An information theoretic approach to select alternate subsets of predictors for data-driven hydrological models

Abstract

This work investigates the uncertainty associated to the presence of multiple subsets of predictors yielding data-driven models with the same, or similar, predictive accuracy. To handle this uncertainty eectively, we introduce a novel input variable selection algorithm, called Wrapper for Quasi Equally Informative Subset Selection (W-QEISS), specically conceived to identify all alternate subsets of predictors in a given dataset. The search process is based on a four-objective optimisation problem that minimises the number of selected predictors, maximises the predictive accuracy of a data-driven model and optimises two information theoretic metrics of relevance and redundancy, which guarantee that the selected subsets are highly informative and with little intra-subset similarity. The algorithm is rst tested on two synthetic test problems and then demonstrated on a real-world streamow prediction problem in the Yampa River catchment (US). Results show that complex hydro-meteorological datasets are characterised by a large number of alternate subsets of predictors, which provides useful insights on the un

Automatic design of basin-specific drought indexes for highly regulated water systems

“…In terms of performance, wrappers are often more accurate than filters, although computationally more intensive (Galelli et al, 2014). In this study, we used W-QEISS as a wrapper (Karakaya et al, 2015;Taormina et al, 2016). The W-QEISS algorithm receives as input the set X of candidate predictors, i.e., X = {x i , .…”

“…A drought is a slowly developing natural phenomenon that occurs in all climatic zones and can be defined as a temporary significant decrease in water availability (Tallaksen and Van Lanen, 2004;Van Loon and Van Lanen, 2012). Drought impacts can propagate to virtually every water-related sector, such as farming and livestock production, industry, power generation, and public water supply (Spinoni et al, 2016).…”

“…Hydrological drought is defined as a period of exceptionally low flows in watercourses, and lake and groundwater levels below normal (Dracup et al, 1980;Van Loon and Van Lanen, 2012). Related indicators mainly focus on streamflow, as the by-product of every hydro-meteorological process taking place in water catchments (Heim Jr, 2002; Figure 1.…”

“…This drought takes place after a prolonged time of low precipitation and deficient soil moisture and its effects are witnessed in the long-term (6-12 months; Zargar et al, 2011). These three categories refer to droughts as a natural hazard, i.e., a threat of a naturally occurring event that negatively effects people or the environment (Gustard and Demuth, 2009;Van Loon and Van Lanen, 2013;Laaha et al, 2016). On the other hand, particularly in highly regulated contexts, a dry spell may be caused by natural scarcity of precipitation as well as inconsiderate overuse and/or mismanagement of water resources.…”

“…Second, we identify Pareto-optimal subsets of variables balancing predictive accuracy and parsimony. In this study, we employed the Wrapper for QuasiEqually Informative Subset Selection (W-QEISS) to perform this operation (Karakaya et al, 2015;Taormina et al, 2016). Traditional variable selection algorithms are conceived to select only one optimal subset of predictors, while W-QEISS identifies one subset with the highest predictive accuracy, and multiple subsets with similar information content, thus providing more informative results.…”