploys 

a weighing precipitation gage, which measures snowfall 

more reliably than the unheated tipping bucket gage at the 

(closer) AGKO station. Growing-season ET data from alfalfa 

and pasture also were retrieved from the KFLO station for 

comparison with measured wetland ET. These ET values were 

not available from the AGKO station Web site.

Evapotranspiration Results from 

Bulrush and Mixed Vegetation Sites

Site Conditions Affecting Evapotranspiration

Peak vegetation heights typically were 1.9 to 2.3 m above 

land surface (fig. 8). Near-peak heights usually occurred from 

early July to early October, forming somewhat of a plateau 

of canopy height during the heart of the growing season. 

The bulrush and cattail typically senesce in late September, 

turning from green to brown, and then lodge over in October 

and November in response to wind and snow loading. The 

bent-over plants merge with and are supported by plants from 

previous years, creating a loosely woven mat of dead plants 

roughly 0.5 to 1 m in height, which becomes the understory 

of the next year’s live canopy (fig. 8). In the spring, new 

shoots sprout from the soil, up through the water column and 

understory, until they emerge into the open space above. Upon 

emergence, the plants grow rapidly to their peak height.

Water level typically fluctuates about 1.3 m annually 

in response to inflows and controlled outflow at the dam, 

resulting in water levels that vary both above and below land 

surface at both sites at times of the year (fig. 8). Minimum 

water levels usually occur in October, and maximum water 

levels occur from April through June. During the study period, 

maximum water level at the bulrush site was 0.89 m above 

land surface, and minimum water level was -0.63 m. Land 

surface is 0.15 m higher at the mixed site than at the bulrush 

site, so maximum and minimum water levels at this site were 

0.15 m lower (fig. 8). During 2008 to 2010, the hydroperiods 

ranged from 7.2 to 5.2 months and from 5.9 to 3.5 months 

at the bulrush and mixed sites, respectively. Minimum 

hydroperiods occurred in 2010 due to unusually low water 

levels, and hydroperiods were substantially shorter than in 

2008 and 2009.
Evapotranspiration Results from Bulrush and Mixed Vegetation Sites 27

Figure 8. Vegetation height, water level, and soil water content at bulrush site during A, 2008, B, 2009, and C, 2010, and at 

mixed site during D, 2008, E, 2009, and F, 2010.

tac12-0777_fig08a-b

−1

0

1

2

Jan. Feb. Mar. Apr. May. Aug. Sept. Oct. Nov. Dec.

−1

0

1

2

EXPLANATION

Measured vegetation height

Estimated vegetation height

Water level

Soil water content

A. Bulrush site, 2008

B. Bulrush site, 2009

June July

Measured vegetation height, in meters

Water level, in meters

Soil water content, in cubic meters per cubic meter
28 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

EXPLANATION

Measured vegetation height

Estimated vegetation height

Water level

Soil water content

C. Bulrush site, 2010

−1

0

1

2

−1

0

1

2

Jan. Feb. Mar. Apr. May Aug. Sept. Oct. Nov. Dec.

D. Mixed site, 2008

June July

Measured vegetation height, in meters

Water level, in meters

Soil water content, in cubic meters per cubic meter

Figure 8.—Continued
Evapotranspiration Results from Bulrush and Mixed Vegetation Sites 29

Measured vegetation height

EXPLANATION

Estimated vegetation height

Water level

Soil water content

E. Mixed site, 2009

F. Mixed site, 2010

−1

0

1

2

−1

0

1

2

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

Measured vegetation height, in meters

Water level, in meters

Soil water content, in cubic meters per cubic meter

Figure 8.—Continued
30 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

Soil water content (θ; fig. 8) was measured using a 30-cm 

long time-domain reflectometer (TDR) installed vertically in 

the soil, which sensed the mean θ from the surface to a depth 

of 30 cm. The TDR probe was not specifically calibrated for 

this soil, so the absolute readings are approximate although 

differences should be qualitatively correct. At both sites, the 

probe was installed in mid-August 2008, about when the 

water level had receded to the land surface. During most 

of the study period, θ at the bulrush site was very steady at 

about 0.82 to 0.9 m3 m-3, a value typical of saturated peat 

(Schedlbauer and others, 2011). During the coldest part of 

both winter periods, the apparent value dropped below this 

range (fig. 8), but this was very likely an artifact of freezing 

temperatures over at least part of the TDR measurement depth 

interval. The TDR responds to the dielectric constant of the 

surrounding (moist) medium, and the dielectric constant of 

ice is about 4 percent that of liquid water. The low readings 

probably were not caused by conditions of partial saturation 

because similarly low readings did not occur at the times 

of minimum water levels each year when partial saturation 

would be most expected (fig. 8). The apparently saturated soil 

(θ=0.85) during the time of minimum water level (-0.63 m) 

in October 2009 suggests that the capillary fringe of the peat 

soil at this site is at least 0.63 m, an unusually high value. In 

contrast, the TDR probe at the mixed site appeared to indicate 

partial dewatering during all 3 years, beginning in August, 

when water level dropped below about 0.2 m below land 

surface (figs. 8D–F). Freezing soil water could not have been a 

factor at this time of year, and the declines in θ mirror declines 

in water level, suggesting a valid instrumental response and a 

more normal capillary fringe height of less than about 0.2 m. 

Soils were not sampled at the two sites, but these substantially 

different estimates of capillary-fringe height suggest that the 

soils differ greatly in mean particle size. In addition, while the 

saturated soil at the bulrush site indicates that the vegetation 

there was never stressed, the decrease in θ at the mixed site 

to values around 0.5 in September (figs. 8D–F) suggests that 

vegetation there may have experienced mild water stress 

toward the end of the growing season each year.

Source Areas and Fetch Considerations of 

Wetland Evapotranspiration Sites

A source-area model (Schuepp and others, 1990) was 

used to estimate the degree to which measured fluxes represent 

fluxes from the wetland surfaces (surfaces of interest) and to 

what extent they are affected (contaminated) by fluxes from 

the upwind open-water or other surfaces. Sensors used in the 

EC method must be placed at least 1.5 times the vegetation 

canopy height above the land (or water) surface to avoid 

measurement artifacts from underlying heterogeneities. 

Consequently, air passing by the EC sensors comes from 

upwind and, therefore, contains attributes (w, Ta, ρv) that 

correspond to fluxes from upwind surfaces. The source-area 

model describes the relative contributions to the measured flux 

signal from upwind surfaces as a function of upwind distance. 

The union of all contributing surfaces is known as the source 

area. The distance to the farthest upwind extent of uniform 

surface of interest is called the fetch.

At both wetland sites, sensor height, canopy height, and 

fetch were used to determine the percentage of the measured 

flux signal originating from the wetland surface. In this 

context, sensor and canopy heights refer to height above land 

surface or height above water surface if standing water is 

present. Canopy height measured at each site was assumed 

to be representative of the whole source area. Source areas 

are smallest in unstable conditions (H > 0, typically occur 

during daytime), somewhat larger in neutral conditions (H ≈ 0, 

typically occur in heavy overcast, high winds, or near sunrise 

and sunset), and largest in stable conditions (H < 0, typically 

occur during nighttime). Neutral conditions were assumed for 

these calculations to produce the most conservative (largest) 

daytime source areas. Nighttime (stable) conditions were 

not evaluated because very little ET occurs at night. Source 

areas also vary in size depending on the canopy roughness 

length (zm) and displacement height (d). The values of zm and 

d were calculated as 0.1 h and 0.65 h, respectively, where h is 

canopy height in meters (Campbell and Norman, 1998, p. 71). 

In general, source area decreases with increasing canopy 

height. At each site, the source-area model is used to compute 

the percentage of the measured flux signal originating from 

within the wetland in the minimum fetch direction and in 

the predominant wind directions for both the minimum and 

maximum source areas occurring during the study. From these 

bounding and predominant conditions, estimates are made of 

the mean percentage of flux signal originating from within 

the wetland.

Minimum fetch at the bulrush site was 2.0 km at 

azimuths of 360° and 180° (due north and due south, fig. 1). 

Maximum source area occurred during the first day of 

data collection (May 1, 2008) when canopy height (h) was 

0.20 m above 0.80 m of standing water (fig. 8A). For these 

conditions, the source-area model indicated that 96.6 percent 

of the flux signal was contained within 2.0 km of the station. 

Near-maximum source areas typically occurred during the 

winter, when canopy height was low. The minimum source 

area occurred at maximum canopy height (2.3 m), typically 

in summer and early fall (figs. 8A–C). In these conditions, 

99.0 percent of the flux signal was contained within 2.0 km 

of the station. Predominant daytime wind directions (both 

during the growing season and year-round) were 305°, 360°, 

and 135°, in decreasing order. Fetches in the 305° and 135° 

directions were 5.1 and 3.0 km (fig. 1), affording 98.6 and 

97.7 percent containment of the maximum source area flux 

signal, and 99.6 and 99.3 percent containment of the minimum 

source area flux signal, respectively. Considering the range 

and likely prevalence of these containment values, the mean 

time-weighted containment of the flux signal by dense wetland 

bulrush is estimated to be about 98 to 99 percent.
Evapotranspiration Results from Bulrush and Mixed Vegetation Sites 31

Minimum fetches at the mixed site were about 0.97 km 

at 90° (or due east) and 1.03 km at 240° (fig. 1) and these 

azimuths also corresponded to the two equally predominant 

wind directions. Minimum fetch is, therefore, estimated 

as the average of these two, or 1.0 km. Maximum source 

area occurred during the first day of data collection (May 1, 

2008) when canopy height (h) was 0.20 m above 0.65 m 

of standing water (fig. 8D). Near-maximum source areas 

typically occurred during the winter, when canopy height was 

low. For these conditions, the source-area model indicated 

that 92.4 percent of the flux signal was contained within 

1.0 km of the station. The minimum source area occurred 

at maximum canopy height (2.30 m; figs. 8D–E). In these 

conditions, 97.8 percent of the source area was within 1.0 km 

of the station. During average growing season conditions, 

95.6 percent of the source area was within 1.0 km of the 

station. In addition, wind directions that afforded 1.5 km or 

more of fetch occurred during about 23 percent of the growing 

season, which provided 97.0 percent or greater containment of 

the source area. Considering the range and likely prevalence 

of these containment values, the mean time-weighted 

containment of the source area by dense wetland mixed 

vegetation is estimated to be about 95 to 96 percent.

The above estimates of flux-signal containment by 

the bulrush and mixed vegetation types indicate that the 

measured fluxes overwhelmingly originated from the surfaces 

of interest—and not from other, dissimilar surfaces farther 

upwind. In addition, the surfaces upwind of the study sites 

in the minimum-fetch directions consisted of open water at 

the mixed site and open water to the south or intermittently 

flooded wetland to the north at the bulrush site. The 

hydroperiod of the wetland to the north was similar to that of 

the bulrush site. During the growing season, ET from these 

surfaces is roughly equal to ET from the surfaces of interest, 

and therefore would have an insignificant effect on measured 

ET. The greatest potential for contrast in ET occurs in the 

fall and early winter, when the wetland vegetation is dormant 

and standing water (from rising lake level) is not yet present 

at the study sites. If the adjacent lake surface is unfrozen 

during this time, it would slightly inflate the measured ET at 

the sites. However, because the measured winter-time ET is 

about 10 percent of its annual mean value and the lake surface 

was frozen during part of this time, the net effect on the 

annual mean is very small. In summary, contamination of the 

measured ET from surfaces surrounding the wetland surfaces 

of interest is very small and probably much smaller than the 

inherent accuracy of the EC method.

Energy-Balance Closure and Trends

A single value of EBR was used to correct Hm and LEm

in this report to avoid the occurrence of unrealistic EBR

values that can occur over shorter time periods. Correction 

on a 30-minute, daily, or biweekly basis is problematic 

because the smaller signal-to-noise ratio can produce very 

large or small values of EBR at times when TF and AE are 

small (near sunrise, sunset, and at night for 30-minute values, 

during overcast winter periods for daily and biweekly values), 

potentially producing unreliable final values of H and LE. 

For example, if EBR is small and values of Hm and LEm are 

of similar magnitude and of opposite sign, they will both be 

inflated to very large numbers; and if Hm exactly equals –LEm, 

division by zero will occur. To compare the use of a single 

EBR with shorter-period EBR, a biweekly EBR value was 

computed, and is shown along with biweekly AE, uncorrected 

TF, and the mean EBR at the bulrush site in figure 9. Biweekly 

EBR is relatively constant during the high-flux time of year: 

March 1 to October 31. During this time, biweekly EBR

ranges from 16 percent greater than, to 12 percent smaller 

than the mean EBR (equal to 0.730), and averages 0.753, or 

3.2 percent greater than the mean EBR. This high-flux EBR

follows a subtle but consistent pattern from year to year, 

resembling the letter m, with maxima around mid-May and 

early September, and minima around mid-March, early July, 

and late October.

During low-flux times of the year, biweekly EBR is more 

variable, unpredictable, and tends to be smaller than the mean 

EBR (fig. 9). Over half are smaller than 60 percent, and one 

value drops as low as -332 percent in December, 2008, when 

AE > 0 and TF < 0. In addition, inter-annual variability is 

much greater than during high-flux times. The unpredictable 

and large variation of EBR during low-flux times probably 

is caused by a low signal-to-noise ratio in the AE and TF

measurements, because those fluxes are small; less than 

70 W m-2, and averaging around 32 W m-2. Because the low 

signal-to-noise ratio creates somewhat random variations in 

EBR, biweekly correction of TF to satisfy these EBR values is 

considered questionable.

