Method, tool and system for forecasting water resource availability

Abstract

A method for forecasting water resource availability at a given calculation time, based on input precipitation data over a predetermined time interval and historical data recorded over a period prior to that given time. This historical data consists of input precipitation data, possibly evapotranspiration data, and output water flow data. The method combines: - a conceptual rainfall-runoff reservoir model, whose parameters are calibrated to match the historical data; - a machine learning model, trained on the historical input precipitation data and output data consisting of a discrepancy observed between: a) a retrospective flow forecast provided by the conceptual reservoir model calibrated on the historical data, at each time point in the historical period.b) the water flow recorded at the same time in the historical period. The forecast consists of: - obtaining, from the conceptual reservoir model calibrated on historical data, a provisional flow forecast at the time of calculation, based on precipitation input data over the predetermined time interval; - obtaining, from the machine learning model, a correction forecast at the same time of calculation and based on the same input data over the predetermined time interval; - combining the provisional forecast and the correction forecast to obtain a flow forecast. The invention also relates to a forecasting tool and system. Figure for the abstract: none.

Description

Title of the invention: Method, tool and system for forecasting water resource availability

[0001] The invention relates to the forecasting of water resource availability at different time horizons.

[0002] Water resources constitute a major issue in the context of climate change and population growth.

[0003] The forecast of the availability of this resource has already been the subject of numerous studies which have led to the construction of different forecasting models.

[0004] There are essentially two main categories of models, namely conceptual models and machine learning models.

[0005] Conceptual models are based on a theoretical approach to flows. A natural basin is considered as a reservoir that fills with rainwater and empties through runoff into lower basins and evaporation. These models are theoretically accurate, but suffer from a lack of spatial knowledge of the modeled objects, such as impermeability limits, the location of karst cavities, surface water evaporation, etc. This is particularly true for hydrogeological models, which raise the difficulty of combining, on the one hand, internal runoff within the carbonaceous rock and diffuse infiltration into upper rock layers, resulting from external runoff over less permeable rocks until it reaches the limestone, and, on the other hand, concentrated flows in karst conduits.

[0006] With perfect modeling of the site under study, a conceptual model should reflect reality with a very low error. This is obviously never the case, given that detailed knowledge of a terrain is very difficult and that simplifications are necessary, precluding a comprehensive approach to the flow phenomena within geological layers.

[0007] A machine learning model is defined as a model whose parameters are defined by learning from observed data. The observed data are used to parameterize the model, so that it becomes capable of providing new output data from new input data. Such models are also referred to as statistical learning or machine learning.

[0008] Methods based on machine learning models rely on data recorded in the past to predict the future. Rainfall data from a site, accumulated over a long period, are compared with availability data. Water resource availability is assessed with a more or less significant time lag. A machine learning algorithm analyzes this data to train a model. Once the model is trained, it can be asked to provide a water resource availability forecast based on recent rainfall measurements, or even weather forecasts.

[0009] Machine learning methods are very promising, particularly thanks to increasing data acquisition and computing capabilities. Rainfall and water flow rates over several years can be recorded with a certain degree of accuracy, which significantly increases the model's effectiveness. With a perfectly trained model, it is also possible to obtain a forecast based on recent rainfall data, or even on meteorological rainfall forecasts.

[0010] One advantage of machine learning methods is that they do not rely on detailed knowledge of the field being studied. However, there appears to be a limit to improving the quality of the predictions, as an increase in the amount of training data is not sufficient to improve the model indefinitely.

[0011] The present invention aims to propose a new way of forecasting water resource availability which provides better results than the methods of the state of the art, without needing to remedy the disadvantages of the two known methods, that is to say without having to increase indefinitely the knowledge of the field studied in order to apply a conceptual method, nor increase indefinitely the amount of training data in order to apply machine learning methods.

