The GR models were initially developed in the 1980s by Claude Michel and his colleagues at Cemagref (that recently became Irstea and then INRAE). The main objective was to design efficient models, starting from a simple structure and gradually adding complexity that proved useful for improving the model's predictive power . This approach prioritized predictive power over explanatory models , finding justification for this from results obtained using large data sets and not from predefined concepts. This led to the development of a family of models that are usually used in lumped mode (i.e., running at the basin scale with aggregated input).

To disseminate their models beyond the Fortran programming community, a long time ago, the developers of the GR models proposed Microsoft Excel spreadsheets containing hydrological models, namely, the GR1A, GR2M, and GR4J models, as well as the CemaNeige snow accumulation and melt model (see next section for a description of these models), accompanied by a dummy dataset (https://gitlab.irstea.fr/HYCAR-Hydro/ExcelGR, last access: 20 July 2023). The rationale behind this approach was dual: easily providing the GR models to external users (researchers and consultants from France and abroad) and illustrating the hydrological concepts to students with the models developed in-house. The relatively high efficiency and low computational time requirements of these models made them easy to run with Microsoft Excel. In addition, the use of Excel macros enabled interactivity (e.g., the possibility to automatically update simulations when parameter values are modified by users), and graphs were predefined.

Later, the airGR R package was developed to propose additional GR models, and the airGRteaching R package was built as an add-on package of airGR. These tools are described in the next sections.

To ease the implementation of the GR models, proposed the airGR package. Gathering seven hydrological models and one snow accumulation and melt model, airGR can be seen as a research tool, as an efficient way for its developers to share research results, and as a tool simple enough to be used by water managers. The hydrological models included in airGR differ in their complexity and time step, with a gradual increase in complexity as the time step decreases, and various application objectives:

GR1A is an annual one-parameter model, used for water resources assessment . It consists of a single equation relating the annual streamflow to antecedent annual precipitation and potential evapotranspiration.

airGRteaching embeds the main features of airGR and offers simplified ergonomics. It therefore uses its basic tools, meaning that all models implemented in airGR are available in airGRteaching. Since these models have relatively simple structures and few parameters, they can be more easily understood by novice users such as students. airGRteaching does not provide “simplified” versions of existing GR models. Thus, students are able to learn hydrological modeling from the same models that are used in practice, not from degraded versions.

To ease hands-on experience, the choice was made to reduce the number of functions to implement a complete modeling exercise (an airGRteaching function therefore embeds several airGR functions). In addition, the number of modeling options has been reduced, which limits the number of arguments to be specified for running a simulation and simplifies the associated documentation. All these choices allow users to focus on the main questions that beginners ask themselves when they start dealing with hydrological modeling.

airGRteaching contains only a few functions, which can be split into two groups:

a small set of functions to prepare data, to calibrate and run hydrological models, and to plot outputs, i.e., the basic functions needed to undertake a hydrological modeling study;

These two levels of use allow teachers to choose between different levels of technical difficulty. They can choose the most adapted use according to the time available for the exercises, the teaching objectives, and the students' skills.

To get started with the package, particular attention was given to the documentation. The user manual describes the implementation of functions precisely and succinctly and provides simple examples (https://cran.r-project.org/web/packages/airGRteaching/airGRteaching.pdf, last access: 30 December 2022). In addition, a website was created to explain how to use the different features step by step and to answer frequently asked questions (https://hydrogr.github.io/airGRteaching/, last access: 30 December 2022).

Table  summarizes the airGRteaching (and airGR) features.

Like any tool, airGRteaching has its limitations. The first one is that so far only GR hydrological models have been available in airGRteaching. Adding other models is feasible, but to do so, they should be implemented to be compatible with the airGR framework (which contains the basic components for airGRteaching). While for the command-line use of airGRteaching (i.e., use of the PrepGR(), CalGR(), and SimGR() functions), this should be easy to implement, the GUI implementation would require more efforts (for instance, it would require the adding of a model scheme for each model; the interface could become less handy, with models presenting over 10 parameters to optimize, and calibration would be far less rapid).

In addition, it is not possible for the user to build their own hydrological model by adding, for example, reservoirs (e.g., with different discharge functions) and unit hydrographs, to help understand each compartment of a model. This is possible with the RS MINERVE software .

Other limitations, as mentioned in Sect. , are that airGRteaching only offers a limited set of modeling options, compared to airGR. This however could also be seen as a strength, as proposing too many options could be cumbersome from a user's perspective, and these limitations are therefore voluntary.

Remote sensing data, other than meteorological or hydrological data, cannot be used in airGRteaching at the moment. In addition, the effect of land cover changes cannot directly be an asset to airGRteaching, as is the case in some physically based models.

Finally, proper uncertainty exercises, apart from the calibration on different periods, have so far not been a part of this tool, which we see as a simple way of starting hydrological modeling. However, it is easy enough to add noise to the input data to assess input uncertainty. Uncertainty arising from model structure can only be studied by changing models (e.g., using GR4J and GR5J models). The uncertainty associated with parameter calibration methods cannot be tested, as only an optimization algorithm is provided (NB: other algorithms can be plugged into airGR). Finally, airGRteaching does not provide turnkey tools for visualizing uncertainty (e.g., error bars or envelopes on streamflow simulation).

