One stumbling block in water resources engineering is the inadequacy of stream flow records. Records available from many streams are of insufficient length for use in design and prediction, and for some streams no streamflow data have been recorded. Risk-based methods may require large sets of possible stream flow scenarios. The goal of this study is to develop a method to extend gage records realistically, and allow synthesis of realistic daily discharge hydrographs. The original purpose of the study was to provide long duration (100-year) daily discharge hydrographs for a mathematical model that predicts bridge pier scour. A Markov model with time-varying parameters is developed and implemented in Matlab. The model captures the annual cycle and day-to-day persistence of daily streamflow, using 10 parameters estimated from gage records, without precipitation input or watershed modeling. The Matlab program reads text files of stream flow records, estimates the model parameters, and saves results in spreadsheet format. Seventy-eight stream gages in Maryland, with drainage areas from 2 to 27000 , are analyzed. Several examples demonstrate the use of the model in synthesis mode. The model will be useful for any prediction or design tool requiring realistic synthetic discharge hydrographs.