A Procedure for Estimating Short-Term Actual

Evapotranspiration

E. W. Harmsen, V. H. Ramirez Builes, J. E. Gonzalez, M. D. Dukes, and X. Jia

The authors are E. W. Harmsen, Associate Professor, Dept. of Agricultural and Biosystems Engineering, University of Puerto Rico. Mayaguez, PR 00681, V. H. Ramirez Builes, Research Assistant, Agronomy and Soils Department, University of Puerto Rico, Mayaguez PR 00681, J. E. Gonzalez, Professor, Santa Clara University, Santa Clara, CA. M. D. Dukes, Assistant Professor and X. Jia, Postdoctoral Fellow, Department of Agricultural and Biological Engineering, University of Florida, Gainesville, FL. Corresponding author: Eric Harmsen, P.O. Box 9030, Dept. of Agricultural and Biosystems Engineering, University of Puerto Rico, Mayaguez, PR 00681-9030; phone: 787-834-2575; fax: 787-265-3853 ; e-mail: eric_harmsen@cca.uprm.edu.

ABSTRACT.

A method is presented for estimating the actual evapotranspiration from short natural vegetation or

agricultural crops. The method consists of equating the ET flux equations based on the generalized Penman-

Monteith (GPM) combination method and a humidity gradient (HG) method. By equating the GPM and HG

expressions, a single unknown parameter, either the bulk surface resistance (rs ) or aerodynamic resistance (ra),

can be determined. In the procedure, the value of the resistance factor is adjusted by trial and error until the

daily ET time series curves from the two methods approximately coincide. This paper provides an overview of

the technical approach used, and presents results of a comparison between the new method and an eddy

covariance system. To illustrate the utility of the method an example is presented in which the ET and the

aerodynamic resistance were estimated for a sugar cane plot using one-hour values of the surface resistance,

based on measured stomatal resistance and leaf area index. A second example is presented in which surface

temperatures obtained by NASA’s airborne Advanced Thermal and Land Applications Sensor (ATLAS) were

corrected to provide accurate estimates of ET using a flux gradient equation, as part of an urban heat island

study conducted in San Juan, Puerto Rico, during February 2004.

Keywords. Evapotranspiration, Penman-Monteith, humidity gradient, Bowen ratio, eddy covariance,

weighing lysimeter, surface resistance, aerodynamic resistance

1

Introduction

Accurate estimates of actual evapotranspiration (ET) are costly to obtain. An inexpensive

alternative is to estimate actual evapotranspiration by multiplying a potential or reference

evapotranspiration by a crop coefficient (Kc) (Jensen et al., 1990). This approach has been promoted

by the United Nations Food and Agriculture Organization (FAO) for almost 30 years through their

Irrigation and Drainage Paper No. 24 (Doorenbos and Pruitt, 1977) and more recently in Paper No. 56

(Allen et al., 1998). Even though they have reported values for K c for numerous crops, many crops

grown in the world are not included in their lists. Although crop coefficients derived in other parts of

the world can be used to provide approximate estimates of evapotranspiration, the crop coefficient in

fact depends upon the specific crop variety and other local conditions (Harmsen, 2003).

To avoid the need for using crop coefficients a direct approach can be used to estimate actual

evapotranspiration. Current methods for estimating actual evapotranspiration include weighing

lysimeter, eddy covariance, and Bowen-ratio methods. Each of these methods has certain limitations

which are discussed below. A method is described in this paper which provides an estimate of the

actual ET from short natural vegetation or agricultural crops and is less expensive than the other

methods mentioned above.

The objectives of this study were

To describe a relatively inexpensive method for estimating short-term (e.g., hourly)

actual evapotranspiration.

Present validation results for the method

Present application example results from two field studies conducted in Puerto Rico.

A short review of direct methods is provided below, including the weighing lysimeter, eddy

covariance, and Bowen ratio systems.

Weighing Lysimeter. Weighing lysimeters are considered to be the most accurate method for

obtaining short-term direct estimates of actual evapotranspiration. The method can be used to

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understand the change in evapotranspiration with specific meteorological conditions, such as the

phenomenon of mid-day wilt, the short-term variation of energy partition, and the relationship between

transpiration and soil moisture tension (Chang, 1968).

Weighing lysimeters determine evapotranspiration by means of measuring the change in weight

in a volume of soil (Malone et al. 1999). The lysimeters are constructed to ensure identical soil and

crop conditions in the lysimeter and the surrounding crop. The disadvantage of the weighing lysimeter

method is that it has a high relative cost, the measurement is intrusive, and it can not be moved, which

implies that only one crop can be evaluated during a crop season.

The weighing lysimeter method estimates actual evapotranspiration by means of a water balance

analysis. The evapotranspiration rate of any crop that is planted on the lysimeter can be determined by

monitoring the change in weight, or equivalently, the change in water storage (S) within the lysimeter

soil. The water balance can be expressed as:

(1)

All terms are expressed in units of water depth relative to the surface area of the tank, where P is

rainfall, I is irrigation, D is drainage, and RO is runoff.

Howell et al. (2004) reviewed the history of lysimeter design and use for ET measurement.

