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A new look at the simplified method for remote sensing of daily evapotranspiration
ELSEVIER
A New Look at the Simplified Method for Remote Sensing of Daily Evapotranspiration Toby N. Carlson,*William J. Capehart,* and Robert R. Gillies* A modification of the so-called "Simplified Method" used to obtain the integrated daily evapotranspiration from surface radiant temperature over variable vegetation cover is proposed. Mathematically, the simplified equation takes the form Rn24 - LEe4 = B(T013- Tal3)", where Rn24 and LE24 are, respectively, the integrated net radiation and evapotranspiration over a 24-h period and Toz3 and Ta13 are, respectively, the surface radiant and the 50-m air temperatures at 1300 local time. B and n are pseudo constants given as functions of the normalized difference vegetation index (ND VI), expressed as a scaled index N*. Both N* and Ta13 a r e obtained with the aid of remotely determined measurements, which are viewed on scatterplots of To13 versus NDVI.
1300 h local time, T013), a corresponding air temperature (usually measured at screen height, T~13), and the net radiation expressed as an integrated value over a 24-h period (Rn24). An equation of the following form has been used by Jackson et al. (1977), Sequin and Itier (1983), and Nieuenhuis et al. (1985): Rn24 - LE24 = B(To,3 - T~13)n,
where B and n are parameters to be determined and RN24 and ET24 are henceforth expressed in units of cm per day. Theoretical justification for Eq. (1) can be made with reference to the surface energy balance integrated over a 24-h day. Neglecting the integrated ground heat flux, the surface energy balance can be written as Rn - LE = H - pCp(To - Ta)
INTRODUCTION The so-called Simplified Method for determining the accumulated daily evapotranspiration from remote surface radiant temperature measurements was first proposed by Jackson et al. (1977) and later taken up by other investigators, such as Itier and Riou (1982), Seguin and Itier (1983), Nieuwenhuis et al. (1985), Carlson and Buffum (1989), Lagouarde (1991), Lagouarde and McAneney (1992), and Sandholt and Andersen (1993). The idea behind the simplified method is that the net integrated daily evapotranspiration at the surface (ETz4) can be estimated from a very few easily obtainable measurements, these being the surface radiant temperature measured near the time of local maximum (about * Department of Meteorology, Penn State University, University Park *Earth System Science Center, Penn State University, University Park Address correspondence to Toby N. Carlson, Dep. of Meteorology, Penn State Univ., University Park, PA 16802. Received 28 December 1994; revised 5 June 1995. REMOTE SENS. ENVIRON. 54:161-167 (1995) ©Elsevier Science Inc., 1995 655 Avenue of the Americas, New York, NY 10010
(la)
(lb)
RH
where H, LE, and Rn are the sensible and latent heat fluxes and the net radiant flux and R,, is an atmospheric resistance to the flux of sensible heat. Integration of Eq. (lb) over a 24-h period yields an expression in which the left-hand side of Eq. (lb) is identical to that in Eq. (la). However, the right-hand side of this equation does not lend itself to such a facile integration; moreover, R, is a highly ambiguous parameter to define over a mixture of vegetated and bare soil surfaces (Carlson et al., 1995b). It is therefore more appropriate to express the integrated form of Eq. (lb) as the simplified Eq. (la), where B can be thought of as an average bulk conductance for the daily integrated sensible heat flux and a nonunity value of n as a correction for nonneutral static stability. Equation (la) is of limited utility in areas where in situ measurements are lacking. Perceiving this limitation, Carlson and Buffum (1989) suggested that air temperatures at 50 m be used instead of those at screen level, because the former is relatively independent of 0034-4257 / 95 / $9.50 SSDI 0034-4257(95)00139-R
162 Carlson et al.
local surface conditions and can be approximated by regional-scale averages of surface air temperatures, such as reported on weather maps, or from the output of regional-scale atmospheric prediction models. Henceforth, T,,~3 will refer to the 50-m air temperature. It is remarkable, however, that such a simplified formula as Eq. (la) is able to successfidly encapsulate the complex physics of evapotranspiration over diverse surfaces with variable vegetation cover. Yet it has been widely applied and is generally thought to be accurate to within about 0.1 c m / d a y (Lagouarde and McAneney, 1992). Nevertheless, a problem exists in the use of this equation, which is that the parameters B and n are not constant. Although n is generally thought to have a value close to 1.0 (Seguin and Itier, 1983), the conductance is highly sensitive to wind speed, roughness, and vegetation amount (Carlson and Buffum; 1989; Lagouarde and McAneney, 1992). Indeed, values of B reported in the literature show considerable variation. Seguin and Itier (1983), for example, reported values of B = 0.025 over a homogeneous grassland in southeastern France, whereas Jackson et al. (1977) found values of B = 0.064 for a large irrigated field of wheat in Arizona. Seguin (private communication) has suggested that B tends to vary from about 0.01 to 0.06, with values increasing with increasing vegetation cover. In contrast, Carlson and Buffum found that both B and n varied by less than about 25% over the normal range of wind speed and surface roughness length for a given vegetation amount. Friedl and Davis (1994), Gillies and Carlson (1995), and Carlson et al. (1995a) show that the surface energy fluxes depend strongly on both surface wetness and fractional vegetation cover (Fr). The method used by Carlson et al. (1995) for obtaining surface evapotranspiration, surface soil moisture availability (ref. Fig. lb) and Fr is called the "'triangle method", so-called because the pattern formed by the envelope of pixels on a scatterplot of surface radiant temperature (To) versus normalized difference vegetation index (NDVI) resembles a triangle (Price, 1990; Carlson et al., 1995a) (ref. Figs• la and lb). (Surface moisture availability, shown in Fig. lb, is here defined as the ratio of surface soil water content to that at field capacity, which is 0.34 by volume for this case.) Simulations with the more recent version of the model discussed by Carlson and Buffum (1989), referred to here as a soil-vegetation-atmosphere transfer (SVAT) model (Gillies and Carlson, 1995), also yield similar triangular patterns for the isopleths of moisture availability when plotted as a function of surface radiant temperature and Fr (Fig. lb). NDVI is customarily defined as NDVI
= ((a,.~ 6 t n i r +- a,~)' avis)
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Figure la. Scatterplot of surf:ace radiant temperature (°C) versus NDVI, adjusted to at-surface values as determined from pixel values measured by an NS001 radiometer (5 m resolution) aboard a C-130 aircraft flying over the Konza Prairie during FIFE on 15 August 1987. The vertical dashed line denotes the screen-level air temperature at flight time and the horizontal lines denote the values of NDVI for N*= 1 and N*= 0.
