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This review paper will deal with the possibilities of applying the R programming language in water resources and hydrologic applications in education and research. The objective of this paper is to present some features and packages that make R a powerful environment for analysing data from the hydrology and water resources management fields, hydrological modelling, the post processing of the results of such modelling, and other task. R is maintained by statistical programmers with the support of an increasing community of users from many different backgrounds, including hydrologists, which allows access to both well established and experimental techniques in various areas.
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International Journal for Innovation Education and Research www.ijier.net Vol:-3 No-10, 2015
International Educative Research Foundation and Publisher © 2015 pg. 97
Using R in Water Resources Education
Milan Cisty, Lubomir Celar
Slovak University of Technology in Bratislava, Slovak Republic
milan.cisty@stuba.sk
Abstract
This review paper will deal with the possibilities of applying the R programming language in water resources
and hydrologic applications in education and research. The objective of this paper is to present some features
and packages that make R a powerful environment for analysing data from the hydrology and water resources
management fields, hydrological modelling, the post processing of the results of such modelling, and other
task. R is maintained by statistical programmers with the support of an increasing community of users from
many different backgrounds, including hydrologists, which allows access to both well established and
experimental techniques in various areas.
1. Introduction
This chapter reviews the possibilities of applying the R programming language in hydroinformatics, e.g., in
applications related to water resources and hydrology. R is an open-source software for statistical computing,
which means that R is freely available, so its users are free to see how it is written and improve or extend its
possibilities. The last characteristic is particularly important from the point of view of this review, because the
possibility of its extension is widely used by R users from many different backgrounds. Consequently, this leads
to one of the best things about R, which is the large amount of existing add-ins (so-called “packages”), which
are aimed at solving various tasks in different fields, including hydrology, water resources, climatology, soil
science and meteorology. These packages can be optionally loaded into the basic R environment, which permits
access to both well-established and experimental computational methods from different fields.
Although R was originally built for statistical tasks, its programming possibilities are not limited to them; it is
a full-featured object-oriented programming language and is suitable for a very broad class of tasks, including
various tasks from the domain of hydrology and related fields. As hydrology is a very data-intensive domain, it
is natural that R could be applied in various statistical or data-mining tasks related to hydrological and water
resources data. Hydrological data are often time series or have a spatial character; such data types also have a
reliable support in R. Furthermore, R is a high-level language in which one can implement new methods from
the area of physical modelling. R has various commands to operate on matrices and for computing integrals,
and it has tools for solving differential equations. Although such modelling is not a typical application of R,
based on these features, R is suitable even for building mathematical and hydrological models in which solving
differential equations is eventually included.
R is rooted in S, a statistical computing and data visualization language, which originated at Bell Laboratories
[1]. In 1993, Robert Gentleman and Ross Ihaka developed an implementation of S, which they called “R”. They
made it open source in 1995. The R language provides a rich environment for working with data, especially
data to be used for statistical modeling or graphics. R offers a wide variety of statistical and graphing techniques
(e.g., linear and nonlinear modeling, classical statistical tests, time-series analysis, classification, clustering,
etc.), and as has already been noted, is highly extensible (there are about 25 packages supplied with the basic R
distribution, and many more are optionally available through the CRAN family of Internet sites).
The R language includes [2]:
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an effective data handling and storage facility,
a suite of operators for calculations on arrays,
a large, coherent and integrated collection of functions and tools for data analysis and for general
programming tasks,
graphic capabilities for data analysis and display either on-screen or on hard copies, and
Simple and effective programming language features, which include conditional statements, loops,
possibilities for the definition of user-defined functions, input and output facilities, etc.
The starting point for getting information about R is the Comprehensive R Archive Network (CRAN) project,
where it is possible to download R and other related resources and obtain help. For instance, a sample
introductory session tutorial is available, along with various manuals edited by the R Development Core Team,
as well as contributed manuals, the R Journal and so-called task views, which are summarizations of R and
contributed R package possibilities for various specialized tasks, which are usually edited by an expert in that
field (e.g., for clustering, time series, machine learning, Bayesian inferences, probability distributions,
optimization, analyses of spatial data, etc.). Another basic information point is the R-project (www.r-
project.org) with links to, e.g., an R-wiki, FAQs, conferences, user groups and mailing groups (hydrology-
related questions could be sent to R-sig-ecology, which is a special interest group for ecology).
R has inbuilt help assistance. To get more information on any specific function, for example, optimise, the
command is:
> help(optimise) or ?optimise
Assistance is available in an HTML format by running:
> help.start()
Which will launch a Web browser that allows the help pages to be browsed with the assistance of hyperlinks.
The sos package [3] provides a means to quickly search the help pages of the contributed packages, which is
particularly important if the user is trying to discover if some tools in the R community exist for a particular
problem. Its findFn function, to which some alphabetic search string can serve as input, returns matches with
this string which were found in all the help pages; they can be sorted and subsetted by user specifications and
viewed in an HTML table. E.g., by typing the following command to the R console, we get 191 results:
> findFn("Regional Frequency Analysis")
“Rseek” is a specialized R search engine (www.rseek.org), and “quick-R” is a handy web page for basic
information about R language (www.statmethods.net/index.html). Many other similar resources exist.
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Figure 1. Two GUIs for R: R-Commander on the left and Rattle on the right side.
The R user interface is an interpreted programming environment with a command line interface (CLI). This
means that when one enter a statement or a group of statements to an R console and hits the Enter key, R
computes and eventually responds with a text or graphic output (in a separate window) as a reaction to this
action. Although this seems very simple and may be unsophisticated from some points of view, the CLI interface
is preferred by power users, because it allows for the direct control of calculations and is more flexible than
menu/icon-driven graphic user interfaces (GUIs). It has advantages from the point of view of reproducible
research, e.g., for verifying, controlling and consulting on the work accomplished, as well as running an analysis
with different data. However, a good knowledge of the language is required. A CLI can therefore be a
disincentive for beginners. The learning curve is typically longer than with a GUI application.
