Tutorial for R package kwb.wtaq
Introduction
Background
Within the OPTIWELLS-2 project, sponsored by Veolia Water, a detailed study was performed for screening available models that:
are able to simulate time-dependent well drawdown
also include the additional drawdown in case of well interference and
are quite easy to parameterise
The semi-analytical groundwater model WTAQ-2 was chosen, because it fitted best with the above defined requirements. However, as the model is programmed in FORTRAN it requires that the user follows the steps that are listed below:
- Step: Definition and parameterisation of text input file,
- Step: Execution of the WTAQ-2 model engine in MS DOS command shell
- Step: Saving of model results in a text output file
- Step: Reading and analysing of model outputs
- Step (in case of well interference): looping through Steps 1-4 for each active production well and superposition of additional drawdowns due to well interference
For simplifying this process it was decided to build an R package that enables to perform all these steps and also includes the WTAQ-2 model engine (for more details see: Sonnenberg et al., 2014). This R package kwb.wtaq was developed by Hauke Sonnenberg at Kompetenzzentrum Wasser Berlin (KWB). It provides an Application Programming Interface (API) to the analytical groundwater drawdown model WTAQ-2, developed by the United States Geological Survey (USGS) and provided for free (for further information on WTAQ-2 see: http://water.usgs.gov/ogw/wtaq/). In the following we will simply use “WTAQ” when referring to the software WTAQ-2.
Objective
The objective of this tutorial is to demonstrate how the functions from the R-package kwb.wtaq can be used to configure and run a WTAQ model setup and to read the resulting groundwater drawdowns from the output files that are generated by the WTAQ model software.
Preparation
In order to use the R package you need to have the R programming environment (in version 3.0 or higher) installed on your computer. You can download it for free from http://cran.rstudio.com/.
As Integrated Programming Interface (IDE) for the R environment we recommend — and for the purpose of this tutorial require — to use the free software RStudio. You can download RStudio from: http://www.rstudio.com/products/rstudio/download/.
The programming environment R is shipped with a basic set of functions. It can be extended by so-called packages that contain user-defined functions. We used this packaging mechanism and provide the access functions to WTAQ in the form of an R package that we named kwb.wtaq.
Before you can start using the functions provided in the package you need to
Install the package into your R programming environment and
Load the package into your current R session.
Installation of required R packages
Since the package kwb.wtaq depends on a number of other packages, not only kwb.wtaq but also all the packages that it depends on need to be installed.
In order to simplify the package installation run the following code:
if(!require("devtools")) { install.packages("devtools") }
devtools::install_github(repo = "KWB-R/kwb.wtaq", dependencies = TRUE)This will download and install the package kwb.wtaq with all required dependencies, i.e.:
publicly available packages from the Comprehensive R Archive Network (CRAN) and
the KWB Github package kwb.utils
If the installation succeeds the messages generated should read like these:
## package 'zoo' successfully unpacked and MD5 sums checked
## package 'hydroGOF' successfully unpacked and MD5 sums checked
## package 'lattice' successfully unpacked and MD5 sums checked
## package 'plotrix' successfully unpacked and MD5 sums checked
##
## The downloaded binary packages are in
## C:\Dokumente und Einstellungen\Key Hauke\Lokale Einstellungen\Temp\RtmpctBYMz\downloaded_packages
## package 'kwb.utils' successfully unpacked and MD5 sums checkedThe installation needs to be done only once. The packages keep
installed until you decide to uninstall them. Uninstalling a package in
RStudio can be done by clicking on the Remove package
button right to the package name on the “Packages” tab.
Loading the package
Once you have installed all the requied packages you are almost ready to use the functions contained in the package kwb.wtaq.
As a last step you need to explicitly load the package into your current R session by running the following R command:
You will see messages stating the progress of loading not only the package kwb.wtaq but also of all the packages that it depends on.
You may see warnings that the packages have been built under R in a higher version compared to the version that you are using:
Unless you are using R in a version prior to 3.0 these messages do not indicate a problem and can be ignored.
Please note that the functions provided in the kwb.wtaq
package can only be used when the package is loaded with
library(kwb.wtaq) as shown here. This needs to be done each
time you start a new R session or each time you open RStudio. If you
write an R script that uses the functions from kwb.wtaq then it
would be a good practice to put library(kwb.wtaq) as one of
the first lines of your script.
Using the package help
A detailed description of the WTAQ model parameters is available in
the WTAQ
documentation. However, within ‘RStudio’ is not always necessary to
consult this manual, because the parameter description is integrated in
the kwb.wtaq package help. These information can be
accessed by pressing Ctrl and Space
simultaneously, if the cursor is located within a function,
e.g. wtConfGeneral():
On the fly help in RStudio
The help file for each R function in RStudio can be
accessed by using the R command help(functionname) or using
? before the functionname, e.g.:
Note: Typing kwb.wtaq:: before the
function name is only needed if you haven’t loaded the package into your
R session with library(kwb.wtaq) (see Loading the package)
In addition, we also provide a full description of all the parameters that are accepted by the configuration functions, which are descriped later in this tutorial.