(just below 0.7 pro) and in the near infrared part of the visible spectrum (just above 0.7 tim). It is generally accepted that NDVI, Fr, and vegetation amount are related and, indeed, various investigators describe monotonic relationships between NDVI and leaf area index (Baret and Guyot, 1991; Price, 1992, Choudhury et al., 1994). As in Choudhury et al., (1994), we (Gillies and Carlson, 1995) define a scaled NDVI (N*), which is defined as N* = (NDVI - NDVI0) (NDVIs - NDVI0),
(3)
where NDVL is the value of NDVI at 100% vegetation cover (N*= 1.0) and NDVI0 is that value for bare soil (N*=0). Corrected for atmospheric attenuation to atsurface values, NDVI tends to vary from about zero for bare soil to about 0.75 at full vegetation cover. The relationship Fr=(U*) 2
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has been found to fit virtually all the images we have analyzed; it is identical to one suggested by Choudhury et al. (1994)• The index N* has the advantage of being relatively insensitive to viewing angle, sensor drift, and uncertainties in atmospheric corrections. Figure la shows that the value of Fr = 0 (N*= 0) corresponds closely to an NDVI of zero; negative values in this scatterplot were
Simplified Method for Remote Sensing of Evapotranspiration
163
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found by inspection of the original image to be representative of artificial surfaces such as roads, which form their own envelope of points below the base of the main triangle. Recent simulations with a later version of the SVAT model used by Carlson and Buffum (1989) further indicate that B may depend much m o r e sensitively on the amount of vegetation than on wind speed or roughness. As vegetation amount increases from a small fraction to dense cover, the difference between the air and surface radiant temperatures trends to diminish, regardless of the soil surface wetness, all other factors being equal. This is illustrated by the scatterplot in Figure la, which shows surface radiant temperature (To) plotted versus normalized difference vegetation index (NDVI). However, our simulations also show a large increase in LE24 from the right-hand (warm) side to the left-hand (cold) side of the pixel envelope, with isopleths of LE24 oriented more or less vertically, similar to the surface moisture availability isopleths shown in Figure lb. The purpose of this article is 1) to present simple relationships between the parameters B and n and N* and 2) to indicate how the surface air t e m p e r a t u r e (T,13) can be obtained solely from the scatterplots of surface radiant t e m p e r a t u r e and NDVI. RESULTS O F SIMULATIONS Eleven sets of simulations were run. These were made using the initial atmospheric and surface conditions corresponding to nine AVHRR and two aircraft (NS001) images. Of the former, five satellite images pertain to
Figure 2. Plot of (To - Ta]3) at 1300 h versus Rn24- LE24 for a fractional vegetation cover, Fr = 0.25. The air temperature is 50 m above the ground level. The solid line represents the linear best fit (Regr.) through the points (ref. Table 1) and the dashed lines represent the root mean square deviation (RMSD) from the regression line. Data were generated from 11 simulations for five cases over Pennsylvania (PA; open circles), four over Newcastle Upon Tyne (UK; squares) and two in FIFE (triangles).
the Susquehanna Watershed in Pennsylvania and four images to the area around Newcastle upon Tyne, England (Gillies and Carlson, 1995). Two images were made by aircraft during intensive field operations in FIFE. As a byproduct of these simulations, series of statistics were generated which were used to obtain the variations in B and n with Fr and therefore with N* using the transformation given in Eq. (3). For each of these 11 cases, the quantities LE24, Rn24, T 0 1 3 (at 1300 local time), and Ta]3 were generated. In each of these simulations Fr was incremented over five values (in steps of 0.25) and surface moisture availability over six values (in steps of 0.2) for a total of 66 points in each of the graphs shown in Figures 2 and 3. Initial conditions for each of these 11 series of simulations varied over a wide range of values; in particular, surface roughness and geostrophic wind speed varied between 2 cm and 30 cm and between 1 m s-1 and 8.5 m s-1, respectively. Although the statistics generated for this article are not site-specific and do not depend on the actual image data, each of the simulations were made to fit the surface moisture availability isopleths to seatterplots for the images. As the initial conditions used for the SVAT model were representative of a realistic range of atmospheric and surface conditions, the scatter of points shown in Figures 2 and 3 can be taken to represent the spurious effects of differing wind speed and surface roughness on B and n. The results are encapsulated in Figure 3. Overall,
164
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the standard error of the estimate (STD ERR), shown in Table 1, is about 0.14 era, while the parameters B and n exhibit a systematic variation with Fr. This is shown in Figure 4. Relationships b e t w e e n Fr and the parameters B and n, were found to be Table 1. Fractional vegetation cover, R'2, Standard Error, and the Parameters B (intercept) and n (slope) for Regression lines in Figure 3 Fr
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Simplified Method for Remote Sensing of Evapotranspiration
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over their full ranges of 0 to 1, B increases from about 0.01 to 0.06, and n decreases from about 1.05 to 0.7.
