# Large-scale seasonal forecasts of river discharge by coupling local and global datasets with a stacked neural network: Case for the Loire River system

M. T. Vu, Abderrahim Jardani, M. Krimissa, F. Zaoui, Nicolas Massei

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M. T. Vu, Abderrahim Jardani, M. Krimissa, F. Zaoui, Nicolas Massei. Large-scale seasonal forecasts of river discharge by coupling local and global datasets with a stacked neural network: Case for the Loire River system. Science of the Total Environment, 2023, 897, 10.1016/j.scitotenv.2023.165494. hal-04290103

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<figure><img src="image_1.png" /></figure>
Large-scale seasonal forecasts of river discharge by
coupling local and global datasets with a stacked neural
network: Case for the Loire River system

M. T. Vu ¹,*, A. Jardani ¹, M. Krimissa², F. Zaoui², N. Massei¹

¹ Université de Rouen, M2C, UMR 6143, CNRS, Morphodynamique Continentale et Côtière, Mont Saint

Aignan, France

² Electricité de France EDF, Le Département Laboratoire National d'Hydraulique et Environnement (LNHE), 6

Quai Watier, Chatou, France

* Corresponding author: minh-tan.vu@univ-rouen.fr

Emails: minh-tan.vu@univ-rouen.fr; abderrahim.jardani@univ-rouen.fr; mohamed.krimissa@edf.fr;

fabrice.zaoui@edf.fr; nicolas.massei@univ-rouen.fr.

*In preparation for Science of the Total Environment*
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**Abstract**

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Accurate prediction of river discharge is critical for a wide range of sectors, from human activities to environmental hazard management, especially in the face of increasing demand for water resources and climate change. To address this need, a multivariate model that incorporates both local and global data sources, including river and piezometer gauges, sea level, and climate parameters. By employing phase shift analysis, the model optimizes correlations between the target discharge and 12 parameters related to hydrologic and climatic systems, all sampled daily. In addition, a stacked LSTM - a more complex neural network architecture - is used to improve information extraction ability.

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Exploring river dynamics in the Loire-Bretagne basin and its surroundings, the investigation delves into predictions in daily time steps for one, three, and six months ahead. The resulting forecast features high accuracy and efficiency in predicting river discharge fluctuations, showcasing superior performance in forecasting drought periods over flood peaks. A detailed examination on data used highlights the significance of both local and global datasets in predicting river discharge, where the former dictates short-term predictions, while the latter drives long-range forecasts. Seasonally extended forecasting confirms a strong connection between the forecast leading time and the shift in data correlation, with lower correlation at a lag of 3 months due to seasonal changes affecting forecast quality, compensated by a higher correlation at a longer lag of 6 months. Such mutual effect in this multi-time-step forecasting improves the predictive quality of a six-month horizon, thus encourages progress in long-term prediction to a seasonal scale. The research establishes a practical foundation for effectively utilizing big data to leverage long-term forecasting of environmental dynamics.

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**Keywords:** Forecast, River discharge, Stacked LSTM, Deep Learning, Big data, Loire Bretagne Basin.

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# 1. Introduction

Accurately predicting streamflow is an important task that impacts many areas, from agriculture and recreation management to industrial purposes and environmental disaster management. Very often, predictive models are designed to prevent extreme events such as floods and droughts which can have dramatic consequences for the environment and human life (Mosavi, et al., 2018; Sit, et al., 2020). In this field, many forecasting models have been developed over the last decade using various physics-based or black-box approaches to help public agencies better anticipate the occurrence of such events at different short- and long-term time horizons. However, in the context of climate change, the agencies increasingly need to elaborate water management plans and environment protections toward long-term forecasts of the basin state that can span over months, seasons, and even years (Karpatne, et al., 2019). As the forecasting horizon lengthens, more data are needed to capture generalized phenomena and processes of different types at different scales that control basin functionality, especially with respect to drought events. This context naturally leads to larger data sets required to build a powerful predictive model that can handle increasingly complex data (Shen, 2018).

Over the past decade, data-driven models have revolutionized the field of water dynamic forecasting with their ability to efficiently approximate nonlinear relationships between the river discharge and the meteorological, geological, and anthropogenic factors that control it. Among these models, artificial neural networks (ANNs) have emerged since the 1960s and now represent an attractive alternative for both short- and long-term forecasting (Dramsch, 2020; Shen, 2018). In recent years, new generations of neural networks have emerged, of which the mechanisms are adapted to process time series by efficiently capturing temporal dependencies while preserving the memory effect, such as the long short-term memory -LSTM (Hochreiter & Schmidhuber, 1997). LSTM has been applied in various ways to improve streamflow forecasting, such as using past streamflow data at the same location as an autoregression to predict future fluctuations (Zhu, et al., 2020; Sahoo, et al., 2019; Mehedi, et al., 2022). It has also been used with the incorporation of multiple data, such as flow data from nearby streams and metrological data (Nguyen, et al., 2022; Fang & Shao, 2022; Vu, et al., 2023). Currently, the latter way, whose hydrologic prediction is based on the extraction of different
features from numerous data sources (e.g., air temperature, precipitation, and potential evapotranspiration), promises the most reliable long-term forecasts (Li & Yuan, 2023; Girihagama, et al., 2022; Xiang, et al., 2020; Natel de Moura, et al., 2022). Despite the abundance of research in the field, the precise functional distribution of individual datasets, at both local and large scales, remains poorly understood. This lack of understanding presents a major obstacle for practitioners, as it impairs their ability to accurately predict short- and long-term outcomes using treated models.