Example sessions
Level 1: One pumping well
Pumping test data
We have provided an example dataset “drawdowns” containing four different pumping tests with measured drawdown time-series in five different wells (production well and four observation wells). You can load the dataset by running:
Let’s have a short look to the dataset. It is a list of four data frames as the R command “str” reveals:
## List of 4
## $ W1:'data.frame': 15 obs. of 6 variables:
## ..$ time.in.seconds: num [1:15] 420 1020 1620 2820 4020 ...
## ..$ W1 : num [1:15] 1.25 1.42 1.46 1.52 1.56 ...
## ..$ W2 : num [1:15] 0.02 0.04 0.05 0.07 0.08 ...
## ..$ W3 : num [1:15] 0 0.01 0.01 0.02 0.03 ...
## ..$ W4 : num [1:15] 0 0 0.01 0.02 0.02 ...
## ..$ W5 : num [1:15] 0 0.01 0.01 0.01 0.01 ...
## $ W2:'data.frame': 15 obs. of 6 variables:
## ..$ time.in.seconds: num [1:15] 120 720 1320 2520 3720 ...
## ..$ W2 : num [1:15] 1.2 1.73 1.62 1.68 1.75 ...
## ..$ W1 : num [1:15] 0.01 0.05 0.06 0.09 0.1 ...
## ..$ W3 : num [1:15] 0 0.02 0.03 0.05 0.06 ...
## ..$ W4 : num [1:15] 0 0 0.01 0.01 0.02 ...
## ..$ W5 : num [1:15] 0 0.01 0.01 0.01 0.01 ...
## $ W4:'data.frame': 15 obs. of 6 variables:
## ..$ time.in.seconds: num [1:15] 60 660 1260 2460 3660 ...
## ..$ W4 : num [1:15] 0.5 0.76 0.79 0.82 0.84 ...
## ..$ W1 : num [1:15] 0 0 0.01 0.02 0.02 ...
## ..$ W2 : num [1:15] 0.01 0.01 0.01 0.02 0.03 ...
## ..$ W3 : num [1:15] 0.01 0.05 0.06 0.08 0.1 ...
## ..$ W5 : num [1:15] 0.01 0.04 0.05 0.07 0.08 ...
## $ W5:'data.frame': 15 obs. of 6 variables:
## ..$ time.in.seconds: num [1:15] 600 1200 1800 2400 3600 5400 7200 10800 15000 21600 ...
## ..$ W5 : num [1:15] 0.73 0.74 0.75 0.77 0.78 ...
## ..$ W1 : num [1:15] 0 0 0 0.01 0.01 ...
## ..$ W2 : num [1:15] 0 0 0 0 0 ...
## ..$ W3 : num [1:15] 0.01 0.01 0.01 0.01 0.02 ...
## ..$ W4 : num [1:15] 0.04 0.04 0.06 0.06 0.07 ...The four list elements represent four different pumping tests (in “W1”, “W2”, “W4” and “W5”. The resulting drawdowns of each pumping test are stored in a data frame of six columns. Column “time.in.seconds” contains the time in seconds since the start of a pumping test. The columns “W1” through “W5” contain the water table drawdowns measured in the corresponding wells “W1” to “W5”,in meters below the initial water table.
For example, the fourth pumping test, during which a discharge of Q = 313 m3/h was measured in Well W5, resulted in the following drawdowns:
## time.in.seconds W5 W1 W2 W3 W4
## 1 600 0.73 0.00 0.00 0.01 0.04
## 2 1200 0.74 0.00 0.00 0.01 0.04
## 3 1800 0.75 0.00 0.00 0.01 0.06
## 4 2400 0.77 0.01 0.00 0.01 0.06
## 5 3600 0.78 0.01 0.00 0.02 0.07
## 6 5400 0.80 0.01 0.01 0.03 0.09
## 7 7200 0.82 0.02 0.01 0.04 0.10
## 8 10800 0.83 0.03 0.02 0.05 0.11
## 9 15000 0.85 0.03 0.03 0.06 0.13
## 10 21600 0.87 0.04 0.04 0.08 0.15
## 11 31200 0.89 0.05 0.05 0.09 0.16
## 12 44400 0.92 0.06 0.06 0.11 0.18
## 13 63600 0.93 0.07 0.07 0.12 0.20
## 14 90600 0.95 0.08 0.08 0.14 0.21
## 15 129600 0.96 0.09 0.09 0.15 0.23It seems as if the drawdowns reach a steady-state after a certain time. This can be judged better by a diagram that can be produced in R by using the xyplot function from the R-package “lattice”:
lattice::xyplot(W1 + W2 + W3 + W4 + W5 ~ time.in.seconds,
data = drawdowns[["W5"]],
type = c("b", "g"), # (b)oth, dots and lines, and a (g)rid
auto.key = list(columns = 5), # legend arranged in five columns
ylim=c(1,-0.1),
ylab= "Drawdown (m)", # label of y-Axis
xlab= "Time in seconds since start of pumping in W5 (s)") # label of y-Axis
Model parameterisation
In a first step a WTAQ input file needs to be defined. This can be realised with two different functions:
wtConfigure(): definition of WTAQ configuration within RwtReadInputFile(): importing of WTAQ configuration from existing WTAQ input text file into R
The WTAQ input file can be directly defined in R using the function
wtConfigure() and saved in the R object
wtaqConfiguration (for a full description of all the
parameters that are accepted by the configuration functions, see: Parameter tables).
