# Regionally improved seasonal forecast of precipitation through Best estimation of winter NAO

### Eroteida Sánchez-García

### José Voces-Aboy

### Beatriz Navascués

### Ernesto Rodríguez-Camino

We describe a methodology for ensemble member's weighting of operational seasonal forecasting systems (SFS) based on an enhanced prediction of a climate driver strongly affecting meteorological parameters over a certain region. We have applied it to the North Atlantic Oscillation (NAO) influence on the Iberian Peninsula winter precipitation.

The first step in the proposed approach is to find the best estimation of winter NAO. Skill and error characteristics of forecasted winter NAO index by different Copernicus SFS are analysed in this study. Based on these results, a bias correction scheme is proposed and implemented for the ECMWF System 5 ensemble mean of NAO index, and then a modified NAO index pdf based on Gaussian errors is formulated. Finally, we apply the statistical estimation theory to achieve the Best linear unbiased estimate of winter NAO index and its uncertainty. For this purpose, two a priori estimates are used: the bias corrected NAO index Gaussian pdf from ECMWF System 5, and a skilful winter NAO index prediction based on teleconnection with snow cover advance with normal distributed errors.

The second step of the proposed methodology is to employ the enhanced NAO index pdf estimates for ensemble member's weighting of a SFS based on a single dynamical model. The new NAO pdfs obtained in this work have been used to improve the skill of the ECMWF System 5 to predict both NAO index and precipitation over the Iberian Peninsula. We show the improvement of NAO prediction, and of winter precipitation forecasts over our region of interest, when members are weighted with the bias corrected NAO index Gaussian pdf based on ECMWF System 5 compared with the usual approach based on equiprobability of ensemble members. Forecast skill is further enhanced if the Best NAO index pdf based on an optimal combination of the two a priori NAO index estimates is used for ensemble member's weighting.

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In this study we present a methodology for ensemble member's weighting of operational seasonal forecasting systems (SFSs) based on the extent that certain climate variables (e.g. temperature, precipitation) are captured by a driver of climate variability, as e.g., the North Atlantic Oscillation (NAO). The role of the NAO as main climate driver influencing winter precipitation over the Iberian Peninsula area is well known (e.g. Rodríguez-Puebla et al., 1998). Based on this fact, we describe and apply a new developed methodology aiming at improving NAO and total precipitation seasonal forecasts for the extended winter (November to March, NDJFM) over this geographical area. It makes use of the predictability associated to this climate variability pattern by assigning a different weight to each ensemble member of a particular operational SFS according to its forecasted winter NAO index.

The first step in the proposed approach is to find the best estimation of winter NAO. Although operational SFSs have until very recently little or no skill in European mid-latitudes for precipitation, some authors have recently started to report that some SFSs based on dynamical models show remarkable skill in predicting winter NAO or the related Arctic Oscillation (AO) (e.g., Riddle et al., 2013; Scaife et al., 2014; Kang et al., 2014; Stockdale et al., 2015; Athanasiadis et al., 2017). It is recognised that interannual variability of the winter NAO is driven by a combination of different external sources and dynamical mechanisms. Among these sources of predictability, it is snow cover extent. Cohen and Jones (2011) have shown that, part of NAO wintertime variability, may be externally forced by the autumn boreal snow cover advance. This permits some predictability with one-month lead time or more using simple statistical predictions based on single predictors. Although dynamical SFSs are able to simulate various existing sources of predictability, their forecasts skill frequently do not overcome those of statistical systems, due to climate models difficulties to adequately reproduce important processes.

Athanasiadis et al. (2017) obtain an enhanced skill of winter NAO forecasts through the combination of three different operational SFSs, giving the same weight to each system. In this work we combine weighted forecasts of winter NAO from different forecasting systems coming mostly, but not only, from SFSs based on dynamical models. Our approach attempts to find the optimal (in a statistical sense) NAO estimate following, in a simplified way, methods used in data assimilation for determining atmospheric initial conditions in Numerical Weather Prediction (NWP).

