Multivariate drought index: An information theory based approach for integrated drought assessment
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2014 Elsevier B.V. Most of the existing drought indices are based on a single variable (e.g. precipitation) or a combination of two variables (e.g., precipitation and streamflow). This may not be sufficient for reliable quantification of the existing drought condition. It is possible that a region might be experiencing only a single type of drought at times, but multiple drought types affecting a region is quite common too. To have a comprehensive representation, it is better to consider all the variables that lead to different physical forms of drought, such as meteorological, hydrological, and agricultural droughts. Therefore, we propose to develop a multivariate drought index (MDI) that will utilize information from hydroclimatic variables, including precipitation, runoff, evapotranspiration and soil moisture as indicator variables, thus accounting for all the physical forms of drought. The entropy theory was utilized to develop this proposed index, that led to the smallest set of features maximally preserving the information of the input data set. MDI was then compared with the Palmer drought severity index (PDSI) for all climate regions within Texas for the time period 1950-2012, with particular attention to the two major drought occurrences in Texas, viz. the droughts which occurred in 1950-1957, and 2010-2011. The proposed MDI was found to represent drought conditions well, due to its multivariate, multi scalar, and nonlinear properties. To help the user choose the right time scale for further analysis, entropy maps of MDI at different time scales were used as a guideline. The MDI time scale that has the highest entropy value may be chosen, since a higher entropy indicates a higher information content.
