Modeling of hydrological drought durations and magnitudes: Experiences on Canadian streamflows

Abstract

Study region: North-west Ontario and eastern Canada. Study focus: This study utilized river flow sequences to predict hydrological drought parameters (duration and magnitude) on annual, monthly and weekly time scales. Analysis was conducted at the median truncation level, using the standardized hydrological index (SHI) series. Two approaches – the extreme number theorem and Markov chain – were used for modeling droughts by analyzing runs of dry and wet periods. New hydrological insights for the region: Approach based on the extreme number theorem predicted satisfactorily drought durations at monthly and annual time scales and was also found comparable to Markov chain of order-one for predicting monthly drought durations. The approach was found less satisfactory for predicting drought durations at weekly time scale but the performance was found to improve with the use of Markov chain of order-two. At annual, monthly, and weekly time scales, the relationship (magnitude = intensity × duration) proved satisfactory for predicting drought magnitudes with the assumption that truncated normal distribution performs well for modeling the drought intensity. For predicting drought magnitudes at monthly and weekly time scales, the Markov chain proved more satisfactory with one order lower than the order that was used for predicting drought durations. Markov chain of order-one modeled durations satisfactorily at weekly time scale with uniform truncation levels corresponding to flows equivalent to 90% and 95%.

Keywords

• Deficit-volume
• Drought parameters
• Extreme number theorem
• Markov chain model
• Standardized hydrological index
• Truncated normal probability distribution