Factors such as size, shape, construction materials, weighing device, as well as personal experience

and cultural operation could all affect the ET accuracy. Some lysimeter experiments showed accuracy

better than 0.05 mm (Allen and Fisher, 1990). On the other hand, Martin et al. (2001) reported that

their weighable lysimeters (0.91 x 1.02 x 0.61 m) had an average uncertainty of 0.43 mm per day for

three growing seasons with shallow-rooted crops in Arizona. Garcia et al. (2004) used two large

drainage lysimeters (2 x 2 x 0.9 m) in an ET investigation and the results from the lysimeter

measurements were only 0.2 mm/d different from the reference ET calculated using FAO56 Penman-

Monteith equation at elevations of 3600 to 4000 m above mean sea level. This indicates the validity of

the FAO56 Penman-Monteith method at high elevations as well as the high accuracy of crop ET

measurements using weighing lysimeters.

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Eddy Covariance System. This method is based on the assumption that the vertical eddy flux can be

determined by simultaneous measurements of the upward wind velocity and the fluctuation in vapor

pressure. ET by the eddy covariance method can be estimated by the product of the vertical wind

velocity (w) and a scalar property of the air such as water vapor density (ρv) (Weaver, 1992):

(2)

Equation 2 may produce errors in ET by as much as 20 percent resulting from changes in air density

caused by warming or cooling at the surface. The following equation can be used to correct for these

errors (Weaver, 1992):

(3)

where T(K) is mean temperature in Kelvin (K).

The eddy covariance method has several advantages over the weighing lysimeter. Its relative cost

is lower than the weighing lysimeter, the eddy covariance station can be moved, the method is non-

intrusive, and it is possible to obtain a surface energy balance by including sensors for net radiation

(Rn) and soil heat flux (G). The latent heat flux is equal to the product of latent heat of vaporization (λ)

and ET, and the sensible heat flux term (H) can be obtained as a residual. If a temperature sensor is

included capable of measuring values of temperature at the same frequency as the anemometer (≥ 10

Hz), then the covariance between vertical wind speed and air temperature (T), when multiplied by the

volumetric heat capacity of air (ρCp), can yield the direct eddy-covariance measurement of sensible-

heat flux (Monteith and Unworthy, 1990):

(4)

where ρa is air density and cp is the air heat-capacity.

4

Bowen Ratio. The Bowen-ratio (ß) is the ratio of the sensible to latent heat fluxes and is estimated by

measuring the temperature and humid at two positions (e.g., 10 cm and 2.0 m) above the ground

(Merva, 1975):

(5)

where γ is the psychometric constant; ∆T is the difference in air temperature at two heights (T 1 – T2);

∆e is the difference in vapor pressure at the two heights (e1 – e2); and H is the sensible heat flux. The

latent-heat flux (λET) is estimated by the following equation:

ETRn G 1

.(6)

Tanner, (1960) compared the Bowen-ratio method with a weighing lysimeter covered with an

alfalfa crop and found good agreement. Prueger et al. (1997) reported that the Bowen-ratio method is

often used because of the simplicity of data collection, and because the robust nature of the system

allows for long-term data acquisition. Tomilson, (1996) found values of ET with the Bowen-ratio

method and weighing lysimeter compared favorably (r2= 0.83); However, Tattari et al. (1995) reported

that the Bowen-ratio method produced unreliable long-term evapotranspiration, caused by unfavorable

weather conditions, and by condensation of water inside the air intake tubing filter of the instrument.

German and Summer (2001) concluded that eddy-covariance and Bowen-ratio give comparable

estimates of the latent heat flux λET, however, an advantage of the eddy-covariance method over the

Bowen ratio method is that it does not rely on mechanical parts and therefore the method is less prone

to failure.

Ham et al. (1991) used the Bowen-ratio method to measure the latent heat flux from soil and the

latent heat flux from a cotton crop canopy using 12-minute measurements throughout the day.

Ashktorab et al. (1994) used the micro-Bowen-ratio method (1cm and 6 cm height) and micro-

5

lysimeter and reported that these systems can be used for determining the soil component of

evapotranspiration from crops.

The Bowen-Ratio has the following limitations (Payero et al., 2003): It produces inaccurate

latent heat fluxes when β ≈ 1, conditions that are frequently encountered at sunrise and sunset, when R n

– G ≈ 0, and with intense advection or precipitation, at midday and early afternoon, under cloudy

conditions. Under certain conditions the calculated Bowen-ratio may produce the wrong sign (Payero

et al., 2003).

Like the weighing lysimeter and eddy covariance methods, the Bowen ratio method requires a

relatively flat topography, no regional advection and upwind fetches of 400 m to 600 m (Hanson and

May, 2004). This reported fetch requirement may be hard to obtain in practice. The generally

accepted figure for fetch to height ratio is 1:100 (Alves et al., 1998), and Heilman et al. (1989) have

reported that a fetch to height ratio as small as 1:20 is acceptable for small values of the Bowen ratio.

Important assumptions upon which the Bowen ratio method is based (Baldocchi, 2005) include steady-

state conditions, and horizontal homogeneity in sources/sinks. Advantages of the method include:

measurement is non-intrusive and measurements made at a point represent an areally-average

ensemble of mass and energy exchange, with a length scale of 100 m to 2 km (Baldocchi, 2005).

