Property:Describe key physical parameters
From CSDMS
This is a property of type Text.
K
Key parameters include the rate of sea level rise, suspended sediment concentration, tidal range (which controls vegetation distribution), critical shear stress for sediment erosion, and the period of time that erosion takes place during each tidal cycle. Parameters controlling the growth pattern of vegetation can easily be modified. +
W
Key physical parameters are:
# flows rivers/stream/canal/open channel networks - 1D St Venant Equations for River Networks with kinematic, diffusive, and fully dynamic wave options,
# flows in overland regime - 2D St Venant Equations with: kinematic, diffusive, and fully dynamic wave options,
# flow in subsurface media - 3D Richard Equation for both vadose and saturated zones,
# salinity, thermal, and sediment transport in river networks and overland regime - modified ddvection-dispersion equations with phenomenological approaches for erosion and deposition, and
# water quality transport for all media - advection-dispersion-reaction equations with reaction-based mechanistic approaches to water quality modeling using a general paradigm.
For details refer to Yeh et al., 2005 Technical Report on WASH123D +
S
Key physical parameters include sediment grain size, sediment, density, water and sediment discharge, run time, the initial surface slope, the threshold sediment flux to propagate a new channel, and the allowed channel superelevation above the surrounding topography before avulsion. These parameters and the governing equations for the model are fully described in Limaye et al. (2023), Effect of standing water on formation of fan-shaped sedimentary deposits at Hypanis Valles, Mars, https://dx.doi.org/10.1029/2022GL102367 +
C
Key physical parameters:
*Q: water discharge upstream crevasse splay;
*Qcs: outflow discharge of crevasse splay;
*Qabove: the water discharge above the bottom of crevasse splay;
*rq: the discharge ratio of Qcs and Qabove;
*hs: channel belt's super-elevation (the elevation of lowest point of channel bed);
*Zcs: bottom elevation of crevasse splay;
*Bcs: width of crevasse splay;
*Hcs: flow depth of crevasse splay;
*Vcs: flow velocity of crevasse splay;
*jcs: slope of the outflow of crevasse splay;
*Zcsb: bottom elevation of a crevasse splay whose flow slope is equal to the channel slope j;
Key physical equations:
*Zcs<=max(hs,Zcsb);
*rq=(1.55-1.45*Fi)*Bcs/wc+0.16*(1-2*Fi), in which Fi is the Fraud number for flow in the trunk channel, wc is width of the trunk channel;
*Hcs=(nc*Qcs/sqrt(jcs)/Bcs)^(3/5);
*Vcs=Qcs/Hcs/Bcs;
*dE=M*(Vcs^2-ucre^2)/ucre^2*dt, where M is M-coefficient for erosion rate for crevasse slpay, ucre is critical velocity for erosion, dt is time step;
*dD=Sv*(1-Vcs^2/ucrd^2)*ws/0.6*dt, where Sv is volume sediment concentration, ucrd is critical velocity for deposition, ws is settling velocity of suspended load, dt is time step. +
G
V
Land Cover can subdivide each grid cell's land cover into arbitrary number of "tiles", each corresponding to the fraction of the cell covered by that particular land cover (e.g. coniferous evergreen forest, grassland, etc.)
geographic locations or configurations of land cover types are not considered; VIC lumps all patches of same cover type into 1 tile
Snow Model
VIC considers snow in several forms: ground snow pack, snow in the vegetation canopy, and snow on top of lake ice. Main features:
Ground snow pack is quasi 2-layer; the topmost portion of the pack is considered separately for solving energy balance at pack surface
Meteorological Input Data
Can use sub-daily met data (prcp, tair, wind) at intervals matching simulation time step
Can use daily met data (prcp, tmax, tmin, wind) for daily or sub-daily simulations
Disaggregates daily met data to sub-daily via Thornton & Running algorithm and others (computes incoming sw and lw rad, pressure, density, vp)
VIC can consider spatial heterogeneity in precipitation, arising from either storm fronts/local convection or topographic heterogeneity. Here we consider the influence of storm fronts and local convective activity. This functionality is controlled by the DIST_PRCP option in the global parameter file. Main features:
Can subdivide the grid cell into a time-varying wet fraction (where precipitation falls) and dry fraction (where no precipitation falls).
The wet fraction depends on the intensity of the precipitation; the user can control this function.
Fluxes and storages from the wet and dry fractions are averaged together (weighted by area fraction) to give grid-cell average for writing to output files.
