The precipitation observational data used in this study come from the SAFRAN (Système d'Analyse Fournissant des Renseignements Atmosphériques à la Neige) analysis, based on the system developed by Météo-France (Durand et al., 1993; Le Moigne et al., 2020). SAFRAN is an operational meteorological analysis scheme that combines ground-based observations, large-scale atmospheric analyses, and orographic information to produce spatially and temporally consistent estimates of near-surface meteorological variables. The dataset provides high-quality precipitation fields at hourly resolution over France, available from 1958 to the present, and is widely used for hydrological and climate studies due to its consistency in time, thorough homogenization technique, and fine scale detail (∼ 8 km × 8 km resolution).

As described earlier, our predictive framework relies on large-scale atmospheric and oceanic indices, specifically the SLP-based modes and Atlantic Multidecadal Variability (AMV) derived from Sea Surface Temperature (SST) anomalies. For this purpose, we used ERA5 reanalysis dataset (Hersbach et al., 2020), which provides global, high-resolution atmospheric and oceanic fields at 0.25° spatial resolution and hourly temporal frequency. The ERA5 data, covering the period 1948 to the present, offers a physically consistent representation of large-scale climate variability and serves as the observational reference for computing both SLP and SST indices used in this study. The exact definition of those indices will be provided later on in the paper.

To predict SLP-based mode and AMV indices, we use the multi-model ensemble of initialized decadal predictions from the Decadal Climate Prediction Project Component A (DCPP-A) within CMIP6 (Boer et al., 2016). The ensemble includes decadal hindcasts from 12 models (see Table A1), with a total of 188 members initialized annually from 1960 to 2014 and run for a decade.

Once the target indices are predicted, we apply a subsampling method (described below) to the outputs from the large ensemble of extended historical simulations from the IPSL-CM6A-LR model, consisting of 32 members covering the period 1850–2059 (Bonnet et al., 2021). IPSL-CM6A-LR model contributed to CMIP6 database. It has a nominal horizontal resolution of approximately 2.5° × 1.25° for the atmosphere and 1° for the ocean. A full description of its main components and climatology can be found in Bonnet et al. (2021).

To identify large-scale drivers of precipitation variability over France, we derive the main SLP pattern that affect precipitation. Then, we combine the results with knowledge from literature-based climate indices. More precisely, the whole process follows the three analytical stages described below.

We apply Empirical Orthogonal Function (EOF) analysis to observed seasonal precipitation anomalies using the eofs Python package (Dawson, 2016). EOF analysis decomposes the covariance matrix of the input data into orthogonal spatial patterns (EOFs) and their corresponding time series called principal components (PCs) (Wilks, 2020).

To emphasize low-frequency variability and reduce the influence of interannual noise, precipitation anomalies are smoothed using a 3-year centered rolling mean, and linear trends are removed. The choice of the averaging window is a compromise between enhanced low-frequency variability and retaining sufficient temporal resolution. Results were qualitatively similar for averaging windows between 2 and 4 years (not shown). We define two 6-month extended seasons: October to March (ONDJFM) and April to September (AMJJAS). We limit our analysis to the first two leading modes of variability from the EOF analysis.

To gain physical understanding of the main mode of variability obtained through EOF, it is interesting to evaluate the frequency of the main variability modes of precipitation over France. Indeed, strong low frequency variability is indicative of some potential for decadal predictability. Although this step is not required in our workflow, it was included in this study to better characterize the variability of precipitation over France, and to explore how this might relate to decadal predictability. The frequency characteristics are further investigated by applying a continuous wavelet transform (CWT) to the first two principal components using the pycwt Python package (Krieger and Freij, 2023; Torrence and Compo, 1998) with a Morlet wavelet. Wavelet analysis allows the examination of multiscale and non-stationary signals by convolving the input time series with scaled and shifted versions of the wavelet. Time-averaged frequency spectra highlight dominant frequencies, while the full CWT spectra show their temporal evolution.

