Water-Resources Investigations Report

U.S. GEOLOGICAL SURVEY

Evapotranspiration from Successional

Vegetation in a Deforested Area of the

Lake Wales Ridge, Florida

Prepared in cooperation with the

St. Johns River Water Management District and the

South Florida Water Management District

96–4244

By D. M. Sumner

Tallahassee, Florida

1996
U.S. DEPARTMENT OF THE INTERIOR

BRUCE BABBITT, Secretary

U.S. GEOLOGICAL SURVEY

Gordon P. Eaton, Director

For additional information write to: Copies of this report can be purchased

from:

U.S. Geological Survey

Information Services

Box 25286

Federal Center

Denver, CO 80225

The use of firm, trade, and brand names in this report is for identification purposes

only and does not constitute endorsement by the U.S. Geological Survey.

District Chief

U.S. Geological Survey, WRD

Suite 3015

227 North Bronough Street

Tallahassee, FL 32301
Contents iii

CONTENTS

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

Introduction ........................................................................................................................................................................... 1

Purpose and Scope....................................................................................................................................................... 2

Description of the Study Site....................................................................................................................................... 2

Methods for Measurement and Estimation of Evapotranspiration........................................................................................ 5

Meteorological Station ................................................................................................................................................ 9

Eddy Correlation Measurement of Evapotranspiration ...............................................................................................11

Penman-Monteith Estimation of Evapotranspiration ..................................................................................................14

Simpler Methods for Estimation of Evapotranspiration..............................................................................................17

Results of Evapotranspiration Measurement and Estimation Measurement of Evapotranspiration .....................................18

Model Calibration Using Measured Evapotranspiration .............................................................................................18

Application of Evapotranspiration Models..................................................................................................................30

Summary and Conclusions ....................................................................................................................................................34

References .............................................................................................................................................................................36

FIGURES

1. Map showing location of study site in Orange County, Florida ................................................................................. 3

2-34. Graphs showing:

2. Average canopy height at study site from September 15, 1993, to August 28, 1994........................................ 4

3. Two-sided leaf area index at study site from September 15, 1993, to August 28, 1994.................................... 4

4. Average soil moisture content in upper 30 centimeters of soil profile at study site

from September 15, 1993, to August 28, 1994 .................................................................................................. 5

5. Water level in surficial aquifer at study site from September 15, 1993, to August 28, 1994............................ 6

6. Rainfall rate at 20-minute resolution at study site from September 15, 1993, to August 28, 1994................... 6

7. Cumulative precipitation at study site from September 15, 1993, to September 15, 1994................................ 7

8. Air temperature at study site from September 15, 1993, to August 28, 1994.................................................... 7

9. Photosynthetically active radiation at study site from September 15, 1993, to August 28, 1994 ..................... 8

10. Vapor-pressure deficit at study site from September 15, 1993, to August 28, 1994.......................................... 8

11. Diurnal variation in photosynthetically active radiation and vapor-pressure deficit at study site on

September 23-24, 1993 ...................................................................................................................................... 9

12. Evapotranspiration measured by eddy correlation energy-balance Bowen ratio method at study site

from September 1993 to August 1994 ...............................................................................................................19

13. Surface energy-balance components on September 23-24, 1993, at study site .................................................19

14. Absolute and relative measures of energy-budget closure for eddy correlation data collected on

September 23-24, 1993, at study site .................................................................................................................20

15. Eddy correlation-measured evapotranspiration on September 23-24, 1993, at study site.................................21

16. Comparison of Penman-Monteith-simulated evapotranspiration and measured evapotranspiration

at study site from September 1993 to August 1994...........................................................................................22

17. Comparison of simulated and measured values of canopy resistance at study site from

September 1993 to August 1994........................................................................................................................22

18. Seasonal distribution of discrepancy between Penman-Monteith-simulated evapotranspiration

and measured evapotranspiration at study site from September 1993 to August 1994 .....................................23

19. Comparison between simulated and measured evapotranspiration on September 23-24, 1993,

at study site.........................................................................................................................................................23

20. Comparison of Penman-Monteith-simulated evapotranspiration and measured evapotranspiration

at study site from September 1993 to August 1994...........................................................................................24
iv Contents

21. Seasonal distribution of discrepancy between Penman-Monteith-simulated evapotranspiration

and measured evapotranspiration at study site from September 1993 to August 1994..................................... 25

22. Comparison of modeled and measured values of canopy resistance at study site from

September 1993 to August 1994 ....................................................................................................................... 25

23. Ratio of Penman-estimate of daily evapotranspiration to Penman-Monteith estimate of daily

evapotranspiration at study site ......................................................................................................................... 26

24. Comparison of Priestley-Taylor-simulated evapotranspiration and measured evapotranspiration

at study site from September 1993 to August 1994 .......................................................................................... 27

25. Seasonal distribution of discrepancy between Priestley-Taylor-simulated evapotranspiration and

measured evapotranspiration at study site from September 1993 to August 1994 ........................................... 27

26. Comparison of simulated and measured values of Priestley-Taylor α at study site from

September 1993 to August 1994 ....................................................................................................................... 28

27. Simulated relations of canopy resistance to environmental variables............................................................... 29

28. Estimated daily evapotranspiration rate at study site from September 16, 1993, to August 28, 1994.............. 31

29. Estimated cumulative evapotranspiration at study site from September 15, 1993, to September 15, 1994 ..... 32

30. Simulated mean daytime Bowen ratio at study site from September 16, 1993, to August 28, 1994 ................ 33

31. Simulated daytime canopy resistance at study site from September 15, 1993, to August 28, 1994 ................. 33

32. Simulated canopy resistance at study site from July 19-23, 1994..................................................................... 34

33. Simulated daytime Priestley-Taylor α at study site from September 15, 1993, to August 28, 1994................ 35

34. Simulated Priestley-Taylor α at study site from July 19-23, 1994 ................................................................... 35

TABLES

1. Study instrumentation............................................................................................................................................. 10

2. Summary of parameters and error statistics for evapotranspiration models........................................................... 21
Contents v

CONVERSION FACTORS, VERTICAL DATUM, ABBREVIATIONS, AND SYMBOLS

___________________________________________________________________________________________________

Multiply By To obtain

 ____________________

Length

millimeter (mm) 0.03937 inch

centimeter (cm) 0.3937 inch

meter (m) 3.281 foot

Area

hectare 2.471 acre

Flux

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

Energy

joule (J) 0.2388 calorie

Energy flux density

watt (W/m2) 0.001433 calorie per square centimeter per minute

Pressure

kilopascal (kPa) 0.2953 inches of mercury

0.1450 pound per square inch

10.0 millibar

Photosynthetically-active radiation

micromoles per square meter per second 6.02 × 1017 photons per square meter per second

(μmoles/(m2⋅s))

______________________________________________________________________________________________________________

Sea level: In this report "sea level" refers to the National Geodetic Vertical Datum of 1929--a geodetic datum derived from a

general adjustment of the first-order level nets of the United States and Canada, formerly called Sea Level Datum of 1929.

Altitude, as used in this report, refers to distance above or below sea level.

Temperature is given in degrees Celsius (o

C), which can be converted to degrees Fahrenheit (oF) by the following equation: oF = 1.8(oC) + 32.

Additional abbreviations

CSI = Campbell Scientific, Inc.

ECEBBR = Eddy correlation energy-balance Bowen ratio method

ECEBR = Eddy correlation energy-balance residual method

PAR = Photosynthetically-active radiation

REBS = Radiation and Energy Balance Systems, Inc.

RMY = R.M. Young, Inc.

TDR = Time domain reflectometry

TE = Texas Electronics, Inc.

USGS = United States Geological Survey
vi Contents

List of Symbols

Roman

b Depth to heat flux plate, in m

C1-C8 Site-specific empirical parameters within evapotranspiration models

Cp Specific heat of air, in J/(g⋅

oC)

Cs Mean specific heat capacity of soil above heat flux plate, in J/(m3⋅

oC)

Csd Mean specific heat capacity of dry soil above heat flux plate, in J/(kg⋅

oC)

Cw Specific heat capacity of water, in J/(kg⋅

oC)

d Momentum displacement height of vegetation, in m

D Vapor pressure deficit, in kPa

e Vapor pressure, in kPa

es Saturation vapor pressure, in kPa

E Evapotranspiration rate, in g/(m2⋅s)

F Factor used in krypton hygrometer correction that accounts for molecular weights of air and

atmospheric abundance of oxygen, equal to 0.229 g⋅

oC/J

G Soil heat flux at land surface, in W/m2

h Average canopy height, in m

H Sensible heat flux, in W/m2

k von Karman’s constant, equal to 0.4, dimensionless

κs Attenuation coefficient of light for the canopy, dimensionless

Ko Extinction coefficient of hygrometer for oxygen, in m3/(g⋅cm)

Kw Extinction coefficient of hygrometer for water, in m3/(g⋅cm)

L Two-sided leaf area index, in m2/m2

Ls Sunlit leaf area per unit area of land, in m2/m2

Lv Green leaf fraction visible to observer, in m2/m2

rc Canopy resistance, in s/m

rh Aerodynamic resistance, in s/m

Rn Net radiation, in W/m2

RPAR Photosynthetically-active radiation, in μmoles/(m2⋅s)

S Rate of change of stored energy in soil above heat flux plate, in W/m2

t Time, in Julian days
Contents vii

Ta Air temperature, in oC

Ti Mean temperature at time step “i” of soil above heat flux plate, in oC

u Horizontal wind speed, in m/s

u* Friction velocity, in m/s

w Vertical wind speed, in m/s

wm Mean gravimetric water content above heat flux plate, in kg/kg

z Height of sensors above land surface, in m

zo Roughness length of canopy for momentum, in m

zh Roughness length of canopy for sensible heat, in m

Greek

α Priestley-Taylor coefficient, dimensionless

∆ Slope of the saturation vapor pressure curve, in kPa/oC

∆t Time interval between soil-temperature measurements, in s

γ Psychrometric “constant”, in kPa/oC

λ Latent heat of vaporization, in J/g

λE Latent heat flux, in W/m2

θ Mean volumetric moisture content in rooting zone, in cm3/cm3

ρ Air density, in g/m3

ρb Mean soil bulk density above heat flux plate, in kg/m3

ρv Vapor density, in g/m3

ω Angular frequency of Earth’s revolution around Sun, in d-1

ψh Stability profile corrector for sensible heat, dimensionless

ψm Stability profile corrector for momentum, dimensionless

ζ Atmospheric stability, dimensionless
viii Contents
Abstract 1

Evapotranspiration from Successional Vegetation in a

Deforested Area of the Lake Wales Ridge, Florida

By D. M. Sumner

ABSTRACT

The suitability of three evapotranspiration

models (Penman-Monteith, Penman, and a modified Priestley-Taylor) was evaluated at a site of

successional vegetation in a deforested area of the

Lake Wales Ridge, Florida. Eddy correlation measurements of evapotranspiration made during 22

approximately 1-day periods at a temporal resolution of 20 minutes from September 1993 to

August 1994 were used to calibrate the evapotranspiration models. Three variants of the eddy

correlation method that ascribe measurement

error to three different sources were considered in

the analysis. The Penman-Monteith and modified

Priestley-Taylor models were successful in

approximating measured 20-minute values of

evapotranspiration (r

2 ≥ 0.918). The most successful approaches were the modified PriestleyTaylor model (r

2 = 0.972) and a nontraditional

and simplified form of the Penman-Monteith

model (r

2 = 0.967). The Penman approach was

unsuccessful as a predictor of evapotranspiration.

The evapotranspiration models were used

to estimate evapotranspiration between measurements. When evapotranspiration values measured

with a Bowen ratio variant of the eddy correlation

method were used for model calibration, estimated daily evapotranspiration rates varied seasonally ranging from 0.2 millimeters per day

(0.008 inch per day) in late December 1993 to

5 millimeter per day (0.2 inch per day) in midJuly 1994. Annual evapotranspiration

(September 15, 1993, to September 15, 1994) was

estimated to be about 680 millimeters (27 inches).