The m pattern evident during the high-flux times extends 

into the low-flux times, although with less definition and 

more variability. The reason for this pattern was investigated 

using graphical and regression analyses, but no significant 

relations to other variables were found. The value of EBR

has frequently been related to friction velocity, u*=(τ/ρa)0.5, 

citing reduced turbulence at low wind speeds as a cause of 

low EBR (for example, Wilson and others, 2002; Aubinet and 

others, 2012, ). However, EBR is virtually unrelated to u* in 

this study. Using all biweekly data, EBR is not significantly 

related to u* (r=-0.318, a negative correlation, opposite to that 

observed elsewhere, and p=0.21). After removing the outlier 

point at EBR=-332 percent, r equals 0.187, and p equals 0.14, 

still an insignificant relation. All biweekly EBR results for the 

mixed site (data not shown) are very similar to those for the 

bulrush site.

Considering the relatively small errors incurred during 

the high-flux times by the use of a single, mean EBR, and 

the difficulty and questionable validity of using a biweekly 

EBR during low-flux times, a single, mean value of EBR was 

chosen to correct the TF in this study. Although ET computed 

this way may be slightly overestimated or underestimated at 

times compared to the use of a biweekly EBR, the study-period 

averages are identical.
32 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

Values of EBR also were computed for six different but 

overlapping full 2-year periods during the study to explore 

whether the EBR calculated for the whole study period 

(2.41 years) was representative of an annual average value. 

The first 2-year period began on the first day of the study, 

and each subsequent 2-year period began 4 weeks later the 

preceding one. The EBRs of the six 2-year periods varied by 

less than ± 1 percent, and the means were within 0.25 percent 

of the full-study period EBR at both sites (data not shown), 

indicating that the full-study period EBR adequately 

approximated the annual EBR, and the annual EBR was 

relatively constant during the study period.

Eddy-covariance sensors functioned correctly during 

84 percent of the study period (table 4), substantially better 

than in higher rainfall locations such as Florida, where 

EC sensors were operational only 51 percent of the time 

during a recent study (Schedlbauer and others, 2011). The 

energy-balance ratio (EBR) was calculated from equation 8 

using only data collected when all energy-balance sensors 

functioned correctly, constituting 63.0 and 70.8 percent of 

the study period at the bulrush and mixed sites, respectively 

(table 4). The EBRs of 0.730 and 0.781 at the bulrush and 

mixed sites, respectively, are slightly below the mean observed 

EBR of about 0.8 (Twine and others, 2000; Wilson and others, 

2002; Foken, 2008), but are well within the range typically 

seen in many studies (Dugas and others, 1991; McCaughey 

and others, 1997; Twine and others, 2000; Mauder and 

others, 2006; Foken, 2008). Measured values of turbulent 

flux (Hm and LEm) were divided by these ratios to obtain 

final values, designated as H and LE. Regressions between 

 −332

percent

−20

−350 −350

0

50

100

150

200

250

300

−20

0

50

100

150

200

250

300

Biweekly energy flux, in watts per square meter

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

Energy balance ratio, in percent

Available energy

EXPLANATION

Uncorrected turbulent flux

Energy balance ratio

Mean energy balance ratio

Figure 9. Biweekly means of available energy, turbulent flux, and energy-balance ratio (EBR) at the bulrush site during the 

study period. Also shown is the mean study-period EBR, equal to 73.0 percent.
Evapotranspiration Results from Bulrush and Mixed Vegetation Sites 33

Table 4. Percentage of time eddy covariance sensors operating (%TimeEC), percentage of time all energy-balance sensors operating 

(%TimeALL), energy-balance ratio (EBR), root-mean-squared error between 30-minute available energy and adjusted turbulent flux 

(RMSE), and coefficient of determination (r 2

) of 30-minute, daily, and biweekly means of available energy and turbulent flux. 

[Only data collected when all energy-balance sensors functioned correctly were used to compute 30-minute r 2, whereas daily and biweekly r 2 values also 

include gap-filled data. Abbreviation: W m-2, watts per square meter]

Site %TimeEC %TimeALL EBR RMSE

(W m-2) 30-minute r 

2 Daily r 2 Biweekly r 2

Bulrush 84.2 63.0 0.730 71.9 0.878 0.928 0.973

Mixed 84.4 70.8 0.781 63.7 0.905 0.959 0.981

30-minute available energy and final turbulent flux yielded 

RMSEs of 71.9 and 63.7 W m-2 which, when compared to a 

range in available energy of about 1000 W m-2, resulted in 

reasonably large r 2 values of 0.878 and 0.905 (table 4). Daily 

and biweekly r 2 values (using both measured and gap-filled 

data) increased substantially (table 4), illustrating that much 

of the error in 30-minute energy-balance data is random, and 

decreases over longer periods.

Daily values of the main energy-balance components (Rn, 

H, and LE) are shown in figure 10. G is not shown because 

the daily mean value (0.9 W m-2) and standard deviation 

(17 W m-2) are both quite small and G contributes little to the 

seasonal changes in energy-balance partitioning. A high degree 

of correlation can be seen between equivalent fluxes at the 

two sites, substantiating the field measurements, which were 

made independently of each other. The upper envelope of Rn

corresponds to clear skies and displays the usual sinusoidal 

shape, with intermittent excursions downward caused by the 

occurrence of clouds. Occasionally, Rn exceeds the upper 

envelope sine curve when clouds are near, but not obscuring, 

the direct solar beam arriving at the site. These clouds can 

forward-scatter short-wave radiation (Monteith and Unsworth, 

1990), raising Rn above clear-sky values.

The available energy delivered to the surface is 

partitioned between H and LE, and this partitioning varies 

considerably during the year as the wetland progresses through 

its annual life cycle (fig. 10). Partitioning is described in terms 

of the ratio of H to LE, known as the Bowen (1924) ratio, β. 

At the beginning of the year, the vegetation canopy is dormant 

and water level is below land surface. The loosely woven 

mat of dead stalks forms a complex surface, at times partially 

covered with snow and ice and partially bare, and at other 

times entirely bare. Snow and ice-covered surfaces contribute 

to LE, whereas bare stalks contribute to H. On average, H

and LE are roughly equal during winter (β ≈ 1), alternating 

positions of dominance as precipitation coats the surfaces, then 

is redistributed and removed by evaporation and sublimation 

(fig. 10). During March, April, and early May, water level 

rises but is mostly shaded by the mat of dead stalks, and 

therefore has a minor effect on the equal partitioning. Both H

and LE steadily grow in response to increasing Rn. The new 

vegetation begins to emerge from the dead stalk mat in May or 

June (fig. 8), which begins to shift the partitioning toward LE, 

reducing β (fig. 10). By mid-June, H begins to decrease (even 

though Rn is still approaching peak values) due to increased 

transpiration from the vigorously growing canopy. This shift 

toward greater LE was somewhat delayed in 2010, a year 

of unusually low water levels early in the growing season. 

Because ample root-zone water was available for transpiration 

during this time, a possible alternate mechanism for the 

delay in 2010 is discussed in Daily Evapotranspiration and 

Crop Coefficients.

By midsummer, energy is partitioned overwhelmingly 

to LE (fig. 10), with typical daily values of β near 0.26 

(bulrush site) and 0.13 (mixed site). This wholesale shift over 

to LE at the expense of H is largely a result of transpiration 

by the growing or mature vegetation, creating an obvious 

gulf between H and LE values in the energy-balance graphs 

(fig. 10). The tendency toward even lower β at the mixed 

site is somewhat unexpected, given the shallower water 

levels there, and suggests either greater partitioning toward 

LE by cattail and wocus transpiration at that site, or toward 

evaporation from areas of open shallow water associated with 

the wocus.

In early September, plants begin to senesce and turn 

brown, initiating a shift back toward equal partitioning 

between H and LE. During this time, H actually increases 

even though Rn rapidly decreases (fig. 10). During most of 

October, H is substantially greater than LE (β ≈ 2) primarily 

because October is dry (precipitation is discussed in Daily 

Evapotranspiration and Crop Coefficients) and above freezing. 

Therefore, what little precipitation falls is rainfall, which 

penetrates through the mostly vertical stalks to the lower 

stalk mat and the soil, where it is effectively decoupled from 

Rn and the overlying atmosphere. During November and 

December, the dead canopy lodges over, making a more 

supportive surface for the substantial snowfall during those 

months and providing a better exposure of the snow to Rn. As 

a result, β again approaches 1, which persists for the rest of the 

winter months.
34 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

tac12-0777_fig10a-b

−100

−50

0

50

100

150

200

250

300

Daily average energy flux, in watts per square meter

−50

0

50

100

150

200

250

300

Daily average energy flux, in watts per square meter

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

Net radiation

EXPLANATION

Sensible-heat flux

Latent-heat flux

A. Bulrush site, 2008

B. Bulrush site, 2009

Figure 10. Daily means of net radiation, sensible-heat flux, and latent-heat flux at bulrush site during A, 2008, B, 2009, and 

C, 2010, and at mixed site during D, 2008, E, 2009, and F, 2010.
Evapotranspiration Results from Bulrush and Mixed Vegetation Sites 35

−100

−50

0

50

100

150

200

250

300

−100

−50

0

50

100

150

200

250

300

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

Daily average energy flux, in watts per square meter Daily average energy flux, in watts per square meter

EXPLANATION

C. Bulrush site, 2010

D. Mixed site, 2008

Net radiation

Sensible-heat flux

Latent-heat flux

Figure 10.—Continued
36 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

tac12-0777_fig10e-f

−100

−50

0

50

100

150

200

250

300

Daily average energy flux, in watts per square meter

−100

−50

0

50

100

150

200

250

300

Daily average energy flux, in watts per square meter

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

E. Mixed site, 2009

EXPLANATION

F. Mixed site, 2010

Net radiation

Sensible-heat flux

Latent-heat flux

Figure 10.—Continued
Evapotranspiration Results from Bulrush and Mixed Vegetation Sites 37

Daily Evapotranspiration and Crop Coefficients

Daily values of ET and ETr at both wetland sites during 

the study period (May 1, 2008, to September 29, 2010) are 

shown in figure 11. This study period brackets three growing 

seasons, from 2008 to 2010. A generally sinusoidal pattern 

in ET and ETr can be seen during all 3 years, superimposed 

with daily variations above and below the mean pattern. The 

mean sinusoidal pattern is largely determined by the Rn input 

(fig. 10), modified somewhat by water level and vegetation 

properties, discussed in this section, below. The daily 

variations are also closely related to variations in Rn (fig. 10), 

and to precipitation, discussed in this section, below. A high 

degree of correlation can be seen between bulrush and mixed 

site ET, and between ETr and ET at both sites. Both short term 

(daily) and longer term (weekly to monthly) variations in ETr

are reflected in the measured ET at both sites. On a daily basis, 

ET and ETr

 alternate relative magnitudes to some degree, 

although on average ETr > ET. Periods when ET is noticeably 

less than ETr tend to be in the spring (May 2008; parts of 

April and May 2009; and parts of March, April, May, and 

June 2010) and fall (most of September and October 2008; late 

August through early October 2009; and parts of September 

2010). During much of winter and late summer, ET is often 

indistinguishable from ETr at the daily time step shown 

in figure 11.

Daily values of Kc at both wetland sites and precipitation 

(P) at the Klamath Falls weather station (KFLO) during the 

study period are shown in figure 12. The KFLO record is 

only an approximate indicator of timing and amount of P at 

the Upper Klamath NWR because the KFLO station is 44 km 

from the study sites. The most obvious feature in these plots 

is that daily Kc is generally predictable and well behaved from 

June through September, whereas Kc is quite variable (noisy) 

the rest of the year. The noisy periods consist of somewhat 

sustained intervals when Kc is generally small, punctuated 

with short-lived spikes in Kc, usually during and just after 

days of P (this relation between Kc and P is only approximate 

because of the distant KFLO location). This seasonal 

dependence of Kc variability is caused by (1) the seasonal 

change in the magnitude of ETr; (2) the seasonal change in 

the amount and frequency of P; and (3) the seasonal change 

in sensitivity of canopy energy partitioning to inputs of P. 

During the growing season, larger ETr provides a more stable 

denominator in the calculation of Kc (Kc=ET/ETr), whereas 

measurement and modeling uncertainty in ETr has a greater 

proportional effect on Kc when fluxes are small, during the 

non-growing season. Coincidentally, very little P falls between 

mid-June and the end of September, but P is instead heavily 

skewed toward the winter months. Therefore, the potential 

for Kc to spike in response to P intercepted by the canopy 

occurs more frequently during the non-growing season. Lastly, 

interception has little effect on energy partitioning during the 

growing season, because (1) transpiration is already large, 

nearly satisfying the atmospheric demand; and (2) the live 

leaves are nearly vertical, shunting the water to lower canopy 

layers where it is less available for evaporation.

During the non-growing season, the bent over, more 

nearly horizontal leaves intercept more rain and snow and 

provide better exposure of the intercepted water to incoming 

radiation and better aerodynamic transport back to the 

atmosphere. This process shifts energy partitioning away 

from H toward LE, causing Kc to spike. For example, note 

the subdued response of Kc to P of 3 mm or more during the 

growing season on August 6, 2008, June 15 and 30, 2009, 

August 6-7, 2009, and July 25, 2010. In contrast, when the 

canopy is dormant, interception greatly enhances the ET rate, 

causing Kc to spike to values well above 1 for short periods, 

while the intercepted water evaporates (numerous examples 

in fig. 12). A reasonable correlation can be seen between the 

magnitude of daily P (measured at KFLO) and Kc during the 

non-growing season (fig. 12).

