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# IN-WOP project WP3 - Seine River study case: Climate change impacts on water resources

David Dorchies, Florian Ricquier

► To cite this version:

David Dorchies, Florian Ricquier. IN-WOP project WP3 - Seine River study case: Climate change impacts on water resources. INRAE. 2024, 64 p. hal-04718224

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# IN-WOP project WP3 - Seine River study case: Climate change impacts on water resources

2024-10-02 | UMR G-EAU

DAVID DORCHIES, FLORIAN RICQUIER
# Contents

<table><tr><td>1</td><td>Introduction</td><td>4</td></tr><tr><td>1.1</td><td>The IN-WOP project</td><td>4</td></tr><tr><td>1.2</td><td>Work package 3: The Seine River Basin study case</td><td>4</td></tr><tr><td>1.3</td><td>Abstract</td><td>5</td></tr><tr><td>2</td><td>Study case and model</td><td>6</td></tr><tr><td>2.1</td><td>The Seine River study case</td><td>6</td></tr><tr><td>2.2</td><td>airGR & airGRiwrm models</td><td>8</td></tr><tr><td>3</td><td>Calibration of the model</td><td>11</td></tr><tr><td>3.1</td><td>Model input</td><td>11</td></tr><tr><td>3.2</td><td>Calibration of the model with influenced flows at gauging stations</td><td>11</td></tr><tr><td>3.3</td><td>Simulation for all intermediate bassin in influenced context</td><td>15</td></tr><tr><td>3.4</td><td>Model performance evaluation</td><td>18</td></tr><tr><td>4</td><td>DRIAS-2020 climate simulations</td><td>25</td></tr><tr><td>4.1</td><td>Data description</td><td>25</td></tr><tr><td>4.2</td><td>Calculation of the intersection of SAFRAN meshes with the contour of intermediate catchment areas</td><td>27</td></tr><tr><td>4.3</td><td>Climate projection bias at the intermediate sub-basin scale</td><td>28</td></tr><tr><td>5</td><td>Climate change impact on the flow without the reservoir influence</td><td>31</td></tr><tr><td>5.1</td><td>De-influencing by simulation</td><td>31</td></tr><tr><td>5.2</td><td>Comparison of uninfluenced simulated past flows with other databases</td><td>32</td></tr><tr><td>5.3</td><td>Simulation of uninfluenced flows forced by climate projections</td><td>32</td></tr><tr><td>5.4</td><td>Impact of climate change on hydrological indicators for flows without reservoir influence</td><td>34</td></tr><tr><td>6</td><td>Current reservoirs management rules: modeling and climate change impact</td><td>40</td></tr><tr><td>6.1</td><td>Modeling of reservoir intake and release flows</td><td>40</td></tr><tr><td>6.2</td><td>Simulation of flows with current rules on the historical period</td><td>41</td></tr><tr><td>6.3</td><td>Current rules under climate change</td><td>49</td></tr><tr><td>7</td><td>Conclusion</td><td>55</td></tr><tr><td>8</td><td>Acknowledgments</td><td>56</td></tr></table>
# 1 Introduction

## 1.1 The IN-WOP project

Current practice in integrated water resources management (IWRM) predominantly make use of multi-objective optimization approaches with aggregated objectives. This biases results towards the status quo and against innovative solutions, can foster stakeholder resistance when they do not recognize their values and objectives in the optimization formulation, while also raising ethical concerns related to the inclusion of undesirable and/or hidden trade-offs. In contrast, many-objective optimization approaches can consider many non-aggregated objectives, which has the potential to enrich the solution space with alternative courses of action that better reflect the diverging perspectives of stakeholders, and align better with ethical concerns. From the viewpoint of ethics, disaggregated assessment criteria are preferred as these may avoid undesirable and hidden trade-offs.

The overarching aim of this project is to investigate the contribution of many-objective optimization approaches to IWRM. For this, we use three water management cases in a comparative evaluation of many-objective approaches in diverse hydrological and cultural settings. In Italy our focus is on the Lake Como Basin located in the Italian Southern Alps, serving irrigated agriculture and competing demands from navigation, fishery, energy production environmental and flood protection. In Tunisia we address the anthropogenic impact on the management of water resources in the Merguellil Basin. In the Seine River, France, we focus on the coordinated regulation of the Seine river discharge to reduce both floods and droughts. The present report is part of the results of this last study case on the Seine River.

## 1.2 Work package 3: The Seine River Basin study case

Our approach of many-objective optimization consists in performing many single-objective optimizations and to derive management rules from prioritization of these objectives.

To do so, we first evaluate the risk of non-achievement of each objective independently for a given climatology and a given state of the system. Then, we derive management rules by prioritizing the riskiest objectives in the daily decision making.

The main tasks performed for the work package 3 are summarized in Figure 1.1.

<figure><img src="image_5.png" /><figcaption>Figure 1.1: Main tasks performed in WP3</figcaption></figure>
First, uninfluenced catchment flows are modeled at a daily time step with a semi-distributed GR4J model based on the airGRiwrm R package (Dorchies, Delaigue, and Thirel 2022) and forced by 11 GCM/RCM climate projections for both RCP4.5 and RCP8.5 between 1950 and 2100.

Then, these flows are used to assess the risk of non-achievement of each objective taking into account the current reservoir volume, the day of the year and a selection of climate scenarios and periods. This assessment is derived from the statistical distribution of the minimum (resp. maximum) volume required in the reservoirs for a given drought (resp. flood) objective calculated by a single objective dynamic programming optimisation.

The result of this assessment is available to the public through an interactive Shiny website (http://irmara.g-eau.fr) that allows to experiment management scenarios in real time.

Finally, “risk-based” management rules are derived by prioritising the riskiest objectives and balancing proactive and reactive decisions taking into account a hedging policy.

At the same time, we modeled the current management rules over historical and future periods and we use these outputs to compare this management over the “risk-based” management rules. Both modelling results are specifically analysed for their distributive justice.

## 1.3 Abstract

This report presents the results of the calibration of the semi-distributed hydrological model of the Seine River Basin up to Vernon, using a set of 156 hydrometric stations. It also presents the simulation of the uninfluenced flow forced by 11 climate projections under RCP 4.5 and 8.5. and the impact of the climate change over the XXI<sup>th</sup> century on the basin hydrology.

This modelling is carried out using the airGRiwrm extension of the airGR package (Dorchies, Delaigue, and Thirel 2022) at daily time step.

The calibration is performed using observed influenced flows and known influence of the reservoirs. We use a collection of hydrological indicators characterizing all regime conditions (including droughts and floods) in order to assess this calibration.

Removing the reservoirs from the model allows one to simulate the flow without the influence of the reservoirs (Terrier et al. 2020). We use then the climate projections to simulate the evolution of these “uninfluenced” flows under climate change.

The simulated “uninfluenced” flows under climate change will be use afterward for assessing the reservoir management risks and for computing the derived “risk-based” rules.

In order to assess the climate change impact on water resources, we compute the evolution of hydrological indicators for the near future (2021-2050), the middle (2041-2070), and the end of the century (2071-2100) compared to the reference situation (1976-2005).
# 2 Study case and model

## 2.1 The Seine River study case

In this study, we focus on the Seine basin, more specifically the area upstream of Vernon, (city located downstream of Paris, between Peris and the Channel) which covers approximately 64,420 km² (Figure 2.1). The topography of the basin is generally flat, with an altitude gradient varying from 31 to 300 metres on average, with the exception of the upstream Morvan region where altitudes can reach 901 metres. The hydrological regime of the Seine basin is influenced by an oceanic climate, resulting in higher flows from November to June and lower flows from July to October. While the impact of snow is generally limited, it becomes more significant during periods of heavy snowfall, particularly in the Morvan region. The study area of this basin covers the main tributaries of the Seine, the Yonne (293 km), the Marne (525 km) and the Aube (248 km).

The Seine basin is subject to a number of anthropogenic influences. The basin has a high demand for water, but also very high pollution pressure, as it is home to around 18 million people, or 27% of the population of metropolitan France, including 12 million in the Île-de-France region alone.

Among the anthropogenic influences, we will limit ourselves to the four reservoir lakes located upstream in the basin, with a total volume of 807.5 Mm³. Built between 1949 and 1990, these reservoirs are managed by EPTB Seine Grands Lacs and have the dual purpose of reducing floods and supporting low-water levels.

EPTB Seine Grands Lacs acts at the level of the upstream basin of the Seine, facilitates and coordinates the public action of local authorities throughout the territory through its missions:

* Managing flood risk in the Seine basin by capping floods.

* Supporting river flow during the dry season.

* Acting for the reduction of vulnerability to floods.

* Providing a role of advice, animation and coordination with the basin communities.

* Preserving the environment.

The UMR G-EAU was involved with the EPTB Seine Grands Lacs in the ClimAware project (ERA-NET IWRM-NET 2011-2013) on the Seine River study case. The objective of this study case was to provide an analysis framework to water managers for evaluating potential consequences of climate change on the river basin hydrology and assessing adaption strategies to cope with these changes. These adaption strategies were developed at tactical (adaption of target reservoir filling curves) and at operational (real-time reservoir management) levels.

Some project outputs were used by the EPTB Seine Grands Lacs such as :

* a flood and droughts risk assessment tools considering the filling of the reservoirs for any period during the year;

* the adaptation of the reservoir filling curves which has been presented at the Technical Coordinating Committee for Studies and Works and has been used to modify the shape of the reservoir filling curves.
<figure><img src="image_6.png" /><figcaption>Figure 2.1: Study area of The Seine River Basin</figcaption></figure>
## 2.2 airGR & airGRiwrm models

Studying the impact of climate change and adapting water resources management requires tools for modelling the rainfall-runoff relationship and uses in spatial terms.

We perform the Seine River basin modelling thanks to the airGRiwrm R package (Dorchies, Delaigue, and Thirel 2022).