VALIDATION Before presenting the results, it is essential to make a statement concerning the validity of the SVAT model, which is used to derive the relationship b e t w e e n the parameters in Eq. (1) and N*. The triangle method has recently been subjected to validation using groundbased measurements of surface evapotranspiration (Gillies et al., 1995). These data were obtained by an NS001 radiometer mounted aboard a C-130 aircraft during three days in FIFE (Hall et al., 1992) and two days
Figure 5. The parameters B and n as a function of N*. Dashed lines have the same significance as in Figure 4.
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Figure 6. Simulated versus measured values of Rn24- LE24 (cm) for eight surface measurement stations on 15 August 1987 in FIFE. One outlying data point was discarded.
during Monsoon-90 (Walnut Gulch, Arizona) (Kustas and Goodrich, 1994). Average root-mean square differenees b e t w e e n measured and simulated values of evapotranspiration for these cases was 37 W m -2, or about 10% of the flux values; R 2 for the five eases was 0.95 (Gillies et al., 1995). The relationships expressed in Eqs. (5) and (6) strictly pertain to a surface radiant temperature at 1300 h local time, but are generally valid in a window between about 1200 h and 1400 h when temperature varies slowly with time. Given this time window, however, only one thermal image could be found which was appropriate for verifying these relationships, that for FIFE on 15 August, 1987. The scatterplot for this case is shown in Figure la, and the evapotranspiration values derived thereof were compared with surface measurements. Figure 6 shows good agreement b e t w e e n measured and simulated values of Rn24-LE24, with a standard error of 0.038 cm. A representative air temperature can also be obtained from the scatterplot. Screen-level air temperature tends to be slightly below the surface radiant temperature of a densely vegetated surface. Accordingly, we have found that a reasonable estimate of the screen level air temperature to be that at the apex of the pixel envelope, which is about 3 3 ° C in Figure la. As the 50-m temperature is likely to be slightly cooler than that at screen level, w e adopted the convention in producing Figure 6 that T013 was I ° C less than that at the top of the NDVI envelope. CONCLUSIONS Simulations with a soil / vegetation / atmosphere transfer model were made for 11 sets of initial conditions repre-
166 Carlson et al.
senting a range of surface roughness and wind speed. This was done to derive relationships between NDVI and the parameters in Eq. (1). Results show that B and n vary systematically with fractional vegetation cover and NDVI, the latter expressed as a scaled vegetation index, N*. Although B and n also vary with wind speed and surface roughness, the present study shows that these parameters depend much more sensitively on vegetation cover, at least within reasonable limits. We do recommend, however, that some adjustment of these two parameters be made to account for differences in wind speed and roughness, as indicated in the results of Carlson and Buffum (1989). A powerful advantage of the proposed method is that the one side of Eq. (1) is obtainable from a knowledge of surface radiant temperature and NDVI with an implied standard error of less than 0.15 cm. The dependence of B on Fr may partially explain the wide range of its values in the literature, such as the difference between the studies of Jackson et al. (1977) and Seguin and Itier (1983). The present study indicates that larger variations in B with vegetation amount than those reported by Carlson and Buffum (1989), with values ranging from about 0.01 for bare soil and 0.06 for a fldl vegetation cover. The value of n, though close to 1.0, also shows systematic differences with changing Fr. Finally, it hardly needs to be pointed out that knowledge of one side of Eq. (1) is not sufficient to obtain the evapotranspiration, as the integrated net radiation must still be determined. An estimate of net radiation can be made with reasonable accuracy for clear sky conditions using the formulae recommended by Shaw (1983) and Shuttleworth (1993). Although remote measurements of radiant surface temperature obtained via satellite are feasible only during clear sky conditions, it should be possible to calculate ET24 without great loss of accuracy over a season, given a measurement of Rn24, by determining the so-called evaporation fraction (ET24 / Rn24) from satellite images for a succession of clear days and interpolating the ratios for cloudy ones. The authors" would like to thank Bernard Seguin for his advice and the U.S. Department of Agriculture, Agriculture Research Service, Beltsville, Maryland, especially Tom Schmugge, for their financial assistance of this research through a cooperative research agreement 58-1270-3030. This project is also motivated by our participation in The Global Water Cycle: Extension Across the Earth Sciences EOS Project within the Earth Science System (;enter (ESSC) under Grant No. NAGW~-2686. We would also like to thank Jie Cui for the use of her figures (la and lb). REFERENCES
Baret, F., and Guyot, G. (1991), Potentials and limits of vegetation studies for LAI and APAR assessment, Remote Sens. Environ. 35:161-174.
