Abstract
Drought conditions at a given location evolve randomly through time and are typically characterized by severity and duration. Researchers interested in modeling the economic effects of drought on agriculture or other water users often capture the stochastic nature of drought and its conditions via multiyear, stochastic economic models. Three major sources of uncertainty in application of a multiyear discrete stochastic model to evaluate user preparedness and response to drought are: (1) the assumption of independence of yearly weather conditions, (2) linguistic vagueness in the definition of drought itself, and (3) the duration of drought. One means of addressing these uncertainties is to re-cast drought as a stochastic, multiyear process using a “fuzzy” semi-Markov process. In this paper, we review “crisp” versus “fuzzy” representations of drought and show how fuzzy semi-Markov processes can aid researchers in developing more robust multiyear, discrete stochastic models.
Highlights
The impacts of drought on water supplies and those dependent on such supplies have long been an important topic for economists and policy makers
As the duration of consecutive years of severe drought increases to three years, the possibility of holding time in a fuzzy semi-Markov process is 0.1406, which is 280 percent higher than the probability assumed in a conventional multiyear discrete stochastic programming approach, 0.0370
The adverse effects of multiyear severe drought on both water supply and the environment are expected to increase as water demand increases, especially in the West
Summary
The impacts of drought on water supplies and those dependent on such supplies have long been an important topic for economists and policy makers. This type of linguistic vagueness of the term “drought” can be illustrated by considering the Palmer Drought Severity Index (PDSI), employed by the National Oceanic and Atmospheric Administration (NOAA) to communicate drought conditions to the public. Peck and Adams [3] developed a multiyear, discrete stochastic model of irrigation water use on a multi-crop farm that faces uncertain surface-water supplies due to the possibility of drought They used the model to identify optimal drought preparedness and response plans and measure associated economic benefits that result as the severity and duration of drought is revealed over a six-year period. These numerical examples highlight potential implications of using fuzzy semi-Markov processes rather than traditional probability-based representations of multiyear drought
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