Agronomy Journal 92:628-632 (2000)
© 2000 American Society of Agronomy
AGROCLIMATOLOGY
Simplifying Daily Evapotranspiration Estimates over Short Full-Canopy Crops
Manuel Ibáñez and
Francesc Castellví
Dep. Medi Ambient i Ciències del Sòl, Universitat de Lleida, Av. Rovira Roure 177, 25198 Lleida, Spain
m.ibanez{at}macs.udl.es
 |
ABSTRACT
|
|---|
A knowledge of daily evapotranspiration (
E) from surface radiative temperature at a regional scale is of interest in agronomy. The aerodynamic formulation and the radiative Bowen ratio–energy balance method provide good estimates of instantaneous E based on remote-sensed canopy temperatures. Instantaneous latent heat flux estimates for the daytime period can be integrated to obtain a value for daily E when detailed crop knowledge and continuous meteorological measurements are available. We propose a different method for estimating daily evapotranspiration for short, unstressed crops with a leaf area index (LAI) > 3. The method is based on the radiative Bowen ratio–energy balance method and on the similarity between the diurnal course of E and solar irradiance. This regression-based approach uses continuous measurements of air vapor pressure, air temperature, surface radiative temperature, and solar irradiance during daylight hours. Moreover, detailed crop knowledge is not required. The method was tested in a Mediterranean area with semicontinental climatic characteristics on grass (Festuca arundinacea Schreb.), wheat (Triticum aestivum L.), and alfalfa (Medicago sativa L.). Daily E was estimated with an error <15% compared with estimates of E made using a Bowen ratio–energy balance equipment. This new approach is promising for remote sensing applications at a regional scale, although it requires further verification for other climatological conditions.
Abbreviations: E, evapotranspiration • DOY, day of year • LAI, leaf area index • RMSE, root mean square error
|
INTRODUCTION
|
|---|
ESTIMATING E RATES for agricultural crops is important for adequate water management in semiarid areas where irrigation is necessary and water is expensive. Some methods exist for estimating instantaneous and daily latent heat flux based on radiative temperature (Kustas et al., 1989; Beljaars and Holstag, 1991; Lhomme et al., 1994). These methods are particularly useful when their application is feasible at a regional scale because of the availability of satellite sensors (Moran et al., 1989; Caselles et al., 1992; Choudhury, 1994; Kustas et al., 1994).
Most methods for estimating E from radiative temperature use the Monin-Obukhov similarity theory, the limitations of which are discussed by Sun and Mahrt (1995) and Verhoef et al. (1997). This method requires the measurement of wind speed and crop height to give instantaneous estimates of E. The method has errors between 10 and 20% for short full-canopy (LAI > 3) crops.
Another approach to estimate E is based on the use of the radiative Bowen ratio (Ibáñez et al., 1998). The radiative Bowen ratio and the aerodynamic Bowen ratio for well-watered (Crop Water Stress Index < 0.4) crops with LAI > 3 are linearly related. The radiative Bowen ratio–energy balance method provides reasonable estimates of midday E rates and errors of 
10% were obtained. It was initially assumed that parameters a and b, which interrelate the two Bowen ratios, were constant throughout the growing season. However, it was observed that seasonal variations in these parameters constituted a major drawback of this method.
Several models have been developed to determine the total amount of water evaporated from a surface during the course of a day. Jackson et al. (1977) suggested that the daily E rate is a function of the difference between midday radiative surface and air temperatures. Later papers (Seguin and Itier, 1983) questioned the accuracy of this approach. Other researchers have devised more detailed surface energy balance models that are capable of incorporating instantaneous measurements (Soer, 1980; Taconet et al., 1986). However, the amount of information required for these models makes it difficult to implement them in areas where limited meteorological, plant physiological, and soil information is available.
A simple yet accurate way of converting instantaneous E values into daily totals makes use of the similarity between the diurnal course of the latent heat flux and that of other meteorological variables. One approach assumes that E follows the course of solar radiation throughout the daylight period. Jackson et al. (1983) showed for clear-sky days that the ratio between total daily solar irradiance and a single measurement taken at midday could be approximated by a sine function. This relationship gives rise to a method that gives a strong correlation between measured and estimated daily E.