Carlson, T. N., and Buffum, M. J. (1989), On estimating total daily evapotranspiration from remote surface temperature measurements, Rein. Sens. Environ. 29:197-207. Carlson, T. N., Gillies, R. R., and Schmugge, T. J. (1995a), An interpretation of NDVI and radiant surface temperature as measures of surface soil water content and fractional vegetation cover, Agric. For. Meteorol., forthcoming. Carlson, T. N., Taconet, O., Vidal, A., Gillies, R. R., Oliosn, A., and Humes, K. (1995b), An overview of the Workshop on Thermal Remote Sensing held at La Lande des Maures, France, September 20-24, 1993, Rein. Sens. Rev., pp. 147158. Choudhury, B. J., Ahmed, N. U., Idso, S. B., Reginato, R. J., and Daughtry, C. S. T. (1994), Relations between evaporation coefficients and vegetation indices studied by model simulations, Remote Sens. Environ. 50:1-17. Friedl, M. A., and Davis, F. W. (1994), Sources of variation in radiometric surface temperature over a Tallgrass prairie, Rem. Sens. Environ. 48:1-17. Gillies, R. R., and Carlson, T. N. (1995), Thermal remote sensing of surface soil water content with partial vegetation cover for incorporation into mesoscale prediction models, J. Appl. Meteorol. 34:745-756. Gillies, R. R., Cui, J., Carlson, T. N., Kustas, W. P., and Humes, K. S. (1995), Verification of a method for obtaining surt:ace soil water content and energy fluxes (submitted to J. Applied Meteor.). Hall, F. G., Huemmrich, K. F., Geotz, S. J., Sellers, P. J., and Nickerson, J. E. (1992), Satellite remote sensing of surface energy balance: success, failures and unresolved issues in FIFE. J. Geophys. Res. FIFE Special Issue: 19,061-19,090. Itier, B., and Riou, C. (1982), Une nouvelle methode de determination de l'evapotranspiration r~elle par thermographie infrarouge, J. Rech. Atmos. 16:113-125. Jackson, R. D., Reginato, R. J., and Idso, S. B. (1977), Wheat canopy temperature: a practical tool for evaluating water requirements, Water Resour. Res. 13:651-656. Kustas, W. P., and Goodrich, D. C. (1994), Preface to special issue of MONSOON 90, Water Resour. Res. 30:1211-1225. Lagouarde, J. P. (1991 ), Use of NOAA-AVHRR data combined with an agrometeorological model for evaporation mapping, Int. J. Remote. Sens.:1853-1864. Lagouarde, J. P., and McAneney, K. J. (1992), Daily sensible heat flux estimation from a single measurement of surt:ace temperature and maximum air temperature, Boundary Layer Meteorol. 59:341-362. Nemani, R., and Running, S. W. (1989), Testing a theoretical climate-soil-leaf area hydrological equilibrium of forests using satellite data and ecosystem simulation, Agric. For. Meteorol. 44:245-260. Nieuenhuis, G. J. A., Schmidt, E. A., and Tunnissen, H. A. M. (1985), Estimation of regional evapotranspiration of arable crops from thermal infrared images, J. Rem. Sens. 6:13191334. Price, J. C. (1990), Using spatial context in satellite data to infer regional scale evapotranspiration, IEEE Trans. Geosci. Remote Sens. 28:940-948. Price, J. C. (1992), Estimating vegetation amount from visible and near infrared refleetances, Remote Sens. Environ. 41: 29-34. Saudholt, I., and Anderson H. S. (1993), Derivation of actual
Simplified Method for Remote Sensing of Evapotranspiration
evapotranspiration in the Senegalese Sahel, using NOAAAVHRR data during the 1987 growing season, Remote Sens. Environ. 46:164-172. Seguin, B. and Itier, B. (1983), Using midday surface temperature to estimate daily evaporation from satellite thermal IR data, Int. J. Remote Sens. 4:371-383.
167
Seguin, B. (1994), personal communication. Shaw, E. M. (1983), Hydrology in Practice, Van Nostrand Reinhold, 569 pp. Shuttleworth, J. S. (1993), Evaporation, in Handbook of Hydrology, 1992 (D. R. Maidment, Ed.), McGraw-Hill, New York.
A New Look at the Simplified Method for Remote Sensing of Daily Evapotranspiration Toby N. Carlson,*William J. Capehart,* and Robert R. Gillies* A modification of the so-called "Simplified Method" used to obtain the integrated daily evapotranspiration from surface radiant temperature over variable vegetation cover is proposed. Mathematically, the simplified equation takes the form Rn24 - LEe4 = B(T013- Tal3)", where Rn24 and LE24 are, respectively, the integrated net radiation and evapotranspiration over a 24-h period and Toz3 and Ta13 are, respectively, the surface radiant and the 50-m air temperatures at 1300 local time. B and n are pseudo constants given as functions of the normalized difference vegetation index (ND VI), expressed as a scaled index N*. Both N* and Ta13 a r e obtained with the aid of remotely determined measurements, which are viewed on scatterplots of To13 versus NDVI.