[0012] The present invention relates to a method for forecasting the availability of water resources at a calculation time, based on input precipitation data over a predetermined time interval and historical data recorded over a historical period prior to said given time, said historical data consisting of input precipitation data and output water flow data,

[0013] characterized by the fact that it combines:

[0014] - a conceptual model with rainfall-runoff reservoirs, the parameters of which are calibrated to coincide with historical data,

[0015] - a machine learning model, the learning of which was carried out on the historical input and output data base consisting of a discrepancy observed between:

[0016] a) a retrospective flow forecast provided by the conceptual reservoir model calibrated on historical data, at each instant of the historical period,

[0017] b) the water flow recorded at the same time in the historical period, the forecast consisting of

[0018] - to obtain, from the conceptual model with reservoirs calibrated on historical data, a provisional flow forecast at the time of calculation, based on input data over a predetermined time interval,

[0019] - to obtain, from the machine learning model, a correction forecast at same calculation time and from the same input data over the predetermined time interval,

[0020] - combine the preliminary forecast and the correction forecast to obtain a flow forecast.

[0021] For the purposes of the invention, the term “calculation time” means a date within a period of time at which a forecast is made. This may be a day or an hour.

[0022] Preferably, the time step between two calculation instants is constant. This is then referred to as a regular time step. However, it is possible, according to the invention, to use an irregular time step.

[0023] Preferably, a specific cleaning algorithm is used to clean and validate the historical data before calibrating the conceptual model and training the machine learning model.

[0024] According to a particular embodiment, evapotranspiration input data are added to the precipitation input data and these precipitation and evapotranspiration data are taken into account as input data by the models.

[0025] According to a particular embodiment of the invention, the reservoir model is the Rural Engineering model with n parameters (designated GRnJ); preferably, n=4 and even more preferably, n=5. The GR5J model is an advanced version of the GR4J model, a description of which can be found, for example, in the article by Pushpalatha, Raji, Charles Perrin, Nicolas Le Moine, Thibault Mathevet, and Vazken Andréassian. 2011. “A Downward Structural Sensitivity Analysis of Hydrological Models to Improve Low-Flow Simulation.” Journal of Hydrology 411(1-2):66-76. doi: 10.1016 / j.jhydrol.2011.09.034.

[0026] According to a particular embodiment of the invention, the machine learning model follows a so-called random forest algorithm.

[0027] In a particular implementation mode, the machine learning model follows a support vector algorithm.

[0028] In a particular embodiment, the method includes a monitoring step consisting of checking whether the forecast is within an interval of so-called acceptable values ​​and triggering an alert if said forecast falls outside said interval of so-called acceptable values.

[0029] According to other optional features of the invention, taken alone or in combination:

[0030] - the GR5J model is modified to optimize the contributing area of ​​the basin,

[0031] - the GR5J model is modified in its search limits of its parameter X4,

[0032] - the GR5J model is modified by increasing the initialization period of the models.

[0033] The invention also relates to a tool for forecasting the availability of water resources, consisting of a computer program product comprising instructions for implementing the process described above.

[0034] The invention also relates to a water resource availability forecasting system, comprising:

[0035] - data carriers capable of containing historical precipitation data and water flow rates recorded over a historical period,

[0036] - computing means having at least read access to data storage media,

[0037] - a storage memory accessible for reading and writing by means of calculation and containing instructions executable by computing means,

[0038] characterized in that said instructions implement, when executed by the computing means:

[0039] - a conceptual model with rainfall-runoff reservoirs, the parameters of which are calibrated to coincide with historical data contained in the data carriers, and

[0040] - a machine learning model, the learning of which was carried out on the historical input data contained in the data storage media and output data consisting of a discrepancy observed between:

[0041] a) a retrospective flow forecast provided by the conceptual reservoir model, calibrated on historical data, at each instant of the historical period,

[0042] b) the water flow recorded at the same instant in the historical period,

[0043] said instructions enabling the obtaining, when executed by the computing means,

[0044] - by implementing the reservoir model calibrated on historical data, a provisional flow forecast at the time of calculation, based on input data over a predetermined time interval,

[0045] - by implementing the machine learning model, a prediction of correction at the same calculation time and from the same input data over the predetermined time interval,

[0046] - a combination of the provisional forecast and the correction forecast for to obtain a flow rate forecast.

