Copper (Cu) is an essential element for plants and microorganisms and at larger concentrations a toxic pollutant. A number of factors controlling Cu dynamics have been reported, but information on quantitative relationships is scarce. We aimed to (i) quantitatively describe and predict soil Cu concentrations (Cu_AR) in aqua regia considering site-specific effects and effects of pH, soil organic carbon (SOC) and cation exchange capacity (CEC), and (ii) study the suitability of mixed-effects modelling and rule-based models for the analysis of long-term soil monitoring data. Thirteen uncontaminated long-term monitoring soil profiles in southern Germany were analysed. Since there was no measurable trend of increasing Cu_AR concentrations with time in the respective depth ranges of the sites, data from different sampling dates were combined and horizon-specific regression analyses including model simplifications were carried out for 10 horizons. Fixed- and mixed-effects models with the site as a random effect were useful for the different horizons and significant contributions (either of main effects or interactions) of SOC, CEC and pH were present for 9, 8 and 7 horizons, respectively. Horizon-specific rule-based cubist models described the Cu_AR data similarly well. Validations of cubist models and mixed-effects models for the Cu_AR concentrations in A horizons were successful for the given population after random splitting into calibration and validation samples, but not after independent validations with random splitting according to sites. Overall, site, CEC, SOC and pH provide important information for a description of Cu_AR concentrations using the different regression approaches.

中文翻译：

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应用混合效应建模和基于规则的模型来解释德国南部土壤剖面中铜的变化

铜 (Cu) 是植物和微生物的基本元素，在较高浓度时是有毒污染物。已经报道了许多控制 Cu 动力学的因素，但关于数量关系的信息很少。我们的目标是 (i) 定量描述和预测王水中的土壤铜浓度 (Cu _AR )，考虑到特定地点的影响以及 pH 值、土壤有机碳 (SOC) 和阳离子交换容量 (CEC) 的影响，以及 (ii) 研究混合效应建模和基于规则的模型对长期土壤监测数据分析的适用性。分析了德国南部 13 个未受污染的长期监测土壤剖面。由于没有可测量的增加 Cu _AR的趋势在站点的各个深度范围内随时间变化的浓度，将来自不同采样日期的数据结合起来，并对 10 个层位进行包括模型简化在内的层位特定回归分析。将站点作为随机效应的固定效应和混合效应模型对于不同的层位很有用，并且 SOC、CEC 和 pH 的显着贡献（主要影响或相互作用）分别存在于 9、8 和 7 个层位。基于地平线的基于规则的立体派模型同样很好地描述了 Cu _{AR数据。Cu AR}的立体模型和混合效应模型的验证在随机拆分为校准和验证样本后，给定人群的 A 水平浓度是成功的，但在根据站点随机拆分的独立验证之后却没有。总体而言，位点、CEC、SOC 和 pH 为使用不同回归方法描述 Cu _AR浓度提供了重要信息。