The bulk elemental composition of soil subsurface (B) horizons is influenced by environmental, biological, geological, and climatic factors. Because fossil soils (paleosols) are common in the geologic record, quantitative models that link climate to paleosol geochemistry are highly desirable in the paleoclimate community. Error associated with these models is typically reported as the root mean square error (RMSE) of a regression analysis and reflects the variability imparted by non-climatic influences on soil formation and the uncertainty associated with model fitting. However, for prediction purposes, the RMSE is well known to underestimate model uncertainty. In this work we re-evaluate a widely used transfer function for mean annual precipitation (MAP) based on the chemical index of alteration minus potassium (CIA-K) using data science best practices on two continental-scale soil data sets. Data set inter-comparisons and cross-validation of exponential regression models indicate that the root mean square prediction error (RMSPE) between CIA-K and MAP for soils representative of climates across the continental United States is around 299 mm, significantly higher than the currently accepted 182 mm RMSE. Further, CIA-K is unable to predict perhumid (>2000 mm MAP) climate zones. We show that transitioning from a simple regression framework to one of recursive partitioning via random forests can significantly increase prediction accuracy while automating variable selection. We introduce two new, widely applicable random forest models for MAP (RF-MAP) that use 10 elemental oxides as input variables and were calibrated on the Baylor University Soil Informatics (BU-SI) data set. RF-MAP version 1.0 (RF-MAP1.0) was generated using the entire BU-SI data set (n = 685) and can predict MAP values up to 6865 mm with a RMSPE of 395 mm. RF-MAP version 2.0 (RF-MAP2.0) was generated using a modification of the BU-SI data set (n = 642) and can predict MAP values up to ∼1600 mm with a RMSPE of 209 mm. Pruned regression trees provide insight into the mechanisms driving the random forest models and demonstrate the first empirical confirmation of the sensitivity of soil elemental responses to global climate zones. The RF-MAP1.0 and RF-MAP2.0 models predict MAP values comparable to independent proxy estimates for a range of deep-time paleosols. We advocate for application of RF-MAP1.0 in settings where no a priori information on paleoclimate is available, and encourage the use of either RF-MAP1.0 or RF-MAP2.0 if users have independent constraints that paleo-MAP was below 1600 mm.

中文翻译：

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递归分区改进了降雨的古土壤代理

土壤地下 (B) 层的整体元素组成受环境、生物、地质和气候因素的影响。由于化石土壤（古土壤）在地质记录中很常见，因此在古气候群落中非常需要将气候与古土壤地球化学联系起来的定量模型。与这些模型相关的误差通常报告为回归分析的均方根误差 (RMSE)，反映了非气候影响对土壤形成的影响以及与模型拟合相关的不确定性。然而，出于预测目的，众所周知，RMSE 会低估模型的不确定性。在这项工作中，我们使用两个大陆尺度土壤数据集的数据科学最佳实践，重新评估了广泛使用的年平均降水量 (MAP) 传递函数，该函数基于变化的化学指数减去钾 (CIA-K)。指数回归模型的数据集相互比较和交叉验证表明，CIA-K 和 MAP 之间代表美国大陆气候的土壤的均方根预测误差 (RMSSPE) 约为 299 毫米，显着高于当前接受 182 毫米均方根误差。此外，CIA-K 无法预测高湿 (>2000 mm MAP) 气候带。我们表明，从简单的回归框架过渡到通过随机森林的递归分区之一可以显着提高预测准确性，同时自动化变量选择。我们介绍两个新的，广泛适用的 MAP 随机森林模型 (RF-MAP)，使用 10 种元素氧化物作为输入变量，并在贝勒大学土壤信息学 (BU-SI) 数据集上进行校准。RF-MAP 1.0 版 (RF-MAP1.0) 是使用整个 BU-SI 数据集（n = 685）生成的，可以预测高达 6865 mm 的 MAP 值，RMSPE 为 395 mm。RF-MAP 2.0 版（RF-MAP2.0）是使用 BU-SI 数据集（n = 642）的修改生成的，可以预测高达 1600 mm 的 MAP 值，RMSPE 为 209 mm。修剪回归树提供了对驱动随机森林模型的机制的深入了解，并证明了土壤元素响应对全球气候区的敏感性的首次实证证实。RF-MAP1.0 和 RF-MAP2.0 模型预测的 MAP 值与一系列深时古土壤的独立代理估计值相当。