old/AvgHydraulics.R
In SGronsdahl/GIFT: Geomorphic instream flow tool for conducting hydraulic-habitat modelling.
### Geomorphic Instream Flow Tool ###
#' A function to execute the GIFT hydraulic simulation for flows below bankfull.
#'
#' This function executes the hydraulic geometry simulator to evaluate reach-averaged depths and velocities
#' generated at flows less than bankfull conditions.
#' For more information about this model see: McParland et al. (2016) and Gronsdahl et al. (XXXX)
#' @param S channel gradient (m/m)
#' @param wb reach averaged bankfull width (m).
#' @param db reach averaged bankfull depth (m).
#' @param db_max Defaults to NULL. reach averaged maximum bankfull depth (m). Specifying db_max is preferred to calculate 'b'.
#' @param b User-specified b-value. Defaults to NULL and calculated within model unless specified.
#' @param D84 grain size (mm)
#' @param xs_output Defaults to TRUE. An expression specifying whether to produce a .csv and .jpg of the simulated channel cross section.
#' @export
#' @return .csv and .jpeg of channel cross section if specified
#' @return data frame of reach-averaged hydraulics
#' AvgHydraulics()
library(dplyr)
library(zoo)
calcWidth <- function(elev, b, wb, db, dmax) {
#To calculate width, the channel is split into 3 segments: left bank, channel and right bank
#using Figure 1 in McParland, D., Eaton, B., and Rosenfeld, J. 2016
#The widths are calculated using the b value following the 2016 paper
width.leftbank = b * wb
width.channel = (0.99-b) * wb
width.rightbank = 0.01*wb
#The depths are defined as db for left bank and dmax for right bank
#The channel depths is the difference between the left and right bank depths
depth.leftbank = db
depth.channel = dmax-db
depth.rightbank = dmax
#there are two different ways to calculate depth, depending on if the channel is fully submerged
if(elev >= depth.channel) {
#channel is fully submerged
#The wetted width is calculated using trigonometry
#Each segment of the channel is a triangle
#We denote the depth a (opposite) in the triangle
#width is b (adjacent) in the triangle
#and the channel bottom is c (hypotenuse) in the triangle
#From the tangent equations in trigonometry, we now that the ratio between the straight lines are constant
#i.e. a1/b1 = a2/b2
#in our case, that means the ratio of the depth to width is the same for the geometry and wetted parts
#so we get segment depth/segment width = wetted depth/wetted width
#We know the wetted depth, so we reorder to get wetted width = segment width * wetted depth/segment depth
#The wetted width becomes a fraction of the segment width, the same ratio as the wetted depth to the segment depth
wetted.depth.leftbank = elev - depth.channel
wetted.width.leftbank = width.leftbank*wetted.depth.leftbank/depth.leftbank
wetted.width.channel = width.channel #the entire channel is submerged, so the wetted width is the segment width
wetted.depth.rightbank = elev
wetted.width.rightbank = width.rightbank*wetted.depth.rightbank/depth.rightbank
} else {
wetted.width.leftbank = 0 #the entire left bank is above water, so wetted width is zero
wetted.depth.channel = elev
wetted.width.channel = width.channel*wetted.depth.channel/depth.channel
wetted.depth.rightbank = elev
wetted.width.rightbank = width.rightbank*wetted.depth.rightbank/depth.rightbank
}
wetted.width = wetted.width.leftbank + wetted.width.channel + wetted.width.rightbank
return(wetted.width)
}
calcArea <- function(elev, b, wb, db, dmax) {
#The area calculation is using the same trigonometry as calcWidth to calculated wetted width
#The area is calculate based on the area of a triangle (width*depth/2)
width.leftbank = b * wb
width.channel = (0.99-b) * wb
width.rightbank = 0.01*wb
depth.leftbank = db