For this reason several projects have developed alternative user interfaces. Approximately 20 such projects
exist; the most well-known are R-commander, Rattle and RStudio. The R-Commander and Rattle GUIs consist
of a window containing several menus, tabs, buttons, and information fields (Figure 1). RStudio is very popular
in the R community; it integrates all of the tools one uses while working and programming in R into a single
environment (Figure 2). It can be run on a desktop (Windows, Mac, or Linux) or even over the web using
RStudio Server. RStudio includes a variety of powerful coding tools designed to enhance productivity (code
completion, searchable history, debugging tools, etc.); it enables quick navigation for inputing files, functions,
help pages, etc. It is the most popular compromise solution between the mouse-clicking GUI and the command
line programming environment in the R community.
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Figure 2. RStudio IDE: a powerful and productive user interface for R.
Most classical statistics and much of the latest methodology are available for use with R, and quite a lot of tools
are also available for hydrology and related subjects in R. Nonetheless, users may need to do a little work to
find them, so the authors of the present paper decided to offer this review, which collects information about
some water resources and hydrology-related methods and tools available in R.
2. Applications of R in Hydrology and Related Subjects
The following text contains a selection of possible applications of R in various hydrology and water resources
management tasks. For some tasks code snippets are provided, even though it is not possible to offer complete
tutorials for the tasks presented while keeping this work to a reasonable length. A brief introduction to R is quite
a good prerequisite for understanding the mentioned code snippets, or some intuition of “what could be what”
in the programming language (based on familiarity with some other programming language) could be useful.
Anyway, this is not necessary if the reader does not need to understand coding, but only seeks an overview of
the features available in R, which are useful in hydrology.
2.1. Data Pre-processing
Hydrological modelers spend a large amount of time on various data pre-processing and post-processing tasks.
R is logically a powerful environment for such tasks, because it is generally oriented towards management of
data and their statistical analysis. Because of the possibility of using basic R literature for this subject, we will
not go into much detail here, and only “water specific” tools in the R description follow.
The waterData package [4] allows users to import the U.S. Geological Survey (USGS) daily hydrological time
series data into R; it cleans, plots and summarizes the imported data and calculates and plots eventual
streamflow anomalies. Although the waterData package provides this functionality only for the USA, this
feature could be useful while testing some methodologies and when one needs some data for such testing. The
remaining features of this package are more generally aplicable. E.g., the fillMiss function from this package
estimates missing values in a time series of hydrological observations. The fillMiss function checks the
percentage of missing values and the size of the largest missing block of the data. If there are very large periods
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with missing values, the data may not be appropriate for analysis. If less than a user-specified percentage of the
data is missing and the largest block is less than a user-specified number of days, the data will be filled in by
using the structural time series model StructTS from the base stats package in R. The fitted structural time series
is then smoothed via a state-space model, tsSmooth, from the base package for statistics in R - stats.
With regard to missing data in general, many modelling functions in R offer options for dealing with missing
values, e.g., for some R functions data should not necessarily have to be complete. Besides this, good missing
data functionality can be accessed through various other (non-hydrological) R packages, e.g., Amelia II [5-8],
which offer general missing data functions that are also suitable for hydrological data sets.
Another interesting package, which contains functions to support the processing and exploration of data, is wq,
which was originally developed for monitoring aquatic ecosystems. The name of the wq [9] package stands for
“water quality” and reflects a focus on time series data describing the physical and chemical properties of water,
as well as plankton. However, many of the functions should be useful for a time series analysis regardless of
the subject matter. E.g., the function mannKen does a Mann-Kendall test of trends in a time series (it includes
a seasonal alteration of this function); the decompTs accomplishes multiplicative and additive decomposition
of time series), etc.
A very interesting R package is hydroTSM [10], which provides functions for the management, analysis,
interpolation and plotting of time series used in hydrology and related environmental sciences. Various
conversion functions are available for obtaining, e.g., monthly, annual or seasonal time series from daily data.
The smry function serves for summarizing data; the fdcu function computes and plots the flow duration curve
(FDC) for stream flows as well as for two uncertainty bounds, with the possibility of plotting an additional FDC
representing, e.g., simulated stream flows, in order to compare both curves. Automatic interpolation for a
hydrological time series with an optional plot could be accomplished by the hydrokrige function from this
package. According to the author's comment, it was originally developed as a way to more easily accomplish
the computation of average precipitation over subcatchments (given as an input in a shapefile map), based on
the values measured at several gauging stations, but it can also be used for interpolating any variable over a grid
given by a raster map [11]. Available algorithms for this task include the inverse distance weighting, ordinary
kriging, and kriging with an external drift. Some functions from this package are applied in an example given
in the following subchapter about statistical analysis.
Various tasks for data preparation in water resources include general tasks in statistics and data mining, for
which many functions are available in R, e.g., the functions for data transformation, data normalisation, the
imputation of missing data, data reductions (variable selections for a given task from an available dataset) or
outlier detection. We will not describe the availability of tools for these tasks in R here; those readers interested
in this important subject can easily find the extensive literature on these topics anywhere (e.g., in the R related
book series UseR! from Springer).
2.2. Statistical Analysis of Hydrological Data
One of the main tasks of hydrological practitioners and scientists is the gathering of information regarding the
presence and availability of water in all its forms on earth. For this reason the collection and evaluation of
hydrological data is particularly important, and various tasks regarding these arise: quality control, the
estimation of errors, correction techniques, and statistical and data mining analyses. These are the main use
areas of the R application, so the possibilities of R being applied for evaluating hydrologic data and for handling
various statistical analysis tasks are very broad. For example, R's available tools include functions for
descriptive statistics, including the very interesting graphing possibilities of R, tools for the evaluation of a
dataset's central tendencies (mean, median, mode, etc.), measurements of a spread such as the variance or
standard deviation, and tools for univariate frequency distributions, bivariate distributions or copulas. The same
is true for inferential statistics, testing hypotheses, trend analyses, multivariate statistics, etc.
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Because of the logical availability of such statistical possibilities in R, we decided to focus this part of the
chapter on only one selected topic or brief “illustration” from statistical hydrology: the extreme value theory.
In the example presented, daily flow data from the Bratislava flow-measuring station (on the Danube River) are
used from the period 1876 - 2006. The data were available in a txt format separated by a tabulator. If the reader
wishes to experiment with his own data and currently does not have enough knowledge of R, it is better to
prepare them in a similar way as the data file which was used in our example (Danube.txt):
ID Time Obs
1 1876-1-1 1768
2 1876-1-2 1765
3 1876-1-3 1722
etc.