Our objective is to present a new method for estimating daily E for well-watered crops with LAI > 3 using remotely sensed surface temperature and meteorological data. The main water requirements of wheat, alfalfa, maize and other crops that reach full canopy cover occur when LAI > 3. Even in the Mediterranean area, winter wheat usually does not need to be irrigated before LAI > 3 is achieved.
The new method is particularly interesting because E is calculated on the basis of continuous daytime measurements of solar irradiance, radiative surface temperature, air temperature and air vapor pressure without any knowledge of wind speed, which varies substantially at the regional scale. This algorithm is useful for remote sensing applications because daily E values are obtained without detailed information about the crop canopy.
|
Materials and methods
|
|---|
Method
The method described here combines the radiative Bowen ratio–energy balance method proposed for obtaining instantaneous measurements and the similarities between the diurnal courses of E and solar irradiance to estimate daily E. Daily and daylight latent heat fluxes are essentially identical because E during the night is often negligible.
The radiative Bowen ratio–energy balance method described in Ibáñez et al. (1999) can be used to calculate instantaneous latent heat flux, E, by
 | (1) |
where Rn is the net irradiance (W m-2), G is the soil heat flux (W m-2), ßr is the radiative Bowen ratio, and a and b are regression coefficients that depend on crop and weather conditions.
Net irradiance can be estimated by
 | (2) |
where 
is the albedo, Rs is the incident solar irradiance (W m-2), 
is the Stefan-Boltzman constant (W m-2 K-4), 
is the surface emissivity, a is the atmospheric emissivity calculated for clear sky conditions (Brutsaert, 1975), and Ta and Tr are the air and radiative surface temperatures (K), respectively. Several authors have validated this expression using surface measurements; e.g., Jackson et al. (1985) for prairie vegetation crops, Starks (1990) for pastures, and Goodin (1995) for semiarid landscapes.
Soil heat flux can be estimated using its strong correlation with net irradiance for full-canopy cover crops. The ratio between the two instantaneous fluxes is around 0.10 for grass (Allen et al., 1994), 0.10 for alfalfa (Clothier et al., 1986), and 0.07 for wheat (Denmead, 1969). More detailed studies indicate that G/Rn varies, but when the data required to determine G are not available, it is possible to assume the mean values proposed above.
The radiative Bowen ratio, ßr, has been expressed in the form
 | (3) |
where 
is the psychrometric constant (kPa K-1), e is the air vapor pressure (kPa), and es(Tr) is the saturation vapor pressure (kPa) at temperature Tr.
Acceptable instantaneous estimates of E from radiative temperature for well-watered full-canopy covers are obtained when parameters a and b are taken as constants (Ibáñez et al., 1999). However, it must be noted that values for a and b may vary according to the stage of crop development and prevailing weather conditions.
Daily estimations of E are derived from instantaneous measurements on the basis of the similarity between the diurnal course of the latent heat flux and solar irradiance (Jackson et al., 1983). This result can be expressed by
 | (4) |
where subindex d refers to daytime accumulated values of Rs and E. This algorithm gives good results when used to determine daily E from instantaneous values (Zhang and Lemeur, 1995).
Two methods for estimating daytime E are tested in this paper. The first uses Eq. [1] to obtain estimations of instantaneous E. These are converted to daily values by integrating over the daytime hours. Parameters a and b are considered to be constant for each crop throughout the growing season according to Ibáñez et al. (1999). Hereafter, this method is referred to as the seasonal method.
In the second method, Eq. [1] is combined with Eq. [4] to obtain
 | (5) |
By rearranging Eq. [5], it is possible to obtain
 | (6) |
where (1 + a)Ed/Rsd and bEd/Rsd are daily constants. Both of these factors can be determined through least square regression when continuous values of Rn - G, Rs, and ßr are available throughout the daytime period.