generalConfiguration <- wtConfigureGeneral(
### title of the project (max. length 70 characters)
title="Example well field, long-term pumping test of well 5"
)
aquiferConfiguration <- wtConfigureAquifer(
aqtype = "WATER TABLE", # aquifer type
bb = 10, # saturated aquifer thickness
hkr = 1E-03, # horizontal hydraulic conductivity
hkz = 3.5E-05, # vertical hydraulic conductivity
ss = 1E-05, # specific storage
sy = 0.05 # specific yield
)
drainageConfiguration <- wtConfigureDrainage(
idra = 0 # = instantaneous drainage in unsaturated zone
)
timesConfiguration <- wtConfigureTimes(
its = 1 # = user-specified time-steps
)In the following we will configure one pumping well and two observation wells (for simplifying the tutorial we restrict ourselves to two instead of four observation wells four which drawdown time series are available).
Since WTAQ allows to define time-series of measured drawdowns for
each well, the corresponding functions
wtConfigurePumpwell() and
wtConfigureObservationWell(), that are described in the
following, also allow to specify these measured drawdown values. For
this example, we want to use the drawdowns of the fourth pumping test,
provided in the example dataset drawdowns. We store it in a
separate variable drawdowns5:
Now we prepare some data frames (a table-like structure in R, defined
by rows and columns, see ?data.frame) representing three
drawdown time series, which are measured at :
the pumping well “PW” and
two different observation wells “OW1” and “OW4”.
By doing this we simplify the programmig code that is used later on:
# the times of observations are the same for all wells:
times <- drawdowns5$time.in.seconds
# observed drawdowns at the pumping well
observed.PW <- data.frame(t = times, dd = drawdowns5$W5)
# observed drawdowns at the observation wells
observed.OW1 <- data.frame(t = times, dd = drawdowns5$W1)
observed.OW4 <- data.frame(t = times, dd = drawdowns5$W4)Let’s start with the configuration of the pumping well:
pumpwellConfiguration <- wtConfigurePumpwell(
### partially penetrating pumped well
ipws = 0,
### finite diameter well
ipwd = 1,
### pumping rate of production well in (here: m3/s)
qq = 0.0869,
### radius of pumped well-screen (here: meter)
rw = 1.5,
### top of filter screen below initial water table (here: meter)
zpd = 0.4,
### bottom of filter screen below initial water table (here: meter)
zpl = 7.8,
### well-bore skin parameter (dimensionless)
sw = 0,
### data.frame with times and measured drawdown data in pumping well
tspw = observed.PW
)Now, let’s define our first observation well:
observationWell1 <- wtConfigureObservationWell(
### name of observation well
obname = "OW1",
### distance from pumping well (here: meters)
r = 309.5,
### partially penetrating observation well
iows = 0,
### delayed response
idpr = 1,
### top of filter screen below initial water table (here: meters)
z1 = 1.8,
### bottom of filter screen below initial water table (here: meters)
z2 = 7.5,
### inside radius of the observation well (here: meters)
rp = 1.5,
### data.frame with times and measured drawdown data in OW1
tsobs= observed.OW1
)In the same way, we define a second observation well “OW4” (in a formally more compact way to save some space here):
observationWell4 <- wtConfigureObservationWell(obname = "OW4", r = 86.6,
iows = 0, idpr = 1, z1 = 1.8, z2 = 7.5, rp = 1.5, tsobs = observed.OW4)Out of these parts of configuration we can build one complete
configuration by using the function wtConfigure(). It
returns a R list structure that represents a model configuration
containing all the necessary information that WTAQ requires to perform a
model run. This information is saved in the R object
wtaqConfiguration and will be used for the following
chapters of this tutorial.
wtaqConfiguration <- wtConfigure(
general = generalConfiguration,
aquifer = aquiferConfiguration,
drainage = drainageConfiguration,
times = timesConfiguration,
solution = wtConfigureSolution(),
pumpwell = pumpwellConfiguration,
obswells = list(observationWell4,
observationWell1)
)Note: Alternatively it is possible to load WTAQ
input text files diretly into R with the function
wtReadInputFile() from an already existing WTAQ input text
file, e.g.:
inputFile <- system.file("extdata", "example1.inp", package = "kwb.wtaq")
wtaqConfiguration2 <- wtReadInputFile(inputFile)However, in this tutorial we just focus on the example that is
stored in the R object wtaqConfiguration.