Obs are observed flows in m3.s-1. The basic settings of the project, the data input from the text file, and some
numerical and graphic data summarizations are executed using the following code:
# setting of the working directory (for input and output data)
# and loading necessary R packages:
setwd("C:\\RStudio\\Danube")
library("Kendall")
library("hydroTSM")
# retrieving data from txt file:
Danube <- read.delim("Danube.txt", header=T)
# transformation of data to "zoo", e.g., time series object
Danube.zoo <- zoo(Danube$obs, as.Date(Danube$time))
# data summary:
smry(Danube.zoo)
hydroplot(Danube.zoo, var.type="Flow", main="at Bratislava",
pfreq = "ma")
hydroplot(Danube.zoo, pfreq="seasonal", FUN=mean)
fdc(daily2monthly(Danube.zoo, FUN=mean))
MannKendall(Danube.zoo)
The next two lines of the previous code after the smry function serve for the application of the hydroplot function
from the hydroTSM package for producing the graphs in Figure 3 and 4, which serve for a description of the
data. The fdc function from the same package produces a flow duration curve. After the application of the
MannKendall function in the last line of the code, the function’s output to the console was the following:
tau = 0.00256 and 2-sided p-value = 0.40179
which means that the null hypothesis concerning no trend cannot be rejected based on this data.
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Figure 3. Graphic description of the historical flows on the Danube in Bratislava by the hydroplot function.
Figure 4. Seasonal graph of the Danube's historical flows by the hydroplot function.
In the next code a trend analysis is presented as another example of the exploratory data analysis of the Danube
data, in which the hydroTSM package and basic R commands are applied. The hydroTSM package offers various
time scale transformation functions, e.g., the daily2monthly function, which is used to transform the daily data
to monthly data using some aggregation function (specified by the FUN parameter). Other similar
transformation functions are available too. The mean is used in the case of the following code, but if it is
desirable, it is possible to use, e.g., the max function for the extraction of a month's maximal values or sum for
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a summarization of the daily data (useful e.g., when working with precipitation data). After the application of
this function, a trend analysis of the monthly values by graphic means is executed by the code.
The scatter.smooth function in this example serves for plotting a scatter graph of the selected month’s average
flows versus the time (130 years) and adds a smooth curve computed by the Loess method to this plot. It is
applied twice (for August and for December), and it can be seen from Figure 5 that for August, around the
midpoint of the period analyzed, the trend line declines as opposed to December, where the trend is rising. The
parameter from (equal to 8 and 12) in the seq function, which is nested in the scatter.smooth function, stands
for the identification of the two months analyzed (August and December). The flow data values of these months
are selected from this starting value (index) by step 12 (parameter by) from all 1572 months of the available
period of the data (1876-2006).
Danube.month <- daily2monthly(Danube.zoo, FUN=mean)
# parameter for specification of more graphs in
# one plot one column with two rows:
par(mfrow=c(2,1))
scatter.smooth(x=c(1876 : 2006),
y=Danube.month[seq(from=8,
to = 1572, by=12)]
col="darkblue", xlab="year",
ylab="August average flow m3/s")
scatter.smooth(x=c(1876 : 2006),
y=Danube.month[seq(from=12,
to = 1572, by=12)],
col="darkblue", xlab="year",
ylab="December average flow m3/s")
Figure 5. Scatter plot with a smooth curve fitted by the Loess method for August and December (helpful for a
trend analysis)
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With the next code, an extreme value analysis is presented by utilizing the possibilities of R in this branch of
statistics. It is necessary to load two packages fitdistrplus [12], which contains several functions to help with
the fit of a parametric distribution. In addition to the maximum likelihood estimation method, the package
provides the moment matching, quantile matching and maximum goodness-of-fit estimation methods. In
addition, the evd package is used; it extends the simulation, distribution, quantile and density functions already
available in the basic distribution of R to various extreme value distributions.
library("fitdistrplus")
library("evd")
# Extraction of the maximal flows for all years
Danube.max <- daily2annual(Danube.zoo, FUN=max)
# Fitting of the generalized extreme value distribution (starting
# values of the location and scale parameters are set
# on the basis of trial and error.
# Actuall values of these parameters were searched for
# with following function by estimating the maximum likelihood):
fgev <- fitdist(as.vector(Danube.max), "gev",
start = list(loc = 5000, scale = 2000))
# Computation of 100-year and 1000-year flows in Bratislava by the
# quantile function of generalized extreme value distribution:
qgev(c(0.99,0.999), fgev$estimate[1],fgev$estimate[2])
# Plotting of the fitted distribution:
plot(fgu, col="turquoise")
The results of the qgev functions for the Danube data were Q100=10 824 m3.s-1 and Q1000=13 784 m3.s-1. The
graph plotted by the last command with a visual evaluation of the fitting procedure is in Figure 6.
Other possibilities are also available in R for extreme value analysis. Sometimes, using only a maximum block
value as in the previous example (e.g., maximal flow in year) can be wasteful as it ignores much of the data
[13]. It is often more useful to look at exceedances over a given threshold instead of simply taking the maximal
annual values (which was done when computing the variable Danube.max). The POT package [14] offers tools
to perform statistical analyses called the “peaks over the threshold” method in univariate and bivariate cases. It
includes some preprocessing tools for data preparation, e.g., flow (data) selection from the base data to the input
data file for the POT analysis, which preserves the independence of the data; numerical and graphic tools for
the choice of a threshold; the definition of the generalized pareto distribution; etc. Although POT includes some
graphic tools for the selection of a threshold, this task is a difficult topic and still an area of active research. So
we did not experiment with this method in this review as a paper more focused on this subject would be more
appropriate.
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Figure 6. Plot of an object with a fitted generalized extreme distribution for the Danube data.
2.3. Hydrological Modeling and the Evaluating Model
Hydrological models are simplified representations of a hydrological cycle and play an important role in many
areas of hydrology, such as flood warnings and management, agriculture studies, dam design, climate change
impact studies, etc. Hydrological modeling can be supported quite well by R.