[0047] The options defined for the above process also apply to the tool and the system. Brief description of the figures

[0048] The invention will be better understood upon reading the following description, given solely by way of example and made with reference to the accompanying drawings in which:

[0049] [Fig. 1] represents flow data for a first source, in their raw form,

[0050] [Fig.2] represents flow data for a second source, in their raw form,

[0051] [Fig.3] represents the flow data of [Fig.1], after cleaning, with meteorological data,

[0052] [Fig.4] represents the flow data of [Fig.2], after cleaning, with meteorological data,

[0053] [Fig.5] is a graph showing the squared error of different models on the first source,

[0054] [Fig.6] is a graph showing the squared error of different models on the second source,

[0055] [Fig.7] is a graph showing the relative error of different models on the first source,

[0056] [Fig.8] is a graph showing the relative error of different models on the second source,

[0057] [Fig.9] is a graph showing the predictions of each of the models tested on the first source,

[0058] [Fig. 10] is a graph showing the predictions of each of the models tested on the second source,

[0059] [Fig. 11] is an illustration of the calibration method for the medium-term test,

[0060] [Fig. 12] is a graph representing the quadratic errors of the different models for the first source,

[0061] [Fig. 13] is a graph representing the quadratic errors of the different models for the second source,

[0062] [Fig. 14] is a graph representing the relative errors of the different models for the first source,

[0063] [Fig. 15] is a graph representing the relative errors of the different models for the second source,

[0064] [Fig. 16] is a graph representing the predictions of each of the models tested for the first source

[0065] [Fig. 17] is a graph representing the predictions of each of the models tested for the second source Detailed description

[0066] It should be noted that the GR4J model (Rural Engineering Model with 4 Daily Parameters) is a two-reservoir rainfall-runoff model developed by Cemagref in the early 1980s. It was developed to link the rainfall depth over a watershed to its outlet. It is based on large datasets and the discovery of the structure that best reproduces the hydrological behavior of a watershed, i.e., the watershed's response to rainfall. It is a hydrological model that performs a triple globalization of the watershed system: at the process, spatial, and temporal levels. Several versions have been proposed over time; the latest is that of Perrin et al. (2003).

[0067] The model parameters are: - XI: The capacity of the soil reservoir (mm) - X2: The coefficient of underground exchange (mm / day) - X3: The one-day capacity of the routing reservoir (mm) - X4: The base time of the unit hydrograph HUI (days) - X5: Dimensionless threshold parameter, which allows the direction of groundwater exchange to be changed during the year according to the water level R in the routing reservoir relative to this threshold.

[0068] The model has a production reservoir and a routing reservoir, unit hydrographs, as well as a function to simulate the most important hydrological behavior of the basin.

[0069] In the context of the invention, the GR5J model is interesting in comparison with the GR4J model in that it has shown a significant improvement in performance, particularly in low flow conditions.

[0070] Figures 1 and 2 represent flow data for two sources, in their raw form.

[0071] Thanks to a cleaning algorithm specific to these two sources, this data was cleaned in preparation for the execution of the models.

[0072] The result of this cleaning is shown in Figures 3 and 4, with the addition of a graphical visualization of the meteorological data.

[0073] The data available for the two sources are precipitation P, potential evapotranspiration ETP and flow at the source Q at daily time steps, over a period of almost 20 years (from 2001 to 2021).

[0074] For tank-equipped models, in the described embodiment, the invention uses the GR4J model and its advanced versions (GR5J and GR6J). The GR4J, GR5J, and GR6J models were compared to select the one with the best performance. As already mentioned, an advantage of the GR5J model led to its selection.