Daily values of Kc greater than about 2 require some 

explanation, considering the proximity of the study sites to 

the AGKO weather station (and the concomitant similarity in 

weather), and the high degree of water availability occurring 

at the study sites and assumed in the computation of ETr using 

AGKO data. At the bulrush site, all days of Kc >2 (n=45) 

occurred either before May 6 or after October 3. At the mixed 

site, all days of Kc > 2 (n=32) occurred either before May 11 

or after November 5. These periods correspond to times 

before the emergence of new growth from the dead canopy 

litter layer in the spring, or after senescence in the fall (that 

is, roughly during the non-growing season). Probably the 

main cause of high Kc values is the assumption of a 45 s m-1

surface resistance in the computation of ETr. During or just 

after precipitation, when the surface is wet, the actual surface 

resistance approaches zero. During the non-growing season, 

when the canopy is lodged over, the nearly horizontal leaf 

surfaces retain precipitation longer, sustaining high ET rates 

for one to a few days, depending on the amount of interception 

and the ensuing atmospheric demand. Once the canopy dries 

out, Kc typically returns to values well below one, reflecting 

dormancy and the lack of transpiration. This mechanism 

probably is compounded by a low signal-to-noise ratio in 

measured wetland ET and in computed ETr, which are both 

relatively small at this time of year. Although Kc appears to 

be rather intractable during the non-growing season, its value 

is relatively unimportant because little ET occurs during this 

time. In addition, aggregation into biweekly periods reduces 

noise through averaging, as seen in the next section, Biweekly 

Evapotranspiration and Crop Coefficients.
38 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

tac12-0777_fig11a-b Evapotranspiration, in millimeters per day

−1

0

1

2

3

4

5

6

7

8

9

10

Evapotranspiration, in millimeters per day

−1

0

1

2

3

4

5

6

7

8

9

10

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

Reference evapotransporation

EXPLANATION

Measured evapotransporation

A. Bulrush site, 2008

B. Bulrush site, 2009

Figure 11. Daily reference evapotranspiration and measured evapotranspiration at bulrush site during A, 2008, B, 2009, 

and C, 2010, and at mixed site during D, 2008, E, 2009, and F, 2010.
Evapotranspiration Results from Bulrush and Mixed Vegetation Sites 39

tac12-0777_fig11c-d Evapotranspiration, in millimeters per day

−1

0

1

2

3

4

5

6

7

8

9

10

Evapotranspiration, in millimeters per day

−1

0

1

2

3

4

5

6

7

8

9

10

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

Reference evapotransporation

EXPLANATION

Measured evapotransporation

C. Bulrush site, 2010

D. Mixed site, 2008

Figure 11.—Continued
40 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

tac12-0777_fig11e-f Evapotranspiration, in millimeters per day

−1

0

1

2

3

4

5

6

7

8

9

10

Evapotranspiration, in millimeters per day

−1

0

1

2

3

4

5

6

7

8

9

10

Jan. Feb. Mar. Apr. May Aug. Sept. Oct. Nov. Dec.

Reference evapotransporation

EXPLANATION

Measured evapotransporation

E. Mixed site, 2009

F. Mixed site, 2010

June July

Figure 11.—Continued
Evapotranspiration Results from Bulrush and Mixed Vegetation Sites 41

−1

0

1

2

3

4

5

6

Jan. Feb. Mar. Apr. June July Aug. Sept. Oct. Nov. Dec.

Daily crop coefficient, unitless, and precipitation, in centimeters Daily crop coefficient, unitless, and precipitation, in centimeters

May

−1

0

1

2

3

4

5

6

B. Bulrush site, 2009

Crop coefficient (Kc)

EXPLANATION

Precipitation

A. Bullrush site, 2008

Figure 12. Daily crop coefficient at bulrush site during A, 2008, B, 2009, and C, 2010, and at mixed site during D, 2008, E, 

2009, and F, 2010, and precipitation measured at Klamath Falls AgriMet station.
42 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

−1

0

1

2

3

4

5

6

−1

0

1

2

3

4

5

6

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

Crop coefficient (Kc)

EXPLANATION

Precipitation

C. Bulrush site, 2010

D. Mixed site, 2008

Daily crop coefficient, unitless, and precipitation, in centimeters Daily crop coefficient, unitless, and precipitation, in centimeters

Figure 12.—Continued
Evapotranspiration Results from Bulrush and Mixed Vegetation Sites 43

−1

0

1

2

3

4

5

6

−1

0

1

2

3

4

5

6

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

Daily crop coefficient, unitless, and precipitation, in centimeters Daily crop coefficient, unitless, and precipitation, in centimeters

Crop coefficient (Kc)

EXPLANATION

Precipitation

E. Mixed site, 2009

F. Mixed site, 2010

Figure 12.—Continued
44 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

An expanded view of daily Kc during the 

growing season of all 3 years is shown in figure 13. 

During the middle of the growing season, daily 

Kc follows a simple pattern rather consistently 

from year to year. From mid-June through 

mid-September, Kc is relatively well behaved and 

follows a concave-downward curve. Although the 

canopy begins growing in early May, Kc values 

in May and early June are still somewhat noisy 

because the new growth has not fully emerged 

from the dead stalk mat and interception causes 

spikes in Kc. During late September, canopy 

senescence has progressed sufficiently that 

interception again begins to cause spikes in Kc. 

A base value of Kc (analogous to base flow in a 

stream) can be established during these periods, 

using the lowest values as a guide to estimate 

dry-canopy Kc. Combining this base value with 

the mean behavior during the middle of the season 

leads to simple piecewise linear descriptions of Kc

at both sites—as shown in figure 13 and quantified 

in table 5, that approximate the concave-downward 

curves. These piecewise linear approximations 

were determined by eye (visual examination). 

Based on spikes occurring from May 1 through about June 20, 

and after about September 15, a suggested value of Kc=1.5 

could be used on days of rainfall >3 mm during these periods 

(superseding the piecewise calculation), or on days following 

rainfall, if the rainfall occurs in the afternoon or evening.

This modeling scheme of daily Kc and ET was tested by 

assuming that all precipitation recorded at the KFLO AgriMet 

station occurred early in the day, triggering the specified 

value of Kc=1.5 on the day of precipitation. A comparison 

of modeled and measured ET is shown in figure 14, and 

associated statistics are presented in table 6. These models are 

only marginally successful, as indicated by large scatter about 

the one-to-one line (fig. 14), small slope, r 2, and coefficient 

of efficiency (CE) values, and large intercept and RMSE

values (table 6). The CE is similar to r 2, except it ranges 

from 1 to -∞, is more rigorous, and requires equality as well 

as correlation between two variables to approach 1 (Nash 

Table 5. Piecewise linear expressions of crop coefficient (Kc) at both 

study sites during the growing season.

[Abbreviation: DOY, day of year]

Site Period Equation

Bulrush May 1–June 6

DOY 121–157

Kc

 = 0.65

June 7–July 31

DOY 158–212

Kc

 = 0.65 + 0.007407×(DOY-158)

August 1–August 23

DOY 213–235

Kc

 = 1.05

August 24–September 30

DOY 236–273

Kc

 = 1.05-0.01622×(DOY-236)

Mixed May 1–June 6

DOY 121–157

Kc

 = 0.64

June 7–July 23

DOY 158–204

Kc

 = 0.64 + 0.007609×(DOY-158)

July 23–August 22

DOY 205–234

Kc

 = 0.99

August 23–September 30

DOY 235–273

Kc

 = 0.99-0.01605×(DOY-235)

Table 6. Results of modeling daily evapotranspiration (ET) during the wetland growing season (May 1–September 30, 2008–2010, 

n = 457) at both sites using piecewise linear models of Kc, superseded by setting Kc = 1.5 during days of precipitation greater than 3 

millimeters.

[Slope and intercept are of ordinary least squares best-fit line between modeled and measured ET. Abbreviations: ET , mean evapotranspiration during the 

2008–2010 growing seasons; mea, measured; mod, modeled; r 2, coefficient of determination; CE, coefficient of efficiency; RMSE, root-mean-square-error; 

mm d-1, millimeters per day]

Site ETmea

(mm d–1)

ETmod

(mm d–1) r 

2 CE Slope Intercept

(mm d–1)

RMSE

(mm d–1)

Bulrush 4.537 4.499 0.710 0.652 0.779 1.033 0.902

Mixed 4.376 4.340 0.733 0.704 0.834 0.756 0.870

and Sutcliffe, 1970). Model performance may improve if the 

actual timing of precipitation were known, allowing the use of 

Kc=1.5 on the day following precipitation when precipitation 

occurs late in the day. Further, if atmospheric demand on 

the day following precipitation is especially low (overcast 

conditions), the use of Kc=1.5 could be extended to the next 

sunny day, possibly creating further improvement. However, 

model accuracy is limited by the 44-km distance between 

the KFLO precipitation measurement and the wetland sites 

(and concomitant decoupling of precipitation), and by the 

simplistic treatment of the complicated interactions between 

canopy structure, interception, and subsequent atmospheric 

demand and evaporation. While these models may provide an 

approximate estimate of daily ET at the wetland sites, much 

of the random variability can be removed by considering 

biweekly time steps, as in the following section.
Evapotranspiration Results from Bulrush and Mixed Vegetation Sites 45

tac12-0777_fig13a-b

2008

EXPLANATION

2009

2010

Piecewise linear fit

A. Bulrush site

B. Mixed site

0

1

2

3

Daily crop coefficient, Kc

May June July Aug. Sept. 0

1

2

3

Daily crop coefficient, Kc

Figure 13. Detailed graph of daily crop coefficient during the growing seasons of all 3 years at A, the bulrush site, and B,

the mixed site, and piecewise linear fits to the means from about June 20 to September 15, and to base values outside of this 

period. Piecewise linear fits determined by eye.
46 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

Figure 14. Comparison of daily evapotranspiration (ET) measured during the growing 

season (May 1–September 30) of 2008 through 2010 with ET modeled using the piecewise 

linear approach for the A, bulrush site and B, mixed site.

tac12-0777_fig14a-b

0

1

2

3

4

5

7

6

8

9

B. Mixed site

Measured evapotranspiration, in millimeters per day

0 1 2 3 4 5 6 7 8 9

0

0

1

1

2

2

3

3

4

4

5

5

7

6

8

6 7 8

9

9

Measured evapotranspiration, in millimeters per day

Modeled evapotranspiration, in millimeters per day

Modeled evapotranspiration, in millimeters per day

A. Bulrush site
Evapotranspiration Results from Bulrush and Mixed Vegetation Sites 47

The rising trend in daily Kc during April through 

mid-July is noticeably delayed at both sites in 2010, a year 

of substantially lower water levels (fig. 8). During this period 

in 2010, ET is also noticeably smaller than in 2008 and 2009 

(fig. 11). The lower Kc values in early 2010 probably were not 

caused by canopy stress because water levels were at or above 

land surface by late February at the bulrush site and by early 

April at the mixed site, well before new growth began. The 

major meteorological variables affecting ET were averaged 

for the period April 1–June 30, and a comparison of these 

averages for 2009 and 2010 is given in table 7. Wind speed 

is not included because its effect on ET is small and variable 

depending on other environmental conditions (Campbell 

and Norman, 1998). Spring 2010 was more overcast, humid, 

and cool, but less rainy than spring 2009. These variables 

all contributed to lower ET in 2010, but the reduced solar 

radiation, vapor pressure deficit, and temperature do not 

account for the small Kc because they affect ETr

 to about the 

same proportion as they affect ET. The similar reduction in 

ETr and ET from these environmental conditions can be seen 

by comparing figures 11B, C, E, and F. The reduced rainfall 

in 2010 probably did contribute to smaller Kc through reduced 

evaporation of intercepted rainfall, but as discussed earlier 

in this section, the effect of rainfall is short-lived, causing 

upward spikes in Kc, and even the base values of Kc (during 

dry periods between rainfall) are substantially lower in 2010 

than in 2009 and 2008 (fig. 12). Apparently some other factor 

contributed to the reduction in ET during spring 2010 without 

a corresponding reduction in ETr, leading to consistently 

smaller values of Kc.

A mechanism for a relation between Kc and standing 

water level has been proposed by German (2000), who 

Table 7. Comparison of environmental variables affecting evapotranspiration from 

April 1 to June 30, 2009 and 2010, at both wetland sites. 

[All values shown are period means, except rainfall, which is period total; Ratio, ratio of 2010 value 

to 2009 value; Diff., 2009 value minus 2010 value. Abbreviations: kPa, kilopascals; mm, millimeter; 

W m–2, watts per square meter; °C, degrees Celsius]

Site

Solar 

radiation

(W m–2)

Vapor 

pressure

deficit 

(kPa)

Air 

temperature

(°C)

Rainfall

(mm)

2009 2010 Ratio 2009 2010 Ratio 2009 2010 Diff. 2009 2010 Ratio

Bulrush 289 274 0.95 0.624 0.517 0.83 10.81 8.17 2.64 249 168 0.68

Mixed 284 263 0.93 0.621 0.500 0.81 10.67 8.10 2.57 289 196 0.68

measured ET at multiple sites in the Florida Everglades—

vegetated with sawgrass, spike rush, muhly grass, and cattail; 

vegetation similar to that at the present study site. If canopy 

biomass is distributed evenly in the vertical direction, light 

penetration from above decreases with depth into the canopy 

approximately according to Beer’s law. Conversely, the 

amount of light reaching an underlying water surface increases 

as water-surface elevation increases. At the Everglades 

site, the density of plant material (primarily the dead stalk 

understory) was greatest near the land surface and decreased 

with distance above land surface (Carter and others, 1999). 

