Published in Agron. J. 96:384-390 (2004).
© American Society of Agronomy
677 S. Segoe Rd., Madison, WI 53711 USA
AGROCLIMATOLOGY
Hourly and Daytime Evapotranspiration from Grassland Using Radiometric Surface Temperatures
Ayman Suleiman*,a and
Richard Cragob
a Cent. for Atmos. Sci., Hampton Univ., Hampton, VA 23668
b Dep. of Civil and Environ. Eng., Bucknell Univ., Lewisburg, PA 17837
* Corresponding author (ayman.suleiman{at}hamptonu.edu).
Received for publication July 14, 2002.
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ABSTRACT
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Determination of evapotranspiration (E) is needed for many applications in agriculture, hydrology, and meteorology. The spatial variability of leaf area index (LAI) and soil water availability makes it impractical to model E over heterogeneous lands using ground-based techniques. Remote sensing can be a good source for both LAI and radiometric surface temperature (Ts) estimates. However, remotely sensed soil moisture content is not suitable for E prediction. In this study, we propose a procedure to estimate E using Ts. The method uses a dimensionless temperature 
T, defined as (Ts – Ta)/(Tmax – Ta), where Ta is the air temperature and Tmax is the surface temperature that would occur if all the net radiation (Rn) was converted to sensible heat flux and no evaporation occurred. This approach has been tested on data from two grassland sites in Oklahoma and Kansas. Root mean square differences between hourly predicted and measured E ranged from 30 to 50 W m–2. The slope and r2 for the zero-intercept linear regression between hourly estimated and measured E ranged from 1.01 to 1.37 and 78 to 0.94, respectively. Daytime conservation of evaporative fraction (EF = E/Rn) was used to extrapolate from hourly to daytime E. The slope and r2 of the linear regression between daytime estimated and measured E ranged from 0.89 to 1.07 and 0.69 to 0.9, respectively. These results demonstrate that, for grassland, the model may give good estimates of E when Ta and Ts are available.
Abbreviations: CASES-97, 1997 Cooperative Atmosphere–Surface Exchange Study (experiment) • CWSI, crop water stress index • LAI, leaf area index • SGP-97, 1997 Southern Great Plains (experiment)
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INTRODUCTION
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MEASUREMENTS of evapotranspiration (E) are needed for many applications in agriculture, hydrology, and meteorology. Ground-based measurement techniques are inadequate to model E over large or heterogeneous areas since variables controlling E, such as canopy density (i.e., LAI), soil water availability, and surface temperature, vary spatially. Visible channels are used to estimate LAI, and infrared channels are used for radiometric surface temperature, Ts, while soil moisture content can be estimated with microwave channels. Soil moisture availability is a key variable as it exerts control over the ratio between actual and potential E. Soil moisture sensing is progressing rapidly, with ambitious field experiments ongoing (e.g., the Soil Moisture Experiments in 2002 (SMEX02 Experiment Plan Summary, http://hydrolab.arsusda.gov/smex02/smex02.htm; verified 21 Dec. 2003). However, remotely sensed soil moisture content data are not always available or accurate, especially for dense vegetation. Moreover, remotely sensed soil moisture does not represent the entire soil water profile that controls E. Therefore, a method is needed to find E directly from Ts, without requiring soil water availability.
Evapotranspiration (expressed in this paper as a latent heat flux by multiplying the mass of water evaporated per unit surface area by the latent heat of evaporation) and surface temperature are linked through the land surface energy budget:
 | [1] |
(e.g., Brutsaert, 1982) where Rn (W m–2) is the net incoming radiation minus the heat flux into the ground (W m–2) and H (W m–2) and E (W m–2) are the sensible and latent (evaporative) heat fluxes into the atmosphere, respectively. For the energy balance to close, any part of Rn that does not contribute to E must be converted into H. In order for that to happen, the surface has to have the right temperature (Ts). This temperature is called the aerodynamic surface temperature and will be discussed later. Although soil water availability is crucial in controlling E, Ts can be used as an indicator of E as will be shown in the Theory section.
