temperatures of hot and cold pixels and available energy of the hot pixel. Results of domain dependence show that the mean absolute percentage difference ...
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, D21107, doi:10.1029/2011JD016542, 2011
How sensitive is SEBAL to changes in input variables, domain size and satellite sensor? Di Long,1 Vijay P. Singh,1,2 and Zhao‐Liang Li3,4 Received 8 July 2011; revised 12 September 2011; accepted 14 September 2011; published 10 November 2011.
[1] Estimation of evapotranspiration (ET) over large heterogeneous areas using numerous satellite‐based algorithms is increasing; however, further analysis of uncertainties is limited. The objective of this study was to evaluate impacts of varying input variables, size of the modeling domain, and spatial resolution of satellite sensors on sensible heat flux (H) estimates from the Surface Energy Balance Algorithm for Land (SEBAL). First, sensitivity analysis of SEBAL is conducted by varying its input variables using Moderate Resolution Imaging Spectroradiometer (MODIS) data for 29 cloud‐free days in 2007 covering the Baiyangdian watershed in North China. Domain dependence of the H estimates is quantified by estimating H for subwatersheds of different sizes and the entire watershed using MODIS data for 4 cloud‐free days in May 2007. Landsat Thematic Mapper (TM) and MODIS based H estimates are compared to evaluate the effect of spatial resolution of satellite sensors. Results of sensitivity analysis indicate that the H estimates from SEBAL are most sensitive to temperatures of hot and cold pixels and available energy of the hot pixel. Results of domain dependence show that the mean absolute percentage difference (MAPD) and root mean square deviation (RMSD) in the H estimates between different domain sizes up to 53.9% and 75.7 W m−2, respectively. Although areally averaged H estimates from MODIS and Landsat TM sensors are similar, the MODIS‐based H estimates show an RMSD of 52.3 W m−2 and a bias of 26.5 W m−2 relative to Landsat TM‐based counterparts. Unlike other models, the standard deviation of H estimates from SEBAL using high spatial resolution images can be smaller than that using low spatial resolution images. Furthermore, H estimates from the input upscaling scheme (aggregating input variables) are generally consistent with those from the output upscaling scheme (aggregating the output) for the same sensor, given similar differences between hot and cold pixels for low and high spatial resolution. The resulting H flux and ET estimates from SEBAL can therefore vary with differing extreme pixels selected by the operator, domain size, and spatial resolution of satellite sensors. This study provides insights into various factors that should be considered when applying SEBAL to estimate ET and helps correctly interpret the SEBAL outputs. Citation: Long, D., V. P. Singh, and Z.‐L. Li (2011), How sensitive is SEBAL to changes in input variables, domain size and satellite sensor?, J. Geophys. Res., 116, D21107, doi:10.1029/2011JD016542.
1. Introduction [2] Combined with rainfall and runoff, evapotranspiration (ET), a critical component of the hydrologic cycle, determines the availability of water on the Earth’s surface [McCabe and Wood, 2006]. Traditionally, measurements of ET have been at local, field, and landscape scales, e.g., weighing lysimeter, Energy Balance Bowen Ratio (EBBR), 1 Department of Biological and Agricultural Engineering, Texas A&M University, College Station, Texas, USA. 2 Department of Civil and Environmental Engineering, Texas A&M University, College Station, Texas, USA. 3 LSIIT, UdS, CNRS, Illkirch, France. 4 State Key Laboratory of Resources and Environment Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, China.