Instantaneous Rn - G and ßr measured or estimated from Ta, Tr, and e, together with Rs data measured throughout the daytime hours, are used to compute (1 + a)Ed/Rsd and bEd/Rsd by applying least square regression in Eq. [6]. The two coefficients depend upon three unknowns: a, b, and Ed. The daily E is calculated assuming a given value for parameter a. When the crop is <1 m tall and well-irrigated, a = 0.1 gives good results. This method is useful because it does not require the use of any crop and soil parameters or windspeed data. This approach assumes a and b to be constant on a daily scale (but not necessarily throughout the season) and is referred to as the daily method.
Materials
Measurements were taken in 1994 and 1997 to test the proposed method on grass, wheat, and alfalfa. Experimental sites were located in the Ebro river basin, a Mediterranean area with semicontinental climatic characteristics. Annual precipitation is <350 mm, with minima in January and July. This semiarid area receives water from the Pyrenees, which makes irrigation possible.
Validation was conducted using Bowen ratio equipment (Campbell Scientific, Logan, UT) and a water content reflectometer (CS615, Campbell Scientific) for measuring soil water content. The Bowen ratio equipment used is described in detail by Tanner et al. (1987). Net irradiance was measured with two radiometers (Model Q6, Radiation and Energy Balance Systems, Seattle, WA) both 1 m above the crop. Thermocouples and air intakes to measure the Bowen ratio were supported on two arms. The height of the arms was 1 m for the lower arm and 2 m for the upper one. The soil heat flux was measured with two plates buried in the soil at 10 cm depth; the average temperature of the soil layer above the plates was measured with two soil thermocouples buried at 3 and 6 cm depth each. No corrections were applied for change in soil thermal conductivity. The soil heat flux was then calculated by adding to the average heat flux the energy stored in the soil layer above the plates (Clothier et al., 1986). Surface radiative temperature was measured with an infrared thermometer (Model 4000BL, Everest Interscience, Tucson, AZ) with an accuracy of ±0.5 K and a field of view of 15°. The data obtained by the infrared thermometer were corrected to account for downward longwave radiation and surface emissivity (Badenas and Caselles, 1992). A pyranometer (Model SP1110, SKYE Instruments, Perth, Australia) and a 2-m-high switching anemometer (Model A100R, Vector Instruments, Rhyl, UK) were used. All measurements were collected every second and were averaged for 20- or 30-min periods.
Irrigation frequencies for the three crops were based on allowable root zone available water depletion, which was maintained below 40% throughout the study period. The crop water stress index, monitored throughout the field tests, never exceeded 0.4.
Grass, wheat, and alfalfa were seeded and monitored on plots at three different geographic locations within large irrigated areas of the Ebro valley. Each of the three plots had sandy loam soils.
Overcast days were discarded from this study and daylight data were only considered when solar irradiance was >25 W m-2. Partly cloudy days were determined by fitting the solar irradiance daylight data to a sine function. The days that gave a coefficient of determination <0.9 were discarded.
Grass Data Set
During the summer of 1994, a field experiment was conducted in Zaragoza (northeast Spain, 41°39' N, 0°53' W, 250 m above sea level). Instruments were placed in the center of a 120- by 100-m field with a dense grass canopy. The infrared thermometer was installed 1.5 m above the surface with a 30° zenith view angle. The grass was irrigated using sprinklers. Data from day of year (DOY) 190 to 209 were used. During this period, grass height increased from 0.06 to 0.2 m.
Wheat Data Set
At a wheat plot in Almacelles (northeast Spain, 41°42' N, 0°26' E, 296 m above sea level), field measurements were taken during the spring of 1997. The fetch for the prevailing wind direction was 150 m. An infrared thermometer was installed 4 m above the ground with a 30° zenith view angle. The wheat was seeded in November and was first irrigated by flooding on DOY 90. Complete canopy cover was considered after this date when LAI > 3. On DOY 114 a hailstorm razed the plot. Data from DOY 93 to 114 were used. The wheat height increased from 0.30 to 0.85 m.