In some agricultural applications, daily evapotranspiration is often needed more than instantaneous rates. With remotely sensed surface temperatures, methods to extend instantaneous to daily evapotranspiration are needed because orbiting satellites usually provide coverage only once daily. One method uses the evaporative fraction, EF = E/Rn, which is commonly used as a dimensionless evaporation rate that characterizes the partition of available energy Rn by the land surface (e.g., Qualls et al., 1999). The evaporative fraction has been found from numerous observations to vary little during the daytime (e.g., Shuttleworth et al., 1989; Gurney and Hsu, 1990, Brutsaert and Chen, 1996; Crago and Brutsaert, 1996). Crago (1996b)(1996c) concluded that a combination of weather conditions, soil moisture, topography, and biophysical conditions contributes to this conservation of EF. Brutsaert and Sugita (1992) showed that cumulative daytime evaporation losses could be accurately estimated by multiplying an instantaneous estimate of EF by the cumulative daytime Rn.
The objective of this work was to develop a procedure to estimate hourly E from radiometric surface temperature measurements. The procedure has been tested on data from the 1997 Southern Great Plains (SGP-97) and the 1997 Cooperative Atmosphere–Surface Exchange Study (CASES-97) field experiments. The hourly evapotranspiration will then be extended to daytime evapotranspiration using the conservation of evaporative fraction. In future work, this procedure will be applied to satellite-based radiometric surface temperatures. To do so, satellite-based LAI will be needed. The MODIS instrument on both Terra and Aqua satellites provides LAI.
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THEORY
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Dimensionless Temperature
The sensible heat flux, H, can be estimated from measurements of air temperature, Ta, and surface temperature, Ts, using the Monin–Obukhov similarity theory (Brutsaert, 1982; Stull, 1988). In the Monin–Obukhov similarity theory, the flux is proportional to the difference between these two temperatures, with the ratio H/(Ts – Ta) depending on variables characterizing the atmospheric turbulence and the land surface. This relationship can be expressed as:
 | [2] |
(e.g., Brutsaert, 1982) where Ts (°C) is the aerodynamic surface temperature, Ta (°C) is the air temperature at a height za (m) in the surface sublayer, k (where k = 0.4) is von-Karman's constant, u* (m s–1) is the friction velocity, 
(kg m–3) is the density of the air, cp (J kg–1 °C–1) is the specific heat at constant pressure, z0h (m) is the scalar roughness length for sensible heat, and d0 (m) is the displacement height. Atmospheric stability, which affects the efficiency of turbulent transport, is included through the variable 
, which is a function of the stability or buoyancy parameter (za – d0)/L, where L (m) is the Obukhov length.
From Eq. [2], when (Ts – Ta) = 0, H = 0 and thus E = Rn [Eq. [1]). A maximum flux temperature Tmax can be defined as the value of Ts in Eq. [2] that gives H = Rn and E = 0. Thus, when (Ts – Ta) = (Tmax – Ta), H = Rn and E = 0 as shown in Fig. 1a
. The figure is found by combining Eq. [1] and [2] and assuming the stability function varies approximately linearly with H. The errors of calculating E or H while implementing this assumption are minimal, particularly when the measurements are taken in the lowest regions of the surface sublayer where stability corrections are small (Brutsaert, 1982). Theoretically, if the actual surface temperature was equal to Tmax, the net radiation (Rn) would be less than the actual Rn due to increased thermal emittance from the surface. Because the difference between this theoretical and actual Rn would be small for a closed canopy and because the use of such theoretical Rn would complicate the calculations, the actual Rn was used in our approach to calculate Tmax. The Bowen ratio (BR = H/E) starts at 0 when (Ts – Ta) is 0, becomes 1 when (Ts – Ta) = 0.5 x (Tmax – Ta), and goes to infinity when (Ts – Ta) goes to (Tmax – Ta), as shown in Fig. 1a. A value of Tmax can be obtained by solving for Ts in Eq. [2], assuming that H equals Rn. A dimensionless temperature (T) can be introduced as:
 | [3] |
From Eq. [1] and [2], H equals 0 and E equals Rn when T is 0 while H equals Rn and E equals 0 when T is 1, as shown in Fig. 1b. The relationship between H and T is linear, with a zero intercept (again assuming varies approximately linearly with H):
 | [4] |
The relationship between E and T is
 | [5] |
and the evaporative fraction EF is
 | [6] |
The dimensionless temperature T can be found from Eq. [3] using radiometric Ts, measured Ta, and Tmax found as described above. These calculations require a value for the scalar roughness length z0h in Eq. [2]; this will be discussed in the next section.
