Create → RTG File for Initial Depth

This routine computes a grid of flow depths for the baseflow case where there is steady-state flow with a given baseflow recharge rate at every grid cell. The derivation begins with the following four equations:

v = n-1 R2/3 S1/2 (Manning)
R = Ac / P
Q = v * Ac
Q = Rb * A

Trapezoidal channel cross-sections are then assumed, with bottom-width, w, and bank-angle, θ, specified as input grids. For such channels we have:

Ac = d * [w + (d * tan(θ))]
P = w + [2 * d / cos(θ)]

These last two equations can be used to show that R = (Ac/P) is closely approximated by the flow depth, d, when (w/d) has a value greater than about 10.

All of these equations can be combined to eliminate v and get a single, nonlinear equation for flow depth, d. This equation is then solved iteratively by grid-based Newton-Raphson iteration; that is, iterated until all grid cells have converged.

Once the initial depth grid has been computed, the corresponding initial velocity grid is computed using the Manning formula.

It is assumed that hillslope pixels have been assigned parameters that are consistent with Manning-type modeling of overland flow. This can be done with the Create → Channel Geometry Grids → With Area Grid dialog or the Create → Channel Geometry Grids → With HS Order Grid dialog.

The variables in the above equations are defined as follows:

Q = discharge [m3/s]
A = basin area [km2]
S = channel slope [none]
v = flow velocity [m/s]
w = bed width [m]
n = Manning roughness parameter [s/m1/3]
Ac = wetted channel cross-section area [m2]
P = wetted channel cross-section permiter [m]
R = hydraulic radius [m] = (Ac / P)
Rb = baseflow recharge rate [mm/year]
d = flow depth [m]