Statistical software hydrology

Moreover, the same script can be reused repeatedly by different people to reproduce a given result avoiding duplication of efforts or to analyse different data, e. Thus, scripts written in R or other languages have wide-ranging benefits, as they facilitate the testing and quality control of the scientific workflow, can be shared and improved by a team of users, lessen the risk of making manual mistakes, and significantly enhance the speed with which analyses can be conducted and updated.

Recent developments in R have contributed to enhancing open science and numerical literacy in the hydrological sciences. Volunteer projects such as the Software Carpentry Wilson , , have been teaching basic computing skills to researchers since , and R now forms a central part of their training. Over the past decade or so, R has become one of the core tools for scientific computation in hydrology. These hosted instances have made the language more accessible to non-specialists due to the large range of pre-installed packages.

Such hosted instances of R remove the initial hurdle of installing R and the required packages i. The R-Hydro community has developed a number of platforms to share computational hydrology analyses, and code is increasingly being shared via repositories see Sect. Code and results can be published as traditional media e.

Dashboards are interfaces that may include a group of related data visualizations such as charts, graphs, tables, and maps e. They can be fixed e. Hydrologists have increasingly employed dashboards to display their analyses in an interactive, user-friendly manner, using packages such as plotly , a graphing library that makes publication-quality graphs online Sievert , , the shiny web application framework Chang et al.

In doing so, these publishing services facilitate immediate interaction and knowledge transfer. Here, a probabilistic time-series GAMLSS model of flood frequency at one gauging station in Ohio, USA, is shown for four different seasons rows and two peak-over-threshold quantities columns: two to four peaks per year.

Source: Neri et al. Figure 5 Use-case scenario for implementation of APIs developed within hydrological sciences. Group A collates the most recent earth- and ground-based observations of land cover, topography, and climate data for an in-house project yet allows an API to interact with an analysis-ready, spatially explicit dataset for their region of interest.

Group B is interested in geomorphological processes and has developed a model to predict likely occurrence of mass movements, which they also provide access to via an API. During a period of extreme rainfall over a scientifically unrelated region, both groups decide to adjust their methods and API to provide pertinent data group A , which feed into predictions of landslide risk group B.

Figure 6 The airGRteaching interface that is used for teaching hydrological modelling. Students can choose a catchment dataset and a hydrological model and activate a snow model on the top left panel of the interface. Modifying the parameters values on the left by using the sliding bars will automatically update the graphs and scores displayed on the right. This interface highlights in an interactive manner the basic principle of the rainfall—runoff relationship and its description in hydrological models.

At the bottom left of the interface, an objective function can be chosen and an automatic calibration procedure can be launched within the interface.

Reproducibility is a key feature of the scientific method and can be broadly defined as the ability for the community to reproduce and verify previous findings. Encouraging reproducible practices helps reduce the likelihood of errors methods can be tested by other researchers while increasing the uptake of any positive developments within a discipline Hutton et al. However, scientific research is increasingly under fire for its lack of reproducibility due to an inadequate methodology description Ceola et al.

True reproducibility requires more than the mere repeatability of results with the same computer code and data: one must also be able to reproduce a study's conclusions when testing the theory with different data or a different model set-up Melsen et al. The open-source nature of R packages and the CRAN repository set-up are one key added value of R to reproducible geoscientific research Pebesma et al.

In addition, packages are citeable in reports and papers together with their version number, allowing the user to track which code was used. Note that many packages are submitted to online repositories such as GitHub that never make it to CRAN for a range of reasons, but this does not necessarily make them less reliable. The journal Nature states that a manuscript can be rejected if the code used to generate new analyses cannot be provided to the editors and reviewers.

Despite the advantages of sharing hydrological code, few computational hydrologists do this because cleaning and annotating the code places an additional burden on the publishing time frame. However, it is reasonable to assume that as more journals require submission of codes with papers, the community of computational hydrologists and associated fields will continue to grow and strengthen the field.

