In this two-part series a stochastic estimation procedure applicable to the analytic streamflow model derived in the companion is introduced. The parameter estimation problem is posed in the framework of maximum likelihood theory, where prior information about the model parameters and a suitable weighting scheme for the error terms in the estimation criterion are included. Various optimization methods are combined for parameter estimation. The issues of model and parameter identifiability, uniqueness, and stability are addressed, and strategies to mitigate identifiability problems in our modeling are discussed. The seasonal streamflow model is applied to a mountainous watershed in southern Arizona, and maximum likelihood estimates of mountain front recharge and other model and statistical parameters are obtained. The analysis of estimation errors is performed in both the eigenspace and the original space of the parameters. ¿ American Geophysical Union 1994