Grid- or pixel-based models, used across various scientific disciplines from microscopic to planetary scales, contain an unquantified error that bias our interpretation of the data. The error is produced by projecting 3D data onto a 2D grid. For Digital Terrain Models (DTMs) the projection error affects all slope-dependent topographic metrics, like surface area or slope angle. Due to the proportionality of the error to the cosine of the slope, we can correct for it. We quantify the error and test the correction using synthetic landscapes for which we have analytical solutions of their metrics. Application to real-world landscapes in California, reveal the systematic underestimation of surface area by up to a third, and mean slope angles by up to 10° in steep topography in current DTMs. Correcting projection errors allow for true estimates of surface areas and slope distributions enabling physics-based models of surface processes at any spatial scale.

中文翻译：

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量化地球地形：比数字地形模型中预测的更陡、更大


基于网格或像素的模型用于从微观到行星尺度的各种科学学科，包含未量化的错误，使我们对数据的解释产生偏差。该误差是通过将 3D 数据投影到 2D 网格上而产生的。对于数字地形模型 (DTM)，投影误差会影响所有与坡度相关的地形指标，例如表面积或坡度角度。由于误差与斜率余弦成比例，我们可以对其进行校正。我们量化误差并使用合成景观测试校正，我们对其指标有分析解。将其应用到加利福尼亚州的真实景观中，揭示了当前 DTM 中陡峭地形中表面积的系统性低估高达三分之一，平均坡度角度高达 10°。校正投影误差可以真实估计表面积和坡度分布，从而在任何空间尺度上建立基于物理的表面过程模型。