German reasoned that this canopy architecture would enhance 

the extinction effect compared to that of an evenly distributed 

canopy, greatly increasing the proportion of water surface 

receiving solar radiation at higher water levels. Greater 

radiation input to the water surface causes greater partitioning 

to LE. At lower water levels, a greater proportion of dead 

plant material per unit horizontal area is exposed to sunlight, 

generating greater H at the expense of LE. We expand on 

German’s (2000) observation by noting that lower water 

levels also increase the aerodynamic resistance from the water 

surface to the free atmosphere, further shifting the energy 

exchange away from the water surface, toward the upper, 

dead canopy. At the current study site, canopy architecture is 

similar to that documented in the Everglades, and although 

detailed measurements were not made, many photographs 

taken during site visits substantiate the greater density of dead 

plant material near the ground. This dependence of energy 

partitioning on water level very likely occurs at the present 

study site, and the unusually small value of Kc during spring 

2010 probably was at least partially related to the unusually 

low water levels during that time.
48 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

Figure 15. Biweekly reference evapotranspiration 

from Agency Lake AgriMet station and measured 

evapotranspiration at bulrush and mixed sites during A, 

2008, B, 2009, and C, 2010.

tac12-0777_fig15a-b-c

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

0

2

4

6

8

0

2

4

6

8

0

2

4

6

8

Biweekly evapotranspiration, in millimeters per day

C. 2010

A. 2008

Bulrush site

Mixed site

EXPLANATION

Reference evapotranspiration

B. 2009

Biweekly Evapotranspiration and 

Crop Coefficients

Biweekly ETr and measured ET at both sites are shown 

by year in figure 15. A reasonable correlation can be seen 

between the two sites and between measured ET and ETr. On 

average, ETr exceeds ET, although some exceptions can be 

seen. Bulrush site ET tends to exceed mixed site ET, also with 

notable exceptions (for example, midsummer, 2008). Although 

the timing of the relation between ET and ETr changes from 

year to year, ET tends to approach ETr most reliably from 

mid‐July to mid-August. During the winter, when fluxes are 

small, ET approaches and even substantially exceeds ETr, but 

no consistent patterns are apparent. In December 2009, ET at 

both sites exceeds ETr by more than a factor of 2.

Biweekly Kc values were computed from the biweekly 

ET and ETr rates, and the Kc values are shown in figure 16, 

along with biweekly precipitation (P) totals. As with daily Kc, 

values are somewhat predictable during the growing season 

(May through September) and are quite variable during other 

times of the year. Values of daily Kc that spike to 5 or 6 in 

November through January (fig. 12) are somewhat moderated 

by aggregation into biweekly periods, but values still exceed 

2 in December 2009 due to the small values of ETr during 

that time. On a biweekly basis, Kc is less correlated with P

than on a daily basis (fig. 16). For example, relatively large P

in early June 2009 and mid-April 2010 did not result in large 

values of Kc; in fact, Kc was smaller in December 2008 than 

in December 2009—although P was greater in 2008. This 

lack of correspondence between P and Kc probably is related 

to: (1) the timing and frequency of P; (2) the tendency for P

to be sequestered by the lower canopy understory and soil; 

and (3) the abundant soil water content during the growing 

season. During the non-growing season, rainfall amounts that 

exceed the interception capacity of the dormant canopy drain 

to lower layers and the soil, where evaporation is reduced due 

to shading and decreased aerodynamic transport. A greater 

percentage of drainage occurs from a few large rainfalls than 

from many small rainfalls of equal total depth, reducing the 

percentage available for evaporation. This mechanism reduces 

the correlation between biweekly Kc and P, instead making Kc

more dependent on the number of rainfall events during the 

period. Snowfall tends to remain more elevated in the canopy 

than rainfall, but wind redistributes the snow to lower levels, 

and solar radiation melts the snow on warmer days, causing 

some drainage and obscuring the linkage between Kc and P. 

During the growing season, evaporation of interception is 

comparable to transpiration due to the ample soil moisture, 

reducing the impact of interception on ET. While interception 

of P causes noticeable spikes in daily Kc, this effect becomes 

masked by other processes on a biweekly basis. Therefore, 

the biweekly magnitude of P does not appear to be useful in 

predicting the biweekly value of Kc.
Evapotranspiration Results from Bulrush and Mixed Vegetation Sites 49

tac12-0777_fig16a-b-c

A. 2008

0

1

2

3

0

1

2

3

B. 2009

Biweekly crop coefficient, Kc and precipitation, in decimeters

C. 2010

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

Bulrush site

Mixed site

Precipitation

EXPLANATION

Figure 16. Biweekly crop coefficients at bulrush and mixed sites, and precipitation at Klamath Falls AgriMet station during 

A, 2008, B, 2009, and C, 2010.
50 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

Ensemble averages of ET and ETr were computed 

using data from all 3 years and were parsed into 26 biweekly 

periods to create a 1-year average record. Ensemble average 

Kc for each biweekly period was then calculated as the 

ratio of average ET to average ETr. By averaging fluxes 

from the corresponding biweekly periods each year, the 

non-linear effects of averaging unusually large or small 

Kc values are removed. Due to the start (May 1, 2008) and 

end (September 29, 2010) of the study period, averages are 

computed from 3 years during the growing season (May 

through September), and 2 years otherwise. The resulting 

time series of ensemble average biweekly Kc is reasonably 

predictable during the growing season and somewhat more 

erratic otherwise (fig. 17). Values of ensemble average Kc

during the growing season are listed in table 8.

During the growing season, ensemble average Kc rises 

almost monotonically from a value near 0.75 on May 1, to 

a peak near 1.0 in mid-August, then declines monotonically 

to a value near 0.5 by late September. The only substantial 

perturbation in this pattern is during late May-early June, 

when Kc is greater than the subsequent 2 or 3 values. This 

boost in ET at both sites may be related to fortuitous timing 

and amounts of rainfall, primarily in 2008 and 2009 (fig. 12). 

On the rising limb of Kc, values at the two sites are nearly 

equal, with the bulrush Kc slightly greater than the mixed 

site Kc on average. On the descending limb, the bulrush Kc is 

substantially and consistently greater than the mixed site Kc. 

The tabled values of ensemble average Kc are used to model 

biweekly ET during the 3 growing seasons, as discussed later 

in this section.

During the non-growing season, ensemble average Kc

varies somewhat unpredictably; large variations occur between 

adjacent periods and between sites (fig. 17). In particular, 

the very large (>2) values in late December 2009 (fig. 16B) 

have been somewhat moderated by the 2008 data, but the 

2-year average still stands out from the rest, especially at the 

bulrush site. In addition, Kc values in October are unusually 

small compared to values during the rest of the non-growing 

season. During the study, October precipitation at the Klamath 

Falls KFLO station was 52 percent of the average for 1999 

through 2011. Part of the random variability in Kc is probably 

related to the small sample size (n=2 years) during the 

non-growing season, combined with the small ETr values as 

described in Daily Evapotranspiration and Crop Coefficients. 

It is therefore suggested that the extreme values of Kc (mostly 

during October and December) are not representative of the 

long-term, and that a single mean value of Kc can adequately 

characterize the whole non-growing season. Consequently, 

Table 8. Ensemble mean crop coefficients (Kc) during growing 

season biweekly periods and mean non-growing season Kc values 

at both study sites.

Period Bulrush Mixed

April 30–May 13 0.760 0.745

May 14–May 27 0.775 0.739

May 28–June 10 0.926 0.900

June 11–June 24 0.836 0.814

June 25–July 8 0.829 0.853

July 9–July 22 0.883 0.903

July 23–August 5 0.965 0.938

August 6–August 19 1.017 0.964

August 20–September 2 0.942 0.864

September 3–September 16 0.757 0.678

September 17–September 30 0.555 0.453

Non-growing season 0.758 0.683

ET and ETr were averaged from October through April, and 

a single non-growing season Kc was computed for each site. 

These values are 0.758 and 0.683 at the bulrush and mixed 

sites, respectively, and are listed in table 8.

Ensemble average values of Kc from the growing season 

(fig. 17; table 8) and mean values from the non-growing 

season (table 8) were multiplied by biweekly values of ETr

to test the adequacy of the average Kc values to reproduce 

the measured ET values at both sites during the entire 

study, consisting of 63 biweekly periods. The results of this 

comparison are shown in figure 18, and associated statistics 

are presented in table 9. Overall, performance of the average 

Kc approach is very good, with r 2 values greater than 0.96, 

RMSE values less than 0.4 mm d-1, and slopes and intercepts 

of best-fit lines near 1 and 0, respectively. This is not the 

most stringent test of the method, because the seasonal Kc

values were determined from the test data rather than from an 

independent data set. However, a fair amount of variability 

in Kc occurred from year to year (during the same biweekly 

period) at both sites (fig. 16), and the ability of the model to 

reproduce the measured ET is still quite good. For example, 

water levels were about 0.5 to 0.2 m lower in 2010 than in 

2008 and 2009 (fig. 8) during the first half of the year. As 

a result of this or other factors, Kc values were noticeably 

lower during the early 2010 growing season (fig. 16), and 

inclusion of these data lends some generality to the Kc model 

by averaging in the unusual year. The resulting model only 

slightly overestimates ET in 2010 (the red squares in fig. 18), 

while still maintaining relatively good accuracy overall.
Evapotranspiration Results from Bulrush and Mixed Vegetation Sites 51

tac12-0777_fig17

0

1

2

Biweekly crop coefficient, Kc

Bulrush site

Mixed site

Bulrush growing season curve

Mixed site growing season curve

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

EXPLANATION

Figure 17. Biweekly ensemble average crop coefficients at bulrush and mixed sites, and fourth-order polynomial fits to the 

crop coefficients during the growing season (May–September).

Table 9. Results of modeling biweekly evapotranspiration (ET) during the study period (n = 63) at both sites using the ensemble-mean 

Kc approach during the growing season and the mean Kc approach during the non-growing season.

[Slope and intercept are of ordinary least squares best-fit line between modeled and measured ET. Abbreviations: CE, coefficient of efficiency; ET , mean ET

during the study period; mea, measured; mod, modeled; mm d-1, millimeters per day; r 2, coefficient of determination; RMSE, root-mean-square-error]

Site mea ET

(mm d-1)

mod ET

(mm d-1)

r 

2 CE Slope Intercept

(mm d–1)

RMSE

(mm d–1)

Bulrush 2.926 2.926 0.962 0.961 0.977 0.067 0.395

Mixed 2.787 2.787 0.971 0.970 0.986 0.039 0.347
52 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

tac12-0777_fig18a-b

0

1

2

3

4

5

6

7

B. Mixed site

Measured evapotranspiration, in millimeters per day

0 1 2 3 4 5 6 7

0

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

Measured evapotranspiration, in millimeters per day

Modeled evapotranspiration, in millimeters per day

Modeled evapotranspiration, in millimeters per day

A. Bulrush site

2008 and 2009

2010

EXPLANATION

Figure 18. Comparison of biweekly evapotranspiration (ET) measured during the entire 

study period with ET modeled using the ensemble average Kc approach for the A, bulrush 

site and B, mixed site.
Evapotranspiration Results from Bulrush and Mixed Vegetation Sites 53

As an alternative to the discrete values of biweekly 

growing season ensemble average Kc in table 8, fourth-order 

polynomials were fit to the biweekly values and the resulting 

curves are shown in figure 17. Information for computing Kc

in this manner is given in table 10. This approach provides 

a more generalized and automated computation of growing 

season Kc, but undoubtedly sacrifices accuracy in modeling 

ET during the study period compared to the Kc table approach 

(fig. 18; table 9). However, over periods of many years, this 

approach may perform equivalently to the Kc table approach.

Study-Period and Annual Evapotranspiration

On average during the study period, Rn at the bulrush and 

mixed sites was 126.4 W m-2 and 113.9 W m-2, respectively. 

The smaller mixed site Rn of about 10 percent probably is 

related to differences in cloudiness, water depth, or vegetation 

type. The 4-component measurements of Rn indicate that this 

10 percent difference is partitioned as follows: 3.8 percent to 

incoming solar, 4.3 percent to reflected solar, 1.5 percent to 

outgoing long-wave, and 0.4 percent to incoming long-wave. 

The smaller incoming solar at the mixed site is likely 

associated with the predominant south-westerly winds at that 

site, issuing from the Cascade Range through the mouth of 

Fourmile Creek at Pelican Bay (fig. 1), entraining montane 

cloudiness preferentially over the mixed site. The bulrush site 

is more removed from the mountains and from the Fourmile 

Creek air stream, as indicated by its more evenly distributed 

wind directions, and the site should experience sunnier skies 

as a result. Mean reflectivity of the bulrush site during the 

study was 0.128, compared to 0.156 at the mixed site. This 

greater retention of solar radiation at the bulrush site was the 

largest factor in the Rn difference and is consistent with the 

deeper water at that site (Sumner and others, 2011). But the 

Rn difference also could be related to differences in vegetation 

color. Deeper water at the bulrush site also would tend to 

keep the surface cooler and account for the reduced outgoing 

long-wave radiation at that site. Although the mixed site was 

located among large patches of open water associated with 

wocus, wocus patches were distant enough from the station 

that they did not affect the measured Rn, but probably did 

affect the measured turbulent fluxes.

Average ET during the study period, during each year 

of study, and during a 3-year period was computed for both 

sites and is presented along with ETr in table 11. The 2008 and 

2010 annual values were computed by filling in the missing 

parts of 2008 (January 1–April 30) and 2010 (September 30–

December 31) with data from the equivalent times in 2009. 

Table 10. Coefficients of fourth-order polynomial fits to biweekly 

growing season ensemble average Kc values. 

[Polynomials are of the form: Kc = C 0+C 1(X)+C 2(X  2)+C 3(X  3)+C 4(X  4), where

X = DOY/100. Because of the powers of X involved, all significant digits shown 

are needed to get accurate results. This number of significant digits did not 

require use of double precision in FORTRAN. Abbreviation: DOY, day of year]

Site

Coefficient

C0 C1 C2 C3 C4

Bulrush -9.411 23.9880 -20.9950 8.09919 -1.15345

Mixed -6.712 17.2984 -15.1276 5.92317 -0.865068

Table 11. Mean evapotranspiration at the study sites and reference evapotranspiration at the Agency 

Lake (AGKO) weather station during the study period (May 1, 2008–September 29, 2010), each year of 

study, and a full 3-year period (January 1, 2008–December 31 2010). 

