Model:TopoFlow-Infiltration-Richards 1D: Difference between revisions

From CSDMS
← Older editNewer edit →
No edit summary
No edit summary
Line 14: Line 14:
  K = Ks * Θeη/λ = hydraulic conductivity (m / s) (see Notes below)
  K = Ks * Θeη/λ = hydraulic conductivity (m / s) (see Notes below)
  ψ = ψB (Θe-c/λ - 1)1/c - ψA    = pressure head (meters) (see Notes below)  
  ψ = ψB (Θe-c/λ - 1)1/c - ψA    = 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.
|/_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.
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.
}}
}}
Line 26: Line 31:
  K = Ks * Θeη/λ = hydraulic conductivity (m / s) (see Notes below)
  K = Ks * Θeη/λ = hydraulic conductivity (m / s) (see Notes below)
  ψ = ψB (Θe-c/λ - 1)1/c - ψA    = pressure head (meters) (see Notes below)  
  ψ = ψB (Θe-c/λ - 1)1/c - ψA    = 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.
|/_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.
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.
}}
}}
Line 46: Line 56:
  K = Ks * Θeη/λ = hydraulic conductivity (m / s) (see Notes below)
  K = Ks * Θeη/λ = hydraulic conductivity (m / s) (see Notes below)
  ψ = ψB (Θe-c/λ - 1)1/c - ψA    = pressure head (meters) (see Notes below)  
  ψ = ψB (Θe-c/λ - 1)1/c - ψA    = 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.
|/_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.
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.
}}
}}
Line 135: Line 150:
  K = Ks * Θeη/λ = hydraulic conductivity (m / s) (see Notes below)
  K = Ks * Θeη/λ = hydraulic conductivity (m / s) (see Notes below)
  ψ = ψB (Θe-c/λ - 1)1/c - ψA    = pressure head (meters) (see Notes below)  
  ψ = ψB (Θe-c/λ - 1)1/c - ψA    = 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.
|/_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.
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.
}}
}}
Line 140: Line 160:
|Describe processes represented by the model=The Richards 1D method for modeling infiltration.
|Describe processes represented by the model=The Richards 1D method for modeling infiltration.
|Describe key physical parameters and equations=Equations Used by the 1D Richards' Equation Method
|Describe key physical parameters and equations=Equations Used by the 1D Richards' Equation Method
  v = K * (1 - ψ_z) = Darcy's Law for vertical flow rate (m / s)
  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
  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_e = (θ - θ_r) / (θ_s - θ_r) = effective saturation or scaled water content (unitless)
  θ_r = θ_s ( |ψ_B| / 10000)^λ = residual water content (unitless)
  θ_r = θ_s (<nowiki>|</nowiki>ψ_B<nowiki>|</nowiki> / 10000)^λ   = residual water content (unitless)
  K = K_s * Θ_e^η/λ = hydraulic conductivity (m / s) (see Notes below)
  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)  
  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.
|Describe length scale and resolution constraints=Recommended grid cell size is around 100 meters, but can be parameterized to run with a wide range of grid cell sizes. DEM grid dimensions are typically less than 1000 columns by 1000 rows.
|Describe length scale and resolution constraints=Recommended grid cell size is around 100 meters, but can be parameterized to run with a wide range of grid cell sizes. DEM grid dimensions are typically less than 1000 columns by 1000 rows.
|Describe time scale and resolution constraints=The basic stability condition is: dt < (dx / u_min), where dt is the timestep, dx is the grid cell size and u_min is the smallest velocity in the grid.  This ensures that flow cannot cross a grid cell in less than one time step. Typical timesteps are on the order of seconds to minutes. Model can be run for a full year or longer, if necessary.
|Describe time scale and resolution constraints=The basic stability condition is: dt < (dx / u_min), where dt is the timestep, dx is the grid cell size and u_min is the smallest velocity in the grid.  This ensures that flow cannot cross a grid cell in less than one time step. Typical timesteps are on the order of seconds to minutes. Model can be run for a full year or longer, if necessary.
Line 154: Line 172:
  K = Ks * Θeη/λ = hydraulic conductivity (m / s) (see Notes below)
  K = Ks * Θeη/λ = hydraulic conductivity (m / s) (see Notes below)
  ψ = ψB (Θe-c/λ - 1)1/c - ψA    = pressure head (meters) (see Notes below)  
  ψ = ψB (Θe-c/λ - 1)1/c - ψA    = 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.
|/_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.
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.
}}
}}
Line 169: Line 192:
  K = Ks * Θeη/λ = hydraulic conductivity (m / s) (see Notes below)
  K = Ks * Θeη/λ = hydraulic conductivity (m / s) (see Notes below)
  ψ = ψB (Θe-c/λ - 1)1/c - ψA    = pressure head (meters) (see Notes below)  
  ψ = ψB (Θe-c/λ - 1)1/c - ψA    = 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.
|/_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.
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.
}}
}}
Line 176: Line 204:
  K = Ks * Θeη/λ = hydraulic conductivity (m / s) (see Notes below)
  K = Ks * Θeη/λ = hydraulic conductivity (m / s) (see Notes below)
  ψ = ψB (Θe-c/λ - 1)1/c - ψA    = pressure head (meters) (see Notes below)  
  ψ = ψB (Θe-c/λ - 1)1/c - ψA    = 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.
|/_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.
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.
}}
}}
Line 185: Line 218:
  K = Ks * Θeη/λ = hydraulic conductivity (m / s) (see Notes below)
  K = Ks * Θeη/λ = hydraulic conductivity (m / s) (see Notes below)
  ψ = ψB (Θe-c/λ - 1)1/c - ψA    = pressure head (meters) (see Notes below)  
  ψ = ψB (Θe-c/λ - 1)1/c - ψA    = 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.
|/_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.
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.
}}
}}
Line 197: Line 235:
  K = Ks * Θeη/λ = hydraulic conductivity (m / s) (see Notes below)
  K = Ks * Θeη/λ = hydraulic conductivity (m / s) (see Notes below)
  ψ = ψB (Θe-c/λ - 1)1/c - ψA    = pressure head (meters) (see Notes below)  
  ψ = ψB (Θe-c/λ - 1)1/c - ψA    = 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.
|/_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.
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.
}}
}}

