Method, tool and system for forecasting the availability of water resources

Abstract

The invention relates to a method for forecasting the availability of water resources at a time of calculation, on the basis of precipitation input data over a predetermined time period and of historical data recorded over a historical period prior to the given time, the historical data consisting of precipitation input data and, optionally, of evapotranspiration and water runoff output data. The method combines: - a conceptual model with rainfall-runoff reservoirs, the parameters of which model are calibrated to coincide with the historical data; - a machine learning model, the learning of which has been carried out on the basis of the historical precipitation input data and of output data consisting of a deviation observed between: a) a retrospective runoff forecast provided by the conceptual model with a reservoir calibrated using the historical data, at each time in the historical period; b) the water runoff recorded at the same time in the historical period, wherein the forecast consists in: - obtaining, from the conceptual model with a reservoir calibrated using the historical data, a provisional runoff forecast at the time of calculation and on the basis of the precipitation input data over the predetermined time period; - obtaining, from the machine learning model, a correction forecast at the same time of calculation and on the basis of the same input data over the predetermined time period; - combining the provisional forecast and the correction forecast to obtain a runoff forecast. The invention also relates to a forecasting tool and system.

Description

Title of the invention: Method, tool and system for forecasting the availability of water resources [1] The invention relates to the forecasting of water resource availability at different time horizons. [2] Water resources are a major issue in the context of climate change and population growth. [3] 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. [4] There are essentially two main categories of models, namely conceptual models and machine learning models. [5] Conceptual models are based on a theoretical approach to flows. A natural basin is considered as a reservoir that fills with rainwater and empties by flows into lower basins and by evaporation. These models are theoretically accurate, but suffer from the lack of spatial knowledge of the modeled objects, such as the limits of impermeability, the location of karst cavities, the evaporation of surface water, etc. This is particularly true for hydrogeological models, which raise the difficulty of combining, on the one hand, internal runoff from the carbonaceous rock itself and diffuse infiltration in upper layers of the rock, resulting from external runoff on less permeable rocks until reaching the limestone rock, and on the other hand, concentrated flows in karst conduits. [6] With perfect modeling of the site studied, a conceptual model should reflect reality with very low error. This is obviously never the case given that detailed knowledge of a terrain is very difficult and simplifications are necessary, prohibiting a global approach to the phenomena of internal flows in geological layers. [7] A machine learning model is 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. [8] 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 water resource availability data with a greater or lesser time lag. A learning algorithm analyzes this data to train a model. Once the model is trained, it can be asked to provide a forecast of water resource availability based on recent rainfall records or even weather forecasts. [9] Machine learning methods are very promising, particularly due to increasing data capture and computational capabilities. Rainfall and water flow over several years can be recorded with a certain precision, which increases the efficiency of the model. With a well-trained model, one can also hope to obtain a forecast from recent rainfall data, or even from meteorological rain forecasts.

[0010] An advantage of machine learning methods is that they do not rely on detailed knowledge of the terrain being studied. However, there appears to be a limit to improving the quality of predictions, as it has been found that increasing 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 the availability of water resources which provides better results than the methods of the state of the art, without having to overcome the drawbacks of the two known methods, that is to say without having to indefinitely increase the knowledge of the terrain studied to apply a conceptual method, nor indefinitely increase the quantity of learning data to apply machine learning methods.

[0012] The subject of the present invention is a method for forecasting the availability of water resources at a calculation time, from precipitation input data over a predetermined time interval and historical data recorded over a historical period prior to said given time, said historical data consisting of precipitation input data and water flow output data, characterized in that it combines: - a conceptual rain-flow reservoir model, whose parameters are calibrated to match historical data, - a machine-learning model, which was trained on the basis of 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 - obtain, from the conceptual reservoir model calibrated on historical data, a provisional flow forecast at the calculation time, from the input data over the predetermined time interval, - obtain, from the machine-learning model, a correction forecast at the same calculation time and from the same input data over the predetermined time interval, - combine the provisional forecast and the correction forecast to obtain a flow forecast.

[0013] For the purposes of the invention, “calculation time” means a date in a period of time for which a forecast is made. This may be a day or an hour.