In most cases, the hydraulic and climatic data processed are collected only on the territory of the basin studied, which limits the possibility of providing a large database to build an effective predictive model to grasp the seasonal hydraulic behavior of the basin. This territorial compartmentalization in the construction of predictive models has been imposed in hydrological studies as a real physical fact, but in practice it is a misconception the model simplification, since involving hydraulic and climatic continuity does not obey this compartmentalization. This means that regional observations, such as precipitation, temperature, or atmospheric pressure, obtained on a large continental or global scale can provide relevant information on the key climatic drivers of seasonal basin dynamics (Murphy, et al., 2010; Karpatne, et al., 2019). The use of local data alone thus entails more of a projection from climate variables than a prediction from the true driving forces. In addition, identifying atmospheric circulation patterns or teleconnections that cause extreme events has been an important step in predicting catchment flow behavior (Hagen, et al., 2021; Murphy, et al., 2010; Massei, et al., 2010). For example, in southeastern Australia, climate forcings influencing droughts originate from atmospheric circulation patterns emanating from the Pacific, Indian, and Southern Oceans (Dikshit, et al., 2021), while in western France they originate from the Atlantic Ocean (Massei, et al., 2010), in both cases related to annual cycles. These results have encouraged researchers to further exploit large-scale climate variables as predictors of long-term water system conditions (Ouma, et al., 2022; Dikshit, et al., 2021; Martin Santos, et al., 2021). However, the concept is still little known in the literature, mainly due to the difficulty of collecting such a large dataset from all over the world, of which the analysis hence requires a high comprehension and computational effort.
The deluge of data in the Earth system has reached unprecedented levels, with storage volumes exceeding tens of petabytes (Shen, 2018), and our ability to make sense of this data has not kept pace with our ability to generate and gather it. The first major challenge, therefore, concerns the data processing: how to extract interpretable information and knowledge from this massive amount of data and integrate it across disciplines to build interpretable models. A common solution is decomposition for dealing with non-linearity and non-stationarity in time series, e.g., wavelet transform (WT), empirical mode decomposition (EMD), and empirical ensemble mode decomposition (EEMD) (Gürsoy & Engin, 2019; Niu, et al., 2019; Zhang, et al., 2018). The combination of data preprocessing techniques and deep learning tools can surpass the performance of traditional models. Nevertheless, a challenge associated with these models is the computationally intensive process of identifying the optimal frequency components for each signal. Implementing these techniques on a large data set containing millions of time series can be daunting. In this study, we propose a simplified variant in which a single frequency is determined by resampling the time series of the input data, where the step size in resampling is chosen based on its ability to optimally reproduce the flow signal in the network output.

The second challenge concerns the neural network employed: More data requires a more complex model to translate the processed data, which often leads to higher-level neural architectures. Several studies have highlighted the exceptional ability of LSTMs to replicate streamflow fluctuations in catchments worldwide and to estimate the associated uncertainty, e.g., (Hunt, et al., 2022; Mehedi, et al., 2022; Natel de Moura, et al., 2022). Benchmarking on 516 basins across the continental United States, Gauch et al. (2021) further discovered that LSTMs trained on reanalysis data can predict streamflow at any given temporal resolution, even at multiple resolutions simultaneously. Training a single LSTM across multiple basins and incorporating data on basin geography outperformed individual LSTMs trained on a per-basin basis, resulting in superior performance even for ungauged basins. Surprisingly, simple LSTM architectures without stacking were performed as well as stacked ones in simulating discharge fluctuations (Le, et al., 2021; Chidepudi, et al., 2023). Although a single LSTM can predict a few time steps ahead, it becomes less effective for long-term forecasting with multiple time horizons, making stacked neural networks more prevalent (Chandra, et al., 2021; Wang
& Zhang, 2020). By incorporating multiple LSTM layers, more advanced neural architecture can extract intricate feature embeddings from diverse databases, resulting in longer and more precise outputs, particularly for multiple time steps. Existing research has predominantly concentrated on predicting individual lead times, limiting our comprehension of the interrelationships between different time step horizons. However, the primary objective of this present study is to overcome this limitation and explore the mutual influence of forecasts across multiple time steps.

This study presents a number of novelties including: i) Combining data sources from different scales and sources to achieve more complete coverage of input data, which improves the interpretability of forecasts. ii) Proposing an efficient technique for preprocessing millions of time series by choosing the optimal sampling frequency for seasonal forecasts. iii) Using a stacked LSTM architecture for seasonal horizon forecasts that evaluates the mutual effects between the multiple datasets and also between multiple time-step responses. The investigation delves deeply into the unique importance of individual datasets in driving predictive performance, as well as the interdependent impact on multi time-step forecasting, which have been relatively unexplored in practical research. Outcomes of this study aim to establish a foundation for exploiting big data to leverage the seasonal forecasting of hydrodynamics, which can also be extended to other environmental dynamics exhibiting similar fluctuation patterns. The proposed method is thus applied to forecast the river discharge in the Loire-Bretagne basin, the largest catchment in France, which is strongly affected by climate change and has experienced severe droughts in recent years. The research result should facilitate the development of an informed water and environmental management plan in the basin, with potential applications in other regions of the world.
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## 2. Study area and Data acquisition

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### 2.1 Study area

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Loire-Bretagne basin is the largest basin in France, with a total area of 155,000 km², representing 28% of the French territory (https://agence.eau-loire-bretagne.fr/). The hydrogeographic basin includes the watershed of Loire River and its tributaries, the coastal basins of the Vilaine, Bretagne and Vendee, and the marshes of the Poitevin. The main channel – the Loire River, is more than 1,000 km long, and its entire hydrographic network covers more than 135,000 km. The basin, with its extensive water system, is connected to a complex water cycle on both regional and global scales.

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The basin, with a coastline of 6,654 km, is first directly under the influence of the Atlantic Ocean forcing, into which it flows with a mean annual discharge of 850 m³/s at its mouth. The maximum mean monthly flow is about 1,630 m³/s in February and the minimum flow is 257 m³/s in August (Petelet-Giraud, et al., 2018), with a strong contrast between the dry and wet seasons. Similar conditions prevail in other rivers in the study area, with seasonal differences of tens to hundreds of times; some flows are even interrupted for days or weeks during dry summers. The cause for this is closely tied to the climatic contrasts between the dry summer and the heavy winter rains.

