tran.volume.1D: 1-D, 2-D and 3-D Volumetric Advective-Diffusive Transport in...
In ReacTran: Reactive Transport Modelling in 1d, 2d and 3d
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
Estimates the volumetric transport term (i.e. the rate of change of the
concentration due to diffusion and advection) in a 1-D, 2-D or 3-D model of
an aquatic system (river, estuary).
Volumetric transport implies the use of flows (mass per unit of time) rather
than fluxes (mass per unit of area per unit of time) as is done in
tran.1D, tran.2D or tran.3D.
The tran.volume.xD routines are particularly suited for modelling
channels (like rivers, estuaries) where the cross-sectional area changes,
but where this area change needs not to be explicitly modelled as such.
Another difference with tran.1D is that the tran.volume.1D
routine also allows lateral water or lateral mass input (as from side rivers
or diffusive lateral ground water inflow).
The tran.volume.2D routine can check for water balance and assume an
in- or efflux in case the net flows in and out of a box are not = 0
Usage
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tran.volume.1D(C, C.up = C[1], C.down = C[length(C)],
C.lat = C, F.up = NULL, F.down = NULL, F.lat = NULL,
Disp, flow = 0, flow.lat = NULL, AFDW = 1,
V = NULL, full.check = FALSE, full.output = FALSE)
tran.volume.2D(C, C.x.up = C[1, ], C.x.down = C[nrow(C), ],
C.y.up = C[, 1], C.y.down = C[, ncol(C)],
C.z = C, masscons = TRUE,
F.x.up = NULL, F.x.down = NULL,
F.y.up = NULL, F.y.down = NULL,
Disp.grid = NULL, Disp.x = NULL, Disp.y = Disp.x,
flow.grid = NULL, flow.x = NULL, flow.y = NULL,
AFDW.grid = NULL, AFDW.x = 1, AFDW.y = AFDW.x,
V = NULL, full.check = FALSE, full.output = FALSE)
tran.volume.3D(C, C.x.up = C[1, , ], C.x.down = C[dim(C)[1], , ],
C.y.up = C[, 1, ], C.y.down = C[, dim(C)[2], ],
C.z.up = C[, , 1], C.z.down = C[, , dim(C)[3]],
F.x.up = NULL, F.x.down = NULL,
F.y.up = NULL, F.y.down = NULL,
F.z.up = NULL, F.z.down = NULL,
Disp.grid = NULL,
Disp.x = NULL, Disp.y = Disp.x, Disp.z = Disp.x,
flow.grid = NULL, flow.x = 0, flow.y = 0, flow.z = 0,
AFDW.grid = NULL, AFDW.x = 1, AFDW.y = AFDW.x,
AFDW.z = AFDW.x,
V = NULL, full.check = FALSE, full.output = FALSE)
Arguments
C
tracer concentration, defined at the centre of the grid cells.
A vector of length N [M/L3] (tran.volume.1D),
a matrix of dimension Nr*Nc (tran.volume.2D) or
an Nx*Ny*Nz array (tran.volume.3D) [M/L3].
C.up
tracer concentration at the upstream interface.
One value [M/L3].
C.down
tracer concentration at downstream interface. One value [M/L3].
C.lat
tracer concentration in the lateral input, defined at
grid cell centres. One value, a vector of length N, or a
list as defined by setup.prop.1D [M/L3].
The default is C.lat = C, (a zero-gradient condition).
Setting C.lat=0, together with a positive F.lat will
lead to dilution of the tracer concentration in the
grid cells.
C.x.up
concentration at upstream boundary in x-direction;
vector of length Ny (2D) or matrix of dimensions Ny*Nz (3D) [M/L3].
C.x.down
concentration at downstream boundary in x-direction;
vector of length Ny (2D) or matrix of dimensions Ny*Nz (3D) [M/L3].
C.y.up
concentration at upstream boundary in y-direction;
vector of length Nx (2D) or matrix of dimensions Nx*Nz (3D) [M/L3].
C.y.down
concentration at downstream boundary in y-direction;
vector of length Nx (2D) or matrix of dimensions Nx*Nz (3D) [M/L3].
C.z.up
concentration at upstream boundary in z-direction;
matrix of dimensions Nx*Ny [M/L3].
C.z.down
concentration at downstream boundary in z-direction;
matrix of dimensions Nx*Ny [M/L3].