[0014] Preferably, a time step between two calculation times is constant. This is called a regular time step. However, it is possible, according to the invention, to use an irregular time step.

[0015] Preferably, a specific cleaning algorithm is used to clean and validate historical data before calibrating the conceptual model and training the machine learning model.

[0016] According to a particular implementation mode, 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.

[0017] According to a particular embodiment of the invention, the reservoir model is the Rural Engineering model with n Daily 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 41 1 (1 - 2):66- 76. doi: 10.1016 / j.jhydrol.201 1.09.034.

[0018] According to a particular embodiment of the invention, the machine learning model follows a so-called random forest algorithm.

[0019] In one particular implementation, the machine-learning model follows a support vector algorithm.

[0020] In a particular implementation mode, the method comprises a monitoring step consisting of checking whether the forecast is included in a range of so-called acceptable values ​​and triggering an alert if said forecast falls outside said range of so-called acceptable values.

[0021] According to other optional features of the invention, taken alone or in combination:

[0022] - the GR5J model is modified to optimize the contributing area of ​​the basin,

[0023] - the GR5J model is modified in its search limits of its X4 parameter,

[0024] - the GR5J model is modified by increasing the initialization period of the models.

[0025] The invention also relates to a tool for predicting the availability of water resources, consisting of a computer program product comprising instructions for implementing the method described above.

[0026] The invention also relates to a system for forecasting the availability of water resources, comprising: - data media capable of containing historical precipitation and water flow data recorded over a historical period, - computing means having at least read access to data media, - a storage memory accessible in reading and writing by the calculation means and containing instructions executable by the calculation means, characterized in that said instructions implement, when they are executed by the calculation means: - a conceptual rain-flow reservoir model, the parameters of which are calibrated to match historical data contained in the data carriers, and - a self-learning model, the learning of which was carried out on the basis of historical input data contained in the data carriers 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, said instructions making it possible to obtain, when executed by the computing means, - by implementing the reservoir model calibrated on historical data, a provisional flow forecast at the calculation time, from the 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.

[0027] The options defined for the above process also apply to the tool and the system. Brief description of the figures

[0028] The invention will be better understood on reading the following description, given solely by way of example and with reference to the appended drawings in which:

[0029] [Fig. 1] represents flow data for a first source, in its raw form,

[0030] [Fig. 2] represents flow data for a second source, in its raw form,

[0031] [Fig. 3] represents the flow data of Figure 1, after cleaning, with meteorological data,

[0032] [Fig. 4] represents the flow data of Figure 2, after cleaning, with meteorological data,

[0033] [Fig. 5] is a graph showing the squared error of different models on the first source,

[0034] [Fig. 6] is a graph showing the squared error of different models on the second source,

[0035] [Fig. 7] is a graph showing the relative error of different models on the first source,

[0036] [Fig. 8] is a graph showing the relative error of different models on the second source,

[0037] [Fig. 9] is a graph showing the predictions of each of the models tested on the first source,

[0038] [Fig. 10] is a graph showing the predictions of each of the models tested on the second source,

[0039] [Fig. 11] is an illustration of the calibration method for the medium-term test,

[0040] [Fig. 12] is a graph representing the squared errors of the different models for the first source,

[0041] [Fig. 13] is a graph representing the squared errors of the different models for the second source,

[0042] [Fig. 14] is a graph representing the relative errors of the different models for the first source,

[0043] [Fig. 15] is a graph representing the relative errors of the different models for the second source,

[0044] [Fig. 16] is a graph representing the predictions of each of the models tested for the first source

[0045] [Fig. 17] is a graph representing the predictions of each of the models tested for the second source Detailed description

[0046] It is recalled 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 with the aim of linking the water layer precipitated on a watershed and its outlet. It is built on the basis of large data sets as well as on the discovery of the structure that best reproduces the hydrological behavior of a watershed, that is to say the response of the watershed to rainfall. It is a hydrological model that operates a triple globalization of the watershed system: at the process, space and time levels. Several versions have been proposed over time, the latest being that of Perrin et al. (2003).