Exercises linking hydrology with other disciplines and scientific communities could be developed by the coupling of the airGRteaching package with other numerical tools and models. First, using actual global (GCM) or regional (RCM) climate model outputs as rainfall-runoff model inputs would illustrate the impact of climate variability or emission scenarios on catchment hydrology, linking climatology and hydrology. In a similar way, streamflows produced by the airGRteaching package could be used as inputs to hydraulic models to produce flood maps in teaching projects involving both hydrological and hydraulic skills. Finally, coupling airGRteaching with models of water uses (e.g., water withdrawal models for drinking water or irrigation) would have interesting teaching applications. Another valuable perspective is to use remote sensing data to perform data assimilation for hydrological forecasting by recovering real-time meteorological (e.g., precipitation measured by rain gauges), hydrological (e.g., streamflow observed from gauging stations), or even satellite data (e.g., MODIS snow cover observations) and using these data as inputs of a rainfall-runoff model in the airGRteaching package, e.g., with the airGRdatassim package . Such applications would illustrate the added value of assimilating hydro-meteorological data for better modeling in hydrology. Other exercises could be centered around uncertainties, through coupling the airGRteaching package with sensitivity analysis methods.

Finally, the airGRteaching package could be used for the development of serious games devoted to hydro-meteorological applications, aiming, for example, to discuss the issues of making better decisions when considering probabilistic forecasts .

The authors' experience with different audiences has shown that airGRteaching is useful in helping students understand a variety of basic concepts: from the choice of an objective function to the sensitivity of model simulations to individual parameters, the difference between model states and model parameters, the difference between automatic and manual calibration, and the informative and complementary value of a variety of plots. Projects that are more elaborate have been developed and are listed in Sect. . For students, depending on the time allotted and their experience, we use the graphical interface with or without the use of computer code. For researchers, it is more a matter of introducing them specifically to GR models, and the interface is used as an introduction of the GR model structure. For engineers working in consulting firms, it is often somewhere in between, depending on their experience and their background. The GUI is frequently used to avoid being bogged down in problems of form and to concentrate exclusively on the underlying concepts of hydrological modeling. The simplified code version allows a smooth transition to the more complex airGR code. For the general public, the aim is usually to introduce them using the airGRteaching GUI to one of the fields of hydrology, to help them understand what a model is, and to raise their awareness of applications such as flood and low-flow forecasting and global change.

The introduction to computer programming is ideal to teach these notions to students. If students are to take this tool into their own hands, they must gradually acquire the concepts without difficulty. It is therefore essential that this is done in a playful way so that they are not discarded. The use of a graphical interface allowing modeling notions to be acquired, while putting aside the programming aspects, allows the different problems to be separated: modeling on the one hand and programming on the other hand. As soon as they wish to go further in the understanding of their subject, students very quickly perceive the limitations that a graphical interface can represent (options too limited, etc.). In addition, use can quickly become daunting if tasks need to be repeated (for example, clicking a large number of times and in a well-defined order to reproduce the results on several datasets). Sometimes there is not enough time to learn programming, justifying the need to use simple tools.

As such, the airGRteaching tool is not intended to be used to realize extended hydrological research studies, and therefore it does not aim to be used to contribute to the actual solving of any of the 23 UPHs (unsolved problems in hydrology; ). However, as it is a tool to teach hydrology, to understand hydrological processes, and to master hydrological modeling, we believe that airGRteaching could be used as a preliminary step in the solving of some UPHs. Namely, UPH19 (“How can hydrological models be adapted to be able to extrapolate to changing conditions, including changing vegetation dynamics?”) and UPH20 (“How can we disentangle and reduce model structural/parameter/input uncertainty in hydrological prediction?”), due to the many model parameter manipulations and calibration–evaluation exercises that airGRteaching proposes, are good candidates. This tool can contribute to UPH21 (“How can the (un)certainty in hydrological predictions be communicated to decision makers and the general public?”) as it has already been used by several decision makers in hydrological training. airGRteaching can be seen as a gateway to mastering airGR and other airGR-dependent packages, thus indirectly helping to solve other UPHs. This is notably the case for questions UPH22 (“What are the synergies and tradeoffs between societal goals related to water management (e.g., water-environment-energy-food-health)?”) and UPH23 (“What is the role of water in migration, urbanization, and the dynamics of human civilizations, and what are the implications for contemporary water management?”), linked to water usage, thanks to the airGRiwrm package , which allows water resources management to be integrated. This package could help to solve problems of spatial heterogeneity and change of scale, namely UPH5 (“What causes spatial heterogeneity and homogeneity in runoff, evaporation, subsurface water and material fluxes (carbon and other nutrients, sediments), and in their sensitivity to their controls (e.g., snowfall regime, aridity, reaction coefficients)?”) and UPH6 (“What are the hydrologic laws at the catchment scale and how do they change with scale?”) because it simplifies the use of airGR in a semi-distributed mode. The airGRdatassim package, which enables data assimilation, could be linked to questions of prediction uncertainty, namely UPH20.