Evapotranspiration models calibrated to the standard eddy correlation method and to an energybalance residual variant provided estimates of

annual evapotranspiration that were about 10 percent lower and higher, respectively. These data

indicate that of the 1,320 millimeters (52 inches)

of precipitation during the 1-year period, about

570 to 700 millimeters (22 to 28 inches)

recharged the surficial aquifer. Evapotranspiration

at this study site probably defines the lower limit

of evapotranspiration from vegetated surfaces in

central Florida because of the shallow-rooted

plants, rapidly-drained soils, and relatively deep

water table.

INTRODUCTION

 The importance of evapotranspiration in the

hydrologic cycle has long been recognized. In Florida,

evapotranspiration is second only to precipitation in

magnitude within the hydrologic budget. Of the

approximately 1,300 mm of mean annual rainfall in

central Florida, 760 to 1,220 mm have been estimated

to return to the atmosphere as evapotranspiration

(Tibbals, 1990). Despite the importance of evapotranspiration in the hydrologic cycle, the magnitude, seasonal and diurnal distributions, and relation to

environmental variables of evapotranspiration remain

relatively unknown. This uncertainty in evapotranspiration is particularly apparent in nonagricultural vegetation, such as successional vegetation in deforested

areas of the Lake Wales Ridge. This successional vegetation is unique in that vegetative cover can be

sparse, the water table is relatively deep, and the sandy

soils are rapidly drained; these characteristics minimize evapotranspiration from this vegetation, which in
2 Evapotranspiration From Successional Vegetation in a Deforested Area of the Lake Wales Ridge, Florida

turn, maximizes recharge to the underlying aquifer.

Accurate estimates of evapotranspiration are fundamental to improving estimates of aquifer recharge in

areas of successional vegetation of the Lake Wales

Ridge.

The eddy correlation method has been used successfully to directly measure evapotranspiration in

Florida (Bidlake and others (1993) and Knowles

(1996)). This micrometeorological method offers several advantages to alternative water-budget

approaches (lysimeter or regional water budget) by

providing more areal integration and less site disruption than lysimeters, eliminating the need to estimate

other terms of a water budget (precipitation, deep percolation, and runoff), and allowing relatively fine temporal resolution (less than 1 hour).

Evapotranspiration can be estimated from

evapotranspiration models. These models also provide

insight into the relative importance of individual environmental variables in the evapotranspiration process.

The Penman-Monteith equation (Monteith, 1965) is a

physics-based evapotranspiration model that is based

on a coupling of energy-budget and aerodynamic considerations. Although the Penman-Monteith equation

is often a theoretically sound model, the equation is

computationally cumbersome. Simpler models such as

the Penman (Penman, 1948) and Priestley-Taylor

(Priestley and Taylor, 1972) equations offer computational ease, but the error introduced by these models

must be evaluated to determine model suitability to a

particular site.

The U.S. Geological Survey (USGS), in cooperation with the St. Johns River Water Management District and the South Florida Water Management

District, began a 4-year study in 1992 to estimate the

annual pattern of evapotranspiration at a site containing successional vegetation; to evaluate the implications of these results on estimation of aquifer recharge;

and to evaluate the suitability of several evapotranspiration models. This analysis can provide guidance in

the estimation of evapotranspiration and aquifer

recharge and in the selection of a reliable and efficient

evapotranspiration model at other sites with similar

environmental characteristics.

Purpose and Scope

This report presents (1) estimates of evapotranspiration during a 1-year period at a site of successional

vegetation in a deforested area of the Lake Wales

Ridge, Florida; and (2) results of an evaluation of the

suitability of three evapotranspiration models—

Penman-Monteith, Penman, and a modified PriestleyTaylor—in evapotranspiration simulation. Evapotranspiration measurements were made approximately

every 2 weeks from September 1993 to August 1994

at a field site in Orange County, Florida, using eddy

correlation instrumentation. Evapotranspiration models were used to estimate evapotranspiration between

direct evapotranspiration measurements and to make a

comparative analysis of the merits of each model.

Estimated annual evapotranspiration and measured

precipitation were used to estimate surficial aquifer

recharge.

Description of the Study Site

The study site is a field of mostly herbaceous,

successional vegetation that typically grows in cleared

areas of central Florida. The site location is in west

Orange County, Florida (fig. 1). The site (about 450 m

by 600 m, or about 27 ha) is bounded by citrus groves,

oak trees, cultivated pine trees, and infiltration basins

for disposal of reclaimed water. The site contains rolling topography; land surface altitude ranges from

about 41 to 46 m above sea level. The site is part of the

Lake Wales Ridge physiographic region (White, 1970,

plate 1-B), which is characterized by sandy, rapidly

drained soils, and hilly, karstic topography.

Vegetation at the site predominantly is natalgrass (Rhynchelytrm repens), dog fennel (Eupatorium

sp.), dwarf horseweed (Conyza canadensis), and ragweed (Ambrosia sp.). The rooting depth for any of the

vegetation rarely exceeds 30 cm. Average canopy

height (considering both living plants and dead residual vegetation from the previous growing season) varies seasonally, ranging from about 25 cm in spring to

75 cm in summer (fig. 2). Green foliage density follows a seasonal pattern, reaching maximum values

during the summer wet period and minimum values

during the winter dry period (fig. 3).

The sandy, rapidly drained soils of this

site—Candler series hyperthermic, uncoated Typic

Quartzipsamments (Doolittle and Schellentrager,

1989)—allow the shallow-rooted plants to become

water stressed during a dry period. Moisture content in

the rooting zone of the soil can be as low as

0.02 cm3/cm3 and drainage of the soil profile following a rainfall event is relatively rapid (fig. 4). The

water table generally is more than a meter below land
Introduction 3

Figure 1. Location of study site in Orange County, Florida.

MAP

AREA

33

27

561

192

FLORIDA’S TURNPIKE

Lake

Minneola

Lake

Minnehaha

Lake

Louisa

Johns

Lake

Lake

Butler

Black

Lake

Lake Avalon

Lake

Hancock

Lake

Speer

Flat

Lake

Lake

Nellie

Lake

Needham

Sawgrass Lake

Bay

Lake

Reedy Creek

Bonnet Creek

LAKE COUNTY POLK COUNTY

ORANGE COUNTY OSCEOLA COUNTY

Hickorynut Lake

Reedy

Lake Lake

Sheen

Lake

Ingram

Lake Apopka

I-4

Lake

Tibet

N

82°45′ 82°30′

28°38′

28°14′

30′

22′

0 1

1

2

2

3

3

4

4

5 KILOMETERS

0 5 MILES

50

545

STUDY SITE
4 Evapotranspiration From Successional Vegetation in a Deforested Area of the Lake Wales Ridge, Florida

20

80

30

40

50

60

70

AVERAGE CANOPY HEIGHT, IN CENTIMETERS

245 275 305 335 30 60 90 120 150 180 210 240 270

1993 1994

JULIAN DAY

SEPT OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1993 1994

0

5

1

2

3

4

TWO-SIDED LEAF AREA INDEX,

IN SQUARE METERS PER SQUARE METER

245 275 305 335 30 60 90 120 150 180 210 240 270

1993 1994

JULIAN DAY

SEPT OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1993 1994

Figure 2. Average canopy height at study from September 15, 1993, to August 28, 1994.

Figure 3. Two-sided leaf area index at study site from September 15, 1993, to August 28, 1994. Note: Leaf

area index is defined as the two-sided, green leaf area per unit area of land surface.
Methods for Measurement and Estimation of Evapotranspiration 5

0

0.10

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

AVERAGE SOIL MOISTURE CONTENT IN UPPER 30 CENTIMETERS,

IN CUBIC CENTIMETERS PER CUBIC CENTIMETER

245 275 305 335 30 60 90 120 150 180 210 240 270

1993 1994

JULIAN DAY

SEPT OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1993 1994

Figure 4. Average soil moisture content in upper 30 centimeters of soil profile at study site from September 15, 1993, to

August 28, 1994.

surface throughout the site. In the upland areas of the

site, water-table depth can be more than 5 m. Fluctuations in the water table exhibit a strong seasonal pattern in response to the seasonal distribution of rainfall

(figs. 5 and 6).

The climate of central Florida is humid subtropical and is characterized by a warm, wet season (JuneSeptember) and a mild, relatively dry season (OctoberMay). More than 50 percent of the annual rainfall generally occurs during the wet season (figs. 6 and 7)

when diurnal thunderstorm activity due to differential

heating of the land and ocean is common. During the

dry season, precipitation commonly is associated with

frontal systems. Mean air temperature at the site is

about 22 oC, ranging from occasional winter temperatures below 0 oC to summer temperatures approaching

35 oC (fig. 8). Diurnal temperature variations at the

site average about 12 oC. Strong seasonal and diurnal

patterns also are exhibited by photosynthetically

active radiation and the vapor-pressure deficit of the

air (figs. 9, 10, and 11). Diurnal solar heating also

leads to a diurnal pattern in wind speed and turbulent

mixing (high during day and low at night).

METHODS FOR MEASUREMENT AND

ESTIMATION OF EVAPOTRANSPIRATION

Evapotranspiration was measured at the study

site using the eddy correlation method in a manner similar to Bidlake and others (1993). Eddy correlation

instrumentation was deployed for 22 measurement

events from September 15, 1993, to August 27, 1994.

The length of each measurement event was about

1 day, with 20-min resolution. A station also was

installed 15 m from the eddy correlation instrumentation to continuously measure meteorological data

needed for evapotranspiration modeling and to provide

ancillary data for the eddy correlation analysis. Measured values of evapotranspiration were used to calibrate evapotranspiration models (Penman-Monteith

and modified Priestley-Taylor). Evapotranspiration was
6 Evapotranspiration From Successional Vegetation in a Deforested Area of the Lake Wales Ridge, Florida

39.4

41.2

39.6

39.8

40.0

40.2

40.4

40.6

40.8

41.0

WATER LEVEL, IN METERS ABOVE SEA LEVEL

245 275 305 335 30 60 90 120 150 180 210 240 270

1993 1994

JULIAN DAY

U.S. GEOLOGICAL SURVEY STATION NUMBER 282901081380301

SURFICIAL AQUIFER WELL

ELEVATION OF LAND SURFACE AT WELL = 43 METERS

SEPT OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1993 1994

0

100

20

40

60

80

RAINFALL RATE FOR 20-MINUTE PERIODS,

 IN MILLIMETERS PER HOUR

245 275 305 335 30 60 90 120 150 180 210 240 270

1993 1994

JULIAN DAY

BEGINNING OF MEASUREMENT PERIOD

END OF MEASUREMENTPERIOD

SEPTEMBER 15, 1993

SEPTEMBER 15, 1994

SEPT OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1993 1994

Figure 5. Water level in surficial aquifer at study site from September 15, 1993, to August 28, 1994.

Figure 6. Rainfall rate at 20-minute resolution at study site from September 15, 1993, to August 28, 1994.
Methods for Measurement and Estimation of Evapotranspiration 7

0

1,400

200

400

600

800

1,000

1,200

CUMULATIVE RAINFALL, IN MILLIMETERS

245 275 305 335 30 60 90 120 150 180 210 240 270

1993 1994

JULIAN DAY

BEGINNING OF MEASUREMENT PERIOD

END OF MEASUREMENT PERIOD

SEPTEMBER 15, 1993

SEPTEMBER 15, 1994

DATA COLLECTED AT FIELD SITE

DATA COLLECTED AT ORLANDO AIRPORT (NOAA, 1994A AND 1994B)

SEPT OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1993 1994

-10

40

0

10

20

30

AIR TEMPERATURE, IN DEGREES CELSIUS

245 275 305 335 30 60 90 120 150 180 210 240 270

1993 1994

JULIAN DAY

SEPT OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1993 1994

Figure 7. Cumulative precipitation at study site from September 15, 1993, to September 15, 1994.

Figure 8. Air temperature at study site from September 15, 1993, to August 28, 1994.
8 Evapotranspiration From Successional Vegetation in a Deforested Area of the Lake Wales Ridge, Florida

0

2,500

500

1,000

1,500

2,000

PHOTOSYNTHETICALLY-ACTIVE RADIATION,

IN MICROMOLES PER SECOND PER SQUARE METER

245 275 305 335 30 60 90 120 150 180 210 240 270

1993 1994

JULIAN DAY

SEPT OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1993 1994

0

4.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

VAPOR PRESSURE DEFICIT, IN KILOPASCALS

245 275 305 335 30 60 90 120 150 180 210 240 270

1993 1994

JULIAN DAY

SEPT OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1993 1994

Figure 9. Photosynthetically active radiation at study site from September 15, 1993, to August 28, 1994.

Figure 10. Vapor-pressure deficit at study site from September 15, 1993, to August 28, 1994.
Methods for Measurement and Estimation of Evapotranspiration 9

0400 0800 1200 1600 2000 0000 0400 0800 1200 1600 2000 0000

SEPTEMBER 23 SEPTEMBER 24, 1993

0000

PHOTOSYNTHETICALLY-ACTIVE RADIATION,

EASTERN

STANDARD

TIME

2,500

2,000

1,500

1,000

500

0

4

3

2

1

0

VAPOR PRESSURE DEFICIT, IN KILOPASCALS

IN MICROMOLES PER SQUARE METER PER SECOND

PHOTOSYNTHETICALLY-ACTIVE RADIATION

VAPOR PRESSURE DEFICIT

JULIAN DAY 266 JULIAN DAY 267

Figure 11. Diurnal variation in photosynthetically active radiation and vapor pressure deficit at study site on

September 23-24, 1993.

estimated during the unmeasured periods between

events (and at times of identifiable and substantial

measurement error during the measured events) using

the calibrated evapotranspiration models. Instrumentation used in the study is detailed in table 1.

Meteorological Station

Data collected at the meteorological station

included air temperature, relative humidity, net radiation, wind speed, photosynthetically active radiation

(PAR), soil heat flux, soil temperature, and soil moisture content. These data, except for soil moisture, were

monitored by a datalogger at 15 s intervals and the

resulting 20-min means were stored. Soil moisture

was measured and stored hourly.

Air temperature and relative humidity were

measured using a probe positioned about 1.7 m above

land surface. Net radiation (Rn) was monitored with a

net radiometer deployed at a height of about 1.6 m

above land surface. Wind-speed measurements were

made at a height of about 1.8 m with an anemometer

and were extrapolated to the height of the net radiometer (assuming logarithmic wind speed profile) and

used to correct for the variations in apparent net radiation caused by the convective effects of wind (empirical correction from C. Fritschen, REBS, oral

commun., 1995). A quantum sensor was deployed to

measure PAR.

Soil heat flux at land surface was estimated

based on measured values of subsurface soil heat flux,

soil temperature, and soil moisture. A trench was dug

about 8 m from the meteorological station and probes

for soil heat flux, temperature, and moisture measurement were installed in the undisturbed trench sidewall.

The trench was backfilled with native soil 2 months

before the initiation of data collection at the site.

Instrumentation consisted of a soil heat-flux plate at a

depth of 8 cm, averaging soil thermocouple probes at

depths of 2 and 6 cm, and Time Domain Reflectometry

(TDR) probes at depths of 4, 10, 18, and 30 cm.
10 Evapotranspiration From Successional Vegetation in a Deforested Area of the Lake Wales Ridge, Florida

Table 1. Study instrumentation

[CSI, Campbell Scientific, Inc.; REBS, Radiation and Energy Balance Systems, Inc.; RMY, R. M. Young, Inc.;

TE, Texas Electronics, Inc.]

Type of measurement Instrument

Air temperature/relative humidity CSI Model HMP35C temperature and relative humidity probe

Net radiation REBS Model Q-6 net radiometer

Wind speed/direction RMY Model 05305-5 Wind Monitor-AQ

Photosynthetically-active radiation LI-COR, Inc. LI90SB quantum sensor

Soil heat flux REBS Model HFT-1 heat flux plate

Soil temperature REBS Model TCAV thermocouple probe

Soil moisture CSI time domain reflectometry system with Tektronix, Inc. 1502B cable tester

 Precipitation TE Model 525 tipping-bucket rain gage with L Model 260-952 windshield

Water level in well Druck, Inc. Model PDCR950 pressure transducer

Evapotranspiration CSI eddy correlation system with Model CA-27 sonic anemometer, Model

KH20 krypton hygrometer, and fine-wire chromel-constantan thermocouple

Datalogging CSI 21X datalogger

Two TDR probes were placed at each depth about 2 m

apart. Each TDR probe consisted of two 30-cm stainless steel rods and a twin-lead cable. Twin-lead cable

was connected through a balancing transformer to

50-ohm coaxial cable which led to two levels of multiplexing that served a cable tester. The rods were

pressed into the soil parallel to each other and to land

surface with 3-cm spacing between rods. The measured values are integrated averages of the moisture

contents of the soil in the near-vicinity of the rods.The

empirical expression of Topp and others (1980) was

used to relate the apparent dielectric constant to volumetric moisture content. The mean moisture content

of the soil above the heat flux plate was estimated

based on the measured values of moisture content at

depths of 4 and 10 cm (moisture-content values determined from equal-depth probes were averaged; moisture content from 0 to 4 cm depth was assumed equal

to that measured at 4 cm; linear change in moisture

content was assumed between 4 and 10 cm). The estimated value of mean moisture content (volumetric

basis) was converted to a value of water content

(gravimetric basis). Soil heat flux at land surface was

estimated as the sum of the heat flux measured at an 8-

cm depth and the rate of change in stored energy in the

soil above the heat flux plate:

S , (1)

Ti Ti – 1 ( ) – bCs

∆t = --------------------------------------

where

S is the rate of change of stored energy within

the soil above heat-flux plate, in watts

per square meter;

Ti is the temperature of the soil above heat flux

plate at the end of the current time

interval, in degrees Celsius;

Ti-1 is the temperature of the soil above heat flux

plate at the end of the previous time

interval, in degrees Celsius;

b is the depth to heat flux plate, equal to

0.08 meter;

∆t is the time interval between temperature measurements, equal to 1,200 seconds; and

Cs is the mean specific heat capacity of soil above

heat flux plate, in joules per

cubic meter per degree Celsius and is given

by:

, (2)

where

ρb is mean dry soil bulk density above heat flux

plate, estimated as 1.45 kilograms per cubic

meter;

wm is mean gravimetric water content of soil

above heat flux plate, in kilograms of water

per kilogram of soil;

Cs ρb Csd wmCw = ( ) +
Methods for Measurement and Estimation of Evapotranspiration 11

Csd is the mean specific heat capacity of the dry

soil above heat flux plate, estimated as

840 joules per kilogram per degree Celsius

based on the mineral nature of the soil only

1.8 percent organic matter in upper 8 cm of

soil (J. A. Tindall, USGS, oral commun.,

1995); and

Cw is the specific heat capacity of water, equal to

4,190 joules per kilogram per degree

Celsius.

The soil moisture measurements were also used

to define the mean soil moisture within the rooting

zone (upper 30 cm) in a manner similar to that used for

the estimation of the mean moisture content of the soil

above the heat flux plate.

Precipitation and water table depth were monitored at the site to further characterize the hydrometeorologic regime during the study period. Rainfall was

measured using a tipping-bucket rain gage with an

accompanying windshield. The water level in a surficial-aquifer well about 90 m from the micrometeorological instrumentation was monitored using a

pressure transducer. Measurements of rainfall and

surficial-aquifer water level were recorded with a datalogger at temporal resolutions of 20 and 60 min,

respectively.

Eddy Correlation Measurement of

Evapotranspiration

The eddy correlation method (Tanner and

Greene, 1989) was used to measure two components

of the energy budget of a plant canopy: latent and sensible heat fluxes. Latent heat flux (λE) represents the

energy removed from the canopy in the liquid-tovapor phase change of evapotranspired water and is

the product of the heat of vaporization of water (λ) and

the evapotranspiration rate (E). Sensible heat (H) represents the heat energy removed from the canopy as a

result of a temperature gradient between the canopy

and the air. Both latent and sensible heat fluxes are

transported advectively by turbulent eddies in the air.

The energy available to generate turbulent fluxes of

vapor and heat is equal to the difference of net radiation (Rn) and heat flux into the soil (G). The net radiation incident on the top of the canopy is the difference

of incoming radiation (shortwave solar radiation and

longwave atmospheric radiation) and outgoing radiation (reflected shortwave radiation and longwave canopy radiation). Energy is transported to and from the

base of the canopy by conduction through the soil.

Assuming that net horizontal advection of energy and

canopy storage of energy are both negligible quantities, the energy budget equation takes the following

form:

, (3)

where

 the left-hand side of equation 3 represents the

available energy, the right-hand side represents the turbulent flux, and

Rn is net radiation to/from plant canopy, in watts

per square meter;

G is soil heat flux at land surface, in watts per

square meter;

H is sensible heat flux, in watts per square meter;

λE is latent heat flux, in watts per square meter;

and

the sign convention is such that Rn and G are

positive downwards and H and λE are

positive upwards.

The eddy correlation method is applicable in

instances of adequate fetch. Fetch is adequate if there

is sufficient upwind homogeneity in the vegetative

cover so that the surface layer has equilibrated with

the vegetative cover from ground surface to at least the

height of the instrumentation. This upwind distance

generally is considered to be about 100 times the

instrumentation height (Stannard, 1993).

The eddy correlation method is a conceptually

simple, one-dimensional approach. The time-averaged

product of measured values of vertical wind speed (w)

and vapor density (ρv) is the estimated vapor flux

(evapotranspiration rate) during the averaging period,

assuming that the net lateral advection of vapor is negligible (fetch is adequate). Because of the insufficient

accuracy of instrumentation available for measurement of actual values of vertical wind speed and vapor

density, this procedure generally is performed by monitoring the fluctuations of vertical wind speed and

vapor density about their means, rather than monitoring their actual values. This formulation is represented

by the following equations:

, (4)

Rn – G = H + λE

E wρv ( )ρ w w+ ' ( v ρv = = + ' )
12 Evapotranspiration From Successional Vegetation in a Deforested Area of the Lake Wales Ridge, Florida

, (5)

and

, (6)

where

overbars and primes indicate means over the

averaging period and deviations from

means, respectively;

E is evapotranspiration rate, in grams per square

meter per second;

ρv is vapor density, in grams per cubic meter; and

w is vertical wind speed, in meters per second.

The first term of equation 5 is approximated as

zero because mass-balance considerations dictate that

mean vertical wind speed is zero—assuming constant

air density (correction for temperature-induced airdensity fluctuations will be noted later in this report).

The second and third terms are zero based on the definition that the mean fluctuation of a variable is zero.

Therefore, it is apparent from equation 6 that vertical

wind speed and vapor density must be correlated for a

non-zero vapor flux to exist. The turbulent eddies that

transport water vapor (and sensible heat) produce fluctuations in both the direction and magnitude of vertical

wind speed. The ascending eddies must generally be

“wetter” than the descending eddies for evapotranspiration to occur; that is, upward air movement must be

positively correlated with vapor density and downward air movement must be negatively correlated with

vapor density.