[0047] The model parameters are: - X1: The capacity of the ground tank (mm) - X2: The underground exchange coefficient (mm / day) - X3: The one-day capacity of the routing tank (mm) - X4: The base time of the unit hydrograph HU1 (days) X5: Dimensionless threshold parameter, which allows the direction of water table exchanges to be modified during the year depending on the water level R in the routing reservoir in relation to this threshold.

[0048] 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.

[0049] 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 under low flow conditions.

[0050] Figures 1 and 2 represent flow data for two sources, in their raw form.

[0051] Using a cleaning algorithm specific to these two sources, this data was cleaned in preparation for running the models.

[0052] The result of this cleaning is presented in Figures 3 and 4, with the addition of a graphical visualization of the meteorological data.

[0053] The data available for both sources are precipitation P, potential evapotranspiration ETP and source discharge Q at daily time steps, over a period of almost 20 years (from 2001 to 2021).

[0054] For the tank models, in the described embodiment, the invention uses the GR4J models 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 indicated, an advantage for the GR5J model gave it preference.

[0055] Three modifications are made to this model to make it suitable for groundwater modeling:

[0056] 1st modification: Optimization of the contributing area of ​​the basin at the same time as the other parameters.

[0057] Knowing the area of ​​a spring's hydrogeological catchment area is a crucial step. Without knowing the area, the GR model is unusable since it uses this area to convert flows expressed in m3 / time step into flows expressed in mm / time step.

[0058] Either the topographic area is available and is then used, or the Turc-Mezentsev equations are used, which relate long-term discharge to long-term precipitation and evapotranspiration. These equations are expressed as follows:

[0059] These two equations allow us to have a first estimate of the surface area S of the watershed from this transformation S = Q / (PE)

[0060] The surface area S thus obtained can sometimes differ from the topographic surface area, in particular due to different hydrogeological and climatic phenomena which govern the flow, i.e. drainage, exchanges with a river, etc.

[0061] A topographic area correction hypothesis is introduced in the form of a new parameter a such that: S e ff = a*S

[0062] This new parameter allows the contribution area of ​​the watershed surface area to the flow to be corrected. It is calibrated with the five other parameters of the GR5J model using the SUBPLEX optimization algorithm described for example in the article Anon. sd “PDA SUBPLX”, accessible at the following address: http: / / star-www.rl.ac.uk / docs / sun194. htx / sun194ss82.html.

[0063] 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. [Table 1]

[0064] 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.

[0065] 3rd modification: Increased the initialization period of the models, because the aquifers have a large storage capacity, which implies that the reservoirs in the model take longer to reach a saturation state.

[0066] The modifications to the GR5J model result in the improvements seen in Table 2 below. [T able 2] X1 X2 X3 X4 X5 a KGE

[0067] The GR4J, GR5J and GR6J models require data at daily time steps, 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 provided) • Maximum, minimum and average temperature are optional

[0068] The variables used for the GR5J model are thus fixed.

[0069] According to the invention, the GR5J reservoir model is combined with a machine learning model that corrects its errors.

[0070] For this purpose, the “random forest” (hereinafter RF) and “support vector” (hereinafter SVM) learning models 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.

[0071] The weekly time step of the machine learning models is retained for this combination.

[0072] 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 sum over 4, 12, 26 and 52 weeks of effective rainfall (translation of monthly, quarterly, half-yearly and annual recharge) • Residual: refers to the difference in flow between two successive weeks £(S)=QsimGR(S)~ Qobs(S)

[0073] The use of deltas overcomes the difficulty that predicting source discharge using the random forest algorithm requires knowing the discharge at two previous time steps. However, if the extreme discharge values ​​during floods and low flows were not provided in the model's training data, the model cannot predict these values. With predictions of increases or decreases in discharge, referred to as deltas, this difficulty is overcome. • A lag over the previous 2 weeks for the residual variable • GR5J flow rate

[0074] Both hybrid models (hybrid RF and hybrid SVM) use all the variables described above to estimate the error of the GR5J model.

[0075] Recall 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 grown by independently sampling values ​​from a random vector with the same distribution for all trees in the forest.

[0076] The random forest technique considers instances individually so that the 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 of the prediction is considered the selected prediction.

