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---
title: "ENVT5503 Hydrus-1D Beginners` Guide"
subtitle: "Remediation of Soil and Groundwater"
author: "Andrew Rate"
date: "`r Sys.Date()`"
output:
html_document:
theme: yeti
code_folding: show
self_contained: no
number_sections: no
smart: no
toc: true
toc_depth: 2
toc_float: true
---
<style type="text/css">
body{
font-size: 12pt;
}
</style>
<p style="text-align:center;">{alt="animation of vertical solute transport pulse" width=200 height=300}<br />
<span style="text-align:center; font-size:10pt;">*Figure 1: Animation representing simulated solute transport, made with the `gganimate`<br />R package. For the `R code` to make this animation and some background information,<br />go to [https://ratey-atuwa.github.io/cybloRg/pulse.html](https://ratey-atuwa.github.io/cybloRg/pulse.html){target="_blank"}.*</span></p>
# Getting Started
This guide should enable you to create a working simulation of solute transport
using Hydrus-1D.
Start by opening the `Project Manager`, and click the `New` button:
{alt="Hydrus-1D startup screen screenshot"}
In the `New Project` dialog box, type the name (and optional description), then click `OK`:
{alt="New Project dialog screenshot"}
This should open the `input dialog` (the sub-window name will be the name you gave it above under `New Project`).
- Double-click on the items in the `Pre-processing` pane (left) to open them, which allows you to change input parameters.
- The right side of the window (`Post-processing`) will have items in it after a Hydrus-1D project is run
{alt="input dialog screenshot"}
Double-clicking on `Main Processes` gives a new dialog box – you should make sure that you check the ☑`Solute Transport` checkbox:
{alt="Main Processes dialog screenshot"}
You can just keep clicking the `Next` button to get to each part of the input set-up:
(Remember you can click the `Help` button for assistance on any screen!)
<p id="geom"> </p>
# Hints for parameter selection in each input dialog
The instructions below get you a very basic simulation with a single
substrate ("soil") material, reacting with a single solute. The
reaction is defined by simple partitioning using a *K*~d~ value, and
equilibrium is achieved instantaneously.
## `Geometry Information`
- Set `Length Units` to desired value<br />(we recommend m, but cm is OK) {align="right" width=393 height=159}
- Use one Soil Material for simple transport, but two or more for reactive barriers *etc*.
- For horizontal transport use `Decline from Vertical...` of ≤ 0.1
- Set `Depth` to desired value – this represents our flow path length, so choose something realistic for groundwater! (*e.g*. if your units are cm, Depth needs to be ≥ 1000)
## `Time Information`
- Set Time Units to desired value (days is OK) {align="right" width=266 height=248}
- Set Final Time to match column length and (later) hydraulic conductivity
- You can scale Initial/Minimum/Maximum Time Step up or down depending on whether you increase or decrease Final Time
- Leave other settings as default (for now)
You may need to return to the `Time Information` dialog later depending on the output of your initial simulation.
## `Print Information`
- Set Number of Print Times to enable plotting profile information at different times (*e.g*. 5-10)
- Then click `Select Print Times...` and click `Default` (you can try the other settings later)
{width=366 height=359} {width=383 height=119}
## `Iteration Criteria`
- Leave these at their default settings for now (we don`t usually need to change these values).
{width=346 height=246 alt="Iteration Criteria dialog screenshot"}
## `Soil Hydraulic Model`
- Leave at default settings for now (the van Genuchten model is a good and widely-used option for relating soil physical properties to the water retention curve.)
{width=392 height=353 alt="Soil Hydraulic Model dialog screenshot"}
## `Water Flow Parameters`
- Select the desired pre-set from the `Soil Catalog` {align="right" width=414 height=229}
`Qr` = Residual soil water content, *q~r~*
`Qs` = Saturated soil water content, *q~s~*
`Alpha` = Parameter *a* in the soil water retention function [L^−1^]
`n` = Parameter *n* in the soil water retention function
`Ks` = Saturated hydraulic conductivity, *K~s~* [LT^−1^]
`l` = Tortuosity parameter in the conductivity function [-]
The individual values can be set manually too.