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The basin is characterized by heterogeneous river drainage between its upper and lower reaches and between the main river and its tributaries. Heterogeneity also exists in the climatic regime, which dominates in the upstream and downstream areas, where precipitation gradually increases towards the coast (downstream). The Loire discharge then increases along the river to the mouth, with an important contribution of the tributaries, especially in the upper and lower parts of the Loire. The discharge in the central part is rather related to the connection with the groundwater, the Beauce aquifer. One of these main aquifers extends into semi-permeable sedimentary rocks with numerous underground inflows into the northern basin. These inflows, however, represent only a few percent of the total river flow (Baratelli, et al., 2016). This therefore highlights an important characteristic of this basin: a weak connection between surface water and groundwater at the watershed scale.

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The basin is characterized by an average altitude of 300 m and mostly low valleys. Only slightly less than 10% of the basin's area is above 800 m with a maximum altitude of 1,500 m (Beaufort, et al., 2020), which explains why snow is rare and most of the natural supply comes from precipitation. Furthermore, precipitation itself varies from year to year between 550 and 2,100 mm/year, and this climatic alternation of wet and dry years determines the long-term hydrologic functioning of the basin. The interannual variation of river discharge is highly related to the North Atlantic Oscillation (NAO), with interannual modes of 17 and 5-7 years (Massei, et al., 2010). This implies that the hydrologic functioning of the basin may be under the influence of a larger and longer climate regime (Murphy, et al., 2010).

<figure><img src="image_2.png" /><figcaption>**Figure 1:** The Loire-Bretagne, the largest basin in France with a crucial environmental importance (modified from Agence de l'eau Loire-Bretagne). The red dots mark representative stations to be studied later.</figcaption></figure>

In terms of water use, the main river - the Loire, has often been referred to as “the last wild river” in Western Europe, due to the relative absence of large dams and the effective protection of natural
conditions along the river (http://www.uicn.org). Although some 35,000 ha of farmland are irrigated, consuming 500 million m³ (Rinaudo, et al., 2020), equivalent to only 2% Loire total annual discharge. The basin has a distinctly rural character highlighted by a low population density, with a total water exploitation of 1,000 million m³ for drinking (~ 4% of the Loire discharge). However, rivers are not the primary source of water use. Water use in this basin is remarkably comes from intense groundwater exploitation where the problem of over-extraction that is more serious than elsewhere in France (Rinaudo, et al., 2020). The rivers themselves also serve other local services, however the total water use of the catchment is relatively small compared to the discharge of all rivers. Due to lack of the water use scheme in detail, we thus consider only the natural variables in this study.

## 2.2 Data acquisition

The objective of the data collection strategy in this study is to relate regional characteristics contained in local hydrologic observations to the climatic cycle at a larger scale, including river discharge, piezometer, sea level, air temperature, atmospheric pressure, precipitation, soil moisture, relative humidity, and evaporation rate. Such a strategy aims to provide as much data as possible for the predictive model at various scales to arrive at a better understanding of the functioning of the water cycle as a whole system. Time series variables are collected from relevant sources that fall into the following categories: a) gauging observations; b) hydrogeo-meteorological datasets (see Table S1.1 in Supplementary 1). In which, the former are punctual ground-based measurements while the latter are interpolated grid analyses.

The punctual ground gauges measure discharges in rivers, water levels in aquifers throughout the watershed, and tides on ocean coasts. In the rivers, the monitoring is recovered from the HYDRO database including the discharge at 1,614 stations over a long span from 1900 to 2022 in daily frequency. Groundwater levels are extracted from the ADES database with records at about 1,700 piezometers from the year 1900 to 2022 (see Figure S1.1). Sea levels are collected from REFMAR database which provide a total of 368 active stations in the oceans, focusing on the coastlines of France and the United States, with up-to-date records from the year 2000 to 2022. Indeed, the
motivation to consider tides in the dataset lies not in the connection between rivers and seas in the tidal zone at river mouths, but in the importance of seawater in the global water cycle. Storing 23 times the water on land and millions of times the water in the atmosphere, the oceans buffer fluxes many times greater than the terrestrial equivalent. Ocean dynamics must therefore be central to the water cycle picture of interactive relationship between ocean, atmosphere, and land, which has received little attention in forecasting models recently. The gridded datasets in this study are gathered from the NOAA reanalysis with daily calibration from 1948 to 2022, including air pressure, air temperature, precipitation rate, volumetric soil moisture, relative humidity, and potential evaporation rate. Spatial coverages are 2×2 and 2.5×2.5 degree in global grids (Kalnay, et al., 1996), of which the parameter properties are given in Table S1.1 and the corresponding maps are exampled in Figure S1.2 with other details in Supplementary 1. Finally, the overall datasets consist of around 1.5 million time series with different physical backgrounds and features.

Note that not all data refer to water, but to temperature and pressure, which are the key parameters controlling the behavior of the water cycle both on the continents and in the oceans. With such a heterogeneous database, we are in fact working with such a complex multiphysical phenomenon as the global water cycle. This big data can provide better insight into global climate dynamics, but also poses a challenge for the data processing to extract meaningful information to feed the forecasting model, which is the subject of the next subsection. The database can indeed be expanded to include other variables, such as solar radiation, cloud cover, or heat flux. As part of the information from these variables may already be embedded in the using data, upscaling the problem only leads to a minimal improvement in accuracy, but no further advances in methodology.

## 3. Data analysis

Data analysis is critical phase in river dynamic forecasting with a data-driven model, in which the quality and quantity of data used for modelling is key to prediction reliability. Analysis is about
underpinning the trend and identifying patterns in the available time series to produce an accurate forecast for the future. Working steps involve pre-processing the data, feature engineering and selecting the most relevant and representative information, all of which have a direct impact on forecast efficiency.