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Fig. 1. Latent heat flux (E), sensible heat flux (H), and Bowen ratio (BR) plotted against: (a) surface temperature (Ts) minus air temperature (Ta) and (b) dimensionless temperature (T). Rn, net radiation (less the ground heat flux); Tmax, the value of Ts in Eq. [2] that gives H = Rn and E = 0.
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The variable T is defined in Eq. [3] as a ratio of two vertical temperature gradients. The evaporative fraction EF (related to T through Eq. [6]) and other dimensionless energy fluxes such as the Bowen ratio H/E and the crop water stress index [defined by CWSI = 1 – E/Ep, where Ep is the rate of potential evapotranspiration (Jackson et al., 1981; Moran et al., 1994)] have long been used to characterize the hydrologic state of vegetated surfaces. Like T, the CWSI can be expressed in the form of a ratio of temperatures—the CWSI is the ratio of (Tc – Ta)m – (Tc – Ta)r to (Tc – Ta)m – (Tc – Ta)x, where Tc is the canopy temperature, Ta is the air temperature in the surface sublayer, and the subscripts m, r, and x refer to minimum, measured, and maximum values, respectively (Moran et al., 1994). However, there are several differences between CWSI and T. First, since the measured air temperature is the same for the minimum, measured, and maximum values, Ta cancels out in CWSI, leaving CWSI = (Tcm – Tcr)/(Tcm – Tcx), which is no longer a ratio of vertical temperature gradients. Second, CWSI is usually determined in practice in terms of species-specific maximum and minimum stomatal resistances while T is defined and determined only in terms of the surface and air temperatures and the available energy. In this respect, T differs also from EF and the Bowen ratio. Thus, T is simple to determine in the field and may serves as an alternate to these other variables that characterize the state of vegetated surfaces. Third, the T 
1 and can be negative when the air temperature is greater than Ts, such as for advection conditions, but CWSI is always between 0 and 1. Fourth, T is derived from a residual energy balance while the CWSI uses the energy balance with an estimate of E based on the vapor pressure gradient.
Roughness Length Parameterization
In Eq. [2], z0h is the scalar roughness length, which is the conceptual height at which the surface sublayer temperature profile described by Eq. [2] reaches the surface temperature. This is analogous to the momentum roughness length, z0, which is the height at which the wind speed reaches its surface value. This definition of z0 is unambiguous because the surface value of the wind speed is well defined, namely zero. However, the surface temperature is not as well defined. For example, Vining and Blad (1992) showed that radiometers measuring surface temperatures of the same plot at the same time but at different zenith view angles generally read different temperatures. This occurs because more soil is usually visible to nadir-viewing radiometers than to those with more oblique views of the canopy and the soil temperature is frequently much warmer than the vegetation (sometimes by over 10 K). Thus, the concept of the surface temperature, even the radiometric surface temperature, is ambiguous and so is the definition of z0h. Any parameterization of z0h must account for variations in the apparent value of z0h with radiometer view angle (Brutsaert and Sugita, 1996; Crago, 1998; Lhomme et al., 2000; Suleiman and Crago, 2002a).