## `Water Flow Boundary Conditions`
- Leave at default settings for now
{width=310 height=311}
<p id="Solute-Transport"> </p>
## `Solute Transport`
- the default `Mass Units` are mmol, but we recommend changing to g.<br />If we set the length units to m earlier, this makes our concentration units g/m^3^, which is equivalent to mg/L
- Make sure `Number of Solutes` = 1
- Choose `Pulse Duration` to be a fraction (*e.g*. ≤ 0.1 × the `Final Time` set earlier)
{width=414 height=347}
<p id="Solute-Transport-Parameters"> </p>
## `Solute Transport Parameters`
- You can leave these at defaults, but FYI: {align="right" width=413 height=230}
(dimensions are in square brackets [ ] )
#### `Soil Specific Parameters`:
`Bulk.d.` = Bulk density, *r* [ML^−3^]
`Disp` = Longitudinal dispersivity, *D~L~* [L]
`Frac` = ...fraction of adsorption sites with instantaneous sorption...; Set = 1 for equilibrium transport
`ThIm` = Immobile water content. Set equal to 0 when *physical nonequilibrium* is not considered.
#### `Solute Specific Parameters`:
`Diffus.W` = diffusion coefficient in water, *D~w~* [L²T^−1^]
`Diffus.G` = diffusion coefficient in soil air, *D~a~* [L²T^−1^]
<p id="STRP"> </p>
## `Solute Transport and Reaction Parameters`
- Set partition coefficient `Kd` > 0 for reactive transport (leave `Kd` = 0 for non-reactive)
- for [more advanced simulations (see below)](#advanced), add a reaction rate constant (`Alpha`) parameter
- Click the `Help` button for details!
{width=680 height=231}
## `Solute Transport Boundary Conditions`
- `Bound. Cond` > 0 for each solute (`Sol. No.`) – this is the initial solute concentration, so it can`t be zero!
- Ensure concentrations are realistic and in the correct units set under `Dimensions`
- Click the `Help` button for details of the other options.
{width=397 height=294}
## `Do you want to run PROFILE application ?`
- Yes, you do! Click [OK].
{width=298 height=93}
<p id="profile"> </p>
# `Profile Information` dialog
- Click `Pressure Head...`, then click the `Edit Condition` button, and select the whole column by clicking top then bottom, then set `Top` and `Bottom` value to 0 (zero) *i.e*. **saturated with water**
- You can also set other soil parameters, *e.g*. material types and observation points
– see the video!
- Make sure you click save 💾 (you might need to press the [`esc`] key first), check the soil profile table display, then you are ready to run Hydrus – see the video!
{alt="Profle Information dialog screenshot" width=1200 height=1131}
<span style="font-size:14pt;">👉</span> When the `Profile Information` window is saved and closed, the
`Soil Profile Summary` will open automatically.
### `Soil Profile Summary`
{align="right" width=367 height=253 alt="Hydrus-1D Soil Profile Summary screenshot"}This is a good opportunity to check that the profile is set up the way you want it to be.
- for groundwater, all values in the `h [m]` column should be zero (you might have `h [cm]` depending on your length units)
- scroll down the `Mat` column to check that all soil materials are at the depth/distance (`z [m]`) that you want them to be
- you can edit the values directly in the `Soil Profile Summary` table
When you click `Next` in the `Soil Profile Summary`, the Hydrus-1D
program will ask `Do you want to run HYDRUS-1D application ?` Usually
you do, so click `OK`.
{width=552 height=320 alt="Hydrus-1D Calculation screenshot"}
Look for the text `Calculations have finished successfully.` If it's
there, press Enter or just close the window.
After a successful Hydrus-1D simulation run, you can use the options in the post-processing window to visualise the output within Hydrus-1D. Alternatively, you can read the data file(s) into Excel® or R and make better graphs!
