Possibility of Cusp Catastrophe in Rainfall-Runoff Processes

During the past few decades, simulation of rainfali-runoff processes hasbeen transformed into a capability in hydrology with well-established models andsoftware tools. however, these models transform rainfall into runoff throughcontinuous mathematical functions overlooking possible discontinuities. the focusof this paper is on unraveling possible discontinuities to gain a better insight into theprocess. it introduces the notion of cusp catastrophe developed by rene thorn(1975) to investigate the behavior of rainfali-runoff processes. the study usesmonthly rainfali-runoff of the river aji basin in northwest iran observed for theperiod of 1980-2000. the results are strong enough to make a case for applying thecusp catastrophe model by indicating catastrophic behavior in the rainfall-runoffhydrology, as the r2 statistic and relative errors for monthly flow discharges areparticularly promising. the simulated results are compared with their correspondingobserved data using a number of performance evaluation criteria. this studyemp.loys the cuspfit program developed by cobb, with improvements by hartelman.