1300 h local time, T013), a corresponding air temperature (usually measured at screen height, T~13), and the net radiation expressed as an integrated value over a 24-h period (Rn24). An equation of the following form has been used by Jackson et al. (1977), Sequin and Itier (1983), and Nieuenhuis et al. (1985): Rn24 - LE24 = B(To,3 - T~13)n,
where B and n are parameters to be determined and RN24 and ET24 are henceforth expressed in units of cm per day. Theoretical justification for Eq. (1) can be made with reference to the surface energy balance integrated over a 24-h day. Neglecting the integrated ground heat flux, the surface energy balance can be written as Rn - LE = H - pCp(To - Ta)
INTRODUCTION The so-called Simplified Method for determining the accumulated daily evapotranspiration from remote surface radiant temperature measurements was first proposed by Jackson et al. (1977) and later taken up by other investigators, such as Itier and Riou (1982), Seguin and Itier (1983), Nieuwenhuis et al. (1985), Carlson and Buffum (1989), Lagouarde (1991), Lagouarde and McAneney (1992), and Sandholt and Andersen (1993). The idea behind the simplified method is that the net integrated daily evapotranspiration at the surface (ETz4) can be estimated from a very few easily obtainable measurements, these being the surface radiant temperature measured near the time of local maximum (about * Department of Meteorology, Penn State University, University Park *Earth System Science Center, Penn State University, University Park Address correspondence to Toby N. Carlson, Dep. of Meteorology, Penn State Univ., University Park, PA 16802. Received 28 December 1994; revised 5 June 1995. REMOTE SENS. ENVIRON. 54:161-167 (1995) ©Elsevier Science Inc., 1995 655 Avenue of the Americas, New York, NY 10010
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(lb)
RH
where H, LE, and Rn are the sensible and latent heat fluxes and the net radiant flux and R,, is an atmospheric resistance to the flux of sensible heat. Integration of Eq. (lb) over a 24-h period yields an expression in which the left-hand side of Eq. (lb) is identical to that in Eq. (la). However, the right-hand side of this equation does not lend itself to such a facile integration; moreover, R, is a highly ambiguous parameter to define over a mixture of vegetated and bare soil surfaces (Carlson et al., 1995b). It is therefore more appropriate to express the integrated form of Eq. (lb) as the simplified Eq. (la), where B can be thought of as an average bulk conductance for the daily integrated sensible heat flux and a nonunity value of n as a correction for nonneutral static stability. Equation (la) is of limited utility in areas where in situ measurements are lacking. Perceiving this limitation, Carlson and Buffum (1989) suggested that air temperatures at 50 m be used instead of those at screen level, because the former is relatively independent of 0034-4257 / 95 / $9.50 SSDI 0034-4257(95)00139-R
162 Carlson et al.
local surface conditions and can be approximated by regional-scale averages of surface air temperatures, such as reported on weather maps, or from the output of regional-scale atmospheric prediction models. Henceforth, T,,~3 will refer to the 50-m air temperature. It is remarkable, however, that such a simplified formula as Eq. (la) is able to successfidly encapsulate the complex physics of evapotranspiration over diverse surfaces with variable vegetation cover. Yet it has been widely applied and is generally thought to be accurate to within about 0.1 c m / d a y (Lagouarde and McAneney, 1992). Nevertheless, a problem exists in the use of this equation, which is that the parameters B and n are not constant. Although n is generally thought to have a value close to 1.0 (Seguin and Itier, 1983), the conductance is highly sensitive to wind speed, roughness, and vegetation amount (Carlson and Buffum; 1989; Lagouarde and McAneney, 1992). Indeed, values of B reported in the literature show considerable variation. Seguin and Itier (1983), for example, reported values of B = 0.025 over a homogeneous grassland in southeastern France, whereas Jackson et al. (1977) found values of B = 0.064 for a large irrigated field of wheat in Arizona. Seguin (private communication) has suggested that B tends to vary from about 0.01 to 0.06, with values increasing with increasing vegetation cover. In contrast, Carlson and Buffum found that both B and n varied by less than about 25% over the normal range of wind speed and surface roughness length for a given vegetation amount. Friedl and Davis (1994), Gillies and Carlson (1995), and Carlson et al. (1995a) show that the surface energy fluxes depend strongly on both surface wetness and fractional vegetation cover (Fr). The method used by Carlson et al. (1995) for obtaining surface evapotranspiration, surface soil moisture availability (ref. Fig. lb) and Fr is called the "'triangle method", so-called because the pattern formed by the envelope of pixels on a scatterplot of surface radiant temperature (To) versus normalized difference vegetation index (NDVI) resembles a triangle (Price, 1990; Carlson et al., 1995a) (ref. Figs• la and lb). (Surface moisture availability, shown in Fig. lb, is here defined as the ratio of surface soil water content to that at field capacity, which is 0.34 by volume for this case.) Simulations with the more recent version of the model discussed by Carlson and Buffum (1989), referred to here as a soil-vegetation-atmosphere transfer (SVAT) model (Gillies and Carlson, 1995), also yield similar triangular patterns for the isopleths of moisture availability when plotted as a function of surface radiant temperature and Fr (Fig. lb). NDVI is customarily defined as NDVI
= ((a,.~ 6 t n i r +- a,~)' avis)
(2)
where a is the surface reflectance and the subscripts vis and ir refer to solar wavelength bands in the visible
KonzaPrairie FIFE-07, Aug--15-1907 N ' = 1.0
,:• ,','i
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.'....it! •
ro
' **'. { *1 .....,.
:
• '. ,.,,
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,
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..,.~, L,,'~,,=.y:. , • ~:,,~u,~,~', -',-~.~-. . . . . '~' ".','~":
315 40 415 50 Surface RadiantTemperature(Centigrade)
515
Figure la. Scatterplot of surf:ace radiant temperature (°C) versus NDVI, adjusted to at-surface values as determined from pixel values measured by an NS001 radiometer (5 m resolution) aboard a C-130 aircraft flying over the Konza Prairie during FIFE on 15 August 1987. The vertical dashed line denotes the screen-level air temperature at flight time and the horizontal lines denote the values of NDVI for N*= 1 and N*= 0.