[Full years of record in 2008 and 2010 were synthesized by using data from equivalent periods in 2009 to fill in missing 

periods in 2008 (January 1–April 30) and 2010 (September 30–December 31). The 3-year period is the mean of 2008, 2009, 

and 2010. Abbreviations: mm d-1, millimeters per day; m yr-1, meters per year]

Site

Study period 2008 2009 2010 3-year period

(mm d–1) (m yr–1) (mm d–1) (m yr–1) (mm d–1) (m yr–1) (mm d–1) (m yr–1) (mm d–1) (m yr–1)

Bulrush 2.93 1.069 2.72 0.995 2.77 1.013 2.33 0.850 2.61 0.953

Mixed 2.79 1.018 2.65 0.966 2.54 0.929 2.23 0.814 2.47 0.903

Reference 3.51 1.283 3.34 1.221 3.10 1.132 2.96 1.083 3.14 1.145
54 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

The 3-year period is the mean of the 3 study years. This 

3-year period was synthesized because the study-period 

average combined 3 growing seasons with 2 non-growing 

seasons and, therefore, is biased high compared to an annual 

average. Little uncertainty is introduced by the substitutions 

because ET is small during the non-growing season. As seen 

in table 11, study period ET was about 5 percent greater at the 

bulrush site than at the mixed site. Because the EC data were 

corrected to close the energy balance, the two factors affecting 

this 5 percent difference are mean values of available energy, 

AE, and how that energy was partitioned between H and LE, 

or the Bowen ratio, β. Mean values of AE during the study 

period were 127.0 and 115.1 W m-2 at the bulrush and mixed 

sites respectively. (These values differ slightly from the Rn

means cited in the previous paragraph by the amounts of mean 

Qx + G, which were -0.6 and -1.2 W m2 at the bulrush and 

mixed sites, respectively.) Although AE is about 10 percent 

greater at the bulrush site than at the mixed site, a greater 

proportion of AE was partitioned into LE at the mixed site, 

reducing the LE (and ET) site difference to about 5 percent. As 

noted earlier, the greater proportion of open water associated 

with stands of wocus at the mixed site possibly resulted in a 

lower mean β at the mixed site (0.450) than at the bulrush site 

(0.525) despite the 0.15-m higher land surface and resulting 

shallower water depths at the mixed site.

A two-sided paired-t test was conducted to determine 

whether daily ET values from the two sites during the study 

period are statistically different at the α=0.05 probability 

level. Site ET differences are normally distributed. This test 

yielded a t-value of 2.067 (p=0.0369), indicating that the null 

hypothesis can be rejected and ET values from the two sites 

are statistically different, but not conclusively. The accuracy 

of EC data is typically given as ±5 to 10 percent under 

ideal conditions (Foken, 2008) such as found here, and the 

corresponding precision (or ability to distinguish differences 

under similar conditions) should be substantially smaller than 

the accuracy, on the order of ±1 to 2 percent. Therefore it 

seems likely, although not conclusively, that ET was slightly 

and significantly greater from the bulrush site than from the 

mixed site.

Variability between years (about ± 8.5 percent) was 

substantially greater than variability between sites (about 

± 2.5 percent). The years of 2008 and 2009 were very 

similar overall; bulrush ET was slightly greater in 2009 

than in 2008, whereas mixed site ET was slightly greater in 

2008 than in 2009 (table 11). In 2010, ET at both sites was 

about 14 to 15 percent less than during the previous 2 years. 

Available energy at the bulrush site was 1 percent greater 

in 2010 than in 2008 through 2009. Available energy at the 

mixed site was 2 percent less than in 2008 through 2009, 

and therefore it cannot account for the lower ET in 2010. As 

discussed earlier, unusually low water levels in the first half of 

2010 probably reduced evaporation from the standing water 

by decoupling the water surface from incoming radiation. In 

addition, synthesized precipitation (P) was 16 percent lower in 

2010 than in 2008–2009 and may have reduced evaporation of 

intercepted water, especially during the non-growing season. 

(Although the last 3 months of the synthesized 2010 data are 

borrowed from 2009, the substitution was made for ET as well 

as P and should preserve any correlation between ET and P.) 

Therefore, lower water levels and precipitation probably were 

the main factors causing the lower ET in 2010.

Maximum annual ET occurred in 2009 at the bulrush 

site and in 2008 at the mixed site. Differences between 

the maximum annual value and the next lower value are 

small (1.8 and 4.0 percent at the bulrush and mixed sites, 

respectively), and the year reversal could be caused either by 

site differences in climate and surface response to climate, 

or simply by random error in the EC method. However, the 

most likely causative climatic variable, available energy, was 

greater at both sites in 2009, suggesting the year reversal may 

be a result of random error.

Overall, the 3-year synthesized average ET values at 

the bulrush and mixed sites are 0.953 m/yr and 0.903 m/yr, 

respectively. The corresponding 3-year synthesized average 

ETr from the Agency Lake weather station is 1.145 m/yr, 

resulting in average annual Kc values of 0.832 and 0.789 

at the bulrush and mixed sites, respectively. These annual 

values fall near the middle of the range of ensemble average 

biweekly Kc values given in figure 17 and table 8. Based on 

our estimate that 70 percent of the Upper Klamath NWR is 

typified by the bulrush site and 30 percent by the mixed site, 

the 3-year average ET value for the whole NWR is 0.938 m/yr. 

The 3-year synthesized average precipitation at the Klamath 

Falls weather station (KFLO) is 0.233 m/yr, equal to about 

25 percent of 3-year average measured ET.

The relation of the 3-year synthesized ET values to 

expected values of long-term ET can be partially investigated 

by comparing relevant climatic variables during the 3-year 

period to their long-term means. In a water-limited system, 

precipitation (P) is probably the most important variable, 

whereas in an energy-limited system, solar radiation (Rs

) and 

temperature assume that role. Although the most relevant 

temperature is that of the evaporating surface, air temperature 

(Ta) is commonly used because it is highly correlated with 

surface temperature and is more readily available. During 

the heart of the growing season, the NWR wetland clearly is 

energy-limited, but at other times of the year, P influences ET

through evaporation of intercepted water. Long-term means of 

Rs, P, and Ta are calculated using data from the nearby Agency 

Lake (AGKO) and Klamath Falls (KFLO) weather stations 

(fig. 1) and are compared to 3-year synthesized study period 
Evapotranspiration Results from Bulrush and Mixed Vegetation Sites 55

means in table 12. Long-term means are calculated from 

water years 2001–2011 (11 years) and the 3-year values are 

synthesized from the same months and years used to compute 

measured ET, to be consistent with those data. The closer 

AGKO station is used when possible (for Rs and Ta), but only 

the KFLO station has a reliable precipitation record during 

the winter, so those data are used to compute P. Although 

the KFLO station record begins in 1999, the first 2 years are 

not used, to be consistent with the full period of record at the 

AGKO station (2001–2011). Solar radiation during the study 

period was about 9.5 percent lower than the 11-year mean, 

which should reduce the study period ET compared to the long 

term. Interestingly, P also was about 17 percent less during 

the study period than its long-term average. Often, reduced P

is associated with greater Rs, but the frequency, duration, and 

intensity of P, as well as the distance between the AGKO and 

KFLO stations, can alter this relation. In this wetland setting, 

reduced P should have little effect on growing-season ET, and 

a mildly inhibiting effect on non-growing season evaporation 

of intercepted water. Finally, the study-period Ta is slightly 

cooler than the long-term mean, which also should slightly 

reduce ET. Overall, the study period was less sunny, drier, and 

cooler than the 11-year average, all of which should reduce 

the study-period ET compared to the norm. While this result 

indicates that the study-period ET given in table 11 probably 

is smaller than the long-term average, the smaller ET should 

have little or no effect on the accuracy of the Kc approach 

developed in this study. The effects of Rs and Ta on ET are 

explicitly included in the Penman-Monteith expression for 

ETr, and the effects of P on annual ET from this well-watered 

wetland are small.

Table 12. Comparison of 3-year study period averages with 

11-year averages of solar radiation, precipitation, and air 

temperature. 

[The 3-year period is synthesized from the actual May 1, 2008–September 29, 

2010 study period, supplemented with data from January 1, 2009–April 30, 

2009 and September 30, 2009–December 31, 2009, to be consistent with 

synthesized 3-yr evapotranspiration (ET) values given in table 11. Solar 

radiation and air temperature data are from the Agency Lake (AGKO) weather 

station, and precipitation data are from the Klamath Falls (KFLO) weather 

station. Abbreviations: mm yr-1, millimeters per year; W m-2, watts per 

square meter; °C, degrees Celsius] 

Period

Solar 

radiation

(W m–2)

Precipitation

(mm yr–1)

Air 

temperature

(°C)

2008–2010 184.7 233 6.98

2001–2011 195.0 280 7.45

Comparison of Wetland Evapotranspiration with 

Evapotranspiration of Local Crops

A comparison of our measured wetland ET with ET of 

crops in the area can be made using data from the Bureau of 

Reclamation AgriMet Web site. Computation of ETr is based 

on an assumption that the alfalfa crop is full sized and green 

year-round, as indicated by an assumed surface resistance (rs) of 

45 s/m at the daily time step, regardless of time of year (Allen 

and others, 2005). In the region of the current study, actual 

alfalfa ET is somewhat less than ETr due to reduced green leaf 

area during the non-growing season and multiple cuttings during 

the growing season. The Bureau of Reclamation AgriMet Web 

site computes and posts values of estimated ET for alfalfa and 

other crops. These ET values are computed using the 1982 

Kimberly-Penman equation to compute ETr, with appropriate 

values of Kc. Although this ETr equation is slightly different 

than the ASCE equation, the Kc values were developed to 

provide best estimates of crop ET using the 1982 ETr equation 

(the AgriMet Web site does not provide estimates of crop 

ET using the more recent ASCE ETr equation). The Web site 

posts crop ET for each growing season, the duration of which 

is established by local conditions and expert opinions year by 

year. We computed wetland ET using our measured data during 

the 2008 through 2010 growing seasons, and the 70 percent 

to 30 percent weighting (for bulrush versus mixed vegetation) 

used earlier in Study-Period and Annual Evapotranspiration. We 

obtained alfalfa and pasture growing-season ET data for 2008 

through 2010 from the Klamath Falls (KFLO) AgriMet Web site 

because crop ET is not computed for the closer AGKO station. A 

comparison of growing-season ET (table 13) shows that wetland 

ET was about 9 percent less than alfalfa ET, and about 18 

percent greater than pasture ET during 2008 through 2010.

Although AgriMet does not compute non-growing-season 

crop ET, a rough comparison of annual wetland and crop ET can 

be made by assuming ET from all vegetated surfaces is equal 

during the non-growing season. This assumption is supported 

by the similar weather and existence of dormant vegetation at 

the locations involved. Although wetland ET probably exceeds 

crop ET in late winter and early spring due to the presence of 

standing water at the wetland, crop ET probably exceeds wetland 

ET during fall and early winter (when standing water is absent) 

because of the greater mulching effect of the more massive 

dormant canopy at the wetland. We compute mean 2008 through 

2010 non-growing season wetland ET using the same synthesis 

methods used in Study-Period and Annual Evapotranspiration

to estimate early 2008 and late 2010 water use. Non-growing 

season crop ET is assumed equal to wetland ET, and annual ET

is computed as the sum of growing-season and non-growingseason ET of both wetland and crops. On an annual basis, 

wetland ET during 2008 through 2010 is estimated to be about 

6 percent less than alfalfa ET and about 14 percent greater than 

pasture ET (table 13).
56 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

Comparison of Wetland Evapotranspiration with 

Previous Studies

Bidlake (2000) conducted a field campaign to 

characterize ET at a site about 200 m northwest of the 

bulrush site during the growing season of 1997. He deployed 

EC sensors during four 1- to 2- day periods (May 29–30, 

July 10–12, August 23–25, and October 11–13), and a 

recording weather station at the same location continuously 

from May 29 to October 13. The EC fluxes were used to 

calibrate a Penman-Monteith (PM) model (similar to the 

one used in the present study to compute ETr at the AGKO 

AgriMet site) by solving for the average surface resistance, 

rs, during each EC deployment, and interpolating rs between 

site visits. The Penman-Monteith model was then used to 

compute daily ET during the entire growing season, and the 

daily values were aggregated into weekly values. Bidlake’s EC 

data were not corrected to force energy-balance closure and, 

therefore, neither were the modeled ET values because they 

were calibrated to match the EC data. For comparison with 

the current study, we divided Bidlake’s ET data by the average 

energy budget ratio (EBR) measured during that study (0.88) 

to force energy-balance closure and improve comparability 

with the current study.

Bidlake’s 1997 adjusted weekly ET (Bidlake, 2000) is 

plotted along with our 2008 through 2010 biweekly bulrush 

ET in figure 19. Compared to our 2008 and 2009 ET data, 

the 1997 ET was somewhat lower in June, nearly equal in 

July, somewhat greater in August, and nearly equal thereafter, 

resulting in very similar growing season totals. June and 

August differences may be attributable to: interpolation of rs

to compute the 1997 ET; the use of relatively short periods 

(29–35 hours) to compute each rs

 interpolation endpoint; 

or to climatic differences between years. Worthy of note 

is that in 1997, June appeared to be cloudier, and August 

clearer, than the corresponding months during the current 

study (fig. 10; Bidlake, 2000, fig. 1), which is consistent with 

the ET differences during those periods. Interestingly, ET

magnitudes during all 4 years are similar from late August to 

early October, a time when the canopy is tall and beginning 

to senesce. Overall, the 1997 growing season ET data are in 

general agreement with the ET measured in the current study 

and help support our results.