C.z
concentration at boundary in z-direction for 2-D models where
masscons = TRUE. Matrix of dimensions Nx*Ny [M/L3].
masscons
When TRUE, will check flow balance in 2D model.
The flow in the third direction will then be estimated.
F.up
total tracer input at the upstream interface. One value [M/T].
F.down
total tracer input at downstream interface. One value [M/T].
F.lat
total lateral tracer input, defined at grid cell centres.
One value, a vector of length N, or a 1D list property as defined by setup.prop.1D,[M/T].
F.x.up
total tracer input at the upstream interface in x-direction.
positive = INTO model domain. A vector of length Ny (2D) or a matrix of dimensions Ny*Nz (3D) [M/T].
F.x.down
total tracer input at downstream interface in x-direction. positive = INTO model domain. A vector of length Ny (2D) or a matrix of dimensions Ny*Nz (3D) [M/T].
F.y.up
total tracer input at the upstream interface in y-direction.
positive = INTO model domain. A vector of length Nx (2D) or a matrix of dimensions Nx*Nz (3D) [M/T].
F.y.down
total tracer input at downstream interface in y-direction. positive = INTO model domain. A vector of length Nx (2D) or a matrix of dimensions Nx*Nz (3D) [M/T].
F.z.up
total tracer input at the upstream interface in z-direction.
positive = INTO model domain. A matrix of dimensions Nx*Ny [M/T].
F.z.down
total tracer input at downstream interface in z-direction. positive = INTO model domain. A matrix of dimensions Nx*Ny [M/T].
Disp.grid
BULK dispersion coefficients defined on all grid cell
interfaces. For tran.volume.2D, should contain two matrices, x.int (dimension (Nx+1)*Ny) and y.int (dimension Nx * (Ny+1)).
For tran.volume.3D should contain three arrays x.int (dim = (Nx+1)*Ny*Nz), y.int (dim = Nx*(Ny+1)*Nz), and z.int (dim = Nx*Ny*(Nz+1))
Disp
BULK dispersion coefficient, defined on grid cell interfaces.
One value, a vector of length N+1, or a 1D list property as defined by setup.prop.1D [L3/T].
Disp.x
BULK dispersion coefficient in x-direction, defined on grid cell interfaces. One value, a vector of length (Nx+1), a prop.1D list created by setup.prop.1D, a (Nx+1)* Ny matrix (2D) or a Nx*(Ny+1)*Nz array (3D) [L3/T].
Disp.y
BULK dispersion coefficient in y-direction, defined on grid cell
interfaces. One value, a vector of length (Ny+1),
a prop.1D list created by setup.prop.1D,
or a Nx*(Ny+1) matrix (2D) or a Nx*(Ny+1)*Nz array (3D)[L3/T].
Disp.z
BULK dispersion coefficient in z-direction, defined on grid cell
interfaces. One value, a vector of length (Nz+1), or a Nx*Ny*(Nz+1) array [L3/T].
flow
water flow rate, defined on grid cell interfaces. One value, a vector of length N+1, or a list as defined by setup.prop.1D [L3/T].
If flow.lat is not NULL the flow should be one value containing the flow rate at the upstream boundary.
If flow.lat is NULL then flow can be either one value, a vector or a list.
flow.lat
lateral water flow rate [L3/T] into each volume box, defined at grid cell centres. One value, a vector of
length N, or a list as defined by setup.prop.1D. If flow.lat has a value, then
flow should be the flow rate at the upstream interface (one value).
For each grid cell, the flow at the downstream side of a grid cell is
then estimated by water balance (adding flow.lat in the cell to
flow rate at the upstream side of the grid cell). If flow.lat is NULL, then it is determined by water balance
from flow.
flow.grid
flow rates defined on all grid cell
interfaces. Can be positive (downstream flow) or negative (upstream flow).
Should contain elements x.int, y.int, z.int (3-D), arrays with the values on the
interfaces in x, y and z-direction [L3/T].
flow.x
flow rates in the x-direction, defined on grid cell
interfaces. Can be positive (downstream flow) or negative (upstream flow).
One value, a vector of length (Nx+1),
a prop.1D list created by setup.prop.1D (2D),
a (Nx+1)*Ny matrix (2D) or a (Nx+1)*Ny*Nz array (3D) [L3/T].
flow.y
flow rates in the y-direction, defined on grid cell
interfaces. Can be positive (downstream flow) or negative (upstream flow).
