Abstract We study the spatial structure of soil moisture fields within savanna ecosystems, whose persistence is vital because it is the driver of the entire ecological structure and function. These include changes in the physical and biogeochemical conditions of the landscape, affecting vegetation state, soil composition, water fluxes, and solar radiation. We focus on computations of the probabilistic structure of islands of soil moisture, known empirically to be related to that of tree clusters, defined as crossing properties of simulated soil moisture fields. Rainfall is modelled via Cox-Isham space-time fields endowed with characteristic scales. Results show that clusters of soil moisture islands are characterized by robust scale-free structures in the region of a phase transition whose order parameter depends on mean soil moisture. Signatures of this fractal structure are well-defined power laws of size distributions of soil moisture clusters; their perimeters-vs-area relations; variance-vs- area of the fields. These characteristics allow for the estimation of the fractal dimension of the field, and its Hurst coefficient. From the general covariance equation of a fractal field, spatial simulations are possible because its mean and variance are known from the probabilistic structure of soil moisture at a point. Our results identify the statistics of hotspots of microbial activity deduced from proper moisture islands, unattainable otherwise, and thus may guide the design of field and remote observations. The critical order parameter characterizing the phase transition establishes where the fractal structure of soil moisture fields exists as a function of the climatic drivers, and the thresholds reflecting where vegetation survives in the field. An example of application of the phase transition diagram presented here is carried out with reference to the Nylsvley savanna in South Africa.

中文翻译：

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土壤水分场的分形结构

摘要 我们研究了稀树草原生态系统中土壤水分场的空间结构，其持久性至关重要，因为它是整个生态结构和功能的驱动力。这些包括景观的物理和生物地球化学条件的变化，影响植被状态、土壤成分、水通量和太阳辐射。我们专注于计算土壤水分岛的概率结构，经验上已知与树群的概率结构相关，定义为模拟土壤水分场的交叉特性。降雨量是通过具有特征尺度的 Cox-Isham 时空场建模的。结果表明，土壤水分岛群在相变区域具有稳健的无标度结构，其顺序参数取决于平均土壤水分。这种分形结构的特征是土壤水分簇大小分布的明确幂律；它们的周长与面积关系；字段的方差与面积。这些特性允许估计场的分形维数及其 Hurst 系数。根据分形场的一般协方差方程，空间模拟是可能的，因为它的均值和方差是从某一点土壤水分的概率结构中得知的。我们的结果确定了从适当的水分岛推断出的微生物活动热点的统计数据，否则无法实现，因此可以指导现场和远程观察的设计。表征相变的临界顺序参数确定了土壤水分场的分形结构作为气候驱动因素的函数存在的位置，以及反映植被在田间生存位置的阈值。此处介绍的相变图的应用示例是参照南非的 Nylsvley 稀树草原进行的。