## 3.1 Data pre-processing

In pre-processing, the time series are cleaned, normalized, and transformed to make them suitable for analysis in the next step, and then fed into the neural network. The goal of this step is to improve the quality and utility of the measured data. The raw data is first processed to remove errors and fill measurement gaps. To limit the errors, the validated dataset is prioritized in this study with some manual intervention to eliminate visual anomalies, while the rest is considered as noise in the modeling which is later based on the neural network functionality. The gaps are filled with an autoregressive algorithm (Akaike, 1969), which is effective for short gaps; records with longer gaps are then left aside in the selection step because they have a lower correlation to the target.

Since processing time series maps require a huge computational memory to extract relevant features (Zhu, et al., 2017), we simply consider time series point by point at each map pixel to select the most relative series. This scheme may minimize large-scale interactions, but simplify processing. However, as discussed in Section 3.3, this simplification only has marginal impact on the resulting data as the behavior of climate parameters is consistent at large scales. The forecast is then established through the joint processing of highly related time series, which enhances the accuracy and reliability of the prediction. In this model, the projection mechanism works by using leading signals (positive lag, detailed in Supplementary 2), which provide early indications of potential changes through a combination of historical and current monitoring, to identify these changes in river dynamics.
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## 3.2 Data feature engineering: correlation between time series

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Hydrological responses are the result of the concomitance of several climatic, geological, anthropogenic, and oceanic factors, involving complex processes and interactions that occur at different time scales and frequencies. The presence of these phenomena leads to a strongly nonlinear behavior of hydrological responses, which makes their prediction a challenge. It is therefore essential to understand these phenomena by analyzing their multi-frequency behavior in order to ensure their usefulness as data in a forecasting procedure. Common methods for analyzing multifrequency signals include wavelet analysis, empirical mode decomposition, or the Fourier transform, which identify and separate different frequency components and model each component individually before combining them for the final prediction. These approaches can lead to accurate modelling, but processing millions of input series in this case requires excessive computational effort. In this approach, we propose a simplified estimation in dealing with time series, where the input data are resampled at a frequency that best fits the target signal, as shown in Figure 2. The figure examples how the time series in the database correlate with the target signal at different frequencies, where the target is the daily river discharge at station No.1, which is located downstream of the Loire River and exhibits minimal influence from human activities.
<figure><img src="image_3.png" /><figcaption>Figure 2: The discharge fluctuation at station No.1 exhibits varying correlations with other datasets sampled at different frequencies ranging from daily to monthly. This multi-frequency behavior highlights the need for thorough data analysis to derive meaningful frequencies for accurate forecasting.</figcaption></figure>

As shown in Figure 2a, the daily discharge at station No.1 shares the most similarity to the weeklies discharges at the other river stations in the basin, reflecting the downstream flow regime, which contains mainly low frequency. The analysis also confirms that the discharges at the stations in the basin are determined by low-frequency features at the basin scale, while the high-frequency signals are otherwise related to local conditions, as discussed in (Vu, et al., 2021) for the Seine catchment. The correlation between station measurements remains significantly high, indicating that flow conditions in the basin are consistent to some extent. Otherwise, the discharge signal agrees well with
the daily observations in the aquifer. The piezometer signal in fact also consists mainly of the low-frequency component and is closely related to recharge from the river flows through the filtration process, resulting in a delay in the piezometer signal compared to the discharge observations, which will be discussed in the next discussion on phase shifting. However, sea level shows little correlation with the river discharge signal in this case because station No.1 is not located in the tidal zone of the Atlantic Ocean. Although there is no direct relationship between the two, both are influenced by large-scale features of the global water system, such as climatic conditions, which causes some similarity between them at a low frequency. A loose relationship in this case complicates the use of sea level signals in the discharge forecasts but may be helpful in other studies where river and sea interact.

Climatic parameters such as temperature, atmospheric pressure, evaporation, and humidity show the strongest correlation with a monthly frequency, reaching a maximum correlation coefficient of about 0.7. This low correlation demonstrates a weak connection between these climatic variables and the river system, which has been backed up by previous research of (Wang, et al., 2022) since the hydrosystem involves multiple interacting variables, and each parameter can have a cascading, direct or indirect impact on the entire system. River discharge, on the other hand, is more closely related to accumulated precipitation (see Figure 2f). It is well known that runoff directly replenishes streamflow, resulting in a clear influence of precipitation on river discharge. A long-term accumulation of precipitation over two to three months exhibits a clear influence on river dynamics, as already mentioned in the drought studies (Sutanto, et al., 2020; Solaraju-Murali, et al., 2019). Soil moisture similarly shows an important impact on river dynamics, as illustrated in Figure 5g, with the highest correlation among the climatic parameters considered. This is also the conclusion of recent research by Chatterjee et al. 2022, in which soil moisture is considered an essential component for describing and predicting large-scale droughts. Indeed, subsurface soil moisture directly determines the effectiveness of runoff and other surface and subsurface discharges into rivers.
3.3 Data feature engineering: time lag between time series

Time lag estimation is important for forecasting dynamics to identify and account for the delay between cause and effect in a multivariate system. Understanding the time lag helps to better foresee how changes in one variable will affect another variable in the coming time steps with some certainty.

To continue the investigation from the previous section, Figure 3 demonstrates the time lag between the discharge signal at station No.1 and other parameters in the database, as well as their correlation.

<figure><img src="image_4.png" /><figcaption>Figure 3: Time lag and correlation between the discharge measurement at station No.1 and other parameters in the database. The analysis highlights the differences between the local and global datasets in predictive performance. While the local data (in figures a and b) mainly</figcaption></figure>
target a short-term lag, the global data (in the remaining figures) provide a much longer lag
with a clear decline in correlation due to the season shifts at the lag of about 90 days.

