A methodology for estimation of surface evapotranspiration

Transcription

1 1 A methodology for estimation of surface evapotranspiration over large areas using remote sensing observations Le Jiang and Shafiqul Islam Cincinnati Earth Systems Science Program, Department of Civil and Environmental Engineering, University of Cincinnati, Cincinnati, Ohio Abstract. We propose a simple scheme to estimate surface evaporation over large heterogeneous areas using remote sensing observations. Our approach is based on a relationship between easily measured surface parameters (e.g. radiometric surface temperature) and a surrogate for effective surface resistance. Preliminary results, using remotely sensed data sets from AVHRR NOAA-14 over the Southern Great Plains, show good agreement. The proposed approach appears to be more reliable and easily applicable for operational estimation of evaporation over large areas. 1. Introduction Accurate knowledge of the distribution of land surface evaporation is critical for studying the interaction between land surface and atmosphere and for many water resources management and agricultural applications over a range of space and time scales. Operational methods using standard meteorological input variables [e.g., Brutsaert, 1982; Parlange et al., 1995] have shown a varying degree of success. A major difficulty in using these methods, however, is that they require near-surface meteorological observations which are not easily available over large heterogeneous areas. Current generation of remote sensors have the potential to provide surface observations of many variables over large heterogeneous land surfaces. However, remote sensors cannot provide critical atmospheric variables like wind speed, air temperature, vapor pressure, and aerodynamic resistance needed to estimate surface fluxes over large areas. Several studies have attempted to estimate evapotranspiration over large areas using a combination of remote sensing observations and ancillary surface and atmospheric data [e.g., Jackson et al., 1977; Bastiaanssen et al., 1996]. Many of the current studies use the energy balance equation to estimate evapotranspiration as a residual term. It is not uncommon to incur greater than 50% errors due to the use of radiometric surface temperature in classical sensible heat flux formulation with an aerodynamic resistance [Stewart et al., 1994]. This motivates us to explore alternative methods of estimating evaporation over large areas using mainly remote sensing observations. 2. Estimation of surface evaporation over large areas using remote sensing data Currently, the residual method is the most commonly used scheme to calculate surface latent heat flux based on the surface energy balance: G = H + λe (1) R n 1

2 2 where R n is the net radiation (including long wave and short wave), G is the soil heat flux, H is the sensible heat flux, and λe is the latent heat flux. We note that uncertainties associated with the estimation of R n and G are common to the residual as well as our proposed method. In addition, significant uncertainty exists in the estimation of H using classical aerodynamic formulation and remotely sensed surface temperature. Thus, we will not attempt to estimate H directly from remote sensing data. Various formulations of evaporation can be expressed in the following general form (for an extensive review see [Brutsaert, 1982; Parlange et al., 1995]): γ λ E = β[ A( R G) B f ( u)( e* n + a e a )] (2) + γ + γ where e is the vapor pressure and e * the saturation vapor pressure (the subscript a indicates values in the atmosphere), is the slope of saturated vapor pressure at the air temperature T a, γ is psychometric constant. The symbol f(u) represents a wind function while parameters A and B depend on the particular model. β is the Budyko-Thornwaite-Mather parameter. Daily estimates of latent heat flux from these formulations are fairly accurate when applied locally but they have been less reliable when applied over large areas. One of the major difficulties in applying Equation (2) is that we are unable to obtain representative values for the free parameters over large areas. One way to estimate large scale evaporation using mainly remote sensing data is to use the Priestley-Taylor Equation [Priestley and Taylor, 1972] which is obtained by putting A=α, β=1.0 and B=0 in Equation (2). In several studies, α has been found to be about 1.26 and is used as a dimensionless parameter to identify potential conditions [Crago and Brutsaert, 1992]. Analysis of data from FIFE, HAPEX-MOBILHY and ARME suggests a concave down relationship between α and conductance [Bastiaanssen et al., 1996]. These observed data indicate that there is a strong relationship between α and certain physical characteristics of the pixel. These physical characteristics may be related to surface wetness, surface conductance and surface temperature. Based on these observational evidence and simplicity of Priestley-Taylor formulation, we propose to simplify Equation (2) as our model of evaporation: λe = φ[( Rn G) ] (3) + γ Equation (3) may be applicable for a range of surface conditions and can be interpreted as the following: R n -G is the driving force for evaporation. ( G) /( + γ ) R n is called equilibrium evaporation [Brutsaert and Chen, 1995], φ represents a complex effects parameter that absorbs the combined effects of Priestley-Taylor α and β. We must emphasize here that the φ in Equation (3), although looks similar to Priestley-Taylor s α, it encompasses a wide range evaporative conditions and can take a range of values. For example, in the absence of significant advection and convection, latent heat flux cannot exceed R n -G, and hence φ has a range between 0 and ( + γ ). There are indications that Priestley-Taylor α, and by extension φ, may not be sensitive to atmospheric conditions [Eichinger et al., 1996]. Also, an advantage of using φ is that aerodynamic resistance is not explicitly needed. One may think, however, φ as a surrogate of surface resistance to 2