Copyright 2011 by the American Geophysical Union. 0148‐0227/11/2011JD016542
and eddy covariance techniques [Twine et al., 2000]. However, such measurements cannot be directly extrapolated to large‐scale ET due to natural heterogeneity of the land surface and complexity of hydrologic processes [Bastiaanssen et al., 2005]. This inability impedes water budget calculations and hydrologic modeling at large scales. A common procedure to estimate ET is based on reference ET, soil moisture reduction, and crop coefficients using the standardized Penman‐Monteith equation (FAO56 equation [Allen, 2000]). It requires information on crop types, growth stages, and field management, thereby highlighting the of ET estimation on excessive ground‐based data. Satellite techniques provide an opportunity to estimate ET at a variety of spatial and temporal scales [Kalma et al., 2008; Li et al., 2008]. Visible, near‐infrared, and thermal infrared band information can be converted into a variety of critical surface and atmospheric variables, such as land surface temperature (LST), Vegetation Index (VI), and atmospheric temperature. These variables
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then serve as inputs to simulate surface fluxes and ET based on the energy balance equation [e.g., Norman et al., 1995; Su, 2002] or by interpreting the LST/VI triangle space [e.g., Nishida et al., 2003]. These satellite‐based approaches do not require information on precipitation and subsurface soil texture or other complex hydrologic processes [Anderson et al., 2007]. [3] The Surface Energy Balance Algorithm for Land [SEBAL; Bastiaanssen et al., 1998a, 1998b] was designed to simulate surface fluxes by incorporating remotely sensed variables and a minimum of ground‐based data. This model has been widely used for estimation of water consumption by natural vegetation and agricultural crops, crop water productivity, and water depletion in a river basin, optimization of irrigation schedules, and assisting in water resources management [Allen et al., 2007; Bastiaanssen et al., 2005]. In hydrologic and atmospheric modeling, SEBAL‐based ET can be utilized to quantify the impact of expanding irrigated agriculture on the regional water balance [Teixeira et al., 2009] and to improve spatial representation of water balance components in hydrologic models [Immerzeel and Droogers, 2008; Schuurmans et al., 2003]. Bastiaanssen et al. [2005] summarized the overall accuracy of SEBAL‐ based ET estimates in terms of its application in more than 30 countries to a variety of climates and ecosystems at different spatial scales. They asserted that for a range of soil wetness and plant community conditions, typical accuracy at the field scale was 85% for 1 day and it increased to 95% on a seasonal or annual basis [Bastiaanssen et al., 2010]. [4] SEBAL is based on a set of formulas involved in each component of the energy balance equation. How different variables/parameters in these equations interact with each other and vary with the domain scale would largely determine the mechanisms of error propagation and the magnitudes of errors in the resulting surface flux estimates. The domain scale is defined here as the actual size of the modeling domain/satellite imagery being used. The domain dependence is referred to as the dependence of the magnitude and distribution of output from a model on the domain scale. SEBAL assumes the difference between the aerodynamic temperature and the air temperature to be linearly proportional to LST. The linear coefficients should be derived from so‐called hot pixel and cold pixel selected by the operator from satellite images. The selection procedure is, however, subjective [Gao et al., 2008; Timmermans et al., 2007; Winsemius et al., 2008]. Performance of SEBAL may depend on the domain scale, if the two extreme pixels differ with varying domain scales. First, varying spatial coverage and quality of satellite images available for the domain of interest may result in varying extreme temperatures and resultant ET estimates. For instance, contamination with clouds blurs or obstructs portions of an image, potentially reducing the domain of interest and shrinking the range of LST. Selection of the cold pixel should be largely impacted by clouds because the cloud pixel is likely to be incorrectly interpreted as the cold pixel [Gao et al., 2008; Marx et al., 2008]. Even though images for absolute clear skies are available, the resulting heat flux estimates would vary with the actual size of images being used. One would derive a subset of an image specifically for a study site, take the entire scene of the image, or even merge multiple scenes of images. This means that varying sizes of images would be used
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because of the placement of a study watershed/region in different hierarchical river basin systems. In this case, locations and corresponding physical and geomorphological features of extremes would probably be different. [5] Second, pixels satisfying the assumptions in SEBAL depend on surface hydrologic contrasts (dry and wet land surface types) that may vary substantially with the study area of interest [French et al., 2005]. It is, however, difficult to properly select pixels representing the extreme hydrologic conditions hypothesized in SEBAL; improper selection may cause large uncertainties in the resulting surface flux estimates [Bastiaanssen et al., 2010; Long and Singh, 2010; Singh et al., 2008; Timmermans et al., 2007]. For instance, if a study site is primarily characterized by crops or vegetated areas, the possibility of the presence of a hot pixel with negligible latent heat flux (LE) in an image would be greatly reduced. Likewise, for a study site where bare soil