In order to do so, some error statistical characteristics of wintertime NAO simulated by different forecasting systems must be previously known. The existence of biases of the SFS ensemble mean of NAO index with comparable magnitude to the interannual anomaly signal is a serious hindrance that must be circumvented. Consequently, biases should be corrected before or within the algorithm using the estimates, as it is routinely done in NWP, e.g. with satellite radiances (Eyre, 2016). Knowledge of error variances for different a priori NAO index estimates is another requirement of optimal estimation method. The distribution of NAO index forecasts by the ensemble members around the ensemble mean NAO is provided by the SFS itself. So, the variance of the NAO index forecast each winter can be obtained from the ensemble spread. In this sense, if this SFS ensemble spread is not realistic as a measure of the NAO index estimate error, error variance of the ensemble mean NAO index may be alternatively modelled. Finally, statistical estimation theory (e.g. Kalnay, 2003) allows to obtain an optimal (Best) linear estimation of winter NAO index and its uncertainty (i.e. an optimal NAO pdf) based on a priori NAO index estimates and their respective error variances. The algorithm is based on minimising the error variance of the optimal estimate. In case of Gaussian error distributions of the a priori estimates, the method is equivalent to the maximum likelihood Bayesian approach followed, e.g. by Coelho and Pezzulli (2004) to estimate ENSO index seasonal forecast distribution.

We analyse the performance of winter NAO (December to February) seasonal forecasts by three different SFS available at the Climate Data Store (CDS) of the Copernicus Climate Change Service (C3S). Ensemble mean of NAO index correlation with observations and NAO index ensemble spread measured as the NAO index variance or standard deviation are calculated. Error histograms and RMSE of these SFS ensemble mean NAO forecasts are also obtained and spread/RMSE ratios are computed. Then, a statistical bias correction scheme is formulated and successfully applied to the SFS showing the highest correlation with observations.

An empirical seasonal forecasting system (named S-ClimWaRe) relying on the October snow advance over continental areas in the Northern Hemisphere and NAO relationship has been developed at AEMET (Voces et al., 2016). The S-ClimWaRe empirical system uses as predictor the Snow Advance Index (SAI) (Cohen and Jones, 2011). SAI is based on daily satellite snow cover data from the Interactive Multisensor Snow and Ice Mapping System (IMS), which generates daily maps of snow, and ice cover derived from visible and microwave satellite imagery (Ramsay, 1998; Helfrich et al., 2007). A NAO index forecast pdf is built using a normal distribution centered at the linearly regressed NAO index value with standard deviation obtained from the regression residuals. In this study, NAO index forecast errors from the S-ClimWaRe system have been analysed in a similar way to those of the three C3S SFSs.

Athanasiadis et al. (2017) largely attribute the high predictive skill for NAO achieved by the multisystem created by averaging three operational SFSs to the increase of the ensemble size (and then the seasonal signal), but also partly to increasing model diversity (due to cancellation of model errors). Unlike Athanasiadis et al. (2017), in our approach we do not increase the ensemble size but only consider the potential benefit brought by increasing model diversity. Among the seasonal forecasting systems analysed, we select for combination the two systems showing the highest NAO forecast performance in terms of biases and correlation with observations. The two a priori estimates selected in this work for applying optimal estimation theory and obtaining the Best NAO estimate pdf are: (i) the ensemble mean of NAO index forecasts from the bias corrected ECMWF S5 SFS,and (ii) the NAO index empirically predicted by the S-ClimWaRe system.

The second step of the methodology proposed in this paper relies on the knowledge of an enhanced winter NAO forecast pdf to weight members of a SFS based on a single dynamical model in order to achieve improved seasonal forecasts. Ensemble members' equiprobability is generally assumed for atmospheric members in SFSs based on a single dynamical model. Weighting of members from an ensemble seasonal forecasting system is not a trivial task and frequently depends on the particular application or target region of the forecast. Riddle et al. (2013) obtained slightly improved AO predictions with a single SFS when they use a weighted ensemble that rewards forecast runs that represent more accurately the Eurasian October snow cover extent. Dobrynin et al. (2018) enhance prediction skill of surface temperature, precipitation and sea level pressure over certain areas in the Northern Hemisphere by retaining only SFS ensemble members whose NAO state is close to a NAO empirical prediction. In our approach, we look for an enhanced precipitation pdf forecast over the Iberian Peninsula produced by an improved NAO pdf forecast. Instead of considering an ensemble sub-sampling, we apply an analytical function of winter NAO index to weight each SFS ensemble member. The weighting function used is the Gaussian NAO index pdf estimate that has been obtained by, either a bias correction procedure of the raw SFS NAO ensemble mean forecast, or an optimal estimation method combining different NAO index forecasts estimates. For a given ensemble member, the resulting member weight assigned depends on the member predicted NAO. So, it is expected that the member's weighting consistently improve the forecasting system skill in predicting both the winter NAO, and precipitation over those areas strongly influenced by this climate driver. Seasonal forecasts of NAO index and of accumulated precipitation for the extended winter over the Iberian Peninsula (NDJFM) are assessed (in a hindcast period) comparing skill of the SFS ensemble using both weighted and customary unweighted ensemble members.