For checking this model parameterisation it can be printed:
## General
## - Title: Example well field, long-term pumping test of well 5
## - Format: DIMENSIONAL
##
## Aquifer
## - Type: WATER TABLE
## - Thickness (bb) ............: 10.000000 (length)
## - Horiz. hydr. conduct. (hkr): 0.001000 (length/time)
## - Vert. hydr. conduct. (hkz): 0.000035 (length/time)
## - Specific storage (ss) .....: 0.000010 (1/length)
## - Specific yield (sy) .......: 0.050000
##
## Drainage
## - Type: Instantaneous drainage (idra = 0)
##
## Times
## - Type: User-specified times (its = 1)
##
## Solution
## - Type: de Hoog algorithm (isoln = 2)
## - Rel. err. for Newton-Raphson iter. (rerrnr) ...................: 0.000000
## - Rel. err. sought for accur. of the num. invers. (error) .......: 0.000100
## - Factor to determ. # terms in finite summations (ntms) .........: 30
## - # terms in summ. of Fourier series for inv. Lapl. transf. (nnn): 6
## - Method used to accelerate convergence of Fourier series .......: 3
##
## Pumped Well ("PW")
## - Type: Partially penetrating pumped well (ipws = 0)
## - Type of diameter: Finite diameter (ipwd = 1)
## - Pumping rate (qq) .......................................: 0.086900 (length^3/time)
## - Radius of screen (rw) ...................................: 1.500000 (length)
## - Inside radius where levels change during pumping (rc) ...: 1.500000 (length)
## - Top of aquifer/initial water table to screen top (zpd) ..: 0.400000 (length)
## - Top of aquifer/initial water table to screen bottom (zpl): 7.800000 (length)
## - Well-bore skin parameter (sw) ...........................: 0.000000
## - Predefined Times (t)/drawdown measurements (dd):
## t dd
## 1 600 0.73
## 2 1200 0.74
## 3 1800 0.75
## 4 2400 0.77
## 5 3600 0.78
## 6 5400 0.80
## 7 7200 0.82
## 8 10800 0.83
## 9 15000 0.85
## 10 21600 0.87
## 11 31200 0.89
## 12 44400 0.92
## 13 63600 0.93
## 14 90600 0.95
## 15 129600 0.96
##
## Observation Well "OW4"
## - Type: Partially penetrating observation well (iows = 0)
## - Delayed response: yes (idpr = 1)
## - Radial dist. from axis of pumped well to obs. well (r) .....: 86.600000 (length)
## - Top of aquifer/initial water table to screen top (z1) ......: 1.800000 (length)
## - Top of aquifer/initial water table to screen bottom (z2) ...: 7.500000 (length)
## - Inside radius of standpipe where levels change (rp) ........: 1.500000 (length)
## - Length of screened interval (xll) ..........................: 5.700000 (length)
## - Predefined Times (t)/drawdown measurements (dd):
## t dd
## 1 600 0.04
## 2 1200 0.04
## 3 1800 0.06
## 4 2400 0.06
## 5 3600 0.07
## 6 5400 0.09
## 7 7200 0.10
## 8 10800 0.11
## 9 15000 0.13
## 10 21600 0.15
## 11 31200 0.16
## 12 44400 0.18
## 13 63600 0.20
## 14 90600 0.21
## 15 129600 0.23
##
## Observation Well "OW1"
## - Type: Partially penetrating observation well (iows = 0)
## - Delayed response: yes (idpr = 1)
## - Radial dist. from axis of pumped well to obs. well (r) .....: 309.500000 (length)
## - Top of aquifer/initial water table to screen top (z1) ......: 1.800000 (length)
## - Top of aquifer/initial water table to screen bottom (z2) ...: 7.500000 (length)
## - Inside radius of standpipe where levels change (rp) ........: 1.500000 (length)
## - Length of screened interval (xll) ..........................: 5.700000 (length)
## - Predefined Times (t)/drawdown measurements (dd):
## t dd
## 1 600 0.00
## 2 1200 0.00
## 3 1800 0.00
## 4 2400 0.01
## 5 3600 0.01
## 6 5400 0.01
## 7 7200 0.02
## 8 10800 0.03
## 9 15000 0.03
## 10 21600 0.04
## 11 31200 0.05
## 12 44400 0.06
## 13 63600 0.07
## 14 90600 0.08
## 15 129600 0.09and also graphically visualised with the function
wtPlotConfiguration(), e.g.:
Model run
For running WTAQ and saving the results in the R object
result we just have do use the function
wtRunConfiguration() with our above defined model
parameterisation wtaqConfiguration:
## Warning in type.convert.default(block[, i]): 'as.is' should be specified by the
## caller; using TRUE
## Warning in type.convert.default(block[, i]): 'as.is' should be specified by the
## caller; using TRUE
## Warning in type.convert.default(block[, i]): 'as.is' should be specified by the
## caller; using TRUE
## Warning in type.convert.default(block[, i]): 'as.is' should be specified by the
## caller; using TRUE
## Warning in type.convert.default(block[, i]): 'as.is' should be specified by the
## caller; using TRUE
## Warning in type.convert.default(block[, i]): 'as.is' should be specified by the
## caller; using TRUE
## Warning in type.convert.default(block[, i]): 'as.is' should be specified by the
## caller; using TRUE
## Warning in type.convert.default(block[, i]): 'as.is' should be specified by the
## caller; using TRUE
## Warning in type.convert.default(block[, i]): 'as.is' should be specified by the
## caller; using TRUE
## Warning in type.convert.default(block[, i]): 'as.is' should be specified by the
## caller; using TRUE
## Warning in type.convert.default(block[, i]): 'as.is' should be specified by the
## caller; using TRUE
## Warning in type.convert.default(block[, i]): 'as.is' should be specified by the
## caller; using TRUEAnalysing results
To print the results of the model run, that are stored in the object
result in the RStudio console we simply
need to enter:
## WELL TIME MEASDD CALCDD RELERR
## 3 PW 600 0.73 3.808e+00 -421.60
## 4 PW 1200 0.74 4.731e+00 -539.40
## 5 PW 1800 0.75 5.033e+00 -571.00
## 6 PW 2400 0.77 5.189e+00 -573.90
## 7 PW 3600 0.78 5.402e+00 -592.50
## 8 PW 5400 0.80 5.640e+00 -604.90
## 9 PW 7200 0.82 5.825e+00 -610.30
## 10 PW 10800 0.83 6.103e+00 -635.30
## 11 PW 15000 0.85 6.338e+00 -645.60
## 12 PW 21600 0.87 6.602e+00 -658.90
## 13 PW 31200 0.89 6.869e+00 -671.80
## 14 PW 44400 0.92 7.123e+00 -674.30
## 15 PW 63600 0.93 7.380e+00 -693.60
## 16 PW 90600 0.95 7.631e+00 -703.20
## 17 PW 129600 0.96 7.883e+00 -721.10
## 20 OW4 600 0.04 2.162e-02 45.94
## 21 OW4 1200 0.04 4.856e-02 -21.41
## 22 OW4 1800 0.06 6.812e-02 -13.53
## 23 OW4 2400 0.06 8.315e-02 -38.59
## 24 OW4 3600 0.07 1.086e-01 -55.15
## 25 OW4 5400 0.09 1.453e-01 -61.41
## 26 OW4 7200 0.10 1.826e-01 -82.61
## 27 OW4 10800 0.11 2.579e-01 -134.50
## 28 OW4 15000 0.13 3.440e-01 -164.60
## 29 OW4 21600 0.15 4.703e-01 -213.50
## 30 OW4 31200 0.16 6.307e-01 -294.20
## 31 OW4 44400 0.18 8.115e-01 -350.90
## 32 OW4 63600 0.20 1.016e+00 -408.10
## 33 OW4 90600 0.21 1.232e+00 -486.60
## 34 OW4 129600 0.23 1.460e+00 -534.60
## 37 OW1 600 0.00 1.659e-05 NA
## 38 OW1 1200 0.00 4.502e-05 NA
## 39 OW1 1800 0.00 7.374e-05 NA
## 40 OW1 2400 0.01 1.039e-04 98.96
## 41 OW1 3600 0.01 1.747e-04 98.25
## 42 OW1 5400 0.01 3.169e-04 96.83
## 43 OW1 7200 0.02 5.106e-04 97.45
## 44 OW1 10800 0.03 1.081e-03 96.40
## 45 OW1 15000 0.03 2.114e-03 92.95
## 46 OW1 21600 0.04 4.682e-03 88.30
## 47 OW1 31200 0.05 1.075e-02 78.49
## 48 OW1 44400 0.06 2.373e-02 60.45
## 49 OW1 63600 0.07 5.076e-02 27.49
## 50 OW1 90600 0.08 9.924e-02 -24.05
## 51 OW1 129600 0.09 1.775e-01 -97.28For plotting the results we can either use the function
wtPlotResult() with the parameter
plottype = "w" to plot for each well measured (MEASDD) and
calculated (CALCDD) drawdowns in one plot:
## Warning: The function hsRenameColumns() is deprecated.
## Please use renameColumns() instead.
or produce a plot that contains measured and calculated drawdowns for
all wells in two separate plots by setting the parameter
plottype = "s":
Model calibration
For this tutorial calibration is realised by using an automatised one-dimensional optimisation approach for the following two model parameters, because these were identified to be the most sensitive ones:
The approach is valid because the calibration of the well-skin
parameter (during Step 2) has no impact on the observation well
drawdowns (Step 1). However, it needs to be stated that conditions could
occur, where a better model fit could be possible (especially if the
mid-term drawdown data are not fitting well) in case that both, vertical
hkz and horizontal hkr hydraulic aquifer
conductivity are varied in tandem.