METHODS

DATA ANALYSIS

The method used in this study consisted of equating the ET flux equations based on the

generalized Penman-Monteith (GPM) combination method (Allen et al., 1998) with a humidity

gradient (HG) method (Monteith and Unsworth, 1990). In the procedure, the value of one of the

resistance factors (either the aerodynamic resistance, ra, or the bulk surface resistance, rs) is adjusted

iteratively in the two equations until their ET time series curves approximately coincide. A similar

6

approach was used by Alves et al. (1998) in which an independent estimate of ET was derived from the

Bowen ratio method, ra was obtained from a theoretical equation, and rs was obtained by inversion of

the Penman-Monteith equation.

The GPM combination equation is given as follows (Allen et al., 1998):

ET

Rn G a cpes ea

ra

1rsra

. (8)

where Δ is slope of the vapor pressure curve, Rn is net radiation, G is soil heat flux density, ρa is air

density, cp is specific heat of air, γ is psychrometric constant, T is air temperature at 2 m height, u 2 is

wind speed at 2 m height, es is the saturated vapor pressure and ea is the actual vapor pressure, ra is the

aerodynamic resistance and rs is bulk surface resistance.

Evapotranspiration can also be estimated by means of a humidity gradient equation,

ET a Kwzqd

d

. (9)

where ρa is the density of air, q is specific humidity of the air, z is the vertical spatial coordinate and Kw

is the transfer coefficient for water vapor in the atmosphere. The functional form of equation 9 used

in this study is given below:

ETa cp

w

vL vH ra rs

.(10)

7

where ρw is the density of water, ρv is the water vapor density of the air, and L and H are vertical

positions above the ground. All other variables were defined previously. The water vapor densities

were calculated based on the ideal gas equation:

vea 18

R T 273.15( )

. (11)

where R is the universal gas constant, 18 is the gram molecular weight of water vapor, and T is air

temperature (oC). The actual vapor pressures (ea) were calculated by first estimating the saturated

vapor pressure (eo) based on the measured air temperature, and then multiplying by the measured

relative humidity (RH):eo 0.6108exp17.27T

T 237.3

ea eoRH100

.(12)

In this study L and H were 0.3 m and 2 m above the ground, respectively. Equation 10 is

essentially identical to the latent heat flux equation presented by Monteith and Unsworth (1990,

equation 15.9) except that their formulation was based on the vapor pressure deficit (VPD). The VPD

is the saturated air vapor pressure minus the actual vapor pressure. In our formulation we rely only on

actual vapor pressures. It is important to note that the resistance factors in equation 10 are identical to

those used in equation 8.

The method, which effectively combines equations 8 and 10 to eliminate one of the resistance

factors, can be applied in two different ways:

1. Use theoretical equation for ra and estimate rs by trial and error procedure. (Similar to the approach

used by Alves et al., 1998)

a. The value of the aerodynamic resistance can be estimated with a theoretical equation, such as

equation 13 below (Allen et al., 1998):

8

ra

lnzm d

zom

lnzh d

zoh

k2 u2

.rau2

.

(13)

where zm is height of wind measurement, zh is height of humidity measurement, d is zero plane

displacement height equal to 0.67 h, h is crop height, zom is roughness length governing

momentum transfer equal to 0.123 h, zoh is roughness length governing transfer of heat and

vapor equal to 0.1 zom, and k is von Karman’s constant (0.41). Allen et al. (1998) reported that

equation 14 and the associated estimates of d, zom and zoh are applicable for a wide range of

crops. Equation 13 is restricted to neutral stability conditions, i.e., where temperature,

atmospheric pressure, and wind velocity distribution follow nearly adiabatic conditions (no

heat exchange). A study of surface and aerodynamic resistance performed by Kjelgaard and

Stockle (2001) determined that equation 13 will produce reliable estimates of ra for small

crops.

b. The bulk surface resistance is estimated by a trial and error procedure, which consists of

adjusting the value of rs until the daily plots of ET from equations 8 and 10 approximately

coincide. Adjustment of rs is considered acceptable when the values of the total daily ET from

the two equations are within 0.01 mm.

2. Measure rs and estimate ra by trial and error procedure.

a. The bulk surface resistance is determined from the equation:

rs = rl / (0.5LAI) (14)

where rl is the measured stomatal resistance, (0.5 LAI) is the sunlit leaf area index and LAI is

the measured leaf area index.

b. The aerodynamic resistance is estimated by a trial and error procedure, which consists of

adjusting the value ζ until the daily plots of ET from equations 8 and 10 approximately

9

coincide. Adjustment of ζ is considered acceptable when the values of the daily ET from the

two equations are within 0.01 mm.

FIELD DATA ANALYSIS

Climatological data were saved on a Campbell Scientific (CS) CRX10 data logger every 10

seconds. Net radiation was measured using a NR Lite Net Radiometer. Wind speed was measured 3

m above the ground using a MET One 034B wind speed and direction sensor. The wind speed at 3 m

was adjusted to the 2 m height using the logarithmic relation presented by Allen et al. (1998). Soil

water content was measured using a CS616 Water Content Reflectometer. Soil temperature was

measured using two TCAV Averaging Soil Temperature probes, and the soil heat flux at 8 cm below

the surface was measured using a HFT3 Soil Heat Flux Plate.

