Stream Runoff

To determine runoff pattern and drainage characteristics of a stream it is first necessary to know the amount and pattern of rainfall. This can be determined by a variety of methods, all of which begin with some form of precipitation measurement device. These devices are typically some type of self-reporting rain station in wilderness areas and a simple rain collection device in more populated regions.

The first and simplest way to determine rain amount over a region is the arithmetic mean. This is done using all of the rain collection data for the basin in question and figuring an average. This may be misleading, however, do to possible changes in topography and non-uniform placement of measuring devices.

The second and third methods for determining precipitation over a basin are the Theissen and isohyetal methods. In essence, these two methods take a weighted average of the rainfall data, taking into account that data from one station my represent a larger area than data from another station. In general, however, the reliability of rainfall measurement is a function of
(1) the distance of the gauge from the representative area,
(2) the size of the area,
(3) topography,
(4) the nature of the rainfall event concerned, and
(5) local storm pattern characteristics.

The isohyetal method greatly resembles a topographical map in that lines of equal rainfall are superimposed over a map of the basin. These lines are based on interpolation between rain gauge stations. The location of each station is first plotted on a map of the basin and after the data is collected the amount of rain for each station is indicated on the map at its respective station. Next, an interpolation between points is performed and rainfall amounts at selected increments are plotted. Points of equal rainfall are then connected forming an isohyet, a line of equal precipitation. By taking the arithmetic mean between isohyet and calculating the area between each isohyet, that area's contribution of rainfall can be determined. After repeating these steps for all areas in the basin, the final average can be determined by multiplying the mean for each area by the area, adding the results, and dividing by the number of areas.

The Theissen method uses areas subdivided into polygons to achieve a weighted average. To develop the polygons a line is drawn between a station and its immediate neighbors. Each line is then bisected with a line perpendicular to the first. This line continues until it reaches the next bisector. This process continues until each station is surrounded and the basin is covered with the polygons. Finally, the area of each polygon is multiplied by the amount of rainfall at the station it surrounds, the results are added, and the sum is divided by the number of stations.

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