According to the article "characterizing the severity and risk of drought in the poudre river, colorado" (j. of water res. planning and mgmnt., 2005: 383–393), the drought length is the number of consecutive time intervals in which the water supply remains below a critical value (a deficit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). the cited paper proposes a geometric distribution with for this random variable.