[0075] Three modifications are made to this model to make it suitable for a model- groundwater treatment:

[0076] 1st modification: Optimization of the basin's contributing area at the same time as the other parameters.

[0077] Knowledge of the area of ​​the hydrogeological catchment of a spring is a crucial step. Without knowing the area, the GR model is unusable since it uses this area to convert flow rates expressed in m³ / time step into flow rates expressed in mm / time step.

[0078] Either the topographic surface is available and is then used, or the Turc-Mezentsev equations are used, which relate long-term discharge with long-term precipitation and evapotranspiration. These equations are expressed as follows: Referenced Streamflow formulation Actual evaporation formulation Parameter TÜrcn954F~ Mezentsev y = p ^[pe + E = [Fn + fi > 0 0955) Eq. 2

[0079] These two equations allow us to obtain a first estimate of the area S of the catchment basin from this transformation

[0080] S = Q / (PE)

[0081] The area S thus obtained may sometimes differ from the topographic area, due in particular to various hydrogeological and climatic phenomena which govern the flow, i.e. drainage, exchanges with a river, etc.

[0082] A topographic surface correction hypothesis is introduced in the form of a new parameter a such that: Seff = a*S

[0083] This new parameter allows for correcting the contribution of the catchment area to the flow rate. It is calibrated with the five other parameters of the GR5J model using the SUBPLEX optimization algorithm described, for example, in the article "PDA_SUBPLX", available at the following address: http: / / star-www.rl.ac.uk / docs / sunl94.htx / sunl94ss82.html.

[0084] 2nd modification: Modification of the search limits of the parameter X4, which represents the base time of the unit hydrograph of the transfer function between the two reservoirs. This parameter, as defined by Perrin et al. (2007), has a median value of 1.7 days, and an 80% confidence interval between 1.1 and 2.9 days, as shown below in Table 1. [Tables 1] Parameter j Median 1 80% Confidence Interval^ Xi (mm) 350 100 at 12:00 | X2 (mm) 0 -5 to 3 >G(mmj T 20 to 300 | X4 (days) j 1.7 | 1.1 to 2.9 I

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092] In the underground context of the invention, the infiltration process takes much longer than the runoff process. This is why the X4 parameter was modified from a maximum of 20 days to a maximum of 365 days. 3rd modification: Increase in the initialization period of the models, because aquifers have a significant storage capacity, which implies that the reservoirs in the model take longer to reach a state of saturation. The modifications to the GR5J model result in the improvements visible in Table 2 below. [Tables 2] XI X2 X3 X4 X5 a KGE Values ​​before modification 1231.5 -7 7630 20 0.2 0.796 Values ​​after modification 953.82 -1.38 11220 23.32 'G 0.5 1 0.76 0.337 The GR4J, GR5J, and GR6J models require daily time-step data, including: • Daily precipitation and evapotranspiration in mm / day • Daily flow rate in mm / day (or m3 / day provided the surface area of ​​the basin is supplied) • Maximum, minimum, and average temperatures are optional The variables used for the GR5J model are thus fixed. According to the invention, the GR5J tank model is combined with a machine learning model that corrects its errors. To this end, the learning models of the “random forest” type (hereafter RF) and of the “support vector” type (hereafter SVM) are used to give rise to a hybrid model resulting from the combination of the previous GR5J conceptual model with, respectively, the random forest model and the support vector model. The weekly time step of the machine learning models is retained for this combination.

[0093] The following explanatory variables are used for the hybrid models: • The weekly sum of precipitation, evapotranspiration and effective rainfall (P, ETP, PE) • A lag over the previous 3 weeks for the variables (P, ETP, PE) • The rolling total over 4, 12, 26 and 52 weeks of effective rainfall (translation (monthly, quarterly, semi-annual and annual top-ups) • Residual: denotes the difference in flow rate between two successive weeks £(S)=QsimGR(S) - Qobs(S)

[0094] The use of deltas overcomes the difficulty that predicting the source flow using the random forest algorithm requires knowing the flow two time steps earlier. However, if the extreme flow values ​​during floods and low flows have not been provided in the model training data, the model cannot predict these values. This difficulty is overcome by forecasting increases or decreases in flow, referred to as deltas. • A lag over the previous 2 weeks for the residual variable • GR5J flow rate

[0095] Both hybrid models (RF hybrid and SVM hybrid) use all the variables described above to estimate the error of the GR5J model.