This paper is structured as follows: Sect. 2 describes some errors statistical characteristics of seasonal forecast systems predicting the winter NAO. The methodology applied to improve the NAO estimates is presented in Sect. 3. The enhancement of NAO index prediction and precipitation forecast skill of a single SFS using weighted ensemble members based on two different NAO pdf estimates is shown in Sect. 4. Finally, Sect. 5 concludes with summary and final remarks.

The study has been carried only with seasonal forecasts initialized in October. The three operational C3S SFSs here analysed are ECMWF System 5, Met Office System 12 and Météo-France System 5 (https://cds.climate.copernicus.eu, Climate Data Store, 2019). As mentioned, the performance of S-ClimWaRe empirical seasonal forecasting system developed at AEMET is also considered.

ERA-Interim (ERAI) reanalysis (Dee et al., 2011) has been used to obtain EOF
patterns and winter NAO index (averaged over December to February, DJF) time
series similarly to Butler et al. (2016). For each of the three SFS
considered and for each of their ensemble members, NAO index has been
obtained by projecting the 1st EOF onto the member DJF averaged Z500 gridded
anomaly. Notice that NAO index has not been standardized. Time series of the
winter NAO index of the SFS ensemble has been compared to that of ERAI.
Figure 1a shows a scatter plot of forecasted winter NAO index computed for
ensemble members and ensemble mean from ECMWF System 5 against the
corresponding winter NAO index value obtained from ERAI reanalysis.
Regression line in Fig. 1a indicates that the ensemble mean of NAO index
and ERAI are correlated. However, it can be seen the great dispersion of
winter NAO index predicted each year by ensemble members and, as a
consequence, that the magnitude of the ensemble mean of NAO index is
underestimated and does not reproduce the amplitude of the observed North
Atlantic Oscillation. Stockdale et al. (2015) also report a winter AO index
highly correlated with observations but with a weak interannual AO signal in
the formerly operational ECMWF System 4 SFS due the high degree of
intraensemble spread in the ensemble members. Figure 1b compares ECMWF
System 5 winter NAO index ensemble mean forecast error (using ERAI NAO
indices as reference) with NAO ensemble variance. It shows that there is a
correlation between ECMWF System 5 ensemble variance and ensemble mean bias
(*R*=0.37). Figure 1b also shows that the size of the absolute error of the
ensemble mean of NAO index predicted by ECMWF System 5 is not correlated
with the NAO index intraensemble variance.

Some verification scores have been obtained to assess the performance of the different SFSs and S-ClimWaRe empirical system to predict the winter NAO. Correlation coefficient between winter NAO index computed from ensemble mean forecasts and from ERAI reanalysis is displayed in Table 1. In order to have a spread/skill evaluation of NAO seasonal forecasts, the ensemble spread each year has been calculated as the intraensemble standard deviation of NAO index. Its average over the hindcast period has been compared to Root Mean Square Error (RMSE) of the NAO index ensemble mean. Table 1 displays the corresponding spread/RMSE ratios for all SFSs analysed. The hindcast common period for the whole NAO error characterization is restricted to 1997–2016 due to the limited availability of S-ClimWaRe input satellite snow cover products. Over this hindcast period, only the ensemble mean of ECMWF System 5 and S-ClimWaRe present a significant correlation with ERA-Interim. However, ECMWF System 5 ensemble is overdispersive according to the spread/RMSE ratio, and the ensemble spread of NAO index largely overestimates the real ensemble mean error. On the contrary, Met Office System 12 ensemble is reliable (spread/RMSE ratio is close to 1), the observed error standard deviation of the ensemble mean of NAO index is well represented by the ensemble spread, but it presents a poor correlation with NAO index obtained from ERAI. Météo-France system 5 correlation with ERAI is low and it is underconfident as ECMWF System 5. S-ClimWaRe empirical system shows to be rather consistent in respect to spread/RMSE ratio (see Table 1)

Histograms in Fig. 2a, b, c, d show distribution of ensemble mean NAO error for all studied SFSs over the available hindcast period for each system. All forecasting systems present biases (underestimation of NAO), being S-ClimWaRe empirical system the least biased. It is noticeable that error distribution of the S-ClimWaRe empirical system has the sharpest histogram and closest to a Gaussian pdf.