Within this tutorial we solve this one-dimensional optimisation problem by using:
the build-in R function
optimise()andthe Root-Mean-Square-Error (RMSE) as the only performance criteria for evaluating the model fitness (i.e. comparision of calculated and measured drawdowns).
For solving this optimisation (or: calibration) problem we define the
R function calibrateModel() which requires the following
four input parameters:
configuration: a valid WTAQ input parameterisation (here:wtaqConfiguration)wellPattern: a regular expression or the well(s) names to be used for the model fit evaluation (here:OW4orPW)parameterName: name of the WTAQ parameter that should be calibrated (here:hkrorsw)parameterRange: allowed value range for calibration parameter (e.g.c(0.0001, 0.1)for parameterhkr)
Firstly this function - and its three dependent helper functions
modelFitness(), modelFitnessAggregated and
fitnessAdaptedModelConfiguration() - need to be loaded in R
by running the following code:
## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric# modelFitness(): called by function modelFitnessAggregated()
modelFitness <- function
(
wtaqResult,
wellPattern
)
{
subResult <- wtaqResult[grep(pattern = wellPattern, wtaqResult$WELL),]
fitness <- t(hydroGOF::gof(sim = subResult$MEASDD, obs = subResult$CALCDD, digits = 3))
colnames(fitness) <- sub(" %", "", colnames(fitness))
### data.frame with plenty of performance indicators: e.g. RMSE, NSE, R2
as.data.frame(fitness)
}
# modelFitnessAggregated: called by function fitnessAdaptedModelConfiguration()
modelFitnessAggregated <- function
(
wtaqResult,
wellPattern
)
{
fitness <- modelFitness(wtaqResult, wellPattern)
### Objective function for the performance criteria that is minimised, here:
fitness$RMSE
}
# fitnessAdaptedModelConfiguration: called by function calibrateModel()
fitnessAdaptedModelConfiguration <- function
(
parameterValue, parameterName, configuration, wellPattern
)
{
configuration <- wtSetParameter(configuration, parameterName, parameterValue)
wtaqResult <- wtRunConfiguration(configuration)
modelFitnessAggregated(wtaqResult, wellPattern)
}
#calibrateModel()
calibrateModel <- function (
### WTAQ parameterisation, e.g. as retrieved by wtConfigure()
configuration,
### regular expression or name of well(s) to be used for calibration: e.g. "OW4"
wellPattern,
### name of ONE WTAQ parameter to be calibrated: e.g. `hkr`, `sw`
parameterName,
### min/max range of possible calibration parameter values
parameterRange
)
{
optResults <- optimise(
f = fitnessAdaptedModelConfiguration,
interval = parameterRange,
parameterName = parameterName,
configuration = configuration,
wellPattern = wellPattern )
### Save calibrated WTAQ configuration:
wtaqConfigurationCalibrated <- wtSetParameter(
configuration = configuration,
parameterName = parameterName,
parameterValue = optResults$minimum)
### Save optimisation results in list
list(parameterName=parameterName,
wellPattern=wellPattern,
optimalParameterValue=optResults$minimum,
minimalPerformanceValue=optResults$objective,
wtaqConfig=wtaqConfigurationCalibrated
)
}Aquifer characteristics: horizontal hydraulic conductivity (Step 1)
# 1.Step: Calibrate aquifer characteristics 'hkr' for OW4-------------------------------
calibratedAquifer <- calibrateModel(
### reference wtaq configuration
configuration = wtaqConfiguration,
### calibrate hydraulic aquifer conductivity
parameterName = "hkr",
### 'hkr' is within 0.0001 - 0.1 m/s
parameterRange = c(0.0001, 0.1),
### only use drawdown time-series of OW4 for calibration
wellPattern = "OW4"
)## Warning in type.convert.default(block[, i]): 'as.is' should be specified by the
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## Warning in type.convert.default(block[, i]): 'as.is' should be specified by the
## caller; using TRUE### Plot the drawdowns with calibrated aquifer characteristics:
wtPlotResult(wtaqResult = wtRunConfiguration(
configuration = calibratedAquifer$wtaqConfig),
main = sprintf("Optimal value of parameter '%s' for %s: %0.4f m/s",
calibratedAquifer$parameterName,
calibratedAquifer$wellPattern,
calibratedAquifer$optimalParameterValue),
plottype = "w")## Warning in type.convert.default(block[, i]): 'as.is' should be specified by the
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## caller; using TRUE## Warning: The function hsRenameColumns() is deprecated.
## Please use renameColumns() instead.
After this step observed and measured drawdowns fit nearly perfectly for
the calibrated observation well “OW4” only by setting the
hkr to 0.0148366 (m/s) , but still the
drawdown in the production well “PW” is underestimated (because it is
still assumed that here are no “well losses”).
Thus the production well characteristics (i.e. the well-skin
parameter sw) need to be calibrated in a next step.
