Journal of

Hydrology ELSEVIER

Journal of Hydrology 188-189 (1997) 749-778

Estimating land surface albedo in the HAPEX-Sahel southern super-site: inversion of two BRDF models against multiple angle ASAS images M.J. Barnsley a'*, P. Lewis b, M. Sutherland b, J.-P.

Muller c

aDepartment of Geography, University of Wales, Swansea, Singleton Park, Swansea SA2 8PP, UK bRemote Sensing Unit, Department of Geography, University College London, 26, Bedford Way, London WCIH OAP, UK CDepartment of Photogrammetry and Surveying, University College London, Gower Street, London WCIE 6BT, UK

Abstract

The provision of spatially and temporally disaggregated values of albedo is critical to an improved understanding of energy interactions at the Earth surface. Remotely sensed estimates of land surface albedo can best be obtained by inverting models of the Bidirectional Reflectance Distribution Function (BRDF) against bidirectional reflectance factor measurements sampled at different sensor view angles and solar illumination angles. This paper describes the preliminary results obtained using such an approach over the HAPEX-Sahel (Hydrological and Atmospheric Pilot Experiment) southern super-site in Niger. Two BRDF models, one empirical (modified-Walthall) and one semi-empirical (a linear kemel-driven model, employing isotropic, geometric and volume scattering kernels), are inverted analytically against each pixel in a set of co-registered multispectral images acquired by NASA's Advanced Solid-state Array Spectroradiometer (ASAS). The paper describes the methods used to register these images to sub-pixel accuracy, to perform radiometric and first-order atmospheric correction of the data, and to invert the BRDF model against the pre-processed image data to yield spatially referenced estimates of the model parameters and angularly integrated terms related to albedo. Spatial patterns, closely related to variations in land cover type, are clearly evident in these data. It is shown that, in this instance, the simple empirical model provides a better fit to the measured data, particularly at red and near-infrared wavelengths. The poorer performance of the semi-empirical model at this particular study site is discussed in terms of the assumptions that the model makes about energy interaction with the land surface. The impacts of changes in the projected instantaneous field-of-view as a function of sensor view angle and of residual image-to-image mis-registration on the derived BRDF model parameters and estimated albedo values are also examined.

* Corresponding author. 0022-1694/97/$17.00 © 1997- Elsevier Science B.V. All rights reserved PII S0022-1 694(96)03169-1

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1. Introduction Soil-vegetation-atmosphere transfer schemes (SVATs) in general circulation models (GCMs) require information on a range of biophysical properties that control water and energy budgets at the Earth surface: for example, the albedo, leaf area index (LAI), aerodynamic surface roughness length (Z0) and temperature of vegetation canopies and soil (Dorman and Sellers, 1989). Unfortunately, direct measurement of these properties in the field is both labour-intensive and time-consuming. Consequently, in situ data are usually only acquired for a very limited number of point samples in most field measurement programmes. For studies of water and energy budgets at regional and global scales, it is clearly not feasible to provide spatially and temporally disaggregated information using standard measurement techniques. Instead, aggregate values are commonly assigned to broad ecological groups in composite, often generalized, land cover maps (Matthews, 1983; Wilson and Henderson-Sellers, 1985). The relatively poor parameterization of SVATs at these spatial scales therefore remains a barrier to our understanding of the Earth surface processes that they describe and of how changes due to anthropogenic activity can affect climate. In principle, satellite remote sensing provides an alternative means of acquiring information on many of the properties that are relevant to SVATs. Digital remotely sensed images represent a dynamic, synoptic and spatially comprehensive source of information, in contrast with the essentially point-based, often static samples provided by conventional ground survey techniques. However, very few biophysical properties can be measured directly using remote sensing methods. Instead, they must be inferred from measurements of spectral directional radiance using some form of mathematical model, or related to surrogate variables (e.g. land cover) that can be derived more readily from remotely sensed data. The accuracy with which these properties can be inferred is therefore dependent on the quality (validity, appropriateness, accuracy, consistency, etc.) of the models and algorithms used to convert the remotely sensed data into estimates of the surface properties concerned, or on the degree of correlation between the surrogate and target variables, together with the accuracy of any land cover classification involved and the appropriateness of the classes that this defines. The estimation of Earth surface albedo represents a prime example of these problems. The spectral (narrow band) albedo (o0 of a surface can be approximated by:

1 Ii*JiO(0, ~b,0', th')btd/zdth

ct "~ -

71"

(1)

where o is the bidirectional reflectance factor, 0 and 4) are the view zenith and azimuth angles, 0' and $' are the illumination zenith and azimuth angles and/~ = cos 0 (HendersonSellers and Wilson, 1983; Lewis and Bamsley, 1994). A single spectral bidirectional reflectance factor (BRF) measurement recorded by a satellite sensor at any given view angle (including nadir) will normally be an unreliable estimate of the surface spectral albedo because few, if any, Earth surface materials scatter radiation equally in all directions (Kimes, 1983; Kimes and Sellers, 1985; Kimes et al., 1987; Ranson et al., 1991). Thus, to derive accurate estimates of surface spectral albedo, a model is required that describes and accounts for the directional distribution of radiation scattered from the Earth

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surface (formally defined by the Bidirectional Reflectance Distribution Function (BRDF); Nicodemus et al., 1977) the parameters of which can be estimated from a relatively limited (angular) sample of Bidirectional Reflectance Factor (BRF) measurements that can be acquired by airborne or satellite sensors (Goel, 1988; Myneni et al., 1989; Barnsley et al., 1994; Meyer et al., 1995). The accuracy with which albedo can be estimated in this way is therefore strongly dependent on both the validity and utility of the BRDF model used, and the angular distribution of BRF measurements obtained (Bamsley et al., 1994). With respect to the latter, the description of surface reflectance as a function of viewing and illumination angles will inevitably involve both interpolation (between the limited sample of BRF measurements) and extrapolation (to viewing and illumination angles outside the sampled BRF domain). In fact, numerous BRDF models have been developed: recent examples include those by Camillo (1987), Ross and Marshak (1988), Ahmad and Deering (1992), Nilson and Kuusk (1989), Pinty et al. (1989), Pinty et al. (1990), Verstraete et al. (1990) and Liang and Strahler (1993, 1994). These models are physically based; that is, they are based on an understanding of the physical processes by which energy interacts with Earth surface materials for most of the model components. All, however, make a number of simplifying assumptions and approximations to derive a tractable set of mathematical functions that can be used to describe and represent the BRDF. In most cases, it is possible to estimate values for the parameters of these models (which may, in turn, be related to measurable biophysical properties) by inverting the model against a set of bidirectional reflectance factor measurements sampled at a limited number of different sensor view angles and solar illumination angles (Goel, 1988; Pinty and Verstraete, 1991). Due to the relative complexity of these models, inversion is typically achieved using numerical methods. This raises difficulties in an operational context, notably because numerical methods are computationally demanding and because it is not always possible to find a unique solution to the minimization of the error function (Privette et al., 1994). Some of these problems can be overcome by defining the BRDF model as a linear combination of component terms; where the terms describe approximations to, for example, the single-scattered and multiple-scattered contributions from volumetric scattering from a turbid medium, and the influence of geometric shadowing phenomena (Wanner et al., 1995). If the terms can be separated into the product of a single model parameter and a model 'kernel' which depends only on the angles of viewing and illumination, then one can describe such models as linear kernel-driven models. Further assumptions are required to make these so-called 'semi-empirical' models linear, but the resultant models have a number of distinct advantages (Lewis, 1995). One important property of this class of model is that an analytical inversion of the model parameters can be derived from sampled BRDF data, overcoming the problems inherent in the use of numerical inversion of non-linear models (Lewis, 1995). The approach of Roujean et al. (1992) is considered a suitable method for the definition of linear kernel-driven models and, as such, has recently been used by Wanner et al. (1995) to define a suite of models which have the general form: k-N,

p(O,e~,o',~')-- ~ fkkk(O,~,O',e~') kffil

(2)

where Nk is the number of kernels used, f are coefficients defining the weight of each