### 2.2.1 The airGR R-package: an R implementation of GR models

The airGR package (Coron et al. 2017) is an open source package available in the R language that provides the GR family of rainfall-runoff models, including GR4J (Perrin, Michel, and Andréassian 2003), and their latest developments. These empirical models, which operate on hourly, daily, monthly and annual time steps, use rainfall and air temperature data to simulate river flows (Perrin, Andréassian, et al. 2018). The package also includes a snow accumulation and melting model, functions for optimising model parameters, assessing model performance and plotting analysis graphs.

For more informations: https://hydrogr.github.io/airGR/

In this study, we use the GR4J model (Perrin, Michel, and Andréassian 2003) which is a simple conceptual model with 4 parameters to be optimised (Figure 2.2). The model has been tested in a large number of studies over the last decades throughout France and also on other continents, particularly in operational research.

Two types of data are required as model input:

* Precipitation, corresponding in this case to daily rainfall totals;

* Potential evapotranspiration, which serves at representing water loss in the catchment area under study.

The first part of the model, known as “interception”, corresponds to a production function used to determine the actual input of raw rainfall, which will be used to estimate the flow. The first free parameter is $x_1$ (mm) corresponding to the maximum capacity of the production reservoir. $S$ corresponds to the quantity of water in this reservoir at time $t$. This reservoir takes rainfall and potential evapotranspiration into account. It can also take into account modules such as CemaNeige, which takes solid precipitation into account (Valéry 2010) and computes snow accumulation and melt thanks to two new parameters.

Then, the transfer function takes into account a unit hydrograph to distribute the slow (90%) and fast (10%) flows from the production function. Both hydrographs depend on the free parameter $x_4$ (d). The slow flows fill a routing reservoir whose volume corresponds to the free parameter $x_3$ (mm). $R$ corresponds to the quantity of water in this reservoir at time $t$.

A fourth free parameter, $x_2$ (mm/d), corresponds to the loss/gain coefficient due to exchanges between basins at subsurface level.

### 2.2.2 The airGRiwrm R-package

The airGRiwrm package is an R package that ‘encapsulates’ airGR, i.e. it uses its GR functionalities and models directly, but systematises their use in a semi-distributed way thanks to a set of new functions enabling a network of models to be set up (Dorchies, Delaigue, and Thirel 2022). In addition, airGRiwrm makes it possible to include water uses in this network, either by injecting measured water intakes or restitutions directly, or by allowing coupling to use models (Figure 2.3). In addition, as uses are subject to management rules or restrictions, it is possible to use ‘controllers’, which implement decision logic and determine, for example, when demand for a use is met or not.

For example, this package can be used to simulate the flows in catchment areas that include reservoirs for flood control or low-water support, canals for inter-basin transfers, and all kinds of abstractions and discharges and their regulation.
<figure><img src="image_7.png" /><figcaption>Figure 2.2: Functional scheme of the GR4J model (Perrin, Michel, and Andréassian 2003)</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Figure 2.3: GRiwrm graph representing the vicinity of the Seine reservoir. In blue, upstream GR hydrological modelling; in green, GR hydrological modelling of intermediate catchment areas; in turquoise, reservoirs; in black, river branches, in dashed red, human diversions.</figcaption></figure>
### 2.2.3 The seinebasin2 R-package

The work carried out for this study and the resulting reports were developed specifically for the project in the form of an R package called **seinebasin2**.

The **seinebasin2** package is built as an extension of the **airGRiwrm** and **airGR** packages. The data are stored on a cloud, and can be automatically loaded with the script directly from the cloud, or copied locally and used locally.

The code below loads the `cfg` configuration, which contains the path to the data folder (by default from the cloud):

```r
library(seinebasin2)
cfg <- loadConfig()
cfgdata=path
#> NULL
```

Data can be downloaded from Nextcloud via this link: https://nextcloud.inrae.fr/s/adinzGa3AmLEXnZ.

See the documentation of the functions `loadConfig` and `-dataPath` of the `seinebasin2` package for more details on data management: https://in-wop.g-eau.fr/seinebasin2
# 3 Calibration of the model

## 3.1 Model input

The semi-distributed hydrological model requires input climate data for the calibration process. On each intermediate sub-catchment (Figure 2.1), it uses precipitation, potential evapotranspiration, and air temperature. Precipitation and temperature data are extracted from the SAFRAN reanalysis database (Vidal et al. 2010). The potential evapotranspiration is calculated from the Oudin formula (Oudin et al. 2005) which only uses temperature, day of the year and geographical latitude as inputs.

For the calibration, we use the complete data set available between the 1st of August 1958 and the 31th of July 2022 at a daily time step.

Observed flow data used for calibration are extracted from the HydroPortail database (https://hydro.eaufrance.fr/) for each of the 152 stations in the study (Leleu et al. 2014). We use all available data also between 1958 and 2022.

The intake and release flow data observed for the 4 reservoir lakes are extracted from the daily operating files supplied by the ETPB Seine Grands Lacs. These data will be used to take into account the influence of the reservoir lakes on river flows.

## 3.2 Calibration of the model with influenced flows at gauging stations

The model contains a schematic representation of the river network in which each intermediate sub-catchment is represented by a node used by the **airGRiwrm** package.

### 3.2.1 Adjustment of the natural hydrological network to integrate Reservoir and Diversion nodes

A modification to the network present in the GRiwrm object is required to incorporate the reservoir influences.

The **airGRiwrm** extension used in **seinebasin2** allows various nodes to be added:

* the **Reservoir** node allows to model the evolution of the volume of a reservoir from one or more upstream nodes for filling and one downstream node for the release (release time series provided by the user);

* the **Diversion** node allows to divert water from an existing node to another (diversion time series provided by the user);

* the **Ungauged** node allows to simulate the flow on the river network on a location not equipped by a gauging station by copying hydrological parameters from a downstream gauged node thanks to a common calibration.

All the reservoirs in the Seine basin can be conceptualized as in Figure 3.1. All the reservoirs have one river outlet that controls the release of the reservoir. A reservoir can be a dam across the river such as for the Pannecière Lake (Yonne River), and in this case, it does not have river inlets that control the filling. Other reservoirs on the Seine basin are derived with one or several river inlets (denoted as *river inlet i* in Figure 3.1). Marne and Seine lakes do not have natural impluvium which is not the case for the Yonne lake naturally filled by the Yonne river, and the Aube lake naturally filled by the Auzon and the Amance rivers. Finally, the Marne and the Aube lakes replenish former rivers that have been cut at the reservoir construction. These replenishments are processed independently from other reservoir rules even if this flow is added to the reservoir release in the model.

The Seine implementation of the Seine reservoir is represented in Figures 3.2 and 3.3.
<figure><img src="image_9.png" /><figcaption>Figure 3.1: Conceptual scheme of reservoir connections with the river system</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Figure 3.2: Diagram of natural network around the lake Seine</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Figure 3.3: Diagram of the network around the lake Seine after reservoir implementation</figcaption></figure>
The Yonne lake, as an inline reservoir, is not complicated to implement as we can see in Figures 3.4 and 3.5.

<figure><img src="image_12.png" /><figcaption>Figure 3.4: Diagram of natural network around the lake Yonne</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Figure 3.5: Diagram of the network around the lake Yonne after reservoir implementation</figcaption></figure>

The Marne lake is provided with 2 inlets on the Marne and Blaise rivers with one outlet (Figure 3.6). The reservoir is partly located on the Aube watershed through the replenishment of the Droyes River which flows to the intermediate sub-catchment “L’Aube à Arcis-sur-Aube” (H1501010). The implementation of the Marne reservoir is represented in Figure 3.8.

<figure><img src="image_14.png" /><figcaption>Figure 3.6: Diagram of natural network around the lake Marne</figcaption></figure>

The Aube reservoir presents a specific context (Figure 3.7). This reservoir is made up of two smaller reservoirs, Lake Auzon-Temple and Lake Amance which are linked by an open canal and are located on two distinct river basins. The first feeds the Auzon river, whose downstream basin is “L’Aube à Arcis-sur-Aube” (H1501010). The second feeds the Amance, whose downstream basin is R_AUBE the release point of the reservoir in the Aube River. The model mimics this behaviour until 1988 when the reservoir was built.

After this date all the flow from the Auzon and Amance rivers is diverted to the reservoir and the replenishment flow for the Auzon river is diverted from R_AUBE to the gauging station H1501010 as illustrated in the Figure 3.8.

As the AMANCE and AUZON stations have no observed flows, we define them as Ungauged. This means that these sub basins are calibrated with and will use parameters derived from the nearest downstream gauged basin, in this case R_AUBE, to simulate flows.

Observed flows at inlets and outlets of the reservoirs are injected in the model through the Diversion and Reservoir nodes in order to process to the calibration using influenced observed flows.

### 3.2.2 Calibration of the 152 stations in the study area, taking reservoirs into account

The calibration process determines the optimized parameters for each catchment.

The AMANCE and AUZON nodes are defined as Ungauged because no observed flow is available to calibrate these catchments. The calibration is then performed following the method “M2” developed by Lobligeois (2014). This calibration consists in defining a “donor” node which has observed flows and is calibrated together with the ungauged node.

Hydrological model parameters are copied from the donor to the ungauged node with the exception that the unit hydrograph parameter X4 depends on the area of the sub-catchment ($S_i$) which is divided by the catchment of the donor catchment ($S_{BV}$) following Equation (3.1).

$$x_{4i} = \left( \frac{S_i}{S_{BV}} \right)^{0.3} X_4 \qquad (3.1)$$
<figure><img src="image_15.png" /><figcaption>Figure 3.7: Diagram of natural network around the lake Aube</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Figure 3.8: Diagram of the network around the lake Aube and Marne after reservoir implementation</figcaption></figure>
The airGRiwrm package natively defines a "donor" for each node in the network. By default, it assigns the first downstream gauged node as donor. As one can see on Figure 3.7, the AMANCE node has the R_AUBE node as donor and the AUZON node should have the H1501010 node as donor. However the implementation of the reservoir (Figure 3.8) adds a connection between the AUZON node and the R_AUBE node through the reservoir. This creates a conflict because H1501010 and R_AUBE become interdependent and should be calibrated all together which is currently not possible. Therefore, we have chosen as well to define R_AUBE as donor for the ungauged AUZON node.