In addition to the sharing of open-source code, reproducibility experts also advocate the use of software tool sets such as version control, scripting, container technology, and computational notebooks to enhance the reproducibility of scientific results Perkel , Hydrological tutorials, vignettes, or teaching documents increasingly implement literate programming Sect. In the hydrological sciences, several ongoing open scientific initiatives can be noted other than the R packages that are discussed in Sect.

These initiatives include the HydroShare web-based system for sharing hydrologic data and models, which allows hydrologists to visualize, analyse, and work with data and models on the HydroShare website e.

The reproducibility agenda has benefited from strong political and financial support, with European Union projects like FOSTER Plus Fostering the practical implementation of Open Science in Horizon and beyond that aim to encourage open science.

As such, open science is expected to encourage interdisciplinary research and is considered a key approach to tackle the grand challenges of our time. There are many different types of software for statistical analysis, but R is still considered the most powerful and popular language and environment for statistical computing. R is GNU S, a language which can be described as the modern implementation of the S language Becker and Chambers , ; Chambers , , and is specifically optimized for statistical computing.

In addition to the standard statistical techniques within base-R i. When comparing R with other similar open-source languages, users often describe R's unique selling point as the vast number of statistical packages which liken it to a free, community-driven statistical software. The statistical and graphical packages provided in R are particularly useful for the hydrological sciences and include techniques such as linear and non-linear modelling, statistical tests, time-series analysis, classification, or clustering.

A description of specific statistical packages relevant to hydrology is provided in Sect. Many different programming languages are used in hydrology, including older languages such as Fortran, developed in the s e. Backus , , and C in e. Ritchie , ; proprietary commercial languages, e. Sanner et al. S and R were both built using algorithms implemented mostly in Fortran and sometimes in C Chambers , , p.

Interconnections between R and other languages can be very useful for taking advantage of each language's strengths or using pre-existing scripts that were originally written in other languages. For example, C and Fortran are both efficient in performing loop tasks.

This is the reason why the apply function loops are coded in C. The airGR hydrological models Coron et al. R can also be connected to different languages using a range of packages, e. Connections to Python can be achieved with the packages reticulate Allaire et al. Additionally, R can also be connected to JavaScript e. Conversely, connecting other languages to R is also possible. One of the major advantages of R is the extensive user community, which provides ample support to newcomers through various initiatives and is growing at a fast pace.

R-Hydro beginners are strongly encouraged to join the discussion on various R-related topics on social media. A wide range of scientific resources, including online manuals and tutorials in several languages, have been developed by the community. Short courses, i. The core aim of the short course is to bring together the R-Hydro community, including both users who are learning to program and advanced users who are either teaching computational hydrology or developing packages for hydrological analysis.

Recent advances in R for hydrology applications are demonstrated during the short course, and a platform for open discussion between guest speakers and course participants is provided. It is also worth noting that a regular short course is also run at the EGU on R package development. The R Consortium provides support to the community in multiple ways. One example of such support is the grant programme run by the R Consortium's Infrastructure Steering Committee ISC , which funds development of projects seeking to promote improvement of the R infrastructure and to achieve long-term stability of the R community.

R is an ever-growing environment, as can be seen in the number of R packages that are developed every year Fig. There are now hydrological packages for every step of a standard hydrological workflow Fig. Setting up a repository with version control i.

A repository is a structured set of files that will track edits any team member makes to the project, similar to the track-changes function in common word processors. There are just a few initial steps to set up a repository.

These include 1 creating a local directory folder to host your RStudio project, 2 creating a Git or a Subversion repository online, and 3 linking the two. Beyond those three steps, all the user needs to do is regularly commit i. These changes can then be uploaded, updating and synchronizing the online repository with labelled annotations username and timestamp.

The repository can be public or private, with different levels of administrator access for users. Many tutorials on how to set up a repository in R can be found online.

Once a project folder or repository has been set up, one might need to identify the most useful R packages and functions for the task at hand. CRAN Task Views were recently developed to provide thematic lists of the packages that are most relevant to specific disciplines. Data retrieval. This includes hydrological data sources surface or groundwater, both quantity and quality and meteorological data e. Data analysis.

