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kinematic
and
A = alpha { Q sup { beta }}
combined into
{{ delta Q } over { delta x }} +
{{ alpha } { beta } { Q sup { beta -1 }}
{{ delta Q } over { delta t }} = q }
with
Q streamflow through channel (m3/sec)
q inflow into the channel (m3/sec)
dt timestep used in the model (sec)
dx channel length through cell (m)
alpha coefficient
beta coefficient
The objective is to solve the equations for
Q tsub {t+1}
(Qnew) at each point in the map, given the channel parameters
alpha
and
beta
, the lateral inflow q and the initial conditions Qold. For each cell calculates the accumulated amount of
material that flows out of the cell into its neighbouring downstream cell. This accumulated amount is the
amount of material in the cell itself plus the amount of material in upstream cells of the cell.
Unlike the accuflux-family of functions this function allows for streamflow calculations in those
situations where the average travel time through a cell is within the magnitude of the model time step.
Notes
This is an experimental implementation of the numerical solutions of the kinematic wave equations. The
stability and accuracy of the equations can not be gauranteed under all circumstances.
The kinematic-operations uses (unlike other pcraster commands) defined units for the calculations.
Whereas other pcraster commands can operate with any consistent system of units, the
kinematic-operation explicitly needs its input parameters in (cubic) meters and seconds, and the result is
in qubic meters per second. This explains the explicit use of dX and dT in the interface of the operator.
Additional sediment flux based on the channel flow calculated with this operator can be obtained by the
code shown in example 1 below.
http://pcraster.geog.uu.nl/documentation/pcrman/r7415.htm (2 van 3) [3/2/2005 5:03:52 PM]