discharge() computes the x, y and z components of the discharge vector for an aem object
at the given x, y and z coordinates.
darcy() computes the x, y and z components of the Darcy flux vector (also called specific discharge vector)
for an aem object at the given x, y and z coordinates.
velocity() computes the x, y and z components of the average linear groundwater flow velocity vector
for an aem object at the given x, y and z coordinates.
domega() computes the complex discharge for an aem or element object
at the given x and y coordinates.
Usage
discharge(...)
darcy(...)
velocity(...)
domega(...)
# S3 method for class 'aem'
discharge(
aem,
x,
y,
z,
as.grid = FALSE,
magnitude = FALSE,
verbose = TRUE,
...
)
# S3 method for class 'aem'
darcy(aem, x, y, z, as.grid = FALSE, magnitude = FALSE, ...)
# S3 method for class 'aem'
velocity(aem, x, y, z, as.grid = FALSE, magnitude = FALSE, R = 1, ...)
# S3 method for class 'aem'
domega(aem, x, y, as.grid = FALSE, ...)
# S3 method for class 'element'
domega(element, x, y, ...)Arguments
- ...
ignored or arguments passed from
velocity()ordarcy()todischarge().- aem
aemobject.- x
numeric x coordinates to evaluate the flow at.
- y
numeric y coordinates to evaluate the flow at.
- z
numeric z coordinates to evaluate at
- as.grid
logical, should a matrix be returned? Defaults to
FALSE. See details.- magnitude
logical, should the magnitude of the flow vector be returned as well? Default to
FALSE. See details.- verbose
logical, if
TRUE(default), warnings with regards to settingQztoNAare printed. See details.- R
numeric, retardation coefficient used in
velocity(). Defaults to 1 (no retardation).- element
analytic element of class
element.
Value
For discharge(), a matrix with the number of rows equal to the number of points to evaluate
the discharge vector at, and with columns Qx, Qy and Qz corresponding to x, y and z components
of the discharge vector at coordinates x, y and z. If as.grid = TRUE, an array of dimensions
c(length(y), length(x), length(z), 3) described by marginal vectors x, y and z (columns, rows and third dimension)
containing the x, y and z components of the discharge vector (Qx, Qy and Qz) as the fourth dimension.
The x component of discharge() is the real value of domega(), the y component
the negative imaginary component and the z component is calculated based on area-sink strengths
and/or the curvature of the phreatic surface.
If magnitude = TRUE, the last dimension of the returned array is expanded to include
the magnitude of the discharge/Darcy/velocity vector, calculated as sqrt(Qx^2 + Qy^2 + Qz^2)
(or sqrt(qx^2 + qy^2 + qz^2) or sqrt(vx^2 + vy^2 + vz^2), respectively).
For darcy(), the same as for discharge() but with the x, y and z components of the
Darcy flux vector (qx, qy and qz). The values are computed by dividing the values of discharge() by
the saturated thickness at x, y and z.
For velocity(), the same as for discharge() but with the x, y and z components of the
average linear groundwater flow velocity vector (vx, vy and vz). The values are computed by dividing
the darcy() values by the effective porosity (aem$n) and the retardation coefficient R.
For domega(), a vector of length(x) (equal to length(y)) with the complex discharge values at x and y,
If as.grid = TRUE, a matrix of dimensions c(length(y), length(x)) described by
marginal vectors x and y containing the complex discharge values at the grid points.
domega() is the derivative of omega() in the x and y directions.
Details
There is no discharge(), darcy() or velocity() method for an object of class element because an aem object is required
to obtain the aquifer base and top.
If the z coordinate is above the saturated aquifer level (i.e. the water-table for unconfined conditions or
the aquifer top for confined conditions), or below the aquifer base, Qz values are set to NA with a warning (if verbose = TRUE).
The Qx and Qy values are not set to NA, for convenience in specifying the z coordinate when only lateral flow
is of interest.
Examples
w <- well(xw = 55, yw = 0, Q = 200)
uf <- uniformflow(gradient = 0.002, angle = -45, TR = 100)
as <- areasink(xc = 0, yc = 0, N = 0.001, R = 500)
rf <- constant(xc = -1000, yc = 1000, hc = 10)
ml <- aem(k = 10, top = 10, base = -15, n = 0.2, w, uf, as, rf)
xg <- seq(-100, 100, length = 5)
yg <- seq(-75, 75, length = 3)
# Discharge vector
discharge(ml, c(150, 0), c(80, -80), z = -10)
#> Qx Qy Qz
#> [1,] 0.02037961 -0.2665091 -0.005060767
#> [2,] 0.32717248 0.0887621 -0.005097869
discharge(ml, c(150, 0), c(80, -80), z = c(2, 5), magnitude = TRUE)
#> Qx Qy Qz Q
#> [1,] 0.02037961 -0.2665091 -0.01720661 0.2678405
#> [2,] 0.32717248 0.0887621 -0.02039148 0.3396121
discharge(ml, xg, yg, z = 2, as.grid = TRUE)
#> , , 1, Qx
#>
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.2578228 0.3171573 0.3438149 0.1945904 0.004180247
#> [2,] 0.2967826 0.4195736 0.7201666 6.5326191 -0.515933946
#> [3,] 0.2578228 0.3171573 0.3438149 0.1945904 0.004180247
#>
#> , , 1, Qy
#>
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] -0.18443819 -0.24730419 -0.37991259 -0.5264566 -0.4159899
#> [2,] -0.14142136 -0.14142136 -0.14142136 -0.1414214 -0.1414214
#> [3,] -0.09840452 -0.03553852 0.09706987 0.2436139 0.1331472
#>
#> , , 1, Qz
#>
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] -0.01728591 -0.01746242 -0.01775486 -0.01791021 -0.01750075
#> [2,] -0.01730880 -0.01756345 -0.01856240 -0.14449874 -0.01783670
#> [3,] -0.01721822 -0.01729328 -0.01736962 -0.01728292 -0.01705172
#>
discharge(ml, c(150, 0), c(80, -80), z = ml$top + c(-5, 0.5)) # NA for z > water-table
#> Warning: Setting Qz values to NA for z above saturated aquifer level or below aquifer base
#> Qx Qy Qz
#> [1,] 0.02037961 -0.2665091 -0.02024307
#> [2,] 0.32717248 0.0887621 NA
# Darcy flux
darcy(ml, c(150, 0), c(80, -80), c(0, 5), magnitude = TRUE)
#> qx qy qz q
#> [1,] 0.000840556 -0.010992156 -0.0006261932 0.01104202
#> [2,] 0.013502552 0.003663251 -0.0008415652 0.01401594
# Velocity
velocity(ml, c(150, 0), c(80, -80), c(0, 5), magnitude = TRUE, R = 5)
#> vx vy vz v
#> [1,] 0.000840556 -0.010992156 -0.0006261932 0.01104202
#> [2,] 0.013502552 0.003663251 -0.0008415652 0.01401594
# Complex discharge
domega(ml, c(150, 0), c(80, -80))
#> [1] 0.02037961+0.2665091i 0.32717248-0.0887621i
# Complex discharge for elements
domega(w, c(150, 0), c(80, -80))
#> [1] -0.1960417+0.1650878i 0.1857511-0.2701835i