surfaces or impervious areas are prevalent, the likelihood that a cold pixel with negligible sensible heat flux (H) could be successfully identified would be decreased. However, uncertainties resulting from domain dependence of SEBAL have not yet been systematically quantified. [6] Satellite‐based ET algorithms are typically developed and tested at the resolution scale of a certain sensor based on the assumption of homogeneity within the pixel resolution. Here, the resolution scale is defined as the spatial resolution of satellite imagery being employed. Likewise, the resolution dependence is referred to as the dependence of the magnitude and distribution of output from a model on the resolution scale. There is a tendency to directly apply the algorithms developed at a finer scale to a coarser scale [Gebremichael et al., 2010]. For instance, SEBAL was first developed and tested at the resolution scale of Landsat Thematic Mapper (TM) images; however, it was asserted that the model can handle thermal infrared images at resolutions between a few meters to a few kilometers [Bastiaanssen, 1995; Bastiaanssen et al., 1998a], and has been applied to a variety of satellite platforms, e.g., Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Gebremichael et al., 2010], Advanced Very High Resolution Radiometer (AVHRR) [Bastiaanssen et al., 2002; Bastiaanssen and Chandrapala, 2003], and Moderate‐resolution Imaging Spectroradiometer (MODIS) [Compaore et al., 2008; Kongo and Jewitt, 2006]. A noteworthy issue is how do surface flux estimates using SEBAL differ with varying resolutions of satellite sensors? Resolution dependence of a model results mostly from the resolution of inputs; uncertainty in model outputs is propagated in a large part by the resolution of inputs rather than the model physics. However, uncertainty due to the resolution dependence of SEBAL may also result in alteration of model physics by changing coefficients a and b in computing H. [7] There have been significant studies on resolution dependence of satellite‐based ET models, e.g., Two‐source Energy Balance (TSEB) [Norman et al., 1995] and Surface Energy Balance System (SEBS) [Su, 2002] across a variety of satellite platforms, e.g., Landsat TM/ETM+, ASTER, and MODIS [Brunner et al., 2008; Kustas et al., 2004; Li et al., 2008; McCabe and Wood, 2006]. These studies provide insights into variations in ET retrievals at varying resolutions and are greatly helpful in building an understanding of heterogeneity involved in coarse resolution image‐based ET retrievals. Allen et al. [2007] proposed the Mapping
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Evapotranspiration at high Resolution with Internalized Calibration (METRIC) model, in which the key component for computing H inherits substantially from SEBAL. However, only a few published studies have addressed domain and resolution dependencies of SEBAL/METRIC, and they have not restrained the misuse of these models in operational ET estimation. [8] Sensitivity analysis is helpful for identifying the most sensitive variables/parameters for quantifying model uncertainty, and consequently provides valuable insights into the degree of effort that should be expended to constrain errors of a model. If the sensitive variables of a model are domain‐ and/or resolution‐ dependent, variations in the model outputs at a variety of scales should be quantified. The H scheme appears to be the most critical component in approaches of computing LE as a residual term of the energy balance equation. However, sensitivity of H estimates from SEBAL to model inputs has not yet been fully examined. [9] Wang et al. [2009] performed a sensitivity analysis of SEBAL on full, half, and sparse cover conditions. We suggest that application of SEBAL does not depend on cover conditions and land use types; the three cover conditions, in fact, only provide three initial value conditions for running the model. A more generalized sensitivity analysis of SEBAL can be achieved by varying inputs under a wider range of initial value conditions. Marx et al. [2008] performed an uncertainty analysis of SEBAL‐based H estimates using Gaussian error propagation, indicating that the computed total relative uncertainty in H ranged from 15 to 20% for two study sites in the central part of West Africa. Nevertheless, they did not quantify influences of the selection of extremes. [10] The objective of this study was to quantify the sensitivity of H estimates from SEBAL to various input variables, domain size, and spatial resolution of satellite images. A detailed sensitivity analysis of the H algorithm of SEBAL was first performed, on the basis of which we performed a systematic investigation into domain and resolution dependencies of SEBAL by applying it to the Baiyangdian watershed in North China and its subwatersheds, and to Landsat TM and MODIS satellite sensors. This study differs from the previous studies in the integration of sensitivity analysis with domain and resolution dependencies. Results of this study should provide a more comprehensive understanding of critical variables for estimating surface fluxes using SEBAL and identify any domain or resolution dependencies of the H estimates.
2. Methods 2.1. Theoretical and Computational Basis of SEBAL [11] SEBAL computes LE as the residual term of the energy balance equation: Rn ¼ G þ H þ LE
ð1Þ
where Rn denotes the instantaneous (typically at the satellite overpass time) net radiation (W m−2) and G denotes the soil heat flux (W m−2). Rn and G are calculated using remotely sensed albedo, LST, surface emissivity, Normalized Difference Vegetation Index (NDVI), and few meteorological data (air temperature, T a, and vapor pressure, ea). The novel component of SEBAL is the H parameterization scheme.
