基于联合多重分形的土壤微量元素协同克立格研究

Spatial variability and scaling analysis of soil properties and processes can answer the question how to execute the transformation of soil property parameters and processes across spatial scales. The scaling relationships between soil properties and environmental factors usually restrain the spatial prediction capability of the Cokriging method. In this study, we will quantify the scaling relationships between the spatial distributions of soil micronutrients and environmental factors through joint multifractal (spectrum) modeling. In addition, we develop a cross semi-variogram model to improve the spatial prediction capability of the Cokriging method based on correlation analysis of the singularity index. The objectives of this study are: to understand the relationships between soil micronutrients and environmental factors at multiple spatial scales; to reveal the practical significance of scaling relationships in the Cokriging analysis, and; to present a joint multifractal-based Cokriging approach, which can provide theoretical and technical support for spatial variability and scaling analysis of soil properties and processes(e.g. micronutrient levels).

土壤性状及过程空间变异与尺度转化研究可以回答"如何实现不同尺度上土壤特性参数和过程相互转换"的科学问题。土壤特性与环境因子空间分布相关关系的尺度效应常常影响协同克立格（Cokriging）方法空间预测能力。本研究拟采用联合多重分形（谱）模型量化土壤微量元素与环境因子空间分布相关关系尺度效应，通过建立基于奇异性指数相关分析的协同变异函数模型优化Cokriging空间预测能力。目的从多尺度上理解土壤微量元素与环境因子空间分布相关性，揭示土壤微量元素与环境因子空间分布相关关系尺度效应在Cokriging研究中实践意义，继而提出基于联合多重分形技术的Cokriging方法，为土壤性状及过程（微量元素）空间变异与尺度转换研究提供理论和技术支撑。

土壤微量元素空间分布具有高度变异性，本项目开展了基于联合多重分形的协同Kriging插值土壤微量元素空间变异与估计研究。与传统协同Kriging插值结果相比较验证，土壤微量元素空间估计结果中的极值范围和较小的均方根误差表明结合尺度效应分析的协同Kriging能够提高土壤微量元素空间估计的预测精确度，研究结果可借鉴到土壤与景观关系和三维地统计研究。项目关键在于联合多重分形能够刻画土壤微量元素空间分布的奇异性及其与环境变量空间相关性的尺度效应，结合尺度效应拟合的变异函数进一步降低了Kriging的平滑效应，使得插值估计更好地保留了土壤微量元素的空间变异特征和局部异常值。综合上述主要结果得出的项目结论与预期研究结果一致。根据追踪国际动态，应用三维地统计方法和基于已有数据挖掘和专家知识的土壤属性(微量元素)空间变异与制图研究是项目组下一步拟开展的主要课题。