Self-similar characteristics of drought duration, total deficit, and intensity curves

Abstract

Droughts are among the creeping extreme events with meteorological, hydrological, agricultural, and even social impacts. Due to their complex occurrences, drought identification and prediction need simple, effective, conceptual, logical, and rational innovative approaches that can help for practical applications. A new approach is being suggested at a set of threshold (or demand) levels to identify drought features such as duration, total deficit, and intensity relations, which depend on the run analysis and standardized precipitation index (SPI) methodology. This concept is applicable to identify mathematical relationships between the threshold values and the drought features. Exponential and power laws appear as straight lines on semi-logarithmic and double-logarithmic papers, respectively. In addition, power law implies self-similarity property with fractal geometrical patterns. As the threshold level increases, so does each one of the drought descriptors. Graphical representations help to identify climate change implications as well as practical design quantity determination. The applications of the suggested methodology are presented for monthly meteorological time series records. This methodology is also considered for the SPI over 6-month and 12-month moving average time scales at seven meteorology stations from different geographical parts of Turkey. The empirical mathematical expressions are obtained between the threshold values and the drought durations, total deficits, and drought intensities, which provide future drought characteristic predictions.