(just below 0.7 pro) and in the near infrared part of the visible spectrum (just above 0.7 tim). It is generally accepted that NDVI, Fr, and vegetation amount are related and, indeed, various investigators describe monotonic relationships between NDVI and leaf area index (Baret and Guyot, 1991; Price, 1992, Choudhury et al., 1994). As in Choudhury et al., (1994), we (Gillies and Carlson, 1995) define a scaled NDVI (N*), which is defined as N* = (NDVI - NDVI0) (NDVIs - NDVI0),
(3)
where NDVL is the value of NDVI at 100% vegetation cover (N*= 1.0) and NDVI0 is that value for bare soil (N*=0). Corrected for atmospheric attenuation to atsurface values, NDVI tends to vary from about zero for bare soil to about 0.75 at full vegetation cover. The relationship Fr=(U*) 2
(_+4.2%)
(4)
has been found to fit virtually all the images we have analyzed; it is identical to one suggested by Choudhury et al. (1994)• The index N* has the advantage of being relatively insensitive to viewing angle, sensor drift, and uncertainties in atmospheric corrections. Figure la shows that the value of Fr = 0 (N*= 0) corresponds closely to an NDVI of zero; negative values in this scatterplot were
Simplified Method for Remote Sensing of Evapotranspiration
163
Fractional Vegetation Cover = 25%
,1:
Me = 0.0 Me = 0,2 Mo = 0.4 Me = 0.6 Me = 0.8 Mo = 1.0 Triangle
0.5
. . . . ' " "
E /"
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122
=o
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.. .. .. ~.. .. .. .. ..
,i
.. .. .. ..
10 (Ts - Ta) @ 1300 LST
i
i ii
100
surface radiant temperature (centigrade)
Figure lb. Moisture availability isopleths (at intervals of 0.2) for the scatterplot in Figure la. The lowest value (0) is on the right and the highest (1.0) is on the left side of the triangle (key). Pixels affected by water, sloping terrain, or urban surfaces are indicated. The dashed lines within the figure denote the envelope of pixels in Figure la.
found by inspection of the original image to be representative of artificial surfaces such as roads, which form their own envelope of points below the base of the main triangle. Recent simulations with a later version of the SVAT model used by Carlson and Buffum (1989) further indicate that B may depend much m o r e sensitively on the amount of vegetation than on wind speed or roughness. As vegetation amount increases from a small fraction to dense cover, the difference between the air and surface radiant temperatures trends to diminish, regardless of the soil surface wetness, all other factors being equal. This is illustrated by the scatterplot in Figure la, which shows surface radiant temperature (To) plotted versus normalized difference vegetation index (NDVI). However, our simulations also show a large increase in LE24 from the right-hand (warm) side to the left-hand (cold) side of the pixel envelope, with isopleths of LE24 oriented more or less vertically, similar to the surface moisture availability isopleths shown in Figure lb. The purpose of this article is 1) to present simple relationships between the parameters B and n and N* and 2) to indicate how the surface air t e m p e r a t u r e (T,13) can be obtained solely from the scatterplots of surface radiant t e m p e r a t u r e and NDVI. RESULTS O F SIMULATIONS Eleven sets of simulations were run. These were made using the initial atmospheric and surface conditions corresponding to nine AVHRR and two aircraft (NS001) images. Of the former, five satellite images pertain to
Figure 2. Plot of (To - Ta]3) at 1300 h versus Rn24- LE24 for a fractional vegetation cover, Fr = 0.25. The air temperature is 50 m above the ground level. The solid line represents the linear best fit (Regr.) through the points (ref. Table 1) and the dashed lines represent the root mean square deviation (RMSD) from the regression line. Data were generated from 11 simulations for five cases over Pennsylvania (PA; open circles), four over Newcastle Upon Tyne (UK; squares) and two in FIFE (triangles).
the Susquehanna Watershed in Pennsylvania and four images to the area around Newcastle upon Tyne, England (Gillies and Carlson, 1995). Two images were made by aircraft during intensive field operations in FIFE. As a byproduct of these simulations, series of statistics were generated which were used to obtain the variations in B and n with Fr and therefore with N* using the transformation given in Eq. (3). For each of these 11 cases, the quantities LE24, Rn24, T 0 1 3 (at 1300 local time), and Ta]3 were generated. In each of these simulations Fr was incremented over five values (in steps of 0.25) and surface moisture availability over six values (in steps of 0.2) for a total of 66 points in each of the graphs shown in Figures 2 and 3. Initial conditions for each of these 11 series of simulations varied over a wide range of values; in particular, surface roughness and geostrophic wind speed varied between 2 cm and 30 cm and between 1 m s-1 and 8.5 m s-1, respectively. Although the statistics generated for this article are not site-specific and do not depend on the actual image data, each of the simulations were made to fit the surface moisture availability isopleths to seatterplots for the images. As the initial conditions used for the SVAT model were representative of a realistic range of atmospheric and surface conditions, the scatter of points shown in Figures 2 and 3 can be taken to represent the spurious effects of differing wind speed and surface roughness on B and n. The results are encapsulated in Figure 3. Overall,
164
Carlson et al.
Fractional Vegetation Cover = 2 5 %
Fractional Vegetation Cover = 0 %
~~
2
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"
~5 ~ °"t B
0.01
,
:
:
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1
:
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:::::,
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,
:
Fractional Vegetation Cover = 5 0 %
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1 A
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= 75%
lO O's - Ta) @ 1300 LST
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.8
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.
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Figure 3. S a m e as F i g u r e 2 trot tbr five different values o f Fr f i o m 0 to l.O.