Lhomme et al. (2000) parameterized z0h in terms of kB–1, defined as ln(z0/z0h), where k is von Karman's constant (k = 0.4). The definition of z0 is unambiguous (e.g., Brutsaert, 1982; Stull, 1988; Chehbouni et al., 2001), and once z0 and B–1 are known, z0h is also known. Lhomme et al. (2000) developed a simple expression for B–1 that fits a large number of simulations under a wide range of conditions using a dual-source model of the land surface. Dual-source models (e.g., Friedl, 1996; Kustas and Norman, 1997; Kustas et al., 1999) consider the soil surface and the foliage to be separate but interacting sources of heat and water vapor, which may have different temperatures. By examining the simulations, Lhomme et al. (2000) determined that LAI and the radiometer view angle were the most important variables affecting B–1. Therefore, they proposed:
 | [7] |
The coefficients a0...a6 in Eq. [7] vary with radiometer view angle (Table 1). In Lhomme et al.'s (2000) model, the zero plane displacement height (d0) and the roughness length for momentum (z0) can be determined as follows (Chehbouni et al., 2001):
 | [8] |
where X = cdLAI,
and
 | [9] |
where cd is the mean drag coefficient within the canopy (cd = 0.2), z0s is the roughness length of the substrate taken to be 0.01 m for bare soil, and h is plant canopy height (m).
Other parameterizations for kB–1 are available that are more firmly based on theory and may give better results overall than Eq. [7], [8], and [9] (e.g., Suleiman and Crago, 2002a; Zibognon et al., 2002; Massman, 1999). However, these models are somewhat more complicated and require more detailed input data. Equations [7], [8], and [9] require only canopy height and LAI and serve to remove the influence of radiometer view angle and anisothermal canopies from the determination of T.
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MATERIALS AND METHODS
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The Data
Data from the SGP-97 experiment and the CASES-97 field campaign were used in this study.
Southern Great Plains Experiment of 1997
During 18 June to 17 July 1997, the SGP-97 experiment was conducted over an area of about 10000 km2 (Jiang and Islam, 2001) centered in Oklahoma. Six eddy covariance (EC) stations and four energy balance Bowen ratio (EBBR) stations were deployed at the three main study areas of SGP-97 to measure the energy budget at the earth's surface. These sites were located at the Department of Energy's Atmosphere and Radiation Measurement Cloud and Radiation Test-Bed (ARM-CART) Central Facility, the USDA's Grazinglands Research Laboratory in El Reno, and within the Little Washita watershed region (Suleiman and Crago, 2002b).
For this work, data were used from the El Reno facility in the central part of Oklahoma (35°29' N, 98°6' W) from a uniform grassland/rangeland site, ER01. One hundred forty-four half-hourly data points were collected on eight different days in 1997 and provided by W. Kustas (personal communication, 2001). Each data point had radiometric surface temperature measured with an Everest infrared radiometer (model 4000) with a 60° field of view. The instrument was located at a height of 1.7 m with a 0° zenith view angle. All of these data were collected between 0800 and 1700 h local time when net radiation was positive. The LAI of this grassland site was 4.0, and the canopy height, h, was 0.6 m. Additional data included net radiation (REBS Q*6), surface sensible and latent heat fluxes, and u* through eddy correlation with a CSI 3-D sonic anemometer (CSAT3) and krypton hygrometer (KH20) at a height of 2 m. Air temperature and humidity at 2 m were measured with a Vaisala HMP45C temperature and humidity probe. Wind speed at 2 m above the ground was measured with an R.M. Young three-cup photo-chop anemometer. Details of the experiment and the site are available at the SGP-97 homepage at http://daac.gsfc.nasa.gov/CAMPAIGN_DOCS/SGP97/sgp97.html (verified 21 Dec. 2003).
