Determining how changing land use conditions will affect the discharge of a nearby stream is important for assessing flooding potential due to increased runoff. Increased development typically results in greater runoff due to the change in impervious cover. The rational method for determining peak discharge is an uncalibrated equation that calculates the maximum discharge in a stream by accounting for the watershed area, the peak rainfall intensity, and the land use characteristics.

The rational method relates the peak discharge in a stream (Q, in ft³/s) to the watershed area (A, acres), rainfall intensity (i, in/hr), and the runoff coefficient (C, dimensionless), such that

The equation is empirical (you can see that units do not work out properly) but is a useful method for assessing changing land use (C) on peak discharge. Watershed area may be measured from topographic maps or GPS (GPS may be preferable if development has changed the drainage pattern in an area, or if more precise areal measurements are desired).

Runoff characteristics range from 0 to 1, and are a function of the soil type, slope, vegetation, and other related factors. Runoff coefficients can be typically found in surface water hydrology textbooks. For example, cultivated land on 0-2% slopes have C = 0.08 and parking lots on >6% slopes have C = 0.97. One great source of C estimates is McCuen, (1998). Runoff coefficients in nonhomogeneous areas are calculated by summing the product of fraction of the watershed composed of a land use type by the runoff characteristic. For example, if 40% of the area is cultivated land on low slope (C = 0.08) and 60% is parking on steep slope (C = 0.97), the overall C is

Peak discharge estimates can then be made using the rational method for a range of rainfall intensities, or for record events by obtaining historic rainfall data from the NWS.

An important application of the rational method is the design of storm water drainage in small urban watershed. Calculating peak discharge through a development will allow planners to place appropriately sized culverts to assure effective storm water flow out of an area.

What is the peak discharge through a single culvert draining a forested watershed of 155 acres with low slope (C = 0.05) during a storm with a rainfall intensity of 6"/hr?

Q = (0.05) x 6 x 155

Q = 46.5 ft³/s