Exploring Topographic Effects on Surface Parameters Over Rugged Terrains at Various Spatial Scales
Hanyu Shi, Zhiqiang Xiao
Abstract
Topography is an inevitable factor when processing remote sensing data. Slope and aspect are sufficient for describing topographic conditions within a fine-scale pixel (e.g., 30 m); the resulting schematic is referred to as a sloping terrain and is modeled as a solo slope. A composite slope, which contains many solo slopes that are collectively referred to as rugged terrain, is needed for coarse-scale pixels (e.g., 1 km). However, many parameter estimation algorithms use topographic approximation methods, such as the assumption of a flat surface, assumption of a solo slope, omission of contributions from adjacent slopes, and usage of the terrain view factor (TVF) to approximate adjacent contributions. These topographic approximations can induce significant errors over mountain areas; however, errors caused by various approximation methods have not been comprehensively analyzed. This study summarizes radiative transfer (RT) processes over rugged terrains, proposes composite-slope models for surface parameters, and analyzes the influences of different topographic approximation methods on surface reflectance ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\rho }$ </tex-math></inline-formula> ), directional brightness temperature ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${T_{b}}$ </tex-math></inline-formula> ), surface net radiation ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${E_{n}}$ </tex-math></inline-formula> ), slope downward radiation ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${E_{d}}$ </tex-math></inline-formula> ), absorbed photosynthetically active radiation (APAR), total emitted solar-induced chlorophyll fluorescence (SIF) by all leaves ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${F_{e}}$ </tex-math></inline-formula> ), SIF observed at the top of the canopy ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${F_{o}}$ </tex-math></inline-formula> ), broadband albedo ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\alpha }$ </tex-math></inline-formula> ), and broadband hemispherical emissivity ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\varepsilon }$ </tex-math></inline-formula> ) at a series of spatial resolutions (30, 90, 270, 540, 1080, and 5400 m). Three surface types are tested: vegetation, soil, and snow. The results demonstrate that: 1) assumptions of a flat surface or a solo slope and the use of the TVF method induce significant errors (1%–58%) in all aforementioned parameters; 2) adjacent contributions can be neglected when simulating <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\varepsilon }$ </tex-math></inline-formula> , APAR, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${F_{o}}$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${F_{e}}$ </tex-math></inline-formula> , and low-reflective <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\rho }$ </tex-math></inline-formula> ; and 3) adjacent contributions should be considered for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${E_{n}}$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${E_{d}}$ </tex-math></inline-formula> , and high-reflective <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\rho }$ </tex-math></inline-formula> , and they are also significant when simulating <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\alpha }$ </tex-math></inline-formula> using fine-resolution data or over snow surfaces. These findings and the composite-slope models developed in this study benefit those who intend to conduct forward modeling and parameter estimation studies over rugged terrains.