A remote sensing surface energy balance algorithm for land (SEBAL). 1. Formulation
Introduction
Land surface processes are of paramount importance for the re-distribution of moisture and heat in soil and atmosphere. The exchanges of radiative, heat and moisture fluxes affect the biosphere development and physical living conditions on earth. The thermo-dynamic equilibrium between turbulent transport processes in the atmosphere and laminar processes in the sub-surface manifests itself in the land surface energy balance, which reads as
Where Q* is net radiation, G0is soil heat flux, H is sensible heat flux and λE is latent heat flux. The sign convention of Eq. (1) is that Q* is considered positive when radiation is directed towards the surface, while G0, H and λE are considered positive when directed away from the land surface. Eq. (1) neglects the energy required for photosynthesis and the heat storage in vegetation. Time integrated values of latent heat flux, λE, are important for different applications in hydrology, agronomy and meteorology. Numerical models for crop growth (e.g. Bouman et al., 1996), watersheds (e.g. Famigliette and Wood, 1994), river basins (e.g. Kite et al., 1994) and climate hydrology (e.g. Sellers et al., 1996) can contribute to an improved future planning and management of land and water resources. The number of these distributed hydrological models and land surface parameterization schemes for climate studies is still growing, while research on techniques as to how to verify model predicted energy balances and evaporation at the landscape and continental scale remains an underestimated issue. Hence, a serious question in regional evaporation studies needs to be addressed: How can regional evaporation predicted by simulation models be validated with limited field data and can remote sensing help this verification process?
Remote sensing data provided by satellites are a means of obtaining consistent and frequent observation of spectral reflectance and emittance of radiation of the land surface on micro to macro scale. Overviews on retrieving evaporation from these spectral radiance’s have been presented by Choudhury (1989); Schmugge (1991); Moran and Jackson (1991); Menenti (1993); Kustas and Norman (1996) and Bastiaanssen (1998). Classical remote sensing flux algorithms based on surface temperature measurements in combination with spatially constant other hydro-meteorological parameters may be suitable for assessing the surface fluxes on micro scale (e.g. Jackson et al., 1977), but not for meso and macro scale. Hence, more advanced algorithms have to be designed for composite terrain at a larger scale with physio-graphically different landscapes. Most current remote sensing flux algorithms are unsatisfactory to deal with practical hydrological studies in heterogeneous watersheds and river basins, because of the following common problems:
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As a result of spatial variations in land use, land cover, soil physical properties and inflow of water, most hydro-meteorological parameters exhibit an evident spatial variation, which cannot be obtained from a limited number of synoptic observations.
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Availability of distributed in-situ measurements of solar radiation, air temperature, relative humidity and wind speed during satellite overpass is restricted. Some remote sensing flux algorithms require reference surface fluxes which are only measured during dedicated field studies.
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The performance of remote sensing flux algorithms in heterogeneous terrain is difficult to quantify. Large scale experimental studies towards the area-effective surface energy balances fail even with 20 flux stations to assess the distributed and area-effective fluxes (e.g. Pelgrum and Bastiaanssen, 1996).
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Remote sensing observations provide basically an instantaneous ‘snapshot’ of the radiative properties of the land surface. A general framework to justify a daytime integration of surface fluxes from instantaneous observations is usually lacking.
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The required accuracy of aerodynamic surface temperature (±0.5 K) to calculate the sensible heat flux from remotely sensed radiometric surface temperature and synoptic air temperature can hardly be met (e.g.Brutsaert et al., 1993).
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A proper quantification of the surface roughness for heat transport from the surface roughness for momentum transport seems only feasible if supported by local calibrations (e.g. Blyth and Dolman, 1995). This correction is required for converting the remotely sensed radiometric surface temperature to aerodynamic temperature (e.g. Norman and Becker, 1995; Troufleau et al., 1997).
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The spatial scales of remote sensing measurements do not necessarily commensurate with those of the processes governing surface fluxes (e.g. Moran et al., 1997).
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Intra-patch advection cannot be accounted for as the surface fluxes are schematised to be vertical.
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Several remote sensing algorithms are often used in conjunction with data demanding hydrological and Planetary Boundary Layer models, which makes an operational application at regional scales cumbersome (e.g. Taconet et al., 1986; Choudhury and DiGirolamo, 1998).
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Information on land use types for the conversion between surface temperature to an expression of latent heat flux (e.g. Nieuwenhuis et al., 1985;Sucksdorff and Ottle, 1990) or for the ascription of hydro-meteoroglogical parameters (e.g. Taylor et al., 1997) are sometimes required. These methods are less suitable for sparse canopies and landscapes with an irregular geometry and complex structure.