There are several steps in hydrological modeling: preprocessing the data, sensitivity analysis (identification of
the responsiveness of the model parameters); calibration, e.g., tuning the model parameters by checking the
results of the modeling against observations by utilizing graphs and various goodness-of-fit statistics, the
modeling itself by various types of models (data driven, conceptual, physically based), the validation of the
model, and evaluating the results and their visualization.
A sensitivity analysis of the models could be supported by the sensitivity and fast packages. The sensitivity R
package [15] contains a collection of functions for a global sensitivity analysis of a model's output. fast is an
implementation of the Fourier Amplitude Sensitivity Test, which is a method used to determine the global
sensitivities of a model’s parameter changes with relatively few runs of the model (which is useful in the case
of, e.g., physically-based models). The R package FME is a modeling package designed to confront a
mathematical model with data. It includes algorithms for sensitivity and Monte Carlo analysis, parameter
identifiability and model fitting; it also provides a Markov-chain based method to estimate parameter confidence
intervals.
Regarding the modeling itself, great support is available for data-driven models; some tools are available for
conceptual models as well as for physically-based hydrological models. Physically-based models solve exact
physical equations (differential equations), usually on the basis of spatially distributed inputs. Although it is
better to accomplish such a type of modeling, which is usually computationally demanding in compiled
languages, there is also some support for this type of modeling in R. The wasim package [16] provides tools for
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processing the data and the visualization of the results of the WASIM-ETH hydrological model. The grid-based
Water Flow and Balance Simulation Model (WASIM) is a deterministic, spatially distributed hydrological
catchment model to simulate the water cycle above and below the land surface.
The R package R-SWAT-FME [17] is a comprehensive modeling framework that adopts an R package Flexible
Modeling Environment [18], and Soil and Water Assessment Tool model [19]. This framework provides the
functionalities of parameter identifiability, model calibration, sensitivity and uncertainty analysis with instant
visualization. The Soil and Water Assessment Tool (SWAT) is a semi-distributed hydrological model jointly
developed by the USDA Agricultural Research Service and the Texas A&M AgriLife Research. SWAT is a
small watershed-to-river basin-scale model to simulate the quality and quantity of surface and ground water and
predict the environmental impact of land use, land management practices, and climate change. In SWAT, a
watershed is divided into multiple subwatersheds, which are then further subdivided into hydrological response
units that consist of homogeneous land use, management, and soil characteristics. SWAT is widely used in
assessing soil erosion prevention and control, non-point source pollution control, and regional management in
watersheds.
Many optimization functions in R allow for the interfacing of any computer simulation model with them in the
calibration process. E.g., function optim from the basic stats package provides an implementation of the
Broyden-Fletcher-Goldfarb-Shanno (BFGS) method, bounded BFGS, conjugate gradient, Nelder-Mead, and
simulated annealing (SANN) optimization methods. The genalg package contains rbga, an implementation of
a genetic algorithm; the DEoptim package provides a global optimizer based on a differential evolution
algorithm; the cmaes package implements a global optimization procedure using a covariance matrix--adapting
evolutionary strategy (CMA-ES). As can be seen from its name, the hydroPSO package [11] is more specific
and is mostly intended for the calibration of environmental and hydrological models. It communicates with a
model through the model's own input and output files, without requiring any access to the model's source code.
Advanced sensitivity analysis functions, which use Latin hypercube sampling and several functions for the post-
processing of the calibration results together with user-friendly plotting summaries that simplify the
interpretation and assessment of the calibration results, are available in this package too. hydroPSO is parallel-
capable in order to facilitate the computational burden of complex models with “long” execution times, which
is typically the case when calibrating spatially - distributed hydrological models. R generally contains more of
such tools for parallel and cloud computing (e.g., the snow package). The mentioned hydroPSO package
includes a vignette (tutorial) that shows how to calibrate the SWAT-2005 and MODFLOW-2005 hydrologic
models in the context of real-world case studies.
Data - driven models analyse and derive results only from the observed input (e.g., in the case of rainfall-runoff
modeling, from temperatures, evapotranspiration or rainfall) and output of a modeled system (e.g., a flow in the
case of modeling watershed processes); they do not use exact physical laws at all. Data-driven modeling
techniques [20-22] may help us understand the value and limitations of what the data can offer. In addition,
such models are powerful mergers of information, which are able to handle any kind of data derived from
different sources and expressed in different ways [23]. R, as a language for statistics, is particularly competitive
in this modeling area in comparison with other software environments. For this reason we will not review in
this chapter potential full extent of this subject (there is too much functionality which R can offer in this area
for one chapter); only the two following suggestions are given.
The caret package [24] contains several tools for developing predictive data-driven models (which could be
applied for regression, time series predictions or classification tasks) using the rich set of models available in
R. The package focuses on simplifying the training and tuning of the model across a wide variety of modeling
techniques (e.g., Neural nets, Random Forest, Gradient Boosting, Machines, SVM, etc.). Using the package, a
practitioner can quickly evaluate many different types of models to find the most appropriate tool for his task.
Package also includes methods for pre-processing data, calculating the importance of variables, and visualizing
models [25]. The second recommendation in the area of supporting the data--driven modeling in R given by the
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authors of this chapter is the rattle package [26], which after loading and starting in the R environment, offers
a clickable GUI, which is specifically designed for data-mining tasks and data-driven modeling (Figure 1).
So-called “conceptual” models describe the main features of an idealized hydrological cycle. The hydromad
package [27] provides a modeling framework, which supports such a model design (a conceptual model could
be composed from the predefined functions of this package), and also offers functions for the simulation,
estimation and visualization of the results modeled. The modeling framework in the hydromad package
(available at hydromad.catchment.org ) is based on a two-component structure: (1) a soil moisture accounting
module (with various options); and (2) a routing or unit hydrograph module (also with more options). The soil
moisture accounting module converts a rainfall and temperature or evapotranspiration into an effective rainfall,
and the routing module converts the effective rainfall into a stream flow. A snow routine is available too.