Instrumentation capable of high-frequency resolution must be used in an application of the eddy correlation method because of the relatively high

frequency of the turbulent eddies that transport water

vapor (and sensible heat). Instrumentation included a

single-axis sonic anemometer; a fine-wire, chromelconstantan thermocouple; and a krypton hygrometer to

measure or infer variations in vertical wind speed, air

temperature, and vapor density, respectively. The

sonic anemometer relies on the sonic transducers,

placed 10 cm apart vertically, to detect wind-induced

phase shifts in emitted sound waves. The thermocouple was laterally displaced 4 cm from the middle of

the sonic transducer pathline. The hygrometer relies

on the attenuation of ultraviolet radiation, emitted

from a source tube, by water vapor in the air along the

1-cm path to the detector tube. The instrument pathwρv wρv

' w'ρv w'ρv = +++ '

w'ρv ≅ ' covariance w, ρv = ( )

line was laterally displaced 10 cm from the middle of

the sonic-transducer pathline and 8 cm from the thermocouple. Hygrometer voltage output is proportional

to the attenuated radiation flux and fluctuations in

attenuated radiation flux can be related to fluctuations

in vapor density by Beer’s Law (Weeks and others,

1987). Eddy correlation instrument-sampling frequency was 10 Hz with 20-min averaging periods.

Data were processed and stored in a datalogger. The

susceptibility of the sonic anemometer transducers and

the thin-wire thermocouple to damage by rainfall prevented the continuous deployment of the eddy correlation instrumentation in the field.

Eddy correlation instrumentation was placed

about 2.0 m above land surface in a relatively flat area

of the site. This measurement height places the sensors

at least 1 m above the canopy at all times, avoiding

sonic transducer “echo” effects. The northern and eastern boundaries of the site were adequately spaced

(about 290 and 430 m, respectively) from the eddy

correlation instrumentation, easily satisfying the 1:100

instrument height-to-fetch rule. However, this ratio

was as low as 1:85 and 1:90 for the southern (170 m

distant) and western site (180 m distant) boundaries,

respectively; arcs of 70 and 57 degrees (to the south

and west, respectively) did not satisfy the 1:100 fetch

rule. Because the 1:100 fetch rule is an empirical

approximation, data collected during times when the

wind direction was within one of these arcs were not

immediately rejected. Rather, energy-budget closure

criteria (discussed later in this section) were used to

eliminate data that did not satisfy the assumption of

one-dimensional vertical transport of turbulent energy.

Latent and sensible heat fluxes were estimated

based on a modified form of equation 6 as:

, (7)

and

, (8)

where

λE is latent heat flux, in watts per square meter;

λE λ w'ρ'

v

------------

ρvH

ρC

p (T a + 273.15 )

--------------------------------------------------

FK0H

Kw (T a + 273.15 )

+ + -----------------------------------------------

   

 

=

H ρC

pw'Ta = '
Methods for Measurement and Estimation of Evapotranspiration 13

λ is latent heat of vaporization of water, estimated as a function of temperature

(Stull, 1988), in joules per gram;

H is sensible heat flux, in watts per square meter;

ρ is air density, estimated as a function of air

temperature, total air pressure, and

vapor pressure (Monteith and Unsworth,

1990), in grams per cubic meter;

Cp is specific heat of air, estimated as a function

of specific humidity (Stull, 1988),

in joules per gram per degree Celsius;

Ta is air temperature, in degrees Celsius;

F is a factor used in krypton hygrometer correction that accounts for molecular

weights of air and oxygen, and atmospheric

abundance of oxygen, equal to

0.229 gram-degree Celsius per joule;

K0 is extinction coefficient of hygrometer for oxygen, estimated as 0.0045 cubic

meters per gram per centimeter (Tanner and

others, 1993);

Kw is extinction coefficient of hygrometer for

water, equal to the manufacturer-calibrated

value, in cubic meters per gram per centimeter;

and overbars and primes indicate means over

the averaging period and deviations from

the means, respectively.

The second and third terms of the right-hand

side of equation 7 account for temperature-induced

fluctuations in air density (Webb and others, 1980) and

for the sensitivity of the hygrometer to oxygen (Tanner

and Greene, 1989).

Previous investigators (Weeks and others, 1987;

Bidlake and others, 1993; and Stannard, 1993) have

described a recurring problem with the eddy correlation method—an occasional inconsistency in the measured latent and sensible heat fluxes with the energybudget equation (eq 3), presumably because of measurement or conceptual errors. The more usual case is

that measured turbulent fluxes (H and λE) have not

been sufficient to account for the measured available

energy. In a manner similar to Stannard (1993), the

energy-budget equation was used as a means of filtering data with large energy-budget discrepancies from

the data set. If the turbulent flux for a given 20-min

time period was more than 20 percent and 20 W/m2

different than the available energy, the evapotranspiration estimate was considered unacceptable. Evapotranspiration during a period of unacceptable energybalance closure was estimated using evapotranspiration models described later in this report.

Relatively small energy-balance discrepancies

commonly remain in an eddy correlation-estimated

evapotranspiration data set after filtering for removal

of large discrepancies. Bidlake and others (1993)

present a technique that acknowledges these discrepancies and offer three alternative estimates of evapotranspiration based on differing assumptions regarding

the source of these discrepancies. The standard eddy

correlation method assumes that error in the measurement of available energy is the source of energy-balance discrepancies and that the measured latent and

sensible turbulent fluxes are correct. The eddy correlation energy-balance Bowen ratio method (ECEBBR)

assumes that error in the sonic anemometer measurements of vertical wind speed accounts for the discrepancies. If the error in wind speed estimation is

assumed to apply proportionally to both latent and

sensible heat fluxes, the Bowen ratio (H/λE) is preserved and the energy-budget equation allows solution

of turbulent fluxes. The eddy correlation energy-balance residual method (ECEBR) assumes that error in

the krypton hygrometer measurements of vapor density accounts for the discrepancies. With this assumption, the measured sensible heat flux and the energybalance equation are used to estimate latent heat flux.

The three alternative eddy correlation methods provide a range of evapotranspiration estimates—the

standard eddy correlation method generally provides

the lower bound of this range, while the ECEBR

method generally provides the upper bound. Bidlake

and others (1993) noted that evapotranspiration estimates from traditional Bowen ratio instrumentation

and the ECEBBR variant of the eddy correlation

method were in approximate agreement.

The measurement of nighttime latent heat flux

with the eddy correlation method generally is not

accurate. Dew formation on the windows of the

hygrometer can produce erroneously high measurements of vapor density. Also, the small nighttime

energy fluxes can be relatively large compared to

instrumentation noise. Fortunately, the fraction of total

nighttime evapotranspiration is relatively small.

Air-flow distortions in the vicinity of the sonic

anemometer can contribute to error in the eddy correlation method. The krypton hygrometer must be

placed near the sonic anemometer in order that nearly

the same turbulent eddies are monitored at any one

time. A negative side effect from this instrument proximity is the flow distortion produced by the hygrometer when this instrument is upwind of the anemometer.
14 Evapotranspiration From Successional Vegetation in a Deforested Area of the Lake Wales Ridge, Florida

“Poor” wind directions for a typical sensor arrangement comprise a 75o sector. To minimize flow distortion error, the eddy correlation instrumentation was

positioned relative to the prevailing wind at the time of

deployment for each of the 22 measurement events.

However, varying wind directions during an event

could have produced flow-distortion errors. Measurements with this type of error were assumed to have

been culled from the data set with the energy-balance

criteria.

Penman-Monteith Estimation of

Evapotranspiration

Penman (1948) developed an expression for

evaporation from open water based on energy budget

and aerodynamic principles. That equation has since

been applied to predict evapotranspiration from a

well-watered, dense agricultural crop (“potential”

evapotranspiration). In the Penman expression, the

transport of latent and sensible heat fluxes from a “big

leaf” to the sensor height is subject to an aerodynamic

resistance. The big leaf assumption implies that the

plant canopy can be conceptualized as a single source

of both latent and sensible heat at a given height and

temperature. Inherent in the Penman approach is an

assumption of a net one-dimensional transport of

vapor and heat between the canopy and the instrumentation, a condition that is met under adequate fetch.

Monteith (1965) modified the Penman equation,

allowing for the possibility of an additional “canopy”

resistance to vapor transport due to plant-canopy resistance. The resulting “Penman-Monteith” equation

takes the following form:

, (9)

where

λΕ is latent heat flux, in watts per square meter;

∆ is slope of the saturation vapor-pressure curve,

estimated as a function of air temperature

using the empirical relation of Lowe (1977),

in kilopascals per degree Celsius;

λE

∆ R( ) n – G ρCp

es ( ) – e

rh

+ ------------------------------

∆ γ rc rh ( ) +

rh

+ ------------------------

= ----------------------------------------------------------------

es is saturation vapor pressure, estimated as a

function of air temperature using the empirical relation of Lowe (1977), in kilopascals;

e is vapor pressure, equal to the product of relative humidity and es, in kilopascals;

Cp is specific heat capacity of the air, computed as

a function of vapor pressure and atmospheric pressure (Stull, 1988), in joules per

gram per degree Celsius;

γ is the psychrometric “constant,” computed as a

function of atmospheric pressure and air

temperature (Fritschen and Gay, 1979), in

kilopascals per degree Celsius;

rh is aerodynamic resistance, in seconds per

meter; and

rc is canopy resistance, in seconds per meter.

The first term in the numerator of the Penman-Monteith equation is known as the energy term and the second is known as the aerodynamic term. The

aerodynamic resistance to the transport of vapor and

heat from the plant canopy to the sensor is assumed to

be the same for both constituents—a consequence of

the big leaf assumption and similarity theory. Aerodynamic resistance was computed in a manner similar to

that described by Stannard (1993) in which an initial

assumption of neutral boundary-layer conditions was

made and the following equations were iteratively

solved in the order indicated until convergence was

achieved:

1.

 . (10)

2.

 . (11)

3. Estimate latent heat flux with Penman-Monteith equation (eq 9).

4. Estimate sensible heat flux with energy-balance equation (eq 8).

u∗ ku

z d – z0 +

z0

----------------------     ln ψm +

= -------------------------------------------------------

rh

z d – zh +

zh

----------------------     ln ψh +

ku∗ = -----------------------------------------------
Methods for Measurement and Estimation of Evapotranspiration 15

5.

 . (12)

6. Estimate stability profile correctors.

 For unstable (ζ < 0) and neutral (ζ = 0)

conditions:

 , (13)

 ,(14)

and

 . (15)

 For stable conditions (ζ > 0):

 , (16)

where

u* is friction velocity, in meters per second;

u is horizontal wind speed at sensor height, in

meters per second;

k is von Karman’s constant, equal to 0.4, dimensionless;

z is height of sensors (wind speed, air temperature, and relative humidity) above land surface, in meters; the height of the

anemometer (1.8 m), rather than that of the

temperature and relative humidity sensors

(1.7 m), was used for this variable, because

vertical gradients of the latter are relatively

small;

d is momentum displacement height of vegetation, in meters;

z0 is roughness length of canopy for momentum,

in meters;

zh is roughness length of canopy for sensible

heat, in meters;

ζ kg z d – z0 – ( ) + ( ) H + 0.07λE

ρCp

Tu∗3 = --------------------------------------------------------------------------

X ( ) 1 16 – ζ 1 4⁄ =

ψm 2atanX π

2 – -- 1 X

2   +  

2 ---------------------- ( ) 1 + X2 ------------------- 2

     

= – ln

ψh

1 X2 ( ) +

2 ---------------------

2

     

= –ln

ψm ψh = = 5ζ

ψm is stability profile corrector for momentum,

dimensionless;

ψh is stability profile corrector for sensible heat,

dimensionless;

ζ is atmospheric stability, dimensionless.

The momentum-displacement height and roughness lengths change with canopy height and density.

Average canopy height, h, was estimated by visual

inspection at the field site about every 2 weeks during

the study period. The empirical relations of Campbell

(1977) for dense canopies were used to estimate

momentum-displacement height and roughness

lengths:

 , (17)

 , (18)

and

 . (19)

The canopy resistance within the PenmanMonteith equation is the equivalent resistance of all

the plant stomatal resistances in parallel and therefore

the resistance increases with increasing stomatal constriction and/or decreasing stomatal (foliage) density.