This includes data tidying e. This includes process-based modelling scripts for preparing inputs and outputs and running process-based models and statistical modelling hydrology-related statistical models.

For example, the Environmetrics Task View contains a Hydrology and Oceanography section, and the High-Performance and Parallel Computing with R Task View can also be useful for hydrologists using large amounts of data. Other relevant Task Views cover a range of topics such as time-series analysis, machine learning, or spatial analysis. One last way of discovering relevant and useful hydrological packages is social media, such as Twitter, where many hydrologists share their most recent publications as well as links to useful resources and packages.

One of the most useful computational advances in recent years has been the development of packages designed specifically to retrieve data from online hydrological archives. Many of these packages provide vignettes that illustrate how to use the functions. Other relevant packages are listed in Table 1. Additionally, many data retrieval packages that are relevant to hydrological analyses have been developed by related scientific disciplines, such as meteorology and climatology.

In the future it seems likely that most water and meteorological agencies around the world will facilitate access to these data via APIs and open-source packages see Sect. Table 1 is far from exhaustive, and there are many other relevant packages that are available on CRAN.

Once data have been retrieved or downloaded, a broad range of packages are available for reading different types of data and their associated metadata.

However, these packages are not specifically hydrological and so will be discussed here with brevity. Note that in many cases, for example with the dataRetrieval package, the data are imported directly into the R workspace.

Basic data formats such as csv and txt can be read with base-R read. The rio package facilitates data import and export by making assumptions about data structure from the file extension Chan et al.

GRIB files can also be handled with packages such as raster or gribr Wendt , For an overview of the different issues with hydrological data, see Wilby et al.

This step may involve handling missing data, checking data completeness, reshaping and aggregating data, or converting strings to date format. We do not develop this section specifically because these are general tasks in R. However, for overviews and tutorials on manipulating and cleaning hydrological data, we point the reader to published resources from the Using R in Hydrology workshop see Sect. In the past, R may have been a less powerful alternative to the more established spatial software for processing large datasets and extracting information.

Now, however, R can be parallelized more easily than other software harnessing the power of multiple processor cores to handle large datasets and can integrate GIS analyses within a complete, automated hydrological workflow, which includes data processing steps before or after any GIS analyses and any subsequent statistical analyses.

It is this integration of GIS as one step within the hydrological workflow that makes R extremely attractive. As a result, in recent years, R has become the go-to method for geocomputation and geostatistics and can now be used as a GIS in its own right. Multiple books have been published on the topic of spatial analysis and mapping with R Brunsdon and Comber , or, more broadly, geocomputation with R Lovelace et al.

Many methods are now implemented within R for handling vectorial data, with packages such as sp Pebesma and Bivand , ; Bivand et al. Version 3. There is also a range of packages for handling raster data, like raster Hijmans , , which can be used to read, write, manipulate, analyse, and model gridded spatial data, and stars Pebesma , b for reading, manipulating, writing, and plotting spatio-temporal arrays.

With all these packages, R now has full cartography and mapping functionality and can produce sophisticated maps that are either static or interactive. Packages such as cartography Giraud and Lambert , or tmap Tennekes , can both be used for creating symbols, choropleth, or other types of maps and for facilitating the visualization of spatial data distributions in thematic maps.

These two packages are quite similar in content but not in form: cartography uses the painter's model, while tmap uses The Grammar of Graphics and allows users to draw static and dynamic maps with the same code.

Additionally, ggmap Kahle and Wickham , is commonly used for visualizing, geolocating, and routing spatial data on top of static maps such as Google Maps; RgoogleMaps is used to interact with Google Maps, while the JavaScript leaflet Cheng et al. R software can also be linked to a range of other GIS software to take advantage of specific capabilities.

Table 2 Examples of packages for hydrological modelling. The next step in a typical hydrological workflow is to conduct hydrological modelling by using the data inputs prepared in previous steps. Hydrological modelling often proceeds by simplifying hydrological processes to test hypotheses about the water cycle, manage water resources, reconstruct incomplete flow time series, predict extreme events floods or low flows , or anticipate the effects of future climatic or anthropogenic changes.