[12] SEBAL assumes the difference between T a at the reference height and the aerodynamic temperature to be linearly related to LST, thereby obviating the need for aerodynamic temperature that is not readily available through conventional methods. Coefficients of the linear relationship are determined by two pixels with extreme hydrologic conditions, termed the hot pixel and the cold pixel, visually identified by the operator from maps of LST and NDVI, and/or LST and albedo [Folhes et al., 2009; Timmermans et al., 2007], and from knowledge on local conditions. For the hot pixel, LE is taken to be zero; thus H for the hot pixel is equal to its available energy. For the cold pixel, H is taken to be zero and LE for the cold pixel is equal to the available energy. H ¼ cp
dT ðaTs þ bÞ ¼ cp rah rah
ð2Þ
where r is the air density (kg m−3); cp is the specific heat of air at constant pressure (J kg−1 K−1); dT is the difference between T a and aerodynamic temperature (K); a (dimensionless) and b (K) are the linear regression coefficients that are scene‐ specific; T s is the LST (K), which should be corrected for altitudinal variations; and rah is the aerodynamic resistance for heat transfer (s m−1), which is a function of friction velocity u* (m s−1) and stability correction factors for momentum and heat transfer y m (dimensionless) and y h (dimensionless): 200 y mð200Þ u* ¼ ku200 = ln zom
ð3Þ
1 z2 ln rah ¼ y hð2Þ þ y hð0:1Þ z1 ku*
ð4Þ
where k is the von Karman constant (0.41); u200 is the wind velocity (m s−1) at an assumed blending height (200 m) where the influence of local‐scale surface heterogeneity on atmospheric turbulence is relatively unimportant; u200 can be inferred using wind velocity at a certain height observed at weather stations; and zom is the roughness length for momentum transfer (m), which can be related to NDVI [Bastiaanssen, 2000]. [13] A reference height z2 (at 2 m) for the upper limit of integration for rah is chosen in SEBAL. The roughness length for heat transfer z1 or zoh (m) involved in other surface flux models is replaced by a fixed value of 0.1 m as the lower limit of integration for rah in SEBAL [Bastiaanssen et al., 2002, 2005]. Embedded in the SEBAL algorithm are assumptions about the behavior of zoh. Any impacts of non‐uniform zoh across a landscape that do not scale linearly with LST are ignored by SEBAL. It is noted that there is also another parameterization of rah in SEBAL, in which a kB−1 parameter (=ln(zom /zoh)) with a fixed value of 2.3 is introduced by taking zoh as a fixed fraction (0.1) of zom [Bastiaanssen, 2000; Kalma et al., 2008; Timmermans et al., 2007]. [14] y m and y h are functions of z/L, where L is the Monin‐ Obukhov length:
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L¼
cp u3* Tv kgH
ð5Þ
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If L < 0, the lower atmospheric boundary layer is unstable and the stability correction factors can then be calculated as follows y mð200Þ
! 1 þ x2ð200Þ 1 þ xð200Þ 2 arctan xð200Þ þ ¼ 2 ln þ ln 2 2 2
ð6Þ
y hð2Þ ¼ 2 ln
y hð0:1Þ ¼ 2 ln
1 þ x2ð2Þ
! ð7Þ
2 1 þ x2ð0:1Þ
! ð8Þ
2
z 0:25 x ¼ 1 16 L
ð9Þ −2
where g is the gravitational acceleration (9.8 m s ), and T v is the virtual temperature (K), which could be replaced by T s in calculation as was done in METRIC [Allen et al., 2007]. Subscripts 200, 2, and 0.1 of x in equations (6)–(8) denote the corresponding z values (m) in equation (9). [15] If L > 0, the lower atmospheric boundary layer is stable and the stability correction factors can then be expressed as 2 y mð200Þ ¼ 5 L
y hð2Þ ¼ 5
y hð0:1Þ
2 L
0:1 ¼ 5 : L
ð10Þ
ð11Þ
ð12Þ
[16] In terms of the assumption regarding the hot and cold pixels, coefficients a and b in equation (2) can be expressed as a¼
rah;hot Rn;hot Ghot hot cp Ts;hot Ts;cold
rah;hot Rn;hot Ghot Ts;cold b¼ hot cp Ts;hot Ts;cold
ð13Þ
ð14Þ
where rah,hot is the aerodynamic resistance for heat transfer for the hot pixel; Rn,hot and Ghot are the instantaneous net radiation and soil heat flux for the hot pixel, respectively; T s,hot and T s,cold are the LST for the hot and cold pixels, respectively; and rhot is the air density of the hot pixel. [ 17 ] Because L is a function of H, equations (2)–(14) require an iterative loop to solve for the implicit presence of H in u* (through y m(200)) and rah (through y h(2) and y h(0.1)). First, the stability correction factors are assumed to be zero and the first approximation of H is calculated. Second, the first approximation of H is used to calculate the stability factors and then a second approximation of H is obtained. These steps are repeated iteratively until coefficients a and b
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converge. In this study, the iterative process was terminated when the absolute values of the differences between the last two estimates of a, b, and H over the previous estimates were