An initial test using two temperature/relative humidity (Temp/RH) sensors simultaneously,

positioned at the same height in close proximity revealed non-constant differences in RH between the

two sensors. Differences in RH ranged from -5% to +8.5% (see Figure 1). Errors of this magnitude

were unacceptable for use in estimating the vertical humidity gradient. Therefore, to obtain accurate

estimates of the humidity gradient, a single Temp/RH sensor (Vaisala HMP45C) was used, which was

automatically moved between two vertical positions (0.3 m and 2 m) over short time periods (2

minutes).

An automated elevator device was developed for moving the Temp/RH sensor between the two

vertical positions. The device consisted of an aluminum frame with a 12 volt DC motor (1/30 hp)

mounted on the base of the frame. One end of a 2-m long chain was attached to a shaft on the motor

and the other end to a sprocket at the top of the frame. Waterproof limit switches were located at the

top and bottom of the frame to limit the range of vertical movement.

For automating the elevator device a Programmable Logic Controller (PLC) was used which is

composed of “n” inputs and “n” relay outputs. To program the device, a ladder logic was used which

is a chronological arrangement of tasks to be accomplished in the automation process. The Temp/RH

10

sensor was connected to the elevator device, which measured RH and temperature in the up position

for two minutes then changed to the down position where measurements were taken for two minutes,

and the process continued indefinitely until the experiment was ended. When the elevator moves to the

up position it activates the limit switch which sends an input signal to the PLC. That input tells the

program to stop and remain in that position for two minutes. At the same time it activates an output

which sends a 5 volt signal to the control port C2 in the CR10X data logger in which a small

subroutine is executed. This subroutine assigns a “1” in the results matrix which indicates that the

temperature and relative humidity correspond to the up position. At the end of the two minutes period

the elevator moves to the down position and repeats the same process, but in this case sending a 5 volts

signal to the data logger in the control port C4, which then assigns a “2” in the results matrix.

To facilitate post-processing of the large data sets generated from the weather station a computer

program (spreadsheet macro) was developed. The program separates the data from the “up” and

“down” positions and calculates the Penman-Monteith reference evapotranspiration, and the actual

evapotranspiration by equation 8 and equation 10.

The new method was verified by comparing ET results for April 5 th and 6th, 2005, with an eddy

covariance system at the University of Florida (UF) Plant Science Research and Education Unit

(PSREU) near Citra, Florida. The eddy station was located in the center of a 23 ha bahia grass field

and the shortest distance from the station to the edge of the field was 230 m.

A Campbell Scientific CSAT3 3D Sonic Anemometer and KH20 krypton Hygrometer are the

major instruments used in the eddy covariance system. The anemometer measured wind speeds and the

speed of sound using three pairs of nonorthogonal sonic transducers to detect any vertical wind speed

fluctuations. The anemometer was set up facing the prevailing wind to minimize the negative effect by

the anemometer arms and other supporting structures. The frequency of the CSAT3 is 10 Hz with

output averaged every 30-minutes The KH20 Krypton Hygrometer was mounted 10 cm from the

center of the CSAT3, with the source tube (the longer tube) on the top and the detector tube (the

shorter tube) on the bottom. The output voltage of the hygrometer is proportional to the attenuated

11

radiation, which is in turn related to vapor density. The frequency of the hygrometer is 10 Hz with an

average output every 30-minute.

Additionally, other meteorological and environmental variables were measured including: air

temperature, relative humidity, wind speed and direction, soil temperature, soil heat flux, precipitation

(tipping bucket), net radiation, and incoming solar radiation.

The eddy covariance system directly measured the high fluctuations of wind speed, vapor density

and air temperature (Tanner and Greene, 1989; Twine et al., 2000). Fluctuations in wind speed, virtual

air temperature, and vapor density were sampled at 10 Hz, and 30-minute average covariance was

calculated to estimate the fluxes. The covariance of wind speed and vapor density fluctuations were

used to compute the latent heat flux and the covariance of wind speed and air temperature were used to

compute the sensible heat flux. The 30-minute latent heat fluxes were corrected for temperature-

induced fluctuations in air density (Webb et al. 1980) and for the hygrometer sensitivity to oxygen

(Tanner and Greene 1989). Sensible heat fluxes were corrected for differences between the sonic

temperature and the actual air temperature (Schotanus et al. 1983). Both the sensible and latent heat

fluxes were corrected for misalignment with respect to the natural wind coordinate system (Baldocchi

et al. 1988). The Bowen-ratio method was used to close the surface energy balance relationship (Twine

et al. 2000). Flux and atmospheric measurements were logged using a CR23X datalogger. During

certain periods, such as early mornings and after precipitation, the hygrometer measurements were not

available due to the moisture obscuring the lens. The data analysis was conducted for daytime

measurements, based on the available energy for evapotranspiration.

