Model:TopoFlow-Infiltration-Richards 1D: Difference between revisions
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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. | ||
|</nowiki>_/_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) | |||
}} | }} | ||
{{Model identity | {{Model identity | ||
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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. | ||
|</nowiki>_/_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) | |||
}} | }} | ||
{{Model technical information | {{Model technical information | ||
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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. | ||
|</nowiki>_/_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) | |||
}} | }} | ||
{{Input - Output description | {{Input - Output description | ||
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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. | ||
|</nowiki>_/_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) | |||
}} | }} | ||
{{Process description model | {{Process description model | ||
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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 ( | 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) | 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 | 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. | ||
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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. | ||
|</nowiki>_/_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) | |||
}} | }} | ||
{{Model testing | {{Model testing | ||
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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. | ||
|</nowiki>_/_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) | |||
}} | }} | ||
{{Users groups model | {{Users groups model | ||
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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. | ||
|</nowiki>_/_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) | |||
}} | }} | ||
{{Documentation model | {{Documentation model | ||
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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. | ||
|</nowiki>_/_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) | |||
}} | }} | ||
{{Additional comments model | {{Additional comments model | ||
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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. | ||
|</nowiki>_/_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) | |||
}} | }} | ||
<!-- PLEASE USE THE "EDIT WITH FORM" BUTTON TO EDIT ABOVE CONTENTS; CONTINUE TO EDIT BELOW THIS LINE --> | <!-- PLEASE USE THE "EDIT WITH FORM" BUTTON TO EDIT ABOVE CONTENTS; CONTINUE TO EDIT BELOW THIS LINE --> |
Revision as of 14:36, 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 |
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