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Newbie

## Tracking the Development of a Storm Using 30 Minute Interval Convolution

By D.M. Griffin, Jr.

• Shows you how to estimate the runoff from a rainfall hyetograph (convolution) using a hydrograph
• Applicable in environmental engineering, hydrology, the sciences, and to anyone learning PTC Mathcad programming and splines
• Performs using hydrographs, hyetographs, convolution equation, linear spline, interpolation, and plots

This worksheet shows you how to use a 15 minute UH hydrograph to estimate the runoff from a rainfall hyetograph, also called convolution. For this worksheet, one must assume that each burst of rainfall occurring on a basin within an interval of time comes off as direct runoff in accordance with a specified unit hydrograph for that basin. Each rainfall burst is multiplied by every ordinate of the unit hydrograph. Then the unit hydrograph is translated in time so that it coincides with the next burst. This must be done for each burst of rain. The runoff contributions of each rainfall burst are then summed with respect to the time interval in which they occurred.

This calculation is demonstrated using a 15 minute UH with 30 minute intervals and a precipitation vector with 30 minute intervals. Once all the data has been calculated, you can pass a smooth curve through the data points using a linear spline with interpolation. This plot can graph the computed direct runoff hydrograph points and spline, along with the rainfall hyetograph.

This problem is one that is a good example of an equation that would be very difficult and time consuming to do by hand, but is much more simple to do in PTC Mathcad.  This worksheet provides you with all data, step by step notation and instruction, definitions, formulas, equations, solutions, and graphs to aid you with your own calculations.