:::::,
100
the standard error of the estimate (STD ERR), shown in Table 1, is about 0.14 era, while the parameters B and n exhibit a systematic variation with Fr. This is shown in Figure 4. Relationships b e t w e e n Fr and the parameters B and n, were found to be Table 1. Fractional vegetation cover, R'2, Standard Error, and the Parameters B (intercept) and n (slope) for Regression lines in Figure 3 Fr
R2
S T D E R R (cm)
B
n
0 0.25 /I.50 0.75 1.0
0.72 1).65 0.54 (I.46 0.46
0.13 O, 13 0.14 1).15 0.16
0.013 0.024 0.036 0.047 0.653
1.16 (/.99 0.87 0.82 0.88
B=0.0175+0.05
(Fr)
(_+0.(}02),
(5a)
n = 1.004 - 0.335 (Fr)
( + 0.053),
(5b)
where Fr is expressed as a fraction between 0 and 1. Values in parentheses represent one standard deviation from the straight line of best fit in Figure 4. Since N D V I and not Fr is m e a s u r e d by satellite, a inure practical result is obtained as functions of N*. This relationship, shown in Figure 5, is expressed mathematically as B = 0.0109 + 0.051 (N*) ,,
= 1 . 0 6 r - o . 3 r e (N*)
( + 0.003),
( _+ 0.089),
(6a)
(6t,)
w h e r e the values in parentheses represent 1 standard deviation from the straight line of best fit in Figure 5. Equations (5) and (6) show that as Fr or N* increase
Simplified Method for Remote Sensing of Evapotranspiration
FIFE
-0.08
1.2
15 August 1987 0.25
-0.07
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1 65
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0.01 100
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Figure 4. The parameters B and n as a function of Fr. The dashed lines represent 1 standard deviation from the data points generated from the simulations. The pair of straight lines represents the linear best fit to these points.
over their full ranges of 0 to 1, B increases from about 0.01 to 0.06, and n decreases from about 1.05 to 0.7.
VALIDATION Before presenting the results, it is essential to make a statement concerning the validity of the SVAT model, which is used to derive the relationship b e t w e e n the parameters in Eq. (1) and N*. The triangle method has recently been subjected to validation using groundbased measurements of surface evapotranspiration (Gillies et al., 1995). These data were obtained by an NS001 radiometer mounted aboard a C-130 aircraft during three days in FIFE (Hall et al., 1992) and two days
Figure 5. The parameters B and n as a function of N*. Dashed lines have the same significance as in Figure 4.
1.2 1
-o.o8
"..+.
1.1
" -0.07 """
,'" •,
~
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0 0.8
]
~
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.
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I
0.00 0.00 0.05 0.10 0.15 0.20 0.25 Measured 2 4 h r (Rn-LE)
Figure 6. Simulated versus measured values of Rn24- LE24 (cm) for eight surface measurement stations on 15 August 1987 in FIFE. One outlying data point was discarded.
during Monsoon-90 (Walnut Gulch, Arizona) (Kustas and Goodrich, 1994). Average root-mean square differenees b e t w e e n measured and simulated values of evapotranspiration for these cases was 37 W m -2, or about 10% of the flux values; R 2 for the five eases was 0.95 (Gillies et al., 1995). The relationships expressed in Eqs. (5) and (6) strictly pertain to a surface radiant temperature at 1300 h local time, but are generally valid in a window between about 1200 h and 1400 h when temperature varies slowly with time. Given this time window, however, only one thermal image could be found which was appropriate for verifying these relationships, that for FIFE on 15 August, 1987. The scatterplot for this case is shown in Figure la, and the evapotranspiration values derived thereof were compared with surface measurements. Figure 6 shows good agreement b e t w e e n measured and simulated values of Rn24-LE24, with a standard error of 0.038 cm. A representative air temperature can also be obtained from the scatterplot. Screen-level air temperature tends to be slightly below the surface radiant temperature of a densely vegetated surface. Accordingly, we have found that a reasonable estimate of the screen level air temperature to be that at the apex of the pixel envelope, which is about 3 3 ° C in Figure la. As the 50-m temperature is likely to be slightly cooler than that at screen level, w e adopted the convention in producing Figure 6 that T013 was I ° C less than that at the top of the NDVI envelope. CONCLUSIONS Simulations with a soil / vegetation / atmosphere transfer model were made for 11 sets of initial conditions repre-