As the station being studied is located downstream, the majority of stations show a positive time lag to station No.1 with a strong correlation (see Figure 3a). This can be attributed to the clear connection in river flow through the stations, as the flow path follows the rivers within the basin, taking several days to a week to reach downstream which associates to a short time lag between flow signals. While such a short delay can be beneficial for short-term forecasting, as is often addressed in the literature (Zhu, et al., 2020; Mehedi, et al., 2022; Sahoo, et al., 2019), it is not sufficient for long-term forecasting, which often deals with monthly to seasonal lead times. In contrast, groundwater measurements in Figure 3b expose a long lag compared to surface water due to the recharge process that connects groundwater from the surface stream. In this case, recharge can take days to months to feed the subsurface aquifer depending on site conditions throughout the basin. As discussed in Section 2, groundwater in this basin does not supply much water to the river stream, with a marginal loading of less than 5% seasonal river flows, primarily around the Beauce Aquifer at the central part of the basin. This particular context in the basin hydrosystem explains the delay of most piezometer fluctuations compared to the river dynamics. Sea level observations otherwise show a discarded time lag, as depicted Figure 3c, with little correlation to river discharge due to the unclear relationship between rivers in the basin and the oceans.

The climate parameters overall exhibit a wide range of time lag and correlation, as indicated in Figure 3d-i, as the climatic signals are recorded worldwide with different temporal and spatial distributions. Nevertheless, a distinct seasonal pattern is evident in the parameter dynamics. The seasonal behavior of climate appears to significantly affect the response of the hydrologic system during certain periods when there is a high correlation between river discharge and climatic observations. Otherwise, the correlation is unstable with weak periods around the 90-day and -90-day lags, which apparently correspond to season changes. Fluctuations in the correlation over the time
lags thus pose a challenge to seasonal forecasting models since the predictive accuracy over the lead time deteriorates in response to such fluctuations. In this approach, this issue is overcome by designing a model with multiple lead times, which mitigates the reduction in predictive accuracy over the lead time range.

## 3.4 Data feature at global scale

In this analysis, the discharge signal at station No.1 is related to climate data at the global scale, with only the positive time lag considered as part of the results shown in Figure 3. The analysis reveals how river discharge in a given location connects to the global climate system by comparing their fluctuation signals over time. Overall, the relationship between river discharge and global variables is complex and varies spatially in both correlation and lag, depending on the background of the parameters. The river discharge is linked not only to local conditions on the French territory, but also to other regions of the world, as expressed by a favorable correlation that shows a strong connection in the climate system and the water system at the global scale.

The mapping in Figure 4a indicates that the discharge signal in the Loire River shows a strong correlation with the temperature fluctuations in the temperate zones where it is located, but shows no correlation with the tropical areas. The correlation seems to express an interdependency of local river dynamics and larger climatic oscillations. However, when arriving an important time lag between river activities and local temperature fluctuations, by more than half a year as in Figure 4a, Loire River activities are indeed out-of-phase with local temperature fluctuations. In France, the highest discharge rate of the Loire River responds to the rainy season, coinciding with the winter and spring periods when local temperatures are at their lowest. This implies that river discharge is more influenced by the accumulation of precipitation during the winter and early spring months, rather than direct temperature effects. Surprisingly, the Loire discharges are in phase with a strong correlation to the temperature on the opposite hemisphere. The observation underscores the complex interplay between local and global climatic factors in shaping river dynamics. Moreover, the diphase
phenomenon exemplifies a typical issue with data-driven correlation relationships, where a high correlation does not necessarily imply causality.

Atmospheric pressure in Figure 4c and d behaves differently on a local scale than other climate parameters and does not appear to be closely related to river dynamics. However, flux variations show a more obvious correlation with climate on the other side of the Asian-European continent. While there is a loose correlation between river activity and local atmospheric pressure, studies have shown that water cycle such as drought are associated with persistent or recurrent atmospheric circulation patterns (Namias, 1985). For example, high-pressure circulations frequently occur during summer droughts in the southeastern United States where the diurnal circulation patterns associated with drought are not significantly different from the patterns that occur during periods without drought. Instead, drought is associated with persistent or recurrent circulations that produce little or no precipitation (Hanson, 1991). River flow therefore associates to water-related parameters rather than other climatic factors, as discussed below.

The relationship between precipitation and river discharge is illustrated in Figure 4e for the correlation and in Figure 4f for the time lag at the global scale. The figures demonstrate that while there is a strong positive correlation and a short lag time between precipitation and river discharge at the regional scale, this relationship becomes more heterogeneous at larger scales. Precipitation distribution is highly variable both spatially and temporally and is strongly influenced by local conditions such as topography, large-scale climatic circulations, or other parameters such as evaporation. Fluctuations in precipitation patterns can lead to changes in the timing, magnitude, and duration of river flow. For instance, prolonged dry periods can lead to a decrease in river flow, whereas intense precipitation events can cause a rapid increase in river flow. In general, an increase in precipitation is expected to result in higher river flow, and a strong positive correlation between the two is usually observed.

Loire River discharge similarly shows a clear relationship to the soil moisture at a continental scale with a high correlation and short lag which confirms a direct impact of soil conditions to the river
flow (see Figure 4g & h). In fact, the moisture in shallow ground plays a crucial role in determining
the water runoff on the surface that feeds the river stream, both in the short term and the long term.
During periods of high soil moisture, such as after heavy rains or during spring thaws, river discharge
may increase rapidly as excess water from the soil enters the river. In contrast, during periods of low
soil moisture, such as during a drought, runoff can decrease significantly as less water is available to
the river. A similar relationship is observed for relative humidity in Figure 4i and j on the continents,
while humidity over the oceans follows a different mechanism. This is also true for potential
evaporation in Figure 4k and l. In fact, soil moisture, relative humidity, and evaporation in the air are
closely related, which together with precipitation defines the water cycle that controls the supply to
rivers and thus determines river dynamics.

