In estimating erosion

Erosion

Erosion is when materials are removed from the surface and changed into something else. It only works by hydraulic actions and transport of solids in the natural environment, and leads to the deposition of these materials elsewhere...

, Playfair's Law is an empirical relationship

Empirical relationship

In science, an empirical relationship is one based solely on observation rather than theory. An empirical relationship requires only confirmatory data irrespective of theoretical basis. Sometimes theoretical explanations for what were initially empirical relationships are found, in which case the...

 that relates the size of a stream to the valley it runs through. The role of the flow regiment requires subject attention; the relation acts fundamentally similar to the functionality of a glacial trough. Since the relationship is case specific, it is a misleading description of the morphology

Geomorphology

Geomorphology is the scientific study of landforms and the processes that shape them...

 of fluvial

Fluvial

Fluvial is used in geography and Earth science to refer to the processes associated with rivers and streams and the deposits and landforms created by them...

 junctions and is better defined as a theory

Scientific theory

A scientific theory comprises a collection of concepts, including abstractions of observable phenomena expressed as quantifiable properties, together with rules that express relationships between observations of such concepts...

 rather than law.

Definition

The law states each stream

Stream

A stream is a body of water with a current, confined within a bed and stream banks. Depending on its locale or certain characteristics, a stream may be referred to as a branch, brook, beck, burn, creek, "crick", gill , kill, lick, rill, river, syke, bayou, rivulet, streamage, wash, run or...

 cuts into its own valley

Valley

In geology, a valley or dale is a depression with predominant extent in one direction. A very deep river valley may be called a canyon or gorge.The terms U-shaped and V-shaped are descriptive terms of geography to characterize the form of valleys...

, that each valley is proportional in size to its stream and that the stream junctions in the valley are proportional in depth in accordance with the stream level. Although there are models, in the most basic sense it simply says that large, fast streams will be in large valleys and vice versa. This is because steady, heavy flow of water will tug surrounding soil and subsequently erode and deepen the valley it cuts through.

Playfair's law also states that at tributary junctions, tributaries will have the same slope as the main channels. This is referred to by saying that the junctions occur "at grade".

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

Parameter

Parameter from Ancient Greek παρά also “para” meaning “beside, subsidiary” and μέτρον also “metron” meaning “measure”, can be interpreted in mathematics, logic, linguistics, environmental science and other disciplines....

 that is dependent on the type of land or soil

Soil

Soil is a natural body consisting of layers of mineral constituents of variable thicknesses, which differ from the parent materials in their morphological, physical, chemical, and mineralogical characteristics...

 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.