Revision as of 14:20, 17 February 2010

Contact

Name Scott Peckham
Type of contact Model developer
Institute / Organization CSDMS, INSTAAR, University of Colorado
Postal address 1 1560 30th street
Postal address 2
Town / City Boulder
Postal code 80305
State Colorado
Country USA"USA" is not in the list (Afghanistan, Albania, Algeria, Andorra, Angola, Antigua and Barbuda, Argentina, Armenia, Australia, Austria, ...) of allowed values for the "Country" property.
Email address Scott.Peckham@colorado.edu
Phone 303-492-6752
Fax



TopoFlow-Infiltration-Richards 1D


Metadata

Summary

Also known as
Model type Single
Model part of larger framework
Note on status model
Date note status model

Technical specs

Supported platforms
Unix, Linux, Mac OS, Windows
Other platform
Programming language

Python

Other program language None (but uses NumPy package)
Code optimized Single Processor
Multiple processors implemented
Nr of distributed processors
Nr of shared processors
Start year development 2001
Does model development still take place? Yes
If above answer is no, provide end year model development
Code development status
When did you indicate the 'code development status'?
Model availability As code, As teaching tool
Source code availability
(Or provide future intension) 		Through CSDMS repository
Source web address
Source csdms web address
Program license type Apache public license
Program license type other
Memory requirements Standard
Typical run time Minutes to hours


In/Output

Describe input parameters The input variables used for modeling infiltration and unsaturated vertical flow with the 1D Richard's equation are defined as follows: 
Ks 	 = saturated hydraulic conductivity (m / s)
Ki 	 = initial hydraulic conductivity (m / s) (typically much less than Ks)
θs 	 = soil water content at ψ = 0 (unitless) (often set to the soil porosity, φ)
θi 	 = initial soil water content (unitless)
θr 	 = residual soil water content (unitless) (must be < θi)
ψB 	 = bubbling pressure head (meters) (also called air-entry pressure, ψae)
ψA 	 = 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. Here is a sample configuration (CFG) file for this component: 