Cooperative Atmosphere–Surface Exchange Study of 1997
This campaign was performed in the Walnut River watershed north of Winfield, KS. Its goal was to observe linkages between the diurnal cycle of the atmospheric boundary layer and soil moisture availability. In this study, data were used from a grassland site at 37°44' N, 97°11' W (for a description of the site and methods, see http://www.joss.ucar.edu/data/cases_97/docs/qualls_readme; verified 21 Dec. 2003). The site was in a rectangular field, with 400-m fetches to the north and south and 200 m to the east and west. Winds were generally from the north to northwest or from the southwest to the southeast, giving a typical fetch of 400 m. Trees about 6 to 8 m tall formed the borders of the field. Eddy correlation measurements of sensible heat fluxes were made with a Campbell Scientific Instruments (CSI) 1-D sonic anemometer at a height of 2.56 m and a sampling rate of 10 Hz. Net radiation was measured with a Radiation and Energy Balance Systems (REBS) Q*7.1 net radiometer. Air temperature and humidity were measured at a height of 2 m using a shielded and aspirated REBS THP. Radiometric surface temperature was measured with an Everest Interscience 4000.4 GL, with a 15° field of view mounted at a height of 1.66 m. An emissivity of 0.97 was assumed. Ground heat flux was measured with a REBS heat flow transducer (HFT 3.1) at a depth of 8 cm.
Ten-minute averages of all data were recorded. Plant canopy height was recorded several times during the measurement period (6 April to 24 May 1997). Leaf area index was 0.5 on 6 April and 1.8 on 24 May 1997 (R. Qualls, personal communication, 2001). These LAI values were not measurements but a rough estimate. An interpolation formula was developed to interpolate between these dates, namely, LAI = 2.92 + 0.81 x ln(h).
Analysis Procedure
At both experiments, the 0.5-h (at SGP-97) and 10-min (at CASES-97) data were averaged over 1 h. A moving average was used, with averaging periods starting every 0.5 h at SGP-97 and every 10 min at CASES-97. No average was calculated if any data were missing. Depending on missing data, a given 0.5-h measurement at SGP-97 or 10-min measurement at CASES-97 might appear in more than 1 h.
The scalar roughness length z0h was calculated using the parameterization of Lhomme et al. (2000). This was used to solve Eq. [2] for Ts using H = Rn so that the resulting Ts was Tmax. This Tmax was used with radiometric Ts and measured Ta to calculate T from Eq. [3]. Evapotranspiration was calculated from Eq. [5]. To obtain daytime average evapotranspiration, EF was calculated from Eq. [6] using a single hourly estimate of T taken at 1145 and 1150 h local time at SGP-97 and CASES-97, respectively. Then cumulative daytime evapotranspiration was found by multiplying this single value of EF by the cumulative Rn between 0800 and 1700 h local time for SGP-97 and for the entire measurement period having net radiation greater than 0 at CASES-97; this time started between 530 and 810 h local time and lasted 6 to 12 hours. This was done for all days having continuous data during this time window.
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RESULTS
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Hourly Evapotranspiration
Eddy correlation evapotranspiration measurements compared well to those estimated with Eq. [2] using the Lhomme et al. (2000) parameterization for SGP-97 (Fig. 2a)
and for CASES-97 (Fig. 2b). A linear regression with zero intercept was developed between measured and estimated hourly evapotranspiration for both experiments. The slope and coefficient of determination, R2, for this regression were 1.01 and 0.79 for SGP-97 (Fig. 2a) and 1.37 and 0.94 for CASES-97 (Fig. 2b), respectively. The high slope of the regression line for CASES-97 may have resulted from underestimation of LAI. Higher R2 for CASES-97 than for SGP-97 may reflect more precise measurements or more nearly ideal conditions at CASES-97. Measured E ranged from about 200 to 1200 W m–2 for SGP-97 and from 300 to 1200 W m–2 for CASES-97. The root mean square difference (RMSD) between estimated and measured E was 50 W m–2 for SGP-97 and 38 W m–2 for CASES-97. Lower RMSD indicated better performance in estimating E at CASES-97 than at SGP-97. The results suggest that good estimates of E can be obtained for dense (SGP-97) or relatively sparse (CASES-97) grassland.