Elevation Bands
VIC can consider spatial heterogeneity in precipitation, arising from either storm fronts/local convection or topographic heterogeneity. Here we consider the influence of topography, via elevation bands. This is primarily used to produce more accurate estimates of mountain snow pack. This functionality is controlled by the SNOW_BAND option in the global parameter file. Main features:
Can subdivide the grid cell into arbitrary number of elevation bands, to account for variation of topography within cell
Within each band, meteorologic forcings are lapsed from grid cell average elevation to band's elevation
Geographic locations or configurations of elevation bands are not considered; VIC lumps all areas of same elevation range into 1 band
Fluxes and storages from the bands are averaged together (weighted by area fraction) to give grid-cell average for writing to output files
However, the band-specific values of some variables can be written separately in the output files
Liang et al. (1999): set QUICK_FLUX to TRUE in global parameter file; this is the default for FULL_ENERGY = TRUE and FROZEN_SOIL = FALSE.
Cherkauer et al. (1999): set QUICK_FLUX to FALSE in global parameter file; this is the default for FROZEN_SOIL = TRUE.
By default, the finite difference formulation is an explicit method.
By default, the nodes of the finite difference formulation are spaced linearly.
These apply to the case QUICK_FLUX = FALSE and FROZEN_SOIL = TRUE, i.e. the formulation of Cherkauer et al. (1999).
L
R
Linear nearshore wave transformation numerical model for estimating wave transformation over an arbitrary bathymetry constrained to have mild bottom slopes. The model is based on the numerical solution of the parabolic approximation of the velocity potential of the forward scattered wave field. +
C
Linearized RANS for turbulent boundary layer over smooth terrain
Shear stress partitioning model (work of Raupach et al 1993)
Vegetation growth parameters (timescale, vegetation height, ratio of frontal to basal area) +
T
Main equations used by this component:
ΔV(i,t) = Δt * ( R(i,t) Δx Δy - Q(i,t) + Σ_k Q(k,t) ) = change in water volume (m^3) (mass cons.)
d = {( w^2 + 4 tan(θ) V / L)^1/2 - w } / (2 tan(θ)) = mean water depth in channel segment (m) (if θ > 0)
d = V / (w * L) = mean water depth in channel segment (m) (if θ = 0)
Δv(i,t) = Δt * (T_1 + T_2 + T_3 + T_4 + T_5) / ( d(i,t) * A_w )= change in mean velocity (m / s) (mom. cons.)
T_1 = v(i,t) * Q(i,t) * (C - 1) = efflux term in equation for Δv
T_2 = Σ_k (v(k,t) - v(i,t) * C) * Q(k,t) = influx term in equation for Δv
T_3 = -v(i,t) * C * R(i,t) * Δx * Δy = "new mass" momentum term in equation for Δv
T_4 = A_w * (g * d(i,t) * S(i,t)) = gravity term in equation for Δv
T_5 = -A_w * (f(i,t) * v(i,t)^2) = friction term in equation for Δv
Q = v * A_w = discharge of water (m^3 / s)
f(i,t) = ( κ / LN ( a * d(i,t) / z_0) )^2 = friction factor (unitless) (for law of the wall)
f(i,t) = g * n^2 / Rh(i,t)^1/3 = friction factor (unitless) (for Manning's equation)
C = A_w / A_t = area ratio appearing in equation for Δv
A_t = w_t * L = top surface area of a channel segment (m2) (L = length)
w_t = w + ( 2 * d * tan(θ) ) = top width of a wetted trapezoidal cross-section (m)
R_h = A_w / P_w = hydraulic radius (m)
A_w = d * (w + (d * tan(θ))) = wetted cross-sectional area of a trapezoid (m2)
P_w = w + (2 * d / cos(θ)) = wetted perimeter of a trapezoid (m)
V_w = d^2 * ( L * tan(θ) ) + d * (L * w) = wetted volume of a trapezoidal channel (m)
(Source: TopoFlow HTML Help System) +
Main equations used by this component:
ET = (1000 * Q_et) / (ρ_water * L_v) = evaporation rate (mm / sec)
Q_et = (Q_SW + Q_LW + Q_c + Q_h) = energy flux used to evaporate water (W / m^2)
Q_c = K_soil * (T_soil_x - T_surf) * (100 / x)= conduction energy flux (W / m^2) (between surf. and subsurf.)