3 3 evapotranspiration which is reasonably accurate to estimate regional scale evaporation. Crago and Brutsaert [1992] used a parameter similar to φ to characterize the dependence of evaporation on soil moisture over the FIFE. We do not expect φ to be related to a single surface attribute; instead, we view φ as a complex surface effects parameter whose spatial variation we expect to detect from contextual information of remotely sensed images. Our use of contextual information to obtain spatially distributed φ makes Equation (3) distinctly different from Priestly-Taylor s equation for evaporation. A key assumption for the implementation of the above methodology over large areas is that areas with very high (or low) evaporation can be identified from contextual remotely sensed information. For example, areas of high evaporation can be detected as pixels with low surface albedo and relatively low surface temperature and high surface wetness. Such a pixel is likely to be inland wetlands, storage reservoirs or dense vegetation stands. While areas with no evaporation will show opposite characteristics, that is, relatively high surface temperature and albedo. Once the pixels with limiting values of φ are identified from regional scale remotely sensed images, one needs to estimate φ values for pixels with intermediate evaporation rates. As discussed earlier, it is likely that there is a singular relationship that relates range of φ values, between zero and ( + γ )/, with certain physical characteristics of the pixel. Air temperature is also needed to compute λ E, however, its effect is implicit through the estimation of. /( + γ) shows a very small sensitivity to air temperature. The quasi-linear relationship between T 0 and T 0 -T a, where T 0 is the remotely sensed radiometric surface temperature and T a is the near surface air temperature, can be used to infer air temperature T a [Bastiaanssen, 1995]. A key advantage of using Equation (3) is that it holds true for a wide of range of surface conditions and possibly valid over a wide range of pixel scales. In addition, all of the four quantities (R n, G, φ, and ) in Equation (3) can be estimated using remotely sensed data. Another attractive feature of our evaporation formulation is that it allows a straightforward estimation of surface evaporative fraction (EF) as EF = φ /( + γ). 3. Experiment 3.1 Description of Data To evaluate the robustness of our proposed approach, we need a set of remotely sensed images over a large area to estimate four variables (R n, G, φ and ) and a set of evaporation measurements to validate our estimates. For a preliminary demonstration of concepts, we will use observed satellite remote sensing data from an AVHRR NOAA-14 afternoon overpass on a clear day (July 1, 1997) during the Southern Great Plains 1997 (SGP97) experiment. The satellite overpass time is 20:18:02 GMT (14:18:02 local time). Each image consists of 500 x 350 pixels with a resolution of 1 km. 3.2 Derivation of R n, G and To provide a preliminary demonstration of the proposed methodology, we will use simplified approaches to derive R n, G and in Equation (3). We will then use contextual spatial interpolation to obtain φ for each pixel. In the following 3

