How to solve the 2D advection-diffusion equation for sediment transport using the PDE toolbox

I need to solve the 2D advection-diffusion equation for sediment transport:

where and D are a prescribed fields of velocity and depth, respectively, that I've obtained solving another pde on the same 2D mesh I am using to solve the adv-diff equation. Therefore, I know the value of and Dat each node at every time. and are source terms wherein is a function of C.

To a first approximation, D can be considered homogeneous in space, but changes through time.

In order to map the problem into the form requested by the pde toolbox, my best guess at the moment is to write the equation in the form:

Even so, how do I properly set the coefficients d,c, and f? I've been reading the PDE toolbox user guide but haven't been able to figured it out yet.

Thanks in advance for the help.