To overcome most of these problems, a physically based ‘multi-step’ Surface Energy Balance Algorithm for Land (SEBAL) has been formulated (Bastiaanssen, 1995). SEBAL uses surface temperature T0, hemispherical surface reflectance, r0 and Normalized Difference Vegetation Index (NDVI), as well as their interrelationships to infer surface fluxes for a wide spectrum of land types. A conceptual scheme of SEBAL is presented in Fig. 1. SEBAL describes λE as the rest term of the instantaneous surface energy balance, λEWhere r0 is the hemispherical surface reflectance, K↓ (Wm−2) is the incoming solar radiation, ε′2 is the apparent thermal infrared emissivity of the atmosphere, ϵ0 is the surface thermal infrared emissivity, T0(K) is the radiometric surface temperature, G0(Wm−2) the soil heat flux, z0m(m) the surface roughness length for momentum transport, kB−1 the relationship between z0m and the surface roughness length for heat transport, u*(ms−1) the friction velocity, L(m) the Monin–Obukhov length and δTa(K) is the near-surface vertical air temperature difference. The (x,y) notation denotes that a particular parameter is variable in the horizontal space domain with a resolution of one pixel. The parameter is considered to be spatially constant if the (x,y) notation is not mentioned explicitly.
Section snippets
Hemispherical surface reflectance, r0(x,y)
Registrations of in-band reflected radiation at the top of atmosphere K↑TOA(b) by operational earth observation satellites are usually acquired from a single direction. Corrections for atmospheric interference are generally based on detailed information on the state of the atmosphere (temperature, humidity and wind velocity at different altitudes), as extracted from radiosoundings. If this data is not available, the hemispherical surface reflectance r0 may be obtained from the broadband
Net radiation
Net radiation Q* (x,y) is calculated from the incoming and outgoing all wave radiation fluxeswhere L↓ is the downwelling long wave radiation and L↓(x,y) is the upwelling long wave radiation. As SEBAL is only meant for cloud free conditions, techniques to assess the degree of cloudiness from remote sensing measurements are not included in the list of equations provided with Appendix A. Solar radiation K↓ is computed according to the zenith angle of each
Soil heat flux
Many studies have shown that the midday G0/Q* fraction is highly predictable from remote sensing determinants of vegetation characteristics such as vegetation indices and LAI (see Daughtry et al., 1990, for a review). The G0/Q* approach fails, however, in sparse canopies, because heat transfer into the soil is becoming a more significant part of the net radiation if soils are bare and dry. An improved version of G0/Q* based on radiometric surface temperature T0 is therefore proposed later.
Momentum flux
The relationship between momentum σ, sensible H and latent λE heat fluxes can be demonstrated easily by:where ρa (kg m−3) is the moist air density, cp (J kg−1 K−1) the air specific heat at constant pressure, u*(ms−1) the friction velocity, T* (K) the temperature scale and q* the humidity scale. Appendix B elaborates the computation of the momentum flux in a tabular format.
Sensible and latent heat fluxes
At wet surfaces where water vapour is released with a rate determined by the atmospheric demand, the vertical difference in air temperature δTa is reduced to a minimum. A downward sensible heat flux to the ground arises if evaporation cools the air, a phenomenon known as ‘advection entrainment’ (McNaughton, 1976). Kalma and Jupp (1990) and Gay and Bernhofer (1991) conducted measurements above wet surfaces under arid conditions, which showed that Ta can exceed T0 by several degrees during
Summary
Net radiation is obtained from distributed hemispherical surface reflectance and surface temperature data in combination with spatially variable zenith angles to account for variable incoming short wave radiation values. Soil heat flux is obtained from an empirical soil heat flux/net radiation fraction that accounts for the phase difference between soil heat flux and net radiation arising during a daytime cycle. Surface temperature is included in the parameterization for soil heat flux to
Conclusions
Contrary to the findings of Hall et al. (1992), realistic H-fluxes can be derived from thermal infrared remote sensing measurements. The solution lies essentially in deducing δTa from a predefined value of kB−1 together with H of non-evaporating land surfaces. It is suggested that this has more potential than calibrating kB−1 for a unique combination of T0, Ta and H. This is considered to be an improvement in assessing the spatial variation of H because the spatial variation of z0h(x,y) is much
Acknowledgements
The authors are indebted to Mrs. Mieke van Dijk for her skilful help in preparing the electronic manuscript. The assistance of Mr. Bram ten Cate in the organisation of the final editing is acknowledged. The helping hand of Dr. Jim Lenahan of the International Water Management Institute at Colombo, Sri Lanka is respectfully appreciated.
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