# Unraveling uncertainties in near-term runoff projections across Europe: the major role of atmospheric noise

Juliette Deman, Julien Boé

► To cite this version:

Juliette Deman, Julien Boé. Unraveling uncertainties in near-term runoff projections across Europe: the major role of atmospheric noise. Environmental Research Letters, 2025, 20 (7), pp.074005. 10.1088/1748-9326/addb66. hal-05131964

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LETTER • OPEN ACCESS

Unraveling uncertainties in near-term runoff projections across Europe: the major role of atmospheric noise

To cite this article: Juliette Deman and Julien Boé 2025 *Environ. Res. Lett.* 20 074005

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LETTER

# Unraveling uncertainties in near-term runoff projections across Europe: the major role of atmospheric noise

Juliette Deman* and Julien Boé

CECI, Université de Toulouse, CERFACS/CNRS/IRD, Toulouse, France
* Author to whom any correspondence should be addressed.

E-mail: deman@cerfacs.fr

**Keywords:** internal variability, SMILEs, near-term projections, uncertainty partitioning, runoff, Europe, North Atlantic multi-decadal variability

Supplementary material for this article is available [online](#).

## Abstract

Internal variability drives large runoff variations across Europe. Disentangling its effects from that of anthropogenic forcing in future regional projections is crucial for effective adaptation planning. Here, we show that internal variability is the main source of uncertainty in near-term changes in Europe compared to model and scenario uncertainty, or as important as model uncertainty for the Mediterranean. The contribution of internal variability is even larger for runoff than for precipitation or evapotranspiration over northern, western and central Europe. The inter-member differences in runoff changes are mainly explained by precipitation changes and indirectly by changes in sea level pressure. In potential disagreement with observational studies, no apparent teleconnection between runoff multi-decadal variability and the Atlantic multi-decadal variability is generally found in climate models. This misrepresentation of teleconnections might affect the multi-decadal variability of annual precipitation and therefore runoff over the Mediterranean. Indeed, the multi-decadal variability in precipitation and sea level pressure over this area is shown to be generally underestimated.

## 1. Introduction

In a climate changing world, understanding and projecting accurately the future evolution of runoff is essential for effective water resource management (Mankin et al 2020). In Europe, anthropogenic climate change causes contrasting hydrological changes, with a decrease in annual runoff over the Mediterranean region, an increase over northern Europe, and no robust change over western and central Europe (Zhao and Dai 2022). These projections are subject to large uncertainties from multiple sources (Hawkins and Sutton 2009, Lehner et al 2020), namely the socio-economic narratives used to derive climate forcings, the resolved physics of climate models and the irreducible intrinsic variability of the earth system (Deser et al 2012). The latter is often the least considered factor, yet it has the potential to strongly amplify, attenuate or even reverse the anthropogenic signal on interannual to multi-decadal timescales, especially at the regional scale (Arnell

2003, Deser et al 2017, Maher et al 2020). It remains an ongoing challenge to quantify accurately the magnitude of runoff variations linked to internal variability in future projections (Lehner and Deser 2023).

Variations in runoff are the result of both variations in climatic conditions and of the catchment's response to these variations (Gudmundsson et al 2011, Zhu et al 2023). The most important variations in climatic conditions with respect to runoff are generally variations in precipitation (Lavers et al 2010, Zhu et al 2023). Variations in precipitation are generally mainly driven by large-scale atmospheric circulation (Boé et al 2009, Lavers et al 2013, Simpson et al 2019). This applies to both interannual and multi-decadal timescales (Dieppois et al 2016, Zhu et al 2023).

Apparent multi-decadal fluctuations in large-scale atmospheric circulation could be the result of high-frequency atmospheric noise integrated over longer timescales (Lehner and Deser 2023) or driven by intrinsic low-frequency oceanic variations, such as
the Atlantic multi-decadal variability (AMV; Simpson *et al* 2018). This distinction is important because some of these low-frequency oceanic variations could be potentially predictable thanks to initialized decadal predictions (Meehl *et al* 2009, Simpson *et al* 2018, Yeager *et al* 2018). Anomalies in sea surface temperature influence the state of atmospheric circulation and vice versa through air-sea coupling (Zhang *et al* 2019). These air-sea interactions lead to teleconnections between the AMV and the European climate (Sutton and Dong 2012). These teleconnections are for example particularly important for precipitation over western UK and Portugal in March (Simpson *et al* 2019) when the variability of the North Atlantic jet stream is at its peak (Simpson *et al* 2018). By combining skillful predictions of multi-year North Atlantic sea surface temperature variability and the observed teleconnections, skillful multi-year predictions of European precipitation or temperature can be obtained (Simpson *et al* 2019, Borchert *et al* 2021). Large teleconnections also exist between the AMV and French river flows in spring (Boé and Habets 2014) or groundwater levels (Bonnet *et al* 2020). Note that whether the observed AMV in the 20th century is really mostly an internal mode of variability or is mostly forced is debated (e.g. Klavans *et al* 2022).

Climate models generally exhibit a lack of skill in representing the multi-decadal variability of North Atlantic atmospheric circulation (Scaife and Smith 2018), particularly during winter (Bracegirdle 2022). This general bias includes, for example, an underestimation of the large multi-decadal variability of the North Atlantic jet stream in March (Simpson et al 2018) and an underestimation of the extreme trends in the North Atlantic Oscillation (Eade et al 2022). Model deficiencies may be due to poor representation of some mechanisms as ocean-atmosphere interactions (Simpson et al 2019, Bracegirdle et al 2022) or stratosphere-troposphere interactions (Omrani et al 2014, Bonnet et al 2024). Potential deficiencies in the models' response to external radiative forcing may also play a role (Klavans et al 2021). The underestimation of atmospheric multi-decadal variability in the North Atlantic, regardless of the underlying causes, could have multiple implications for future European climate projections. For instance, it could result in an underestimation of the magnitude and/or frequency of future extremes, which may typically be favored by high or low states of multi-decadal climate variability (O'Reilly et al 2021, Qasmi et al 2021, Baulon et al 2022).

The main objective of this study is to assess the uncertainties due to internal variability in near-term projections of the hydrological cycle over Europe, and to characterize the associated mechanisms. The role of large-scale atmospheric circulation and potentially predictable low-frequency oceanic variability is investigated in this context. An additional objective

of this study is to determine whether the underestimation of the multi-decadal variability in the North Atlantic found in previous studies could lead to an underestimation of the uncertainties in near-term runoff projections. This would indeed have important implications for water resource management, which needs to take into account a realistic full range of possible future evolutions in the context of climate change adaptation.

The data and methods are presented in section 2. In section 3, the contribution of internal variability to the uncertainties in future runoff projections over Europe is assessed. In section 4, we investigate the drivers of the intrinsic uncertainties in future runoff projections. Then, we assess the realism of the simulated multi-decadal variability of these drivers in the 20th century in section 5. Finally, the main conclusions of the study are drawn in section 6.

## 2. Data and methods

### 2.1. Data

Nine single model initial-condition large ensemble (SMILEs) of at least 30 members (simulations from the same model and forcing, differing only in initial conditions) from the Coupled Model Intercomparison Project phase 6 (CMIP6; Eyring et al 2016) are studied. We consider historical simulations and simulations forced by the SSP3-7.0 scenario (O'Neill et al 2016). To assess the contribution of scenario uncertainty, we also use simulations forced by the SSP1-2.6, SSP2-4.5 and SSP5-8.5 scenarios. A comprehensive list of the simulations studied is provided in table 1. The European continent is subdivided into three regions, following the latest IPCC report (Iturbide et al 2020): Northern Europe (NEU), Western and Central Europe (WCE), and the Mediterranean (MED) (figures 4(a), (c) and (e)).

The simulated low-frequency variability is evaluated using reanalysis and observational data. Two twentieth-century reanalyses are used for the evaluation of large-scale atmospheric circulation through sea level pressure: the European Centre for Medium-Range Weather Forecasts' (ECMWF) ERA20C (Poli et al 2016) and the National Oceanic Atmospheric Administration's (NOAA) 20 CRv3 (Compo et al 2011). Two observational datasets are used for the evaluation of continental precipitation: the CRU time series version 4.07 (Harris et al 2020) and the Global Precipitation Climatology Center version 2022 (Rustemeier et al 2022). The evaluation is done on the overlapping period between the reanalyses and precipitation observations, i.e. 1901–2010. Eight of the nine SMILEs are used for the evaluation of multi-decadal variability in the 20th century in section 5. The EC-Earth3 ensemble was not used as its simulations start in 1970. The six SMILEs with the necessary scenarios are used to analyze future projections.
<table><caption>**Table 1.** Single model initial-condition large ensemble (SMILEs) analyzed in this study, with the corresponding periods and number of members for each experiment and reference.</caption><thead><tr><th>Model version</th><th>Years</th><th>Forcing (number of members)</th><th>References</th></tr></thead><tbody><tr><td>ACCESS-ESM1-5</td><td>1850–2100</td><td>Historical (40), SSP1-2.6 (40), SSP2-4.5 (40), SSP3-7.0 (40), SSP5-8.5 (40)</td><td>Ziehn et al 2020</td></tr><tr><td>CanESM5</td><td>1850–2100</td><td>Historical (50), SSP1-2.6 (50), SSP2-4.5 (50), SSP3-7.0 (50), SSP5-8.5 (50)</td><td>Swart et al 2019</td></tr><tr><td>CESM2</td><td>1900–2100</td><td>Historical (100), SSP3-7.0 (100) (only 80 members for mrro and 90 for hfls)</td><td>Rodgers et al 2021</td></tr><tr><td>CNRM-CM6-1</td><td>1850–2014</td><td>Historical (30)</td><td>Voldoire et al 2019</td></tr><tr><td>EC-Earth3</td><td>1970–2100</td><td>Historical (50), SSP1-2.6 (50), SSP2-4.5 (50), SSP3-7.0 (50), SSP5-8.5 (50)</td><td>Wyser et al 2021</td></tr><tr><td>HadGEM3-GC31-LL</td><td>1850–2014</td><td>Historical (55)</td><td>Kuhlbrodt et al 2018</td></tr><tr><td>IPSL-CM6A-LR</td><td>1850–2014</td><td>Historical (32)</td><td>Boucher et al 2020</td></tr><tr><td>MIROC6</td><td>1850–2100</td><td>Historical (50), SSP1-2.6 (50), SSP2-4.5 (50), SSP3-7.0 (50), SSP5-8.5 (50)</td><td>Tatebe et al 2019</td></tr><tr><td>MPI-ESM1-2-LR</td><td>1850–2100</td><td>Historical (50), SSP1-2.6 (50), SSP2-4.5 (50), SSP3-7.0 (50), SSP5-8.5 (50)</td><td>Olonscheck et al 2023</td></tr></tbody></table>

## 2.2. Low-frequency variability

In order to estimate the intrinsic low-frequency variability, the observations and model annual time series are first linearly detrended and then low-pass filtered using a Lanczos filter with a cut-off frequency of 1/20 years and 21 weights. The first and last 10 years are not considered in the analyses.

## 2.3. Uncertainty partitioning

We assess the respective importance of three main sources of uncertainties in climate projections following the work of Lehner *et al* (2020). The uncertainties are computed separately. First, for each SMILE separately, the variance across members is calculated. Then, the multi-model mean across the 6 SMILES is calculated, to obtain the internal variability uncertainty *I*. The model uncertainty *M* is calculated for the SSP3-7.0 scenario. First, for each SMILE separately, the multi-member mean is calculated. Then, the variance across the 6 SMILES is calculated to obtain *M*. To calculate the scenario uncertainty *S*, first for each SMILE separately and for each scenario, the multi-member mean is calculated. The multi-member means are then averaged across the SMILES for each scenario. Finally, the variance across the 4 scenarios is calculated to obtain *S*. Five SMILES are available for the SSP1-2.6, SSP2-4.5 and SSP5-8.5 scenarios, and six SMILEs are available for the scenario SSP3-7.0 (see table 1).

The total uncertainty *T* is the sum of the internal variability uncertainty, model uncertainty and scenario uncertainty: $T = I + M + S$. For each time step, the fractional uncertainties are calculated as the ratio between the uncertainty of each source and the total uncertainty: $frac_I = I/T$, $frac_M = M/T$ and $frac_S = S/T$.

The partitioning of uncertainties is done on absolute annual anomalies using the 1995–2014 reference period. We have chosen to partition the uncertainty using SMILEs, rather than using all available CMIP6

models. Indeed, most of the CMIP6 models provide only one or a few members. As shown in Lehner *et al* (2020), it is more accurate to estimate the climate change signal using a large ensemble of members rather than using a statistical approach with a single member. Prior to calculating the different uncertainties, the annual time series are smoothed with a 10-year running mean as in Lehner *et al* (2020), in order to focus on decadal timescales and therefore on long-term climate changes, more relevant to develop long-term adaptation strategies (Hewitt *et al* 2020). This smoothing step leads to a reduction of the uncertainty due to internal variability (Hawkins and Sutton 2009).

In this study, we often refer to inter-member differences. These are the differences, for a given SMILE and scenario, between members that differ only in initial conditions. Inter-member differences are therefore only due to internal variability. We also refer to inter-model differences. These are the differences of multi-member means obtained with different SMILEs for a given scenario, and they are due to model uncertainty.

## 2.4. The surface water balance equation

Throughout the study, we refer to the surface water balance equation to analyze the changes in runoff:

$$ \Delta S / \Delta t = P - E - R $$

with, at annual level, $\Delta S / \Delta t$ the change of water storages from one year to another, *P* the precipitation, *E* the evapotranspiration and *R* the runoff.

## 3. Influence of internal variability in future runoff projections

In the near term, future changes in annual runoff are projected to be positive over NEU and negative over WCE and MED (figure 1). The multi-model mean of the relative changes is more pronounced
<figure><img src="image_7.png" /><figcaption>**Figure 1.** Annual runoff changes between 2025–2044 and 1995–2014, averaged over NEU (a), (d), WCE (b), (e) and MED (c), (f) projected by six CMIP6 SMILEs. Absolute changes ((a)–(c); mm d⁻¹) and relative changes ((d), (f); %). The box shows the median, the 1st and 3rd quartiles of the distribution. The whiskers extend to the 5th percentile and 95th percentile of the distribution. Values smaller than the 5th percentile and greater than the 95th percentile are shown with diamonds. The golden line represents the multi-model mean.</figcaption></figure>

over MED (figures 1(d)–(f)), although the absolute changes over this region are relatively small due to the low climatological values (figures 1(a)–(c)). For all regions, the models are in agreement on the sign of the change, except for CanESM5, which shows a slight increase over WCE. However, there is a discrepancy between models in terms of inter-member spread and mean signal, especially over MED. The largest climate change signals are projected by CESM2 and MIROC6 over MED, with decreases in annual runoff of –30% and –25% respectively, but even in these models the sign of future changes is not consistent across members.

As suggested in figure 1 by the large inter-member spread, the uncertainty associated with internal variability is large and exceeds or equals the other sources of uncertainty in runoff projections over Europe in the near term (figures 2(a), (d) and (g)). This remains true over the entire 21st century over NEU and WCE, while over MED model uncertainty becomes largely dominant as soon as the mid 21st century.

In order to gain further insight into the drivers of uncertainty in future runoff changes, the partitioning of uncertainty is also shown for precipitation and evapotranspiration (figures 2(b), (c), (e), (f), (h) and (i)). The uncertainties time series of the three variables along the mean signal are given in figure S1. The changes in runoff are almost equal to the difference between changes in precipitation and changes in evapotranspiration (Zhao and Dai 2022), based on the surface water budget equation (section 2.4). Indeed, the variation of water storages from one year

to another is generally negligible compared to the water fluxes (*P*, *E* and *R*). This hypothesis is robust over NEU and WCE and to a lesser extent over MED (not shown). Uncertainty in runoff is therefore structurally linked to uncertainties in precipitation and evapotranspiration, and their co-variability is very important in this context.

Fundamental differences in the partitioning of uncertainties between MED and NEU are not only seen for runoff, but also for evapotranspiration and precipitation. While the contribution of model uncertainty is much larger for runoff than for precipitation or evapotranspiration over MED, the opposite is true for NEU (figure 2). The model uncertainty in precipitation and evapotranspiration therefore tends to cancel-out over NEU and WCE (figure 2). Such a cancellation does not take place over MED. Although there is a strong inter-model correlation between precipitation and evapotranspiration changes everywhere, there is also a very strong inter-member correlation over MED, but not over NEU (figures 3(a)–(c)). This is likely because over MED, the internal variations in evapotranspiration are generally more driven by the availability of water at surface (hence the large correlation with precipitation) rather than by the energy available at surface, while the opposite is true over NEU (e.g. Boé and Terray 2008), which is consistent with figure 3. In the end, both inter-model and inter-member uncertainties in precipitation and evapotranspiration tend to cancel-out over MED, while only inter-model uncertainties in precipitation and evapotranspiration tend to cancel-out
<figure><img src="image_8.png" /><figcaption>**Figure 2.** Fractional contribution of the three sources of uncertainty to total uncertainty for absolute anomalies smoothed with a 10-year running mean, for annual changes in runoff (a), (d), (g), precipitation (b), (e), (h) and evapotranspiration (c), (f), (i). The anomalies are computed using the 1995–2014 period as reference and averaged over NEU (a)–(c), WCE (d)–(f) and MED (g)–(i). Six SMILEs from CMIP6 and four scenarios are used (see Data & Methods), except for CESM2 for which a large ensemble of simulations is available only for the SSP3-7.0 scenario.</figcaption></figure>

over NEU. This leads to a much more prominent role of internal variability in runoff changes over NEU than MED, while an intermediate situation is noted over WCE. Note that the result of the partitioning of uncertainty is expected to be somewhat influenced by the sample of models used. For example, the very large model uncertainty in future runoff changes over MED is sensitive to the inclusion of CESM2 (figure S2), which shows a particularly large decrease in runoff there (figure 1(f)). Additionally, the combination of model and internal variability uncertainty is somewhat smaller in the SMILEs sub-ensemble compared to the full CMIP6 ensemble (figure S3).

Finally, large scenario uncertainty is seen over MED, which exceeds the role of other sources of uncertainty for precipitation and evapotranspiration changes around 2080.

## 4. Mechanisms controlling internal variability uncertainty in future projections

As shown in the previous section, internal variability plays a major role in the uncertainties in future changes in runoff over Europe. We now investigate the mechanisms behind the large inter-member spread seen for the six SMILES. In each model and for each region, changes in runoff are highly correlated with changes in precipitation (figures 3(d)–(f)) and much less correlated with changes in evapotranspiration (figures 3(g)–(i)). Over NEU, there is no relationship between changes in runoff and changes in evapotranspiration across the members of a same model (figure 3(g)). Changes in precipitation are largely responsible for the internal variability uncertainty in near-term changes in runoff.
<figure><img src="image_9.png" /><figcaption>**Figure 3.** Pearson correlation coefficient between changes in precipitation and changes in evapotranspiration (a)–(c), changes in precipitation and changes in runoff (d)–(f) and changes in evapotranspiration and changes in runoff (g)–(i), between the periods 2025–2044 and 1995–2014, over NEU (a), (d), (g), WCE (b), (e), (h) and MED (c), (f), (i). The correlation is computed across the members of each SMILEs (first six vertical bars of each sub-plot) and across the multi-member mean of the six SMILEs (last vertical bar of each sub-plot). The dark blue (light blue) bars indicates that the inter-member (inter-model) correlation is significant (*p* < 0.05). The grey bars indicate that the correlation is not significant (*p* ≥ 0.05).</figcaption></figure>

Changes in precipitation and changes in runoff are strongly linked to changes in atmospheric circulation (figure 4). Indeed, the inter-member differences in changes in runoff and precipitation are strongly anti-correlated with changes in sea level pressure over the region of interest, i.e. the members of each model with the larger increases in precipitation and runoff over NEU (WCE or MED, respectively) are also characterized by the larger decreases in sea level pressure over NEU (WCE or MED, respectively). These correlation patterns are robust across models (figure S4) and are very similar for precipitation and runoff (correlation values on figure S4). This relationship between precipitation and sea level pressure is well understood physically. Negative sea level pressure anomalies are associated with increased vertical velocity in the mid-troposphere above, which enhances cyclonic development and favors local precipitation. Negative sea level pressure anomalies also strengthen

westerly winds, increasing moisture transport from the Atlantic to the continent (Sapiano et al. 2006).

The observed multi-decadal variability of atmospheric circulation over the North Atlantic and Europe has been suggested to be linked to the multi-decadal variability in sea surface temperature over the North Atlantic (Sutton and Dong 2012, Boé and Habets 2014, Simpson et al. 2018, 2019). Yet, no significant inter-member correlation is generally found between changes in sea surface temperature and changes in sea level pressure over the area correlated with changes in precipitation and runoff for the three regions of interest (green box in figures 5(a), (d), (g)). Only over the Labrador Sea for WCE, do the models agree on a significant inter-member anti-correlation between changes in sea level pressure and changes in sea surface temperature. There is generally a large inter-model spread in the relationship between changes in sea level pressure and sea
<figure><img src="image_10.png" /><figcaption>**Figure 4.** Multi-model ensemble mean of the inter-member correlation between changes in sea level pressure at every grid point and, changes in runoff (a), (c), (e) and changes in precipitation (b), (d), (f) averaged over NEU (a), (b), WCE (c), (d) and MED (e), (f). The changes are computed between 2025–2044 and 1995–2014 for the SSP3-7.0 scenario. The inter-member correlation is computed for the six SMILEs and then averaged. The hatching indicates where the correlation is significant (*p* < 0.05) in all SMILEs. For each region, the spatial correlation coefficient between the correlation pattern of sea level pressure changes/runoff changes and the correlation pattern of sea level pressure changes/precipitation changes is given in the lower left corner of the right panels.</figcaption></figure>

surface temperature (figure S5). In particular, EC-Earth3 shows very strong negative inter-member correlations between changes in sea level pressure averaged over the relevant domains and sea surface temperature over a large part of the North Atlantic. This may be related to a higher than usual AMV variance during winter in this model (Bonnet *et al* 2024). Results for changes in runoff and precipitation over NEU, WCE and MED are consistent with those obtained for sea level pressure, with no robust relationship across models with changes in sea surface temperature over the North Atlantic (figures 5(b), (c), (e), (f), (h) and (i)). These results suggest a small contribution from low frequency oceanic variability to runoff multi-decadal variability in the SMILEs and instead a major role of atmospheric noise.

**5. Evaluation of the past multi-decadal variability of the SMILEs**

In the previous sections, we have shown that internal variability plays a major role in the uncertainties of runoff changes over the next two decades for Europe, and even over the entire 21st century for NEU and WCE (figure 2). A key question is whether these uncertainties related to internal variability are realistic in climate models. We have shown that, in the models studied, the inter-member spread in precipitation changes is driven by changes in sea level pressure and drives the inter-member spread in runoff. Yet, some studies have suggested that the multi-decadal variability in atmospheric circulation over the North Atlantic, which is responsible for the inter-member spread in changes in sea level pressure, may
<figure><img src="image_11.png" /><figcaption>**Figure 5.** Same as figure 4 but the inter-member correlation is computed between changes in sea surface temperature at each grid point and changes in sea level pressure averaged over the green box indicated on each panel of the first column (a), (d), (g). The green boxes are meant to capture the area of strong inter-member correlation between sea level pressure changes and runoff/precipitation changes as seen in figure 4. Same as (a), (d), (g) for changes in sea surface temperature and changes in runoff averaged over NEU, WCE or MED (b), (e), (h). Same as (a), (d), (g) for changes in sea surface temperature and changes in precipitation averaged over NEU, WCE, or MED (c), (f), (i).</figcaption></figure>

be underestimated in climate models (Simpson et al 2018, Bracegirdle 2022). This would impact runoff based on our results. The simulated multi-decadal variability in runoff cannot be directly evaluated due to a lack of comparable observations, but observational estimates over the 20th century exist for precipitation and sea level pressure, which are the main drivers of runoff, as shown in section 4.

There is a strong relationship between past multi-decadal variability in precipitation and sea level pressure in most SMILEs in all regions (figures 6(a)–(c)). Conversely, there is no relationship between the multi-decadal variability in the AMV and in precipitation in the climate models (figure S6). The SMILEs are generally consistent with observational estimates for precipitation over NEU and WCE (figures 6(a) and (b)). However, most members of IPSL-CM6A-LR show less multi-decadal variability in precipitation over NEU than observed. Over MED, the observations are on the upper side of the SMILEs distribution for both the multi-decadal variability in precipitation and sea level pressure, except for ACCESS-ESM1-5 precipitation (figure 6(c)). In particular, most members of MIROC6 strongly underestimate the observed multi-decadal variability in precipitation and sea level pressure over MED. This is likely due to a weak multi-decadal variability in sea

level pressure over this region. Given these potential biases in the multi-decadal variability in precipitation, and the relationship that exists between the multi-decadal variability in runoff and precipitation (figures 6(d)–(f)), it is reasonable to assume that the multi-decadal variability in runoff may also be underestimated over MED by most SMILEs. Note that a linear trend is used as a simple estimate of the forced signal in these analyses and therefore the multi-decadal variations characterized in figure 6 may not be purely internal.

## 6. Conclusions

This study shows that internal variability is the main source of uncertainty in near-term changes in runoff across Europe, and a major source of uncertainty over the entire 21st century for NEU and WCE. Model uncertainty becomes substantial over NEU and WCE from 2050 onwards while it is already considerable over MED before 2040. There is no perfect agreement between members on the sign of near-term runoff changes in any model or region (figure 1). This intrinsic uncertainty is substantially greater for runoff changes than for precipitation and evapotranspiration changes over NEU and WCE (figure 2). Note that our estimate of model uncertainty in projected
<figure><img src="image_12.png" /><figcaption>**Figure 6.** Observed and simulated multi-decadal variability in precipitation and sea level pressure, simulated multi-decadal variability in runoff. (a) Standard deviation on 1901–2010 of low-pass filtered precipitation averaged over NEU (y-axis, mm d⁻¹) and sea level pressure averaged over the green box in figure 5(a) (x-axis, hPa) for each SMILE. The light circles show individual members, the dark ones show the multi-member mean. The colored solid lines are the linear regression between the multi-decadal variability of precipitation and the multi-decadal variability of sea level pressure. “r” is the Pearson correlation coefficient. Values in bold indicate that the correlation is significant (*p* < 0.05). The horizontal and vertical solid black lines correspond to the values in the observational datasets, estimated as for the models. The ensemble member distribution of the standard deviations is shown for each model along the x-axis and y-axis (normalized arbitrary values) (b), (c) same as (a) but averaged over WCE, MED for precipitation and averaged over the green boxes shown in figures 5(d) and (g) for sea level pressure. (d)–(f) same as (a)–(c) but with runoff on the x-axis. In (d)–(f), for both precipitation and runoff, the standard deviation of the low-pass filtered time series is divided by the standard deviation of the annual time series (no units).</figcaption></figure>

runoff may be affected by the small size of the CMIP6 SMILEs ensemble, which may not be perfectly representative of the full CMIP6 ensemble, and where an outlier model can easily influence model and scenario uncertainties. In these regions, future changes in precipitation and evapotranspiration are weakly correlated between members of a SMILE, while over MED, where evapotranspiration is strongly limited by soil-moisture, the inter-member correlation between evapotranspiration and precipitation changes is very large. Over NEU and WCE, the impacts of intrinsic evapotranspiration and precipitation changes on runoff changes do not cancel-out (figure 3).

Inter-member variations in near-term changes in runoff are mostly driven by variations in precipitation, themselves driven by sea level pressure variations. No robust impact of variations in North Atlantic sea surface temperature is generally noted in this context. Near-term changes in runoff over Europe are therefore mainly explained by atmospheric noise in current climate models over NEU and WCE. Since climate predictability on multi-year

timescales largely stems from sea surface temperature variability, the predictability of runoff (which has little relationship with sea surface temperature in most SMILEs) is likely to be low. A model (EC-Earth3) still shows a strong teleconnection between North Atlantic sea surface temperature and runoff, which might be linked to a stronger than usual AMV variability (Bonnet et al. 2024). The representation of the AMV, in terms of persistence, variance and basin-scale spatial coherence, varies largely between models and leads to important differences in teleconnections over Europe, at least for summer surface temperature (Qasmi et al. 2017).

As shown based on different observational datasets, the CMIP6 SMILEs tend to underestimate the multi-decadal variability of precipitation and sea level pressure over MED. It is therefore very likely that the multi-decadal variability in runoff over this region could also be underestimated too, given the strong relationship between runoff and precipitation. Clearly, underestimating the impact of internal variability in future runoff projections would have serious implications for impact assessment
and adaptation. Internal hydrological variability over MED therefore needs to be further investigated, especially since this region is particularly at risk in the face of anthropogenic climate change (MedECC 2020).

This study focuses on runoff, which is a good indicator of the future evolution of water resources, especially at larger scales. However, runoff is a climate model variable that is difficult to measure in practice and that is not directly relevant for water managers or stakeholders. For practical applications, studying river flows would be more pertinent. It would require additional steps such as downscaling and hydrological modeling, both of which are also associated with substantial uncertainties.

Given the importance of internal variability in near-term changes in runoff, it should be properly characterized and communicated in an adaptation context. The storyline approach (Shepherd et al 2018) could also be very useful for internally driven changes. In Liné et al (2024), future regional projections from a large multi-member ensemble are conditioned on the prevailing state of the main modes of internal climate variability. Storylines based on the state of the North Atlantic jet are also used for near-term projections of precipitation and temperature changes over the UK (Harvey et al 2023). It would be interesting to apply such approaches to runoff changes over Europe.

## Data availability statement

The CMIP6 data are publicly available through the Earth System Grid Federation (https://esgf-node.ipsl.upmc.fr/search/cmip6-ipsl/). The CESM2-LE model output is available at www.cesm.ucar.edu/projects/community-projects/LENS2/data-sets.html. The CRU-TS data are available at https://cran.r-project.org/cru/data/hrg/cru_ts_4.07/. The Global Precipitation Climatology Project (GPCP) Monthly Analysis Product data are provided by the NOAA PSL, Boulder, Colorado, USA, from their website at https://psl.noaa.gov. ERA20C is available from the C3S store (www.ecmwf.int/en/forecasts/dataset/ecmwf-reanalysis-20th-century, ECMWF 2023). The 20CRv3 (www.psl.noaa.gov/data/gridded/data.20thC_ReanV3.html, NOAA PSL 2024) are provided by the NOAA Earth System Research Laboratory Physical Sciences Division (PSD), Boulder, Colorado, USA, from their website.

All data that support the findings of this study are included within the article (and any supplementary files).

## Acknowledgment

We acknowledge the World Climate Research Programme's Working Group on Coupled Modeling responsible panel for CMIP6. We also thank the climate modeling groups for producing and making available their model output. We acknowledge the

CESM2 Large Ensemble Community Project and supercomputing resources provided by the IBS Center for Climate Physics in South Korea.

## Author contribution

J D and J B designed the study. Analyses were performed by J D. The first draft of the manuscript was written by J D, J B and J D commented on previous versions of the manuscript. All authors read and approved the final manuscript.

## Conflict of interest

The authors declare that they have no conflict of interest.

## ORCID iDs

Juliette Deman https://orcid.org/0009-0003-4790-3960

Julien Boé https://orcid.org/0000-0003-2965-4721

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