In short, this data-driven approach uses correlation-based data selection through identifying
relationships between different variables that need not always have a physical basis. This means that
the relationships identified using this approach do not always reflect the underlying physical processes
that control the climate system. In reality, however, the relationships among different climate
parameters are complex and can vary at different scales. Many climate phenomena occur in large
cycles that can span continents or oceans and exhibit a long-term cyclical pattern that ranges from
monthly to annually to decades. These cycles can be influenced by a number of factors, including
changes in temperature, precipitation, and atmospheric circulation patterns. A holistic understanding
of the physical processes that control the climate system includes, but cannot account for, the complex
interactions among various climate parameters at multiple scales and the underlying physical
mechanisms that drive these interactions. Consequently, before switching to a better strategy that
considers the underlying physics, it is preferable to work with a simplified idea in this technique.
Correlation

<figure><img src="image_5.png" /><figcaption>c) Air Pressure at Sea Level</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>e) Precipitation Rate</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>g) Volumetric Soil Moisture BGL 10cm</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>i) Relative Humidity</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>k) Potential Evaporation Rate</figcaption></figure>

<figure><img src="image_10.png" /></figure>

Lag Time

<figure><img src="image_11.png" /><figcaption>d) Air Pressure at Sea Level</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>f) Precipitation Rate</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>h) Volumetric Soil Moisture BGL 10cm</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>j) Relative Humidity</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>l) Potential Evaporation Rate</figcaption></figure>

<figure><img src="image_16.png" /></figure>
**Figure 4: Correlation and time lag of the discharge signal at station No.1 (the red cross) to climate parameters. Each parameter demonstrates a distinct pattern of correlation and time lag with the discharge signal, but the extensive areas with high correlation provide evidence that global-scale datasets are useful for local-scale prediction.**

# 4. Methodology and model design

Phase shift forecast forms the basis of the model that allows detection and prediction of changes from underlying patterns in hydrological and climatic dynamics. Processing the phase shift prediction involves: 1) estimating the phase shift and the correlation between the target and the time series in the database; 2) selecting the most relevant series; 3) design the neural network, training the model and performing the prediction. It should be noted that only the most relevant time series from the database are used to ensure computational efficiency and to avoid noise in forecasting. The first two steps were described in the previous section; this section briefly discusses the methodology for designing the neural network. The result is presented in the next section with discussions.

In this study, our main objective is to design a forecasting model that can accurately predict river discharge over an extended period of time. To achieve this, we intend to use a Long Short-Term Memory (LSTM) neural network that can perform multiple time steps ahead, with the longest prediction horizon being 180-time steps (more details in Supplementary 3). To ensure the accuracy of the model, we intend to incorporate multivariate inputs from both local and global data sources that come from different physical backgrounds, frequencies, and observational sources. However, the complexity of the input data requires an effective neural network that can interpret complex features at the input and produce accurate long-term predictions. As a result, we propose the use of a stacked LSTM that can effectively capture the complex relationships between input and output variables and produce reliable and accurate predictions.
<figure><img src="image_17.png" /><figcaption>Figure 5: Stacked neural network composing multiple LSTM layers in vertical direction.</figcaption></figure>

Stacked LSTMs were introduced by (Graves, et al., 2013) in their application of LSTMs to speech recognition, which outperformed a benchmark on a challenging standard problem. They found that the depth of the network is more significant than the number of memory cells in a given layer. Indeed, Deep learning is built around a hypothesis that a deep/hierarchical model can be exponentially more efficient than a shallow model at representing some features. To make a neural network deeper, additional hidden layers can be added. Of which, each layer processes a portion of the task and passes it to the next, turning the deep neural network into a processing pipeline that solves a portion of the task until the last layer provides the output. These additional layers recombine the learned representation from prior layers to create new representations at higher levels of abstraction, for instance from lines to shapes, then to objects. Although a neural network with a single hidden layer can approximate most functions, increasing the depth of the network provides an alternative solution that requires fewer neurons and trains faster.

The proposed neural network optimized in this case consists of two LSTM layers, of which the neurons are optimized for each corresponding problem (see Figure 5). However, in all cases, the neural networks provide a sequence output instead of a single value output in the classical LSTM
model. As long-term forecasts are associated with low frequencies, the operation of the neural network is optimized with an output sequence composing various frequencies, the further the lower.

For a six-month forecast horizon, the predictions are daily for the first week, every four days for the next three weeks, weekly for the following two months, and two-weekly for the later periods.

Forecasting is performed daily after updating the measurement.

The composition of input data selection aligns with the previously mentioned time step ahead design, where the selection is divided into groups based on specific thresholds. In detail, we have maximum four groups (for six-month horizon): the first week with a daily time step, the next three weeks with a four-day time step, the subsequent two months with a weekly time step, and the remaining period with a two-weekly time step. As the correlation is computed for each time-lag, the selection of time series relies on threshold the correlation over the time lag group which corresponds to the time step ahead group at the output. The group-based assessment ensures the stability of the approach performance at the output, which enhances the interconnection in multiple time-step forecasting. The selection for each group is then combined to construct the input dataset that feeds into the neural network. To optimize the accuracy of the forecasting results for each station, the thresholds in this process are manually determined through trial tests. However, it is important to note that this threshold optimization process can be computationally intensive, as it involves parallel optimization of the neural network structure detailed in the following paragraph. This challenge is commonly encountered when dealing with multiple time step forecasts using a large database.