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kernel and kk is the kernel, a function of viewing and illumination angles (Roujean et al., 1992; Lewis, 1995; Wanner et al., 1995) and where it is understood that the terms k and f vary with respect to wavelength. This approach offers considerable flexibility in terms of defining a model of the BRDF. Note that the parameters used in models such as those described by Roujean et al. (1992) and Wanner et al. (1995) may be functionally related to measurable biophysical parameters, such as LAI, leaf reflectance, soil reflectance, etc. A number of simpler, empirical models has also been developed - the best known being the one developed by Walthall et al. (1985), subsequently modified by Nilson and Kuusk (1989) to satisfy the reciprocity relationship for viewing and illumination angles. In general, empirical models seek to describe, rather than to account for, the shape of the BRDF. Consequently, the parameters of these models are not directly related to identifiable biophysical properties, although it may be possible to establish statistical relationships between them using least-squares regression techniques. Interest in such models stems from their computational simplicity and the fact that they make few, if any, assumptions about the nature of the reflecting surface (Bamsley, 1994). Empirical BRDF models can also usually be inverted analytically (Lewis, 1995; Wanner et al., 1995). One problem with such models, however, is their known weakness in extrapolating reflectance values to viewing and illumination angles larger than those at which the sampled BRF data were acquired. This paper describes the preliminary results obtained using two BRDF models (one empirical, the other semi-empirical, linear, kernel-driven) to derive spatially referenced data sets of the model parameters from multiple-view-angle image data acquired by NASA's ASAS (Advanced Solid-state Array Spectroradiometer) instrument over a small section of the HAPEX-Sahel southern super-site in Niger. These data are subsequently used to calculate the spectral albedo (or, more formally, the spectral directional-hemispherical reflectance) for this area. The study area, which is fairly flat and level, comprises mainly millet crops, with some areas of bare soil/sand, and a sparse covering of trees and bushes. The BRDF models selected for analysis represent two of a number of candidate models being used in this and related work in BRDF modelling and albedo derivation from forthcoming satellite sensor programmes, including ATSR-2 (Along-Track Scanning Radiometer), MODIS (Moderate Resolution Imaging Spectrometer) and MISR (Multi-angle Imaging SpectroRadiometer) on EOS (Earth Observing System), SPOT-4 VEGETATION (Systeme Probatoire pour l'Observation de la Terre) and POLDER (Polarization and Directionality of Reflectance) on ADEOS (Advanced Earth Observation Satellite) (Barnsley et al., 1994; Strahler et al., 1995a, b). The paper also describes the methods used to register the images to sub-pixel accuracy, to perform radiometric and atmospheric correction of the data and to invert the BRDF models against the pre-processed image data to yield estimates of the model parameters. The study complements previous work by Rahman et al. (1993) and, more especially, Cabot et al. (1994). Cabot et al. (1994) used a somewhat more extensive suite of BRDF models (including physically based, semi-empirical and empirical models) applied to ASAS data acquired over an area of intensive agriculture in Arizona, USA. They note that the semi-empirical and empirical models exhibited the best fits to the observed data. The present study effectively extends their analysis in two ways: first, results are presented for a very different physical environment (semi-arid vegetation and sparse crops, as opposed to intensive agricultural farmland); second, the results of the BRDF model

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inversions are presented in the form of images, so that spatial variation in the retrieved model parameter and albedo values can be explored and compared with the distribution of different land cover types evident in the original ASAS images.

2. Description of the ASAS image data set ASAS is a 'pushbroom' sensor (Irons et al., 1991). By pointing the scanner forward, nadir and aft of the aircraft on which it is mounted, it is possible to record images at up to ten different sensor view angles during a single over pass using this instrument (Fig. 1). These are nominally centred on 75 °, 60 °, 45 °, 30 ° and 15 ° forward of the aircraft, nadir (0°), and 15 °, 30 °, 45 ° and 55 ° aft of the aircraft. Note that pixels located away from the centre of the swath are sampled at a sensor view angle different from these nominal values due to the effect of the instrument's 25 ° cross-track field-of-view (FOV). Attitudinal variations in the C-130 aircraft on which ASAS is mounted also introduce perturbations about these nominal angles. The version of the ASAS instrument used here records images in 64 spectral wavebands in the range 400 nm to 1060 ran, each with a spectral resolution of approximately 10 nm (Irons et al., 1991). Three of these have been selected for detailed investigation here, namely Bands 15 (centred on 555 nm; green), 24 (645.6 rim; red) and 45 (862 nm;

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