One value, a vector of length (Ny+1),
a prop.1D list created by setup.prop.1D (2D),
a Nx*(Ny+1) matrix (2D) or a Nx*(Ny+1)*Nz array [L3/T].
flow.z
flow rates in the z-direction, defined on grid cell
interfaces. Can be positive (downstream flow) or negative (upstream flow).
One value, a vector of length (Nz+1),
or a Nx*Ny*(Nz+1) array [L3/T].
AFDW
weight used in the finite difference scheme for advection,
defined on grid cell interfaces; backward = 1, centred = 0.5, forward = 0;
default is backward. One value, a vector of length N+1, or a
list as defined by setup.prop.1D [-].
AFDW.grid
weight used in the finite difference scheme for advection
in the x-direction, defined on grid cell interfaces; backward = 1,
centred = 0.5, forward = 0; default is backward.
For tran.volume.3D should contain elements x.int, y.int, z.int (3D), for tran.volume.2D should contain elements x.int and y.int. [-].
AFDW.x
weight used in the finite difference scheme for advection
in the x-direction, defined on grid cell interfaces; backward = 1,
centred = 0.5, forward = 0; default is backward.
One value, a vector of length (Nx+1),
a prop.1D list created by setup.prop.1D,
a (Nx+1)*Ny matrix (2D) or a (Nx+1)*Ny*Nz array (3D) [-].
AFDW.y
weight used in the finite difference scheme for advection
in the y-direction, defined on grid cell interfaces; backward = 1,
centred = 0.5, forward = 0; default is backward.
One value, a vector of length (Ny+1),
a prop.1D list created by setup.prop.1D,
a Nx*(Ny+1) matrix (2D) or a Nx*(Ny+1)*Nz array [-].
AFDW.z
weight used in the finite difference scheme for advection
in the z-direction, defined on grid cell interfaces; backward = 1,
centred = 0.5, forward = 0; default is backward.
One value, a vector of length (Nz+1),
a prop.1D list created by setup.prop.1D,
or a Nx*Ny*(Nz+1) array [-].
V
grid cell volume, defined at grid cell centres [L3]. One value, a
vector of length N, or a list as defined by setup.prop.1D.
full.check
logical flag enabling a full check of the consistency
of the arguments (default = FALSE; TRUE slows down execution
by 50 percent).
full.output
logical flag enabling a full return of the output
(default = FALSE; TRUE slows down execution by 20 percent).
Details
The boundary conditions are of type
1. zero-gradient (default)
2. fixed concentration
3. fixed input
The bulk dispersion coefficient (Disp) and the flow rate
(flow) can be either one value or a vector of length N+1, defined at
all grid cell interfaces, including upstream and downstream boundary.
The spatial discretisation is given by the volume of each box (V),
which can be one value or a vector of length N+1, defined at the centre of
each grid cell.
The water flow is mass conservative. Over each volume box, the routine
calculates internally the downstream outflow of water in terms of the
upstream inflow and the lateral inflow.
Value
dC
the rate of change of the concentration C due to transport,
defined in the centre of each grid cell [M/L3/T].
F.up
mass flow across the upstream boundary, positive = INTO
model domain. One value [M/T].
F.down
mass flow across the downstream boundary, positive = OUT
of model domain. One value [M/T].
F.lat
lateral mass input per volume box, positive = INTO model
domain. A vector of length N [M/T].
flow
water flow across the interface of each grid cell. A vector
of length N+1 [L3/T]. Only provided when (full.output = TRUE
flow.up
water flow across the upstream (external) boundary, positive = INTO
model domain. One value [L3/T]. Only provided when (full.output = TRUE)
flow.down
water flow across the downstream (external) boundary, positive = OUT
of model domain. One value [L3/T]. Only provided when
(full.output = TRUE)
flow.lat
lateral water input on each volume box, positive = INTO model
domain. A vector of length N [L3/T]. Only provided when
(full.output = TRUE)
F
mass flow across at the interface of each grid cell. A vector
of length N+1 [M/T]. Only provided when (full.output = TRUE)
Author(s)
Filip Meysman <filip.meysman@nioz.nl>,
Karline Soetaert <karline.soetaert@nioz.nl>
References
Soetaert and Herman (2009) A practical guide to ecological modelling -
using R as a simulation platform. Springer.