In the neural network, each LSTM layer is followed by a dropout layer to reduce the problem of overfitting. The number of neurons in each LSTM layer is optimized by the trial test where the number of neurons varies from 10 to 150. For training, the ADAM algorithm is used with a constant learning rate of 0.01 in 250 epochs. To select the best performing model, the three most frequently used evaluation metrics in time series analysis were selected. The model that shows the best performance on most of the evaluation metrics is selected as the most efficient and accurate model for predicting water dynamics. For these evaluation metrics, *x* represents the actual value, *y* represents the predicted value, and *n* represents the total number of test samples.
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# 5. Result and discussion

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This section presents the forecast results for 18 representative stations across the Loire-Bretagne basin, including one station from a neighboring basin, the Charente, to demonstrate the proposed model effectiveness (see **Figure 1**). Of the 18 stations, five are located in the mainstream of the Loire River, with one downstream, two in the middle, and two upstream. Additionally, six stations are regularly located in the Loire distributary, providing insight into the flow regime in the Loire connectors. Five other stations are located in small rivers in the Bretagne sub-basin, which are not directly connected to the Loire. Finally, one additional station (No. 5) is included from a neighboring basin to further evaluate the methodology performance in an extended context. The neural networks will be trained with a data set of 18 years and tested in the following 4 years until the current year 2022. The forecast at each station is examined with different time horizons, ranging from 1 month to 6 months ahead. The details of input data and neural networks used in the forecasting are listed in Table S4.1 and the results of which are summarized in Table S4.2, both of which are in Supplementary 4.

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## 5.1 Forecast of 1 month ahead

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The forecast of river discharge is first performed for a one-month horizon of 31 days ahead using a Stacked-LSTM model, which provides highly accurate results as shown in Figure 6. To provide a comprehensive view of the study, five distinct cases are selected for detailed presentation. Case a, which involves a downstream station No.1 with a large discharge and mainly low frequency, is forecasted with remarkable accuracy. In Case b, the station located at the basin center with a large stream and certain abrupt changes in river flow presents some difficulties for prediction. Case c, which involves station No.11 attached to the Loire tributary with a small proportion to the main river stream, where experienced highly fluctuated flow with long droughts and short floods, posing significant challenges to forecast. In Case d, the station is located in the Bretagne sub-basin, with
short rivers and small flow through a natural park less influenced by human activities, which allows better forecasting. Case e concerns the Charente River at station No.5 in the neighboring basin, which exhibits different flow features, especially at high frequency, with lower dynamics compared to the Loire, but some correlation to low frequency. The transfer of information between the two basins included in the data used data worked favorably, indicating the strength of data-driven method in building forecasting models at large scales.
<figure><img src="image_18.png" /><figcaption>Figure 6: Forecasts of river discharge for 31 days ahead at five representative stations, the resulting forecasts are of good accuracy with some losses of extreme events.</figcaption></figure>

In this short time horizon, the forecasting model relies mainly on the local data (see Table S4.1) with the gauge records in the rivers and in the basin itself. These measurements are associated with the transit time of water through the regional system and contribute significantly to the predictive
capabilities of the model. The model effectiveness is thus closely linked to the specific features of the local region, as broader scale data proves to be less insightful. By focusing on local data, the model can capture the typical dynamics and behavior of the river system in the region, which have been reported extensively in the literature (Sit, et al., 2020). In more detail, the prediction of discharge is highly dependent on the frequency and dynamics of the discharge, which is confirmed in Section 2.3. Low-frequency discharges with similar rhythm and seasonal behavior are easier to predict because measurements throughout the basin have a low-frequency basis. High-frequency discharges, on the other hand, are challenging because they depend on local conditions, both human and natural. For example, the Loire River is heavily stressed by dams, reservoirs, and irrigation activities, making it difficult to accurately predict high-frequency discharges. In addition, the method used in the study has some limitations in dealing with extreme events and accidents. This is because the Long Short-Term Memory (LSTM) model is well suited for trend data and frequently occurring events, but not for infrequent incidents. Other methods such as inference techniques or physical models may be better suited for these types of incidents. Finally, it should be noted that only observational data of natural phenomena are used in the study, reflecting only natural behavior, and excluding human interactions.

## 5.2 Forecast of 3 months ahead

To extend the forecast to a three-month horizon, the model mobilizes more data compared to the previous shorter horizon forecasts. This includes both local and global datasets to support the multiple time step ahead forecast where local data is crucial for short terms, while global data is essential for longer-term forecasts because they possess a longer time lag to discharge signals. The added complexity of the input data is expected to improve the predictive information, resulting in more accurate and reliable forecasts. Although a model with a longer time horizon mobilizes more input data sets, the increase is only slight compared to the previous case with a one-month forecast. This is because the correlation between data may decrease due to seasonal changes, which can make it challenging to select better data with high correlation to improve the forecasting process. This
physical constraint further adds complexity to solving long-term predictions, especially for seasonal forecasts as in this case.

<figure><img src="image_19.png" /><figcaption>**Figure 7:** Forecasts of 90 days ahead at five representative stations, showing a good trend, albeit with lower accuracy compared to a shorter horizon as in Figure 6. The predictions lose the floods, but favorable for the drought forecast.</figcaption></figure>
To demonstrate the effectiveness of our proposed model, we draw on cases from the previous study in Section 4. In most cases, the predictions correctly reproduce the flow dynamics trend with a high correlation coefficient. The models produce mainly low-frequency results, which is to be expected for long-term forecasts, the accuracy of which is lower for shorter time horizons, as shown in the previous section. The prediction is not suited to capture the peak flood events, which are often triggered by rapid surface runoff due to precipitation. This influence of precipitation on the long-term operation of the basin remains unclear because of the limited connection between surface water and subsurface aquifers in this basin and the lack of the physical properties of the catchment such as the topography and land cover that control the rapid events. On the other hand, low water levels that prevail during the dry season in summer are properly captured by the proposed models. In fact, the recharge of the river is minimal during the dry season, mainly due to low rainfalls and narrow aquifers, although the aquifers contribute little to the river discharge. This particularity of the Loire, with its serious lack of recharge sources, seems to facilitate the prediction of low water levels.