<div id="advanced" style="border: 2px solid #039; background-color:#f0f0f0; padding: 8px;">
For many applications we would want to include more complexity into
our simulation. For example, in the ENVT5503 class, we set an
assignment to simulate remediation of groundwater contamination with a
permeable reactive barrier (PRB). In this case we should consider
including:
- at least 2 'soil' materials with different properties to represent the aquifer material and the PRB (see the [`Geometry Information` dialog](#geom))
* this would be further defined as a depth range in the `Material Distribution` options of the [`Profile Information` dialog](#profile)
- a One-site sorption model (Chemical Nonequilibrium) (in the [`Solute Transport` dialog](#Solute-Transport))
- a diffusion coefficient for our solute in water (`Diffus. W.` in the [`Solute Transport Parameters` dialog](#Solute-Transport-Parameters))
- a `Frac = 1` value of zero to match non-equilibrium conditions (in the [`Solute Transport Parameters` dialog](#Solute-Transport-Parameters))
- a non-zero `Kd` value for the material representing the PRB (and potentially a lower `Kd` value for the surrounding material) in the [`Solute Transport and Reaction parameters` dialog](#STRP)
- an `alpha` value (first-order reaction rate constant) for each material (in the [`Solute Transport and Reaction parameters` dialog](#STRP) - scroll to the right; `alpha` is at the end)
</div>
```{r table1, message=FALSE, warning=FALSE, echo=FALSE}
windowsFonts(fixed=windowsFont("Courier New"))
library(flextable)
library(officer)
set_flextable_defaults(theme_fun = "theme_zebra",
font.size = 11, font.family = "Arial",
padding = 2, text.align = "right")
BorderDk <- officer::fp_border(color = "#B5C3DF", style = "solid", width = 1)
BorderLt <- officer::fp_border(color = "#FFFFFF", style = "solid", width = 1)
table1 <- data.frame(filename=c("Nod_Inf.out","Obs_Node.out",
"Solute1.out\n(& Solute2.out,...)"),
Contents=c("Separate data matrices at selected `Print times` during simulation.\nUseful columns: Depth, Conc(1..NS), Sorb(1..NS)",
"Side-by side data matrices for each node depth.\nUseful columns: time, theta, conc",
"Single data matrix for each solute. Contains columns for time, fluxes and concentrations (including cumulative values) at start of flow path (Top), Root zone, end of flow path (Bot)."))
flextable(table1) |> width(j=c(1,2), width=c(6,14), unit="cm") |>
valign(valign = "top", part="body") |>
border_outer(border=BorderDk) |> border_inner(border=BorderLt) |>
set_header_labels(filename="File name") |> fontsize(size=11, part="all") |>
set_caption(caption="Table 1: The following HYDRUS-1D output files contain useful data.", align_with_table=F, fp_p=fp_par(text.align = "left", padding.bottom = 6))
```
More detail is available in the Hydrus-1D manual. We recommend the [Hydrus-1D Tutorial (Rassam *et al*. 2018)](https://www.pc-progress.com/Downloads/Public_Lib_H1D/HYDRUS-1D_Tutorial_V1.00_2018.pdf){target="_blank"}.
Various versions of Hydrus manuals are available at [https://www.pc-progress.com/](https://www.pc-progress.com/en/Default.aspx?Downloads){target="_blank"}, the most relevant probably being Šimůnek *et al*. (2008).
# Reading HYDRUS-1D data into `R`
Users of
[Hydrus-1D](https://www.pc-progress.com/en/Default.aspx?H1d-downloads){target="_blank"}
either need to use the limited graphics in Hydrus itself, open the
output files in Excel, or devise a way of using more flexible
software like `R`.
## Reading data copied from a Hydrus-1D plot
{width=262 height=315 align="right" alt="Profile information output window opened from Hydrus-1D Post-processing pane, with Concentration selected at Horizontal Variable"} This is an easier alternative to reading the data stored in the
`Nod_Inf.out` file ([described below](#reading-data-in-hydrus-1d-output-files)).
Right-click on Hydrus-1D plot of Profile Information: Concentration,
and select Copy; this will copy the data table for the plot in
tab-separated format.
Then run the following code:
```{r read-hydrus-clipboard, eval=FALSE}
hydrus0 <- read.table("clipboard", header=TRUE, sep="\t")
```
On some Mac computers this does not work, giving an error message such as:<br />
`Error in file(file, "rt") : X11 module cannot be loaded`
In that case, copy the data from the Hydrus-1D plot into Excel, and
save as a `.csv` file (*e.g*. `hydrus1.csv`) into your current RStudio
working directory.
Then just use `read.csv` to input the Hydrus-1D data:
```{r read-hydrus-csv}
hydrus0 <- read.csv("hydrus1.csv") # remember what name you gave the file!
```
<p id="settimes">Then it's useful to input some of the Hydrus-1D information
(`Final Time` (≡ total time), and number of `Print Times`):</p>
```{r set-finaltime-nprinttimes}
# specify Final Time here
# (from Hydrus-1D 'Time Information' input)
# 👇
ft <- 365 # run this line!
# specify number of Print times here
# (from Hydrus-1D 'Print Information' input)
# 👇
pt <- 10 # run this line!