Equation 10 is a finite-difference form of the gradient flux equation and assumes that humidity

varies linearly between the vertical positions L and H. This assumption was verified in this study by

manually measuring the vertical humidity profile for a grass (Star Grass, Cynodum. Spp) and

sugarcane (Sacharum officinarum) crop. The temperature and RH data for the grass were collected at a

commercial turf grass farm (La Fé Agricola Company) in Hormigueros, PR on May 3rd, 2005. The

temperature and RH data for the sugar cane were collected at the UPR Agricultural Experiment Station

12

at Lajas, PR, on February 2, 2005. On the days that data were collected, the grass and the sugarcane

had attained heights of 15 cm and 150 cm, respectively.

Temperature profiles were also obtained. The vertical measurements of temperature and relative

humidity were carried out at six levels above the ground: 0.1 m, 0.5 m, 1.0 m, 1.5 m, 2.0 m, and 2.5 m.

Every fifteen minutes the Temp/RH sensor measurements were taken during a one minute period at

each vertical position. During the one minute interval the data logger saved six readings.

Additionally, net radiation, wind speed, wind direction, soil heat flux, soil moisture, and soil

temperature were saved to the CR10X data logger.

RESULTS

For convenience, the equipment used in this study involving a standard weather station and an

elevator device for obtaining the temperature and humidity gradients, will be referred to as the ET

station. On April 5th and 6th, 2005, the ET station was set up next to an eddy covariance station

described previously. The goal of the experiment was to compare the ET estimates from the ET

station, eddy covariance system, and three weighing lysimeters. Unfortunately, the grass on the

weighing lysimeters was damaged from a recent herbicide application, and consequently the data from

the lysimeters could not be used. Therefore, validation of the ET station was limited to comparisons

with the eddy covariance system.

During the two day experiment the weather was excellent with relatively few clouds. On both

days, except for early morning, the relative humidity was in the range of 40 to 60% and high

temperatures were around 28 oC. The field was covered with bahiagrass (Paspalum notatum), having

average height of 15 cm which receives irrigation regularly via a linear-move irrigation system. On the

night of April 4th, just before the beginning of the experiment, the field received 15 mm of irrigation.

To estimate the ET using data from the ET station the following steps were used:

1. The data were read into the spreadsheet macro which, among other things, separated the “up”

and “down” humidity and temperature data, and calculated actual vapor pressures.

13

2. The approach used in this case was to estimate the aerodynamic resistance (r a) using equation

13 based on a 15 cm plant height, which yielded a value of ζ = 191.

3. The ET estimates from equations 8 and 10 were plotted together on the same graph, and the

value of rs was adjusted until the two datasets approximately coincided. The two datasets were

considered to be in agreement when their total daily ET was within 0.01 mm of each other.

As an example, Figure 2 shows the short-term estimates of ET on April 6 th, 2005 at the PSREU

near Citra, Florida. The total daily ET for both methods was 3.66 mm, and the final value of r s was

equal to 160 sm-1. Based on our experience, the HG method is generally much more variable than the

GPM method. The fluctuations in the GPM ET data in Figure 2 were primarily due to fluctuations in

the net radiation. It is interesting to note that the HG ET data, which is a function of the water vapor

density gradient and the wind velocity (via ra), follows the pattern of the GPM method quite well, and

the GPM ET data were well correlated with net radiation.

Figure 3 shows a 15-minute period of RH readings. The figure also shows the value of the square

wave (i.e., the value 1 or 2 sent from the PLC to the data logger). A square wave value of 1 signified

that the Temp/RH sensor was in the up position and a 2 signified that the Temp/RH sensor was in the

down position. Figure 4 shows the actual vapor pressures for April 6 th, 2005, separated into the up and

down positions as determined by the spreadsheet macro. The figure also shows the difference in the

actual vapor pressures for the two vertical positions.

Table 1 lists the estimated daily ET data from the eddy covariance system and the ET station for

April 5th and 6th, 2005. The ET estimates by the two methods are in reasonably good agreement. The

daily average crop coefficients (Kc) in Table 1 are in the range reported for mature turf grass (cool

season 0.95, warm season 0.85) (Allen et al., 1998). The table also includes the parameters ζ and r s.

Values of ζ and rs for the reference evapotranspiration were obtained from Allen et al. (1998) for the

imaginary reference grass (ζ = 208 and rs = 70 s m-1). Figure 5a and 5b show the ET as determined

from the eddy covariance system and the ET station for April 5 th and 6th, 2005, respectively. The

Penman-Monteith reference evapotranspiration is also shown in the figure. An interesting fact is that

14

the eddy covariance ET exceeded the reference evapotranspiration several times during the two days

experiment.

To test the assumption of linearity in the humidity gradient, experiments were conducted to

measure the RH and temperature at six heights above the ground for a grass and sugarcane crop.

Figure 6 and 7 show the vertical distribution of actual vapor pressure and air temperature, respectively,

for the grass and sugarcane crop. A linear trend can be observed for the average actual vapor pressure

(Figure 6) with height up to around 2 meters above the ground. The shape of the sugarcane curve was

more linear than the idealized vertical vapor pressure profile presented by Monteith and Unsworth

(1990). The deviation from the idealized actual vapor pressure profile may be because the data was

collected within a small test plot, adjacent to a pasture (upwind). Consequently, the conditions present

almost surely precluded the development of an idealized wind profile and an aerodynamic resistance as

calculated by equation 13.