We compute correlation maps between the first two principal components of precipitation anomalies (PCs) and SLP anomalies over the North Atlantic sector (20–85° N, 85° W–40° E), for both extended warm and cold seasons. The significance of the correlation coefficients is assessed using a block bootstrap procedure (1000 samples) with a block size of 3 years, where correlations are considered significant if zero is outside the 95 % confidence interval of the bootstrap distribution. Based on the significant correlation patterns and previous literature, candidate SLP indices for decadal precipitation prediction are identified (see Sect. 3.1 for further discussion). From these patterns and previous literature, we identified four atmospheric indices most relevant for France:

For the winter season, those are:

The North Atlantic Oscillation Index (wNAO), calculated for DJFM (December to March) as the difference in mean SLP between two zonal boxes spanning the North Atlantic-European sector – subtropical (35–40° N, 80° W–30° E) and subpolar (63–67° N, 80° W–30° E) – following Jianping and Wang (2003). This formulation reduces sensitivity to east-west shifts in the centers of action that can happen within climate models.  It should be noted that unlike Jianping and Wang (2003), here the indices are not normalized.

For the summer season, they are:

The Summer North Atlantic Oscillation index (hereafter sNAO), defined for AMJJAS (April to September) as the sea level pressure (SLP) difference between two regions: one located west of England and France (45–55° N, 20° W–12° E) and another south of Greenland (55–69° N, 60–45° W). This definition is adapted from previous studies (Dunstone et al., 2023; Folland et al., 2009; Wang and Ting, 2022) to better capture the observed correlations between precipitation principal components and SLP.

The relevance of these indices is evaluated by computing Pearson correlation coefficients with the corresponding principal components at two temporal scales. Correlations are first computed between the PCs based on 3-year mean precipitation and the climate indices smoothed using a 3-year rolling mean. Then, lower-frequency variability of around 8 years is assessed by applying another 6-year rolling mean to the previous PCs and 3-year means climate indices.

To extract atmospheric indices, observations and model outputs are remapped to a common 2° × 2° regular grid using bilinear interpolation prior to spatial averaging over the index definition regions. For observations and the uninitialized IPSL ensemble, 8-year rolling means are first computed from the raw seasonal values, and anomalies are then obtained by subtracting the climatological mean of these smoothed times series, estimated over the full 1966–2019 period. For DCPP boosted predictions (see Sect. 2.2.2), the 8-year aggregation follows the lead-time-aware method of (Alkama et al., 2026); anomalies are subsequently computed relative to the same 1966–2019 climatological baseline.

In addition to the atmospheric indices, we include an AMV index to capture potential low-frequency oceanic influences on European climate (Sutton and Hodson, 2005). The AMV describes the evolution of the dominant mode of North Atlantic SST variability over multidecadal timescales (Schlesinger and Ramankutty, 1994). We define the index used here as the area-weighted mean of annual-mean SST over the North Atlantic domain (0–60° N, 76° W–0° E). For models with curvilinear or irregular ocean grids, weighting is performed using the model-native grid-cell area field; for models on regular latitude-longitude grids, cosine-of-latitude weighting is used. To avoid making any hypothesis to remove the global warming trend, we just use this raw and unadjusted times series that we call uAMV (e.g., Michel et al., 2022) since this does not correspond to classical definitions from the literature, where the trend is removed using various approaches (e.g., Terray, 2012; Trenberth and Shea, 2006). We retain here the externally forced signal in the uAMV index as well as the internal signal, because both signals are used in the subsampling procedure described below (Sect. 2.2.3) to select model members that best reproduce both internal variability and forced trends, which may be misrepresented in models (Kharin et al., 2012). Removing the forced component consistently across observations, initialized, and uninitialized simulations is challenging; thus, keeping the raw signal improves consistency and preserves important multidecadal trends.

We apply the post-processing method developed by Alkama et al. (2026) that improves the earlier work by Marcheggiani et al. (2023) and Smith et al. (2020). This approach includes two key steps:

The DCPP-A ensemble mean is aggregated across lead times using an optimized averaging scheme. For each target 8-year calendar window, rather than combining members from four consecutive start dates as in Smith et al. (2020) – which introduces a systematic two-year lag between the predicted and observed periods – Alkama et al. (2026) restrict averaging to hindcast years that fall within the target calendar window. Specifically, for each calendar year in the window, the predicted values from all contributing hindcast start dates (lead years 2–9) are first averaged, before computing the 8-year mean. This ensures temporal synchronization between predictions and observations and increases the ACC of the boosted winter NAO from 0.58 to 0.83 (Alkama et al., 2026). Here, the method is applied using lead times 2–10, rather than 2–9 in Alkama et al. This does not extend the 8-year averaging window, but increases the number of hindcast members contributing to each calendar year within that window, thereby marginally increasing the effective ensemble size and potentially improving skill.

