664 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 42, NO. 3, MARCH 2004 Simulation Study of View Angle Effects on Thermal Infrared Measurements Over Heterogeneous Surfaces Laurent Coret, Xavier Briottet, Yann H. Kerr, Senior Member, IEEE, and Abdelghani Chehbouni Abstract—The issue of deriving cross-scale aggregation rules has been extensively investigated over the last two decades. A widely used approach consists of formulating grid-scale surface radiances using the same equations that govern the patch-scale behavior but whose arguments are the aggregate expressions of those at the patch-scale. This approach derives the area-averaged or effective radiative surface temperature as might be observed using low spatial resolution satellite data. The problem however is that such satellite data exhibit large directional effects and no study has addressed this issue. The present work tackles this problem in the thermal infrared domain. The directional effects are studied by modeling. Thus, an infrared sensor observing a two-dimensional (2-D) heterogeneous plane surface is modeled. The 2-D heterogeneous plane surface is simulated by a grid with two homogeneous elements (vegetation-bare soil). The angular properties of the local surfaces, assumed homogeneous, are calculated by a multiple scattering model. The equivalent angular radiance of the complete heterogeneous scene is then determined by applying the aggregation method. This radiance is very sensitive to the surface heterogeneity, especially when the spatial variation of the surface temperature is significant and when the directional behavior of the surface is non-Lambertian. As a result, an angular variation of 6% on radiance was obtained on a heterogenous surface between a zenith angle of 70 and on-nadir measurements. Index Terms—Change of scale, directional effect, heterogeneity, infrared radiometry. I. INTRODUCTION S URFACE temperature is a key parameter in the study of nat- ural surfaces because it results directly from the energy bal- ance equation. The transport of energy occurs by three types of processes: convection, conduction and radiation. Temperature is a common element among all three but the relationship between temperature and heat transport is different for each process. For example, convective fluxes are linked to a temperature, called the aerodynamic temperature, which when combined with air temperature and a resistance provides an estimate of the surface sensible heat flux [1]. In fact, this temperature intervenes more directly in the surface energy budget and thus constitutes a key parameter. In the case of terrestrial surface, infrared remote sensing mea- surements probably represent the best practical means for ob- serving something near the surface temperature. This is why it Manuscript received January 13, 2003; revised August 25, 2003. X. Briottet are with the Département d’Optique Théorique et Appliquée, Of- fice National d’Études et de Recherches Aérospatiales (ONERA/DOTA), 31055 Toulouse, France. L. Coret, Y. H. Kerr, and A. Chelbouni are with the Centre d’Etudes Spatiales de la Biosphére, Centre National d’Etudes Spatiales (CNES-CNRS-IRD-UPS), 31401 Toulouse Cedex 9, France. Digital Object Identifier 10.1109/TGRS.2003.819443 has often been used to study the variations over time of surface fluxes on a wide range of spatial scales. However, the use of thermal infrared (TIR) satellite data still involves many method- ological and measurement problems, such as the following. • Directional effects must be more accurately known both to evaluate the bias they introduce in the measurements and to use the information they contain. • A good understanding of the effects induced by soil het- erogeneity is required for changes of scale (from field or local scale, for ground measurements for instance, to the “regional” or landscape scale, for airborne or satellite measurements). • The quality of sensible heat flux estimates depends on how well the relations between radiative and aerodynamic tem- peratures on heterogeneous surfaces are known [2] insofar as the turbulent flux equations require the aerodynamic temperature, not the radiative temperature. One method for overcoming the latter problem is to deter- mine the aerodynamic surface temperature analytically. Using a two-layer formulation, this temperature is expressed as a func- tion of the soil, vegetation and air temperatures and the corre- sponding resistances [3]–[5]. However, the temperatures of each surface element (soil and vegetation) are not directly accessible by remote sensing. A number of radiometric models have been developed [6]–[12] to separate the contributions of each component of the heterogeneous surface (ground, vegetation) using angular measurements in the thermal infrared. Interest in multidirec- tional IRT measurements should increase when data from the Advanced Along Track Scanning Radiometer (AATSR) instru- ment, aboard the Environment Satellite (ENVISAT) become available (and also with the ATSR Along Track Scanning Radiometer European Remote Sensing Satellite (ERS-1) [13]). When the observed surface is heterogeneous, the total sur- face temperature has a directional character. The impact of the heterogeneities on this temperature and especially on the signal measured, i.e., directional radiance, is not well known. Our objective is the development of a radiative transfer model for complex surfaces (in particular, with relief) for a better un- derstanding of the signal measured by an infrared instrument in the case of a heterogeneous surface. Until now, this ques- tion was not studied in detail, except for homogeneous surfaces. To improve our comprehension, we set up a field measurement campaign to investigate directional effects over heterogeneous surfaces in the infrared. The present study was undertaken in preparation of this experimentation. For a better comprehension of heterogeneous surfaces, it is necessary to use a large viewing angle. Indeed, for complex sur- faces, in particular with relief (topography or roughness effects), 0196-2892/04$20.00 © 2004 IEEE