Various statistics used in the hydrological modeling evaluation framework and optimization functions are
available to fit a hydromad model, e.g., a shuffled complex evolution algorithm, differential evolution
algorithm, covariance matrix adaptation evolution strategy or differential evolution adaptive metropolis
algorithm. The last named is a Markov Chain Monte Carlo (MCMC) algorithm, which gives estimates of the
joint probability distribution of parameters according to a likelihood function. The fitting function returns the
maximum likelihood model, but the full MCMC results are also available. Various other tools are available in
the hydromad package, e.g., tools for the identification and separation of discrete events (both precipitation and
flow events) from time series and the application of various graphing and computational functions to them. A
graphic user interface for defining discrete events in a time series is also available for this purpose. The
estimateDelay function uses cross-correlation to estimate the delay between an input time series and (rises in)
the corresponding output time series.
Another conceptual hydrological model is available in the TUWmodel package. The TUWmodel [28] is a lumped
conceptual rainfall-runoff model, which follows the structure of the well-known HBV model. The model runs
on a daily time step and consists of a snow routine, a soil moisture routine, and a flow routing routine. An
example of the model`s calibration, modeling, and evaluation of the results follows.
The variable modeled by the TUWmodel was the flow of the Laborec River at the Humenne station (Slovak
Republic). As the input data, a time series of precipitation, temperatures, potential evapotranspiration and flows
from the period 1981-2005 were used. In the present chapter the authors will not deal with the data preparation,
although several functions are available in R for this important task. If, e.g., precipitation data are available for
more stations in a watershed, it is possible to use Thiessen polygons to get areas with the precipitation associated
with each station (and then it is possible to compute the weighted average of the precipitation). The dirichlet
function from the statstat package and other packages and functions are available for this task. The idw function
from the spatstat package performs a spatial smoothing of the numerical values observed at a set of irregular
locations using inverse-distance weighting and could also be used for averaging of the precipitation and similar
tasks. The values of the potential evapotranspiration, which are necessary for running the TUWmodel, can be
obtained by the application of various functions from the sirad, SPEI, EcoHydRology or r2dRue packages. In
the case of climate change impact studies, a weather generator could be useful for preparing the data in the
modeling. The RMAWGEN package [29] contains functions for the spatial multi-site stochastic generation of
daily time series of temperatures and precipitation.
In the following example of the application of the TUWmodel, such data preparation tasks are skipped, and it is
assumed that the input data are already available in the following format (text file). In the case of using own
data, it must be prepared similarly:
DATE Q Z T PET
1981-3-2 11.27 0.790 -1.064 0.238
1981-3-3 10.86 8.701 -0.151 0.91
1981-3-4 10.30 0.261 2.046 0.834
...
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The dataset was divided into the calibration (1981-1995) and validation periods (1996-2005), and then it was
read to the R environment by the following statements:
LABORECcal <- read.delim("E:/RStudio/Laborec/LABORECcal.txt")
LABORECval <- read.delim("E:/RStudio/Laborec/LABORECval.txt")
The modeling itself is accomplished by the TUWmodel function. The details about this function can be obtained
by a ?TUWmodel statement written to the R console. These details are mainly information about the parameters
which should be specified in this function. These are input data (precipitation, temperatures, evapotranspiration,
and the watershed area) and the model parameters, which are necessary to determine for this task. There are 15
such parameters in the TUWmodel, which are described in the mentioned help page together with the intervals
in which the parameter`s values lie. In the following code, a differential evolution - one of the many optimization
functions available in R - is applied to this calibration task, e.g., to searching for the exact values of these 15
parameters within these intervals.
# definition of the objective function, necessary for optimization
# task:
fitness<-function(x){
# running TUWmodel with parameters defined by actual chromosome x,
# which is generated by differential evolution function DEoptim:
simLAB=TUWmodel(prec=as.vector(LABORECcal$Z),
airt=as.vector(LABORECcal$T),
ep=as.vector(LABORECcal$PET),
area=1281, param= as.vector(x))
# extraction of the simulated flows from the simLAB object:
sim<-as.vector(t(simLAB$q))
# computation of the Nash/Sutcliffe coefficient of efficiency
# by the function from the hydroGOF package:
nash<-NSE(sim, as.vector(LABORECcal$Q))
# value of the objective function:
objF=1-nash #difference from 1 (ideal model) should be minimized
return(objF)
}
# code for running differential evolution, the lower and upper
# are border values for the searched TUWparameters:
DEOP<-DEoptim(fitness,
lower=c(0.9,0,1,-3,-2,0,0,0,0,2,30,1,0,0,0),
upper = c(1.5,5,3,1,2,1,600,20,2,30,
250,100,8,30,50),
control = list (itermax=200, NP=200, trace=5))
# modeling of the flows in validation period with optimal
# parameters, which were found by a differential evolution:
simLAB=TUWmodel(prec=as.vector(LABORECval$Z),
airt=as.vector(LABORECval$T),
ep=as.vector(LABORECval$PET),
area=1281,param=DEOP$optim$bestmem)
# evaluation of the results by the ggof function from the hydroGOF
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# package (the result is displayed in Figure 7)
ggof(as.vector(t(simLAB$q)), as.vector(LABORECval$Q),
dates=as.Date(c(as.Date("1996-01-1"):
as.Date("2005-12-31"))),
ftype="dm", FUN=mean)
Figure 7. Examination of the modeling results from the output of the ggof function.
In Figure 7 the results from the application of the calibrated model to the validation data are evaluated. The
graph and associated statistics are produced by the ggof function from the hydroGOF package [30]. There are
various options as to how the resulting graphic evaluation will look when this function is applied in the case
in Figure 7; the daily and monthly evaluations were accomplished by setting the ftype="dm" option. The
hydrological goodness-of-fit statistics are printed for both of these time scales on the right side of the associated
graph (the meaning of the abbreviations is on the help page of this function). It is also possible to obtain these
values in a text form with the gof function. As can be seen, quite a bit better statistical values are obtained when
the same computation is evaluated in a monthly time step, e.g., it might be interesting to compare whether it is
not better in the case of modeling monthly flows to use daily inputs and not monthly averages. For more
information about this function, it is necessary to write the statement? gof on the R console and press Enter.
2.4. Spatial Data Manipulation
R's ability to analyze and visualize data makes it a good choice for spatial data analysis. For some spatial
analysis projects, using only R may be sufficient. In many cases, however, R can be used in conjunction with
GIS software. It is better not to try to substitute GIS with R if it is necessary to do specialized GIS tasks, e.g.,
an interactive display or the editing of spatial data. The core R engine was not designed specifically for the
display and analysis of maps, and the limited interactive facilities it offers have drawbacks in this area [31].
