# A New Method for Calculating a Mathematical Expression for Streamflow Recession

*by*Albert T. Rutledge, U.S. Geological Survey, Richmond, United States,

**Abstract:**An empirical method has been devised to calculate the master recession curve, which is a mathematical expression for streamflow recession during times of negligible direct runoff. The method is based on the assumption that the storage-delay factor, which is the time per log cycle of streamflow recession, varies linearly with the logarithm of streamflow. The resulting master recession curve can be nonlinear. The method can be executed by a computer program that reads a data file of daily mean streamflow, then allows the user to select several near-linear segments of streamflow recession. The storage-delay factor for each segment is one of the coefficients of the equation that results from linear least-squares regression. Using results for each recession segment, a mathematical expression of the storage-delay factor as a function of the log of streamflow is determined by linear least-squares regression. The master recession curve, which is a second-order polynomial expression for time as a function of log of streamflow, is then derived using the coefficients of this function.

**Subject Headings:**Streamflow | Curvature | Linear functions | Hydrologic models | Water resources | Water storage | Least squares method

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