(simTimes <- seq(0,ft, len=pt+1))
colnames(hydrus0)[seq(2,ncol(hydrus0),2)] <- paste("Day",round(simTimes))
colnames(hydrus0)[seq(3,ncol(hydrus0),2)] <- paste0("Dist",round(simTimes))
```
Then, **reformat the data for easier plotting** using `melt()` from
the `reshape2` package. If `Distance` is negative, we make it
positive. To enhance plots, strip off the last concentration at each time step.
```{r melt-pasted-data}
library(reshape2)
# convert to long-form using melt()
hydrus1 <- melt(hydrus0[,2:ncol(hydrus0)],
id.vars = c("T0"),
measure.vars = paste("Day",round(simTimes)))
colnames(hydrus1) <- c("Distance","Time","Concentration")
# reverse sign of distance variable
if(min(hydrus1$Distance)<0) hydrus1$Distance <- -1*hydrus1$Distance
# make final concs NA
hydrus1[which(hydrus1$Distance==max(hydrus1$Distance)),"Concentration"] <- NA
```
Check the data file:
```{r check-melted-data}
str(hydrus1)
```
### Plot the data (option 1: symbols only)
We plot the concentration (*y-axis*) *vs*. distance (*x-axis*) since
this is relevant to horizontal transport, such as flow of
**groundwater** containing solute(s).
```{r plot-melted-1, fig.width=8, fig.height=4, fig.cap="Figure 2: Plot of simulated solute concentration vs. horizontal distance for each simulation time step (showing individual simulation points), using Hydrus-1D", results='hold'}
par(mar=c(4,4,1,1), mgp=c(1.7,0.3,0), tcl=0.25,
font.lab=2, cex.lab=1.2)
palette(c("black",viridis::plasma(pt, alp=0.7)))
with(hydrus1, plot(Distance, Concentration, type="b",cex=1,
pch=rep(c(21:25),3)[Time],
bg=seq_along(simTimes)[Time],
xlab="Distance (m)",
ylab="Solute concentration (mg/L)"))
legend("topright", bty="n", inset=0.02, ncol=2,
title=expression(italic("Simulation times [days]")),
legend=round(simTimes[-1]), pt.bg=seq_along(simTimes)+1,
pch=c(22:25,21:25,21), pt.cex=1.2)
```
### Plot the data (option 2: just the lines)
If you don't like all the symbols in the plot above, try the following
(or, you can adapt the code to plot concentration on the horizontal
axis - [see below](#vert)):
```{r plot-melted-2, fig.cap="Figure 3: Plot of simulated solute concentration vs. horizontal distance for each simulation time step (showing smooth lines only), fig.height=4, fig.width=8, paged.print=FALSE, using Hydrus-1D", results='hold'}
par(mar=c(4,4,1,1), mgp=c(1.7,0.3,0), tcl=0.25,
font.lab=2, cex.lab=1.2)
palette(c("black",viridis::turbo(pt)))
with(subset(hydrus1, hydrus1$Time==levels(hydrus1$Time)[1]),
plot(Concentration ~ Distance, type="l",
ylim=c(0, max(hydrus1$Concentration, na.rm=TRUE)),
xlab="Distance (m)", ylab="Solute concentration (mg/L)") )
for (i in 2:(pt+1)){
with(subset(hydrus1, hydrus1$Time==levels(hydrus1$Time)[i]),
lines(Concentration ~ Distance, col=i,lwd=3,lty=i))
}
legend("topright", bty="n", inset=0.02, ncol=2,
title=expression(italic("Simulation times [days]")),
lty=seq_along(simTimes)+1, seg.len=4.5, legend=round(simTimes[-1]),
col=seq_along(simTimes)+1, pch=NA, lwd=rep(3,pt),
x.intersp=0.5)
```
### Of course you can use ggplot if you want!
Note that the legend uses the levels names for the factor `Time` that we made after setting the Final Time and number of Print Times ([above](#settimes)).
```{r hydrus-plot-gg, fig.width=10, fig.height=4, fig.cap="Figure 4: Plot of simulated solute concentration vs. horizontal distance for each simulation time step, using Hydrus-1D (the `ggplot` version).", message=FALSE, warning=FALSE, results='hold'}
require(ggplot2)
ggplot(hydrus1) +
geom_line(aes(x=Distance, y=Concentration, colour=Time,
linetype=Time), linewidth=1.5) +
scale_color_manual(values=c("grey",viridis::turbo(10, beg=0.05))) +
guides(color=guide_legend(title="Simulation times")) +
guides(linetype=guide_legend(title="Simulation times")) +
labs(x="Distance (m)", y = "Concentration (mg/m³)") +
theme_bw() +
theme(axis.title = element_text(face="bold", size=14),
legend.key.width = unit(4, "line"),
legend.title = element_text(face="bold", size=12))
```
## Reading data in Hydrus-1D output files
Here's my code to read the node (Profile) information
output files from Hydrus-1D (`Nod_Inf.out` in the relevant Hydrus-1D
project folder) into an **R** data frame.
