Equation
By modeling Playfair's Law in the following mathematical scheme, we can find the incision rate of the stream into the valley by following:
- where
- is the is erosion (or incision), and is therefore equal to the incision rate
- is an erosion parameter (see below)
- is the area drained by the stream
- is the local gradient of the channel
- stream parameters (see below)
In evaluating the case specific parameters, we regard as a parameter that is dependent on the type of land or soil that the stream is penetrating. Also, can be estimated by first assuming that at the junction the law holds over the distance used to determine S and taking their ratios (m/n) at different points, then substitution.
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