166 Carlson et al.
senting a range of surface roughness and wind speed. This was done to derive relationships between NDVI and the parameters in Eq. (1). Results show that B and n vary systematically with fractional vegetation cover and NDVI, the latter expressed as a scaled vegetation index, N*. Although B and n also vary with wind speed and surface roughness, the present study shows that these parameters depend much more sensitively on vegetation cover, at least within reasonable limits. We do recommend, however, that some adjustment of these two parameters be made to account for differences in wind speed and roughness, as indicated in the results of Carlson and Buffum (1989). A powerful advantage of the proposed method is that the one side of Eq. (1) is obtainable from a knowledge of surface radiant temperature and NDVI with an implied standard error of less than 0.15 cm. The dependence of B on Fr may partially explain the wide range of its values in the literature, such as the difference between the studies of Jackson et al. (1977) and Seguin and Itier (1983). The present study indicates that larger variations in B with vegetation amount than those reported by Carlson and Buffum (1989), with values ranging from about 0.01 for bare soil and 0.06 for a fldl vegetation cover. The value of n, though close to 1.0, also shows systematic differences with changing Fr. Finally, it hardly needs to be pointed out that knowledge of one side of Eq. (1) is not sufficient to obtain the evapotranspiration, as the integrated net radiation must still be determined. An estimate of net radiation can be made with reasonable accuracy for clear sky conditions using the formulae recommended by Shaw (1983) and Shuttleworth (1993). Although remote measurements of radiant surface temperature obtained via satellite are feasible only during clear sky conditions, it should be possible to calculate ET24 without great loss of accuracy over a season, given a measurement of Rn24, by determining the so-called evaporation fraction (ET24 / Rn24) from satellite images for a succession of clear days and interpolating the ratios for cloudy ones. The authors" would like to thank Bernard Seguin for his advice and the U.S. Department of Agriculture, Agriculture Research Service, Beltsville, Maryland, especially Tom Schmugge, for their financial assistance of this research through a cooperative research agreement 58-1270-3030. This project is also motivated by our participation in The Global Water Cycle: Extension Across the Earth Sciences EOS Project within the Earth Science System (;enter (ESSC) under Grant No. NAGW~-2686. We would also like to thank Jie Cui for the use of her figures (la and lb). REFERENCES
Baret, F., and Guyot, G. (1991), Potentials and limits of vegetation studies for LAI and APAR assessment, Remote Sens. Environ. 35:161-174.
Carlson, T. N., and Buffum, M. J. (1989), On estimating total daily evapotranspiration from remote surface temperature measurements, Rein. Sens. Environ. 29:197-207. Carlson, T. N., Gillies, R. R., and Schmugge, T. J. (1995a), An interpretation of NDVI and radiant surface temperature as measures of surface soil water content and fractional vegetation cover, Agric. For. Meteorol., forthcoming. Carlson, T. N., Taconet, O., Vidal, A., Gillies, R. R., Oliosn, A., and Humes, K. (1995b), An overview of the Workshop on Thermal Remote Sensing held at La Lande des Maures, France, September 20-24, 1993, Rein. Sens. Rev., pp. 147158. Choudhury, B. J., Ahmed, N. U., Idso, S. B., Reginato, R. J., and Daughtry, C. S. T. (1994), Relations between evaporation coefficients and vegetation indices studied by model simulations, Remote Sens. Environ. 50:1-17. Friedl, M. A., and Davis, F. W. (1994), Sources of variation in radiometric surface temperature over a Tallgrass prairie, Rem. Sens. Environ. 48:1-17. Gillies, R. R., and Carlson, T. N. (1995), Thermal remote sensing of surface soil water content with partial vegetation cover for incorporation into mesoscale prediction models, J. Appl. Meteorol. 34:745-756. Gillies, R. R., Cui, J., Carlson, T. N., Kustas, W. P., and Humes, K. S. (1995), Verification of a method for obtaining surt:ace soil water content and energy fluxes (submitted to J. Applied Meteor.). Hall, F. G., Huemmrich, K. F., Geotz, S. J., Sellers, P. J., and Nickerson, J. E. (1992), Satellite remote sensing of surface energy balance: success, failures and unresolved issues in FIFE. J. Geophys. Res. FIFE Special Issue: 19,061-19,090. Itier, B., and Riou, C. (1982), Une nouvelle methode de determination de l'evapotranspiration r~elle par thermographie infrarouge, J. Rech. Atmos. 16:113-125. Jackson, R. D., Reginato, R. J., and Idso, S. B. (1977), Wheat canopy temperature: a practical tool for evaluating water requirements, Water Resour. Res. 13:651-656. Kustas, W. P., and Goodrich, D. C. (1994), Preface to special issue of MONSOON 90, Water Resour. Res. 30:1211-1225. Lagouarde, J. P. (1991 ), Use of NOAA-AVHRR data combined with an agrometeorological model for evaporation mapping, Int. J. Remote. Sens.:1853-1864. Lagouarde, J. P., and McAneney, K. J. (1992), Daily sensible heat flux estimation from a single measurement of surt:ace temperature and maximum air temperature, Boundary Layer Meteorol. 59:341-362. Nemani, R., and Running, S. W. (1989), Testing a theoretical climate-soil-leaf area hydrological equilibrium of forests using satellite data and ecosystem simulation, Agric. For. Meteorol. 44:245-260. Nieuenhuis, G. J. A., Schmidt, E. A., and Tunnissen, H. A. M. (1985), Estimation of regional evapotranspiration of arable crops from thermal infrared images, J. Rem. Sens. 6:13191334. Price, J. C. (1990), Using spatial context in satellite data to infer regional scale evapotranspiration, IEEE Trans. Geosci. Remote Sens. 28:940-948. Price, J. C. (1992), Estimating vegetation amount from visible and near infrared refleetances, Remote Sens. Environ. 41: 29-34. Saudholt, I., and Anderson H. S. (1993), Derivation of actual
Simplified Method for Remote Sensing of Evapotranspiration
evapotranspiration in the Senegalese Sahel, using NOAAAVHRR data during the 1987 growing season, Remote Sens. Environ. 46:164-172. Seguin, B. and Itier, B. (1983), Using midday surface temperature to estimate daily evaporation from satellite thermal IR data, Int. J. Remote Sens. 4:371-383.
167
Seguin, B. (1994), personal communication. Shaw, E. M. (1983), Hydrology in Practice, Van Nostrand Reinhold, 569 pp. Shuttleworth, J. S. (1993), Evaporation, in Handbook of Hydrology, 1992 (D. R. Maidment, Ed.), McGraw-Hill, New York.