The average of the 15-minute actual vapor pressure data for the grass showed less linearity than the

sugar cane (Figure 6). The increasing ea for the grass above 150 cm could be due to a combination of

factors including the fact that the soil was relatively dry on the day of the data collection and the ET

may have been low due to water-limiting conditions. Also the study area, although having an upwind

fetch greater than 100 meters, was bordered by a forest, which may have been the source of the higher

humidity above 150 cm above the ground. Nevertheless, from the data presented for 15 cm and 150

cm tall crops the assumption of linearity in the vertical humidity gradient appears to be reasonable.

The average vertical air temperature distributions for the grass and sugar cane (Figure 7) indicate some

non-linearity in the temperature gradients, however, the overall variations in temperatures were small

(< 0.5oC ).

Application Study 1

A study was conducted to determine the value of ζ for a sugar cane (Sacharum officinarum)

plot located at the UPR Agricultural Experiment Station at Lajas, PR, on November 9, 2004. The

experimental plot was 230 m2 in area and contained 305 sugar cane plants. The average plant height

15

was 1.5 m and the leaf area index (LAI) based on the leaf area (1.79 m 2 per plant) for the day of the

experiment was 2.4. Stomatal resistance measurements were taken on 20 leaves each hour using a

Delta-T AP4 porometer. The estimated surface resistance (equation 14) throughout the day is shown

in Figure 8. Employing equations 8 and 10, the final adjusted value of ζ was equal to 305, and the

estimated values of ra are shown in Figure 10. The ζ is higher than the value that would have been

estimated using equation 13. Equation 13 would not be applicable as the sugar cane plants did not

fully cover the ground as is a requirement for using the equation (i.e., full cover). Furthermore the

fetch to height ratio was only 14.5 which is less than the minimum value of 20 recommended by

Heilman et al. (1989) for small values of β. The ET throughout the day of the experiment is shown in

Figure 9. The total ET for the day was only 1.3 mm owing to the cloudy conditions. Figure 10 shows

the net radiation throughout the day of the experiment. For comparison the net radiation from a

relatively cloudless day (October 31, 2004) at the same location is shown.

Application Study 2

The ability to estimate short-term fluxes of water vapor from a growing crop or natural vegetation

is necessary for validating estimates from remote sensing techniques, such as NASA’s Advanced

Thermal and Land Applications Sensor (ATLAS). On February 11th through February 16th, 2004, the

airborne ATLAS instrument was used to evaluate the Urban Heat Island Effect within the San Juan

Metropolitan area. To validate energy flux estimates from ATLAS, a ground study was conducted at

the University of Puerto Rico Agricultural Experiment Station at Rio Piedras, PR (located within the

metropolitan area). The ET station was located on a grass-covered field in the Jardin Botanica Sur.

The objective of this study was to adjust, if necessary, the ATLAS surface temperatures so that

accurate values of evapotranspiration from vegetated areas could be estimated with the ATLAS

instrument. Various efforts have been made to estimate the latent heat flux using remote sensing

techniques (e.g., Jarvis 1981; Luvall et al., 1990; Holbo and Luvall, 1989; Quattrochi and Luvall,

1990; Turner and Gardner, 1991). These methods typically rely on an equation of the following form

(Luvall et al., 1990):

16

ETa cp

v vs rs

.

(15)

where ρv is water vapor density of the air based on measurements of air temperature and RH at the

ground surface, and ρvs is saturated water vapor density of the air at the vegetation canopy, based on

surface temperature obtained by remote sensing. All other parameters were previously defined.

The following methodology was used to correct the ATLAS surface temperature data:

1. The average surface temperature was obtained for a small group of contiguous pixels in the study

area from the ATLAS surface temperature (TST) image, produced from a flight-line covering the UPR

Agricultural Experiment Station on February 11th, 2004.

2. The canopy temperature was iteratively adjusted in equation 15 (via equation 11 replacing e a with es)

until the ET equaled the ET obtained from equations 8 and 10 at the time of the fly-over (2 PM). The

corrected value of the canopy temperature was considered to be the effective surface temperature (TST-

eff).

3. A surface temperature correction factor (STCF) was obtained from TST-TST-eff. The STCF can be

subtracted from all TST pixel values in the San Juan area to obtain estimates for use in calculating

evapotranspiration for similar land surface conditions (i.e., grass).

Figure 12 shows the surface temperature image of the study area (circled) and the surrounding

vicinity obtained from the ATLAS instrument on February 11, 2005, at 2 PM. In one pixel of 5 square

meters (resolution of the ATLAS instrument), in which the ET station was located, the average air

temperature, average soil temperature and ATLAS surface temperature (pixel containing the ET

station) were 28.9˚C, 27.9˚C and 32.0oC, respectively. The average surface temperature derived from

the ATLAS instrument for a group of twelve contiguous pixels within the study area was 33.0oC.

Figure 12 shows the estimated ET for February 11, 2004, as determined by the GPM method, the

HG method, and the average of the two methods. The value of ζ was set equal 208 and the estimated

daily average bulk surface resistance 90 sm-1.