Well characteristics: well-bore skin parameter of production well (Step 2)
#2.Step: Calibrate well-bore skin parameter 'sw' for PW-------------------------------
calibratedAquiferAndWellSkin <- calibrateModel(
#### WTAQ configuration with calibrated aquifer (Step1)
configuration = calibratedAquifer$wtaqConfig,
### calibrate well-bore skin parameter
parameterName = "sw",
### 'sw' within 0 - 100 (dimensionless)
parameterRange = c(0, 100),
### only use drawdown time-series of PW for calibration
wellPattern = "PW"
)## Warning in type.convert.default(block[, i]): 'as.is' should be specified by the
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## caller; using TRUE### Plot the drawdowns with calibrated aquifer & well-bore skin characteristics:
wtPlotResult(wtaqResult = wtRunConfiguration(
configuration = calibratedAquiferAndWellSkin$wtaqConfig,
),
main = sprintf("Optimal value of parameter '%s' for %s: %2.4f (dimensionless)",
calibratedAquiferAndWellSkin$parameterName,
calibratedAquiferAndWellSkin$wellPattern,
calibratedAquiferAndWellSkin$optimalParameterValue),
plottype = "w")## Warning in type.convert.default(block[, i]): 'as.is' should be specified by the
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## caller; using TRUE## Warning: The function hsRenameColumns() is deprecated.
## Please use renameColumns() instead.
By calibrating the well-skin parameter sw to 2.0150393 the drawdown in the production well “PW” now also fits nearly perfectly the observed drawdown values, without impacting the fit for the observation wells.
Note: There might be cases where the calibration
results by following the methodology defined above is not satisfying.
This can be possibly solved by calibrating multiple parameters in
parallel (e.g. horizontal hkr and vertical hydraulic
aquifer conductivity hkz). For this a more complex
algorithm (e.g. build-in R function optim()), which is able
to solve multi-dimenional optimisation problems, might be usefull.
However, this goes beyond the scope of this tutorial.
Level 2: Multiple pumping wells
Note: For performing this example session it is required to perform all steps of the Level 1: one pumping well example session first, because this example session requires some data of the Level 1: one pumping well example
One challenge of using WTAQ for multiple wells is that the drawdown simulation for each model run is limited to:
one active production well and
up to 25 observation wells
This means that the model parameterisation for the pumping (e.g. pumping rate) and observation wells (e.g. distance to pumping well) needs to be adapted for each model run manually by using the Level 1 function (see: Level 1: one pumping well example).
For avoiding such time consuming task additional Level 2 functions were developed and included in the kwb.wtaq package that simplify using WTAQ on the well-field scale. The usage of these functions is described in the following:
Model parameterisation
Well field
In a first step the well field is defined, by creating a R object
owWellfieldConf that contains the following properties for
each well, i.e.:
Location
x,y,Well diameter
r,Depth of filter screen top
z1and bottomz2below initial groundwater levelWell-skin parameter
sw
For all production wells the well-skin parameter
sw is set to wellSkin, because this value
achieved the best-model fit during calibration
for W5
### Well-skin parameter from calibration of W5 for all wells of the well field
wellSkin <- calibratedAquiferAndWellSkin$optimalParameterValue
sprintf("Well-skin parameter value: %2.6f (dimensionless)", wellSkin)## [1] "Well-skin parameter value: 2.015039 (dimensionless)"# Example well field configuration with 5 wells
owWellfieldConf <- rbind(
owConfigureWell(
wellName = "W1", x = 807679.64, y = 2091015.29,
r = 1.5, z1 = 2, z2 = 4, sw = wellSkin),
owConfigureWell(
wellName = "W2", x = 807608.66, y = 2091018.51,
r = 1.7, z1 = 4.2, z2 = 7, sw = wellSkin),
owConfigureWell(
wellName = "W3", x = 807558.27, y = 2091090.30,
r = 1.5, z1 = 1.8, z2 = 8, sw = wellSkin),
owConfigureWell(
wellName = "W4", x = 807509.29, y = 2091161.80,
r = 1.5, z1 = 1.8, z2 = 7.5, sw = wellSkin),
owConfigureWell(
wellName = "W5", x = 807458.95, y = 2091232.26,
r = 1.5, z1 = 0.4, z2 = 7.8, sw = wellSkin))Note:
On the Level 2 function level it is now not
necessary to define well distances (this was required in the Level 1: one pumping well example.