depth.channel = dmax-db
depth.rightbank = dmax
if(elev >= depth.channel) {
#channel is fully submerged
wetted.depth.leftbank = elev - depth.channel
wetted.width.leftbank = width.leftbank*wetted.depth.leftbank/depth.leftbank
wetted.area.leftbank = wetted.width.leftbank*wetted.depth.leftbank/2
#the entire channel is submerged, so the wetted area is the triangle for the width and depth of the channel
#and the rectangle from the channel depth up to the water elevation
wetted.area.channel = width.channel*depth.channel/2 + width.channel*(elev-depth.channel)
wetted.depth.rightbank = elev
wetted.width.rightbank = width.rightbank*wetted.depth.rightbank/depth.rightbank
wetted.area.rightbank = wetted.width.rightbank*wetted.depth.rightbank/2
} else {
wetted.area.leftbank = 0 #the entire left bank is above water, so zero area
wetted.depth.channel = elev
wetted.width.channel = width.channel*wetted.depth.channel/depth.channel
wetted.area.channel = wetted.width.channel*wetted.depth.channel/2
wetted.depth.rightbank = elev
wetted.width.rightbank = width.rightbank*wetted.depth.rightbank/depth.rightbank
wetted.area.rightbank = wetted.width.rightbank*wetted.depth.rightbank/2
}
wetted.area = wetted.area.leftbank + wetted.area.channel + wetted.area.rightbank
return(wetted.area)
}
calcP <- function(elev, b, wb, db, dmax) {
#The bottom length is calculated using the Pythagorean theorem: a^2+b^2=c^2
#For our purpose, that means wetted depth ^ 2 + wetted width ^ 2 = wetted bottom length ^ 2
#Reorderede get wetted bottom length = sqrt(wetted depth ^ 2 + wetted width ^ 2)
#wetted width are calculated as in calcWidth
width.leftbank = b * wb
width.channel = (0.99-b) * wb
width.rightbank = 0.01*wb
depth.leftbank = db
depth.channel = dmax-db
depth.rightbank = dmax
if(elev >= depth.channel) {
#channel is fully submerged
wetted.depth.leftbank = elev - depth.channel
wetted.width.leftbank = width.leftbank*wetted.depth.leftbank/depth.leftbank
length.bottom.leftbank = sqrt(wetted.width.leftbank^2+wetted.depth.leftbank^2)
#the entire channel is submerged, so wetted width and depth is the same as channel width and depth
length.bottom.channel = sqrt(width.channel^2+depth.channel^2)
wetted.depth.rightbank = elev
wetted.width.rightbank = width.rightbank*wetted.depth.rightbank/depth.rightbank
length.bottom.rightbank = sqrt(wetted.width.rightbank^2+wetted.depth.rightbank^2)
} else {
length.bottom.leftbank = 0 #the entire left bank is above water
wetted.depth.channel = elev
wetted.width.channel = width.channel*wetted.depth.channel/depth.channel
length.bottom.channel = sqrt(wetted.width.channel^2+wetted.depth.channel^2)
wetted.depth.rightbank = elev
wetted.width.rightbank = width.rightbank*wetted.depth.rightbank/depth.rightbank
length.bottom.rightbank = sqrt(wetted.width.rightbank^2+wetted.depth.rightbank^2)
}
p = length.bottom.leftbank + length.bottom.channel + length.bottom.rightbank
return(p)
}
# Velocity function per Ferguson 2007
calcUi <- function(Ri, D84, S) {
D.84 <- D84 / 1000 #D84 grain size in m
g <- 9.81 # gravity
a1 <- 6.5
a2 <- 2.5
Res <- a1 * a2 * (Ri / D.84) /
(a1^2 + a2^2 * (Ri / D.84) ^ (5/3)) ^ (1/2)
Ui <- Res * sqrt(g * Ri * S) # Velocity (m/s)
return(Ui)
}
AvgHydraulics <- function(S, wb, db, db_max = NULL, b_value = NULL,
D84, xs_output = TRUE) {
#####################################################
# input validation
if(!is.numeric(S)) {stop("AvgHydraulics expects 'S' to be numeric")}
if(S <= 0 ) {stop("AvgHydraulics expects 'S' to be a positive number")}
if(!is.numeric(wb)) {stop("AvgHydraulics expects 'wb' to be numeric")}
if(wb <= 0 ) {stop("AvgHydraulics expects 'wb' to be a positive number")}
if(wb > 100 ) {warning("Warning: width outside of recommended range")}
if(!is.numeric(db)) {stop("AvgHydraulics expects 'db' to be numeric")}