See Also
advection.volume.1D, for more sophisticated advection schemes
Examples
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## =============================================================================
## EXAMPLE : organic carbon (OC) decay in a widening estuary
## =============================================================================
# Two scenarios are simulated: the baseline includes only input
# of organic matter upstream. The second scenario simulates the
# input of an important side river half way the estuary.
#====================#
# Model formulation #
#====================#
river.model <- function (t = 0, OC, pars = NULL) {
tran <- tran.volume.1D(C = OC, F.up = F.OC, F.lat = F.lat,
Disp = Disp, flow = flow.up, flow.lat = flow.lat,
V = Volume, full.output = TRUE)
reac <- - k*OC
return(list(dCdt = tran$dC + reac, Flow = tran$flow))
}
#======================#
# Parameter definition #
#======================#
# Initialising morphology estuary:
nbox <- 500 # number of grid cells
lengthEstuary <- 100000 # length of estuary [m]
BoxLength <- lengthEstuary/nbox # [m]
Distance <- seq(BoxLength/2, by = BoxLength, len =nbox) # [m]
Int.Distance <- seq(0, by = BoxLength, len = (nbox+1)) # [m]
# Cross sectional area: sigmoid function of estuarine distance [m2]
CrossArea <- 4000 + 72000 * Distance^5 /(Distance^5+50000^5)
# Volume of boxes (m3)
Volume <- CrossArea*BoxLength
# Transport coefficients
Disp <- 1000 # m3/s, bulk dispersion coefficient
flow.up <- 180 # m3/s, main river upstream inflow
flow.lat.0 <- 180 # m3/s, side river inflow
F.OC <- 180 # input organic carbon [mol s-1]
F.lat.0 <- 180 # lateral input organic carbon [mol s-1]
k <- 10/(365*24*3600) # decay constant organic carbon [s-1]
#====================#
# Model solution #
#====================#
#scenario 1: without lateral input
F.lat <- rep(0, length.out = nbox)
flow.lat <- rep(0, length.out = nbox)
Conc1 <- steady.1D(runif(nbox), fun = river.model, nspec = 1, name = "OC")
#scenario 2: with lateral input
F.lat <- F.lat.0 * dnorm(x =Distance/lengthEstuary,
mean = Distance[nbox/2]/lengthEstuary,
sd = 1/20, log = FALSE)/nbox
flow.lat <- flow.lat.0 * dnorm(x = Distance/lengthEstuary,
mean = Distance[nbox/2]/lengthEstuary,
sd = 1/20, log = FALSE)/nbox
Conc2 <- steady.1D(runif(nbox), fun = river.model, nspec = 1, name = "OC")
#====================#
# Plotting output #
#====================#
# use S3 plot method
plot(Conc1, Conc2, grid = Distance/1000, which = "OC",
mfrow = c(2, 1), lwd = 2, xlab = "distance [km]",
main = "Organic carbon decay in the estuary",
ylab = "OC Concentration [mM]")
plot(Conc1, Conc2, grid = Int.Distance/1000, which = "Flow",
mfrow = NULL, lwd = 2, xlab = "distance [km]",
main = "Longitudinal change in the water flow rate",
ylab = "Flow rate [m3 s-1]")
legend ("topright", lty = 1:2, col = 1:2, lwd = 2,
c("baseline", "+ side river input"))
ReacTran documentation built on May 2, 2019, 9:38 a.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
Estimates the volumetric transport term (i.e. the rate of change of the concentration due to diffusion and advection) in a 1-D, 2-D or 3-D model of an aquatic system (river, estuary).
Volumetric transport implies the use of flows (mass per unit of time) rather
than fluxes (mass per unit of area per unit of time) as is done in
tran.1D, tran.2D or tran.3D.
The tran.volume.xD routines are particularly suited for modelling
channels (like rivers, estuaries) where the cross-sectional area changes,
but where this area change needs not to be explicitly modelled as such.
Another difference with tran.1D is that the tran.volume.1D
routine also allows lateral water or lateral mass input (as from side rivers
or diffusive lateral ground water inflow).