[0077] It is also recalled that support vector models are neural networks whose training is based on structural risk minimization instead of empirical risk minimization of artificial neural networks. The support vector algorithm simultaneously minimizes the empirical error and the complexity of the model, which can improve the generalization ability of the model for classification or regression problems in many disciplines. This is achieved by minimizing an upper bound on the test error rather than minimizing the training error.

[0078] For each week S, the residuals of the two previous weeks are used to estimate the residual of week S. e(ti) = model[£(ti-i), e(ti-2), other variables] for week 1 of prediction e(t2) = model[£(ti), £(ti-i), other variables] for week 2 of prediction £(t) = model[£(ti-i), £(ti-2), other variables] after week 2 of prediction

[0079] The terms £(ti-i) and E(ti-2) signify the difference between the measured flow rate and the flow rate modeled by the GR5J model, respectively 1 and 2 weeks before the first week of prediction.

[0080] The flow rate is finally obtained by the equation Qsim(S)=QsimGR(S) - £(S) with: Qsim: Predicted flow rate QsimGR: Flow predicted by GR5J, also called provisional flow £: the estimated residual

[0081] Thus, a method for determining the predicted flow consists of obtaining from the conceptual model, here the GRJ5 model, a provisional flow for a given instant, here a week S, obtaining from the machine learning model, here either the random forest type algorithm or the support vector algorithm, an estimated residual for this given instant. The method for determining the flow finally consists of obtaining the predicted flow by combining the provisional flow and the estimated residual.

[0082] Advantageously, the method comprises a monitoring step, also called a surveillance step, consisting of checking whether the predicted flow rate is within a range of so-called acceptable values ​​and triggering an alert if the predicted flow rate falls outside said range of so-called acceptable values.

[0083] To evaluate the performance of the models, two errors were calculated, the relative error RE in %, and the squared error RMSE. with : Qobs: Observed flow rate Qsim: Predicted flow rate

[0084] The relative error (RE) provides information on the percentage error in terms of the total quantity of water predicted compared to the actual one over the prediction period, while the square error (RMSE) allows models to be compared with each other in terms of general performance (underestimation, overestimation, quantity, etc.)

[0085] First, we check the short-term performance of the models. We therefore seek to predict the flow rate for the two weeks following the calibration date.

[0086] 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.

[0087] The squared error of the different models for a first and a second source is illustrated by the graphs in Figures 5 and 6.

[0088] The relative error of the different models for a first and a second source is illustrated by the graphs in Figures 7 and 8.

[0089] We see that for both sources, the 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. The hybrid models with average relative errors of order 1% for the first source, and 3.5% for the second source, are very acceptable, taking into account the fact that they catch up with the GR5J error which is very high; namely 3.8% for the first source and 8.1% for the second source.

[0090] The predictions of each of the tested models are visible in Figures 9 and 10. We can see that the predictions of the hybrid_RF and hybrid_SVM models follow the actual flow rate.

[0091] The medium-term performance of the models is then checked.

[0092] The available data set is divided into a calibration part and a test part.

[0093] The years 2013 to 2022 serve as test years for the first source, the rest is used for calibration and training. For the second source, the years 2011 to 2018 are chosen for testing.

[0094] The performance evaluation of each model is done as illustrated in Figure 1 1: • Model calibration over the 10 years prior to March of the test year. • Test over the period from April to December of the test year.

[0095] The squared errors of the different models are illustrated by the graphs in Figures 12 and 13 for each of the two sources.

[0096] The relative errors of the different models are illustrated by the graphs in Figures 14 and 15 for each of the two sources.

[0097] The hybrid models are found to have the best performance for the first source with an average error of about 1.5%, with a slight advantage for the random forest-based model.

[0098] The predictions of each of the tested models are visible in Figures 16 and 17. We can see that the predictions of the hybrid_RF and hybrid_SVM models follow the actual flow rate.

[0099] The performance of the models is checked on ensemble forecasts.

[0100] An ensemble forecast in hydrology is a type of forecast based on running multiple simulations of a numerical prediction model 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, discharges, and precipitation.

[0101] Ensemble forecasts in hydrology are used to provide information on flood risks and drought conditions, which can 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.

[0102] Ensemble forecasts in hydrology are a valuable tool because they provide a range of possible outcomes for future hydrological conditions, allowing for better risk assessment and informed water management decisions.

