basins,
Python
K_s = saturated hydraulic conductivity (m / s) K_i = initial hydraulic conductivity (m / s) (typically much less than K_s) θ_s = soil water content at ψ = 0 (unitless) (often set to the soil porosity, φ) θ_i = initial soil water content (unitless) θ_r = residual soil water content (unitless) (must be < θ_i) ψ_B = bubbling pressure head (meters) (also called air-entry pressure, ψ_ae) ψ_A = pressure head offset parameter (meters) λ = pore-size distribution parameter (unitless) (alt. notation = 1/b ) η = 2 + (3 * λ) (unitless) (see Notes) c = transitional Brooks-Corey curvature parameter (unitless) (see Notes) dznodes = vertical distance between nodes (meters) nnodes = number of subsurface vertical nodes
The behavior of this component is controlled with a configuration (CFG) file, which may point to other files that contain input data.
v = K * (1 - ψ_z) = Darcy's Law for vertical flow rate (m / s) v_z = J - θ_t = conservation of mass, with source/sink term J Θ_e = (θ - θ_r) / (θ_s - θ_r) = effective saturation or scaled water content (unitless) θ_r = θ_s ( abs(ψ_B) / 10000)^λ = residual water content (unitless) K = K_s * Θ_e^η/λ = hydraulic conductivity (m / s) (see Notes below) ψ = ψ_B (Θ_e^-c/λ - 1)^1/c - ψ_A = pressure head (meters) (see Notes below)
These equations are used to compute the time evolution of 1D (vertical, subsurface) profiles for (1) soil moisture, θ, (2) pressure head, ψ, (3) hydraulic conductivity, K and (4) vertical flow rate, v. TopoFlow solves these equations separately to get time-evolving profiles for every grid cell in a DEM. The result is a 3D grid for each of these four variables that spans the unsaturated zone. The third equation above just defines a variable that is used in the 4th and 5th equations, so the coupled set constitutes 4 equations to be solved for 4 unknowns. These equations can be combined into one nonlinear, parabolic, second-order PDE (partial differential equation) known as the one-dimensional Richards' equation.
This part will be filled out by CSDMS staff
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