By dynamically adjusting the size of the stomatal

openings in response to PAR, leaf-air vapor pressure

difference, leaf-water potential, ambient carbon dioxide concentration, and leaf air temperature (Jarvis,

1976), plants optimize their growth and survival. During plentiful PAR and high ambient concentrations of

carbon dioxide, the stomata of plants (excluding succulents) tend to be relatively open to increase the carbon dioxide flux to the plant while the energy to

photosynthetically fix carbon is available. Plant stomata tend to constrict under conditions of high atmospheric demand (large leaf-air vapor pressure

difference) or low leaf-water potential (reduced plant

turgor pressure, leading to wilting). Stomatal opening

is restricted at low and high leaf temperatures and is

least constricted at intermediate temperatures. As foliage or leaf density increases through seasonal or

growth cycles of the plant, the number of stomata

available for plant-to-atmosphere vapor transport

changes, therefore changing the canopy resistance to

vapor flux.

d = 0.64h

z0 = 0.13h

zh 0.20z0 =
16 Evapotranspiration From Successional Vegetation in a Deforested Area of the Lake Wales Ridge, Florida

Canopy resistance generally is estimated by

either (1) upscaling porometer measurements of stomatal conductance (reciprocal of resistance) on individual plant leaves, or by (2) use of the PenmanMonteith equation (eq 9) along with an independently

estimated value of evapotranspiration (for example,

using eddy correlation or Bowen ratio methodologies)

and other measured meteorological variables to “backsolve” for canopy resistance. The first method has

been used successfully (Abtew, 1995), but is subject to

the subjectivity of upscaling approaches and to the

impracticality of achieving high temporal resolution

over long time periods (field personnel required at site

to perform porometer measurements). The second

method is not subject to these limitations and has been

used (Stannard, 1993) to obtain estimates of canopy

resistance that are consistent, within the framework of

the Penman-Monteith equation, with measured values

of evapotranspiration. This second method was used

in the investigation described in this report.

Eddy correlation measurements made periodically from September 1993 to August 1994 were evaluated for acceptable energy-balance closure. Only

those measurements that met the closure criteria were

used to estimate canopy resistance. Previous investigators have used parameterized forms of canopy-resistance functions (Jarvis, 1976; Avissar and others,

1985; Stewart, 1988; and Stannard, 1993). The form

of these functions generally was based on the results

of experiments conducted in controlled, laboratory

environments with a plant monoculture. A variety of

functional forms of canopy resistance were evaluated

in this study as a means of expressing the dependence

of this variable on environmental variables identified

by Jarvis (1976) as being important factors in stomatal

constriction. As part of this evaluation, field measurements were made of these environmental variables or

of more easily measured variables that are highly correlated with the variables identified by Jarvis. Fieldmeasured environmental variables were PAR, vaporpressure deficit of air (a surrogate for leaf-air vapor

pressure difference), soil moisture content (a surrogate

for leaf-water potential), and air temperature (a surrogate for leaf temperature). The effect of carbon dioxide concentrations on canopy resistance was not

considered in this study. Parameters within the canopy-resistance functions were estimated through an

optimization procedure—the Powell algorithm (Press

and others, 1989)—which minimized the sum of

squared differences between the Penman-Monteith

simulated and measured values of evapotranspiration.

This procedure was followed for each of the three

alternative estimates of the eddy correlation method.

Next, the “calibrated” canopy-resistance functions

were used in conjunction with the Penman-Monteith

equation and environmental data monitored during the

study period to estimate evapotranspiration at times

during which the eddy correlation data did not meet

energy-balance closure criteria and at times between

eddy correlation measurement events.

The Penman-Monteith equation was not applied

to nighttime computation of evapotranspiration; an

evapotranspiration rate of zero was assumed during

this time. Similar to Stannard (1993), this assumption

was made because (1) evapotranspiration from vegetation is relatively small at night and (2) the iterative

calculation of u* in the Penman-Monteith model often

becomes unstable for nighttime data, preventing the

accurate estimation of evapotranspiration and dew formation. PAR was used to provide a quantitative daynight demarcation (nighttime defined as PAR < 1

μmoles/( )).

Dew formation is frequent in humid areas such

as Florida. If dewfall is substantial but nighttime vapor

fluxes are not explicitly measured, evapotranspiration

will be overestimated (nighttime dewfall is not measured, but early-morning dew evaporation is measured). Therefore, a methodology to exclude earlymorning dew evaporation was needed in this investigation. Abtew and Obeysekera (1995) noted that the

mean time to evaporate dew from a cattail marsh in

south Florida was 78 minutes after the onset of positive net radiation. In the present study, this criterion

(assumed time-invariant and rounded to 80 minutes)

was used to prescribe evapotranspiration as zero during times of expected dew evaporation. This approach

assumes that dew formed nightly during the study

period and that negligible transpiration occurred in the

presence of dew.

Leaf-area index was estimated (by visual

inspection) for possible use within the canopy-resistance function in a manner similar to that described by

Stannard (1993). This method is based on an application of Beer’s Law for attenuation of radiation in a

medium (Monteith and Unsworth, 1990):

 , (20)

m

2 ⋅ s

Ls

1 e

κs

L

2 – --

–      

κs

= ---------------------------
Methods for Measurement and Estimation of Evapotranspiration 17

where

Ls is sunlit leaf area per unit area of land, in

square meters per square meter;

κs is attenuation coefficient of light for the canopy, dimensionless;

L is two-sided leaf area per unit area of land

(leaf-area index), in square meter per square

meter.

Assuming that the leaf-angle distribution is

ellipsoidal, the attenuation coefficient is equal to about

one when the solar elevation is 30o (Monteith and

Unsworth, 1990, p. 76). To an observer viewing the

canopy at an angle of 30o below the horizon, the green

leaf-area fraction visible, Lv, is equal to the sunlit leafarea fraction at a solar elevation of 30o. Therefore,

 . (21)

To estimate leaf-area index using this method,

site vegetation was photographed at an angle of 30o

below the horizon about every 2 weeks during the

study period. Leaf-area index was estimated at

unmonitored times with linear interpolation of measured values.

Simpler Methods for Estimation of

Evapotranspiration

Two simpler alternatives to the Penman-Monteith method were considered in this study. These

alternatives - the Penman and Priestley-Taylor methods - require less meteorological data and are less

computationally demanding than the Penman-Monteith method.

As discussed previously, the Penman method

estimates potential evapotranspiration assuming a

dense canopy without moisture stress. Computationally, this assumption is equivalent to assuming a negligible canopy resistance within the Penman-Monteith

approach. Consequently, the challenge of estimating

this empirical term is eliminated. The Penman equation takes the following form:

 , (22)

L 2 1 Lv = – ln ( ) –

λE

∆ R( ) n – G ρCp

es ( ) – e

rh

+ ------------------------------

∆ γ + = ----------------------------------------------------------------

where

all variables have been previously defined

(see eq 9).

Although the assumption of ample soil moisture

and dense canopy coverage often is not met in the

upland, nonirrigated areas of Florida, the possibility

remains that potential evapotranspiration might

exceed actual evapotranspiration by some consistent

and quantifiable degree and therefore could serve as a

reliable estimator of actual evapotranspiration. The

usefulness of the Penman equation in this regard was

examined within this investigation.

Priestley and Taylor (1972) proposed a simplification of the Penman equation for the case of saturated

atmosphere (e = es), where the aerodynamic term of

the Penman equation (eq 22) is zero:

 . (23)

However, Priestley and Taylor (1972) noted that

empirical evidence suggests that evaporation from

extensive wet surfaces is greater than this amount, presumably because the atmosphere generally does not

attain saturation. Therefore, the Priestley-Taylor coefficient, α, was introduced as an empirical correction to

the theoretical expression (eq 23):

 . (24)

The value of was estimated to be 1.26. Eichinger and others (1996) have shown that the empirical

value of α has a theoretical basis—a nearly constant

value of α is expected under the existing range of

Earth-atmospheric conditions.

Previous studies (Flint and Childs, 1991; Stannard, 1993) have examined the use of a modified form

of the Priestley-Taylor equation. The approach in these

studies relaxes the assumption of a free-water surface

or a dense, well-watered canopy by allowing α to be

less than 1.26 and to vary as a function of environmental factors. Stannard (1993) noted that the PriestleyTaylor approach to simulation of observed evapotranspiration rates was superior to that of Penman-Monteith

for a site of wildland vegetation in semiarid rangeland.

In this investigation, the utility of the Priestley-Taylor

equation to estimate evapotranspiration was evaluated.

The functional form of the Priestley-Taylor α was estimated in a manner analogous to that described for the

Penman-Monteith rc.

λE

∆ R( ) n – G

∆ γ + = --------------------------

λE α

∆ R( ) n – G

∆ γ + = --------------------------

α
18 Evapotranspiration From Successional Vegetation in a Deforested Area of the Lake Wales Ridge, Florida

RESULTS OF EVAPOTRANSPIRATION

MEASUREMENT AND

ESTIMATION MEASUREMENT OF

EVAPOTRANSPIRATION

The 20-min resolution eddy correlation measurements of evapotranspiration that met the energybalance criteria provided good temporal coverage—both diurnally and seasonally (fig. 12). There

were a total of 538 daytime (following estimated time

of complete dew evaporation) measurements that were

considered acceptable; about half of the daytime

evapotranspiration measurements were discounted

using the energy-balance criteria. Results for the first

of the 22 measurement events are shown in figures

13-15. All energy terms—net radiation, soil heat flux,

sensible heat flux, and latent heat flux—exhibit a

strong diurnal pattern (fig. 13). Net radiation generally

is the dominant energy term. During daytime, net radiation and soil heat flux are relatively high and positive

(net downward flux) and are relatively low and negative (net upward flux) during nighttime as the soil radiates heat to the atmosphere. The effect of intermittent

cloud cover is evident as sharp variations in these

energy fluxes.

Absolute energy-balance closure (available

energy minus turbulent flux) was relatively good at

night (low energy flux environment) (fig. 14). However, the relative energy-budget closure (turbulent flux

energy divided by available energy) was poor, probably because of dew formation on the hygrometer and

the relative magnitudes of energy fluxes and instrumentation noise. Conversely, daytime absolute energybalance closure was relatively poor, but the relative

energy-budget closure was good. The absolute energybalance closure generally was positive, indicating

either an overestimation of available energy or an

underestimation of turbulent flux. The three variants

of the eddy correlation method, which ascribe energybalance error to three different sources, are exemplified in figure 15. Because of the generally positive

absolute energy-balance closure, the highest, intermediate, and lowest estimates of evapotranspiration are

provided by the ECEBR, ECEBBR, and standard eddy

correlation methods, respectively.

Model Calibration Using Measured

Evapotranspiration

The 538 measurements of daytime evapotranspiration deemed acceptable provided a standard with

which to calibrate the evapotranspiration

models—Penman-Monteith, Penman, and modified

Priestley-Taylor equations. The functional form of

Penman-Monteith canopy resistance that was initially

considered was based on a composite of empirical

models proposed by Jarvis (1976) and Stewart (1988);

terms are included in this model to account for the

dependence of canopy resistance on leaf-area index,

vapor-pressure deficit, PAR, air temperature, and rooting zone soil moisture. Canopy resistance within this

traditional approach (“method 1” in this report) takes

the following form:

(25),

where

D is vapor pressure deficit (equal to es-e), in

kilopascals;

RPAR is photosynthetically active radiation, in

micromoles per square meter per second;

Ta is air temperature, in degrees Celsius;

θ is mean moisture content in rooting zone

(upper 30 cm of soil), in cubic centimeters

per cubic centimeter;

C1-C8 are site-specific empirical parameters; and

other terms are as previously defined.

The parameter C8, equal to the moisture content at

which canopy resistance is infinite, was set equal to

zero; evapotranspiration was measured at the site

when θ was as low as 0.02 cm3/cm3, implying that

canopy resistance was finite above this moisture

content.

The results of estimation of the parameters in

equation 25, using evapotranspiration estimates provided by the ECEBBR method, are shown in table 2.