[0103] The skill score is a statistical indicator used to assess the quality of hydrological forecasts. It is also used for weather forecasts. It measures the difference between observed and predicted values, taking into account the natural variability of the phenomenon studied.

[0104] The skill score compares the performance of a forecast against a reference, which can 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.

[0105] If the score is positive, it indicates that the model predicts better than the baseline model. If the score is negative, it means that the model performs worse than the baseline model. A skill score of zero indicates that the model and the baseline model have equivalent performance.

[0106] For each test year, the 20 climate scenarios preceding the year are selected to construct a set of climate scenarios. The models are then relaunched on each scenario, constructing 20 hydrological scenarios per model. These are averaged to obtain a representative scenario on which a skill score is calculated. calculated in relation to a reference model, which is - for each time step - the average of historical flows over 20 rolling years.

[0107] The skill score used for this study is the SSRMSE defined by the following formula: RMSE(model) SS RM SE — 1 RMSE(reference) With : • RMSE(model): is the squared error of the model studied • RMSE(reference): is the squared error of the reference model.

[0108] Tables 3 and 4 below summarize the performances of the different models over the medium term, with the weather ({ModelName} + Weather) and with the forecast ensemble ({ModelName} + Scenario), as well as the skill scores linked to these performances.

[0109] Table 3 shows the RMSE squared error of the different models and the reference model for each year for the first source. [Table 3]

[0110] 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. [Table 4]

[0111] Advantageously, a system for determining the predicted flow rate comprises data carriers, calculation means and a storage memory. The data carriers are advantageously capable of containing historical precipitation and water flow data recorded over a historical period. The calculation means are advantageously configured to access the data carriers at least in read mode. storage memory is advantageously configured to be accessible in reading and writing by the calculation means. Advantageously, the storage memory comprises instructions executable by the calculation means. When the instructions are executed, they implement the method for determining the predicted flow rate.

[0112] In particular, when the instructions are executed, they implement the conceptual reservoir model and the machine learning model, in order to obtain the provisional flow rate, the estimated residual and to obtain the predicted flow rate by combining the provisional flow rate and the estimated residual.

[0113] The invention is not limited to the embodiments presented and other embodiments will become apparent to those skilled in the art.

[0114] In the definitions given in this description, when steps follow one another, the order indicated is only imposed to the extent that a result used in one step is obtained in a previous step. Otherwise, the order of the steps can be any.

Claims

Claims

1. Method for determining a predicted flow rate at a calculation time, from precipitation input data over a predetermined time interval and historical data recorded over a historical period prior to said given time, said historical data consisting of precipitation input data and water flow output data, characterized in that it combines: - a conceptual rain-flow reservoir model, whose parameters are calibrated to match historical data, - a machine-learning model, the training of which was carried out on the basis of 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 method consisting of - obtain, from the conceptual reservoir model calibrated on historical data, a provisional flow rate at the calculation time, from the input data over the predetermined time interval, - obtain, from the machine learning model, an estimated residual at the same calculation time and from the same input data over the predetermined time interval, - obtain the predicted flow rate by combining the provisional flow rate and the estimated residual.

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, comprising using a specific cleaning algorithm 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. Method according to any one of the preceding claims, according to 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 predicted flow rate is included in an interval of so-called acceptable values ​​and triggering an alert if the predicted flow rate falls outside said interval of so-called acceptable values.

9. A system for determining predicted flow rate, comprising - data media capable of containing historical precipitation and water flow data recorded over a historical period, - computing means having at least read access to data media, - a storage memory accessible in reading and writing by the calculation means and containing instructions executable by the calculation means, characterized in that said instructions implement, when they are executed by the calculation means - a conceptual rain-flow reservoir model, the parameters of which are calibrated to match historical data contained in the data carriers, and - a self-learning model, which was trained on the basis of historical input data contained in the data carriers and output data consisting of a deviation 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, 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 rate at the time of calculation, from the input data of precipitation and evapotranspiration over the predetermined time interval, - by implementing the machine learning model, a residual estimated at the same calculation time and from the same input data over the predetermined time interval, - a predicted flow rate, by combining the provisional flow rate and the estimated residual.

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