Non-Linear Approaches to Assess Water and Soil Quality

Abstract

Systematic monitoring is indispensable for a thorough water and soil management. However, large data sets with many variables, natural heterogeneities, and a variety of (possible) influencing factors require new approaches for processing and visualization of the data. A variety of advanced techniques has been developed recently in different disciplines. Some of them have been tested for application in water and soil resources management and exhibited very promising results. Two out of these approaches are presented here by application to a data set of shallow groundwater quality that has been complied during a five years period in a small catchment in Northeast Germany. Measured variables of soil or water quality usually reflect effects of various processes. On the other hand, single processes usually affect more than one variable and thus generate a characteristic “fingerprint” that can be used in an inverse approach to identify this process based on observed measured variables. Other processes differ with respect to their “fingerprints” and thus can be differentiated in a large data set. This is the basic idea of applying dimensionality reduction approaches. Every single sample can be ascribed a score of a component that is a quantitative measure for the impact of the respective process on the given sample. Usually, a small number of components (or processes, respectively) accounts for a large fraction of the variance in a data set with many variables. This “dimensionality reduction” helps a lot to gain better understanding of the prevailing processes, of spatial and temporal patterns, and of the reasons for conspicuous data. The larger a given data set, and the larger the number of variables, the more advanced methods of data visualization are required. Modern visualization techniques pave the way for efficient use of the most powerful interface between data stored on a computer and the human brain. A single non-linear projection of high-dimensional data on a two-dimensional graph provides comprehensive information about outliers, clusters, linear and non-linear relationships, spatial patterns, multivariate trends, etc. in the data. This approach could usefully be combined with other dimensionality reduction techniques. This chapter can serve only as an appetizer. A variety of sophisticated new methods exist. These techniques still are not part of textbooks of hydrology or soil science. They require an open mind and some initial training. Then a wealth of powerful tools are at hand as a base for thorough water and soil resources management.