The resulting predictions are referred to as 'boosted' decadal predictions. For some indices (wWEPA, sNAO, and sMedScand), the predicted linear trend is opposite in sign to the observed trend (Fig. S1). In these cases, the predicted trend is adjusted to match the observed trend over the historical period, following (Kharin et al., 2012); for future forecasts, this correction is applied by extending the historical observed trend.

To transfer predictability from large-scale indices to precipitation, we adopt an index-based subsampling strategy inspired by the NAO-matching method (Alkama et al., 2026; Smith et al., 2020). The idea of selecting climate simulations based on predicted or observed criteria has been employed in various contexts: in seasonal forecasting (Ding et al., 2018) and on decadal-to-multi-decadal timescales (Befort et al., 2020; Mahmood et al., 2021, 2022, 2025). Smith et al. (2020) introduced the NAO-matching method by selecting a subset of 20 members from multi-model decadal simulations at each 8-year window whose NAO values best match the NAO prediction from the whole DCP predictions ensemble mean. Climate variables (e.g., precipitation) are then extracted from this subset, yielding “NAO-matched precipitation” predictions expected to improve skill.

Alkama et al. (2026) applied NAO-matching to an uninitialized large ensemble from CESM2, showing skill improvements compared to initialized multi-model, also subsampled on NAO predictions, especially in extended-winter precipitation, though with limited skill over France. This might be related to the fact that initialized predictions can show strong drift in the first few years, contrary to uninitialized large ensemble (e.g., Polkova et al., 2023).

Motivated by these findings, we apply the subsampling method to the large ensemble of extended historical IPSL-CM6A-LR model (32 members), spanning 1850–2059 (Bonnet et al., 2021), hereafter called “uninit IPSL”. The subsampling method selects relevant uninitialized ensemble members separately for each 8-year mean window. The 8-year mean climate index centered in t is predicted by each 32 uninitialized ensemble members (ui(t),∀i∈[1,32]), and by the boosted DCP ensemble mean (f(t)). We select the five uninitialized ensemble members minimizing D defined as: 1Dit=uit-ft2,∀i∈[1,32]

We name “Sub(X)” the selected ensemble where X denotes the climate index used (e.g., Sub(wNAO)). The procedure can be applied using any SLP or SST index individually or combined. In the case of combined selection, the five selected uninitialized ensemble members minimize: 2Di(t)=d1i(t)/σ12+d2i(t)/σ22,∀i∈[1,32], where σ=STD{dj(x)}j=1,…32;xϵT and di(t)=ui(t)-f(t) for each index. Standard deviations are computed over the entire historical period rather than at each individual date to provide a stable normalization that is not influenced by the small sample size at any given window.

For extended summer precipitation prediction, we combine the sNAO, sMedScand SLP indices and the uAMV. The corresponding selected ensembles are called “Sub(sNAO+uAMV)” and “Sub(sMedScand+uAMV)”. The subsampling procedure is applied on the entire historical period from 1961 to 2024, allowing to extract precipitation – or other variables – predictions from the selected ensembles. The skill of this system is assessed on 8-year means computed from ensemble members that can be different at successive 8-year periods. The resulting prediction shows reduced temporal coherence that is not directly comparable to the smoothed rolling means applied to observations. To ensure consistent autocorrelation properties, we apply to the selected members the aggregation of the post-processing method described in Sect. 2.2.2 – specifically, the 8-year running mean aggregation with the lead-time weighting scheme.

The SAFRAN reanalysis provides high-quality precipitation observations at an 8 km resolution across France and has become a reference dataset for hydrological applications, water resource management, and impact studies (Labrousse et al., 2020; Seyedhashemi et al., 2023; Vidal et al., 2010). Developing decadal precipitation forecasts at the same spatial scale would directly support these operational needs by bridging the gap between coarse-scale climate predictions and local-scale decision-making. Correcting the bias of the prediction is also necessary in order to use them in impact studies.