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Fig. 2. Measured (Em) and estimated (Ee) hourly evapotranspiration for (a) 1997 Southern Great Plains (SGP-97) experiment and (b) 1997 Cooperative Atmosphere–Surface Exchange Study (CASES-97).
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Daytime Total Evapotranspiration
The eddy correlation measurements of EF for day of year 119 from CASES-97 are shown in Fig. 3
, showing that EF exhibits relatively little variation between midmorning and late afternoon, with an EF of approximately 0.45. It is noticeable that the midday value of EF is less than that at the beginning or the end of the day. However, this difference of EF values should generally not cause a significant discrepancy in the estimates of daytime E since midday energy fluxes are usually greater than those at the beginning and end of the day. Use of the value of EF during the period of greatest flux (i.e., at midday) is thus generally appropriate. In Fig. 4a
(for SGP-97) and 4b (for CASES-97), eddy correlation measurements of cumulative daytime evapotranspiration (Em) (defined in the Analysis Procedure section) are compared with cumulative evapotranspiration found by: (i) multiplying cumulative Rn by the measured midday (i.e., 1145 and 1150 h local time at SGP-97 and CASES-97, respectively) eddy correlation values of EF (Em11.45), (ii) adding up the cumulative evapotranspiration using hourly estimates found using T (Ee), and (iii) multiplying cumulative Rn by the estimated midday EF using T (Ee11.45). For every day, Em was greater than Em11.45, and Ee was greater than Ee11.45 for SGP-97 and CASES-97 because midday EF is an underestimate of EF for the entire day as shown in Fig. 3. A more complicated approach (not assuming EF is constant all day but rather imposing a characteristic shape to the temporal progression of EF) could reduce the gap between Em and Em11.45 and Ee and Ee11.45. Figures 5a
(for SGP-97) and 5b (for CASES-97) compare the daytime total evapotranspiration measured by eddy correlation (Em) with that calculated by multiplying daytime total Rn by estimated midday EF using T (Ee11.45). The slope and R2 for a regression with zero intercept were 0.89 and 0.69 for SGP-97 and 1.07 and 0.90 for CASES-97. These results suggest that assuming EF is constant during the daytime has not resulted in significant errors in the daytime evapotranspiration estimates.
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Fig. 3. Progression of evaporative fraction (EF) for a typical day (day of year 119) from 1997 Cooperative Atmosphere–Surface Exchange Study (CASES-97).
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Fig. 4. Daytime cumulative evapotranspiration (E) at Southern Great Plains in 1997 (SGP-97) found by various methods: (i) measured, Em; (ii) measured net radiation (Rn) multiplied by midday measured evaporative fraction (EF), Em11.45; (iii) estimated from Eq. [2], [3], and [5] for each hour during the daytime, Ee; and (iv) estimated from measured Rn multiplied by midday estimated EF from Eq. [6], Ee11.45 at (a) SGP-97 and (b) Cooperative Atmosphere–Surface Exchange Study of 1997 (CASES-97).
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Fig. 5. Daytime evapotranspiration estimated from measured net radiation (Rn) multiplied by midday estimated evaporative fraction (EF) from Eq. [6] (Ee11.45) compared with measured values (Em) at (a) Southern Great Plains in 1997 (SGP-97) and (b) Cooperative Atmosphere–Surface Exchange Study of 1997 (CASES-97).
