Flood Frequency Analysis Using the Cox Regression Model

Procedures for incorporating time‐varying exogenous information into flood frequency analyses are developed using the Cox regression model for counting processes. In this statistical model the probability of occurrence of a flood peak in a short interval [ t , t + dt ) depends in an explicit manner on the values at t of k “covariate” processes Z 1 , …, Z k . Specifically, letting dN ( t ) be 1 if a flood peak occurs in [ t , t + dt ) and 0 otherwise, dN ( t ) = a ( t ) exp {∑ j=1 k b j Z j ( t )} + dM ( t ) where a , the “baseline intensity,” is an unknown function, b is a vector of unknown “regression” parameters, and the error dM ( t ) is (conditionally) orthogonal to the past history. Two applications, assessment of relative importance of physical processes such as snow melt or soil moisture storage on flood frequency at a site and derivation of time‐varying flood frequency estimates, are considered.