The calibration consists in finding the model parameters which optimized a performance criterion. We use here a composite criterion containing a parameter regularization as defined by de Lavenne et al. (2019) which adds a priori information on optimal parameter sets for each modeling unit of the semi-distributed model. Calibration iterations are then performed by jointly maximizing simulation performance and minimizing drifts from the a priori parameter sets.

As proposed by de Lavenne et al. (2019), we use the Kling-Gupta Efficiency (KGE) criterion (Gupta et al. 2009) (Equation (3.2)) calculated on the square root of the discharge.

$$KGE = 1 - \sqrt{(r-1)^2 + (\alpha-1)^2 + (\beta-1)^2} \qquad (3.2)$$

* α : Ratio between simulated and observed flow variances

* β : Model bias

* r : Correlation coefficient between observed and simulated flow rates

This criterion is used to quantify a bias between observed flow values and simulated model output values. This criterion varies between -inf and 1, and the closer it is to 1, the smaller the difference between the simulated and observed values.

## 3.3 Simulation for all intermediate bassin in influenced context

The maps below show the spatial variability of the four parameters defined during the calibration process with reservoir influence:

* x₁ corresponds to the maximum capacity of the production reservoir (mm);

* x₂ corresponds to the loss/gain coefficient due to inter-basin exchanges at the underground level (mm/d);

* x₃ is the capacity at one-time step of the routing reservoir (mm);

* x₄ is the unit hydrograph (day).

Stations H1501010, R_MARNE and R_SEINE show simulated regimes that are close to those observed. However, for station H20201010, the simulated flows barely match with observed ones (Figure 3.10). The simulation is less good during the period from June to November, when the model overestimates the flows. We did not succeed to find out why we get this poor result on this gauging station. The most probable reason would be a poor rating curve on this gauging station.

For each station, a summary sheet of the flow, rainfall and regime records used for calibration is recorded and available here: https://nextcloud.inrae.fr/s/dweGCFJoke5R6qc
<figure><img src="image_17.png" /><figcaption>Figure 3.9: Maps of calibration parameters including the influence of the reservoirs</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>Figure 3.10: Simulated and observed flow regimes incorporating the influence of reservoirs</figcaption></figure>
## 3.4 Model performance evaluation

We use the Kling-Gupta Efficiency (KGE) criterion defined in Equation (3.2) calculated from the output of the simulation with reservoir influence in order to evaluate the results of the model taking into account the influence of the four reservoir lakes.

For most of the intermediate basins, the KGE criterion is between 0.8 and 1 (Figure 3.11) which reflects an accurate representation of observed flows. The “no data” areas correspond to the Amance and Auzon sub basins where the KGE indicator cannot be calculated because of the lack of observed flows.

<figure><img src="image_19.png" /><figcaption>Figure 3.11: Maps of KGE criteria for calibration with the integration of the influence of reservoirs</figcaption></figure>

The simulation performances are also assessed with hydrological indicators related to mean flow, high-flows and low-flows. We here use these indicators which were already used in the Explore 2070 project (Chazot et al. 2012):

* The mean annual discharge “QA” provides a general measure of the quantity of water flowing over a year.

* The “VCN10” and “VCN30” low-flow indicators are respectively the average annual minimum flows over periods of 10 and 30 consecutive days.
* The "QMNA2" and "QMNA5" low-flow indicators are the lowest average monthly flows over a year with a return period of respectively 2 and 5 years.

* The "QJXA2", "QJXA10" and "QJXA20" high-flow indicators are the annual maximum daily flows over a return period of 2, 10 and 20 years respectively.

Low-flow indicators are computed from a statistical adjustment of a Galton distribution, and high-flow indicators are computed from a statistical adjustment of a Gumbel distribution.

The accuracy of the models used in the study are assessed from ratios "R-" between these indicators calculated from simulated and observed flows as illustrated in Equation (3.3).

$$R-QA = \frac{QA_{simulated}}{QA_{observed}} \qquad (3.3)$$

The following maps illustrate the ratios calculated between simulated and observed flows for various hydrological indicators in all 152 intermediate catchments except for the AMANCE and AUZON, which have no observed data.

### 3.4.1 Calibration performance on QA (average flow)

The "R-QA" indicators reflects that the simulated flows produced a good interannual volume of water. It is a key indicator in terms of water resource management at annual scale.

In all the intermediate catchments, the values of "R-QA" are generally between 0.9 and 1.1, which indicates that the annual mean of the simulated flows is similar to the observed flows (Figure 3.12).

This result is not surprising since the mean flow bias is used in the KGE criterion chosen for the calibration (Equation (3.2)).

### 3.4.2 Calibration performance on VCN30 with a 2-year return period

As far as low-flow indicators are concerned, most of the intermediate catchment areas show ratios between 0.75 and 0.9, suggesting an underestimation of simulated flows of the order of 10 to 25% (Figure 3.13). For the other basins, the ratios vary considerably, sometimes going as far as a very pronounced underestimation (close to 0.25) or a significant overestimation (close to 2) for some upstream basins.

### 3.4.3 Calibration performance on QMNA5

The Figure 3.14 shows the map of the "R-QMNA5" ratios. These results are quite similar as those obtained on the "R-VCN30-2" ratios.

### 3.4.4 Calibration performance on QJXA10

For maximum daily flows with a 10-year return period, the ratios are generally between 0.75 and 1.5.

### 3.4.5 Overview of all calibration performance indicators

We highlight 9 hydrometric stations used as monitoring stations for the assessment of the reservoir management performance (Dorchies, Thirel, Jay-Allemand, et al. 2014). The spider diagram below shows all the hydrological indicator ratios for these stations.

Of the nine stations, the model underestimates the simulated flows for low-flows ("VCN" and "QMNA" indicators) at seven of them (by an average of 0.75). Only the COURL and ALFOR stations reproduce the data accurately.

For high flows ("QJXA" indicators), the ARCIS station is clearly underestimated, while the other stations are around 1, with the exception of the COURL, ALFOR and CHALO stations, which are overestimated by around 25%. The NOGEN station is the most overestimated, approaching 30%.
<figure><img src="image_20.png" /><figcaption>Figure 3.12: Map of R-QA indicators for simulated flows with observed reservoir influences calculated on period 1959-2022</figcaption></figure>
<figure><img src="image_21.png" /><figcaption>Figure 3.13: Map of R-VCN30-2 indicators for simulated flows with observed reservoir influences calculated on period 1959-2022</figcaption></figure>
<figure><img src="image_22.png" /><figcaption>Figure 3.14: Map of R-QMNA5 indicators for simulated flows with observed reservoir influences calculated on period 1959-2022</figcaption></figure>
<figure><img src="image_23.png" /><figcaption>Figure 3.15: Map of R-QJXA10 indicators for simulated flows with observed reservoir influences calculated on period 1959-2022</figcaption></figure>
<figure><img src="image_24.png" /><figcaption>Figure 3.16: Ratio between hydrological indicators calculated on simulated and observed influenced flows on the period 1959-2022</figcaption></figure>

Hydrological indicators for observed and simulated flows are recorded here in the same format as will be used to analyse historical and projected natural flows.

These indicators can be downloaded from : https://nextcloud.inrae.fr/s/adinzGa3AmLEXnZ/download?path=%2F02-calibration&files=Q_indicators_with.csv
# 4 DRIAS-2020 climate simulations

## 4.1 Data description

The DRIAS2020 dataset (http://www.drias-climat.fr/) consists of 42 climate simulations, 12 simulations for the past period (before 2005) and for the future period (2006-2100) respectively 8, 10 and 12 climate projections for the scenarios RCP2.6, RCP4.5 and RCP8.5. The simulations are carried out using regional climate models (RCM) implemented at a resolution of 0.11° (EUR11, about 12km) over the same domain covering Europe. They are controlled at their edges by global climate models (GCM, for General Climate Model) of the CMIP5 programme.

Finally, the data is projected on an 8 km resolution grid and corrected for biases using the ADAMONT method (Verfaillie et al. 2017) extended over France (implemented by Météo-France) based on the analysis of SAFRAN observation data (Vidal et al. 2010).

<figure><img src="image_25.png" /><figcaption>Figure 4.1: Downscaling steps from global to regional modelling to disaggregation at small spatial scales (excerpt from DRIAS2020)</figcaption></figure>

For this study, we choose to work with 11 climate projections from the DRIAS2020 data set completed by some projections added for the Explore2 project (Sauquet 2022) forced by representative concentration pathways (RCP) 4.5 and 8.5.

The RCP 4.5 corresponds to a mitigation scenario with a peak of emission by 2040, while the RCP 8.5 corresponds to a “no-policy” scenario with a continuous huge use of fossil fuels (Moss et al. 2010). As shown in Figure 4.2, these 2 emission scenarios are the more likely to happen considering the current trajectory of historical emissions.

Recently, there was a debate on the opportunity to continue to use RCP 8.5 in prospective studies, because of its weak probability to happen (Ritchie and Dowlatbadi 2017). However, Schwalm, Glendon, and Duffy (2020) argue that *not only are the emissions consistent with RCP8.5 in close agreement with historical total cumulative CO₂ emissions (within 1%), but RCP8.5 is also the best match out to mid-century under current and stated policies with still highly plausible levels of CO₂ emissions in 2100.*

Even if the climate projection data set available for the Explore2 project has more climate projections, since we wanted to have the same projections for each RCP in order to make them comparable, the number of available common scenarios was limited to 11 (Table 4.1)<fnref n="1" />.

