A Simplified Model for Predicting Drought Magnitudes: a Case of Streamflow Droughts in Canadian Prairies

The model for prediction of drought magnitudes is based on the multiplicative relationship: drought magnitude (M)=drought intensity (I) × drought duration (L), where I, L, and M are presumed to obey respectively the truncated normal probability distribution function (pdf), the geometric pdf, and the normal pdf. The multiplicative relationship is applied in the standardized domain of the streamflows, named as SHI (standardized hydrological index) sequences, which are treated equivalent to standard normal variates. The expected drought magnitude E(M <Subscript> T </Subscript>), i.e. the largest value of M over a sampling period of T-time units (T-year, T-month, and T-week) is predicted for hydrological droughts using streamflow data from Canadian prairies. By suitably amalgamating E(L <Subscript> T </Subscript>) with mean and variance of I in the extreme number theorem based relationship, the E(M <Subscript> T </Subscript>) is evaluated. Using Markov chain (MC), the E(L <Subscript> T </Subscript>) is estimated involving the geometric pdf of L. The Markov chains up to order one (MC-1) were found to be adequate in the proposed model for the annual to weekly time scales. For a given level of drought probability (q) and a sampling period T-time units; the evaluation of E(M <Subscript> T </Subscript>) requires only 3 parameters viz. lag-1 autocorrelation (ρ <Subscript> 1 </Subscript>), first order conditional probability (q <Subscript> q </Subscript>, present instant being a drought given past instant was a drought) in SHI sequences and a parameter ø (value 0 to 1), which were estimated from historical data of streamflows. A major strength of the proposed model lies in the use of simple and widely familiar normal and geometric pdfs as its basic building blocks for the estimation of drought magnitudes. Copyright Springer Science+Business Media Dordrecht 2014