In Table 2 we highlight some of the key packages that facilitate the implementation of certain hydrological models in R. As R can be used for every step within the hydrological modelling process, from importing and cleaning data to exploratory analyses, data modelling, data analysis, and graphical visualization, it represents an ideal language for hydrological modellers. Some packages also include degree-day snow models e. Many of the models included in these packages are lumped i. Some packages, such as TUWmodel and topmodel , allow a spatial distribution of the hydrological processes.

TUWmodel , for instance, allows the user to implement a semi-distributed application with differentiation into elevation zones, while topmodel allows the user to make topographic index classes from a topographic index map. The vast majority of the models in the above packages are deterministic; however, the fuse package can also provide ensembles of conceptual lumped hydrological models, and the hydromad package is intended to provide a flexible framework for assembling different soil moisture accounting and routing schemes.

The above packages typically allow the user to run the hydrological models, and usually provide some sample input data, with executable examples.

Some packages provide optimization algorithms, criteria calculation, and dedicated plotting functions e. Developing hydrological modelling packages in R is relatively straightforward because of the language's flexibility; additionally, as discussed in Sect. This property allows R users to embed model codes that already exist into R and provides a more friendly environment, as many packages ease the analysis of data and model simulations.

R was initially developed as a statistical computing language and is still the primary language in which novel statistical methods are coded and distributed. Statistical approaches are employed for an extremely wide range of tasks in hydrology, and it is virtually impossible to give complete coverage of all possible packages that might be useful to hydrologists.

The skimr package provides compact and flexible summaries of data; it can be used with pipes and displays nicely in the console. Many estimating procedures can be carried out using the base-R stats package, which includes, for example, correlation analysis and Mann—Kendall testing, linear regression, Poisson regression, and Gamma regression.

There are also generalist packages for non-parametric trend tests such as trend Pohlert , , which includes a broad range of tests for trend detection, correlation, and detection of change points or non-randomness.

Many general modelling packages have been found to be useful by hydrologists, for example mgcv Wood , , VGAM Yee et al. While mgcv can be useful for more complex smoothing approaches e. A hydrologist might therefore choose which package to use depending on the most likely distribution of the data which are being analysed and the complexity of the analysis.

The caret package Kuhn et al. There are many packages available for common hydrological tasks. A comprehensive set of functions for carrying out extreme value analysis Coles , can be found in the extRemes package Gilleland and Katz , , and a more complete overview can be found in the CRAN Extreme Value Analysis Task View.

L-moments can be implemented using the lmom Hosking b package, while the lmomRFA package Hosking , a enables regional frequency analysis. The lfstat Koffler et al. Many of the standard model evaluation metrics are provided directly within these packages. The caret package, for instance, imports other packages, such as ModelMetrics Hunt , , to facilitate model evaluation directly.

A range of packages have also been developed specifically for model evaluation. The hydroGOF package Zambrano-Bigiarini , a provides goodness-of-fit functions specifically for comparison of simulated and observed hydrological time series. In Table 3 we present a brief overview of some other packages for hydrological statistics. Table 3 Examples of packages for hydrological statistics.

Data visualizations play an important role in hydrological analysis: R makes them straightforward to implement and allows considerable flexibility. R includes three main families of graphics packages: a painter model, natively present in R and based on the S language's GR-Z model Becker and Chambers , , the trellis graphs e. The last two families are both based on the grid package R Core Team , , a low-level abstraction layer that allows the development of graphical packages with different philosophies, which means that the created graphics can be stored in objects to be updated and plotted again later.

Visualizations are produced in base-R using the graphics package R Core Team , , which relies on the philosophy of superimposing elements of the graphics with no provision for deleting an element once it is drawn and includes a range of functions to add straight lines, arrows, axes, boxes, grids, legends, or annotation to a plot.

Figure 4 provides a hydrological example of faceting where a statistical model is visualized for different seasons rows and different peak-over-threshold quantities columns. Dynamic charts — where the user can, for instance, hover over one or multiple points to read the associated data or metadata e.