<footnote n="1">¹It should be noted that, as part of the Explore2 project, two simulations (IPSL_WRF and CNRM_RACMO) have been finally withdrawn from the ensemble for the production of hydrological simulations due to projected temperature and precipitation changes over France outside the confidence intervals of the new CMIP6 global simulations, analysed in particular in the IPCC's 6th Assessment Report</footnote>
<figure><img src="image_26.png" /></figure>

<figure><img src="image_27.png" /><figcaption>Figure 4.2: Global fossil fuel CO2 emissions (left) and total CO2 emissions from fossil fuels and land use (right) for historical observations and RCP, SRES, and IS92 scenarios. Credit: Glen Peters.</figcaption></figure>

<table><caption>Table 4.1: Climate projections used for the climate change impact assessment</caption><thead><tr><td>GCM</td><td>RCM</td></tr></thead><tbody><tr><td>CNRM-CERFACS-CNRM-CM5</td><td>CNRM-ALADIN63</td></tr><tr><td>CNRM-CERFACS-CNRM-CM5</td><td>KNMI-RACMO22E</td></tr><tr><td>ICHEC-EC-EARTH</td><td>KNMI-RACMO22E</td></tr><tr><td>ICHEC-EC-EARTH</td><td>SMHI-RCA4</td></tr><tr><td>IPSL-IPSL-CM5A-MR</td><td>IPSL-WRF381P</td></tr><tr><td>IPSL-IPSL-CM5A-MR</td><td>SMHI-RCA4</td></tr><tr><td>MOHC-HadGEM2-ES</td><td>CLMcom-CCLM4-8-17</td></tr><tr><td>MPI-M-MPI-ESM-LR</td><td>CLMcom-CCLM4-8-17</td></tr><tr><td>MPI-M-MPI-ESM-LR</td><td>MPI-CSC-REMO2009</td></tr><tr><td>NCC-NorESM1-M</td><td>DMI-HIRHAM5</td></tr><tr><td>NCC-NorESM1-M</td><td>GERICS-REMO2015</td></tr></tbody></table>
The DRIAS2020 project defines 4 periods for assessing the climate change impact:

* current climate reference (1976-2005): This is a standard period of 30 years of the recent past, which corresponds to the most recent 30-year period possible in the historical simulations and the current reference used in the DRIAS portal.

* near future (2021-2050)

* medium-term future (2041-2070)

* far future (2071-2100)

We use these periods for assessing the impact of climate change through the evolution of hydrological indicators.

## 4.2 Calculation of the intersection of SAFRAN meshes with the contour of intermediate catchment areas

The Figure 4.3 illustrates the intersection between the cells of the 8x8 km SAFRAN grid and the Seine River intermediate sub-basins of the **seinebasin2** model.

<figure><img src="image_28.png" /><figcaption>Figure 4.3: Merging of the SAFRAN layer with that of the intermediate catchment areas of the Seine catchment at Vernon</figcaption></figure>

For each intermediate sub-basin, we compute which cells and proportion of them are concerned in order to compute the mean meteorological data at this scale. The Table 4.2 shows an excerpt of the resulting conversion table with *x* and *y* the coordinates of the SAFRAN cell centroid, *CODE* the gauging station identifier, *area* the area of the intersection in km², and *prop* the proportion of the intersection area compared to the sub-basin area.
<table><caption>Table 4.2: Conversion table for aggregating meteorological data at the intermediate sub-basin scale (excerpt)</caption><thead><tr><th>x</th><th>y</th><th>CODE</th><th>area</th><th>prop</th></tr></thead><tbody><tr><td>820000</td><td>2449000</td><td>H6102010</td><td>6.112018</td><td>0.0216247</td></tr><tr><td>828000</td><td>2417000</td><td>H6102010</td><td>18.732000</td><td>0.0662751</td></tr><tr><td>828000</td><td>2425000</td><td>H6102010</td><td>27.565881</td><td>0.0975300</td></tr><tr><td>828000</td><td>2433000</td><td>H6102010</td><td>10.824818</td><td>0.0382990</td></tr><tr><td>828000</td><td>2441000</td><td>H6102010</td><td>0.233000</td><td>0.0008244</td></tr><tr><td>820000</td><td>2345000</td><td>H5042010</td><td>2.560719</td><td>0.0151647</td></tr><tr><td>820000</td><td>2353000</td><td>H5042010</td><td>19.777100</td><td>0.1171213</td></tr><tr><td>820000</td><td>2361000</td><td>H5042010</td><td>12.243082</td><td>0.0725043</td></tr><tr><td>828000</td><td>2337000</td><td>H5042010</td><td>2.339519</td><td>0.0138548</td></tr><tr><td>828000</td><td>2345000</td><td>H5042010</td><td>57.788381</td><td>0.3422266</td></tr><tr><td>828000</td><td>2353000</td><td>H5042010</td><td>47.727632</td><td>0.2826462</td></tr><tr><td>828000</td><td>2361000</td><td>H5042010</td><td>6.433868</td><td>0.0381018</td></tr><tr><td>836000</td><td>2337000</td><td>H5042010</td><td>2.882932</td><td>0.0170729</td></tr><tr><td>836000</td><td>2345000</td><td>H5042010</td><td>14.895000</td><td>0.0882092</td></tr><tr><td>836000</td><td>2353000</td><td>H5042010</td><td>2.211768</td><td>0.0130982</td></tr></tbody></table>

## 4.3 Climate projection bias at the intermediate sub-basin scale

The climate projections have been unbiaised by the ADAMONT method (Verfaillie et al. 2017) and are supposed to produce a similar climate than the one historically observed over the past period (1976-2005).

The Figures 4.4, 4.5, and 4.6 show respectively the correspondence of the monthly mean precipitation, daily mean temperature, and potential evapotranspiration between historical observations and climate projections over the reference period (1976-2005). Climate projections of temperature and potential evapotranspiration match very well with historical data. Results on precipitation is a bit more spreaded, this is due to the fact that the ADAMONT method was applied at a seasonal time scale and here we analyse results at a monthly time scale. Nevertheless, all climate projections are converging around historical value at the year scale and the general monthly trend is respected.

<figure><img src="image_29.png" /><figcaption>Figure 4.4: Monthly mean precipitation for the intermediate sub-basin at Paris (H5920010) calculated on period 1976-2005: comparison between observations and climate projections</figcaption></figure>
<figure><img src="image_30.png" /><figcaption>Figure 4.5: Monthly mean daily temperature for the intermediate sub-basin at Paris (H5920010) calculated on period 1976-2005: comparison between observations and climate projections</figcaption></figure>
<figure><img src="image_31.png" /><figcaption>Figure 4.6: Monthly mean potential evapotranspiration for the intermediate sub-basin at Paris (H5920010) calculated on period 1976-2005: comparison between observations and climate projections</figcaption></figure>
# 5 Climate change impact on the flow without the reservoir influence

In the Section 3, we carried out a calibration of a hydrological model over the historical period, explicitly taking into account the influence of the four major reservoirs in the basin.

In order to perform the risk assessment of the reservoir management, we need to simulate hydrological flows without the reservoir influences.

## 5.1 De-influencing by simulation

Of the various methods available for de-influencing flows (Terrier et al. 2020), we opted for the simulation method. This approach involves simulating the catchment using parameters that have been calibrated on a model taking into account human influences (see Section 3), while eliminating human influences from the model.

As the reservoir influences are the only human influences explicitly integrated in the model, the naturalization is not complete and does not take into account all other usages (withdrawals for drinking water, irrigation, industries...).

The uninfluenced flow regime downstream the reservoirs is highly different from the measured (i.e. influenced) one as illustrated in Figure 5.1 for the Aube River at Arcis-sur-Aube. De-influenced flows are higher than observed influenced flows during winter and spring, when the reservoir located upstream the station is filling, and lower during summer and autumn, when the reservoir releases for supporting low-flows.

<figure><img src="image_32.png" /><figcaption>Figure 5.1: De-influenced and observed flow regimes for station H1501010 - the Aube at Arcis-sur-Aube forced by SAFRAN reanalysis (1959-2022)</figcaption></figure>

Simulation outputs and hydrological indicators for uninfluenced simulated flows computed for the period 1959-2022 can be downloaded from the following address: https://nextcloud.inrae.fr/s/jH5FFGbLXSsBGoA.
## 5.2 Comparison of uninfluenced simulated past flows with other databases

In this approach, we compare the uninfluenced data simulated by our model with the data from the So-greah/Hydratec database (Hydratec 2011) which is the uninfluenced flow database formerly used by the ETPB for their studies, including the model developed for the ClimAware project (Dorchies, Thirel, Jay-Allemand, et al. 2014; Dorchies, Thirel, Perrin, et al. 2016; Ficchì et al. 2015). This database contains 25 gauging stations that are in common with the 152 stations contained in the *seinebasin2* model.

For this comparison, the EPTB wanted to focus on the VCN10 annual indicator which corresponds to the minimum mean flow calculated over 10 consecutive days. This indicator is used to evaluate the maximum flow released by the reservoirs during the worst low-flow period in the year.

The Figure 5.2 shows that the annual VCN10 indicators for the two data sets at La Seine à Paris are quite similar (The difference between the two sources is displayed as a grey line). Although for some stations we observe values ranging from simple to double, the values remain in the same range, between 25 m³/s and 150 m³/s.

<figure><img src="image_33.png" /><figcaption>Figure 5.2: Annual VCN10 of Hydratec and seinebasin2 uninfluenced flows at Paris for the historical period</figcaption></figure>

The plot for the 24 other gauging stations can be downloaded at: https://nextcloud.inrae.fr/s/iJJeHpBr56mDHBd

## 5.3 Simulation of uninfluenced flows forced by climate projections

The model calibrated on influenced flows over the period 1958-2020 is now forced by 11 climate projections for both RCP 4.5 and 8.5 in a configuration without reservoirs.

The simulation outputs of these resulting uninfluenced simulated flows are available at the URL: https://nextcloud.inrae.fr/s/adinzGa3AmLEXnZ?path=%2F03-naturalised_flows%2Fv2.0%2FDRIAS2020_NEW

As a first result we can compare the uninfluenced flow of the *seinebasin2* model (noted as Inrae) database on the annual VCN10 indicator for the gauged station located at Paris forced by the SAFRAN reanalysis and the DRIAS climate projections and we extend the period over 2100 with climate projections.

The Figure 5.3 shows the results for the climate projections forced by RCP 4.5, and the Figure 5.4 for RCP 8.5.

