Statistical learning theory: Concepts and applications in water resources management.

摘要

Most hydrologic quantities are variable in time and space, and hence, hydrologists are confronted with challenges of predicting these quantities (e.g., groundwater head, stream flows, etc.). Traditionally, empirical models based on classical statistics that treat the hydrologic system as a "black box" and infer input/output relations without trying to understand the exact form of the underlying relationships are used when data are scarce to justify physically based models. These models are developed for large samples and based on various types of a priori information. On the other hand, physically based hydrological models represent the underlying physical or other processes as they are best understood. There is a need to bridge the gap between these two extreme approaches for, at least, two reasons: (1) there is still a need to inject domain knowledge into dependency estimation problems rather than just using input/output of state variables and assuming a priori form of this relationship; and (2) when data are scarce and underlying physical and/or other processes are poorly understood, one would still like to come up with a reasonable model that would let the data "speak."; The concept of statistical learning theory (SLT), which was developed for small data samples and does not rely on prior knowledge of the problem to be solved, is primarily used in fields of computer science and statistics. It is used in the present study to bridge the gap between classical regression-based and physically based hydrological models. While estimating functional dependency, SLT considers two components of the estimation problem: one related to the regularization of a solution (i.e., the estimated function will always tend to be flat, avoiding over fitting) and the second related to the goodness-of-fit (closeness to data). The SLT methodology is explored in this study to solve few real-life water resources management problems, including (1) snow/runoff modeling; (2) chaotic time series learning and prediction; and (3) design of groundwater quality and quantity monitoring networks. The results of these applications show the extent to which the SLT theory may be adapted in hydrological sciences and its limitation in addressing real-life problems.