Q_h = ρ_air * c_air * D_h * (T_air - T_surf) = sensible heat flux (W / m^2)
D_n = u_z * κ^2 / LN((z - h_snow) / z0_air)^2 = bulk exchange coeff. (neutrally stable conditions) (m / s)
D_h = D_n / (1 + (10 * Ri)), (T_air > T_surf) = bulk exchange coeff. for heat (m / s) (stable)
= D_n * (1 - (10 * Ri)), (T_air < T_surf) = bulk exchange coeff. for heat (m / s) (unstable)
Ri = g * z * (T_air - T_surf) / (u_z^2 (T_air + 273.15)) = Richardson's number (unitless) +
Main equations used by this component:
ΔV(i,t)= Δt * ( R(i,t) Δx Δy - Q(i,t) + Σk Q(k,t) ) = change in water volume (m^3), mass conservation
d = {( w^2 + 4 tan(θ) V / L)^1/2 - w } / (2 tan(θ)) = mean water depth in channel segment (m) (if θ > 0)
d = V / (w * L) = mean water depth in channel segment (m) (if θ = 0)
Q = v * Aw = discharge of water (m^3 / s)
v = n^(-1) * Rh^(2/3) * S^(1/2) = section-averaged velocity (m / s), Manning's formula
v = ( g * Rh * S)^(1/2) * LN( a * d / z0) / κ = section-averaged velocity (m / s), Law of the Wall
Rh = Aw / Pw = hydraulic radius (m)
Aw = d * (w + (d * tan(θ))) = wetted cross-sectional area of a trapezoid (m^2)
Pw = w + (2 * d / cos(θ)) = wetted perimeter of a trapezoid (m)
Vw = d^2 * ( L * tan(θ) ) + d * (L * w) = wetted volume of a trapezoidal channel (m)
(Source: TopoFlow HTML Help System) +
Main equations used by this component:
ET = (1000 * Q_et) / (ρ_water * L_v) = evaporation rate (mm / sec)
Q_et = α * (0.406 + (0.011 * T_air)) * (Q_SW + Q_LW - Q_c) = energy flux used to evaporate water (W / m^2)
Q_c = K_soil * (T_soil_x - T_surf) * (100 / x) = conduction energy flux (W / m^2) +
Main equations used by this component:
ΔV(i,t) = Δt * ( R(i,t) Δx Δy - Q(i,t) + Σ_k Q(k,t) ) = change in water volume (m^3), mass conservation
d = {( w^2 + 4 tan(θ) V / L)^1/2 - w } / (2 tan(θ)) = mean water depth in channel segment (m) (if θ > 0)
d = V / (w * L) = mean water depth in channel segment (m) (if θ = 0)
Q = v * A_w = discharge of water (m3 / s)
v = n^-1 * R_h^2/3 * S^1/2 = section-averaged velocity (m / s), Manning's formula
v = ( g * Rh * S)^1/2 * LN( a * d / z_0) / κ = section-averaged velocity (m / s), Law of the Wall
R_h = A_w / P_w = hydraulic radius (m)
A_w = d * (w + (d * tan(θ))) = wetted cross-sectional area of a trapezoid (m2)
P_w = w + (2 * d / cos(θ)) = wetted perimeter of a trapezoid (m)
V_w = d^2 * ( L * tan(θ) ) + d * (L * w) = wetted volume of a trapezoidal channel (m) +
M
Many, see Mudd et al. (2009) ECSS v 82(3) 377-389 +
E
Model governing equations express the conservation of sand and mud in the floodplain and in the channel. Water depth and shear stress are computed with a Chezy formulation for a composite rectangular cross section. Total ((bedload plus suspended load) sand transport capacity is computed with an Engelund and Hansen-type of bulk load relation (see Parker, 2004). The mean annual sand load is determined by averaging the sand transport capacities over the flow duration curve. Channel migration rate is computed as in Eke et al. (2014). Overbank deposition rates are computed with the approach presented in Parker et al. (1996).
References
Eke, E., Parker, G. & Shimizu, Y. (2014). Numerical modeling of erosional and depositional bank processes in migrating river bends with self-formed width: Morphodynamics of bar push and bank pull, Journal of Geophysical Research: Earth Surface 119, 1455-1483.
Parker, G. (2004). 1D sediment transport morphodynamics with applications to rivers and turbidity currents e-book available at http://hydrolab.illinois.edu/people/parkerg/morphodynamics_e-book.htm .
Parker, G., Cui, Y., Imran, J. & Dietrich, W. E. (1996). Flooding in the lower Ok Tedi, Papua New Guinea due to the disposal of mine tailings and it’s amelioration, International Seminar on Recent trends of floods and their preventive measures, 20-21 June, Sapporo, Japan. +
F
Momentum and continuity differential equations are solved for each layer. Closure equations are solved for bed-load discharge and entrainment/deposition. +
T
Navier-Stokes equation in Bousinessq approximations: to describe the ambient fluid's motion
Transport equation(s): to describe the particle and/or salinity concentration field evolution.
Reynolds number, Peclet number, particle settling velocities. +
R
Navier-Stokes primitive equations. Bio-optical, biogeochemical, and ecosystem models equations. Cohesive and non cohesive sediment equations. Several vertical turbulece equations (KPP, GLS, MY-2.5). Air-Sea interaction coupling equations (COARE). Bottom boundary layer model equations. +
C