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Various R packages for spatial data exist. They mainly address two areas: moving spatial data into and out of
R, and analyzing spatial data in R. There are a number of packages for spatial analysis; what follows is only the
tip of the iceberg.
The basic package for the definition of the various types of spatial object structures (e.g., points, lines, polygons
or grids) in R is sp [31]. Several utility functions are provided in sp, e.g., for conversion between data formats,
plotting maps, spatial selection and overlays, as well as methods for retrieving coordinates, or for subsetting,
printing, summarizing data, etc.
Various packages serve for accessing vector data, e.g., RArcInfo [32] allows ArcInfo v.7 binary files and *.e00
files to be read; also the maptools [33] and shapefiles [34] packages read and write ArcView shapefiles and
various other formats. The maptools package includes a number of useful functions for reading, writing,
converting, and otherwise handling spatial objects in R. Unlike their rgdal counterparts, the maptools functions
neither read nor write projection information, leaving it up to the user to manage these details manually. The
maptools package includes support for the creation of KML files: the file format is used to display geographic
data in an Earth browser such as Google Earth, Google Maps, and Google Maps for mobile. The mentioned
rgdal package [35] provides functions to read and write a lot of grid and vector formats, and it provides access
to projection and transformation operations. The rgdal package provides an interface to the GDAL/OGR library,
which powers the data import and export capabilities of many geospatially aware software applications. The
package includes the readOGR and writeOGR functions for reading and writing not only shapefiles, but also
numerous other vector-based file formats. In addition, the ogrInfo function is useful for retrieving details about
a file without reading in the full dataset. These functions are all capable of automatically reading and writing
projection information if available.
The following code is a basic demonstration of the reading and visualization of a grid and vector data by the
maptools and sp packages. Again, running it with own data is easy, only 2 shapefiles and one ascii grid file is
necessary.
setwd("E:\\RStudio\\Bela") # set working directory
library(maptools) # load package for reading GIS data
library(lattice) # graphing package
# read the DEM and the vectors in shape files by maptools package
# functions to objects):
bela_DEM <- readAsciiGrid("elevation.asc")
bela_rivers <- readShapeLines("rivers")
bela_border <- readShapeLines("watershed")
# defining the vectors and their basic properties for plotting
# (color and width of lines):
rivers <- list("sp.lines",bela_rivers, col="blue", lwd=0.5)
border <- list("sp.lines",bela_border, col="black", lwd=1)
# defining various other objects and texts to draw:
scale <- list("SpatialPolygonsRescale",
layout.scale.bar(height=0.05),
offset = c(-357500,-1194000),
scale = 5000, fill=c("transparent","black"))
text1 <- list("sp.text", c(-357500,-1195000), "0")
text2 <- list("sp.text", c(-351700,-1195000), "5 km")
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text3 <- list("sp.text", c(-368000,-1178000),
"Bela river watershed",
cex=1.5)
arrow <- list("SpatialPolygonsRescale",
layout.north.arrow(type=1),
offset = c(-355500,-1193000), scale = 2000)
# set some nice topographic colors
colors <- terrain.colors(1000)
trellis.par.set(sp.theme(regions=list(col = colors)))
#final plot plotted by sp package function spplot: (Figure 8)
spplot(bela_DEM,draw = T, colorkey=list(space="right",
height=0.5),
cuts=500,scales=list(draw=T),
sp.layout=list(scale,text1,text2,text3,
arrow,rivers,border))
Figure 8. Simple display of GIS data by spplot function.
The raster package [36] provides access to data in raster formats and includes analytical tools for this type of
spatial data. Raster data divides space into cells of equal size. Such continuous spatial data are also referred to
as “grid” data, and can be contrasted with vector-based spatial data (points, lines, polygons). The raster package
provides, among other things, the creation of raster objects from scratch or from a file, the handling of extremely
large raster files, raster algebra and overlay functions, distance functions, polygons, lines and points to raster
conversion, summarizing raster values, easy access to raster cell values, plotting, reading and writing various
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raster file types. The rasterVis package complements [37] the raster package, which provides a set of methods
for enhanced visualization and interaction.
Vector data manipulation, e.g., topology operations on geometries, are accessible with the help of the functions
from the rgeos package [38]. It contains many functions for handling, combining, and querying points, lines,
and polygon types of spatial data. The package's functionality is based on the GEOS library, which is a C++
port of the Java Topology Suite (JTS). The available functions fall into three main classes: miscellaneous
functions such as gArea (which calculates the area of a given geometry), topological queries (e.g., gContains -
a function for testing whether one geometry is contained within another geometry), and topological operations
(e.g., gIntersection - a function for determining the intersection between two given geometries). Some
operations are unary, taking one vector object, while others are binary, taking two objects. There is more than
one hundred of such functions available in the rgeos package.
The gstat package [39] offers a wide range of univariable and multivariable geostatistical modeling
methodologies, prediction and simulation functions, variogram modeling, variogram map plotting, everything
from simple global kriging to local universal cokriging, multivariate geostatistics, block kriging, etc. The geoR
package [40] includes functions and methods for reading and preparing the data, exploratory analysis, inferences
of model parameters, including variogram-based and likelihood-based methods, and spatial interpolation.
Furthermore, it implements simple, ordinary, universal and external trend kriging. The package also implements
Bayesian methods, which take the parameter uncertainties into account when making predictions at specified
locations.
The mapplots package [41] serves for visualization purposes; its main purpose is to add sub-plots to a map. The
basemap function from this package creates a blank map. Other GIS layers can be added with a function for
drawing shape files. For univariate data, functions for bubble plots and heat maps are available; multivariate
data can be displayed with square pie plots, pie plots or barplots.
The RPyGeo package [42] provides access to (virtually any) ArcGIS geoprocessing tool from within R by
running Python scripts without writing Python code or the direct usage of ArcGIS GUI. At least the ArcGIS
version 9.2 and a suitable version of Python are required. The spgrass6 [43] package offers an interface between
the GRASS 6+ geographical information system and R. The interface between GRASS 6 and R has been used
in research in a number of fields, for example, by Haywood and Stone [44], which is interesting in that it uses
the interface to apply the Weka machine learning software suite, which itself is interfaced to R through the
RWeka package [45]. R then becomes a useful bridge between various tools that open up other possibilities
beyond R. RSAGA provides access to the geocomputing and terrain analysis functions of SAGA from within
R by running the command line version of SAGA (www.sourceforge.net/projects/saga-gis/files/).