Alternative, simplified versions of equation 25, in

which individual terms were eliminated, were used to

examine the extent to which these terms were superfluous. Results indicated that all terms (particularly the

term involving PAR) make a significant contribution

to the description of canopy resistance. Values of

parameters C5 and C6 selected by the parameter optimization procedure produced the best match between

simulated and measured values of evapotranspiration;

r

c C1L

C2

C2 + D -----------------       RPARRPAR C3 + ----------------------------       Ta C5 –     C6 Ta –    

C4

     

1 e

C7 θ C8 –    

–       –1=
Results of Evapotranspiration Measurement and Estimation Measurement of Evapotranspiration 19

0

20

5

10

15

EVAPOTRANSPIRATION,

0 365 100 200 300

JULIAN DAY

1994 1993

J FMAM J J ASOND

IN MILLIMETERS PER DAY

Figure 12. Evapotranspiration measured by eddy

correlation energy-balance Bowen ratio method at

study site from September 1993 to August 1994.

Note: Measurements shown include only daytime

(following estimated time of complete dew

evaporation) values that met the energy-balance

criteria.

Figure 13 (Below). Surface energy-balance

components on September 23-24, 1993, at

study site. Note: Sensible and latent heat

flux were estimated with the standard eddy

correlation method.

700

600

500

400

300

200

100

 0

-100

0400 0800 1200 1600 2000 0000 0400 0800 1200 1600 2000 0000

SEPTEMBER 23 SEPTEMBER 24, 1993

0000

ENERGY FLUX, IN WATTS PER SQUARE METER

EXPLANATION

NET RADIATION

SOIL HEAT FLUX

SENSIBLE HEAT FLUX

LATENT HEAT FLUX

EASTERN

STANDARD

TIME
20 Evapotranspiration From Successional Vegetation in a Deforested Area of the Lake Wales Ridge, Florida

however, these values probably are not physically

realistic. The coefficients C5 and C6 are defined as the

lower and upper temperatures, respectively, at which

canopy resistance is infinite. The coefficient C5 is

equal to -91  ̊C, implying that full stomatal closure

does not occur until that temperature is reached; stomatal closure probably would occur just below freezing, at the coldest. Also, the selected values of C4, C5,

and C6 imply that the optimal (lowest) value of canopy

resistance occurs at a temperature of -39  ̊C; optimal

values of canopy resistance are expected to occur at

temperatures above freezing. This anomalous relation

of canopy resistance to air temperature probably is the

result of inadequacies in the model (eq 25) or because

of correlation between the independent variables of

the model that obscure a unique definition of the

model parameters.

Comparisons between modeled and measured

values of evapotranspiration and canopy resistance are

shown in figures 16 and 17, respectively. The model

generally performed better in estimating evapotranspi0400 0800 1200 1600 2000 0000 0400 0800 1200 1600 2000 0000

SEPTEMBER 23 SEPTEMBER 24, 1993

0000

300

200

100

0

-100

-200

-300

ABSOLUTE ENERGY-BUDGET CLOSURE

RELATIVE ENERGY-BUDGET CLOSURE,

2

1

0

-1

-2

RELATIVE ENERGY-BUDGET CLOSURE

ABSOLUTE ENERGY-BUDGET CLOSURE

Region of acceptable absolute

energy-budget closure

Region of acceptable relative

energy-budget closure

IN WATTS PER SQUARE METER

(AVAILABLE ENERGY - TURBULENT FLUX ENERGY),(TURBULENT FLUX ENERGY/AVAILABLE ENERGY)

EASTERN

STANDARD

TIME

Figure 14. Absolute and relative measures of energy-budget closure for eddy correlation data collected on September

23-24, 1993, at study site. Note: Evapotranspiration measurements were considered “unacceptable” if the

measurement did not meet either the absolute energy-budget closure criterion (turbulent flux within 20 W/m2 of

available energy) or the relative energy-budget closure criterion (turbulent flux energy within 20 % of available energy.

ration than in estimating canopy resistance. Because

simulation of evapotranspiration—rather than canopy

resistance—was the objective of the study, the mismatch in canopy-resistance values points out the

importance of calibrating the canopy-resistance model

on measured values of evapotranspiration, rather than

“measured” values of canopy resistance. As also noted

by Stannard (1993), the mismatch in canopy-resistance values generally occurred during times of low

turbulent flux (shortly after sunrise or before sunset)

when instrumentation error is relatively high. Because

the latent heat flux was low at these times, error in

simulating canopy resistance did not seriously degrade

estimating daily evapotranspiration. The model exhibited substantial seasonal bias (fig. 18), generally overpredicting evapotranspiration during the months of

July to October and under-predicting evapotranspiration during other periods. An example of the ability of

the model to simulate diurnal patterns of evapotranspiration is shown in figure 19.
Results of Evapotranspiration Measurement and Estimation Measurement of Evapotranspiration 21

Table 2. Summary of parameters and error statistics for

evapotranspiration models

[Method 1, see equation 25; method 2, see equation 26; Priestley-Taylor,

see equation 27; SEE, Standard error of estimate (in millimeters per day);

 --, not applicable]

PenmanMonteith

(method 1)

PenmanMonteith

(method 2)

PriestleyTaylor

Parameters

C1 0.000000388 -0.144 -0.0000978

C2 1.30 157 .0118

C3 1,800 -1,920 4.64

C4 1.78 313. .508

C5 -91.0 .504 -.349

C6 53.5 305 294

C7 -32.0 -- --

C8 .0 -- --

Error statistics

r

2 .918 .967 .972

SEE 1.33 .84 .77

15

10

0

5

0000 0400 0800 1200 1600 2000 0000 0400 0800 1200 1600 2000 0000

SEPTEMBER 23 SEPTEMBER 24, 1993

EVAPOTRANSPIRATION, IN MILLIMETERS PER DAY

STANDARD EDDY CORRELATION METHOD

EDDY CORRELATION ENERGY-BALANCE BOWEN RATIO METHOD (ECEBBR)

EXPLANATION

EDDY CORRELATION ENERGY-BALANCE RESIDUAL METHOD (ECEBR)

EASTERN

STANDARD

TIME

Figure 15. Eddy-correlation-measured evapotranspiration on September 23-24, 1993, at study site.

 A nontraditional model for canopy resistance

also was considered, referred to as “method 2” in this

report. This model assumed a linear relation between

all environmental variables and canopy resistance.

Also, a sinusoidal function of Julian day with a wavelength of 1 year was used as a surrogate for leaf-area

index:

(26)

where

ω is 2π/365 per day;

t is Julian day; and

C1-C6 are site-specific empirical parameters.

The results of parameter estimation are shown in

table 2. An additional linear term in equation 26

r

c C1RPAR C2D C3θ C4 + ++     C5 ω t C6 –       sin  + 1   =  
22 Evapotranspiration From Successional Vegetation in a Deforested Area of the Lake Wales Ridge, Florida

0

20

5

10

15

SIMULATED EVAPOTRANSPIRATION (METHOD 1),

IN MILLIMETERS PER DAY

0 20 5 10 15

MEASURED EVAPOTRANSPIRATION,

IN MILLIMETERS PER DAY

line of equality

r

2 = 0.918

root-mean-squared error =

 1.33 millimeters per day

Figure 16. Comparison of Penman-Monteithsimulated evapotranspiration (method 1) and

measured (eddy correlation energy-balance

Bowen ratio method) evapotranspiration at study

site from September 1993 to August 1994.

10

100,000

100

1,000

10,000

SIMULATED CANOPY RESISTANCE (METHOD 1),

10 100,000 100 1,000 10,000

MEASURED CANOPY RESISTANCE,

IN SECONDS PER METER

IN SECONDS PER METER

line of equality

Figure 17. Comparison of simulated (method 1)

and measured values of canopy resistance at

study site from September 1993 to August 1994.

Note: Measured values of canopy resistance

computed using values of latent and sensible

heat flux measured with the eddy correlation

energy-balance Bowen ratio method.
Results of Evapotranspiration Measurement and Estimation Measurement of Evapotranspiration 23

0 365 100 200 300 -4

4

-3

-2

-1

0

1

2

3

MODEL EVAPOTRANSPIRATION ERROR

(SIMULATED (METHOD 1) - MEASURED),

IN MILLIMETERS PER DAY

JULIAN DAY

1994 1993

J FMAM J J ASOND

Figure 18. Seasonal distribution of discrepancy

between Penman-Monteith-simulated

evapotranspiration (method 1) and measured

(eddy correlation energy-balance Bowen ratio

method) evapotranspiration at study site from

September 1993 to August 1994.

Figure 19: (Below) Comparison between

simulated and measured evapotranspiration

on September 23-24, 1993, at study site.

15

10

5

0000 0400 0800 1200 1600 2000 0000 0400 0800 1200 1600 2000 0000

SEPTEMBER 23 SEPTEMBER 24, 1993

EVAPOTRANSPIRATION, IN MILLIMETERS PER DAY

PRIESTLEY-TAYLOR ESTIMATE OF EVAPOTRANSPIRATION

PENMAN-MONTEITH ESTIMATE (METHOD 2) OF EVAPOTRANSPIRATION

EXPLANATION

PENMAN-MONTEITH ESTIMATE (METHOD 1) OF EVAPOTRANSPIRATION

EASTERN

STANDARD

TIME

MEASURED VALUE OF EVAPOTRANSPIRATION WITH ACCEPTABLE ENERGY-BALANCE CLOSURE

EDDY CORRELATION

 INSTRUMENTATION DEPLOYED

JULIAN DAY 266 JULIAN DAY 267

0
24 Evapotranspiration From Successional Vegetation in a Deforested Area of the Lake Wales Ridge, Florida

involving air temperature was shown to contribute a

negligible amount of unique information to simulation

of canopy resistance and was eliminated.

Canopy resistance, modeled with method 2, provided a correspondence between measured and simulated evapotranspiration that was superior to that of

method 1 (table 2; figs. 16 and 20), in spite of the relative simplicity of method 2 (6 parameters, rather than

7). The standard error of estimate was reduced from

1.33 mm/d (method 1) to 0.84 mm/d (method 2).

Additionally, the strong seasonal error bias noted with

method 1 (fig. 18) is not apparent with method 2

(fig. 21). Canopy resistance also is simulated better

with method 2 than with method 1 (figs. 17 and 22),

although substantial error remains for high resistance/low turbulent flux conditions.

Calibration of the Penman-Monteith (method 2)

model with estimates of evapotranspiration provided

by eddy correlation variants other than the ECEBBR

method (standard eddy correlation and ECEBR methods) produced canopy-resistance functions that were

structurally similar to that obtained using the

ECEBBR method. Also, the standard errors of evapo

0

20

5

10

15

SIMULATED EVAPOTRANSPIRATION (METHOD 2),

IN MILLIMETERS PER DAY

0 20 5 10 15

MEASURED EVAPOTRANSPIRATION,

IN MILLIMETERS PER DAY

line of equality

r

2 = 0.967

root-mean-squared error =

 0.84 millimeter per day

Figure 20. Comparison of Penman-Monteith-simulated evapotranspiration (method 2)

and measured (eddy correlation energy-balance Bowen ratio method) evapotranspiration

at study site from September 1993 to August 1994.

transpiration estimate produced using these variants of

the eddy correlation method were approximately equal

to that produced using the ECEBBR method. However, the canopy-resistance values obtained in this

manner were slightly higher with the standard eddy

correlation estimates and slightly lower with the

ECEBR estimates than with the ECEBBR estimates of

evapotranspiration.

Evapotranspiration estimated by the Penman

equation was compared to that estimated by the more

rigorous Penman-Monteith equation (method 2). The

relative discrepancy between the two estimates was

somewhat erratic, although a seasonal trend was

apparent (fig. 23). This discrepancy was not unexpected given the variable soil-moisture content and

canopy coverage noted at the site. The lack of a consistent relation between the evapotranspiration estimates of the Penman and Penman-Monteith equations

precludes the use of the Penman equation as a reliable,

and simple, estimator of evapotranspiration from nonirrigated vegetation in central Florida. However, Bidlake and others(1993) note that the Penman equation

may be useful in estimating evapotranspiration from a

marsh vegetation type.
Results of Evapotranspiration Measurement and Estimation Measurement of Evapotranspiration 25

3

-3

-2

-1

0

1

2

MODEL EVAPOTRANSPIRATION ERROR

(SIMULATED (METHOD 2) - MEASURED),

IN MILLIMETERS PER DAY

0 365 100 200 300

JULIAN DAY

-4

4

1994 1993

J FMAM J J ASOND

Figure 21. Seasonal distribution of discrepancy between Penman-Monteith-simulated

evapotranspiration (method 2) and measured (eddy correlation energy-balance Bowen

ratio method) evapotranspiration at study site from September 1993 to August 1994.