```{r set-hydrus-dir-dontshow, message=FALSE, warning=FALSE, include=FALSE}
MyPC <- "C:/Users/00028958/OneDrive - The University of Western Australia/My Documents/aaTeaching/"
```
```{r read Nod_Inf.out, results='hide'}
# R code to read Hydrus-1D Nod_Inf.out files into an R data frame
# set full path to Hydrus-1D project directory (folder)
# -=-=-=-=- EDIT THIS TO MATCH THE FOLDER ON YOUR COMPUTER ! -=-=-=-=-
PCdir <- paste0(MyPC,"ENVT5503/Hydrus1D ENVT5503/PRB")
# read Nod_Inf.out file into a vector of character (text) strings
Nod_Inf_out <- readLines(paste0(PCdir,"/","Nod_Inf.out"))
# View(Nod_Inf_out) # optionally check what we just read
# find indices of some rows we want to delete
head_rows <- grep("Node", Nod_Inf_out)
# use indices to delete the rows
Nod_Inf_out <- Nod_Inf_out[-c(seq(1,7),head_rows-2, head_rows-1,
head_rows+1, head_rows+2)]
# find indices of some more rows we want to delete
ends <- grep("end",Nod_Inf_out)[-1*NROW(grep("end",Nod_Inf_out))]
# use indices to delete the rows
Nod_Inf_out <- Nod_Inf_out[-c(ends, ends+1, ends+2)]
# find indices of rows that have the Hydrus-1D print times
time_rows <- grep("Time:", Nod_Inf_out)
# extract the rows with Hydrus-1D print times into a vector
timz <- Nod_Inf_out[time_rows]
# get rid of text around the Hydrus-1D print time values...
timz <- gsub("Time: ","",timz)
timz <- gsub(" ","",timz)
# ...and convert to numbers...
timz <- as.numeric(timz)
# ...then delete the Hydrus-1D print time rows
Nod_Inf_out <- Nod_Inf_out[-c(time_rows)]
# find the rows with column names for each block of print data...
head_rows <- grep("Node", Nod_Inf_out)
# and remove all except the first one
Nod_Inf_out <- Nod_Inf_out[-c(head_rows[-1])]
# strip out all but single spaces from data...
while(NROW(grep(" ", Nod_Inf_out)) > 0) {
Nod_Inf_out <- gsub(" "," ", Nod_Inf_out)
}
# ...and (finally!) delete the very last row (an 'end' statement)
Nod_Inf_out <- Nod_Inf_out[-1*NROW(Nod_Inf_out)]
#
# write the edited output to a file...
writeLines(Nod_Inf_out, con="./NodInf3.out")
# ...and read the file in as space-delimited
node_data <- read.table(file = "NodInf3.out", header = TRUE, sep = " ")
# the is a blank column 1; rename it to "Time"
colnames(node_data)[1] <- "Time"
# use the print times vector to make a vector with
# the relevant time repeated for each block
timz0 <- rep(timz[1], NROW(node_data)/NROW(timz))
for (i in 2:NROW(timz)) {
timz0 <- append(timz0, rep(timz[i], NROW(node_data)/NROW(timz)))
}
# replace the Time colum with the vector we just made...
node_data$Time <- timz0
# ...and convert Time to a factor
node_data$Time <- as.factor(node_data$Time)