if(db <= 0 ) {stop("AvgHydraulics expects 'db' to be a positive number")}
if(db > 5 ) {warning("Warning: db outside of recommended range")}
if(!is.numeric(D84)) {stop("AvgHydraulics expects 'D84' to be numeric")}
if(D84 <= 1 ) {warning("Warning: Confirm D84 is entered in mm")}
if(D84 > 400 ) {warning("Warning: D84 may be outside of recommended range")}
if(is.null(db_max)){
} else {
if(db > db_max) {stop("AvgHydraulics expects db < db_max")}
}
deltaX = 0.0001
deltaY = 0.001
#############################################################
##### Simulate Hydraulics #####
# Ferguson model's shape factor (b): define based on specified inputs
if(is.null(b_value) == FALSE){
b <- b_value # option 1: user specified
} else if (is.null(db_max) == FALSE) {
b <- 1 - (db / db_max) # option 2: incorporates db_max values
} else {
b <- (wb / db) / 100 # option 3: uses mean width
}
# b value input validation
if(b > 0.7 ) {warning("Warning: b_value outside of recommended range")}
# estimate max depth using b-value
dmax <- (1 + (b / (1 - b))) * db
# generate xs_corrdinates
X <- c(0, b * wb, 0.99 * wb, wb)
Y <- 5 * db- c(0, db, dmax, 0) # depths are relative
# Interpolate the distribution onto an xs raster
Xgrid <- wb * seq(0, 1, deltaX)
Ygrid <- matrix(unlist(approx(X, Y, Xgrid)), ncol = length(Xgrid), byrow = TRUE)[2,]
# Specify water surface elevations for which to calculate Wi
Zw <- 5 * db - dmax + seq(0.02 * dmax, dmax, deltaY * dmax)
######################################################
# For loop to calculate the width and discharge for each chosen water level
# create objects to hold store results
simulated <- data.frame(Zw=Zw, Q = NA, Ai = NA, Wi = NA, di = NA, Ui = NA, elev = NA)
results <- list()
for (j in 1:length(Zw)) {
#j = 20
elev = Zw[j] - min(Ygrid)
Wi = calcWidth(elev, b, wb, db, dmax)
Ai = calcArea(elev, b, wb, db, dmax)
Pi = calcP(elev, b, wb, db, dmax)
di <- Ai / Wi
Ri <- Ai/Pi
Ui = calcUi(Ri, D84, S)
Q = Ui * Ai
simulated$elev[j] = elev
simulated$Wi[j] = Wi
simulated$Ai[j] = Ai
simulated$Pi[j] = Pi
simulated$di[j] = di
simulated$Ri[j] = Ri
simulated$Ui[j] = Ui
simulated$Q[j] = Q
}
# set up data frame of outputs with varying streamflow intervals
Q <- c(seq(0.001, 0.1, 0.001), seq(0.11, 1, 0.01), seq(1.1, 10, 0.1),
seq(11, 100, 1), seq(110, 1000, 10), seq(1100, 10000, 100))
# add modelled hydraulics to output dataframe
Ai <- approx(simulated$Q, simulated$Ai, xout = Q)[2]
Wi <- approx(simulated$Q, simulated$Wi, xout = Q)[2]
di <- approx(simulated$Q, simulated$di, xout = Q)[2]
Ui <- approx(simulated$Q, simulated$Ui, xout = Q)[2]
# filter results
mod_hyd <- data.frame(Q, Ai = Ai$y, Wi = Wi$y, di = di$y, Ui = Ui$y) %>%
filter(is.na(Ai) == FALSE)
#####################################################
# Prepare graph of cross section
if(xs_output == TRUE){
# output coordinates
if(is.null(db_max) == TRUE){
plot_y <- c(0, (db * -1), (dmax * - 1), 0)
} else {
plot_y <- c(0, (db * -1), (db_max * - 1), 0)
}
# set up x-values to plot
plot_x <- c(0, (b * wb), (0.99 * wb), wb )
# write channel cross section
channel_xs <- data.frame(x = plot_x, y = plot_y)
write.csv(channel_xs, "channel_xs.csv", row.names = FALSE)
# plot simple figure
jpeg("channel_xs.jpeg", width = 6, height = 4, units = "in", res = 300)
par(mar = c(4.5, 4.5, 1, 1))
plot(plot_x, plot_y, type = "l",
xlab = "Width (m)",
ylab = "Depth (m)",
ylim = c((min(plot_y) * 1.2), 0), cex.lab = 0.8, cex.axis = 0.8,
)
abline(a = (db * -1), 0, lty = 2, col = "grey")
legend("bottomleft", col = c("black", "grey"), bty = "n",
lty = c(1, 2), cex = 0.86,
legend = c("Channel cross section", "Average depth"))
dev.off()
} else {
}
# return modelled hydraulics
return(mod_hyd)
}
SGronsdahl/GIFT documentation built on Dec. 18, 2021, 11:59 a.m.
