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According to the equations, a basin with high drainage density, the contribution of surface runoff to stream discharge will be high, while that from baseflow will be low. Conversely, a stream in a low drainage density system will have a larger contribution from baseflow and a smaller contribution from overland flow. [8] [9]
The amplified drainage equation uses an hydraulic equivalent of Joule's law in electricity. It is in the form of a differential equation that cannot be solved analytically (i.e. in a closed form ) but the solution requires a numerical method for which a computer program is indispensable.
The discharge may also be expressed as: Q = − dS/dT . Substituting herein the expression of Q in equation (1) gives the differential equation dS/dT = A·S, of which the solution is: S = exp(− A·t) . Replacing herein S by Q/A according to equation (1), it is obtained that: Q = A exp(− A·t) .
Dissolved load is the portion of a stream's total sediment load that is carried in solution, especially ions from chemical weathering. It is a major contributor to the total amount of material removed from a river's drainage basin , along with suspended load and bed load .
Results showed that this approximation does not affect the calculated infiltration flux because the diffusive flux is small and that the finite water-content vadose zone flow method is a valid solution of the equation [13] is a set of three ordinary differential equations, is guaranteed to converge and to conserve mass. It requires the ...
A drainage basin is an area of land in which all flowing surface water converges to a single point, such as a river mouth, or flows into another body of water, such as a lake or ocean. A basin is separated from adjacent basins by a perimeter, the drainage divide , [ 1 ] made up of a succession of elevated features, such as ridges and hills .
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:
This is an important distinction because, for example, the vertical velocity cannot be zero when the floor changes depth, and thus if it were zero only flat floors would be usable with the shallow-water equations. Once a solution (i.e. the horizontal velocities and free surface displacement) has been found, the vertical velocity can be ...