This is the simplest fluxing procedure that will work for steep areas, where the flow is entirely driven by the gradient. We assume that fluxes are already known (say defined by a Stella Module). For each cell in the StudyArea we calculate the amount of water that is to be moved with the flux to the next cell 'downhill'. Then we update the Surface Water variable, adding/subtracting the water moved. Also move 'Stuff' together with water, in proportion to the amount of water moved. 'Stuff' can be dissolved (nutrients), or suspended (detritus, sediment). It has to be uniformly distributed in the cell volume, so that its flux can be assumed proportional to water transport.
This may be repeated over the whole area several times, in which case we get the multiple cell algorithm. In this case over one time step the water from a cell ends up several cells downhill. The number of iterations niter can be adjusted to satisfy the Courant condition, that is necessary for the model to be stable:
dx/dt ≥ F/S,
where, F - is the flux of water (m3/d), and S - is the area (m2) of the surface water in the cell. This condition implies that to make the model stable we need to reduce the time step, when we need to run the model at a finer spatial resolution.
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This is the simplest fluxing procedure that will work for steep areas, where the flow is entirely driven by the gradient. We assume that fluxes are already known (say defined by a Stella Module). For each cell in the StudyArea we calculate the amount of water that is to be moved with the flux to the next cell 'downhill'. Then we update the Surface Water variable, adding/subtracting the water moved. Also move 'Stuff' together with water, in proportion to the amount of water moved. 'Stuff' can be dissolved (nutrients), or suspended (detritus, sediment). It has to be uniformly distributed in the cell volume, so that its flux can be assumed proportional to water transport.
This may be repeated over the whole area several times, in which case we get the multiple cell algorithm. In this case over one time step the water from a cell ends up several cells downhill. The number of iterations niter can be adjusted to satisfy the Courant condition, that is necessary for the model to be stable: