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Goodness-of-fit measures: what do they tell about vegetation variable retrieval performance from Earth observation data

机译：拟合优度度量：它们从地球观测数据中了解植被变量的检索性能

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摘要

The capability of models to predict vegetation biophysical variables is usually evaluated by means of one or several goodness-of-fit measures, ranging from absolute error indices (e.g. the root mean square error, RMSE) over correlation based measures (e.g. coefficient of determination, R~2) to a group of dimensionless evaluation indices (e.g. relative RMSE). Hence, the greatest difficulty for the readers is the lack of comparability between the different models' accuracies. Therefore, the objective of our study was to provide an overview about the quantitative assessment of biophysical variable retrieval performance. Furthermore, we aimed to suggest an optimal set of statistical measures. This optimum set of statistics should be insensitive to the magnitude of values, range and outliers. For this purpose, a literature review was carried out, summarizing the statistical measures that have been used to evaluate model performances. Followed by this literature review and supported by some exemplary datasets, a range of statistical measures was calculated and their interrelationships analyzed. From the results of the literature review and the test analyses, we recommend an optimum statistic set, including RMSE, R~2, the normalized RMSE and some other indicators. Using at least the recommended statistics, comparability of model prediction accuracies is guaranteed. If applied, this will enable a better intercomparison of scientific results urgently needed in times of increasing data availability for current and upcoming EO missions.
机译：通常通过一种或几种拟合优度度量来评估模型预测植被生物物理变量的能力，范围从绝对误差指数（例如均方根误差，RMSE）到基于相关性的度量（例如确定系数， R〜2）到一组无量纲的评估指标（例如相对RMSE）。因此，对读者来说最大的困难是不同模型精度之间缺乏可比性。因此，我们的研究目的是提供有关生物物理变量检索性能的定量评估的概述。此外，我们旨在建议一套最佳的统计指标。最佳的统计数据集应该对值的大小，范围和离群值不敏感。为此，进行了文献综述，总结了用于评估模型性能的统计方法。在此文献综述之后，并得到一些示例性数据集的支持，计算了一系列统计量度并分析了它们之间的相互关系。根据文献综述和检验分析的结果，我们推荐一个最佳统计集，包括RMSE，R〜2，归一化RMSE和其他一些指标。至少使用推荐的统计数据，可以保证模型预测准确性的可比性。如果应用，这将使现有和未来的驻外任务的数据可用性不断提高时，急需更好地相互比较科学结果。

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