These dynamic graphics are particularly useful in inspecting data, such as outliers, or explaining an analysis when teaching hydrology in the classroom e. Dynamic graphics including maps can be created by using the plotly package Sievert , , a graphic library that allows the user to make graphs interactive with minimal extra code.

A number of JavaScript-based visualization libraries can also help achieve dynamic graphics. For interactive time-series data requiring axis display features such as zooming and panning and highlighting of series and points, the dygraphs package Vanderkam et al. The manipulate package Allaire , allows the user to easily add sliders and other control tools to otherwise static plots. We encourage the reader to explore these HTML widgets, as they show how simple it is to implement dynamic graphics with just a line or two of R code.

Choosing the appropriate colour gradients for hydrological graphs and maps is key. It is widely accepted now that certain colour schemes, and notably the infamous rainbow colour scale, are poor choices for data visualization Light and Bartlein , ; Stauffer et al.

The rainbow scheme has been shown to distort perceptions of data and alter meaning by creating false boundaries between values; additionally it is not colourblind-safe, and other alternatives like perceptually uniform colour maps have been suggested Crameri , The R language is strong in the area of colour gradients, and there are many colourblind-friendly palettes available for hydrology that follow effective data visualization guidelines Kelleher and Wagener , There are both manually defined and predefined palettes using packages such as RColourBrewer Neuwirth , , colorspace Zeileis et al.

A vast array of packages have been developed in R for creating dynamic presentations and documents, which are particularly useful for illustrating hydrological concepts. Dynamic interfaces and web-based applications can be created with shiny Chang et al. R can also be used to generate animated GIF files for presentations, for example to highlight temporal changes in land cover or reservoir levels from earth observation. Additionally, various packages have been designed to produce interactive maps, such as leaflet Cheng et al.

R also offers many tools for creating websites or blog posts, with packages like rmarkdown Allaire et al. Presentations, books, reports, and documents can be generated in LaTeX, or Markdown, natively with Sweave functionalities or with packages such as knitr Xie , , markdown Allaire et al.

These packages facilitate the automation of such documents e. For most hydrologists who are new to R, the initial hurdle is understanding how to install libraries and use packages to explore their own datasets. The book R packages Wickham , is freely available online and explains everything from the basic installation of packages to the role of metadata, understanding documentation, the role of vignettes, and best practice on GitHub one common collaboration and version control platform.

R packages centralized on CRAN are structured similarly, with a reference manual, source code, a license file, and other common elements. The code and documentation of all packages is verified before they are uploaded to CRAN. R packages ideally provide two forms of documentation: a short form help pages and a long form vignettes , which are both complementary and serve different purposes Wickham , The help pages explain what each function does, describe the required input and the produced output, and usually include a section with executable examples.

Vignettes, in contrast, are tutorials that illustrate how R packages and their functions are used, often with discussion of the outputs. However, not all packages include a link to a vignette on the CRAN repository, as this is not compulsory. Developing clear and useful vignettes is one of the key challenges in facilitating the uptake of new packages and methods; in fact these are key to reducing the misuse of software and ensuring that the package users understand the methods.

Use cases can be written as blog posts or tutorial-style papers, with explanation of how to correctly interpret and implement a specific method and helping the community move forward.

IDEs are software applications that are used to facilitate coding by providing the code editor, compiler, or interpreter and debugger within a single graphical user interface GUI. Neil , RStudio facilitates the uptake of R by hydrologists by providing a helpful research tool and training environment to new and experienced programmers alike.

RStudio is available in two editions: an open-source edition and an enterprise edition with a commercial license. Most hydrologists use the free RStudio Desktop edition, although university departments and companies increasingly offer server editions too.

RStudio's features include a console; a syntax-highlighting editor that supports direct code execution; integrated R help and documentation; support for version control systems; and tools for plotting, history, debugging, and workspace management.

The RStudio environment makes it straightforward for hydrologists to conduct a range of tasks e. Other advantages of RStudio include the easy access to the help window, the ease of package management and updating, code debugging, or even the easy development of packages in one location. All of these benefits contribute to facilitating open hydrological science. RStudio version 1.