17

Equation 15 was set equal to 0.53 mm/hr, the average ET at the time of the ATLAS fly-over

(2:00 PM). Backing out an effective surface temperature from the saturated water vapor density (ρ vs)

term, resulted in an unrealistically low surface temperature equal to 21.2 oC. Therefore, a modification

was made to equation 15 by replacing ρvs with ρv-canopy, where ρv-canopy is the water vapor density of the

air near the canopy based on the actual vapor pressure. Using this approach an effective surface

temperature of 29.8oC was obtained. Therefore the average correction to the ATLAS surface

temperature was 33.0 oC – 29.8 oC= 4.2 oC. A study is currently in progress to estimate ET for

February 11, 2004, throughout the San Juan and surrounding rural areas for similar land cover. It is

hypothesized that an “Urban Evapotranspiration Island” exists for San Juan. Evapotranspiration will

also be estimated using a net radiation approach, which is one of the parameters that the ATLAS

instrument measures.

Because of the relatively low cost of the method described in this paper numerous stations could

be deployed over a region with the purpose of validating or calibrating remote sensing estimates of ET.

Figure 13 shows the relative costs of the current methods available for estimating actual

evapotranspiration. The system described in this paper is approximately 20 and 7 times less expensive

than the weighing lysimeter and eddy covariance methods, respectively. The Bowen Ratio method,

although relatively inexpensive, nevertheless is about twice the cost of the system described in this

paper.

CONCLUSION

This paper described a method for estimating of the actual ET that is equally accurate

and is less expensive than the weighing lysimeter, eddy covariance and Bowen ratio methods.

The method used in this study consisted of equating the ET flux equations based on the generalized

Penman-Monteith combination method with a humidity gradient method. In the procedure, the value

of one of the resistance factors (either the aerodynamic resistance, ra, or the bulk surface resistance, rs)

is adjusted iteratively in the two equations until their ET time series curves approximately coincide.

18

The method was validated by comparison with an eddy covariance station located at the

University of Florida Plant Science Research and Education Center near Citra, FL on April 5 th and 6th,

2005. Two application examples were presented: one in which the surface resistance was estimated

throughout the day at the UPR Agricultural Experiment station in Lajas, PR, within a sugar cane plot

on November 9th, 2004, and the aerodynamic resistance was obtained as a residual of the procedure. In

the second application example, the method was used to obtain a surface temperature correction factor

for the airborne ATLAS instrument as part of the Urban Heat Island project conducted in San Juan, PR

during February 2004.

ACKNOWLEDGEMENTS

This material is based on research supported by NASA-EPSCoR (NCC5-595), NOAA-

CREST, USDA-TSTAR, NASA-URC, and UPRM-TCESS. We would like to thank the following

individuals for their contributions to this paper: Javier Chaparro, Antonio Gonzalez, Richard Diaz, Jose

Paulino-Paulino, and Dr. Ricardo Goanaga of the USDA Tropical Agricultural Research Station in

Mayaguez, PR.

The ATLAS Sensor was provided by NASA Stennis Space Center and the Lear Jet Plane was

provided by NASA Glenn Research Center. Special thanks to Dr. Jeffrey Luvall who coordinated the

remote sensing data collection and post-processing, Pieter Van Der Meer and Porfirio Beltrán for

coordinating the mission from the ground, and to the flight crew: James Demers, Kirk Blankenship,

Olen Read and to the instrument operator Duane O’Neal.

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23

24

Table 1. ET as determined from the eddy covariance system and the ET station. The Penman-Monteith reference

evapotranspiration, daily average crop coefficients (Kc), and values of ζ, and ra are also included.

Date Method

Daily ET

(mm) Kc ζrs

(s/m)

4/5/2005PM - ETo 4.37   208 70

Eddy Covariance 3.92 0.90    ET station 4.11 0.94 191 157

4/6/2005PM - ETo 4.06   208 70

Eddy Covariance 3.78 0.93    ET station 3.66 0.90 191 160

25

-6

-4

-2

0

2

4

6

8

10

0 4 8 12 16

Time (hours)

RH

Diff

eren

ce (%

) .

Figure 1. Difference between RH measured by two RH sensors held in close proximity. Differences in RH

ranged from -5% to +8.5%.

0.0

0.2

0.4

0.6

0.8

8:30 AM 10:54 AM 1:18 PM 3:42 PM 6:06 PM

Time

Eva

potra

nspi

ratio

n (m

m/h

r) .

Penman-Monteith Method

Humidity Gradient Method

Figure 2. Example of the estimated short-term ET using the GPM and HG equations. Values of the daily

average surface resistance (rs) were adjusted until the two datasets approximately coincided. The final value of rs was

154 s m-1, and ζ was equal to 191. The data used to estimate ET was obtained on April 6, 2005 at the University of

Florida Plant Science Research and Education Center near Citra, FL.

26

0.5

1

1.5

2

2.5

2:15 PM 2:17 PM 2:20 PM 2:23 PM 2:26 PM 2:29 PMTime

Squ

are

Wav

e

40

44

48

52

56

60

Rel

ativ

e H

umid

ty (%

) .

SW

RH

Figure 3. Example of the measured relative humidity for a fifteen-minute period measured on April 6, 2005 at

the University of Florida Plant Science Research and Education Unit near Citra, FL. A 1 on the square wave (SW) axis

indicates that the RH /temperature sensor was up (2 m) and a 2 that the sensor was down (0.3 m).

