Measurements of land surface temperature (LST) performed in the thermal infrared (TIR) domain are prone to strong directional anisotropy. Instead of detailed analytical physical TIR models requiring too much input information and computational capacities, simplified parametric approaches capable to mimic and correct with precision the angular effects on LST will be deemed suitable for practical satellite applications. In this study, we present a simple two parameters model, so-called RL (Roujean-Lagouarde), which shows capabilities to properly depict the directional signatures of both urban and vegetation targets within an accuracy better than 1 °C. This latter value is the RMSE (root mean square error) obtained as the best adjustment of the RL model against in situ datasets. Then the RL approach was compared to a synthetic dataset generated by the model Soil Canopy Observation, Photochemistry and Energy fluxes (SCOPE) in which large variability in meteorological scenarios, canopy structure and water status conditions was accounted for. Results indicate RMSE ≤0.6 °C which is a very hopeful result. Besides, the RL model performs even better than the popular parametric model of Vinnikov that encompasses two unknowns. The ability of RL model to better reproduce the hotspot phenomenon explains this feature.
The RL model appears as a potential candidate for future operational processing chains of TIR satellite data because it fulfills the requirements of both simple analytical formulation and limited number of input parameters. Efforts nevertheless remain to be done on inversion methodologies.
Thermal infrared (TIR) measurements are widely used to retrieve land surface temperature (LST) which is a useful proxy to derive surface fluxes, especially evapotranspiration. However these measurements are prone to strong directional anisotropic effects. Those can be defined as the difference between off-nadir and nadir temperatures. Such difference can reach up to 15 °C according to various authors (Kimes and Kirchner, 1983; Lagouarde et al., 2014).
Efforts have been made in the past to model the TIR radiation anisotropy in following geometric, radiative transfer, 3-dimensional and parametric approaches. A review can be found in Verhoef et al. (2007). Duffour et al. (2015b) recently demonstrated the ability of the Soil-Vegetation-Atmosphere Transfer (SVAT) model SCOPE (Van der Tol et al., 2009) which combines a detailed description of both physical and physiological processes to simulate TIR directional anisotropy. Actually, TIR data processing is in need of simple models for several purposes. First reason is to be able to correct TIR remote sensing data from directional effects using a fast and computationally efficient method. For such, one must only consider algorithms (i) requiring a few input data and (ii) being analytically interpretable for ease of implementation into operational satellite data processing chains. Secondly, simple models are very helpful for a rapid assessment of the impact of the angular sampling, which is particularly relevant for the design of experimental campaigns with the concern of optimizing the instrumental protocol.
Simple parametric models are attractive in many ways. Because of their limited number of input parameters, the inversion procedure is more certain. Another asset is that they can be relevant at any spatial scale, in particular when linearity of the model is possible. Moreover, parametric models may be more robust to measurement noise compared to deterministic models which are affected by the cumulative uncertainties of the large input datasets they require. Parametric models can be totally empirical or based on physical assumptions. Although parametric models are widely used to correct optical BRDF (Bi-directional Reflectance Distribution Function), such an approach has not yet been developed so far to process and analyze TIR data. One limitation however would be the prescription of a priori values for the input parameters, unless their physical meaning may be well determined through field experiments for instance.
When approaching TIR satellite measurements through modeling, a primary assumption is that any sensor pixel is the sum of dissociated elementary photometric quantities. These latter can be further modeled as a linear combination of mathematical functions sketched by kernels being trigonometric functions of the geometry of observation. In the optical domain, the kernel approach has been successful to mimic the BRDF (Wanner et al., 1995; Jupp, 2000; Bréon et al., 2002; Vermote et al., 2009). In the TIR domain, it has been applied to simulate the directional anisotropy of surface emissivity (Snyder and Wan, 1998; Su et al., 2002). In order to model the radiation anisotropy on TIR signal and further on temperature from geostationary satellites observations, Vinnikov et al. (2012) developed a parametric model of TIR anisotropy based on only two kernels.
Generally speaking, the solution to the inverse problem may be obtained by generating first Look Up Tables (LUTs) issued from simulations of a sophisticated TIR model, at the cost of some training for initiate some machine learning. Even so, and to our knowledge, this possibility has not been evaluated yet in the TIR domain. However, in the context of remote sensing applications, the robustness of the solution is indeed a real concern in order to comply with possibly noisy and sparse observations.
This justifies for another approach here consisting in the derivation of analytical expressions departing from simplified assumptions on the physics. For instance Roujean (2000) and Bréon et al. (2002) have proposed two models of hot spot simplifying the radiative transfer processes inside canopies for optical remote sensing applications. In the TIR, Lagouarde and Irvine (2008) adapted the Roujean (2000) model to derive a parametric expression of directional anisotropy requiring two parameters only to be known or adjusted. A first favorable test was obtained against experimental measurements acquired over an urban canopy. The simplicity of the model makes it very attractive to characterize the directional anisotropy.
Nevertheless it still requires to be extensively evaluated. Such is the goal of this paper. In a first section, the model will be described and its ability to simulate DA over vegetation demonstrated. The scarcity of available experimental DA datasets providing both azimuth and zenith angular information led us to assess the reliability of the model in a second step by testing it against a synthetic dataset generated by a deterministic model, SCOPE. Here, SCOPE is used as a data generator, for a large range of realistic conditions that can be met: structure of the canopy, water status, meteorological forcing. A third section finally proposes a comparison with the Vinnikov's approach which was considered to correct satellite data for DA effects. Since to our knowledge, Vinnikov's model has no equivalent so far, the mutual assets of both approaches for remote sensing applications are further discussed.