The tran.volume.2D routine can check for water balance and assume an
in- or efflux in case the net flows in and out of a box are not = 0
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | tran.volume.1D(C, C.up = C[1], C.down = C[length(C)],
C.lat = C, F.up = NULL, F.down = NULL, F.lat = NULL,
Disp, flow = 0, flow.lat = NULL, AFDW = 1,
V = NULL, full.check = FALSE, full.output = FALSE)
tran.volume.2D(C, C.x.up = C[1, ], C.x.down = C[nrow(C), ],
C.y.up = C[, 1], C.y.down = C[, ncol(C)],
C.z = C, masscons = TRUE,
F.x.up = NULL, F.x.down = NULL,
F.y.up = NULL, F.y.down = NULL,
Disp.grid = NULL, Disp.x = NULL, Disp.y = Disp.x,
flow.grid = NULL, flow.x = NULL, flow.y = NULL,
AFDW.grid = NULL, AFDW.x = 1, AFDW.y = AFDW.x,
V = NULL, full.check = FALSE, full.output = FALSE)
tran.volume.3D(C, C.x.up = C[1, , ], C.x.down = C[dim(C)[1], , ],
C.y.up = C[, 1, ], C.y.down = C[, dim(C)[2], ],
C.z.up = C[, , 1], C.z.down = C[, , dim(C)[3]],
F.x.up = NULL, F.x.down = NULL,
F.y.up = NULL, F.y.down = NULL,
F.z.up = NULL, F.z.down = NULL,
Disp.grid = NULL,
Disp.x = NULL, Disp.y = Disp.x, Disp.z = Disp.x,
flow.grid = NULL, flow.x = 0, flow.y = 0, flow.z = 0,
AFDW.grid = NULL, AFDW.x = 1, AFDW.y = AFDW.x,
AFDW.z = AFDW.x,
V = NULL, full.check = FALSE, full.output = FALSE)
|
Arguments
C |
tracer concentration, defined at the centre of the grid cells. A vector of length N [M/L3] (tran.volume.1D), a matrix of dimension Nr*Nc (tran.volume.2D) or an Nx*Ny*Nz array (tran.volume.3D) [M/L3]. |
C.up |
tracer concentration at the upstream interface. One value [M/L3]. |
C.down |
tracer concentration at downstream interface. One value [M/L3]. |
C.lat |
tracer concentration in the lateral input, defined at
grid cell centres. One value, a vector of length N, or a
list as defined by |
C.x.up |
concentration at upstream boundary in x-direction; vector of length Ny (2D) or matrix of dimensions Ny*Nz (3D) [M/L3]. |
C.x.down |
concentration at downstream boundary in x-direction; vector of length Ny (2D) or matrix of dimensions Ny*Nz (3D) [M/L3]. |
C.y.up |
concentration at upstream boundary in y-direction; vector of length Nx (2D) or matrix of dimensions Nx*Nz (3D) [M/L3]. |
C.y.down |
concentration at downstream boundary in y-direction; vector of length Nx (2D) or matrix of dimensions Nx*Nz (3D) [M/L3]. |
C.z.up |
concentration at upstream boundary in z-direction; matrix of dimensions Nx*Ny [M/L3]. |
C.z.down |
concentration at downstream boundary in z-direction; matrix of dimensions Nx*Ny [M/L3]. |
C.z |
concentration at boundary in z-direction for 2-D models where
|
masscons |
When |
F.up |
total tracer input at the upstream interface. One value [M/T]. |
F.down |
total tracer input at downstream interface. One value [M/T]. |
F.lat |
total lateral tracer input, defined at grid cell centres.
One value, a vector of length N, or a 1D list property as defined by |
F.x.up |
total tracer input at the upstream interface in x-direction. positive = INTO model domain. A vector of length Ny (2D) or a matrix of dimensions Ny*Nz (3D) [M/T]. |
F.x.down |
total tracer input at downstream interface in x-direction. positive = INTO model domain. A vector of length Ny (2D) or a matrix of dimensions Ny*Nz (3D) [M/T]. |
F.y.up |
total tracer input at the upstream interface in y-direction. positive = INTO model domain. A vector of length Nx (2D) or a matrix of dimensions Nx*Nz (3D) [M/T]. |
F.y.down |
total tracer input at downstream interface in y-direction. positive = INTO model domain. A vector of length Nx (2D) or a matrix of dimensions Nx*Nz (3D) [M/T]. |
F.z.up |
total tracer input at the upstream interface in z-direction. positive = INTO model domain. A matrix of dimensions Nx*Ny [M/T]. |
F.z.down |
total tracer input at downstream interface in z-direction. positive = INTO model domain. A matrix of dimensions Nx*Ny [M/T]. |
Disp.grid |
BULK dispersion coefficients defined on all grid cell
interfaces. For |
Disp |
BULK dispersion coefficient, defined on grid cell interfaces.
