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Flood Frequency Analysis Using the Cox Regression Model
Author(s) -
Smith James A.,
Karr Alan F.
Publication year - 1986
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr022i006p00890
Subject(s) - flood myth , covariate , regression analysis , regression , statistics , mathematics , proportional hazards model , hydrology (agriculture) , geology , geography , geotechnical engineering , archaeology
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.