# remove temporary objects...
rm(list = c("i","head_rows","Nod_Inf_out","timz","timz0","ends"))
# ...and check the cleaned-up data
str(node_data)
```
### Plot concentration *vs*. depth
<p id="vert">This is the type of plot we would use for vertical transport, such as leaching through a soil profile.</p>
```{r conc-depth, fig.width=4, fig.height=6, fig.cap="Figure 5: Plot of simulated solute concentration vs. vertical depth for each simulation time step, using Hydrus-1D", results='hold'}
# check it with a plot
# plot as concentration vs. depth
palette(c("black",viridis::rocket(6, beg=0.15, end=0.7)))
par(mar = c(1,4,4,1), mgp = c(1.7,0.3,0), tcl = 0.3, font.lab=2)
plot(-1*(node_data$Depth) ~ node_data[,13],
type = "l", col = 1,
xlim = c(0, max(node_data[,13], na.rm=T)),
ylim = c(-1*min(node_data$Depth, na.rm=T), 0),
subset = node_data$Time==levels(node_data$Time)[1],
xaxt = "n", xlab = "", ylab = "Depth (cm)")
axis(3)
mtext("Concentration", side = 3, line = 1.7, font = 2)
symz <- c(15,19,17,8,12,9)
for (i in 2:nlevels(node_data$Time)) {
points(-1*node_data$Depth ~ node_data[,13], col = i,
subset = node_data$Time==levels(node_data$Time)[i],
type = "o", pch = symz[i-1], cex = 0.6)
}
legend("bottomright", legend = levels(node_data$Time),
col = seq(1,nlevels(node_data$Time)),
pch = c(NA,symz),
lwd = 1,
pt.cex=0.85, bty = "n", inset = 0.02,
title = expression(bold("Time (days)")))
```
### Plot as concentration *vs*. horizontal distance
This type of plot is relevant to horizontal transport, such as flow of
**groundwater** containing solute(s).
```{r conc-hdist, fig.width=8, fig.height=4, fig.cap="Figure 6: Plot of simulated solute concentration vs. horizontal distance for each simulation time step, using Hydrus-1D", results='hold'}
palette(c("black",viridis::plasma(6)))
symz <- rep(21:25,2)
par(mar = c(4,4,1,1), mgp = c(1.7,0.3,0), tcl = 0.3, font.lab=2)
node_data$Distance <- -1*node_data$Depth
plot(node_data[,13] ~ -1*node_data$Distance,
type = "l", col = 1,
ylim = c(0, max(node_data[,13], na.rm=T)),
xlim = c(0, max(node_data$Distance, na.rm=T)),
subset = node_data$Time==levels(node_data$Time)[1],
ylab = "Concentration", xlab = "Distance (cm)")
for (i in 2:nlevels(node_data$Time)) {
points(node_data[,13] ~ -1*node_data$Distance, bg = i,
subset = node_data$Time==levels(node_data$Time)[i],
type = "o", pch = symz[i-1], cex = 1)
}
legend("topright", legend = levels(node_data$Time),
pt.bg = seq(1,nlevels(node_data$Time)),
pch = c(NA,symz),
lwd = 1,
pt.cex=1, bty = "n", inset = 0.02,
title = expression(bold("Time (days)")))
```
# References
Rassam, D., J. Šimůnek, D. Mallants, and M. Th. van Genuchten, *The HYDRUS-1D Software Package for Simulating the One-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably-Saturated Media: Tutorial*, CSIRO Land and Water, Adelaide, Australia, 183 pp., ISBN 978-1-4863-1001-2, 2018. [https://www.pc-progress.com/Downloads/Public_Lib_H1D/HYDRUS-1D_Tutorial_V1.00_2018.pdf](https://www.pc-progress.com/Downloads/Public_Lib_H1D/HYDRUS-1D_Tutorial_V1.00_2018.pdf){target="_blank"}
Šimůnek, J., M. Šejna, H. Saito, M. Sakai, and M. Th. van Genuchten, *The Hydrus-1D Software Package for Simulating the Movement of Water, Heat, and Multiple Solutes in Variably Saturated Media*, Version 4.0, HYDRUS Software Series 3, Department of Environmental Sciences, University of California Riverside, Riverside, California, USA, pp. 315, 2008. ([PDF 2.7MB](https://www.pc-progress.com/downloads/Pgm_Hydrus1D/HYDRUS1D-4.08.pdf){target="_blank"})
# R packages
Garnier S, Ross N, Rudis R, Camargo AP, Sciaini M, Scherer C (2024). `viridis(Lite)` - Colorblind-Friendly Color Maps for R. `viridis` package version 0.6.5. [https://sjmgarnier.github.io/viridis/](https://sjmgarnier.github.io/viridis/){target="_blank"}
Wickham, H. (2007). Reshaping Data with the `reshape` Package. *Journal of Statistical Software*, **21(12)**, 1-20. URL [http://www.jstatsoft.org/v21/i12/](http://www.jstatsoft.org/v21/i12/){target="_blank"}.
Wickham, H. (2016). `ggplot2`: *Elegant Graphics for Data Analysis*. Springer-Verlag: New York. [https://ggplot2.tidyverse.org](https://ggplot2.tidyverse.org){target="_blank"}