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DISCUSSION
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The results presented in Fig. 2 show that, for the sites and conditions studied, radiometric surface temperatures are helpful to give good estimates of E for dense (SGP-97) or relatively sparse (CASES-97) grassland. The results presented in Fig. 5 show that midday estimates of evaporative fraction EF can be extrapolated to give estimated daytime total evapotranspiration. Daily (24-h) evapotranspiration is typically 1.1 to 1.2 times the daytime total evapotranspiration (Brutsaert and Sugita, 1992), so good estimates of weekly to monthly evapotranspiration may be available if estimates of midday evapotranspiration and daily available energy are available.
Differences between calculated and measured E may result from several sources, including: measurement errors in radiometric surface temperature, net radiation, or E; errors in finding the correct value of scalar roughness length or kB–1; errors in other parameters such as LAI and wind speed; and errors associated with the model assumptions. Measurement errors may be large. For example, errors in measurements of E of around 20% using Bowen ratio or eddy correlation instrumentation are commonly cited (e.g., Zhan et al., 1996).
The approach taken here for hourly evapotranspiration involves calculating T and/or EF as intermediate steps. However, if Rn and z0h are known (z0h could be known from Eq. [7], [8], and [9]), evapotranspiration can be calculated directly from Eq. [1] and [2]. This more direct method has the advantage that the influence of the stability (buoyancy) correction function need not be assumed to vary approximately linearly with H, as it was in the development of Fig. 1 and Eq. [3]. The results presented here would be nearly identical if this more direct calculation of evapotranspiration was used. The present approach was taken because it shows that the evaporative fraction EF can be written in terms of surface and air temperatures, without reference to soil moisture. For characterizing the hydrologic budget or the climate of a site, EF serves as a dimensionless evaporation rate that incorporates vegetation, the dryness of the air, and the soil moisture content. That is, sparse vegetation, dry soils, and nearly saturated air all tend to decrease EF while dense vegetation, moist soils, and dry air all tend to increase EF, regardless of the available energy. The daytime value of EF may thus serve as an indicator of the evaporative state of a site, with large EF values indicating healthy, transpiring vegetation and low values indicating moisture stress. In the context of agronomy, decreasing EF over time during the growing season could serve as an indicator of moisture stress. Evapotranspiration could not serve in this role because it depends on the available energy. The CWSI could not be used as easily as T in this role since it generally requires specification of maximum and minimum stomatal resistances.
To illustrate the importance of EF, Qualls et al. (1999) analyzed spatial covariability among EF, soil moisture content, and the diurnal range of radiometric surface temperature at a large grassland area. They concluded that two sites in a region (for example, in a single cell of a numerical weather prediction or general circulation model) are not hydrologically similar unless all three variables are similar at the sites. With the present method, two of these three variables can be expressed in terms of surface temperatures, available from remote sensing, and air temperature, available from a large existing network of observing stations.
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SUMMARY AND CONCLUSIONS
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Equations based on Monin–Obukhov similarity theory and the land surface energy budget have been presented, including a dimensionless temperature variable T and the evaporative fraction, EF, that can be expressed in terms of surface and air temperatures. Hourly evapotranspiration rates at two grassland sites matched well with rates measured by the eddy correlation method. Daytime and even daily evapotranspiration can be estimated from a single midday estimate of evapotranspiration by assuming that EF is constant during the daytime. This is often a reasonable assumption (e.g., Crago, 1996a). At the two sites studied, daytime evapotranspiration matched well with measured amounts. The method presented has the conceptual advantage that it produces EF, which is a key variable to characterize the hydrology of a site, directly in terms of surface and air temperatures. Instantaneous (or hourly) evapotranspiration can be extrapolated to daily evapotranspiration by assuming a constant EF, regardless of the method used to estimate the midday evapotranspiration rate.
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ACKNOWLEDGMENTS
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We thank Dr. Russell Qualls and Dr. William Kustas for providing the data used in this paper from CASES-97 and SGP-97, respectively. This work has been supported in part by NASA grants NAG5-8699 and NAG5-8679.
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ABSTRACT
INTRODUCTION
