Precipitation statistics Cumulative probability of events Exceedance probability Return period Depth-Duration-Frequency Analysis

Statistical basis of hydrology Meteorological events characterized by statistical variability – precipitation inputs to watersheds - atmospheric forcing – resulting runoff, groundwater recharge, streamflow e.g. What is the largest rainfall event expected in a year? 10 years? 100 years? Ditto for flood events or drought intensity e.g. What is the probability of receiving more than 5 inches of rainfall in a day in any year? Of a flood exceeding a specific discharge or stage? Need statistical tools to make these estimates – often based on assumption of stationarity (historical record is representative of the future)

Precipitation probability distribution as a function of duration: shorter duration: skewed, extreme value distributions longer duration -> more normal distribution