10

100,000

100

1,000

10,000

MODELED CANOPY RESISTANCE (METHOD 2),

10 100,000 100 1,000 10,000

MEASURED CANOPY RESISTANCE,

IN SECONDS PER METER

IN SECONDS PER METER

line of equality

Figure 22. Comparison of modeled (method 2) and measured values of canopy

resistance at study site from September 1993 to August 1994. Note: Measured

values of canopy resistance computed using values of latent and sensible heat flux

measured with the eddy correlation energy-balance Bowen ratio method.
26 Evapotranspiration From Successional Vegetation in a Deforested Area of the Lake Wales Ridge, Florida

Evapotranspiration was modeled relatively well

with the modified Priestley-Taylor equation (figs. 24

and 25). The results of this model were slightly superior to those of the Penman-Monteith equation; standard error of estimate was 0.77 mm/d (modified

Priestley-Taylor) as compared to 0.84 mm/d (PenmanMonteith - method 2). The Priestley-Taylor α was formulated as a function of several environmental variables (PAR, vapor-pressure deficit, soil-moisture

content, air temperature, and Julian day) in a fashion

similar to that for Penman-Monteith canopy resistance

(method 2):

. (27)

Initially, wind speed and air temperature were

included as independent variables in this expression.

However, these variables contributed negligible information to simulation of measured evapotranspiration

values and were eliminated from the function for

Priestley-Taylor α. The results of estimation of the

parameters in equation 27 are shown in table 2. A simplified 4-parameter version of equation 27, which

included only soil-moisture content and Julian day as

0

10

2

4

6

8

RATIO OF PENMAN-ESTIMATE TO

OF DAILY EVAPOTRANSPIRATION

245 275 305 335 30 60 90 120 150 180 210 240 270

1993 1994

JULIAN DAY

SEPT OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1993 1994

PENMAN-MONTEITH-ESTIMATE

Figure 23. Ratio of Penman-estimate of daily evapotranspiration to Penman-Monteith estimate of daily evapotranspiration

at study site. Note: Estimated Penman-Monteith evapotranspiration is based on calibration (method 2) of the PenmanMonteith equation to evapotranspiration values measured by the eddy correlation energy-balance Bowen-ratio method.

α C1RPAR C2∆e C3θ C4 + ++     C5 ω t C6 –       sin  + 1   =  

independent variables, produced results comparable to

those with the 6-parameter Penman-Monteith canopyresistance function (method 2)—standard error of estimate was 0.84 mm/d in both cases. These results were

unexpected given the more rigorous nature of the Penman-Monteith model as compared to the PriestleyTaylor model, but are not unprecedented (Stannard

(1993)). A comparison of simulated and measured

Priestley-Taylor α (fig. 26) reveals that simulation of

this parameter generally is good. However, similar to

simulation of Penman-Monteith canopy-resistance

values, substantial mismatches sometimes occurred

during times of low turbulent flux.

The poor performance of the Penman-Monteith

model with a traditional formulation of canopy resistance (method 1) relative to that of a nontraditional

Penman-Monteith model (method 2) or the modified

Priestley-Taylor model was unexpected. Possible reasons for the relative differences in model performance

might include:

(1) The models neglect possible synergistic

interactions of environmental variables on model

parameters (Penman-Monteith canopy resistance or

Priestley-Taylor α). This neglect is possibly most
Results of Evapotranspiration Measurement and Estimation Measurement of Evapotranspiration 27

line of equality

r

2 = 0.972

root-mean-squared error =

 0.77 millimeter per day

0

20

5

10

15

SIMULATED EVAPOTRANSPIRATION (METHOD 2),

IN MILLIMETERS PER DAY

0 20 5 10 15

MEASURED EVAPOTRANSPIRATION,

IN MILLIMETERS PER DAY

Figure 24. Comparison of Priestley-Taylor-simulated

evapotranspiration and measured (eddy correlation energy-balance

Bowen ratio method) evapotranspiration at study site from

September 1993 to August 1994.

3

-3

-2

-1

0

1

2

MODEL EVAPOTRANSPIRATION ERROR

(SIMULATED (PRIESTLEY-TAYLOR) - MEASURED),

IN MILLIMETERS PER DAY

0 365 100 200 300

JULIAN DAY

-4

4

1994 1993

J FMAM J J ASOND

Figure 25. Seasonal distribution of discrepancy between PriestleyTaylor-simulated evapotranspiration and measured (eddy correlation

energy-balance Bowen ratio method) evapotranspiration at study site

from September 1993 to August 1994.
28 Evapotranspiration From Successional Vegetation in a Deforested Area of the Lake Wales Ridge, Florida

apparent in the Penman-Monteith (method 1) model,

in which a given change in an environmental variable

will produce a constant proportional change in the

canopy resistance regardless of the state of the other

variables. The structural form of the other models

allows for a nonproportional change in the model

parameter with a change in an environmental variable,

which perhaps more satisfactorily accommodates synergistic interactions.

(2) The models do not explicitly incorporate the

seasonally changing relative distribution of species at

the site within the model parameter function. Also,

although vegetation at the site progresses yearly from

juvenile to mature status, the possible effect of these

phenological changes on the parameter function of the

model are neglected. The “sine” term within the

parameter functions for the Penman-Monteith (method

2) and Priestley-Taylor models may somewhat incorporate the effects of these seasonal changes, as well as

the changing canopy coverage. Foliage seasonality is

incorporated in the Penman-Monteith (method 1)

model only through a specified leaf-area index, which

considers only changes in canopy coverage.

(3) The model inputs are subject to field measurement error. In particular, estimation of leaf-area

0 2.0 0.5 1.0 1.5

MEASURED α

0

2.0

0.5

1.0

1.5

SIMULATED MODELED

α

line of equality

Figure 26. Comparison of simulated and measured values of PriestleyTaylor α at study site from September 1993 to August 1994. Note:

Measured values of Priestley-Taylor α computed using values of latent

heat flux measured with the eddy correlation energy-balance Bowen

ratio method.

index, as part of the Penman-Monteith (method 1)

model, is prone to subjectivity.

Values of Penman-Monteith rc or PriestleyTaylor α demonstrated substantial sensitivity to environmental variables (fig. 27). The Priestley-Taylor

model incorporates the effects of plant stomatal sensitivity to environmental variables in a different framework than do the Penman-Monteith models, resulting

in a different expression of this sensitivity. Correlation

between environmental variables further confounds a

unique definition of parameter sensitivity. For these

reasons, the functions for rc and α described in this

report should be viewed as a general guide, rather than

as a definitive description of stomatal response of site

vegetation to environmental variables. However, the

fact that the models successfully reproduced 538 measurements of site evapotranspiration over a wide range

of seasonal and diurnal values lends credence to the

ability of the models to estimate evapotranspiration at

the site. This observation is particularly appropriate in

the case of interpolation of evapotranspiration

between measured values. More caution would need

to be observed in the case of extrapolation of the models beyond the measured values of evapotranspiration,

or beyond the range of meteorologic conditions used

to calibrate the models.
Results of Evapotranspiration Measurement and Estimation Measurement of Evapotranspiration 29

0 5 1 2 3 4

TWO-SIDED LEAF AREA INDEX

0

1,000

200

400

600

800

CANOPY RESISTANCE, IN SECONDS PER METER

0 4 1 2 3

VAPOR PRESSURE DEFICIT, IN KILOPASCALS

1.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

PRIESTLEY-TAYLOR

α

0.3

0 35 5 10 15 20 25 30

AIR TEMPERATURE, IN DEGREES CELSIUS

CANOPY RESISTANCE, IN SECONDS PER METER

0

1,000

200

400

600

800

0 1,000 2,000 3,000

PHOTOSYNTHETICALLY-ACTIVE RADIATION,

IN MICROMOLES PER SECOND PER SQUARE METER

0.3

1.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

PRIESTLEY-TAYLOR

α

Figure 27. Simulated relations of canopy resistance to environmental variables. Note: Base values are: two-sided leaf

area index =3; air temperature = 25 oC; vapor pressure deficit = 1.5 kPa; photosynthetically-active radiation = 1,000

μmoles/m2.s) average moisture content in upper 30 cm of soil = 0.05; Julian day = 100. (Figure 27 continued on next

page.)
30 Evapotranspiration From Successional Vegetation in a Deforested Area of the Lake Wales Ridge, Florida

Application of Evapotranspiration Models

The calibrated evapotranspiration models

described in the previous section were applied to the

estimation of evapotranspiration, aquifer recharge,

partitioning of available energy between latent and

sensible heat, Penman-Monteith rc, and PriestleyTaylor α.

Estimated daily and cumulative evapotranspiration for September 15, 1993, to August 27, 1994, are

shown in figures 28 and 29, respectively. The strong

seasonal pattern of evapotranspiration is evident in

these graphs. Daily evapotranspiration varied over an

order of magnitude during the study period (from less

than 0.2 mm/d in late December to almost 5 mm/d in

mid-July). The cumulative evapotranspiration estimates from this period were linearly extrapolated to

estimate annual evapotranspiration. Annual evapotranspiration (September 15, 1993, to September 15,

1994) was estimated to be about 680 mm with either

of the more accurate evapotranspiration models

0.02 0.04 0.06 0.08 0.10

SOIL VOLUMETRIC MOISTURE CONTENT

0 30 60 90 120 150 180 210 240 270 300 330 360

JULIAN DAY

CANOPY RESISTANCE, IN SECONDS PER METER

1.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

PRIESTLEY-TAYLOR

α

0 0.3

1,000

200

400

600

800

J FMAM J J ASOND

CANOPY RESISTANCE (METHOD 1)

CANOPY RESISTANCE (METHOD 2)

PRIESTLEY-TAYLOR α

EXPLANATION

Figure 27. Simulated relations of canopy resistance to environmental variables. Note: Base values are: two-sided leaf

area index =3; air temperature = 25 oC; vapor pressure deficit = 1.5 kPa; photosynthetically-active radiation = 1,000

μmoles/m2.s) average moisture content in upper 30 cm of soil = 0.05; Julian day = 100 —Continued.

(Penman-Monteith (method 2) and modified PriestleyTaylor). Using the less accurate Penman-Monteith

(method 1) model, only 560 mm of annual evapotranspiration was estimated. Annual evapotranspiration values estimated using the Penman-Monteith (method 2)

model calibrated using the alternatives to the

ECEBBR eddy correlation variant were 620 mm (standard eddy correlation method) and 750 mm (ECEBR

method). The modified Priestley-Taylor model

produced similar alternative estimates of annual

evapotranspiration.

The 620 to 750 mm estimated range for evapotranspiration produced by the most successful models

(Penman-Monteith method 2 and the modified

Priestley-Taylor method) can be used to make a water

budget-based estimate of aquifer recharge. The sandy

soils of the site readily accept infiltration, producing

little overland flow. Therefore, assuming a negligible

change in storage in the unsaturated zone during the

study period, these data imply that of the 1,320 mm of
Results of Evapotranspiration Measurement and Estimation Measurement of Evapotranspiration 31

rainfall during the 1-year estimation period about

570 to 700 mm contributed to aquifer recharge. These

relative values of evapotranspiration and recharge

probably approach the low and high bounds, respectively, for these terms of the water budget in central

Florida. The rapidly drained soils, shallow-rooted vegetation, and relatively deep water table of this site are

very conducive to minimizing evapotranspiration and

maximizing recharge. Results of this investigation

indicate that the minimum possible annual evapotranspiration probably is lower for central Florida than that

suggested by Tibbals (1990).