In the early years of R, the software was unable to handle large data files exceeding millions of rows or complex data formats. However, both of these limitations have since been overcome. Some of the early packages for handling large data files include bigmemory Kane et al. More recently, the package data. In hydrology, some of the spatial data handling packages are particularly relevant, such as the sf package Pebesma , a for large shape files or the feather Wickham , a package for feather files, a lightweight binary columnar data store designed for maximum speed.

Distributed data frames can be implemented using packages such as sparklyr Luraschi et al. As the volume of available data increases and hydrologists use a greater number of models and ensembles, parallel computing — where many calculations are carried out simultaneously instead of sequentially — has become an essential tool in computational hydrology and has sped up analyses.

For instance, instead of using traditional for-loops an approach where one action is carried out over a dataset iteratively , the data may be broken down into groups e. The performance boosts that can be achieved by parallelizing the code i. Even without access to a high-performance computer or cluster, it is possible to perform hydrological tasks faster, since most local machines now have between 4 to 16 cores.

R has multiple facilities and packages for enabling the parallelization of code execution. At the most simple level, base-R functions like lapply and sapply can be used to apply a specific function to a vector or list input, which can speed up analyses considerably. For instance, the base-R parallel package for distributed computing provides methods to access additional computational power by allocating available processing cores into a cluster.

Other packages that are widely used for parallel computing in hydrology and other areas include the snowfall Knaus , package, which facilitates the development of parallel R programs, e.

Additionally, some packages have parallel functionalities that are integrated directly within the package, such as the h2o package LeDell et al. As we have shown above, the development of R fosters progress in hydrology. In this section we discuss what we perceive as some of the future avenues for enhancing hydrological research or operational hydrological practice with R and how we can achieve these as a community. Open research practices bring significant benefits to researchers McKiernan et al.

There are many different platforms for sharing and publishing R code such as GitHub, Figshare, and RPubs or Plotly also for dashboards and interactive plots. To obtain a DOI, users may wish to use repositories such as Zenodo, a general purpose open-access repository which allows researchers in the sciences and humanities to deposit datasets, research software, and create reports.

The data publisher PANGAEA, additionally, is specifically tailored to archiving, publishing, and reuse of data in earth and environmental sciences. For further guidance, some of these platforms are discussed in the code and data policy section of the open-access journal Geoscientific Model Development.

The consistent stream of new R packages has been a great driver for progress not only in hydrology but even in science more broadly, as packages favour the uptake and development of methods. Additionally, the open-source nature of R packages means that different users can contribute feedback to R package developers and help enhance existing code.

R users can raise issues for certain packages directly on online platforms hosting the repositories such as GitHub or GitLab to foster an online-documented discussion with the package developers generating interaction in the community. Package authors can also add a bug report link or an email address in their package description file common best practice for developers to specify how they prefer to receive bug reports.

This feedback between users and developers is one key route to scientific progress. Users can identify issues or suggest improvements by commenting on online collaboration platforms e. GitHub or GitLab or by emailing the developer or maintainer. Most packages are hosted on these repository hosting platforms before becoming available via the CRAN archive, ensuring that a certain standard and best practice are met.

Although CRAN itself does not have any mechanism to check the quality or cleanness of the code, there is a suite of packages that are used to i ensure clean code and documentation that follow a widely accepted style guide, such as the lintr Hester , , goodpractice Csardi and Frick , , and hunspell Ooms , packages and to ii rigorously test the functions against predefined outcomes, using for example the testthat package Wickham , In comparison with GitHub, CRAN is an organized repository which provides executables for several platforms, whereas finding an hydrological R package on GitHub can be difficult.

The comparison between the two is somewhat like visiting a curated art auction versus an antique store. Developing an R package requires a structured approach, just like writing a scientific paper. The main requirements for publishing a package are listed on the CRAN website. Providing documentation and tutorials, e. Package authors can also provide user-friendly and modular functions to aid maintenance and future development e.