During the growing season of 2000, Bidlake (2002) 

measured ET from three fallowed agricultural fields in the Tule 

Lake National Wildlife Refuge in northern California, about 

83 km southwest of the present study site. During the previous 

year (1999), the three sites were sown to barley and irrigated, 

and had variously evolved into a patchwork of harvested, 

unharvested, and burned (by wildfire) areas by spring 2000. 

One of the sites was tilled and sown to rye in February 2000 

to simulate a dry-land cover crop that might be used during 

future fallowing. During the growing season of 2000, surface 

coverage consisted of a mixture of stubble and other crop 

residues, weedy volunteer species, small grain plants sprouted 

from the seeds of previous crops, bare soil, and rye (at the one 

site planted with rye). All sites were un-irrigated during 2000. 

Water table depths averaged about 1.1 m below land surface 

during the growing season, ranging from about 0.7 to 1.4 m. 

Evapotranspiration was measured or estimated from May 1 to 

October 31 (184 days, designated as the growing season) using 

the Bowen-ratio method, supplemented with modeling during 

data gaps. The Priestley-Taylor method (with variable α) was 

used during short (< 2 hr) gaps, and a reference ET (ETr) 

method was used for longer gaps. Daily ETr was obtained 

from a University of California weather station about 8 km 

north, and daily Kc values were computed by interpolation 

between, or extrapolation beyond periods when Bowen-ratio 

sensors were operational. Extended gaps occurred at the 

beginning and end of the growing season, approximately the 

Table 13. Comparison of mean 2008–2010 growing season, non-growing 

season, and annual evapotranspiration (ET) of alfalfa, pasture, and Upper 

Klamath Lake NWR wetland, in meters.

[Alfalfa and pasture growing-season duration and ET determined from Bureau of 

Reclamation AgriMet Web site. Wetland ET measured using eddy covariance method 

(this study). Non-growing season alfalfa and pasture ET assumed equal to wetland ET

during the same period. Annual ET is the sum of growing season and non-growing 

season ET. Abbreviation: NWR, National Wildlife Refuge]

Alfalfa comparison

(190 day average 

growing season)

Pasture comparison

(195 day average 

growing season)

Alfalfa ET Wetland ET Pasture ET Wetland ET

Growing season 0.838 0.779 0.671 0.789

Non-growing season 0.159 0.159 0.149 0.149

Annual 0.997 0.938 0.820 0.938
Evapotranspiration Results from Bulrush and Mixed Vegetation Sites 57

tac12-0777_fig19

0

1

2

3

4

5

6

7

8

9

Biweekly evapotranspiration, in millimeters per day

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

EXPLANATION

Bulrush Site, 2008

Bulrush Site, 2009

Bulrush Site, 2010

Bidlake Site, 1997

Figure 19. Comparison of biweekly evapotranspiration (ET) measured at the bulrush site 

during the current study with weekly ET measured and modeled by Bidlake (2000) at a 

nearby site during May 28–October 12, 1997.

first half of May, and the last two-thirds of October, at all 

3 sites. Because ET at these times was small, little error in 

the seasonal totals was incurred by the use of the ETr model. 

Although timing of peak ET varied substantially between the 

fields, the growing-season totals were quite similar, ranging 

from 0.426 to 0.444 m, and averaging 0.435 m.

We computed 2008 through 2010 wetland 

growing-season ET using our measured data from the same 

growing season as in Bidlake (2002), again weighting the 

bulrush and mixed site ET 70 percent-30 percent, respectively. 

Growing-season ET data from October 2009 were substituted 

for the October 2010 period, which occurred after the study 

period. Wetland growing-season ET was about 65 percent 

greater than ET from the fallowed cropland (table 14). 

Although Bidlake did not compute non-growing season ET at 

the fallowed crop sites, a rough comparison of annual wetland 

and fallowed-crop ET can be made by assuming ET from both 

vegetated surfaces is equal during the non-growing season, 

as was assumed for alfalfa and pasture. We compute mean 

2008 through 2010 non-growing season wetland ET using 

the same synthesis methods used in Study Period and Annual 

Evapotranspiration to estimate early 2008 and late 2010 water 

use. Non-growing season fallowed-crop ET is assumed equal 

to wetland ET, and annual ET is computed as the sum of 

growing-season and non-growing-season ET of both wetland 

and fallowed crops. On an annual basis, wetland ET during 

2008–2010 is estimated to be about 43 percent greater than 

fallowed-cropland ET during 2000 (table 14).

Table 14. Mean growing season, non-growing season, and 

annual evapotranspiration (ET) of Tule Lake NWR fallowed 

cropland during 2000, and Upper Klamath Lake NWR wetland 

during 2008–2010, in meters. 

[Fallowed cropland growing-season ET is from Bidlake (2002). Wetland ET

measured using eddy covariance method (this study). Non-growing season 

fallowed cropland ET assumed equal to wetland ET during the same time of 

year. Annual ET is the sum of growing season and non-growing season ET. 

Abbreviations: NWR, National Wildlife Refuge]

Tule Lake NWR

fallowed crops

Upper Klamath Lake

NWR wetland

Growing season 0.435 0.718

Non-growing season 0.220 0.220

Annual 0.655 0.938
58 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

Open-Water Evaporation Results

Average open-water evaporation rates during the energy 

budget periods ranged from 2.8 mm d-1 in early October 2008 

at the MDL site (MDN was not usable in 2008) to as much as 

7.0 mm d-1 during mid-July 2010 at the MDL site (table 15). 

Evaporation totals from June 12, 2009, to October 2, 

2009, were 615 and 601 mm at the MDL and MDN sites, 

respectively. The difference between totals at the sites was 

about 2.3 percent. Evaporation during the same period in 2010 

was slightly larger, totaling 636 and 611 mm at MDL and 

MDN, respectively. Evaporation totals for the entire period 

of data for 2010, May 29 through October 2, which was two 

weeks longer than the data collection period in 2009, were 

701 and 675 mm at the MDL and MDN sites, respectively. 

The difference between the 2010 totals at the two sites was 

about 3.8 percent.

Open-water evaporation measurements generally 

correspond to the period from June through September. About 

61 percent of annual pan evaporation at Klamath Falls occurs 

during this period, based on mean monthly values from 

1949 to 2004 (Western Regional Climate Center, 2012). The 

surface of Upper Klamath Lake is typically frozen during 

winter months.

Table 15. Mean surface temperatures (Ts), Bowen ratios (β), net radiation (Rn), net water advected energy (Qv), energy transferred 

to lakebed (Qb), net change in energy stored in the lake (Qx

), and energy-budget evaporation rates (Eeb) for biweekly budget periods in 

2008, 2009, and 2010.

[Abbreviation: MDL, midlake site; MDN, midlake north site; mm d-1, millimeters per day; W m-2, watts per square meter; °C, degrees Celsius]

Year

Budget

period

dates

Budget 

period

number

Ts

(MDL) 

(°C)

Ts

(MDN) 

(°C)

β

(MDL)

β

(MDN)

Rn

(W m-2)

Qv

(W m-2)

Qb

(W m-2)

Qx

(W m-2)

Eeb

(MDL) 

(mm d-1)

(MDN) 

(mm d-1)

2008 07-24–08-06 7 21.8 0.102 211.73 -8.64 4.07 1.21 6.2

08-07–08-20 8 22.0 0.072 174.35 -9.86 2.57 -19.27 5.8

08-21–09-03 9 18.9 0.159 158.64 -9.30 0.92 -31.28 5.3

09-04–09-17 10 18.2 0.024 132.33 -6.49 -0.79 2.87 4.1

09-18–10-01 11 16.2 0.101 92.47 -4.31 -2.44 -18.00 3.4

10-02–10-15 12 11.4 0.296 48.74 -1.36 -3.96 -51.83 2.8

2009 06-12–06-25 17 18.7 18.5 0.214 0.221 220.43 -2.11 6.78 8.99 5.7 5.7

06-02 –07-09 18 21.0 21.5 0.098 0.120 223.22 -11.52 6.17 2.41 6.3 6.2

07-10–07-23 19 22.0 22.2 0.070 0.092 229.65 -11.42 5.20 19.00 6.2 6.1

07-24–08-06 20 23.6 24.5 0.060 0.098 179.06 -13.01 3.94 -37.24 6.4 6.2

08-07–08-20 21 19.8 20.3 0.110 0.139 192.02 -8.99 2.44 -0.09 5.6 5.4

08-21–09-03 22 20.4 20.5 0.065 0.100 158.84 -11.65 0.81 -17.46 5.3 5.1

09-04–09-17 23 18.2 18.9 0.108 0.155 135.12 -7.19 -0.87 -16.14 4.5 4.3

09-18–10-01 24 17.1 17.5 0.144 0.171 98.92 -6.47 -2.50 -34.35 3.9 3.8

2010 05-29–06-11 29 14.0 13.9 0.187 0.193 189.62 4.32 6.82 27.82 4.6 4.6

06-12–06-25 30 17.9 16.8 0.230 0.192 233.84 1.48 6.82 31.70 5.5 5.7

06-26–07-09 31 19.2 20.0 0.111 0.138 234.69 -3.70 6.43 12.86 6.5 6.4

07-10–07-23 32 21.8 22.6 0.046 0.075 231.08 -5.92 5.66 5.24 7.0 6.8

07-24–08-06 33 22.9 23.1 0.084 0.109 197.11 -4.79 4.57 -9.81 6.2 6.1

08-07–08-20 34 22.4 22.3 0.096 0.111 188.66 -7.61 3.21 -13.62 6.0 5.9

08-21–09-03 35 17.0 19.2 0.061 0.181 158.97 -6.47 1.67 -26.14 5.7 5.2

09-04–09-17 36 15.0 17.1 0.025 0.194 141.93 -4.01 0.03 -14.46 5.1 4.4

09-18–10-01 37 16.6 16.6 0.165 0.219 112.48 -0.95 -1.61 0.58 3.3 3.2
Open-Water Evaporation Results 59

During the study period, water surface temperatures of 

the lake were highest from late July through the first week 

of August. In 2008, however, the highest biweekly average 

surface temperature occurred during the period that extends 

through mid-August (table 15). Peaks in average surface 

temperatures tended to lag peaks in net radiation (fig. 20; 

table 15). Energy-budget evaporation rates are generally at 

their highest when net radiation is highest (fig. 21), but rates 

are also affected by other factors, chiefly net changes in energy 

stored in the lake and the dominant type of heat transfer 

occurring in the lake as described by Bowen ratios (table 15).

Where data were available to calculate evaporation at 

both the MDL and MDN sites, differences in evaporation 

rates averaged about 0.2 mm/d, and the median difference 

for all energy budget periods was 0.1 mm/d. The maximum 

difference observed was 0.7 mm/d (table 15). The similarity 

of evaporation rates determined at the geographically separate 

MDL and MDN sites indicates that, at the time scales of 

the 2-week energy-budget periods, the physical conditions 

controlling the Bowen ratio were similar at both sites. Given 

that water depth and fetch conditions at these two sites 

are representative of most of the lake, and that the lake is 

reasonably well mixed, results from the MDL and MDN sites 

should be reasonably representative of the lake as a whole.

EXPLANATION

Lake surface temperature, MDL (midlake) site

Lake surface temperature, MDN (midlake north) site

Rn (net radiation)

Budget period start date

0

5

10

15

20

25

30

Temperature, in degrees Celsius

0

50

100

150

200

250

July 24

August 7

August 21

September 4

September 18

October 2

June 12June 26

July 10July 24

August 7

August 21

September 4

September 18

May 29

June 12June 26

July 10July 24

August 7

August 21

September 4

September 18

2008 2009 2010

Net radiation, in watts per square meter

Figure 20. Average lake surface temperatures at the midlake (MDL) and midlake north (MDN) sites plotted on the left 

vertical axis and net radiation (Qn) plotted on the right vertical axis for the budget periods extending from July 2008 to 

September 2010. Changes in surface temperatures generally lag changes in net radiation.
60 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

Figure 21. Average evaporation rates at the midlake (MDL) and midlake north (MDN) sites plotted on the left vertical axis 

and net radiation (Qn) plotted on the right vertical axis for the budget periods from July 2008 to September 2010.

tac12-0777_fig21

0

50

100

150

200

250

0

1

2

3

4

5

6

7

8

July 24

August 7

August 21

September 4

September 18

October 2

June 12June 26

July 10July 24

August 7

August 21

September 4

September 18

May 29

June 12June 26

July 10July 24

August 7

August 21

September 4

September 18

2008 2009 2010

Energy budget evaporation rate, in millimeters per day

Net radiation, in watts per square meter

EXPLANATION

MDL (midlake) site

MDN (midlake north) site

Rn (net radiation)

Budget period start date

Comparison of Open-Water Evaporation 

with Previous Studies and With 

Wetland Evapotranspiration

Biweekly energy-budget evaporation rates calculated 

for budget periods in 2008, 2009, and 2010 are similar to 

evaporation rates determined in previous studies of Upper 

Klamath Lake. Janssen (2005) determined that 2003 energy 

budget evaporation rates from June 7 to September 30 

averaged 4.2 mm/d, somewhat less than the 5.5 mm/d 

average measured during a similar period in 2009 and 2010 

in this study in spite of slightly warmer monthly average 

temperatures in 2003. Janssen’s average, however, excludes 

data from 2 days in late June along with a period of 13 days 

between June 26 and July 8. Because near-peak evaporation 

occurs during these missing periods, Janssen’s average 

probably would have been greater if the missing data had 

been available.