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### Geomorphic Instream Flow Tool ###
#' A function to execute the GIFT hydraulic simulation for flows below bankfull.
#'
#' This function executes the hydraulic geometry simulator to evaluate reach-averaged depths and velocities
#' generated at flows less than bankfull conditions.
#' For more information about this model see: McParland et al. (2016) and Gronsdahl et al. (XXXX)
#' @param S channel gradient (m/m)
#' @param wb reach averaged bankfull width (m).
#' @param db reach averaged bankfull depth (m).
#' @param db_max Defaults to NULL. reach averaged maximum bankfull depth (m). Specifying db_max is preferred to calculate 'b'.
#' @param b User-specified b-value. Defaults to NULL and calculated within model unless specified.
#' @param D84 grain size (mm)
#' @param xs_output Defaults to TRUE. An expression specifying whether to produce a .csv and .jpg of the simulated channel cross section.
#' @export
#' @return .csv and .jpeg of channel cross section if specified
#' @return data frame of reach-averaged hydraulics
#' AvgHydraulics()
library(dplyr)
library(zoo)
calcWidth <- function(elev, b, wb, db, dmax) {
#To calculate width, the channel is split into 3 segments: left bank, channel and right bank
#using Figure 1 in McParland, D., Eaton, B., and Rosenfeld, J. 2016
#The widths are calculated using the b value following the 2016 paper
width.leftbank = b * wb
width.channel = (0.99-b) * wb
width.rightbank = 0.01*wb
#The depths are defined as db for left bank and dmax for right bank
#The channel depths is the difference between the left and right bank depths
depth.leftbank = db
depth.channel = dmax-db
depth.rightbank = dmax
#there are two different ways to calculate depth, depending on if the channel is fully submerged
if(elev >= depth.channel) {
#channel is fully submerged
#The wetted width is calculated using trigonometry
#Each segment of the channel is a triangle
#We denote the depth a (opposite) in the triangle
#width is b (adjacent) in the triangle
#and the channel bottom is c (hypotenuse) in the triangle
#From the tangent equations in trigonometry, we now that the ratio between the straight lines are constant
#i.e. a1/b1 = a2/b2
#in our case, that means the ratio of the depth to width is the same for the geometry and wetted parts
#so we get segment depth/segment width = wetted depth/wetted width
#We know the wetted depth, so we reorder to get wetted width = segment width * wetted depth/segment depth
#The wetted width becomes a fraction of the segment width, the same ratio as the wetted depth to the segment depth
wetted.depth.leftbank = elev - depth.channel
wetted.width.leftbank = width.leftbank*wetted.depth.leftbank/depth.leftbank
wetted.width.channel = width.channel #the entire channel is submerged, so the wetted width is the segment width
wetted.depth.rightbank = elev
wetted.width.rightbank = width.rightbank*wetted.depth.rightbank/depth.rightbank
} else {
wetted.width.leftbank = 0 #the entire left bank is above water, so wetted width is zero
wetted.depth.channel = elev
wetted.width.channel = width.channel*wetted.depth.channel/depth.channel
wetted.depth.rightbank = elev
wetted.width.rightbank = width.rightbank*wetted.depth.rightbank/depth.rightbank
}
wetted.width = wetted.width.leftbank + wetted.width.channel + wetted.width.rightbank
return(wetted.width)
}
calcArea <- function(elev, b, wb, db, dmax) {
#The area calculation is using the same trigonometry as calcWidth to calculated wetted width
#The area is calculate based on the area of a triangle (width*depth/2)
width.leftbank = b * wb
width.channel = (0.99-b) * wb
width.rightbank = 0.01*wb
depth.leftbank = db
depth.channel = dmax-db
depth.rightbank = dmax
if(elev >= depth.channel) {