4 4 procedure, we use primarily the remote sensing information. Due to brevity of space, we cannot provide all the detailed description for the estimation of R n and G. We must emphasize, however, uncertainties associated with the estimation of R n and G are common to the proposed as well as the commonly used residual method. Briefly, each component of R n in Equation (4) can be derived primarily based on remote sensing information. R = ( 1 r0 R + L L (4) n ) Both the downward short wave radiation (R s ) and albedo (r 0 ) are estimated using empirical and physically based models [Iqbal, 1983; Bastiaanssen, 1995]. Long wave upward radiation L = ε 0 σ T 4 0, where σ is the Stefan-Boltzmann constant and surface emissivity ε 0 is estimated as a function of NDVI [Bastiaanssen, 1995]. T 0 is determined using the split window algorithm of Coll et al. [1994]. For the calculation of soil heat flux, we use the scheme by Moran et al. [1989]: G = 0.583exp( 2.13NDVI ) R n (5) This scheme is used for NDVI > 0.0. For pixels with NDVI < 0.0 (e.g. water bodies), G is taken to be a constant fraction of R n (i.e. G = R n ). is estimated from the gradient of saturation vapor pressure evaluated at T=T a. Although T a is easily obtained from routine meteorological stations, we will not assume the availability of T a over large areas. Rather, we will use strong linear relationship between T 0 -T a and T 0 to derive T a [Bastiaanssen, 1995]. 3.3 Spatial interpolation of φ A key aspect of the proposed methodology is the presence of a relationship between φ and remotely detectable spatial variables, such as land surface temperature, surface reflectance and NDVI, or a combination of these parameters. For example, for a given net radiation, wet pixels will be identified with low reflectance and low temperature, while dry pixels will have high reflectance and high temperature. In this preliminary demonstration, we explore possible relationships among surface temperature, NDVI, and φ. Figure 1 shows a scatter plot of 175,000 pixels for the derived surface temperature T 0 and NDVI for the SGP97 July 01, 1997 overpass of NOAA-14 AVHRR. The pixels with negative NDVI can be identified as water body while the φ values for these pixels reach a maxima (i.e. H = 0, LE =R n - G, and φ = φ max = ( + γ )/ ). For the pixels with NDVI > 0.0, it appears that almost all the points are bounded by a triangle. An extensive discussion on such a triangular bound can be found in Price [1990], and Calson et al. [1995]. Such a bound may be attributed to physical states of the land surface. For this particular site, the land surface types range from bare soil to densely vegetated soil with increasing amount of vegetation (i.e., NDVI). Within each type of land surface (i.e. same NDVI), the surface temperature varies from minimum (i.e. maximum evaporative cooling) to maximum (minimal evaporative cooling). For a given level of net radiation, such a temperature variation may be associated with variations of surface soil moisture or resistance to evaporation for a particular surface type. From Figure 1, we also notice that as the vegetation amount (NDVI) increases, the range of surface temperature variation decreases. We will use these signatures from Figure 1 to obtain φ value for each pixel in an image. s 4