Web-based services are becoming ever more important channels for exchanging spatial data. The RgoogleMaps
[46] package provides tools to access Google Maps data in an image form using the Google Static Maps API,
in order to permit background maps to be used in R. The ggmap package allows for the easy visualization of
spatial data on top of Google Maps, OpenStreetMaps, Stamen Maps, or CloudMade Maps using ggplot2.
ggplot2 [47] is one of the most popular packages in R intended as an alternative for data visualization; it is
based on Leland Wilkinson's grammar of graphics. It provides a scheme for data visualization, which breaks up
the creation of graph into a layers. In ggmap usage, a basic layer, e.g., from Google Maps, is firstly downloaded,
and then its object is created in R. Then other layers with lines, points, polygons, texts and other features from
various sources are added to it according to its rules of syntax. Vector data from OpenStreetMap is also available
for downloading by using the recently contributed osmar package [48].
2.4. Soil Hydrology
The soilwater package [49] provides soil water retention functions, soil hydraulic conductivity functions, and
pedotransfer functions. The water retention curve is one of the main hydraulic soil properties, which is used in
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simulating the water regime of soils. It represents the relationship between the water content and the soil water
potential (the potential energy of water per unit volume, which quantifies the tendency of water to move from
one place to another). This curve is distinctive for different types of soil. It is used to predict soils water storage,
the water supply to plants, and other tasks in soil water modelling. Pedotransfer functions are used for
determining the water retention curve from more easily available soil properties such as particle size
distribution, dry bulk density, organic C content, etc.
The soilwaterfun package [50] is a collection of widely used soil water retention functions by various authors
[51] and soil hydraulic conductivity functions (Mualem-van Genuchten, Brooks & Corey, Campbell). The
soilwaterptf package [52], is a collection of so-called “pedotransfer functions” (PTFs) for estimating the
parameters of soil water retention and hydraulic conductivity functions from easily available soil properties
(typically the texture, organic carbon content and bulk density). The package provides functions that implement
pedotransfer functions for predicting the parameters of the Mualem and the van Genuchten water retention
functions and hydraulic conductivity functions. These functions are used to predict soil hydraulic properties
when no measurements are available.
Other projects exist that provide useful soil-related R functions, e.g:
The soiltexture package [53], which provides functions for soil texture data in R. The available functions
can (1) plot soil texture data (2) classify soil texture data, (3) transform soil texture data from and to
different systems of particle size classification systems, and (4) provide some tools to 'explore' soil
texture data (in the sense of a statistical visual analysis).
HydroMe [54] - estimation of soil hydraulic parameters from experimental data. The HydroMe package
estimates the parameters in infiltration and water retention models by the curve-fitting method. The
models considered are those that are commonly used in soil science.
The ZeBook package [55] is an R package accompanying the book “Working with Dynamic Models for
Agriculture and the Environment” [56]. It contain the well-known Watbal water balance model, which
calculate soil water over a designated time period and various dynamic models of crop growth.
3. Conclusions
In this chapter a selection of possibilities offered by the R development core team, as well as by the work of
various contributors in the areas of hydrology and water resources management, was described. Because of the
limited space, this chapter was not intended as a detailed description with tutorials; instead, it is an overview of
the possibilities available in this software environment, which could serve as an inspiration for readers if they are
considering using R in their hydrological analyses. Some hydrologic topics are presented only briefly, and some
subjects were not described at all, although the tools for them exist in R (e.g., weather and climate--related
subjects, time series, regional hydrology, etc.). As can be seen, there are a useful collection of options, even on a
level where the user is actually not programming something. It is necessary to know the basic syntax of the
language, but what was basically presented in the chapter were ready-made functions. The only obstacle for less-
experienced users could be that these functions are not managed by a clickable GUI, but through a command line
interface. Moreover, in the case of also exploiting all the programming possibilities of R, the effect of using R
for water practitioners or scientists will be even more useful.
Although having a tool is not enough for serious work which involves other subject-related theoretical and
practical knowledge and skills, a tool such as R is very useful, e.g., in the process of learning some difficult
subject related to an analysis of hydrological data (e.g., copulas, to mention one). In R one has the possibility of
easily trying corresponding computations, which are otherwise only described by complicated theories. Of
course, it is necessary to know the background of the computations, but it is very helpful in the process of learning
some intimidating and complicated subject, if one knows that he can do the very thing which he is trying to
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understand. This is supported by a unified system as to how the so-called S3 and S4 functions of R are written.
For the R user it means that there is not a big difference in exploiting R's possibilities if he is interested in the
capabilities of GIS or the mentioned copula computations. R is also an interesting social phenomenon with
enthusiastic features in its user community; often someone makes such complicated tasks easier by offering
appropriate tools, e.g., GUIs, which help to do basic tasks in such areas easily and intuitively (e.g., from the items
described hereinbefore, the extremes package for an extreme value analysis is a good example of this point, which
is a de facto wizard that uses computational engines from other packages). Many R functions are wrap programs,
which are written in FORTRAN, Java, C++, etc., which often makes it easier to use these programs. Moreover,
an advantage is obtained when the opportunity arises to use them in a stream with the other software packages
available in R. This could produce an interesting synergistic effect, at least in terms of productivity.
Because the packages contributed are the result of voluntary efforts, there is no guarantee which methods based
on such a genesis exist in R. As has already been mentioned, users may need to be prepared to do a little work
to find what they need, e.g., to be prepared sometimes for a little digging. Besides the disadvantages associated
with it (e.g., we will not find something, because no one has done this very thing, or because somebody stopped
caring about it), due to the enthusiastic elements in the R community, some existential pleasure, which is
associated with treasure hunting, as a result of such digging, is often attained as a reward.