[0096] It is recalled that random forest algorithms work by constructing groups of decision trees during the calibration process, representing a distinct instance of the data input classification. Each tree is developed by independently sampling the values ​​of a random vector with the same distribution for all trees in the forest.

[0097] The random forest technique considers instances individually so that trees are executed in parallel; there is no interaction between these trees during tree construction. The prediction with the majority of votes or an average prediction is considered the selected prediction.

[0098] It is also worth recalling that support vector models are neural networks whose learning is based on minimizing structural risk rather than the empirical risk of artificial neural networks. The support vector algorithm simultaneously minimizes empirical error and model complexity, which can improve the model's generalizability for classification or regression problems in many disciplines. This is achieved by minimizing an upper bound on the test error rather than minimizing the learning error.

[0099] For each week S, the residuals of the two previous weeks are used to estimate the residual of week S.

[0100] e(ti) = model[e(ti i), e(ti2), other variables] for week 1 of prediction

[0101] e(t2) = model[e(ti), e(t; i), other variables] for week 2 of prediction

[0102] e(ti) = model[e(ti i), e(ti2), other variables] after prediction week 2

[0103] The terms rit, J and e(ti2) mean the difference between the measured flow rate and the flow rate modeled by the GR5J model, respectively at 1 and 2 weeks before the first week of prediction.

[0104] The flow rate is finally obtained by the equation

[0105] Qsim(S)=QsimGR(S) - e(S)

[0106] with:

[0107] Qsim: Predicted flow rate

[0108] QsimGR: Throughput predicted by GR5J

[0109] To evaluate the performance of the models, two errors were calculated, the relative error RE in %, and the root mean square error RMSE. ER = Çï-----------% / Y". iQobsfi)—Qsim(i)]2 RMSE = f --~— VN

[0110] with:

[0111] Qobs: Observed flow rate

[0112] Qsim: Predicted Flow Rate

[0113] The relative error (RE) indicates the percentage error in terms of the total quantity of water predicted compared to the actual quantity over the prediction period, while the root mean square error (RMSE) allows comparison of the models with each other in terms of general performance (underestimation, overestimation, quantity...)

[0114] First, the short-term performance of the models is checked. Thus, the aim is to predict the flow rate two weeks after the calibration date.

[0115] The available data series is almost 20 years long. The year 2021, with its 53 weeks, is used as the test period. The models are trained up to week S of 2021 and predict the flow rate for weeks S+1 and S+2.

[0116] The squared error of the different models for a first and a second source is illustrated by the graphs in Figures 5 and 6.

[0117] The relative error of the different models for a first and second source is illustrated by the graphs in Figures 7 and 8.

[0118] It is observed that for both sources, machine learning models are the best, with average relative errors of less than 0.5% for the first source and 2.5% for the second source. Hybrid models with average relative errors of around 1% for the first source, and 3.5% for the second source, are very acceptable, taking into account that they make up for the error of the GR5J which is very high; namely 3.8% for the first source and 8.1% for the second source.

[0119] The predictions of each of the tested models are visible in figures 9 and 10. It can be seen that the predictions of the hybrid_RF and hybrid_SVM models follow the actual throughput.

[0120] The medium-term performance of the models is then checked.

[0121] The available data series is divided into a calibration part and a part test.

[0122] The years 2013 to 2022 serve as test years for the first source; the remainder is used for calibration and training. For the second source, the years 2011 to 2018 are chosen for testing.

