Soil Moisture, Subsurface Storage and Runoff as a Low Dimensional Dynamical System

小行星9418674 本研究将验证一个假设，即土壤径流过程可以表示为一个低维动力系统，地形，土壤，地质和气候变化的影响。 通过“低维“，我们的意思是最小数量的状态变量所需的近似过程作为一个系统的非线性常微分方程。 我们研究的情况下，控制多孔土壤和浅层地下水循环，并在集水区的能力，以存储水和产量径流取决于系统的存储-通量关系的性质。 蒸散作为土壤水分储存的参数函数的作用也将被检查。 “低维”模型将作为一个基于物理的替代非线性偏微分方程（理查德方程）代表当地的过程。 在构建动力学模型时，关键问题是分离或区分流域动力学的空间和时间分量，以便阐明所涉及过程的重要机制，而不损失关键的非线性结构。 （1）通过对饱和-非饱和渗流偏微分方程有限元解的数值试验，建立了与地形相关的本构关系（如蓄量-流量关系）。 建议的研究将建立在一系列稳态数值试验（Lee，1993; Duffy，1994）上，用于具有均匀土壤性质的二维山坡几何形状。 以前的工作发现，补给地下水位和地下水流的流至少有两个状态变量的非线性函数：综合土壤水分和综合饱和存储。 目前的目标是将这些实验扩展到全三维和时变流的情况下，并测试土壤分层和非线性存储通量关系和径流响应的变化的作用。 (2)开发和测试程序的缩放和空间整合的状态变量和通量的页岩山流域，8公顷，森林，集水区在中央PA（J.林奇等人，1976年）。 页岩山是一个独特的实验在20世纪70年代的网站，以评估先前的土壤水分对暴雨流量和时间的影响。 人工降雨应用于8个事件，初始湿度从干燥到非常潮湿。 对整个流域的土壤水分和饱和贮量进行了综合核算。 虽然它似乎是一个简单的问题，分散的现场观测的空间整合需要一个适当的加权函数。 Duffy（1994）提出了一种基于高程分布的加权函数，并对每个山坡或零阶盆地的山坡轨迹进行了局部重标度。 将对Shale Hills数据库采用这种比例和平均方法。 将把实地估算的储水量-通量关系与（1）中的数值试验进行比较。 (3)被称为适当的正交分解（POD）的一个独立的方法，允许的基本空间结构的动态重建直接从随机场数据或从执政的PDE的。 该方法被广泛应用于探测流体动力学湍流（Lumley，1967）、气候场演化（North et al，1982）和非线性振动（Cusumano，and Bai，1993，Cusumano et al，1993，Lin and Cusumano，1993，Cusumano et al，1994）中的相干结构。 POD方法将应用于页岩山实验的现场数据和理查德方程，以提供对系统建模所需的维数或状态变量数量的测量。

9418674 Duffy This research will test the hypothesis that the rainfall-runoff process can be represented as a low-dimensional dynamical system, forced by topographic, soil, geologic and climatic variability. By "low-dimensional " we mean the minimum number of state variables required to approximate the processes as a system of nonlinear ordinary differential equations. We examine the case where rainfall-runoff is controlled by porous soils and shallow groundwater circulation, and where the ability of the catchment to store water and yield runoff depends on the nature of the storage-flux relationships of the system. The role of evapotranspiration as a parametic function of soil-moisture storage will also be examined. The "low-dimensional" model will serve as a physically-based alternative to the nonlinear partial differential equations (Richard's equation) representing the local processes. In constructing the dynamical model, the essential problem is to separate or distinguish among spatial and temporal components of watershed dynamics, such that the important mechanics of the processes involved are elucidated, without loss of critical nonlinear structure. The research has the following elements: (1) Comprehensive numerical experiments based on finite element solutions to the partial differential equations for saturated-unsaturated flow will be performed To establish terrain-integrated constitutive relations (e.g. storage-flux relations). the proposed research will build on a series of steady-state numerical experiments (Lee, 1993; Duffy, 1994) for two dimensional hillslope geometry with uniform soil properties. This previous work found that recharge to the water table and subsurface flow to the stream were nonlinear functions of at least two state variables: the integrated soil moisture and integrated saturated storage. The present objective is to extend these experiments to the case of fully three dimensional and time varying flow, and test the role of soil stratification and variability on nonlinear storage-flux relations and runoff response. (2) Develop and test procedures for scaling and spatial integration of the state variables and fluxes for the Shale Hills watershed, 8 hectare, forested, catchment in central PA (J. Lynch et al, 1976). Shale Hills was the site of a unique experiment in the 1970's to evaluate the effects of antecedent soil moisture on stormflow volume and timing. Rainfall was artificially applied for 8 events with initial moisture ranging from dry to very wet. a comprehensive accounting of soil moisture and saturated storage at multiple depths was made over the entire watershed. Although if may seem to be a straight forward problem, spatial integration of scattered field observations requires an appropriate weighting function. Duffy (1994) has proposed weighting function derived from the hypsometric distribution, and a local rescaling of hillslope trajectories for each hillslope or zero-order basin. This scaling and averaging method will be carried out for the Shale Hills data base. Field-estimated storage-flux relations will be compared with the numerical experiments in (1). (3) An independent method known as proper orthogonal decomposition (POD), allows the essential spatial structure of the dynamics to be reconstructed directly from random field data or from the governing pde's. The method is widely applied to detecting coherent structures in hydrodynamics turbulence (Lumley, 1967), the evolution of climatic fields (North et al, 1982), and nonlinear vibration (Cusumano, and Bai, 1993, Cusumano et al, 1993, Lin and Cusumano, 1993, Cusumano et al, 1994). The POD method will be applied to the field data of the Shale Hills experiment and the Richard's equation to provide a measure of the dimensionality, or number of state variables required to model the system.