Building a simple delta numerical model: Part V

Now we need to add a routine to update the channel bed, based upon the calculated change in sediment transport over space from the previous step. We’ll use the calculation from the last Part of the tutorial (get_dqsdx) in order to update the channel bed (\(\eta\)) at the end of each timestep. Define the following parameters

phi = 0.6; 	% bed porosity
If = 0.2; 	% intermittency factor

where If is an intermittency factor representing the fraction of the year that the river is experiencing significant morphodynamic activity. We are basically assuming that the only major change to the river occurs when the river is in flood. One year is the temporal resolution for the model, which we’ll define in the next Part.

function [eta] = update_eta(eta, dqsdx, phi, If, dtsec)
	eta0 = eta;
	eta = eta0 - ((1/(1-phi)) .* dqsdx .* (If * dtsec));
end

This module works simply by multiplying our vector for change in sediment transport capacity over space to the Exner equation (reproduced below) to evaluate the change in bed elevation over time (i.e., at the next timestep).

\[(1-\lambda_p) \frac{\partial \eta}{\partial t} = - \frac{\partial q_s}{\partial x}\]

There isn’t really anything exciting to show at this stage, as we’ve only calculated the change in the bed for a given dqsdx vector, which represents only a single timestep. In the next Part, we’ll add a time routine to the model, completing the setup required for the simple delta model.

This material is based upon work supported by the National Science Foundation (NSF) Graduate Research Fellowship under Grant No.145068 and NSF EAR-1427177. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.