Method code:            4                                                   
Method name:            Richards_1D                                          
Number of layers:       3                                                    
Time step:              Scalar         60.0                    (sec)         
Ks:                     Scalar         7.20000010915e-06       (m/s)         
Ki:                     Scalar         9.84968936528e-08       (m/s)         
qs:                     Scalar         0.485                   (none)        
qi:                     Scalar         0.375807627781          (none)        
qr:                     Scalar         0.0815254493977         (none)        
pB:                     Scalar         -0.785999984741         (m)           
pA:                     Scalar         0.0                     (m)           
lambda:                 Scalar         0.188679238493          (none)        
c:                      Scalar         1.0                     (none)        
dz:                     Scalar         0.03                    (m)           
nz:                     Scalar         20                      (none)        
Closest soil_type:      silt_loam                                            
Ks:                     Scalar         6.94999995176e-06       (m/s)         
Ki:                     Scalar         3.29297097399e-08       (m/s)         
qs:                     Scalar         0.451                   (none)        
qi:                     Scalar         0.328764135306          (none)        
qr:                     Scalar         0.071217406467          (none)        
pB:                     Scalar         -0.477999992371         (m)           
pA:                     Scalar         0.0                     (m)           
lambda:                 Scalar         0.185528761553          (none)        
c:                      Scalar         1.0                     (none)        
dz:                     Scalar         0.03                    (m)           
nz:                     Scalar         20                      (none)        
Closest soil_type:      loam                                                 
Ks:                     Scalar         2.45000002906e-06       (m/s)         
Ki:                     Scalar         3.11491927151e-08       (m/s)         
qs:                     Scalar         0.476                   (none)        
qi:                     Scalar         0.412771789613          (none)        
qr:                     Scalar         0.15295787535           (none)        
pB:                     Scalar         -0.63                   (m)           
pA:                     Scalar         0.0                     (m)           
lambda:                 Scalar         0.117370885713          (none)        
c:                      Scalar         1.0                     (none)        
dz:                     Scalar         0.03                    (m)           
nz:                     Scalar         20                      (none)        
Closest soil_type:      clay_loam                                            
Save grid timestep:     Scalar         60.00000000             (sec) 
Save v0 grids:          0              Case5_2D-v0.rts         (m/s) 
Save q0 grids:          0              Case5_2D-q0.rts         (none) 
Save I  grids:          0              Case5_2D-I.rts          (m) 
Save Zw grids:          0              Case5_2D-Zw.rts         (m) 
Save pixels timestep:   Scalar         60.00000000             (sec) 
Save v0 pixels:         0              Case5_0D-v0.txt         (m/s) 
Save q0 pixels:         0              Case5_0D-q0.txt         (none) 
Save I  pixels:         0              Case5_0D-I.txt          (m) 
Save Zw pixels:         0              Case5_0D-Zw.txt         (m) 
Save stack timestep:    Scalar         60.00000000             (sec) 
Save q stacks:          0              Case5_3D-q.rt3          (none) 
Save p stacks:          0              Case5_3D-p.rt3          (m) 
Save K stacks:          0              Case5_3D-K.rt3          (m/s) 
Save v stacks:          0              Case5_3D-v.rt3          (m/s) 
Save profile timestep:  Scalar         60.00000000             (sec) 
Save q profiles:        0              Case5_1D-q.txt          (none) 
Save p profiles:        0              Case5_1D_p.txt          (m) 
Save K profiles:        0              Case5_1D_K.txt          (m/s) 
Save v profiles:        0              Case5_1D_v.txt          (m/s)
Input format ASCII, Binary
Other input format
Describe output parameters
Output format ASCII, Binary
Other output format
Pre-processing software needed? Yes
Describe pre-processing software Another program must be used to create the input grids. This includes a D8 flow grid derived from a DEM for the region to be modeled. The earlier, IDL version of TopoFlow can be used to create some of these.
Post-processing software needed? Yes
Describe post-processing software None, except visualization software. Grid sequences saved in netCDF files can be viewed as animations and saved as movies using VisIt.
Visualization software needed? Yes
If above answer is yes
Other visualization software VisIt


Process

Describe processes represented by the model The Richards 1D method for modeling infiltration.
Describe key physical parameters and equations Equations Used by the 1D Richards' Equation Method 
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 ('"`UNIQ--nowiki-00000000-QINU`"'ψ_B'"`UNIQ--nowiki-00000001-QINU`"' / 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)
Describe length scale and resolution constraints Recommended grid cell size is around 100 meters, but can be parameterized to run with a wide range of grid cell sizes. DEM grid dimensions are typically less than 1000 columns by 1000 rows.
Describe time scale and resolution constraints The basic stability condition is: dt < (dx / u_min), where dt is the timestep, dx is the grid cell size and u_min is the smallest velocity in the grid. This ensures that flow cannot cross a grid cell in less than one time step. Typical timesteps are on the order of seconds to minutes. Model can be run for a full year or longer, if necessary.
Describe any numerical limitations and issues This model/component needs more rigorous testing.


Testing

Describe available calibration data sets This model/component is typically not calibrated to fit data, but is run with a best guess or measured value for each input parameter.
Upload calibration data sets if available:
Describe available test data sets Available test data sets:
  • Treynor watershed, in the Nishnabotna River basin, Iowa, USA.
  • (Two large rainfall events.)
  • Small basin in Kentucky.
  • Inclined plane for testing.
  • Arctic watershed data from Larry Hinzman (UAF).
  • See /data/progs/topoflow/3.0/data on CSDMS cluster.
Upload test data sets if available:
Describe ideal data for testing Several test datasets are stored on the CSDMS cluster at: /data/progs/topoflow/3.0/data.


Other

Do you have current or future plans for collaborating with other researchers? Collaborators include: Larry Hinzman (UAF), Bob Bolton, Anna Liljedahl (UAF), Stefan Pohl and others
Is there a manual available? Yes
Upload manual if available:
Model website if any This site.
Model forum / discussion board
Comments About this component:
  • This component was developed as part of the TopoFlow hydrologic model, which was originally written in IDL and had a point-and-click GUI. For more information on TopoFlow, please goto: http://csdms.colorado.edu/wiki/Model:TopoFlow.
  • When used from within the CSDMS Modeling Tool (CMT), this component has "config" button which launches a graphical user interface (GUI) for changing input parameters. The GUI is a tabbed dialog with a Help button at the bottom that displays HTML help in a browser window.
  • This component also has a configuration (CFG) file, with a name of the form: <case_prefix>_channels_diff_wave.cfg. This file can be edited with a text editor.
  • The Numerical Python module (numpy) is used for fast, array-based processing.
  • This model has an OpenMI-style interface, similar to OpenMI 2.0. Part of this interface is inherited from "CSDMS_base.py".

Introduction

History

Papers

Issues

Help

Input Files

Output Files

Download

Source

Retrieved from "https://csdms.colorado.edu/csdms_wiki/index.php?title=Model:TopoFlow-Infiltration-Richards_1D&oldid=12336"