[0123] The performance evaluation of each model is carried out as illustrated in [Fig.11]: • Calibration of the model over the 10 years prior up to March of the test year. • Testing over the period from April to December of the test year.

[0124] The quadratic errors of the different models are illustrated by the graphs in Figures 12 and 13 for each of the two sources.

[0125] The relative errors of the different models are illustrated by the graphs in Figures 14 and 15 for each of the two sources.

[0126] Hybrid models prove to have the best performance for the first source with an average error of about 1.5%, with a slight advantage for the model based on random forests.

[0127] The predictions of each of the tested models are visible in Figures 16 and 17. It can be seen that the predictions of the hybrid_RF and hybrid_SVM models follow the actual throughput.

[0128] The performance of the models is checked on ensemble forecasts.

[0129] An ensemble forecast in hydrology is a type of forecast based on execution Multiple simulations of a numerical forecasting model are run with slightly different initial conditions or model parameters. The results of these simulations are used to generate a range of possible outcomes for future hydrological conditions, including river water levels, flows, and precipitation.

[0130] Ensemble forecasts in hydrology are used to provide information on flood risks and drought conditions, which may have significant impacts on communities, agriculture and the environment. They are used by water managers to plan the use of water resources, including irrigation activities, recreational activities and flood management projects.

[0131] Ensemble forecasts in hydrology are a valuable tool because they provide a range of possible outcomes for future hydrological conditions, which allows for better risk assessment and informed water management decisions.

[0132] The “skill score” is a statistical indicator used to assess the quality of hydrological forecasts. It is also used for meteorological forecasts. It measures the difference between observed and predicted values, taking into account the natural variability of the phenomenon studied.

[0133] The skill score compares the performance of a forecast against a reference, which may be a climatological average, a forecast based on simpler methods, or a previous observation. It thus makes it possible to determine whether a forecast is better than the reference used.

[0134] A positive score indicates that the model predicts better than the reference model. A negative score indicates that the model performs worse than the reference model. A performance score of zero indicates that the model and the reference model have equivalent performance.

[0135] For each test year, the 20 climatological scenarios preceding the year are selected to construct a set of climate scenarios. The models are then rerun for each scenario, generating 20 hydrological scenarios per model. These are averaged to obtain a representative scenario on which a skill score is calculated relative to a reference model, which is—for each time step—the average of historical flows over a rolling 20-year period.

[0136] The skill score used for this study is the SSrmse defined by the following formula: RMSE (model) SS Ji A.fait — 1- ---------;........................ RMSE (reference)

[0137] With: • RMSE(model): is the root mean square error of the model being studied • RMSE(reference): is the root mean square error of the reference model.

[0138] The following tables 3 and 4 summarize the performance of the different models over the medium term, with the weather ( {ModelName} + Weather) and with the forecast set ( {ModelName} + Scenario), as well as the skill scores related to these performances.

[0139] Table 3 shows the RMSE root mean square error of the different models and of the reference model for each year for the first source. [Tables 3] hW : K m > / 1 / VS ", f A / » । R / <,Jt 1K<. i AiüfMfW «Jj Ji / Ï ? vX' ÿ ' ■* 2W - 4 aa • ' 2b J y WU* w S *4' 2^ »? <.7 OO I 2^^ B \xx? 5« "ÎX'. 2' / 2b'. K:.....to?.....1 2( / 2 / I22I4É2IIIIO Ws* xt<- w ] 2 22 xMJ? 4:2:24::2 : : : € xi! 7M> i ï2^2 : 55P£ ■ i / / )355!

