Dimensionality reduction in drought modelling

Abstract

For monitoring hydrological events characterized by high spatial and temporal variability, the number and location of recording stations must be carefully selected to ensure that the necessary information is collected. Depending on the characteristics of each natural process, certain stations may be spurious or redundant, whereas others may provide most of the relevant data. With the objective of reducing the costs of the monitoring system and, at the same time, improving its operational effectiveness, three procedures were applied to identify the minimum network of rain gauge stations able to capture the characteristics of droughts in mainland Portugal. Drought severity is characterized by the standardized precipitation index applied to the timescales of 1, 3, 6 and 12 consecutive months. The three techniques used to reduce the dimensionality of the network of rain gauges were as follows: (i) artificial neural networks with sensitivity analysis, (ii) application of the mutual information criterion and (iii) K‐means cluster analysis using Euclidean distances. The results demonstrated that the best dimensionality reduction method was case dependent in the three regions of Portugal (northern, central and southern) previously identified by cluster analysis. All the reduction techniques lead to the selection of a subset of rain gauges capable of reproducing the original temporal patterns of drought. For specific severe drought events in Portugal in the past, the comparison between drought spatial patterns obtained with the original stations and the selected subset indicated that the subset produced statistically satisfactory results (correlation coefficients higher than 0.6 and efficiency coefficients higher than 0.5). Copyright © 2012 John Wiley & Sons, Ltd.

Entropy Applications to Water Monitoring Network Design: A Review

“…Applications found in the literature have taken the reasonable approach of using entropy to reduce network density for comparison to a network that included all stations. In Portugal, Santos et al [50] compared artificial neural networks, K-means clustering and mutual information (MI) criteria for reducing the density of a precipitation network for drought monitoring at different time scales. They found the best performing reduction method was case dependent depending on the region and time scale applied, but noted that all methods performed well.…”

Development of an annual drought classification system based on drought severity indexes

“…Because it is a natural, recurrent and complex event, attempts are made to predict its beginning, end, and severity. This process involves the calculation of drought indices, which incorporate hydrometeorological data that provide information on historical droughts to monitor current conditions (Santos et al 2013). Fernandes et al (2010) state that drought rates are, however, important for adopting different indices for a performance assessment.…”

An information theoretic alternative to model a natural system using observational information alone

“…Past applications of the above mentioned PMI criterion to hydrological or hydrometeorological problems is indicative of the possible hydrological problems the proposed criterion could be used for. These past applications include those for identifying the optimal rain gauge density for characterizing droughts [ Santos et al ., ], characterizing epistemic and aleatory uncertainty in modeled streamflow using a range of conceptual hydrologic models [ Gong et al ., ], predicting and characterizing water quality using models whose inputs have been ascertained partly using PMI [ He et al ., ; May et al ., ], identifying time‐lagged predictors for ecohydrological modeling and in a range of scenarios [ Ruddell and Kumar , ], and applications to reservoir operation and forecasting where the definition of the system requires identification of the most causative climatic and catchment predictor variables [ Sankarasubramanian et al ., ], along with a host of other applications where the intent is to define the inputs most suitable for predicting an observed response. Many of the above papers go on to specify the system being modeled using inputs determined by PMI but do not use a systematic approach for identifying the optimal number of predictor variables, or account for the relative contribution each predictor should have in determining the Euclidean distance needed for issuing predictions.…”