Parameterization, Spatial Simulation, and Quantified Effects of Non-linear Spatial Dependence

Abstract:

The structure of a pathway pertains to the arrangement of the system components that determine the flow of water; this structure can vary in space and in time. This presentation demonstrates a method that is: (1) capable of describing a varying arrangement for different separation distances, and (2) based on measurements. The focus lies on saturated hydraulic conductivity (K), but the method is easily extensible to parameters describing variably saturated flow or karst networks.

The key advantage of the method presented is its capability to describe non-linear spatial dependence. Such asymmetric spatial dependence is encountered ubiquitously in nature and originates in the generating processes (examples based on hydraulic conductivity and regional groundwater quality data-sets are shown). The kind of dependence varies for different separation distances and even the type of dependence as measured by symmetry might change for different separation distances. Different degrees of dependence can be described and modeled for different measurement values (quantiles). We present metrics to quantify the type and degree of dependence based on data, as well as parameter estimation techniques for the simulation methods. This approach does not require the common, but limiting, assumption of multivariate normal spatial dependence, and hence neither the assumption of a (log-) normal distribution of the marginal values.

The effects of the spatial dependence structure of K on dependent physical / chemical properties such as solute transport behavior are demonstrated and relevant metrics such as connectivity and capacity are quantified. These properties deviate systematically from expected Gaussian behavior as the multivariate dependence deviates from Gaussian dependence, despite identical correlation. This can have significant implications for water resources management (e.g. peak breakthrough concentration, earliest arrival).