The plots for all the gauging stations in the Hydratec data set are available at: https://nextcloud.inrae.fr/s/adinzGa3AmLEXnZ?path=%2F03-naturalised_flows%2Fv1.0
<figure><img src="image_34.png" /></figure>

Figure 5.3: VCN10 30-years moving average of uninfluenced flows over historical period and future period forced by RCP 4.5 on the Seine River at Paris

<figure><img src="image_35.png" /></figure>

Figure 5.4: VCN10 30-years moving average of uninfluenced flows over historical period and future period forced by RCP 8.5 on the Seine River at Paris
## 5.4 Impact of climate change on hydrological indicators for flows without reservoir influence

Although, the Explore2 project outputs (Sauquet 2022) will provide an up to date overview of the impact of climate change impact on water resources in France, the present study on the Seine River cannot be compared to the work done in Explore 2. Indeed, even if this study uses some identical GCM/RCM projections, the Explore2 project will produce more robust projections based on multiple bias correction methods, multiple hydrological models, and will identify the uncertainties in the model chain using uncertainty components partitioning (Evin et al. 2019).

The evolution of hydrological indicators is assessed as the ratio between the indicator calculated for the future period (near:2021-2050, medium-term: 2041-2070, far: 2071-2100) over the one calculated on the reference period (1976-2005).

Evolution indicators are computed separately for each climate projection forced by RCP 4.5 and 8.5 and we show the minimum, median and maximum evolution encountered over the 11 climate projections.

### 5.4.1 List of indicators

#### 5.4.1.1 Monthly indicators

Monthly indicators for uninfluenced simulated flows are:

* monthly mean of daily mean flow rate (m³/s)

* low-flow monthly mean for a 5 year return period (m³/s)

#### 5.4.1.2 Synthetic indicators

We use the same indicators defined in Section 3.4

For low-flows the indicators are: "VCN10", "VCN30", and "QMNA" for a return period of 2, 5, and 10 years computed on a statistical adjustment on a Galton distribution. For high flows: "QJXA" for a return period of 2, 10, and 20 years computed on a statistical adjustment on a Gumbel distribution. For both low-flows and high-flows: quantiles 95% and 10% of daily mean flows.

The calculation method for all these indicators are detailed in Chazot et al. (2012).

### 5.4.2 Results on monthly flows without reservoir influence

The mean monthly flow at Paris (H5920010) for the reference period (1976-2005) and for the distant future period (2071-2100) are respectively shown in Figures 5.5 and 5.6. We can notice that, for reference period, simulated flows forced by climate projections shows a bias in autumn with a simulated flow dryer than the simulated flows forced by SAFRAN observations. Despite this bias, simulated flows forced by climate projection on period 2071-2100 shows significant increasing of high flows and decreasing of low flows for almost all projections.

### 5.4.3 Evolution of hydrological indicators

We propose synthetic tables providing minimum, median, and maximum evolution among the 11 climate projections for each station for both monthly indicators such as in the Table 5.1, and hydrological indicators such as in Table 5.2 for Paris-Austerlitz gauging station (H5920010) between 1976-2005 and 2071-2100 in RCP 8.5.

In this configuration (RCP 8.5 and evolution between 1976-2005 and 2071-2100), the Figure 5.7 shows the median value of the evolution of the QA indicator which is likely to remain stable downstream Paris with a contrasted light increase for the major part of the basin except for the Beauce natural region where it decreases. The median evolution of the QMNA5 low-flow indicator shows a decrease between 10 and 50% on the major part of the basin (Figure 5.8). The QJXA10 high-flow indicator shows an increase between 25 and 50% on a majority of gauging stations (Figure 5.9).
<figure><img src="image_36.png" /><figcaption>Figure 5.5: Monthly mean flows at Paris (H5920010) calculated on period 1976-2005: comparison between observed (obs), simulated with influences (sim), simulated without influences (nat), and simulated without influence forced by climate projections</figcaption></figure>

<figure><img src="image_37.png" /><figcaption>Figure 5.6: Monthly mean flows at Paris (H5920010): comparison between observed (obs), simulated with influences (sim), simulated without influences (nat) calculated on period 1976-2005, and simulated without influence forced by RCP8.5 climate projections calculated on period 2071-2100</figcaption></figure>
<table><caption>Table 5.1: Absolute values over 1976-2005 and min, max and median evolution of mean monthly uninfluenced flows at Paris-Austerlitz between 1976-2005 and 2071-2100 for RCP 8.5 (%)</caption><thead><tr><th></th><th>Q~obs~ (m^3/s)</th><th>Q~sim~ (m^3/s)</th><th>Q~nat~ (m^3/s)</th><th>Δ Q~nat~ min (%)</th><th>Δ Q~nat~ med (%)</th><th>Δ Q~na</th></tr></thead><tbody><tr><td>January</td><td>540.4</td><td>533.9</td><td>627.4</td><td>+0.3</td><td>+21.6</td><td>+</td></tr><tr><td>February</td><td>587.6</td><td>573.9</td><td>676.8</td><td>+4.9</td><td>+30.7</td><td>+</td></tr><tr><td>March</td><td>498.6</td><td>488.7</td><td>573.3</td><td>-20.2</td><td>+9.1</td><td>+</td></tr><tr><td>April</td><td>418.1</td><td>406.6</td><td>499.5</td><td>-20.9</td><td>+7.5</td><td>+</td></tr><tr><td>May</td><td>316.1</td><td>306.6</td><td>357.9</td><td>-21.6</td><td>-5.8</td><td>+</td></tr><tr><td>June</td><td>228.7</td><td>219.4</td><td>235.7</td><td>-38.5</td><td>-15.6</td><td>+</td></tr><tr><td>July</td><td>181.4</td><td>174.6</td><td>170.2</td><td>-53.4</td><td>-24.0</td><td>+</td></tr><tr><td>August</td><td>162.6</td><td>147.7</td><td>110.6</td><td>-54.5</td><td>-31.5</td><td>+</td></tr><tr><td>September</td><td>163.4</td><td>149.5</td><td>99.4</td><td>-58.4</td><td>-35.4</td><td>+1</td></tr><tr><td>October</td><td>218.5</td><td>206.1</td><td>177.3</td><td>-64.8</td><td>-43.9</td><td>+</td></tr><tr><td>November</td><td>280.5</td><td>297.5</td><td>308.9</td><td>-56.7</td><td>-20.2</td><td>+1</td></tr><tr><td>December</td><td>423.1</td><td>429.4</td><td>492.3</td><td>-27.0</td><td>+5.0</td><td>+1</td></tr></tbody></table>

<table><caption>Table 5.2: Absolute values over 1976-2005 and min, max and median evolution of hydrological indicators of uninfluenced flows at Paris-Austerlitz between 1976-2005 and 2071-2100 for RCP 8.5 (%)</caption><thead><tr><th></th><th>Q~obs~ (m^3/s)</th><th>Q~sim~ (m^3/s)</th><th>Q~nat~ (m^3/s)</th><th>Δ Q~nat~ min (%)</th><th>Δ Q~nat~ med (%)</th><th>Δ Q~na</th></tr></thead><tbody><tr><td>QA</td><td>335.4</td><td>329.2</td><td>359.3</td><td>-18.0</td><td>6.7</td><td></td></tr><tr><td>VCN10_2</td><td>114.7</td><td>98.4</td><td>65.1</td><td>-52.5</td><td>-33.2</td><td></td></tr><tr><td>VCN30_2</td><td>126.6</td><td>107.8</td><td>72.5</td><td>-54.1</td><td>-33.8</td><td></td></tr><tr><td>QMNA2</td><td>133.9</td><td>113.5</td><td>78.9</td><td>-53.9</td><td>-33.4</td><td></td></tr><tr><td>VCN10_5</td><td>91.3</td><td>73.0</td><td>46.8</td><td>-51.5</td><td>-28.9</td><td></td></tr><tr><td>VCN30_5</td><td>99.5</td><td>79.6</td><td>51.5</td><td>-53.0</td><td>-29.9</td><td></td></tr><tr><td>QMNA5</td><td>104.9</td><td>84.0</td><td>54.7</td><td>-51.6</td><td>-30.2</td><td></td></tr><tr><td>VCN10_10</td><td>81.0</td><td>62.4</td><td>39.4</td><td>-50.9</td><td>-26.6</td><td></td></tr><tr><td>VCN30_10</td><td>87.7</td><td>67.9</td><td>43.0</td><td>-52.4</td><td>-27.7</td><td></td></tr><tr><td>QMNA10</td><td>92.4</td><td>71.7</td><td>45.2</td><td>-50.3</td><td>-28.5</td><td></td></tr><tr><td>QJXA2</td><td>1076.2</td><td>1126.0</td><td>1373.0</td><td>1.4</td><td>21.7</td><td></td></tr><tr><td>QJXA10</td><td>1527.7</td><td>1669.8</td><td>1928.8</td><td>10.1</td><td>30.3</td><td></td></tr><tr><td>QJXA20</td><td>1700.3</td><td>1877.6</td><td>2141.2</td><td>7.9</td><td>31.3</td><td></td></tr></tbody></table>
<figure><img src="image_38.png" /><figcaption>Figure 5.7: Map of median scenario evolution of indicator QA between 1976-2005 and 2071-2100 for RCP 8.5</figcaption></figure>
<figure><img src="image_39.png" /><figcaption>Figure 5.8: Map of median scenario evolution of indicator QMNA5 between 1976-2005 and 2071-2100 for RCP 8.5</figcaption></figure>
<figure><img src="image_40.png" /><figcaption>Figure 5.9: Map of median scenario evolution of indicator QJXA10 between 1976-2005 and 2071-2100 for RCP 8.5</figcaption></figure>
# 6 Current reservoirs management rules: modeling and climate change impact

The modeling of the current reservoirs management rules allows to get simulated flows influenced by these rules in a simulation forced by climate projections, and it provides a base line for comparison with new management rules that will be processed in the report "IN-WOP project WP3 - Seine River study case: Risk-based management rules and assessment of fairness under climate change".

The so-called "Current reservoir management rules" are used by the EPTB Seine-Grands-Lacs for operating the AUBE, SEINE, MARNE and YONNE lakes. These management rules are described in Dehay (2012) and has already been modeled in the ClimAware project (Dorchies, Thirel, Jay-Allemand, et al. 2014; Dorchies, Thirel, Perrin, et al. 2016).