#channel is fully submerged
wetted.depth.leftbank = elev - depth.channel
wetted.width.leftbank = width.leftbank*wetted.depth.leftbank/depth.leftbank
wetted.area.leftbank = wetted.width.leftbank*wetted.depth.leftbank/2
#the entire channel is submerged, so the wetted area is the triangle for the width and depth of the channel
#and the rectangle from the channel depth up to the water elevation
wetted.area.channel = width.channel*depth.channel/2 + width.channel*(elev-depth.channel)
wetted.depth.rightbank = elev
wetted.width.rightbank = width.rightbank*wetted.depth.rightbank/depth.rightbank
wetted.area.rightbank = wetted.width.rightbank*wetted.depth.rightbank/2
} else {
wetted.area.leftbank = 0 #the entire left bank is above water, so zero area
wetted.depth.channel = elev
wetted.width.channel = width.channel*wetted.depth.channel/depth.channel
wetted.area.channel = wetted.width.channel*wetted.depth.channel/2
wetted.depth.rightbank = elev
wetted.width.rightbank = width.rightbank*wetted.depth.rightbank/depth.rightbank
wetted.area.rightbank = wetted.width.rightbank*wetted.depth.rightbank/2
}
wetted.area = wetted.area.leftbank + wetted.area.channel + wetted.area.rightbank
return(wetted.area)
}
calcP <- function(elev, b, wb, db, dmax) {
#The bottom length is calculated using the Pythagorean theorem: a^2+b^2=c^2
#For our purpose, that means wetted depth ^ 2 + wetted width ^ 2 = wetted bottom length ^ 2
#Reorderede get wetted bottom length = sqrt(wetted depth ^ 2 + wetted width ^ 2)
#wetted width are calculated as in calcWidth
width.leftbank = b * wb
width.channel = (0.99-b) * wb
width.rightbank = 0.01*wb
depth.leftbank = db
depth.channel = dmax-db
depth.rightbank = dmax
if(elev >= depth.channel) {
#channel is fully submerged
wetted.depth.leftbank = elev - depth.channel
wetted.width.leftbank = width.leftbank*wetted.depth.leftbank/depth.leftbank
length.bottom.leftbank = sqrt(wetted.width.leftbank^2+wetted.depth.leftbank^2)
#the entire channel is submerged, so wetted width and depth is the same as channel width and depth
length.bottom.channel = sqrt(width.channel^2+depth.channel^2)
wetted.depth.rightbank = elev
wetted.width.rightbank = width.rightbank*wetted.depth.rightbank/depth.rightbank
length.bottom.rightbank = sqrt(wetted.width.rightbank^2+wetted.depth.rightbank^2)
} else {
length.bottom.leftbank = 0 #the entire left bank is above water
wetted.depth.channel = elev
wetted.width.channel = width.channel*wetted.depth.channel/depth.channel
length.bottom.channel = sqrt(wetted.width.channel^2+wetted.depth.channel^2)
wetted.depth.rightbank = elev
wetted.width.rightbank = width.rightbank*wetted.depth.rightbank/depth.rightbank
length.bottom.rightbank = sqrt(wetted.width.rightbank^2+wetted.depth.rightbank^2)
}
p = length.bottom.leftbank + length.bottom.channel + length.bottom.rightbank
return(p)
}
# Velocity function per Ferguson 2007
calcUi <- function(Ri, D84, S) {
D.84 <- D84 / 1000 #D84 grain size in m
g <- 9.81 # gravity
a1 <- 6.5
a2 <- 2.5
Res <- a1 * a2 * (Ri / D.84) /
(a1^2 + a2^2 * (Ri / D.84) ^ (5/3)) ^ (1/2)
Ui <- Res * sqrt(g * Ri * S) # Velocity (m/s)
return(Ui)
}
AvgHydraulics <- function(S, wb, db, db_max = NULL, b_value = NULL,
D84, xs_output = TRUE) {
#####################################################
# input validation
if(!is.numeric(S)) {stop("AvgHydraulics expects 'S' to be numeric")}
if(S <= 0 ) {stop("AvgHydraulics expects 'S' to be a positive number")}
if(!is.numeric(wb)) {stop("AvgHydraulics expects 'wb' to be numeric")}
if(wb <= 0 ) {stop("AvgHydraulics expects 'wb' to be a positive number")}
if(wb > 100 ) {warning("Warning: width outside of recommended range")}
if(!is.numeric(db)) {stop("AvgHydraulics expects 'db' to be numeric")}
if(db <= 0 ) {stop("AvgHydraulics expects 'db' to be a positive number")}