[0140] Table 4 shows the skill score of the different models (zero value not significant) for the reference model) for each year for the first source. [Tables 4] 1 ><• The fl '' , P iiiiiiiiiiii ïV P ' lîiiiiilMiiSI A< $•<;<«' ss ,n^ 2 _________________; :1 ..... Sìiiliiiiii^OiSisiO . <Jÿs llliiBl BOmiIBBBB J...... tf JWJ| 1111¾¾ IIIIII^^ illll® <>iiiHiiiii im®n 2:2:2:2::^2:3:2:2:2:2: 2fi^^ «^iS ...................................... 1111222111 2:2:2:2:032:2:2:2): it ^2t :333222222222224sssssssssssss32: lllloOlill illiiilll t: iiïHiii 21110222 :2:2:2434^:2:2:: 1 x ÿ.Cx I <l.r r ». i 7 u

[0141] The invention is not limited to the embodiments shown and other embodiments will be obvious to a person skilled in the art.

[0142] In the definitions given in this description, when steps follow one another, the order indicated is only imposed insofar as a result used in a step is obtained in a previous step. Otherwise, the order of the steps may be arbitrary.

Claims

Claims

1. Method for forecasting the availability of water resources at a calculation time, from input precipitation data over a predetermined time interval and historical data recorded over a historical period prior to said given time, said historical data consisting of input precipitation data and output water flow data, characterized in that it combines: - a conceptual rain-flow reservoir model, the parameters of which are calibrated to coincide with the historical data, - a machine-learning model, the training of which has been carried out on the basis of the historical input data and output data consisting of a difference observed between: a) a retrospective flow forecast provided by the conceptual reservoir model calibrated on the historical data, at each instant of the historical period,b) the water flow recorded at the same instant of the historical period, the forecast consisting of - obtaining, from the conceptual model with a reservoir calibrated on the historical data, a provisional flow forecast at the calculation instant, from the input data over the predetermined time interval, - obtaining, from the machine-learning model, a correction forecast at the same calculation instant and from the same input data over the predetermined time interval, - combining the provisional forecast and the correction forecast to obtain a flow forecast.,

2. Method according to claim 1, according to which a time step between two calculation instants is constant.

3. A method according to any preceding claim, wherein a specific cleaning algorithm is used to clean and validate the historical data before calibrating the conceptual model and training the machine learning model.

4. A method according to any preceding claim, wherein evapotranspiration data is added to the precipitation data and these precipitation and evapotranspiration data are taken into account as input data by the models.

5. A method according to any preceding claim, according to in which the reservoir model is the Rural Engineering model with n Daily parameters (designated GRnJ), with, preferably, n=4 and even more preferably, n=5

6. A method according to any preceding claim, wherein the machine-learning model follows a so-called random forest algorithm.

7. A method according to any one of claims 1 to 5, wherein the machine-learning model follows a support vector algorithm.

8. Method according to any one of the preceding claims, comprising a monitoring step consisting of checking whether the forecast is included in an interval of so-called acceptable values ​​and triggering an alert if said forecast falls outside said interval of so-called acceptable values.

9. Water resource availability forecasting tool consisting of a computer program product comprising instructions for implementing the method according to any one of the preceding claims.

10. System for forecasting the availability of water resources, comprising: - data carriers capable of containing historical precipitation and water flow data recorded over a historical period, - calculation means having at least read access to the data carriers, - a storage memory accessible in read and write mode by the calculation means and containing instructions executable by the calculation means, characterized in that said instructions implement, when executed by the calculation means: - a conceptual model with rain-flow reservoirs, a model whose parameters are calibrated to coincide with historical data contained in the data carriers, and - a machine-learning model,whose learning was carried out on the basis of historical input data contained in the data media and output data consisting of a difference observed between: a) a retrospective flow forecast provided by the conceptual reservoir model, calibrated on the historical data, at each instant of the, historical period, (b) the water flow recorded at the same time in the historical period, said instructions making it possible to obtain, when executed by the calculation means, - by implementing the reservoir model calibrated on historical data, a provisional flow forecast at the calculation time, from the precipitation and evapotranspiration input data over the predetermined time interval, - by implementing the machine learning model, a correction forecast at the same calculation time and from the same input data over the predetermined time interval, - a combination of the provisional forecast and the correction forecast to obtain a flow forecast.

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