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... Furthermore, some introductory statistics textbooks also focus on R [9], [10], [11]. Applications of R include experimental design [12], analyzing means [13], dose-response analysis [14], big data [15], and water resources [16], among many more. The function plotDist plots probability density functions (pdfs) and cumulative distribution functions (cdfs), and is described in Section 2. The function shadeDist shades area under the curve of a probability density function, while computing the corresponding probability, and is described in Section 3. Additional useful classroom-type examples based on plotDist and shadeDist are given in Section 4. The function shadePhat, which illustrates probabilities based on a sample proportion, p, and the function plotLine, which fits a simple linear regression line to a scatterplot and computes the equation of the fitted line, are described in Section 5. A brief discussion is given in Section 6. ...
... For example, Figure 6a also can be produced using the command > shadeDist( 0.2, "dprop", 10, 0.4 ) # Figure 6a for vectors x and y. An example using data (x, y) = { (2,12), (3,16), (6,14), (9,17)} based on the command > plotLine( c( 2, 3, 6, 9 ), c( 12, 16, 14, 17 ) ) # Figure 7 is shown in Figure 7. Suppose the data are in a data frame, such as the following: > x = c ( 2,3,6,9 ) ; y = c ( 12,16,14,17 ) ; d = data.frame( x=x, y=y ) ...
... For example, Figure 6a also can be produced using the command > shadeDist( 0.2, "dprop", 10, 0.4 ) # Figure 6a for vectors x and y. An example using data (x, y) = { (2,12), (3,16), (6,14), (9,17)} based on the command > plotLine( c( 2, 3, 6, 9 ), c( 12, 16, 14, 17 ) ) # Figure 7 is shown in Figure 7. Suppose the data are in a data frame, such as the following: > x = c ( 2,3,6,9 ) ; y = c ( 12,16,14,17 ) ; d = data.frame( x=x, y=y ) ...
... used environment for statistical analysis. As the open-source software, R based on the S programming language is developed by Chambers et al. at Bell Labratories in 1960 and enables running of wide-variety of computations with the help of numerous packages(Cisty and Celar, 2015). ...
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Impacts of climate change on hydrology is inevitable due to the direct and indirect linkages. Therefore, considering the significance of the hydrology of the Kura River and its tributaries for the basin countries and increasing intensity of the climate change, the research aimed at assessing the climate change impacts on the hydrology of the basin. To achieve this research aim, statistical methods were utilized to identify the trends and change points in hydroclimatic variables and to detect the correlation between hydrological and climatic indices. Based on the results of the trend analysis, certain patterns both in terms of streamflow and climatic indices were captured. While in Georgia streamflow of the Kura River experienced an increasing trend, especially during cold months, a serious decrease was detected in Azerbaijan for most months. Furthermore, the analysis of climatic indices also signals certain patterns aligning with climate change characteristics such as an increase in precipitation in cold months as well as an increase in temperature generally. Correlation analysis further carried out also highlighted the impacts of these changes since due to the early snowmelts caused by the increasing temperature and precipitation, the Kura River experienced an increase in streamflow for the cold months, while for the dry months certain decrease is the case due to the increase in temperature of the region. To conclude, the results explain that impact of climate change on the hydrology of the study area is already observed and by time, it is more likely to be intensified due to the increasing temperature and changes in rainfall.
... The freely available hydroTSM [65] package in R was applied to extract and visualise the extreme data values (maximum, minimum, and mean monthly discharges) from river daily discharges. This package has robust capability functions in the management, analysis, and visualisation of the time series of hydrological flows [66]. Flood flow extreme value analysis was done by fitting a parametric distribution to the extremal data using fitdistrplus [67], which is also a free package. ...
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... The method of analysis was RStudio (2014 version) which is an integrated development environment (IDE) for the R programming language. The hydroTSM [21] package in Rstudio was used for analysis of river discharges and rainfall because of its capability functions in the management, analysis, and interpolation and plotting of time series (monthly, annual and seasonal) from daily and monthly data [22]. Mann-Kendall test [20] is a non-parametric test for randomness against time for correlation and has, in the last half decade, become useful in water resources research for examining significance in trends within river basins [6,[23][24][25]. ...
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This study investigated temporal variabilities and trends of rainfall and discharges in Tana River Basin in Kenya using Mann-Kendall non-parametric test. Monthly rainfall data from ten stations spanning from 1967 to 2016 and daily streamflow data time series of observations from 1941 to 2016 (75 years) were analyzed with the aim of capturing and detecting multiannual and seasonal variabilities and monotonic trends. The results for the datasets suggested that the streamflow is largely dependent on increasing rainfall at the highlands. The rainfall trends seemed to have been influenced by altitudinal factors. The coefficient of variation of the ten rainfall stations ranged from 12% to 17% but 70% of rainfall stations showed negative monotonic trends and 30% show significant trends. The streamflow showed statistically significant upward monotonic trend and seasonal variability indicating a substantial change in the streamflow regime. Although the increasing trend of the streamflow during this period may not pose future risks and vulnerability of energy and irrigated agricultural production systems across the basin, variability observed indicates the need for enhanced alternative water management strategies during the low flow seasons. The trends and time series data indicate the potential evidence of climate and land use change and their impacts on the availability of water and sustainability of ecology and energy and agricultural production systems across the basin. Variability and trends of rainfall and streamflow are useful for planning studies, hydrological modeling and climate change impacts assessment within Tana River Basin.
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This is an R package for estimating parameters in infiltration and water retention models by curve-fitting methods
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Chapter
When predicting a categorical outcome, some measure of classification accuracy is typically used to evaluate the model’s effectiveness. However, there are different ways to measure classification accuracy, depending of the modeler’s primary objectives. Most classification models can produce both a continuous and categorical prediction output. In Section 11.1, we review these outputs, demonstrate how to adjust probabilities based on calibration plots, recommend ways for displaying class predictions, and define equivocal or indeterminate zones of prediction. In Section 11.2, we review common metrics for assessing classification predictions such as accuracy, kappa, sensitivity, specificity, and positive and negative predicted values. This section also addresses model evaluation when costs are applied to making false positive or false negative mistakes. Classification models may also produce predicted classification probabilities. Evaluating this type of output is addressed in Section 11.3, and includes a discussion of receiver operating characteristic curves as well as lift charts. In Section 11.4, we demonstrate how measures of classification performance can be generated in R.