## 5.3 Forecast of 6 months ahead

To further explore the effectiveness of our forecasting model, the time horizon in forecasting is extended to 6 months, a seasonal model that reaches the range of 180-time steps ahead. This extension will provide us with a more comprehensive understanding of system dynamics and enable us to make better decisions regarding hazard mitigation and other related issues. Extending the seasonal forecasts offer a more profound understanding of how the nature of data types interacts with the forecasting time spans.
<figure><img src="image_20.png" /><figcaption>Figure 8: Forecasts of 180 days ahead reflect the trend of dynamics, though with lower accuracy compared to 3 months ahead in Figure 7. A mutual effect over different time horizons in forecasting is observed at station No16 (Figure 8d) that enhances the forecast accuracy.</figcaption></figure>
To ensure the performance of the model, a stacked LSTM neural network is retrieved and optimized with two LSTM layers, which allows the model to learn more intricate patterns in the data and better capture long-term dependencies. The model continues to utilize both local and global data, which has proven to be effective in previous analysis. The forecast accuracy for longer-term forecasts of 6 months ahead is generally lower than that of the 3-month forecasts in the previous section. The results show promise in capturing the trend in water dynamics for low-frequency components, although there is a significant loss in high-frequency dynamics (see Figure 8). While flooding patterns are absent from the forecast, droughts are well traced over years. However, as shown for station No.16 in Figure 8d and stations No.9,15, and 18 in Table S4.2 a longer time horizon associated with lower accuracy is not always the case when long-term leading information can enhance the accuracy of shorter-term forecasts. As discussed in Section 3.4, data correlation is higher at a six-month lag than at a three-month lag, so this more relevant information strengthens the ability to predict the longer range. This is the reason why, in this case, doubling the time horizon from 3 to 6 months changes the forecast quality only slightly. The mutual effect of time span in forecasting emphasizes the importance of considering multivariate systems with multiple time ahead in dynamic predictions, which can help compensate for differences among datasets and time step ahead, which is the novelty of this research.

As summarized in Table S4.1, the global data set has a significant presence in this case compared to the local data set. This finding, along with the previous two cases, reaffirms the importance of large-scale data in making long-term predictions. Since the models combine data from all climatic parameter fields, the abundance of datasets furthers the predictive capacity of the proposed approach. Even though climate parameters are not uniformly present in the global datasets at the model input, with an emphasis on measurements of soil moisture, relative humidity, and evaporation rate, which restates the discussion in Section 3.4 above. In addition, large-scale data provide the average of spatial information, especially when it comes to large-scale climate variability such as the North Atlantic Oscillation (NAO), the data mainly reflect information about long-term trends. While details and high frequencies are strongly determined by local conditions including water management plans, irrigation schemes, and other natural and human activities, where they are associated with temporal variations
that lend themselves to short-term prediction. As a result, forecast accuracy is better in Bretagne sub-basin as shown in Figure 8d, which has shorter rivers and is less influenced by human activities, so the high-frequency components are lower. This otherwise highlights the importance of considering local conditions for developing accurate forecasts, which are often inadequate in both time and space due to the complexity of management systems in practice.

## Conclusion

This work presents a multivariate model designed to make long-term prediction of river discharges in the Loire-Bretagne basin, which is crucial for effectively managing and preserving the environmental conditions in this region. To ensure comprehensive coverage, the model integrates data from both local and global sources, including river and piezometer gauging within the basin, sea level, and climate parameters on the global scale. The database utilizes a total of 12 parameters related to both the hydrologic and climate systems, which are sampled at a daily frequency. Processing data operates on the principle of phase shift analysis, wherein data selection is performed by identifying the best correlations through frequency analysis of the time series. To adapt to the dynamics of river discharge, a calibration of frequency analysis is employed to optimize the correlation and time lag between parameters owning different physical background and frequency. The proposed approach promises long-term predictions of river discharge that can extend up to seasonal time horizons, where the output is presented in a sequence format that spans multiple time ranges and is updated daily to perform forecasts. To improve information extraction in the processing, the model uses the concept of stacked LSTM, a deeper and more complex neural network architecture, to achieve better coverage of database diversity.

The developed model performs forecasting of river dynamics at representative stations throughout the region and in the neighboring basin - Charente - for periods of one, three and six months, with a horizon of up to 180-time step ahead. Overall, the model provides favorable accuracy and efficiency
in predicting river dynamics over the years. Here, the prediction quality depends on the complexity of river dynamics, with better performance for low frequencies and some losses for high frequencies.

The models perform better in predicting drought periods, but may lose accuracy in predicting flood peaks. By using both data types at the input, the resulting forecast emphasizes the importance of both local and global datasets in predicting river discharge, where local datasets determine short-term predictions while global datasets drive long-range predictions. An interaction between the time range in forecasts and the shift in data correlation is also observed, with lower correlation at a lag of about 3 months due to seasonal changes affecting the quality of the forecast, but compensated by a higher correlation at longer lag of 6 months. Such compensation improves the quality of the forecast at a six-month horizon, and opens the door for a very long-term forecast with a time horizon of seasonal scale.

Since this long lag corresponds well with the large-scale data sets, this reaffirms the importance of including large-scale data for long-term forecasting. This research study establishes a solid practical groundwork to enhance the utilization of big data in order to facilitate accurate and reliable long-term forecasting of hydrodynamics that are also applicable to environmental dynamics with similar variability behavior.

In this study, the database are limited to natural parameters and do not include human activities or accidents; therefore, the predictions are more accurate for rivers with low levels of intervention in the Bretagne sub-basin. In addition, no uncertainty analysis was performed, and the point data used in the study do not provide in-depth information that could incorporate spatial dynamics on a regional or larger scale. Future work should also focus on the explainability of this deep learning model to determine the significance of each dataset used, which may improve the accuracy and reliability of the predictions.
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Seasonal forecasting

<figure><img src="image_21.png" /></figure>