Using a 1-D surface energy balance model to produce 

simulations of Upper Klamath Lake daily evaporation for 

1950 through 2005, Hostetler (2009) found average May 

to September evaporation totaled 707 mm. This compares 

favorably with the late-May to September 2010 totals of 

698 and 680 mm measured at the MDL and MDN sites, 

respectively, during this study.

Seasonal trends in open-water evaporation and wetland 

ET were similar (figs. 15, 21). In general, open-water 

evaporation exceeded wetland ET during the periods when 

both were measured. As expected, E–ET was greatest during 

the late summer periods (late August to October), due to the 

greater release of stored heat in the lake compared to the 

land surface. Differences were smaller during midsummer 

(late June to early August), a time when vegetation was at 

full height and stored heat was not yet a factor. A notable 

exception occurred in late June through mid-July 2010, 

when E–ET was unusually large. The low lake levels 

in 2010 probably contributed to this difference through 

reduced evaporation of standing water from the wetland, as 

discussed in Daily Evapotranspiration and Crop Coefficients. 

Early-season (late May to mid-June) data are spotty (only 

three periods), but consistently show substantially greater 

open-water evaporation, as the green vegetation canopy has 

not fully emerged from the dead stalk mat, and replaced it 

as the primary exchange surface. Overall, during the periods 

of open-water data collection, open-water evaporation (the 

mean of the MDL and MDN sites) was 20 percent greater than 

wetland ET (a 70 percent-30 percent weighted mean of the 

bulrush and mixed sites, respectively).
Summary and Conclusions 61

Summary and Conclusions

Water allocation in the Klamath Basin is important 

to many different groups of people, and to the health and 

well-being of many ecosystems within the basin. Competition 

for the limited water supply in this semiarid basin is intense, 

and knowledge of water losses to evapotranspiration (ET) is 

key information for deciding optimal water-use strategies. 

One of the central hubs for water distribution in the basin 

is Upper Klamath Lake, near Klamath Falls, Oregon. 

The U.S. Geological Survey (USGS) and the Bureau of 

Reclamation conducted a study to quantify ET from extensive 

wetlands in the Upper Klamath National Wildlife Refuge 

(NWR) at the northwest periphery of the lake, and evaporation 

from the open-water portion of the lake. Data collection 

spanned the period from May 1, 2008, to September 29, 2010.

Two wetland sites were selected for study to typify 

vegetation communities and hydrologic conditions most 

frequently occurring in the NWR. Vegetation at one wetland 

site consisted of a virtual monoculture of bulrush (formerly 

Scirpus acutus, now Schoenoplectus acutus), while the other 

site was a mixture dominated by bulrush, with minor amounts 

of cattail (Typha latifolia), wocus (Nuphar polysepalum), open 

water, and trace amounts of other vegetation. The bulrush site 

is at an altitude of 1,262.03 m (4,140.02 ft) asl and the mixed 

site is about 0.15 m (0.50 ft) higher. As a result of controlled 

lake levels, the wetlands are periodically inundated with lake 

water on an annual basis. Standing water typically occurs 

from January or February through July or August, for an 

average hydroperiod of about 6 months at the bulrush site and 

5 months at the mixed site. Water level typically fluctuates 

about 1.3 m, from about 0.8 to 0.9 m above land surface at 

the bulrush site in spring and early summer to about 0.4 to 

0.5 m below land surface in October, with correspondingly 

lower levels at the mixed site. Minimum lake level in fall 

2009 was unusually low, resulting in a late water-level rise 

and reduced maximum water level in 2010. The root zone of 

the bulrush site remained saturated during the entire study 

period (volumetric water content, θ, was 0.8–0.9 m3/m3), 

whereas the mixed site root zone partially dewatered to a θ of 

around 0.5 m3/m3 during late summer and re-saturated in late 

winter or spring. Canopy height at both sites typically reaches 

a maximum of 2.2 to 2.3 m during the summer, although 

maximum height at the mixed site in 2010 was only 1.9 m. 

When the canopy senesces in October, the dead stalks remain 

vertical for some time, and eventually lodge over in response 

to snow and wind loading. The bent-over stalks form a loosely 

distributed mat, generally about 0.6 to 1.0 m high.

The eddy-covariance (EC) method was used to measure 

ET from two wetland sites. A source-area model estimates 

that at the bulrush site, 98 to 99 percent of the measured ET

originated from within the wetland, and at the mixed site, 

95 to 96 percent originated from within the wetland, indicating 

that contamination of the EC measurement by other surface 

types was insignificant. A chronic inability to close the 

surface energy balance using the EC method was remedied 

by adjusting the turbulent flux upward to equal the long‐term 

available energy, while maintaining the ratio between the 

sensible- and latent-heat fluxes (the Bowen ratio, or β). 

This common adjustment (Foken, 2008) made the estimates 

of wetland and open-water evaporation consistent with 

one another.

Partitioning of available energy (AE) into sensible-heat 

flux (H) and latent-heat flux (LE) varies dramatically during 

the seasonal cycle (LE is the energy equivalent of the ET

rate). At the beginning of the calendar year, the remnant dead 

vegetation mat from previous years is the dominant exchange 

surface with the atmosphere and solar radiation, although 

rising water levels soon overtop the land surface, forming 

a secondary, mostly shaded water surface beneath the dead 

canopy. When the canopy is dry, β tends to be greater than 

one. Precipitation briefly shifts the balance toward LE for 

one to a few days, dropping β below 1, but evaporation and 

infiltration of intercepted water to lower layers soon return 

the partitioning to β >1. As a result of these repeated rapid 

reversals, on average, β ≈ 1 during most of the winter. As 

AE increases with growing sun angles in the spring, both H

and LE grow in response, maintaining a β of around one. 

The new green transpiring vegetation typically emerges 

from the water and dead stalk mat in May or June, at which 

time partitioning begins to shift rapidly toward LE. By July 

LE has reached peak values, and H has actually decreased 

from its spring values, even though AE has increased to peak 

values. Through much of the growing season, LE is much 

greater than H, as indicated by β values around 0.26 at the 

bulrush site and 0.13 at the mixed site. Possibly the greater 

partitioning toward LE at the mixed site is in response to the 

greater proportion of open water at that site, in spite of lower 

standing water levels. As the vegetation canopy senesces 

during September, transpiration decreases, and partitioning 

ceases to favor LE. During the study, the Octobers were 

unusually dry, receiving 52 percent of mean 1999 through 

2011 precipitation at Klamath Falls. This lack of precipitation 

and transpiration, coupled with water levels below land 

surface, typically resulted in β of around 2 or 3. Greater 

precipitation in November and December (the two greatest 

precipitation months historically) again restores the average β 

to around one.
62 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

Measured ET at the wetland sites is compared to 

reference ET (ETr) computed from data collected at the 

nearby Bureau of Reclamation Agency Lake weather station 

(AGKO), to compute crop coefficients (Kc) at daily, biweekly, 

and annual time steps. Approximate formulas are given to 

estimate daily values of growing season Kc, thereby allowing 

computation of daily ET using ETr from the AGKO weather 

station. Biweekly values of growing season Kc are computed 

from ensemble average values of ET and ETr during the 3-year 

study period growing seasons, and a single, mean value of 

Kc is computed for the non-growing season. Together, these 

provide relatively accurate estimates of biweekly ET during 

the study (RMSE=0.396 and 0.347 mm d-1, r 2=0.962 

and 0.971 at the bulrush and mixed sites, respectively). 

A fourth‐order polynomial fit of the growing season 

values to day of year provides a more automated form of 

ET computation.

Annual values of ET from both study sites are computed 

for the calendar years of 2008, 2009, and 2010. Annual 

values for 2008 and 2010 are synthesized by substituting 

non-growing season ET data from 2009 for periods before 

the study began (January 1–April 30, 2008) and after the 

study ended (September 30–December 31, 2010). Little 

uncertainty is introduced by this substitution because ET

is small during these times. Annual ET at the bulrush site 

ranged from 0.850 to 1.013 m/yr, with a 3-year mean of 

0.953 m/yr (table 11). Annual ET at the mixed site ranged from 

0.814 to 0.966 m/yr, with a 3-year mean of 0.903 m/yr. Based 

on a satellite-image estimate that the bulrush site typifies 

70 percent of the Upper Klamath Lake National Wildlife 

Refuge (NWR) and the mixed site typifies 30 percent, the 

resulting estimate of mean NWR ET during the 3 years is 

0.938 m/yr. At both sites, minimum annual ET occurred 

during 2010, a year of unusually low water level during 

spring and early summer, and a year that had 16 percent less 

precipitation than in 2008 through 2009. Although the lower 

2010 water level almost surely did not stress the vegetation, 

the water surface remained more shaded and decoupled from 

the atmosphere, leading to less surface water evaporation. 

Interannual variability (about ± 8.5 percent) was substantially 

greater than intersite variability (about ± 2.5 percent). A 

paired t-test conducted on site differences indicated that 

daily ET values from the two sites were statistically, but only 

marginally different from one another at the α=0.05 level.

Study-period averages of solar radiation (Rs), air 

temperature (Ta), and precipitation (P) measured at nearby 

AgriMet stations all were lower than their corresponding 

11-year averages from 2001–2011. Normally, lower Rs is 

associated with greater P, but in this case, the study period 

was less sunny and drier than the long-term average. These 

climatic conditions all suggest that ET measured during the 

study period probably is less than the expected long-term 

average. However, because Rs and Ta appear in the expression 

for reference ET (ETr), and the effect of P on ET in this 

wetland setting is minor, the crop coefficient approach 

developed here should remain relatively robust in other 

climatic settings.

A comparison of measured growing-season wetland ET

with alfalfa and pasture ET was made by tabulating alfalfa and 

pasture ET totals posted for the Klamath Falls station (KFLO) 

on the Bureau of Reclamation AgriMet Web site (http://www.

usbr.gov/pn/agrimet/ETtotals.html) and obtaining growing 

season durations (http://www.usbr.gov/pn/agrimet/chart/

kflo08et.txt). During the 190-day average alfalfa growing 

seasons from 2008 through 2010, wetland ET at our study 

sites was 0.779 m, about 7 percent less than alfalfa mean ET

of 0.838 m. During the 195-day average pasture growing 

seasons from 2008 through 2010, wetland ET at our study 

sites was 0.789 m, about 18 percent greater than pasture 

mean ET of 0.671 m. A comparison of annual ET can be 

made by assuming alfalfa and pasture ET are equal to wetland 

ET during the non-growing season. This assumption leads 

to annual estimates for 2008 through 2010 of 0.997, 0.938, 

and 0.820 m of ET from alfalfa, wetland, and pasture land 

covers, respectively.

An earlier ET study of this wetland used short-term 

(1- to 2-day) EC measurements of ET made four 

times during the growing season of 1997 to calibrate a 

Penman-Monteith ET model, driven by continuous onsite 

weather data, to compute growing-season ET (Bidlake, 

2000). The study site was located about 200 m northwest 

of our bulrush site, with virtually identical vegetation 

and altitude. Total growing-season ET from that study 

was comparable to our 2008 and 2009 ET, with notable 

short-term differences that appear to be related to differences 

in cloudiness. The two studies are consistent, and together 

they provide a well-documented estimate of Upper Klamath 

NWR evapotranspiration.

Bidlake (2002) also studied ET from fallowed cropland 

in the Tule Lake NWR during the growing season of 2000, 

using the Bowen-ratio energy balance method supplemented 

with modeling to fill in data gaps when sensors malfunctioned, 

and to extend the period of record to the full growing season 

(defined as May 1–October 31 in that study). Although the 

seasonal timing of ET varied considerably among the three 

types of fallow surfaces studied, total ET was remarkably 

constant, at 0.435 ± 0.009 m during the growing season. 

During the same months, mean ET measured at the Upper 

Klamath Lake NWR wetland in the current study was 0.718 m, 

or about 65 percent greater than the fallowed-cropland ET. If 

the non-growing-season ET measured at the wetland (0.220 m) 

also is assumed to occur from the fallowed cropland, the 

resulting annual ET from the wetland during 2008 through 

2010 (0.938 m) is about 43 percent greater than the fallowed 

cropland ET (0.655 m) during 2000.
References Cited 63

Open-water evaporation was measured at two midlake 

locations during 23 warm season biweekly periods during 

the study, using the Bowen-ratio energy balance method. 

Seasonal patterns of open-water evaporation were similar to 

those of wetland ET, but exhibited less of a seasonal cycle. 

Open-water and wetland magnitudes were nearly equal during 

late June to early August, when wetland vegetation was green 

and abundant. During late summer, open-water evaporation 

consistently exceeded wetland ET as the vegetation canopy 

began to senesce, while the lake released much of the 

energy stored during the summer, as latent‐heat flux. Spring 

comparison data are few, but suggest that open-water 

evaporation exceeds wetland ET when emergence of the 

new vegetation canopy out of the old, dead stalk mat is not 

complete. Overall, measured open-water evaporation was 

20 percent greater than wetland ET during the same periods.

References Cited

Allen, R.G., Pereira, L.S., Raes, D., and Smith, M., 1998, 

Crop evapotranspiration—Guidelines for computing crop 

water requirements: United Nations Food and Agriculture 

Organization Irrigation and Drainage Paper no. 56, 300 p.

Allen, R.G., Walter, I.A., Elliott, R.L., Howell, T.A., Itenfisu, 

D., and Jensen, M.E., 2005, The ASCE standardized 

reference evapotranspiration equation: Reston, Va., 

American Society of Civil Engineers, 196 p.

Anderson, E.R., 1954, Energy-budget studies, in Harbeck, 

G.E., and others, Water-loss investigations: Lake Hefner 

studies: U.S. Geological Survey Professional Paper 269, 

p. 71–119.

Aubinet, M., Vesala, T., and Papale, D., 2012, Eddy 

covariance—A practical guide to measurement and data 

analysis: Dordrecht, Germany, Springer, 438 p.

