Over multi-decadal time scales, assuming that changes in subsurface water storage are negligible, the continental precipitative water flux, P, can be divided into two principal components, Q (run-off, including soil infiltration and groundwater recharge) and ET (evapotranspiration). Taking into account a broadly applied Budyko's phenomenology to describe the relationship of ET/P as a function of PET/P, where PET is the potential evapotranspiration, we propose a theoretical framework for predicting characteristics of the water cycle from scaling relationships. In this framework, the ecosystem net primary productivity is expressed in terms of soil formation and vegetation growth, which is mathematically optimized with respect to the water partitioning, generating directly the value ET/P. The mathematical optimization is based on the general ecological principle that dominant ecosystems tend to be those that, for any given conditions, maximize conversion of atmospheric carbon to biomass. It is shown that application of the results of mathematical optimization to water-limited ecosystems is possible by applying the optimization only to a vegetation covered portion of the surface. For energy-limited ecosystems, the optimization can be applied only to a portion of the precipitation equal to PET, assuming that the remaining P simply runs off. We use theoretical and actual values of plant root fractal dimensionalities, d_f, to predict ranges of ET/P as a function of PET/P for 0 ≤ PET/P ≤ 1 and compare with annual and multi-decadal means of ET/P. By comparing the developed approach with a large amount of data collected from the literature, we demonstrate its successful applications to both water- and energy-limited systems.

中文翻译：

---

从比例关系预测水循环的特征

在几十年的时间尺度上，假设地下蓄水量的变化可以忽略不计，大陆降水通量P可以分为两个主要成分，Q（径流，包括土壤入渗和地下水补给）和 ET（蒸散）。考虑到广泛应用的 Budyko 现象学来描述 ET/ P作为 PET/ P函数的关系，其中 PET 是潜在的蒸散量，我们提出了一个理论框架，用于根据比例关系预测水循环的特征。在此框架中，生态系统净初级生产力以土壤形成和植被生长的形式表示，在水分配方面进行数学优化，直接产生价值 ET/ P. 数学优化基于一般生态学原理，即主导生态系统往往是那些在任何给定条件下最大限度地将大气碳转化为生物量的生态系统。结果表明，通过仅将优化应用于植被覆盖的地表部分，可以将数学优化的结果应用于限水生态系统。对于能量有限的生态系统，假设剩余的P直接流失，优化只能应用于等于 PET 的一部分降水。我们使用植物根分形维数的理论值和实际值d _f来预测 ET/ P 的范围作为 PET/ P的函数，对于 0 ≤ PET/ P ≤ 1 并与 ET/ P 的年度和多年平均值进行比较。通过将开发的方法与从文献中收集的大量数据进行比较，我们证明了其在水资源和能源有限的系统中的成功应用。