Alfalfa Data Set
During the summer of 1997, data were collected from Altorricon (northeast Spain, 41°50' N, 4°03' E, 220 m above sea level). The equipment was set up in a large field of alfalfa with a minimum fetch of 300 m. The infrared thermometer was installed 3.5 m above the ground with a 30° zenith view angle. Data from DOY 195 to DOY 228 were used. During this period, alfalfa height increased from 0.20 to 0.90 m. The crop was irrigated by flooding.
|
Results and discussion
|
|---|
Values of a and b obtained from daily least square regressions of measured Bowen ratio versus calculated radiative Bowen ratio are plotted in Fig. 1
. The coefficient of determination was always >0.90 (13 d for grass, 16 d for wheat, and 25 d for alfalfa). The mean values given in Table 1
are similar to those obtained by Ibáñez et al. (1999) for a shorter time range around midday. There is appreciable scatter around these mean values, as shown in Figure 1. A relationship between the parameters and DOY was expected due to variations in canopy phenology. It was thought that an increase in leaf area index would result in a change in the parameters, but this was only observed on grass. Although parameters a and b vary, taking them as constants throughout the growing season provides an operative approximation for estimating instantaneous latent heat flux. The standard deviation of daily computed values presented in Table 1 indicates the variability of these two parameters. In all three data sets, the standard deviation of parameter a is similar; however, there are major deviations for b between crops. In each case, b values are about 25% of the mean.
View larger version (20K):
[in this window]
[in a new window]
|
Fig. 1 Values for parameter a and b plotted against the day of year (DOY) for (a) and (b) grass (13 data points), (c) and (d) wheat (16 data points), and (e) and (f) alfalfa (25 data points)
|
|
Figure 2
shows the qualitative relationship between a and b and the meteorological conditions. For wheat, it appears that increases in the value of b relate to corresponding decreases in the value of a (Fig. 2a). Figures 2b, 2c, and 2d show parameter b plotted against daytime mean solar irradiance, vapor pressure deficit, and wind speed. No reliable conclusion can be proposed from these figures, because too few daily data are available for each crop.
View larger version (20K):
[in this window]
[in a new window]
|
Fig. 2 Parameter b obtained from the wheat data set plotted against (a) parameter a, (b) mean solar irradiance (Rs), (c) mean daytime vapor pressure deficit (VPD), and (d) mean daytime wind speed (U)
|
|
Our main objective was to test the daily method. In Table 2
, the root mean square error (RMSE) of daily E estimated from the daily method compared with the Bowen ratio–energy balance method estimates using different values of a is shown. Lower RMSE values (Table 2) were obtained when daily latent heat fluxes were calculated using values for a that were closest to the mean computed value (Table 1). Table 3
presents the percentage of error for each case. Overall errors were relatively small when a = 0.1 was used, so we used this value for applications of the daily method on short crops.
View this table:
[in this window]
[in a new window]
|
Table 2 Root mean square error of daily E estimations from the daily method (RMSED) with different values for parameter a versus daily Bowen ratio–energy balance estimated latent heat fluxes for the three crops
|
|
View this table:
[in this window]
[in a new window]
|
Table 3 Percentage of error in daily E calculations (RMSED/EBR) from daily method with different values for parameter a for the three data sets
|
|
The performance of the daily method compared with the Bowen ratio–energy balance method estimates of daily E is shown in Table 3. Two conclusions may be drawn:- When the method is applied for a known crop, the value of a can be estimated and daily values for E can be calculated with a margin of error of 10%. Using a = 0 for alfalfa, a = 0.1 for grass, and a = 0.2 for wheat, the daily method gives estimates with 7, 6, and 10% errors, respectively.
- When the crop is not known, a value of a = 0.1 permits daily E estimates with an error <15% compared with the estimates made using Bowen ratio–energy balance method.
These results suggest that reasonable estimates of daily E can be made using a value of a = 0.1 and continuous measurements of Ta, Tr, e, and Rs, even when the phenological stage and the weather conditions are not known.