This section therefore focuses on integrating these rules into the model *seinebasin2* and assess the evolution of hydrological indicators in the light of climate projections.

## 6.1 Modeling of reservoir intake and release flows

As the current reservoir management rules are essentially local and not centralized, it's possible to compute reservoir intake and release flows off line, from the simulated uninfluenced flows.

All these constraints are compliant with the conceptualization of reservoir connections described in Figure 3.1.

The management constraints are modeled in this order (constraints are overwritten if several apply):

* define intake or release flow in order to follow the objective curve

* release water to support low-flow to meet the reserved flow

* limit the intake in order to respect the reserved flow

* fill the reservoir in order to maintain the flow under the so called “reference” flow

* limit the release in order to not exceed the reference flow

* limit the intake and the release to the capacity of their respective canals (Table 6.1)

* add the replenishment of natural rivers if so

* limit daily variation of the release at Lake Yonne ($\Delta Q_{max} = 2 \text{ m}^3/\text{s}$)

* limit intake and release in order to stay in the range of minimum and maximum capacities of the reservoir (Table 6.2)

Intake and release flows are determined at each time step with the rules presented above from a state based on:

* the simulated uninfluenced flows;

* the lake volumes updated from the previous time step.

These data are then included in the modeling process in order to get simulated flows influenced by current reservoir management rules.
<table><caption>Table 6.1: Characteristics of the reservoir connections</caption><thead><tr><td>Reservoir ID</td><td>Connection ID</td><td>Max flow rate (m^3/s)</td></tr></thead><tbody><tr><td>LAC_AUBE</td><td>P_AUBE</td><td>135</td></tr><tr><td>LAC_AUBE</td><td>R_AUBE</td><td>35</td></tr><tr><td>LAC_MARNE</td><td>P_MARNE</td><td>375</td></tr><tr><td>LAC_MARNE</td><td>P_BLAISE</td><td>33</td></tr><tr><td>LAC_MARNE</td><td>R_MARNE</td><td>50</td></tr><tr><td>LAC_SEINE</td><td>P_SEINE</td><td>200</td></tr><tr><td>LAC_SEINE</td><td>R_SEINE</td><td>35</td></tr><tr><td>LAC_YONNE</td><td>CHAUM_07</td><td>0</td></tr><tr><td>LAC_YONNE</td><td>H2021010</td><td>16</td></tr></tbody></table>

<table><caption>Table 6.2: Characteristics of the reservoirs</caption><thead><tr><td>Reservoir ID</td><td>Min. volume (mcm)</td><td>Max. volume (mcm)</td><td>Storage capacity (mcm)</td></tr></thead><tbody><tr><td>LAC_AUBE</td><td>2.3</td><td>183.5</td><td>181.2</td></tr><tr><td>LAC_MARNE</td><td>10.0</td><td>364.5</td><td>354.5</td></tr><tr><td>LAC_SEINE</td><td>6.6</td><td>219.5</td><td>212.9</td></tr><tr><td>LAC_YONNE</td><td>8.5</td><td>82.5</td><td>74.0</td></tr></tbody></table>

## 6.2 Simulation of flows with current rules on the historical period

The simulation has been performed on the historical period and we compare the simulated influenced flows with the observed ones in order to assess the quality of the “current rules” model.

The location where the influence is at its greatest is immediately downstream of the reservoirs. Figure 6.1 presents the comparison of the hydrological regime on the stations R_AUBE (AUBE), R_MARNE (MARNE), R_SEINE (SEINE) and H2021010 (YONNE).

On Aube, Seine and Marne lakes, the model correctly reproduced the observed flow. However, the low-flow period downstream the Aube Lake has a significant gap.

On the Yonne Lake (station H2021010), the gap is similar as the one already observed on the calibration results where the observed reservoir releases were directly used in the model. No explanation to this gap has been emerged so far.

As one can see in Figure 6.2, the hydrological regime is perfectly reproduced at Paris.

A global assessment is also performed with the same indicators used during the calibration process (Chazot et al. 2012).

The ratio between simulated and observed mean flows for all sub-basin is shown on Figure 6.3. We see an error inferior at 10% on all sub-basins downstream the reservoir.

On the VCN30 of 2 years return period (Figure @ref{fig:05-plotVCN30Y2}), the model usually underestimates the flow by 25 to 50% and we see the same trend on the QMNA5 (Figure 6.5).

Flood indicators QJXA10 (Figure 6.6) show better results with a light overestimation fading away downstream Paris.

All the ratio indicators provided by Chazot et al. (2012) are compiled in one radar plot Figure 6.7 for the 9 monitoring stations used to assess the management performance.

Simulated flows with modeled current rules forced by historical climate are available via this link: https://nextcloud.inrae.fr/s/adinzGa3AmLEXnZ?path=%2F04-current_rules%2Fv2.0%2Fhistorical%2Fdata
<figure><img src="image_41.png" /><figcaption>Figure 6.1: Hydrological regimes on gauging stations downstream the reservoirs Aube, Marne, Seine, and Yonne respectively with observed flows in black and flows simulated with modeled current rules in orange for the period 1959-2022</figcaption></figure>
<figure><img src="image_42.png" /><figcaption>Figure 6.2: Simulated hydrological regime at Paris with the modeled current rules (1959-2020)</figcaption></figure>
<figure><img src="image_43.png" /><figcaption>Figure 6.3: Map of R-QA indicators for simulated flows influenced by modeled reservoir current rules calculated on period 1959-2022</figcaption></figure>
<figure><img src="image_44.png" /><figcaption>Figure 6.4: Map of R-VCN30-2 indicators for simulated flows influenced by modeled reservoir current rules calculated on period 1959-2022</figcaption></figure>
<figure><img src="image_45.png" /><figcaption>Figure 6.5: Map of R-QMNA5 indicators for simulated flows influenced by modeled reservoir current rules calculated on period 1959-2022</figcaption></figure>
<figure><img src="image_46.png" /><figcaption>Figure 6.6: Map of R-QJXA10 indicators for simulated flows influenced by modeled reservoir current rules calculated on period 1959-2022</figcaption></figure>
<figure><img src="image_47.png" /><figcaption>Figure 6.7: Ratio between hydrological indicators calculated on simulated flows with current management rules and observed influenced flows on the period 1959-2022</figcaption></figure>
## 6.3 Current rules under climate change

### 6.3.1 Modeling current rules forced by climate projections

Calculations of intakes and releases at the reservoirs (See section 6.1) are performed from the outputs of the simulation of the uninfluenced flows forced by climate projections. The simulation of the current rules is then performed by injecting these influences in the model as it has been previously done for historical climate.

Simulated flows for all climate projections are available via this link: https://nextcloud.inrae.fr/s/adinzGa3AmLEXnZ?path=%2F04-current_rules%2Fv2.0%2FDRIAS2020_NEW

### 6.3.2 Impact of climate change on simulated current rules

We perform the same assessment as the one performed for climate change impact on simulated uninfluenced flows in Section 5.4.

#### 6.3.2.1 Results on monthly flows simulated with modeled current rules

The Figures 6.8 and 6.9 show the monthly flow simulated with modeled current rules and forced by climate projections for the reference period (1976-2005) and the end of century period (2071-2100) respectively.

<figure><img src="image_48.png" /></figure>

Figure 6.8: Monthly mean flows at Paris (H5920010) calculated on period 1976-2005: comparison between observed (obs), simulated with observed influences (sim), simulated without influences (nat), and simulated with modeled influences forced by climate projections

#### 6.3.2.2 Evolution of hydrological indicators

The same evolution table as the one provided in section 5.4.3 has been produced.

These synthetic tables providing minimum, median, and maximum evolution among the 11 climate projections for each stations for both monthly indicators such as in the Table 5.1, and hydrological indicators such as in Table 5.2 for Paris-Austerlitz gauging station (H5920010) between 1976-2005 and 2071-2100 in RCP 8.5.

In this configuration (RCP 8.5 and evolution between 1976-2005 and 2071-2100), the comparison of the median value of the evolution of the QA indicator between the Figure 5.7 for uninfluenced flows and the Figure 5.7 for
<figure><img src="image_49.png" /><figcaption>Figure 6.9: Monthly mean flows at Paris (H5920010): comparison between observed (obs), simulated with observed influences (sim), simulated without influences (nat) calculated on period 1976-2005, and simulated with modeled influences forced by RCP8.5 climate projections calculated on period 2071-2100</figcaption></figure>