One value, a vector of length N+1, or a 1D list property as defined by |
Disp.x |
BULK dispersion coefficient in x-direction, defined on grid cell interfaces. One value, a vector of length (Nx+1), a |
Disp.y |
BULK dispersion coefficient in y-direction, defined on grid cell
interfaces. One value, a vector of length (Ny+1),
a |
Disp.z |
BULK dispersion coefficient in z-direction, defined on grid cell interfaces. One value, a vector of length (Nz+1), or a Nx*Ny*(Nz+1) array [L3/T]. |
flow |
water flow rate, defined on grid cell interfaces. One value, a vector of length N+1, or a list as defined by |
flow.lat |
lateral water flow rate [L3/T] into each volume box, defined at grid cell centres. One value, a vector of
length N, or a list as defined by |
flow.grid |
flow rates defined on all grid cell interfaces. Can be positive (downstream flow) or negative (upstream flow). Should contain elements x.int, y.int, z.int (3-D), arrays with the values on the interfaces in x, y and z-direction [L3/T]. |
flow.x |
flow rates in the x-direction, defined on grid cell
interfaces. Can be positive (downstream flow) or negative (upstream flow).
One value, a vector of length (Nx+1),
a |
flow.y |
flow rates in the y-direction, defined on grid cell
interfaces. Can be positive (downstream flow) or negative (upstream flow).
One value, a vector of length (Ny+1),
a |
flow.z |
flow rates in the z-direction, defined on grid cell interfaces. Can be positive (downstream flow) or negative (upstream flow). One value, a vector of length (Nz+1), or a Nx*Ny*(Nz+1) array [L3/T]. |
AFDW |
weight used in the finite difference scheme for advection,
defined on grid cell interfaces; backward = 1, centred = 0.5, forward = 0;
default is backward. One value, a vector of length N+1, or a
list as defined by |
AFDW.grid |
weight used in the finite difference scheme for advection
in the x-direction, defined on grid cell interfaces; backward = 1,
centred = 0.5, forward = 0; default is backward.
For |
AFDW.x |
weight used in the finite difference scheme for advection
in the x-direction, defined on grid cell interfaces; backward = 1,
centred = 0.5, forward = 0; default is backward.
One value, a vector of length (Nx+1),
a |
AFDW.y |
weight used in the finite difference scheme for advection
in the y-direction, defined on grid cell interfaces; backward = 1,
centred = 0.5, forward = 0; default is backward.
One value, a vector of length (Ny+1),
a |
AFDW.z |
weight used in the finite difference scheme for advection
in the z-direction, defined on grid cell interfaces; backward = 1,
centred = 0.5, forward = 0; default is backward.
One value, a vector of length (Nz+1),
a |
V |
grid cell volume, defined at grid cell centres [L3]. One value, a
vector of length N, or a list as defined by |
full.check |
logical flag enabling a full check of the consistency
of the arguments (default = |
full.output |
logical flag enabling a full return of the output
(default = |
Details
The boundary conditions are of type
1. zero-gradient (default)
2. fixed concentration
3. fixed input
The bulk dispersion coefficient (Disp) and the flow rate
(flow) can be either one value or a vector of length N+1, defined at
all grid cell interfaces, including upstream and downstream boundary.
The spatial discretisation is given by the volume of each box (V),
which can be one value or a vector of length N+1, defined at the centre of
each grid cell.
The water flow is mass conservative. Over each volume box, the routine calculates internally the downstream outflow of water in terms of the upstream inflow and the lateral inflow.