The seasonal method is applied with the mean values for parameters a and b given in Table 1. The seasonal method and the daily method are compared in Table 4
. The daily method gave better estimates of latent heat flux than the seasonal method for the three crops. The mean values of daytime E estimated with the three methods are shown for each crop in Table 5
. Both the daily and seasonal methods give mean values similar to the daily levels of E estimated by the Bowen ratio–energy balance method.
The stated accuracy of ±0.5 K is difficult to achieve with current radiometers. Because of this, the sensitivity of the method to measurement errors of the radiative temperature has been studied. The ßr estimation sensitivity is
 | (7) |
where des(Tr)/dTr is the slope of the saturation vapor pressure curve at Tr.
When the mean values and estimated errors Ta = 297 K, Tr = 305 K, e = 2.0 kPa, and 
Tr = ±2 K are considered, the results are ßr = 0.20 and ßr = ±0.01. This small error in the determination of the radiative Bowen ratio leads to an error of 5% in the estimation of E when the daily method is applied.
|
Conclusions
|
|---|
The values for parameters a and b expressed in the relationship between radiative and aerodynamic Bowen ratio were not constant over the measurement period. Some of the observed variations around the mean value could be attributed to meteorological and phenological differences.
The method proposed for calculating daytime E over well-watered, short full-cover crops, based on the radiative Bowen ratio–energy balance method and the similarity between the diurnal course of E and solar radiation, gives an acceptable level of relative error for partly cloudy days. Root mean square errors of <15% of the average E estimated with Bowen ratio equipment were obtained when the crop was unknown. The margin of error was reduced to 10% when the crop was known and its characteristic value for parameter a was applied. Integrations of daytime instantaneous values of E, taking parameters a and b as seasonal constants, gave larger errors. To apply the seasonal method, the crop and its phenological stage should be well known, and parameters a and b relating to these conditions need to have been previously determined.
The daily method discussed here is particularly interesting because E can be adequately calculated on the basis of continuous daytime measurements of solar irradiance, radiative surface temperature, air temperature, and air vapor pressure. These meteorological variables are usually known at the regional scale when automatic meteorological station and satellite image data are available. This algorithm is useful for remote sensing applications because E values are obtained without detailed information about the crop canopy. In general, the results obtained by applying this methodology are promising, although the method still requires further verification for a wider range of crops and climatological conditions.
|
ACKNOWLEDGMENTS
|
|---|
This study was supported by the Ministerio de Educación under research project HID96-1295-C04-03 and by the Centre de Tecnologia Forestal de Catalunya under research project Interreg II. The authors acknowledge the Servicio de Investigaciones Agrarias (DGA, Zaragoza) for the use of the experimental site and the Confederación Hidrográfica del Ebro for the use of the Centro Agronómico La Melusa. We thank Ma. Rosa Teira and Malcom Hayes for their work on the revision of the manuscript.
Received for publication March 4, 1999.
|
REFERENCES
|
|---|
- Allen R.G., Smith M., Pereira L.S., Perrier A. An update for the calculation of reference evapotranspiration. ICID Bull. 1994;43:35-91.
- Badenas C., Caselles V. A simple technique for estimating surface temperature by means of thermal infrared radiometer. Int. J. Remote Sens. 1992;13:2951-2956.
- Beljaars A.C.M., Holstag A.A.M. Flux parameterization over land surfaces for atmospheric models. J. Appl. Meteorol. 1991;30:327-341.
- Brutsaert W. On a derivable formula for long-wave radiation from clear skies. Water Resour. Res. 1975;11:742-744.
- Caselles V., Delegido J., Sobrino J.A., Hurtado E. Evaluation of the maximum evapotranspiration over the La Mancha region, Spain, using NOAA AVHRR data. Int. J. Remote Sens. 1992;13:939-946.
- Choudhury B.J. Synergism of multispectral satellite observations for estimating regional land surface evaporation. Remote Sens. Environ. 1994;49:264-274.
