Abstract Thermal anisotropy is an important phenomenon in thermal infrared remote sensing as it restricts the retrieval accuracy of surface longwave radiation (SLR). Topography is an essential controlling factor for the directionality of SLR for high-relief regions (e.g., mountain regions) where there is land surface heterogeneity and non-isothermal properties at pixel scales. However, satellite sensors can only receive radiance from a specific surface object at a small number of simultaneous viewing angles, which makes the quantitative modeling of thermal anisotropy challenging. Therefore, we developed the topographic longwave radiation model (TLRM) to describe the directionality of SLR components taking into account the variability of both subpixel topography and thermal anisotropy in high-relief regions. The reliability of TLRM was validated using the Discrete Anisotropic Radiative Transfer (DART) model over two typical geomorphic areas: a valley scene and a peak scene. The preliminary validation shows good agreement in terms of surface upward longwave radiance, which confirms the potential of TLRM for capturing the anisotropic patterns of land surfaces. The radiance values simulated by the DART model were first revised for the spectral mismatch. Then, they are used to correct residual deviation for TLRM using linear regressions. The root mean square error (RMSE) and coefficient of determination (R2) were 0.830 W/(m2 ∙ sr) and 0.746 for the valley scene, respectively, and 0.239 W/(m2 ∙ sr) and 0.711 for the peak scene, respectively. Compared with TLRM, models that do not consider terrain effects generate significant discrepancies in high relief SLR components. The differences in downward longwave radiation can reach −60 W/m2 in valleys without considering terrain effects. Based on the reference of hemispherical upward longwave radiation, surface upward longwave radiation estimated by the direct estimation method had a bias of 11.41 W/m2 and standard deviation (STD) of 7.30 W/m2, while the directional upward longwave radiation had a bias of 5.99 W/m2 and STD of 4.08 W/m2, showing lower estimation variation. The discrepancy between surface net longwave radiation (NLR) and terrain-corrected NLR ranged between 50 and −130 W/m2 with clear negative biases mainly occurring in valleys. With higher spatial resolutions of remotely sensed imagery, the influence of complex terrain on land surface radiative flux has become more significant. This parameterization scheme is expected to better represent the topographic effects on SLR, enhance understanding of thermal anisotropy in non-isothermal mixed pixel areas of high relief, and improve the inversion accuracy of SLR.

中文翻译：

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模拟高起伏地形上的表面长波辐射

摘要 热各向异性是热红外遥感中的一个重要现象，它限制了地表长波辐射（SLR）的反演精度。对于在像素尺度上存在陆面异质性和非等温特性的高地貌区域（例如山区），地形是 SLR 方向性的重要控制因素。然而，卫星传感器只能以少量的同时视角接收来自特定表面物体的辐射，这使得热各向异性的定量建模具有挑战性。因此，我们开发了地形长波辐射模型 (TLRM) 来描述 SLR 组件的方向性，同时考虑到高浮雕区域中亚像素地形和热各向异性的可变性。TLRM 的可靠性使用离散各向异性辐射传输 (DART) 模型在两个典型地貌区域进行验证：山谷场景和峰值场景。初步验证在地表向上长波辐射方面显示出良好的一致性，这证实了 TLRM 在捕获地表各向异性模式方面的潜力。由 DART 模型模拟的辐射值首先针对光谱失配进行修正。然后，它们用于使用线性回归校正 TLRM 的残余偏差。山谷场景的均方根误差 (RMSE) 和决定系数 (R2) 分别为 0.830 W/(m2 ∙ sr) 和 0.746，峰值场景分别为 0.239 W/(m2 ∙ sr) 和 0.711 . 与 TLRM 相比，不考虑地形影响的模型会在高浮雕 SLR 组件中产生显着差异。在不考虑地形效应的情况下，山谷中向下长波辐射的差异可以达到-60 W/m2。以半球向上长波辐射为参考，直接估算法估算的地表向上长波辐射偏差为11.41 W/m2，标准差（STD）为7.30 W/m2，而定向向上长波辐射偏差为11.41 W/m2 5.99 W/m2 和 STD 为 4.08 W/m2，显示较低的估计变异。地表净长波辐射 (NLR) 和地形校正 NLR 之间的差异介于 50 和 -130 W/m2 之间，明显的负偏差主要发生在山谷中。随着遥感影像空间分辨率的提高，复杂地形对地表辐射通量的影响更加显着。该参数化方案有望更好地反映地形对SLR的影响，增强对高地貌非等温混合像素区域热各向异性的理解，提高SLR反演精度。