<table><caption>Table 6.3: Evolution of mean monthly simulated influenced flows at Paris-Austerlitz between 1976-2005 and 2071-2100 for RCP 8.5 (%)</caption><thead><tr><th></th><th>obs</th><th>sim</th><th>nat</th><th>min</th><th>med</th><th>max</th></tr></thead><tbody><tr><td>M1</td><td>540.4</td><td>571.9</td><td>627.4</td><td>-5.5</td><td>15.7</td><td>103.9</td></tr><tr><td>M2</td><td>587.6</td><td>618.8</td><td>676.8</td><td>6.9</td><td>37.5</td><td>84.4</td></tr><tr><td>M3</td><td>498.6</td><td>521.0</td><td>573.3</td><td>-17.2</td><td>15.3</td><td>54.2</td></tr><tr><td>M4</td><td>418.1</td><td>430.7</td><td>499.5</td><td>-20.1</td><td>9.9</td><td>35.8</td></tr><tr><td>M5</td><td>316.1</td><td>322.5</td><td>357.9</td><td>-20.0</td><td>-3.4</td><td>19.3</td></tr><tr><td>M6</td><td>228.7</td><td>224.9</td><td>235.7</td><td>-20.5</td><td>6.3</td><td>48.1</td></tr><tr><td>M7</td><td>181.4</td><td>155.7</td><td>170.2</td><td>-35.3</td><td>-14.0</td><td>13.6</td></tr><tr><td>M8</td><td>162.6</td><td>113.8</td><td>110.6</td><td>-38.8</td><td>-20.8</td><td>36.5</td></tr><tr><td>M9</td><td>163.4</td><td>108.3</td><td>99.4</td><td>-39.5</td><td>-27.9</td><td>49.7</td></tr><tr><td>M10</td><td>218.5</td><td>170.5</td><td>177.3</td><td>-66.2</td><td>-55.0</td><td>36.4</td></tr><tr><td>M11</td><td>280.5</td><td>284.1</td><td>308.9</td><td>-59.8</td><td>-23.4</td><td>139.5</td></tr><tr><td>M12</td><td>423.1</td><td>453.1</td><td>492.3</td><td>-33.8</td><td>3.2</td><td>115.7</td></tr></tbody></table>
<table><caption>Table 6.4: Evolution of hydrological indicators of simulated influenced flows at Paris-Austerlitz between 1976-2005 and 2071-2100 for RCP 8.5 (%)</caption><thead><tr><th></th><th>obs</th><th>sim</th><th>nat</th><th>min</th><th>med</th><th>max</th></tr></thead><tbody><tr><td>QA</td><td>335.4</td><td>329.9</td><td>359.3</td><td>-18.1</td><td>6.8</td><td>62.3</td></tr><tr><td>VCN10_2</td><td>114.7</td><td>67.5</td><td>65.1</td><td>-55.2</td><td>-38.5</td><td>36.5</td></tr><tr><td>VCN30_2</td><td>126.6</td><td>74.6</td><td>72.5</td><td>-58.1</td><td>-42.4</td><td>40.9</td></tr><tr><td>QMNA2</td><td>133.9</td><td>80.6</td><td>78.9</td><td>-57.8</td><td>-41.4</td><td>38.1</td></tr><tr><td>VCN10_5</td><td>91.3</td><td>50.6</td><td>46.8</td><td>-56.9</td><td>-40.1</td><td>31.3</td></tr><tr><td>VCN30_5</td><td>99.5</td><td>55.2</td><td>51.5</td><td>-55.7</td><td>-44.4</td><td>33.5</td></tr><tr><td>QMNA5</td><td>104.9</td><td>58.1</td><td>54.7</td><td>-55.5</td><td>-39.8</td><td>30.1</td></tr><tr><td>VCN10_10</td><td>81.0</td><td>43.5</td><td>39.4</td><td>-58.2</td><td>-41.0</td><td>28.7</td></tr><tr><td>VCN30_10</td><td>87.7</td><td>47.1</td><td>43.0</td><td>-58.0</td><td>-42.2</td><td>29.8</td></tr><tr><td>QMNA10</td><td>92.4</td><td>49.0</td><td>45.2</td><td>-57.4</td><td>-36.1</td><td>26.1</td></tr><tr><td>QJXA2</td><td>1076.2</td><td>1196.7</td><td>1373.0</td><td>4.0</td><td>23.7</td><td>74.2</td></tr><tr><td>QJXA10</td><td>1527.7</td><td>1770.2</td><td>1928.8</td><td>12.8</td><td>26.9</td><td>77.1</td></tr><tr><td>QJXA20</td><td>1700.3</td><td>1989.3</td><td>2141.2</td><td>11.2</td><td>29.5</td><td>81.2</td></tr></tbody></table>

influenced flows with the current management rules shows no differences. Indeed, as the management of the reservoir in annual, we can't see any effect of them on the inter-annual mean flow.

The comparison of the median evolution of the QMNA5 low-flow indicator (Figure 6.11) shows that the impact is the same as for uninfluenced flows 5.8 at almost all gauging stations except on the Marne river and downstream where the impact is increased for influenced flows. The reservoir influence, at least with the current rules, seems therefore to increase the vulnerability to water shortages as noticed by Di Baldassarre et al. (2018).

The comparison between Figures 5.9 and 6.12 for the QJXA10 high-flow indicator shows no difference except a mitigation of the impact with the influenced flows on the sub-basin straight downstream the Aube lake.

All simulated flows, indicators and maps are available via the link: https://nextcloud.inrae.fr/s/adinzGa3AmLEXnZ?path=%2F04-current_rules%2Fv2.0%2FDRIAS2020_NEW
Evolution of QA for RCP8.5 median projection (%)

<figure><img src="image_50.png" /><figcaption>Figure 6.10: Map of median scenario evolution of indicator QA between 1976-2005 and 2071-2100 for RCP 8.5 with simulated influenced flows</figcaption></figure>
<figure><img src="image_51.png" /><figcaption>Figure 6.11: Map of median scenario evolution of indicator QMNA5 between 1976-2005 and 2071-2100 for RCP 8.5 with simulated influenced flows</figcaption></figure>
<figure><img src="image_52.png" /><figcaption>Figure 6.12: Map of median scenario evolution of indicator QJXA10 between 1976-2005 and 2071-2100 for RCP 8.5 with simulated influenced flows</figcaption></figure>
# 7 Conclusion

A semi-distributed hydrological model of the Seine River Basin has been set up. It used the **airGRiwrm** R package which allows the integration of anthropogenic influences in the modeled flows. The model has been calibrated with influenced flows on more than 150 gauging stations using observed influences on the 4 reservoirs managed by the EPTB Seine Grands Lacs. The calibrated model shows good performances on mean flows, an slight underestimation of low-flows and a good performance of high-flows.

Climate projections has been used to perform both uninfluenced flow simulations and influenced flows with modeled current rules of the reservoirs.

The impact of climate change has been assess through hydrological indicators and it shows that the impact is more important for influenced flows with current management rules on low-flow indicators.

These outputs will be used afterward in the report "IN-WOP project WP3 - Seine River study case: Risk-based management rules and assessment of fairness under climate change".

Uninfluenced flows will serve to compute the risk assessment on the management of the reservoirs and influenced flows with modeled current rules will serve as a comparison base line for the management performance assessment of the risk based rules developed in this report.
8 Acknowledgments

This report is one of the reports produced as part of the Seine River case study (WP3) within the IN-WOP project.

The authors would like to thank the European Commission and the French National Research Agency (ANR) for funding in the frame of the collaborative international consortium IN-WOP financed under the 2018 Joint call of the WaterWorks2017 ERA-NET Cofund. This ERA-NET is an integral part of the activities developed by the Water JPI.

2018 JOINT CALL

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# 9 About this report

This document has been produced trying to follow the FAIR principles of reproductibility (Wilkinson et al. 2016). It's source code is available within an R package names seinebasin2, containing this report in bookdown format (Xie 2016) generated by the InraeThemes package (Carayon 2020).

The seinebasin2 R-package documentation is available at https://in-wop.g-eau.fr/seinebasin2

The package code and the source code of this report can be downloaded at: https://forgemia.inra.fr/in-wop/seinebasin2
Bibliography

Carayon, David (2020). *Collection Non Officielle de Templates (R markdown) et de Thèmes (Ggplot) Qui Respectent La Charte Graphique INRAE*. manual. URL: https://github.com/davidcarayon/InraeThemes.

Chazot, Sébastien et al. (Feb. 10, 2012). *Explore 2070 - Lot Hydrologie de Surface - A2 - Résultats : Fiches, Cartes et Graphes*. Ministère de l'écologie, du développement durable, des transports et du logement, p. 36.

Coron, L. et al. (Aug. 1, 2017). "The Suite of Lumped GR Hydrological Models in an R Package". In: *Environmental Modelling & Software* 94, pp. 166-171. ISSN: 1364-8152. DOI: 10.1016/j.envsoft.2017.05.002. URL: http://www.sciencedirect.com/science/article/pii/S1364815217300208 (visited on 01/07/2021).

De Lavenne, Alban et al. (2019). "A Regularization Approach to Improve the Sequential Calibration of a Semidis-tributed Hydrological Model". In: *Water Resources Research* 55.11, pp. 8821-8839. ISSN: 1944-7973. DOI: 10.1029/2018WR024266. URL: https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2018WR024266 (visited on 06/07/2021).

Dehay, F. (2012). "Etude de l'impact du changement climatique sur la gestion des lacs-réservoirs de la Seine". other. Diplôme d'ingénieur de l'ENGEES, Strasbourg, p. 74. URL: https://hal.inrae.fr/hal-02597326 (visited on 02/12/2021).

Di Baldassarre, Giuliano et al. (Nov. 2018). "Water Shortages Worsened by Reservoir Effects". In: *Nature Sustainability* 1.11 (11), pp. 617-622. ISSN: 2398-9629. DOI: 10.1038/s41893-018-0159-0. URL: https://www.nature.com/articles/s41893-018-0159-0 (visited on 07/21/2023).

Dorchies, David, Olivier Delaigue, and Guillaume Thirel (Mar. 7, 2022). *airGRiwrm: Modeling of Integrated Water Resources Management Based on airGR. R Package Version 0.6.1*. Dorchies, David; Delaigue, Olivier; Thirel, Guillaume, 2022, "airGRiwrm: Modeling of Integrated Water Resources Management based on airGR. R Package version 0.6.1", https://doi.org/10.15454/3CVD1I, Recherche Data Gouv, V1. DOI: 10.15454/3CVD1I. URL: https://data.inrae.fr/dataset.xhtml?persistentId=doi:10.15454/3CVD1I (visited on 03/07/2022).

Dorchies, David, Guillaume Thirel, Maxime Jay-Allemand, et al. (July 3, 2014). "Climate Change Impacts on Multi-Objective Reservoir Management: Case Study on the Seine River Basin, France". In: *International Journal of River Basin Management* 12.3, pp. 265-283. ISSN: 1571-5124. DOI: 10.1080/15715124.2013.865636. URL: http://dx.doi.org/10.1080/15715124.2013.865636 (visited on 04/15/2015).

Dorchies, David, Guillaume Thirel, Charles Perrin, et al. (Oct. 2016). "Climate Change Impacts on Water Resources and Reservoir Management in the Seine River Basin (France)". In: *La Houille Blanche* 5, pp. 32-37. ISSN: 0018-6368, 1958-5551. DOI: 10.1051/lhb/2016047. URL: http://www.shf-lhb.org/10.1051/lhb/2016047 (visited on 01/04/2018).