if(db > 5 ) {warning("Warning: db outside of recommended range")}
if(!is.numeric(D84)) {stop("AvgHydraulics expects 'D84' to be numeric")}
if(D84 <= 1 ) {warning("Warning: Confirm D84 is entered in mm")}
if(D84 > 400 ) {warning("Warning: D84 may be outside of recommended range")}
if(is.null(db_max)){
} else {
if(db > db_max) {stop("AvgHydraulics expects db < db_max")}
}
deltaX = 0.0001
deltaY = 0.001
#############################################################
##### Simulate Hydraulics #####
# Ferguson model's shape factor (b): define based on specified inputs
if(is.null(b_value) == FALSE){
b <- b_value # option 1: user specified
} else if (is.null(db_max) == FALSE) {
b <- 1 - (db / db_max) # option 2: incorporates db_max values
} else {
b <- (wb / db) / 100 # option 3: uses mean width
}
# b value input validation
if(b > 0.7 ) {warning("Warning: b_value outside of recommended range")}
# estimate max depth using b-value
dmax <- (1 + (b / (1 - b))) * db
# generate xs_corrdinates
X <- c(0, b * wb, 0.99 * wb, wb)
Y <- 5 * db- c(0, db, dmax, 0) # depths are relative
# Interpolate the distribution onto an xs raster
Xgrid <- wb * seq(0, 1, deltaX)
Ygrid <- matrix(unlist(approx(X, Y, Xgrid)), ncol = length(Xgrid), byrow = TRUE)[2,]
# Specify water surface elevations for which to calculate Wi
Zw <- 5 * db - dmax + seq(0.02 * dmax, dmax, deltaY * dmax)
######################################################
# For loop to calculate the width and discharge for each chosen water level
# create objects to hold store results
simulated <- data.frame(Zw=Zw, Q = NA, Ai = NA, Wi = NA, di = NA, Ui = NA, elev = NA)
results <- list()
for (j in 1:length(Zw)) {
#j = 20
elev = Zw[j] - min(Ygrid)
Wi = calcWidth(elev, b, wb, db, dmax)
Ai = calcArea(elev, b, wb, db, dmax)
Pi = calcP(elev, b, wb, db, dmax)
di <- Ai / Wi
Ri <- Ai/Pi
Ui = calcUi(Ri, D84, S)
Q = Ui * Ai
simulated$elev[j] = elev
simulated$Wi[j] = Wi
simulated$Ai[j] = Ai
simulated$Pi[j] = Pi
simulated$di[j] = di
simulated$Ri[j] = Ri
simulated$Ui[j] = Ui
simulated$Q[j] = Q
}
# set up data frame of outputs with varying streamflow intervals
Q <- c(seq(0.001, 0.1, 0.001), seq(0.11, 1, 0.01), seq(1.1, 10, 0.1),
seq(11, 100, 1), seq(110, 1000, 10), seq(1100, 10000, 100))
# add modelled hydraulics to output dataframe
Ai <- approx(simulated$Q, simulated$Ai, xout = Q)[2]
Wi <- approx(simulated$Q, simulated$Wi, xout = Q)[2]
di <- approx(simulated$Q, simulated$di, xout = Q)[2]
Ui <- approx(simulated$Q, simulated$Ui, xout = Q)[2]
# filter results
mod_hyd <- data.frame(Q, Ai = Ai$y, Wi = Wi$y, di = di$y, Ui = Ui$y) %>%
filter(is.na(Ai) == FALSE)
#####################################################
# Prepare graph of cross section
if(xs_output == TRUE){
# output coordinates
if(is.null(db_max) == TRUE){
plot_y <- c(0, (db * -1), (dmax * - 1), 0)
} else {
plot_y <- c(0, (db * -1), (db_max * - 1), 0)
}
# set up x-values to plot
plot_x <- c(0, (b * wb), (0.99 * wb), wb )
# write channel cross section
channel_xs <- data.frame(x = plot_x, y = plot_y)
write.csv(channel_xs, "channel_xs.csv", row.names = FALSE)
# plot simple figure
jpeg("channel_xs.jpeg", width = 6, height = 4, units = "in", res = 300)
par(mar = c(4.5, 4.5, 1, 1))
plot(plot_x, plot_y, type = "l",
xlab = "Width (m)",
ylab = "Depth (m)",
ylim = c((min(plot_y) * 1.2), 0), cex.lab = 0.8, cex.axis = 0.8,
)
abline(a = (db * -1), 0, lty = 2, col = "grey")
legend("bottomleft", col = c("black", "grey"), bty = "n",
lty = c(1, 2), cex = 0.86,
legend = c("Channel cross section", "Average depth"))
dev.off()
} else {
}
# return modelled hydraulics
return(mod_hyd)
}
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Add the following code to your website.
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