Abstract Remote measurements of land surface temperature are prone to significant directional anisotropy. This anisotropy is strong over urban surfaces because of three-dimensional structures and the resulting heterogeneous temperature distributions. However, the development of models that correct urban thermal anisotropy and consider the two factors is rare. In this study, with the assumption of random building orientations, we developed a Geometric model to simulate Thermal Anisotropy over a sparse Urban surface (GUTA-sparse), which does not consider the mutual shadowing effect. GUTA-sparse assumes that anisotropy is the sum of three parts: the vertical wall background temperature contribution, vertical wall orientation effects and shadow contribution. The simulation data provided by the 3-D Discrete Anisotropic Radiative Transfer (DART) model and airborne measurements over the city of Marseille were employed to evaluate model performance. The results show that in this model, the solar zenith angle influences the ability of the fitted coefficients to characterize surface features. GUTA-sparse is applicable over urban surfaces that have aspect ratios smaller than 1.0, where the mutual shadowing effect is negligible. The proposed model can also well simulate the airborne measured anisotropy with root mean square errors (RMSEs) of 0.44, 0.44, 0.56 and 0.40 K, and the anisotropy amplitudes at the four flight times all exceed 8 K. The model is independent of surface parameters that are difficult to obtain, which makes it suitable for remote sensing applications. Because the model is linear with respect to surface parameters, it can be applied to heterogeneous urban surfaces. This model aids in better understanding the relationships among urban surface geometry, component temperatures and thermal anisotropy, and this model may potentially correct the directional temperature values to a common viewing geometry.

中文翻译：

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模拟稀疏城市表面热各向异性的几何模型（GUTA-sparse）

摘要 地表温度的远程测量容易产生显着的方向各向异性。由于三维结构和由此产生的不均匀温度分布，这种各向异性在城市表面上很强。然而，开发校正城市热各向异性并考虑这两个因素的模型是罕见的。在本研究中，假设建筑物方向随机，我们开发了一个几何模型来模拟稀疏城市表面（GUTA-sparse）上的热各向异性，该模型不考虑相互阴影效应。GUTA-sparse 假设各向异性是三部分的总和：垂直壁面背景温度贡献、垂直壁面取向效应和阴影贡献。3-D 离散各向异性辐射传递 (DART) 模型提供的模拟数据和马赛市上空的空中测量被用来评估模型性能。结果表明，在该模型中，太阳天顶角影响拟合系数表征表面特征的能力。GUTA-sparse 适用于纵横比小于 1.0 的城市表面，其中相互阴影效应可以忽略不计。该模型还可以很好地模拟机载实测各向异性，均方根误差（RMSE）分别为0.44、0.44、0.56和0.40 K，四个飞行时间的各向异性幅度均超过8 K。该模型与表面参数无关很难获得，这使得它适用于遥感应用。由于该模型相对于表面参数是线性的，因此它可以应用于异质的城市表面。该模型有助于更好地理解城市表面几何形状、组件温度和热各向异性之间的关系，并且该模型可能会将定向温度值校正为常见的观察几何形状。