Barr, A.G., Betts, A.K., Desjardins, R.L., and MacPherson, J.I, 

1998, Comparison of regional surface fluxes from boundary 

layer budgets and aircraft measurements above boreal 

forest: Journal of Geophysical Research, v. 102, no. D24, 

p. 29213–29218.

Bidlake, W.R., 2000, Evapotranspiration from a bulrushdominated wetland in the Klamath Basin, Oregon: Journal 

of the American Water Resources Association, v. 36, no. 6, 

p. 1309–1320.

Bidlake, W.R., 2002, Evapotranspiration from selected 

fallowed agricultural fields on the Tule Lake National 

Wildlife Refuge, California, during May to October 2000: 

U.S. Geological Survey Water-Resources Investigations 

Report 02–4055, 59 p.

Blanken, P.D., Black, T.A., Yang, P.C., Neumann, H.H., Nesic, 

Z., Staebler, R., den Hartog, G, Novak, M.D., and Lee, 

X., 1998, Energy balance and canopy conductance of a 

boreal aspen forest: Partitioning overstory and understory 

components: Journal of Geophysical Research, v. 102, 

no. D24, p. 28915–28927.

Bossong, C.R., Caine, J.S., Stannard, D.I., Flynn, J.L., 

Stevens, M.R., and Heiny-Dash, J.S., 2003, Hydrologic 

conditions and assessment of water resources in the Turkey 

Creek Watershed, Jefferson County, Colorado, 1998–2001: 

U.S. Geological Survey Water-Resources Investigations 

Report 03–4034, 140 p.

Bowen, I.S., 1926, The ratio of heat losses by conduction and 

by evaporation from any water surface: Physical Review, 

v. 27, p. 779–787.

Brutsaert, W., 1982, Evaporation into the atmosphere: Boston, 

D. Reidel Publishing Co., 299 p.

Bureau of Reclamation, 2005, Natural flow of the upper 

Klamath River—Phase I: Prepared by the Technical Service 

Center, Denver, Colo., for U.S. Department of the Interior, 

Bureau of Reclamation, Klamath Basin Area Office, 

Klamath Falls, Oreg., November.

Campbell, G.S., 1980, Long-wave radiation emission 

and absorption by domes of polyethylene shielded net 

radiometers: Pullman, Wash., Washington State University, 

12 p.

Campbell, G.S., and Norman, J.M., 1998, An introduction to 

environmental biophysics (2d ed.): New York, SpringerVerlag, 286 p.

Carter, V., Reel, J.T., Rybicki, N.B., Ruhl, H.A., Gammon, 

P.T., and Lee, J.K., 1999, Vegetative resistance to flow in 

south Florida—Summary of vegetation sampling at sites 

NESRS3 and P33, Shark River Slough, November 1996: 

U.S. Geological Survey Open-File Report 99–218, 90 p.

Dingman, S.L., 2002, Physical hydrology: New Jersey, 

Prentice Hall, 646 p.

Dugas, W.A., Fritschen, L.J., Gay, L.W., Held, A.A., Matthias, 

A.D., Reicosky, D.C., Steduto, P., and Steiner, J.L., 1991, 

Bowen ratio, eddy correlation, and portable chamber 

measurements of sensible and latent heat flux over irrigated 

spring wheat: Agricultural and Forest Meteorology, v. 56, 

p. 1–20.

Dyer, A.J., 1961, Measurements of evaporation and heat 

transfer in the lower atmosphere by an automatic eddycorrelation technique: Quarterly Journal of the Royal 

Meteorological Society, v. 87, p. 401–412.

Engineering Toolbox, 2011, Water vapor-specific heat: 

Engineering Toolbox, accessed October 13, 2012, at http://

www.engineeringtoolbox.com/water-vapor-d_979.html
64 Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010

Foken, T., 2008, The energy balance closure problem—

An overview: Ecological Applications, v. 18, no. 6, 

p. 1351–1367.

Garratt, J.R., 1992, The atmospheric boundary layer: 

Cambridge, Cambridge University Press, 316 p.

Gash, J.H.C., and Dolman, A.J., 2003, Sonic anemometer 

(co)sine response and flux measurement I. The potential 

for (co)sine error to affect sonic anemometer-based flux 

measurements: Agricultural and Forest Meteorology, v. 119, 

p. 195–207.

German, E.R., 2000, Regional evaluation of 

evapotranspiration in the Everglades: U.S. Geological 

Survey Water-Resources Investigations Report 00–4217, 

48 p.

Halldin, S., and Lindroth, A., 1992, Errors in net radiometry—

Comparison and evaluation of six radiometer designs: 

Journal of Atmospheric and Oceanic Technology, v. 9, 

p. 762–783.

Hansen, K., 1959, The terms gyttja and dy: Hydrobiologia, 

v. 13, no. 4, p. 309–315.

Hostetler, S.W., 2009, Use of models and observations to 

assess trends in the 1950–2005 water balance and climate of 

Upper Klamath Lake, Oregon: Water Resources Research, 

v. 45, W12409, doi:10.1029/2008WR007295, 14 p.

Hubbard, L.L., 1970, Water budget of Upper Klamath Lake, 

southwestern Oregon: U.S. Geological Survey Hydrologic 

Investigations Atlas HA–351, 1 sheet.

Janssen, Kenneth D., 2005, Daily energy-budget and Penman 

evaporation from Upper Klamath Lake, Oregon: Portland, 

Oreg., Portland State University, M.S. thesis, 131 p.

Kann, P., and Walker, W.W., 1999, Nutrient and hydrologic 

loading to Upper Klamath Lake, Oregon, 1991–1998: Draft 

report prepared for Klamath Tribes Natural Resources 

Department and Bureau of Reclamation, Klamath Falls, 

Oreg., 48 p. plus appendices.

Kiehl, J.T., and Trenberth, K.E., 1997, Earth’s annual 

global mean energy budget: Bulletin of the American 

Meteorological Society, v. 78, no. 2, p. 197–208.

Koberg, G.E., 1964, Methods to compute long-wave radiation 

from the atmosphere and reflected solar radiation from 

a water surface: U.S. Geological Survey Professional 

Paper 272–F, p. 107–136.

Lowe, P.R., 1976, An approximating polynomial for 

the computation of saturation vapor pressure: Journal 

of Applied Meteorology, v. 16, no. 1, p. 100–103. 

(Also available at http://dx.doi.org/10.1175/1520-

0450(1977)016<0100:AAPFTC>2.0.CO;2.)

Massman, W.J., 2000, A simple method for estimating 

frequency response corrections for eddy covariance 

systems: Agricultural and Forest Meteorology, v. 104, 

p. 85–198.

Mauder, M., Liebethal, C., Gockede, M., Leps, J.P., Beyrich, 

F., and Foken, T., 2006, Processing and quality control 

of flux data during LITFASS–2003: Boundary-Layer 

Meteorology, v. 121, p. 67–88.

McCaughey, J.H., Lafleur, P.M., Joiner, D.W., Bartlett, P.A., 

Costello, A.M., Jelinski, D.E., and Ryan, M.G., 1997, 

Magnitudes and seasonal patterns of energy, water, and 

carbon exchanges at a boreal young jack pine forest in 

the BOREAS northern study area: Journal of Geophysical 

Research, v. 102, no. D24, p. 28977–29007.

Monteith, J.L., and Unsworth, M.H., 1990, Principles of 

environmental physics (2d ed.): London, Edward Arnold, 

291 p.

Nash, J.E., and Sutcliffe, J.V., 1970, River flow forecasting 

through conceptual models—Part 1–A discussion of 

principles: Journal of Hydrology, v. 10, p. 282–290.

National Research Council, 2007, Hydrology, ecology, and 

fishes of the Klamath River Basin: Washington, D.C., The 

National Academies Press, 249 p.

Paw U, K.T., Baldocchi, D.D., Meyers, T.P., and Wilson, 

K.B., 2000, Correction of eddy-covariance measurements 

incorporating both advective effects and density fluxes: 

Boundary-Layer Meteorology, v. 97, p. 487–511.

Pearce, C.D., and Gold, L.W., 1959, Observations of ground 

temperature and heat flow at Ottawa, Canada: Journal of 

Geophysical Research, v.64, p. 1293–1298.

Sass, J.H., and Sammel, E.A., 1976, Heat Flow Data and Their 

Relation to Observed Geothermal Phenomena near Klamath 

Falls, Oregon: Journal of Geophysical Research, v. 81, 

p. 4863–4868.

Schedlbauer, J.L., Oberbauer, S.F., Starr, G., and Jimenez, 

K.L., 2011, Controls on sensible heat and latent energy 

fluxes from a short-hydroperiod Florida Everglades marsh: 

Journal of Hydrology, v. 411, p. 331–341.

Schotanus, P., Nieuwstadt, F.T.M., and deBruin, H.A.R., 1983, 

Temperature measurement with a sonic anemometer and its 

application to heat and moisture fluxes: Boundary-Layer 

Meteorology, v. 26, p. 81–93.

Schuepp, P.H., LeClerc, M.Y., Macpherson, J.I., and 

Desjardins, R.L., 1990, Footprint prediction of scalar 

fluxes from analytical solutions of the diffusion equation: 

Boundary Layer Meteorology, v. 50, p. 355–373.
References Cited 65

Snyder, D.T., and Morace, J.L., 1997, Nitrogen and 

phosphorous loading from drained wetlands adjacent to 

Upper Klamath and Agency Lakes, Oregon, U.S. Geological 

Survey Water-Resources Investigations Report 97–4059, 

67 p.

Stannard, D.I., 1997, A theoretically based determination 

of Bowen-ratio fetch requirements: Boundary-Layer 

Meteorology, v. 83, p. 375–406.

Stannard, D.I., Rosenberry, D.O., Winter, T.C., and Parkhurst, 

R.S., 2004, Estimates of fetch-induced errors in Bowenratio energy-budget measurements of evapotranspiration 

from a prairie wetland, Cottonwood Lake area, North 

Dakota, USA: Wetlands, v. 24, no. 3, p. 498–513.

Sturrock, A.M., Winter, T.C., and Rosenberry, D.O., 1992, 

Energy budget evaporation from Williams Lake—A closed 

lake in north-central Minnesota: Water Resources Research, 

v. 28, no. 6, p. 1605–1617.

Sumner, D.M., Wu, Q, and Pathak, C.S., 2011, Variability of 

albedo and utility of the MODIS albedo product in forested 

wetlands: Wetlands, v. 31, no. 2, p. 229–237.

Tanner, B.D., and Greene, J.P., 1989, Measurement of 

sensible heat and water-vapor fluxes using eddy-correlation 

methods—Final report prepared for U.S. Army Dugway 

Proving Grounds: U.S. Army, Dugway, Utah, 17 p.

Tanner, C.B., and Thurtell, G.W., 1969. Anemoclinometer 

measurements of Reynolds stress and heat transport in 

the atmospheric surface layer—Final report prepared for 

U.S. Army Electronics Command: Fort Huachuca, Ariz., 

Atmospheric Sciences Laboratory, 10 p.

Twine, T.E., Kustas, W.P., Norman, J.M., Cook, D.R., Houser, 

P.R., Meyers, T.P., Prueger, J.H., Starks, P.J., and Wesely, 

M.L., 2000, Correcting eddy-covariance flux underestimates 

over a grassland: Agricultural and Forest Meteorology, 

v. 103, p. 279–300.

Webb, E.K., Pearman, G.I., and Leuning, R., 1980, Correction 

of flux measurements for density effects due to heat and 

water vapour transfer: Quarterly Journal of the Royal 

Meteorological Society, v. 106, p. 85–100.

Western Regional Climate Center, 2012, Historical climate 

data: Western Regional Climate Center, accessed April 2, 

2012, at http://www.wrcc.dri.edu/Climsum.html.

Wilson, Kell, Goldstein, Allen, Falge, Eva, Aubinet, Marc, 

Baldocchi, Dennis, Berbigier, Paul, Bernhofer, Christian, 

Ceulemans, Reinhart, Dolman, Han, Field, Chris, Grelle, 

Achim, Ibrom, Andreas, Law, B.E., Kowalski, Andy, 

Meyers, Tilden, Moncrieff, John, Monson, Russ, Oechel, 

Walter, Tenhunen, John, Valentini, Ricardo, and Verma, 

Shashi, 2002, Energy balance closure at FLUXNET sites: 

Agricultural and Forest Meteorology, v. 113, p. 223–243.

Winter, T.C., Rosenberry, D.O., and Sturrock, A.M., 2003, 

Evaporation determined by the energy-budget method 

for Mirror Lake, New Hampshire: Limnology and 

Oceanography, v. 48, no. 3, p. 995–1009.

Wood, T.M., Hoilman, G.R., and Lindenberg, M.K., 2006, 

Water-quality conditions in Upper Klamath Lake, Oregon, 

2002–04: U.S. Geological Survey Scientific Investigations 

Report 2006–5209, 52 p.

Wood, T.M., and Gartner, J.W., 2010, Use of acoustic 

backscatter and vertical velocity to estimate concentration 

and dynamics of suspended solids in Upper Klamath Lake, 

south-central Oregon— Implications for Aphanizomenon 

flos-aquae: U.S. Geological Survey Scientific Investigations 

Report 2010–5203, 20 p.
This page intentionally left blank.
Publishing support provided by the U.S. Geological Survey 

Publishing Network, Tacoma Publishing Service Center

For additional information contact:

Director, Oregon Water Science Center

U.S. Geological Survey

2130 SW 5th Avenue

Portland, Oregon 97201

http://or.water.usgs.gov
Stannard and others— Evapotranspiration from Wetland and Open-Water Sites at Upper Klamath Lake, Oregon, 2008–2010—Scientific Investigations Report 2013–5014