Value
dC |
the rate of change of the concentration C due to transport, defined in the centre of each grid cell [M/L3/T]. |
F.up |
mass flow across the upstream boundary, positive = INTO model domain. One value [M/T]. |
F.down |
mass flow across the downstream boundary, positive = OUT of model domain. One value [M/T]. |
F.lat |
lateral mass input per volume box, positive = INTO model domain. A vector of length N [M/T]. |
flow |
water flow across the interface of each grid cell. A vector
of length N+1 [L3/T]. Only provided when ( |
flow.up |
water flow across the upstream (external) boundary, positive = INTO
model domain. One value [L3/T]. Only provided when ( |
flow.down |
water flow across the downstream (external) boundary, positive = OUT
of model domain. One value [L3/T]. Only provided when
( |
flow.lat |
lateral water input on each volume box, positive = INTO model
domain. A vector of length N [L3/T]. Only provided when
( |
F |
mass flow across at the interface of each grid cell. A vector
of length N+1 [M/T]. Only provided when ( |
Author(s)
Filip Meysman <filip.meysman@nioz.nl>, Karline Soetaert <karline.soetaert@nioz.nl>
References
Soetaert and Herman (2009) A practical guide to ecological modelling - using R as a simulation platform. Springer.
See Also
advection.volume.1D, for more sophisticated advection schemes
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 | ## =============================================================================
## EXAMPLE : organic carbon (OC) decay in a widening estuary
## =============================================================================
# Two scenarios are simulated: the baseline includes only input
# of organic matter upstream. The second scenario simulates the
# input of an important side river half way the estuary.
#====================#
# Model formulation #
#====================#
river.model <- function (t = 0, OC, pars = NULL) {
tran <- tran.volume.1D(C = OC, F.up = F.OC, F.lat = F.lat,
Disp = Disp, flow = flow.up, flow.lat = flow.lat,
V = Volume, full.output = TRUE)
reac <- - k*OC
return(list(dCdt = tran$dC + reac, Flow = tran$flow))
}
#======================#
# Parameter definition #
#======================#
# Initialising morphology estuary:
nbox <- 500 # number of grid cells
lengthEstuary <- 100000 # length of estuary [m]
BoxLength <- lengthEstuary/nbox # [m]
Distance <- seq(BoxLength/2, by = BoxLength, len =nbox) # [m]
Int.Distance <- seq(0, by = BoxLength, len = (nbox+1)) # [m]
# Cross sectional area: sigmoid function of estuarine distance [m2]
CrossArea <- 4000 + 72000 * Distance^5 /(Distance^5+50000^5)
# Volume of boxes (m3)
Volume <- CrossArea*BoxLength
# Transport coefficients
Disp <- 1000 # m3/s, bulk dispersion coefficient
flow.up <- 180 # m3/s, main river upstream inflow
flow.lat.0 <- 180 # m3/s, side river inflow
F.OC <- 180 # input organic carbon [mol s-1]
F.lat.0 <- 180 # lateral input organic carbon [mol s-1]
k <- 10/(365*24*3600) # decay constant organic carbon [s-1]
#====================#
# Model solution #
#====================#
#scenario 1: without lateral input
F.lat <- rep(0, length.out = nbox)
flow.lat <- rep(0, length.out = nbox)
Conc1 <- steady.1D(runif(nbox), fun = river.model, nspec = 1, name = "OC")
#scenario 2: with lateral input
F.lat <- F.lat.0 * dnorm(x =Distance/lengthEstuary,
mean = Distance[nbox/2]/lengthEstuary,
sd = 1/20, log = FALSE)/nbox
flow.lat <- flow.lat.0 * dnorm(x = Distance/lengthEstuary,
mean = Distance[nbox/2]/lengthEstuary,
sd = 1/20, log = FALSE)/nbox
Conc2 <- steady.1D(runif(nbox), fun = river.model, nspec = 1, name = "OC")
#====================#
# Plotting output #
#====================#
# use S3 plot method
plot(Conc1, Conc2, grid = Distance/1000, which = "OC",
mfrow = c(2, 1), lwd = 2, xlab = "distance [km]",
main = "Organic carbon decay in the estuary",
ylab = "OC Concentration [mM]")
plot(Conc1, Conc2, grid = Int.Distance/1000, which = "Flow",
mfrow = NULL, lwd = 2, xlab = "distance [km]",
main = "Longitudinal change in the water flow rate",
ylab = "Flow rate [m3 s-1]")
legend ("topright", lty = 1:2, col = 1:2, lwd = 2,
c("baseline", "+ side river input"))
|
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