Derivation of streamflow statistics based on a filtered point process

This work presents the derivation of general streamflow cumulants from dail y rainfall time series. The general streamflow cumulants can be used to com pute basic streamflow statistics such as mean, variance, coefficient of ske wness, and correlation coefficient. Streamflow is considered as a filtered point process where the input is a daily rainfall time series assumed to be a marked point process. The marks of the process are the daily rainfall am ounts which are assumed independent and identically distributed. The number of rainfall occurrences is a counting process represented by either the bi nomial, the Poisson, or the negative binomial probability distribution depe nding on its ratio of mean to variance. The first three cumulants and the c ovariance function of J-day averaged streamflows are deduced based on the c haracteristic function of a filtered point process. These cumulants are fun ctions of the stochastic properties of the daily rainfall process and the b asin-response function representing the causal relationship between rainfal l and runoff.