0.0

0.1

0.2

0.3

0.4

0.5

8:00 AM 10:24 AM 12:48 PM 3:12 PM 5:36 PM

Time

Act

ual V

apor

Pre

ssur

e

Diff

eren

ce (K

Pa)

.

0.0

0.5

1.0

1.5

2.0

2.5

Act

ual V

apor

Pre

ssur

e (K

Pa)

.Actual Vapor Pressure Difference

Up Position Actual Vapor Pressure

Dow n Position Actual Vapor Pressure

Figure 4. Example of the estimated actual vapor pressure in the up and down positions, and the vapor pressure

difference between the two vertical positions measured at on April 6, 2005 at the University of Florida Plant Science

Research and Education Center near Citra, FL.

27

0.0

0.2

0.4

0.6

0.8

8:30 AM 10:54 AM 1:18 PM 3:42 PM

Time

Evap

otra

nspi

ratio

n (m

m/h

r) .

EToEddy Covariance SystemPM ET

(a)

0.0

0.2

0.4

0.6

0.8

1.0

8:30 AM 10:54 AM 1:18 PM 3:42 PM 6:06 PM

Time

Eva

potra

nspi

ratio

n (m

m/h

r) . ETo

Eddy Covariance SystemET Station

(b)

Figure 5. Evapotranspiration estimated using the eddy covariance system and ET station on (a) April 5th, 2005

and (b) April 6th, 2005 at the University of Florida Plant Science Research and Education Center near Citra, FL. ET

estimates from ET station are average of GPM and HG methods. Reference evapotranspiration is also presented.

28

0

50

100

150

200

250

300

1.5 1.7 1.9 2.1 2.3 2.5

Actual Vapor Pressure (KPa)

Hei

ght a

bove

gro

und

(cm

) .

GrassSugar Cane

Figure 6. Vertical distribution of actual vapor pressure for a grass and sugar cane crop. Actual vapor pressures

represent averages of 15-minute readings over a several hour period. The straight lines represent the distributions of

actual vapor pressure implicitly assumed when using equation 10.

0

50

100

150

200

250

300

27.0 28.0 29.0 30.0 31.0 32.0

Temperature (oC)

Hei

ght a

bove

gro

und

(cm

) .

Sugar caneGrass

Figure 7. Vertical distribution of air temperature for a grass and sugar cane crop. Temperatures represent

averages of 15-minute readings during a several hour period.

29

y = 12564x2 - 12139x + 3065.7

0

200

400

600

800

1000

1200

7:00 AM 9:24 AM 11:48 AM 2:12 PM 4:36 PM 7:00 PM

Time

Res

ista

nce

(s/m

) .

Aerodynamic Resistance

Surface Resistance

Poly. (Surface Resistance)

Figure 8. Estimated surface and aerodynamic resistance for a sugar cane plot at the UPR Agricultural

Experiment Station at Lajas on November 9, 2004. The second order polynomial (Poly.) curve is the best fit equation

for the surface resistance data. Aerodynamic resistance was estimated by trial adjustment using the GPM and HG

equations.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

7:00 AM 8:12 AM 9:24 AM 10:36 AM 11:48 AM 1:00 PM 2:12 PM 3:24 PM 4:36 PM 5:48 PM

Time

Eva

potra

nspi

ratio

n (m

m/h

r) .

HG method

GPM method

Average of HG and GPMmethods

Figure 9. Evapotranspiration estimated using the ET station for a sugar cane plot at the UPR Agricultural

Experiment Station at Lajas on November 9, 2004. HG is the humidity gradient method; GPM is the generalized

Penman-Monteith method; the solid bold line is the average of the two methods.

30

-200

-100

0

100

200

300

400

500

600

700

6:00:00 8:24:00 10:48:00 13:12:00 15:36:00 18:00:00

Time

Net

Rad

iatio

n (W

/m2)

.

31-Oct-049-Nov-04

Figure 10. Measured net radiation in a sugar cane plot at the UPR Agricultural Experiment Station at Lajas on

the day in which porometer readings were taken (November 9, 2004). For comparison, data from a relatively cloudless

day (October 31, 2004) at the same location is also shown.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

10:00 AM 11:55 AM 1:50 PM 3:45 PM 5:40 PM

Time

ET

(mm

/hr)

GPM method

HG methodAverage of GPM and HG methods

Figure 11. Estimated evapotranspiration (ET) obtained on February 11th, 2004 at the UPR Agricultural

Experiment Station, Rio Piedras Puerto Rico (Jardin Bontanico Sur). Surface temperatures were obtained for the

study area by the airborne ATLAS instrument a 2 PM.

31

Figure 12. ATLAS surface temperature image. Circled area is the study area where the ET station was located.

Figure 13. Cost comparison of three common direct evapotranspiration measurement systems with

the system described in this paper.

32

60

52

46

39

33

26

19

12

6

Degrees oC

WeighingLysimeter

EddyCovariance

Bowen Ratio Systemdescribed in

this paper

Evapotranspiration Measurement System

Rel

ativ

e C

ost

+

33