Evin, Guillaume et al. (Apr. 15, 2019). "Partitioning Uncertainty Components of an Incomplete Ensemble of Climate Projections Using Data Augmentation". In: *Journal of Climate* 32.8, pp. 2423-2440. ISSN: 0894-8755, 1520-0442. DOI: 10.1175/JCLI-D-18-0606.1. URL: http://journals.ametsoc.org/doi/10.1175/JCLI-D-18-0606.1 (visited on 07/18/2023).

Ficchì, A. et al. (July 15, 2015). "Optimal Operation of the Multireservoir System in the Seine River Basin Using Deterministic and Ensemble Forecasts". In: *Journal of Water Resources Planning and Management*, p. 05015005. ISSN: 0733-9496, 1943-5452. DOI: 10.1061/(ASCE)WR.1943-5452.0000571. URL: http://ascelibrary.org/doi/10.1061/%28ASCE%29WR.1943-5452.0000571 (visited on 07/16/2015).

Gupta, Hoshin V. et al. (Oct. 2009). "Decomposition of the Mean Squared Error and NSE Performance Criteria: Implications for Improving Hydrological Modelling". In: *Journal of Hydrology* 377.1-2, pp. 80-91. ISSN: 00221694. DOI: 10.1016/j.jhydrol.2009.08.003. URL: http://linkinghub.elsevier.com/retrieve/pii/S0022169409004843 (visited on 12/13/2012).

Hydratec (2011). *Actualisation de La Base de Données Des Débits Journaliers 'Naturalisés' - Phase 2*. 26895 - LME/TL, p. 31.
5.1 Absolute values over 1976-2005 and min, max and median evolution of mean monthly uninfluenced flows at Paris-Austerlitz between 1976-2005 and 2071-2100 for RCP 8.5 (%) 36

5.2 Absolute values over 1976-2005 and min, max and median evolution of hydrological indicators of uninfluenced flows at Paris-Austerlitz between 1976-2005 and 2071-2100 for RCP 8.5 (%) 36

6.1 Characteristics of the reservoir connections 41

6.2 Characteristics of the reservoirs 41

6.3 Evolution of mean monthly simulated influenced flows at Paris-Austerlitz between 1976-2005 and 2071-2100 for RCP 8.5 (%) 50

6.4 Evolution of hydrological indicators of simulated influenced flows at Paris-Austerlitz between 1976-2005 and 2071-2100 for RCP 8.5 (%) 51

List of Figures

1.1 Main tasks performed in WP3 4

2.1 Study area of The Seine River Basin 7

2.2 Functional scheme of the GR4J model (Perrin, Michel, and Andréassian 2003) 9

2.3 GRiwrn graph representing the vicinity of the Seine reservoir. In blue, upstream GR hydrological modelling; in green, GR hydrological modelling of intermediate catchment areas; in turquoise, reservoirs; in black, river branches, in dashed red, human diversions. 9

3.1 Conceptual scheme of reservoir connections with the river system 12

3.2 Diagram of natural network around the lake Seine 12

3.3 Diagram of the network around the lake Seine after reservoir implementation 12

3.4 Diagram of natural network around the lake Yonne 13

3.5 Diagram of the network around the lake Yonne after reservoir implementation 13

3.6 Diagram of natural network around the lake Marne 13

3.7 Diagram of natural network around the lake Aube 14

3.8 Diagram of the network around the lake Aube and Marne after reservoir implementation 14

3.9 Maps of calibration parameters including the influence of the reservoirs 16

3.10 Simulated and observed flow regimes incorporating the influence of reservoirs 17

3.11 Maps of KGE criteria for calibration with the integration of the influence of reservoirs 18

3.12 Map of R-QA indicators for simulated flows with observed reservoir influences calculated on period 1959-2022 20

3.13 Map of R-VCN30-2 indicators for simulated flows with observed reservoir influences calculated on period 1959-2022 21

3.14 Map of R-QMNA5 indicators for simulated flows with observed reservoir influences calculated on period 1959-2022 22

3.15 Map of R-QJXA10 indicators for simulated flows with observed reservoir influences calculated on period 1959-2022 23

3.16 Ratio between hydrological indicators calculated on simulated and observed influenced flows on the period 1959-2022 24
<table>
  <tbody>
    <tr>
      <td>4.1</td>
      <td>Downscaling steps from global to regional modelling to disaggregation at small spatial scales (except from DRIAS2020)</td>
      <td>25</td>
    </tr>
    <tr>
      <td>4.2</td>
      <td>Global fossil fuel CO2 emissions (left) and total CO2 emissions from fossil fuels and land use (right) for historical observations and RCP, SRES, and IS92 scenarios. Credit: Glen Peters.</td>
      <td>26</td>
    </tr>
    <tr>
      <td>4.3</td>
      <td>Merging of the SAFRAN layer with that of the intermediate catchment areas of the Seine catchment at Vernon</td>
      <td>27</td>
    </tr>
    <tr>
      <td>4.4</td>
      <td>Monthly mean precipitation for the intermediate sub-basin at Paris (H5920010) calculated on period 1976-2005: comparison between observations and climate projections</td>
      <td>28</td>
    </tr>
    <tr>
      <td>4.5</td>
      <td>Monthly mean daily temperature for the intermediate sub-basin at Paris (H5920010) calculated on period 1976-2005: comparison between observations and climate projections</td>
      <td>29</td>
    </tr>
    <tr>
      <td>4.6</td>
      <td>Monthly mean potential evapotranspiration for the intermediate sub-basin at Paris (H5920010) calculated on period 1976-2005: comparison between observations and climate projections</td>
      <td>30</td>
    </tr>
    <tr>
      <td>5.1</td>
      <td>De-influenced and observed flow regimes for station H1501010 - the Aube at Arcis-sur-Aube forced by SAFRAN reanalysis (1959-2022)</td>
      <td>31</td>
    </tr>
    <tr>
      <td>5.2</td>
      <td>Annual VCN10 of Hydratec and seinebasin2 uninfluenced flows at Paris for the historical period</td>
      <td>32</td>
    </tr>
    <tr>
      <td>5.3</td>
      <td>VCN10 30-years moving average of uninfluenced flows over historical period and future period forced by RCP 4.5 on the Seine River at Paris</td>
      <td>33</td>
    </tr>
    <tr>
      <td>5.4</td>
      <td>VCN10 30-years moving average of uninfluenced flows over historical period and future period forced by RCP 8.5 on the Seine River at Paris</td>
      <td>33</td>
    </tr>
    <tr>
      <td>5.5</td>
      <td>Monthly mean flows at Paris (H5920010) calculated on period 1976-2005: comparison between observed (obs), simulated with influences (sim), simulated without influences (nat), and simulated without influence forced by climate projections</td>
      <td>35</td>
    </tr>
    <tr>
      <td>5.6</td>
      <td>Monthly mean flows at Paris (H5920010): comparison between observed (obs), simulated with influences (sim), simulated without influences (nat) calculated on period 1976-2005, and simulated without influence forced by RCP8.5 climate projections calculated on period 2071-2100</td>
      <td>35</td>
    </tr>
    <tr>
      <td>5.7</td>
      <td>Map of median scenario evolution of indicator QA between 1976-2005 and 2071-2100 for RCP 8.5</td>
      <td>37</td>
    </tr>
    <tr>
      <td>5.8</td>
      <td>Map of median scenario evolution of indicator QMNA5 between 1976-2005 and 2071-2100 for RCP 8.5</td>
      <td>38</td>
    </tr>
    <tr>
      <td>5.9</td>
      <td>Map of median scenario evolution of indicator QJXA10 between 1976-2005 and 2071-2100 for RCP 8.5</td>
      <td>39</td>
    </tr>
    <tr>
      <td>6.1</td>
      <td>Hydrological regimes on gauging stations downstream the reservoirs Aube, Marne, Seine, and Yonne respectively with observed flows in black and flows simulated with modeled current rules in orange for the period 1959-2022</td>
      <td>42</td>
    </tr>
    <tr>
      <td>6.2</td>
      <td>Simulated hydrological regime at Paris with the modeled current rules (1959-2020)</td>
      <td>43</td>
    </tr>
    <tr>
      <td>6.3</td>
      <td>Map of R-QA indicators for simulated flows influenced by modeled reservoir current rules calculated on period 1959-2022</td>
      <td>44</td>
    </tr>
    <tr>
      <td>6.4</td>
      <td>Map of R-VCN30-2 indicators for simulated flows influenced by modeled reservoir current rules calculated on period 1959-2022</td>
      <td>45</td>
    </tr>
    <tr>
      <td>6.5</td>
      <td>Map of R-QMNA5 indicators for simulated flows influenced by modeled reservoir current rules calculated on period 1959-2022</td>
      <td>46</td>
    </tr>
    <tr>
      <td>6.6</td>
      <td>Map of R-QJXA10 indicators for simulated flows influenced by modeled reservoir current rules calculated on period 1959-2022</td>
      <td>47</td>
    </tr>
    <tr>
      <td>6.7</td>
      <td>Ratio between hydrological indicators calculated on simulated flows with current management rules and observed influenced flows on the period 1959-2022</td>
      <td>48</td>
    </tr>
  </tbody>
</table>
6.8 Monthly mean flows at Paris (H5920010) calculated on period 1976-2005: comparison between observed (obs), simulated with observed influences (sim), simulated without influences (nat), and simulated with modeled influences forced by climate projections 49

6.9 Monthly mean flows at Paris (H5920010): comparison between observed (obs), simulated with observed influences (sim), simulated without influences (nat) calculated on period 1976-2005, and simulated with modeled influences forced by RCP8.5 climate projections calculated on period 2071-2100 50

6.10 Map of median scenario evolution of indicator QA between 1976-2005 and 2071-2100 for RCP 8.5 with simulated influenced flows 52

6.11 Map of median scenario evolution of indicator QMNA5 between 1976-2005 and 2071-2100 for RCP 8.5 with simulated influenced flows 53

6.12 Map of median scenario evolution of indicator QJXA10 between 1976-2005 and 2071-2100 for RCP 8.5 with simulated influenced flows 54
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