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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 .
We obtain the distribution of the property i.e. a given two dimensional situation by writing discretized equations of the form of equation (3) at each grid node of the subdivided domain. At the boundaries where the temperature or fluxes are known the discretized equation are modified to incorporate the boundary conditions.
In hydrology, discharge is the volumetric flow rate (volume per time, in units of m 3 /h or ft 3 /h) of a stream. It equals the product of average flow velocity (with dimension of length per time, in m/h or ft/h) and the cross-sectional area (in m 2 or ft 2). [1] It includes any suspended solids (e.g. sediment), dissolved chemicals like CaCO
Shallow-water equations, in its non-linear form, is an obvious candidate for modelling turbulence in the atmosphere and oceans, i.e. geophysical turbulence. An advantage of this, over Quasi-geostrophic equations, is that it allows solutions like gravity waves, while also conserving energy and potential vorticity.
Infiltration is a component of the general mass balance hydrologic budget. There are several ways to estimate the volume and water infiltration rate into the soil. The rigorous standard that fully couples groundwater to surface water through a non-homogeneous soil is the numerical solution of Richards' equation.