5 5 We propose a two-step linear interpolation scheme to obtain φ value for each pixel that has NDVI > 0. First, we need to get upper and lower bounds of φ values for a specific interval of NDVI. The global minimum and maximumφ values can be easily determined i.e., φ min = 0 on the driest bare soil pixel, and φmax is found on the pixel with large NDVI and low T 0. Given these two extremes (NDVI = 0, φ min ), (NDVI = NDVI max, φ max ) and the range of NDVI from min 0 to NDVI max, the φ i can be interpolated (linearly) for each max NDVI interval (NDVI i ). The φ i for each NDVI i is easily calculated using the lowest surface temperature pixel within that NDVI interval. After the lower and upper bounds of φ values for each NDVI class have been determined, the second step is to linearly interpolate within each NDVI class between the lowest temperature pixel ( min max Ti, φ i ), and the highest max min temperature pixel ( Ti, φ i ). The underlying assumption of the above interpolation scheme is that for the homogeneous vegetation type (i.e. same NDVI), φ is linearly related to surface temperature. Given this two steps, φ values for each pixel can now be determined from the spatial context of derived surface temperature and NDVI. An interesting point to note here is that the upper bound of our derived φ for each NDVI class is very close to Given φ values for each pixel and the Equation (4), a spatially distributed λ E map is easily obtained for the SGP97 site as shown in Figure Validation Using SGP97 Data As ground based observations are essentially discrete and limited in numbers, to generate a spatially distributed field of observed evaporation, that is consistent with the remotely sensed evaporation map, one needs to use some form of empirical interpolation. Errors associated with interpolation may be comparable or even larger than model estimation error. In addition, since several types of sensors and measurement techniques were used to obtain surface fluxes during SGP97, a random comp onent is expected to occur in the observations. It is conceivable that random components would also arise in the estimated evaporation map due to measurement error in underlying remote sensors. To minimize the effects of such random components and empirical interpolation schemes, we will first compare statistical moments of spatially average quantities. During the satellite overpass on July 01, 1997, only five ground based flux stations provided reliable observations. The observed latent heat flux for these five stations has a mean of Wm -2, and a standard deviation of Wm -2. Table 1 compares and contrasts the estimation of latent heat flux by the proposed method to those of observations. With a two-variable descriptor (i.e. surface temperature and NDVI) for φ, the proposed method shows encouraging results. Overall, bias is low and the root mean square error is also low compared to process variability (i.e. observed standard deviation) for the derived evaporation. Estimation error (RMSE is 8.67% of the observed mean) is small compared to uncertainties in the observations for the derived λ E. We note here that correlation between the observed and derived λ E (column 3 in Table 1) is somewhat low. To isolate the influence of errors, we have also calculated λ E by using observed R n -G (column 6 of Table 1). With observed R n -G, estimation accuracy for λ E has substantially Figure 1. Figure 2. Table 1. 5

6 6 improved. For instance, bias has reduced from Wm -2 to 5.3 Wm -2, and correlation coefficient has increased from 0.47 to In addition, as a baseline comparison, we estimated λ E using φ = (column 5 and 7 in Table 1). This may be viewed as a direct application of Priestley- Taylor s equation to estimate λ E. Clearly, our proposed approach provides much better estimate of λ E in both cases. As a point of comparison, we also estimate a global mean (evaporation averaged over 175,000 pixels) of Wm -2 with a standard deviation of 91.2 Wm -2. We must emphasize that a key motivation for our approach is to provide a spatially distributed λ E map. Comparison in Table 1, however, cannot quantify differences in spatial structures of the observed and estimated fields. Given the number of ground based observations available, it is not feasible to provide a comprehensive spatial comparison. Nevertheless, to provide a basis for comparison, we show a point-by-point comparison of observed and estimated latent heat fluxes in Table 2. Despite the limited number of stations for ground validation, these five locations (marked as + in Figure 2) show some interesting features. For example, there appears to be two evaporative regimes: two stations with greater than 500 Wm -2 of latent heat flux and the other three with a latent heat flux less than 365 Wm -2. It is interesting to note that our proposed method, using contextual spatial information, has captured the general spatial structure of λ E pretty well. These results are further improved by using observed R n -G. Table 2 5. Conclusions A simple scheme is developed to estimate surface evaporation over large heterogeneous areas using mainly remote sensing data. The results show that the method is operationally feasible and can provide reasonable estimation accuracy with minimum number of free parameters. Given common uncertainties in R n and G, the proposed approach appears to be more reliable and practical considering the complexity associated with the residual method for the estimation of spatially distributed latent heat flux. More importantly, each module of the estimation procedure (such as R n and G) can be imp roved separately. Little supervision is needed for the estimation of spatially distributed φ values from contextual information of remotely sensed surface variables by current generation satellites. Comparisons with ground based data show promising results. These results suggest the potential applications of this technique to remote regions of the globe where in-situ data are not readily available. Our estimated evaporation maps, similar to other estimation procedures that simultaneously utilize remote sensing and in-situ data, are essentially instantaneous and the temporal frequency of such estimates will depend on the temporal frequency of remote sensors. Yet, such evaporation maps can be used to obtain daytime average evaporation by invoking certain assumptions related to midday evaporative fractions and daytime average evaporation. Acknowledgments. Data were obtained from the Atmospheric Radiation Measurement Program sponsored by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research, Environmental Sciences Division. Support of NASA Earth System Science Fellowship and NSF grant (NSF ) are gratefully acknowledged. 6