The well distances will be set later automatically for each model run
based on both, the x y coordinates:
## Well distance matrix table:## W1 W2 W3 W4 W5
## W1 71.1 142.7 224.7 309.5
## W2 71.1 87.7 174.4 261.0
## W3 142.7 87.7 86.7 173.3
## W4 224.7 174.4 86.7 86.6
## W5 309.5 261.0 173.3 86.6and on the information which well is operating. For example column “W2” is used if the pumping Well is “W2”
Basic model parameterisation
In a next step we define we use the Level 2 function
owConfigure() to prepare the constant parts of the WTAQ
configuration parameterisation (wellfield,
aquifer and drainage) and store them in the
object owConf:
# Create constant components of WTAQ configuration
owConf <- owConfigure(wellfield = owWellfieldConf,
aquifer = calibratedAquiferAndWellSkin$wtaqConfig$aquifer,
drainage = wtConfigureDrainage(idra = 0)
)Note: For the parameter aquifer we
simply use the calibrated parameter setting, that we obtained after the
Level 1 model calibration, which is
stored in the R object:
## $aqtype
## [1] "WATER TABLE"
##
## $bb
## [1] 10
##
## $hkr
## [1] 0.01483664
##
## $hkz
## [1] 3.5e-05
##
## $ss
## [1] 1e-05
##
## $sy
## [1] 0.05The well field configuration can be plotted with the function
owPlotConfiguration() (top view & side view). By
setting the parameter referenceWell=1 the Well 1 is
selected as reference well for plotting:
Time-varying model parameteristion
The time-variant model parameterisation contains:
the pumping rates (
pumpingRates) of each well (here: defined inowWellfieldConf) andthe times for which the drawdowns should be calculated (
timesForDDcalculation)
These are defined in the following code:
Model run
Now we have all parts for parameterising WTAQ and calulating the drawdowns easily on the well field scale (i.e. running WTAQ multiple times in the background).
For this we use the function owGetDrawdowns() with the
following parameters:
ddlist <- owGetDrawdowns(
owConf=owConf,
Q = pumpingRates,
times = timesForDDcalculation,
### required for using the function wtPlotResults()
to.matrix=FALSE
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## caller; using TRUEddmatrix<- owGetDrawdowns(
owConf=owConf,
Q = pumpingRates,
times = timesForDDcalculation,
### saves results in "matrix" format: required for function owSuperposeDrawdowns()
to.matrix=TRUE
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## caller; using TRUEThe switch to.matrix=TRUE is required in case one would
like to calculate the total drawdown in each well including well
interference with the function owSuperposeDrawdowns():
Analysing results
Quantifying the impact of well interference
Finally the modelling results can be analysed. For example it is possible to quantify the additional drawdown due to well interference, e.g. for “W1”:
myWell <- "W1"
DD_inProductionWell_withInterference <- drawdownsWithWellInterference[,myWell]
DD_inProductionWell_withoutInterference <- ddmatrix[[myWell]][,myWell]
diffDrawdown <- DD_inProductionWell_withInterference-DD_inProductionWell_withoutInterference
data.frame(time.in.seconds=drawdownsWithWellInterference[,1],
additionalDrawdown.due.to.wellInterference.in.meter=diffDrawdown)## time.in.seconds additionalDrawdown.due.to.wellInterference.in.meter
## 1 1 0.000000000
## 2 5 0.000016160
## 3 10 0.000116362
## 4 30 0.001717690
## 5 60 0.007218800
## 6 600 0.101305000
## 7 1200 0.119617000
## 8 2400 0.140303000
## 9 3600 0.159315000
## 10 10000 0.242770000
## 11 50000 0.483100000
## 12 100000 0.607290000
## 13 300000 0.810100000Plotting of well drawdowns (without well interference):
for (wellName in owWellfieldConf$wellName)
{
index <- which(owWellfieldConf$wellName==wellName)
wellQ <- pumpingRates[index]
if (wellQ > 0)
{
wtPlotResult(wtaqResult = ddlist[[wellName]],
plottype = "s",
ylab = "Drawdown (m)",
xlab = "Time in seconds since start of pumping (s)",
main = sprintf("Pumping well: %s (Q: %3.1f m3/h)",
wellName,
wellQ*3600))
}
}
Plotting of well drawdowns (with well interference):
plotWellInterference <- function(wellName, Q=NULL)
{
if (is.null(Q)) {
label <- sprintf("%s ",wellName)
} else {
label <- sprintf("%s (%3.1f m3/h) ",wellName, Q*3600)
}
drawdown <- data.frame(SCENARIO="no well interference",
TIME=ddmatrix[[wellName]][,"TIME"],
CALCDD=ddmatrix[[wellName]][,wellName])
drawdownWithInterference <- data.frame("SCENARIO"="with well interference",
TIME=drawdownsWithWellInterference[,"TIME"],
CALCDD=drawdownsWithWellInterference[,wellName])
res <- rbind(drawdown, drawdownWithInterference)
print(lattice::xyplot(CALCDD ~ TIME,
groups = SCENARIO,
ylim=rev(extendrange(res$CALCDD)),
ylab = "Drawdown (m)",
xlab = "Time in seconds since start of pumping (s)",
type="b",
auto.key = list(columns=2),
data=res,
main = label))
}
for (wellName in owWellfieldConf$wellName)
{
index <- which(owWellfieldConf$wellName==wellName)
wellQ <- pumpingRates[index]
plotWellInterference(wellName = wellName, Q = wellQ)
}