Authoring hydrology-based R packages that can stand up to scientific scrutiny and ensure user-friendliness is not a minor task, and such investment should be recognized within the community.

Fuelling the development and dissemination of new R-based methods is therefore the joint responsibility of developers, authors, and journal editors. If developers include digital object identifiers DOIs as well as instructions for citation within their software, then authors can subsequently cite these packages.

The adequate reference or references can be obtained with the citation function for every package. The references generally comprise a reference to the package with CRAN link and package version, which is key for encouraging reproducibility and sometimes also include an additional journal paper reference.

If both are available, then ideally both must be cited to provide recognition of computational scientists' contribution to the hydrological community and to enhance the reproducibility of the research. Editors might also support reproducibility via special issues or sections for technical notes.

Dedicated software journals such as the Journal of Open Source Software can be used to publish brief, technical descriptions of R packages. Any potential apprehensions for publishing such methods e. It is worth noting that when writing new packages, the open-source approach has both pitfalls risk of errors in new packages and strengths community review and range of tests that can be implemented via the above-mentioned packages.

One of the main challenges today for hydrological workflow harmonization is to standardize calls for data which are structured in different ways by data providers around the world.

While the number of packages for hydrological data retrieval has grown considerably see Table 1 , the packages are structured differently because they were set up independently and because the underlying hydrological and hydrometric datasets differ from country to country. As more nations develop similar hydrological data acquisition packages, we believe it would be worth implementing a common syntax and data output form.

For example, it would be ideal to use consistent APIs and output objects across packages. There is currently no effort to combine data retrieval packages from different regions, but it might be worth implementing a meta-package with functions that convert hydrometric data from other packages to a standard format or one for hydrological models to be run within the same framework.

Additionally, the growing tendency towards data standardization at the global level may facilitate the development of consistent data retrieval packages. Examples of global data standards include WaterML, the Open Geospatial Consortium standards for hydrological time series, or TimeseriesML, a more generic candidate standard currently under discussion. As more water agencies and data providers adopt such standards, it will become much easier to develop consistent data retrieval packages, and in theory we may no longer require different packages for data retrieval because the only component that should change is the server endpoint.

APIs play a key role in hydrological data acquisition and provision and are likely to become increasingly important in the future. An API is a set of code which usually includes subroutine definitions, communication protocols, and tools for building software and interacting with different datasets.

These packages provide means of posting requests via the R command line and then return an R object for subsequent manipulation. Internally, the source code translates all inputs and outputs to and from HTTP. Programmatically accessing a variety of vast online resources i. Recent developments, however, have opened up a new, and arguably under-utilized, approach to APIs for the R community: rather than exploiting an existing interface, R users can now increasingly rely on a set of tools to develop and make their own APIs accessible for use by third parties via HTTP.

API development is likely to become a major avenue of future advances in scientific computing within the hydrological community as well as interaction beyond the scientific realm. Such APIs can provide access to the latest raw or analysis-ready data, methods, or even entire statistical models written in R.

The simplicity and ubiquitous implementation of HTTP have vast implications, of which we highlight four. This means, for the first time, that fully seamless interaction between research groups working in different languages is possible e.

Skip to main content Skip to table of contents. Advertisement Hide. This service is more advanced with JavaScript available. Fundamentals of Statistical Hydrology. Editors view affiliations Mauro Naghettini. Describes up-to-date methods for statistical analysis of hydrological variables Includes numerous worked out examples with solutions, exercises with answers, and summaries for descriptors of the main probability distributions Takes a not-too-simple and not-too-difficult approach, suitable for students with a basic-to-moderate background in mathematics Contains useful reviews of mathematical concepts and listings of the hydrological data used within the book.

Front Matter Pages i-xi. Introduction to Statistical Hydrology. Pages Preliminary Analysis of Hydrologic Data. Elementary Probability Theory. Parameter and Quantile Estimation. Statistical Hypothesis Testing. Correlation and Regression. Regional Frequency Analysis of Hydrologic Variables. Introduction to Bayesian Analysis of Hydrologic Variables.