- Clothier B.E., Clawson K.L., Pinter P.J., Moran M.S., Reginato R.J., Jackson R.D. Estimation of soil heat flux from net radiation during the growth of alfalfa. Agric. For. Meteorol. 1986;31:319-329.
- Denmead O.T. Comparative micrometeorology of a wheat field and a forest of Pinus Radiata. Agric. Meteorol. 1969;6:357-371.
- Goodin D.G. Evaluation of a combined modelling–remote sensing method for estimating net radiation in a wetland: A case study in the Nebraska Sand Hills, U.S.A. Int. J. Remote Sens. 1995;16:1481-1494.
- Ibáñez M., Pérez P.J., Caselles V., Castellví F. A simple method for estimating the latent heat flux over grass from radiative Bowen ratio. J. Appl. Meteorol. 1998;37:386-392.
- Ibáñez M., Pérez P.J., Rosell J.I., Castellví F. Estimation of the latent heat flux over full canopy covers from radiative temperature. J. Appl. Meteorol. 1999;38:423-431.
- Jackson R.D., Reginato R.J., Idso S.B. Wheat canopy temperature: A practical tool for evaluating water requirements. Water Resour. Manage. 1977;13:651-656.
- Jackson R.D., Hatfield J.L., Reginato R.J., Idso S.B., Pinter P.J. Estimation of daily evapotranspiration from one-time day measurements. Agric. Water Manage. 1983;7:351-362.
- Jackson R.D., Pinter P.J., Reginato R.J. Net radiation calculated from remote multispectral and ground station meteorological data. Agric. For. Meteorol. 1985;35:153-164.
- Kustas W.P., Choudhury B.J., Moran M.S., Reginato R.J., Jackson R.D., Gay L.W., Weaver H.L. Determination of sensible heat flux over sparse canopy using thermal infrared data. Agric. For. Meteorol. 1989;44:197-216.
- Kustas W.P., Perry E.M., Doraiswamy P.C., Moran M.S. Using satellite remote sensing to extrapolate evapotranspiration estimates in time and space over a semiarid rangeland basin. Remote Sens. Environ. 1994;49:275-286.
- Lhomme J.P., Monteny B., Amadou M. Estimating sensible heat flux from radiometric temperature over sparse millet. Agric. For. Meteorol. 1994;68:77-91.
- Moran M.S., Jackson R., Raymond L.H., Gay L.W., Slater P.N. Mapping surface energy balance components by combining Landsat thematic mapper and ground-based meteorological data. Remote Sens. Environ. 1989;30:77-87.
- Seguin B., Itier B. Using midday surface temperature to estimate daily evaporation from satellite thermal IR data. Int. J. Remote Sens. 1983;4:371-383.
- Soer G.J.R. Estimation of regional evapotranspiration and soil moisture conditions using remotely sensed crop surface temperatures. Remote Sens. Environ. 1980;9:27-45.
- Starks P.J. Measured and modeled radiation fluxes from prairie vegetation at the FIFE study site. Lincoln: Ph.D. diss. Univ. of Nebraska, 1990.
- Sun Y., Mahrt L. Relationship of surface heat flux to microscale temperature fluctuations. Boundary-Layer Meteorol. 1995;76:292-301.
- Taconet O., Carlson T.N., Bernard R., Vidal-Madjar D. Evaluation of a surface/vegetation parameterization using satellite measurements of surface temperature. J. Clim. Appl. Meteorol. 1986;25:1752-1767.
- Tanner B.D., Greene J.P., Bingham G.E. A Bowen-ratio design for long term measurements. St. Joseph, MI: ASAE, 1987 ASAE Paper No. 87-2503..
- Verhoef A., De Bruin H.A.R., van den Hurk B.J.J.M. Some practical notes on the parameter kB-1 for sparse vegetation. J. Appl. Meteorol. 1997;26:560-572.
- Zhang L., Lemeur R. Evaluation of daily evapotranspiration estimates from instantaneous measurements. Agric. For. Meteorol. 1995;74:139-154.
TOP
ABSTRACT
INTRODUCTION
