To make predictions about the carbon cycling consequences of rising global surface temperatures, Earth system scientists rely on mathematical soil biogeochemical models (SBMs). However, it is not clear which models have better predictive accuracy, and a rigorous quantitative approach for comparing and validating the predictions has yet to be established. In this study, we present a Bayesian approach to SBM comparison that can be incorporated into a statistical model selection framework. We compared the fits of linear and nonlinear SBMs to soil respiration data compiled in a recent meta-analysis of soil warming field experiments. Fit quality was quantified using Bayesian goodness-of-fit metrics, including the widely applicable information criterion (WAIC) and leave-one-out cross validation (LOO). We found that the linear model generally outperformed the nonlinear model at fitting the meta-analysis data set. Both WAIC and LOO computed higher overfitting risk and effective numbers of parameters for the nonlinear model compared to the linear model, conditional on the data set. Goodness of fit for both models generally improved when they were initialized with lower and more realistic steady-state soil organic carbon densities. Still, testing whether linear models offer definitively superior predictive performance over nonlinear models on a global scale will require comparisons with additional site-specific data sets of suitable size and dimensionality. Such comparisons can build upon the approach defined in this study to make more rigorous statistical determinations about model accuracy while leveraging emerging data sets, such as those from long-term ecological research experiments.

中文翻译：

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土壤生物地球化学模型评估的贝叶斯方法

为了预测全球地表温度上升的碳循环后果，地球系统科学家依靠数学的土壤生物地球化学模型（SBM）。但是，尚不清楚哪种模型具有更好的预测准确性，并且尚需建立用于比较和验证预测的严格的定量方法。在这项研究中，我们提出了一种贝叶斯SBM比较方法，可以将其纳入统计模型选择框架。我们将线性和非线性SBM的拟合与土壤呼吸数据进行了拟合，该数据是在最近对土壤变暖场实验进行的荟萃分析中汇编的。使用贝叶斯拟合优度指标对拟合质量进行量化，包括广泛适用的信息标准（WAIC）和留一法交叉验证（LOO）。我们发现，在拟合荟萃分析数据集时，线性模型通常要优于非线性模型。与线性模型相比，根据数据集，WAIC和LOO都为非线性模型计算了更高的过拟合风险和有效参数数量。当使用较低且更切合实际的稳态土壤有机碳密度进行初始化时，两个模型的拟合优度通常都会提高。尽管如此，要测试线性模型是否在全局范围内是否比非线性模型具有绝对优越的预测性能，将需要与其他具有适当大小和尺寸的特定地点数据集进行比较。此类比较可以基于本研究中定义的方法，以便在利用新兴数据集的同时，对模型的准确性进行更严格的统计确定，