The simulation of catchment dynamics using a physically based overland flow model is well
established in hydraulic and hydrologic engineering practice (Ponce 1986).
The diffusion wave model is an improvement over the kinematic wave model because the former
is grid independent, while the latter is not. In fact, it can be
shown that the outflow hydrograph generated
by the diffusion wave model does not vary with the choice of grid size, while the same statement does not
hold true for the kinematic wave model.
This correct numerical behavior is due to the fact that the diffusion wave model
matches the physical diffusivity of Hayami with the numerical diffusivity of Cunge (Ponce 1989).
In addition to matching diffusivities,
ONLINE OVERLAND minimizes numerical dispersion by specifying the grid ratio such that the
Courant number is equal to 1.
This leads to
a simulation that is as numerically and physically accurate as it is
possible under the open-book schematization.
The specification of the
dynamic hydraulic diffusivity, replacing the kinematic hydraulic diffusivity,
the diffusion wave model to the realm of dynamic waves (Ponce 1991).
This assures the physical accuracy of the overland flow model
through a wide range of Vedernikov numbers.
ONLINE OVERLAND uses the diffusion wave model
to calculate overland flow in an open-book schematization, using one book.
The appropriate specification of Courant number and
dynamic hydraulic diffusivity assures
a simulation that is as physically and numerically accurate as it is
possible in deterministic catchment modeling.
Ponce, V. M. 1986. Diffusion wave modeling of catchment dynamics. Journal of Hydraulic Engineering, 112(8), August, 716-727.
Ponce, V. M. 1989. Engineering Hydrology: Principles and Practices. Prentice Hall, Englewood Cliffs, New Jersey.
Ponce, V. M. 1991. New perspective on the Vedernikov number. Water Resources Research, 27(7), July, 1777-1779.
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