To achieve this, we use the Cumulative Distribution Function-transform (CDF-t) method (Michelangeli et al., 2009), a widely used quantile-mapping technique. CDF-t adjusts the statistical distribution of modeled precipitation to match that of observations while preserving the model's representation of large-scale variability.

This method allows to statistically downscale the subsampled precipitation outputs (∼ 150 km resolution) onto the SAFRAN 8-km grid using available observation. Such an approach is necessary and widely used for impact studies.

This method also accounts for changes in the distribution between historical and forecast periods through a transfer function that aligns modeled and observed daily cumulative distributions and therefore remove the bias in prediction at the daily timescale. The CDF-t technique has been extensively validated for precipitation bias correction and regional climate projection studies (Gogien et al., 2023; Sauquet et al., 2026; Vrac et al., 2012).

We assessed the skill of 8-year precipitation predictions against SAFRAN observations using deterministic and probabilistic metrics (see details in Appendix B). Those skill scores are:

Anomaly Correlation Coefficient (ACC). It measures the ability of the ensemble mean to predict temporal variations of observed precipitation anomalies (Wilks, 2020).

Statistical significance of ACC, RCC and CRPSS is assessed using a block bootstrap with 1000 samples and block size of eight years to account for temporal autocorrelation (Rousselet et al., 2021; Smith et al., 2020). The p-values are estimated as the proportion of bootstrap scores falling below zero (Goddard et al., 2013). To account for the multiplicity problem arising from simultaneous testing across all grid points (Wilks, 2020), significance is assessed using the False Discovery Rate (FDR) correction with αFDR=2×αglobal and αglobal=0.05 following (Wilks, 2016) (see Supplement Sect. S9).

Before evaluating forecast skill, the variance of both the subsampled predictions and the uninitialized full ensemble are rescaled to match that of the observations. Because observations represent a single realization of the climate system, while ensemble means (five-member subsampled and 32-member uninitialized) inherently smooth variability through averaging, their standard deviations are artificially reduced. To ensure statistical consistency and comparability with the observed variance, we apply a variance-scaling correction. Each ensemble member is multiplied by σo/σm, where σo and σm are the standard deviations of the observations and the ensemble member, respectively, computed on the entire historical period. This adjustment does not affect ACC but improves CRPSS by preventing the prediction ensemble from being too narrow, which would lead to underconfident forecast. CRPSS maps computed from the raw, uncorrected predictions are provided in the Supplement (Fig. S10).

The forecast skill is also evaluated against the raw DCPP-A ensemble mean. The DCPP ensemble includes 11 models (and not 12 because precipitation data for CESM1-1-CAM5-CMIP5 are unavailable on ESGF). Drift is removed from DCPP-A predictions by computing precipitation anomalies relative to a lead-time-dependent climatology for each model. Eight-year means are computed by averaging lead times 2–9. The multi-model ensemble mean is then formed by averaging the individual model ensemble means.

The comparison between the two prediction systems is not straightforward due to their different spatial resolutions. DCPP-A predictions are available at a coarse native resolution of approximately 2°, while our subsampling-based predictions have been statistically downscaled at 8 km resolution. To ensure inter-model comparability, we first remapped all DCPP-A outputs to a common 2° resolution grid. Remapping these predictions to a finer scale would not be physically meaningful given the models' native resolution. Concerning the subsampling-based predictions, they have been downscaled and bias-corrected against the SAFRAN observational dataset (∼ 8 km, ∼ 0.08° resolution). Remapping the downscaled subsampling predictions to a 2° is not straightforward. Indeed, since these predictions are only available over metropolitan France, regridding to a 2° would result in incomplete coverage of several coarse grid cells at the domain boundaries, introducing artefacts in the skill computation.

For consistency, ACC from both prediction systems (raw DCPP and subsampled predictions) are compared using ERA5 dataset. DCPP-A predictions are compared against ERA5 remapped to 2°, while subsampling predictions are compared against ERA5 at 0.25° resolution. Note that the subsampling predictions are spatially interpolated onto the 0.25° ERA5 grid for this comparison, no additional bias correction is applied at this stage.