A statistical framework we call CQUESST (Carbon Quantification and Uncertainty from Evolutionary Soil STochastics), which models carbon sequestration and cycling in soils, is applied to a long-running agricultural experiment that controls for crop type, tillage, and season. The experiment, known as the Millenium Tillage Trial (MTT), ran on 42 field-plots for ten years from 2000-2010; here CQUESST is used to model soil carbon dynamically in six pools, in each of the 42 agricultural plots, and on a monthly time step for a decade. We show how CQUESST can be used to estimate soil-carbon cycling rates under different treatments. Our methods provide much-needed statistical tools for quantitatively inferring the effectiveness of different experimental treatments on soil-carbon sequestration. The decade-long data are of multiple observation types, and these interacting time series are ingested into a fully Bayesian model that has a dynamic stochastic model of multiple pools of soil carbon at its core. CQUESST's stochastic model is motivated by the deterministic RothC soil-carbon model based on nonlinear difference equations. We demonstrate how CQUESST can estimate soil-carbon fluxes for different experimental treatments while acknowledging uncertainties in soil-carbon dynamics, in physical parameters, and in observations. CQUESST is implemented efficiently in the probabilistic programming language Stan using its MapReduce parallelization, and it scales well for large numbers of field-plots, using software libraries that allow for computation to be shared over multiple nodes of high-performance computing clusters.

翻译：我们提出了一种称为CQUESST（碳量化与演化土壤随机不确定性）的统计框架，该框架模拟土壤中的碳封存与循环过程，并将其应用于一项长期运行的农业试验中。该试验名为千年耕作试验（MTT），通过控制作物类型、耕作方式和季节变量，在42块田间样地上持续开展了从2000年至2010年共十年的观测。本研究运用CQUESST框架，以月度时间步长动态模拟了42个农业样地中六个碳库的土壤碳动态。我们展示了如何利用CQUESST估算不同处理条件下的土壤碳循环速率。该方法为定量推断不同实验处理对土壤碳封存效果的影响提供了亟需的统计工具。长达十年的观测数据包含多种类型，这些相互关联的时间序列被整合到一个完全贝叶斯模型中，该模型的核心是基于多碳库土壤碳动态的随机模型。CQUESST的随机模型受基于非线性差分方程的确定性RothC土壤碳模型启发而构建。我们演示了CQUESST如何在承认土壤碳动态、物理参数及观测数据不确定性的前提下，估算不同实验处理下的土壤碳通量。CQUESST通过概率编程语言Stan实现高效计算，利用其MapReduce并行化技术，并借助支持高性能计算集群多节点分布式计算的软件库，能够良好适应大规模田间样地的分析需求。