**U.S. Geological Survey Water-Resources Investigations Report 91-4194
Lansing, Michigan 1992**

Statistical models for estimating daily streamflow were analyzed for 25 pairs of streamflow-gaging stations in Michigan. Stations were paired by randomly choosing a station operated in 1989 at which 10 or more years of continuous flow data had been collected and at which flow is virtually unregulated; a nearby station was chosen where flow characteristics are similar. Streamflow data from the 25 randomly selected stations were used as the response variables; streamflow data at the nearby stations were used to generate a set of explanatory variables. Ordinary-least-squares regression (OLSR) equations, autoregressive integrated moving-average (ARIMA) equations, and transfer-function-noise (TFN) equations were developed to estimate the log transform of flow for the 25 randomly selected stations. The precision of each type of equation was evaluated on the basis of the standard deviation of the estimation errors. OLSR equations produced one set of estimation errors, while ARIMA and TFN models each produced l set of estimation errors corresponding to the forecast lead. The standard deviation of composite errors varied throughout the length of the estimation interval and generally was at maximum near the center of the interval. The mean standard deviation of length-l composite errors were generally less than the standard deviation of the OLSR errors for l RECORD ID: 9302669

F&G CODE: 02e; 07c

**Publication**

Holtschlag, D.J., Salehi, H., 1992, Statistical Models for Estimating Daily
Streamflow in Michigan: Available from the US Geological Survey, Books and
Open-File Reports Section; Box 25425, Denver, CO 80225. Water-Resources
Investigations Report 91-4194, 54p, 17 fig, 4 tab, 14 ref. Prepared in
cooperation with the Michigan Department of Natural Resources.

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