Annual recharge estimates may be in error by as

much as 20 percent based on the 130-mm error band

of annual evapotranspiration determined from the

three variants of the eddy correlation method. However, for sites in which evapotranspiration is a higher

proportion of precipitation, the method described in

this report can produce substantially greater relative

0

5.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

DAILY EVAPOTRANSPIRATION, IN MILLIMETERS

245 275 305 335 30 60 90 120 150 180 210 240 270

JULIAN DAY

1993 1994

SEPT OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1993 1994

Figure 28. Simulated daily evapotranspiration rate at study site from September 16, 1993, to August 28, 1994.

Note: Estimated values based on calibration of Penman-Monteith model (method 2) to evapotranspiration rates

measured by the eddy correlation energy-balance Bowen ratio method.

error in estimating aquifer recharge. For example,

annual evapotranspiration at a marsh site probably

approaches the potential value (about 1,200 mm). An

error band of 130 mm in estimated evapotranspiration

in this case can result in an error of over 100 percent in

estimating recharge.

Most of the energy available for turbulent

energy fluxes was partitioned as sensible heat from

October to May (fig. 30) when there was relatively

little canopy coverage (fig. 3) and soil conditions were

dry (fig. 4). Most of the available energy was partitioned as latent heat flux during conditions of relatively dense canopy coverage and moist soil from June

to September. Therefore, canopy coverage and soilmoisture content act as important constraints on

evapotranspiration at the study site.

Site precipitation (figs. 6 and 7) for the study

period was about average for the area in both temporal

distribution and total magnitude. The distribution and
32 Evapotranspiration From Successional Vegetation in a Deforested Area of the Lake Wales Ridge, Florida

magnitude of precipitation can strongly affect soil

moisture. Because of the strong dependence of evapotranspiration-model parameters and canopy coverage

on soil moisture, the annual value of site evapotranspiration could be higher or lower during wet and dry

years, respectively, than that reported here. Also, during a year in which total precipitation is similar to that

of the study period, evapotranspiration might be considerably different than that in the study period

because of differences in the temporal pattern of rainfall between the two years. A relatively large fraction

of the rainfall from a pattern of low-frequency, highintensity storm events is expected to escape evapotranspiration because much of the water percolating

through the sandy soil moves quickly below the shallow rooting zone. Site vegetation is susceptible to

stress because of relatively low soil moisture during

extended dry periods between storm events, and

evapotranspiration is reduced as stomata constrict and

800

0

100

200

300

400

500

600

700

CUMULATIVE EVAPOTRANSPIRATION, IN MILLIMETERS

245 275 305 335 30 60 90 120 150 180 210 240 270 SEPTEMBER 15, 1993 SEPTEMBER 15, 1994

PENMAN-MONTEITH-SIMULATED CUMULATIVE EVAPOTRANSPIRATION

1993 1994

JULIAN DAY

METHOD 1

METHOD 2

PRIESTLEY-TAYLOR-SIMULATED CUMULATIVE EVAPOTRANSPIRATION

END OF MEASUREMENT PERIOD

SEPT OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1993 1994

EXTRAPOLATED EVAPOTRANSPIRATION

Figure 29. Simulated cumulative evapotranspiration at study site from September 15, 1993, to September 15, 1994.

Note: Estimated values are based on calibration of Penman-Monteith and Priestley-Taylor models to

evapotranspiration values measured by the eddy correlation energy-balance Bowen ratio method.

canopy coverage decreases. Conversely, a pattern of

high-frequency storm events, even those of low intensity, can lead to high evapotranspiration because site

vegetation is less susceptible to moisture stress.

Application of the evapotranspiration models

for simulation of Penman-Monteith canopy resistance

and Priestley-Taylor α is useful for understanding the

models. Estimates of canopy resistance (method 2)

showed strong seasonal and diurnal fluctuations

(figs. 31 and 32). Canopy resistance is relatively low

during the wet summer season (June-September) when

foliage is dense, soil is moist, and PAR is high. Diurnal fluctuations in canopy resistance generally follow

the diurnal pattern of vapor-pressure deficit (fig. 11),

increasing from low morning values to a peak value a

few hours after midday and decreasing to low values

at sunset. The effect of diurnal variations in PAR on

estimated canopy resistance is second to that of vaporpressure deficit and opposite in direction. Canopy-
Results of Evapotranspiration Measurement and Estimation Measurement of Evapotranspiration 33

Figure 30. Simulated mean daytime Bowen ratio at study site from September 16, 1993, to August 28, 1994. Note:

Estimated values are based on calibration (method 2) of the Penman-Monteith equation to evapotranspiration values

measured by the eddy correlation energy-balance Bowen ratio method.

0

5

1

2

3

4

MEAN DAYTIME BOWEN RATIO (METHOD 2)

245 275 305 335 30 60 90 120 150 180 210 240 270

JULIAN DAY

1993 1994

BOWEN RATIO =

LATENT HEAT FLUX

SENSIBLE HEAT FLUX

SEPT OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1993 1994

245 275 305 335 30 60 90 120 150 180 210 240 270

JULIAN DAY

1993 1994

0

1,000

200

400

600

800

DAYTIME CANOPY RESISTANCE (METHOD 2),

IN SECONDS PER METER

SEPT OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1993 1994

Figure 31. Simulated daytime canopy resistance at study site from September 15, 1993, to August 28, 1994. Note:

Estimated values are based on calibration of the Penman-Monteith equation (method 2) to evapotranspiration values

measured by the eddy correlation energy-balance Bowen ratio method.
34 Evapotranspiration From Successional Vegetation in a Deforested Area of the Lake Wales Ridge, Florida

resistance values simulated by method 1 are similar to

those simulated by method 2 during most of the day.

However, canopy-resistance values simulated using

method 1 rose rapidly as sunset approached, but simulated values using method 2 decreased slightly at this

time (fig. 32). A similar effect would be noted in the

morning were it not for the exclusion of the earlymorning period of dew evaporation from model simulation.

The Priestley-Taylor α generally was well

below the empirical value of 1.26 for a well-watered

canopy, although for short periods in the wet season

(June through August) this value was approached

(fig. 33). This parameter was relatively low during the

dry season. Diurnal fluctuations in α are exemplified

in figure 34. The diurnal pattern of α is “concave up”

and responds largely to variations in PAR. Vaporpressure deficit has only a small effect on estimated

Priestley-Taylor α. in contrast to the strong sensitivity

evident in the estimated Penman-Monteith canopy

resistance.

200

400

600

800

CANOPY RESISTANCE, IN SECONDS PER METER

EXPLANATION

METHOD 1

METHOD 2

NIGHTTIME OR PRE-DEW EVAPORATION PERIOD;

CANOPY RESISTANCE NOT ESTIMATED

JULIAN DAY (1994)

1,000

200 201 202 203 204 205 0

JULY 19, 1994 20 21 22 23

Figure 32. Simulated canopy resistance at study site from July 19-23, 1994.

SUMMARY AND CONCLUSIONS

A study was conducted to: (1) estimate evapotranspiration and aquifer recharge over a 1-year period

at a site of successional vegetation in a deforested area

of the Lake Wales Ridge, Florida; and (2) to evaluate

the suitability of several evapotranspiration models

(Penman-Monteith, Penman, and modified PriestleyTaylor) for evapotranspiration simulation. Vegetation

at the site consisted of natalgrass, dog fennel, dwarf

horseweed, ragweed, and other nonagricultural plants.

Site evapotranspiration probably defines the lower

limit of evapotranspiration from vegetated surfaces in

central Florida because of the shallow-rooted plants,

rapidly drained soils, and relatively deep water table.

Eddy correlation measurements of evapotranspiration

were made during 22 events from September 1993 to

August 1994. Each measurement event was about

1 day in length with a temporal measurement resolution of 20 minutes. Eddy correlation measurements

were used to “calibrate” evapotranspiration models to

estimate evapotranspiration at unmeasured times.
Summary and Conclusions 35

275 305 335 30 60 90 120 150 180 210 240 270

JULIAN DAY

1993 1994

0.3

SIMULATED PRIESTLEY-TAYLOR

α

1.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

245

SEPT OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1993 1994

Figure 33. Simulated daytime Priestley-Taylor α at study site from September 15,1993, to August 28, 1994.

Note: Estimated values are based on calibration of the Priestley-Taylor equation to evapotranspiration values

measured by the eddy correlation energy-balance Bowen ratio method.

JULIAN DAY (1994)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

PRIESTLEY-TAYLOR α

EXPLANATION

PRIESTLEY-TAYLOR α

NIGHTTIME OR PRE-DEW EVAPORATION PERIOD;

PRIESTLEY-TAYLOR α NOT ESTIMATED

1.3

1.2

JULY 19, 1994 20 21 22 23

200 201 202 203 204 205

Figure 34. Simulated Priestley-Taylor α at study site from July 19-23, 1994.
36 Evapotranspiration From Successional Vegetation in a Deforested Area of the Lake Wales Ridge, Florida

The Penman-Monteith and Priestley-Taylor

models reproduced the 538 measured values of evapotranspiration very well. A nontraditional functional

form of the Penman-Monteith canopy resistance

proved superior (r

2 = 0.967; standard error of estimate

= 0.84 millimeter per day (mm/d)) to forms used by

previous investigators (r

2 = 0.918; standard error of

estimate = 1.33 mm/d) in evapotranspiration simulation at the site. This nontraditional approach conceptualized canopy resistance as a simple linear function of

photosynthetically active radiation, vapor-pressure

deficit, mean moisture content in the rooting zone, and

a seasonal term intended to incorporate changes in

canopy coverage, relative species density, and plant

phenological stages. A simple modified Priestley-Taylor model simulated evapotranspiration slightly better

(r

2 = 0.972; standard error of estimate = 0.77 mm/d)

than did the best Penman-Monteith model. Thus, the

simple Priestley-Taylor model would be preferable to

the Penman-Monteith model for general usage at sites

similar to the study site because the Priestley-Taylor

model simulates evapotranspiration well, is computationally much simpler than the Penman-Monteith

model, and does not require collection of wind speed

and relative humidity data.

The Penman model of evapotranspiration was a

poor predictor of measured evapotranspiration at the

study site. No relation was evident between Penmansimulated evapotranspiration and measured evapotranspiration. As expected, the discrepancy between

this model and measured values was most extreme

when canopy coverage and soil moisture were relatively low.

Daily evapotranspiration rates (simulated by

nontraditional Penman-Monteith and Priestley-Taylor

models calibrated to a Bowen ratio variant of the eddy

correlation method) varied seasonally, ranging from

about 0.2 mm/d in late December 1993 to about

5 mm/d in mid-July 1994. Most of the available

energy for turbulent energy fluxes is distributed to sensible heat during times of relatively sparse canopy

coverage and dry soil (generally October-May). Most

of the available energy is dissipated as latent heat flux

during times of relatively dense canopy coverage and

moist soil (generally June-September). Annual evapotranspiration (September 15, 1993, to September 15,

1994) was estimated to be about 680 millimeters

(mm). Evapotranspiration models, calibrated to the

standard eddy correlation method and to an energybalance residual variant, provided estimates of evapotranspiration that were about 10 percent lower and

higher, respectively, than the above estimates provided

by the Bowen ratio variant.

Measured precipitation over the study period

(1,320 mm) was about equal to mean annual precipitation for the area (1,300 mm). Neglecting changes in

storage of water above the water table and assuming

negligible surface runoff, the measured data imply that

about 570 to 700 mm of recharge to the surficial aquifer occurred over the 1-year study period. However,

the dependence of evapotranspiration-model parameters on environmental variables (particularly soil

moisture content) suggests the possibility that evapotranspiration during years of nontypical rainfall might

vary from that measured in this study.

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38 Evapotranspiration From Successional Vegetation in a Deforested Area of the Lake Wales Ridge, Florida