7 7 References Bastiaanssen, W. G., M. Pelgrum, M. Menenti and R. A. Feddes, Estimation of surface resistance and Priestley Taylor α - parameter at different scale, in Scaling up in Hydrology using Remote Sensing,, pp , edited by Stewart, J., E. Engman, R. Feddes and Y. Kerr, Bastiaannssen, W. G. M., Regionalization of surface flux densities and moisture indicators in composite terrain A remote sensing approach under clear skies in Mediterranean climates, Ph.D. thesis, 273pp., Agri. Univ., Wageningen (The Netherlands), Brutsaert, W., Evaporation into the Atmosphere: Theory, History and Applications, 229 pp., D. Reidel Publishing Company, Brutsaert, W. and H. Chen, Desorption and the two stages of drying of natural tallgrass prairie, Water Resour. Res., 31(5), , Carlson, T. N., R. R. Gillies, and T. J. Schmugge, An interpretation of methodologies for indirect measurement of soil water content, Agricultural and Forest Meteorology, 77, , Coll, C., V. Casselles, and T. J. Schmugge, Estimation of land surface emissivity differences in the split-window channels of AVHRR, Remote Sens. Environ., 47, 1-25, Crago, R. D. and W. Brutsaert, A comparison of several evaporation equations, Water Resour. Res., 28(3), , Eichinger, W. E., M. B. Parlange and H. Stricker, On the concept of equilibrium evaporation and the value of the Priestley-Taylor coefficient, Water Resour. Res., 32 (1), , Iqbal, M., An introduction to solar radiation, 390 pp., Academic Press, Jackson, R. D., R. J. Reginato and S. B. Idso, Wheat canopy temperature: A practical tool for evaluating water requirements, Water Resour. Res., 13, , Moran, M. S., R. D. Jackson, L. H. Raymond, L. W. Gay and P. N. Slater, Mapping surface energy balance components by combining Landsat thermatic mapper and ground-based meteorological data, Remote Sens. of Enviro., 30, 77-87, Parlange, M. B., W. E. Eichinger, and J. D. Albertson, Regional scale evaporation and the atmospheric boundary layer, Rev. of Geophysics, 33(1), , Price, J. C., Using spatial context in satellite data to infer regional scale evapotranspiration, IEEE Trans. Geosci and Remote Sens., 28(5), , Priestley, C. H. B. and R. J. Taylor, On the assessment of surface heat flux and evaporation using large scale parameters, Mon. Wea. Rev., 100, 81-92, Stewart, J. B., W. P. Kustas, K. S. Humes, W. D. Nichols, M. S. Moran and H. A. R. De Bruin, Sensible heat flux radiometric surface temperature relationship for eight semiarid areas, J. Appl. Meteor., 33, , (Received April 13, 1999; revised June 21, 1999; accepted July 15, 1999) 7

8 8 Figure 1. Scheme to interpolate φ for each pixel. Figure 2. Derived surface evaporation map (Wm -2 ). 8

9 9 Table 1. Statistical comparison of derived λ E with 5 points observations Metrics λ E observed λ E derived λ E derived with φ = λ E derived using observed R n-g λ E derived using observed R n-g and φ = 1.26 Mean (Wm -2 ) St. Dev. (Wm -2 ) Bias (Wm -2 ) RMSE (Wm -2 ) Corr. coef

10 10 Table 2. Point-by-point comparison of derived λ E with observed λ E (Lat, Lon) Grid λ E observed (Wm -2 ) λ E derived (Wm -2 ) λ E derived with φ = 1.26 (Wm -2 ) λ E derived using observed R n-g (Wm -2 ) λ E derived using observed R n-g and φ = 1.26 (Wm -2 ) (36.841N, W) (224, 270) (36.431N, W) (269, 104) (38.306N, W) ( 59, 192) (35.564N, W) (366, 220) (36.061N, W) (311, 28)

11 11 φ min ( NDVI, max min i T i, φi ) Figure 1. φ max ( NDVI, i T i min, φ max i ) Le Jiang and Shafiqul Islam 11

12 12 Figure 2. Le Jiang and Shafiqul Islam 12