## 3.1 Correction of NAO index error and reduction of ECMWF S5 ensemble spread

ECMWF System 5 NAO presents the highest correlation with ERAI, but it is biased. Using results obtained above (see Fig. 1b), a bias correction has been performed to the ensemble mean of NAO index of this SFS. The bias correction scheme here proposed is based on a linear model using ensemble variance of NAO index as predictor. Taking this predictor in the bias correction algorithm means that negative biases of ensemble mean NAO are related to small NAO ensemble variances whereas the largest NAO ensemble variances are linked to positive biases of ensemble mean NAO. As it is shown in Fig. 1a, the magnitude of the ensemble mean of NAO index is underestimated. So, in case of large positive/negative observed NAO index (obtained from ERAI), ECMWF System 5 ensemble mean of NAO index generally presents a negative/positive bias that the bias correction scheme will partially correct according to Fig. 1b, because this bias is associated to a small/large NAO ensemble variance. The aim of this bias correction is to alleviate the underestimation of the ensemble mean of NAO index. It can be applied because ECMWF System 5 is providing information about the sign of biases through the magnitude of the NAO index ensemble variance. In other words, it seems that, in case of a positive/negative NAO index forecast the SFS NAO ensemble variance tends to be smaller/larger.

The coefficient of the predictor of the bias correction regression is trained separately for each year in the hindcast period. This is done by leaving out the current year NAO index error and using a data sample with the remaining years.

Figure 2e depicts the errors histogram of the ECMWF System 5 ensemble mean
of NAO index after the bias correction procedure. We call
NAO_{BC_ECMWF-S5_mean} to this ensemble
mean of NAO index after the bias correction. A much sharper and less biased
errors distribution is obtained as compared to Fig. 2a. The corrected
winter NAO time series still presents a high correlation with ERAI, being
only slightly lower than that of the uncorrected ensemble mean of NAO index
with ERAI (see columns 2–3 of Table 2).

A Gaussian model centred in the corrected NAO value, NAO_{BC_ECMWF-S5}= N (NAO_{BC_ECMWF-S5_mean},
*σ*_{BC_ECMWF-S5}), has been finally adopted to
represent every year the NAO errors probability density function. The error
standard deviation of the bias corrected NAO index provides the width of
this Gaussian pdf, *σ*_{BC_ECMWF-S5}. A similar
procedure to the one used to train the bias coefficient each year is
employed to calculate *σ*_{BC_ECMWF-S5}. An example
of the Gaussian NAO pdf for the winter 2012–2013 is displayed in red in
Fig. 3.

## 3.2 Optimal estimation of the NAO pdf

The first step of the methodology presented in this paper ends with the
optimal estimation of the winter NAO. Two a priori NAO estimates are
considered in this work. The first one is the ECMWF System 5 bias corrected
NAO index with Gaussian errors distribution described in Sect. 3.1
(NAO_{BC_ECMWF-S5}= N (NAO_{BC_ECMWF-S5_ mean}, *σ*_{BC_ ECMWF-S5})).
The second a priori estimate of winter NAO index comes from S-ClimWaRe
empirical prediction (NAO_{S-ClimWaRe}). We call
NAO_{S-ClimWaRe_fc} to the NAO index forecasted empirically
each year. The S-ClimWaRe NAO index errors pdf is represented similarly to
those of ECMWF System 5 bias corrected NAO, with a normal distribution using
RMSE of the empirical NAO index forecasts as the standard deviation *σ*_{S-ClimWaRe}. So, NAO_{S-ClimWaRe}= N
(NAO_{S-ClimWaRe_fc}, *σ*_{S-ClimWaRe}).

These two a priori NAO estimates with Gaussian errors pdfs present
significant correlation with ERAI (see Tables 1 and 2). Application of
statistical estimation theory provides the optimal estimation of winter NAO
index and its uncertainty. According to Kalnay (2003), the “Best” estimate
of the truth, that minimizes the error variance and maximizes the a
posteriori probability in a Bayesian approach, is a sharper Gaussian pdf,
NAO_{Best}= N (NAO_{Best_mean}, *σ*_{Best}).
This optimal estimate will be unbiased if the two a priori estimates are.

The mean of this Best NAO Gaussian pdf estimate, NAO_{Best_mean}, is obtained by linear combination of the ECMWF System 5 bias
corrected ensemble mean of NAO index, NAO_{BC_ECMWF-S5_mean}, and the S-ClimWaRe NAO index empirical
forecast,

Being the optimal coefficients *a*_{BC_ECMWF-S5} and
*a*_{S-ClimWaRe} dependent on the relative errors of each estimate:

The NAO optimal estimate has a reduced error standard deviation *σ*_{Best}:

Figure 3 shows NAO_{BC_ECMWF-S5} (red),
NAO_{S-ClimWaRe} (green), and NAO_{Best} (blue) Gaussian pdfs
obtained for the 2012–2013 winter. Figure 2f displays the errors histogram
for the mean of this Best NAO Gaussian estimate, NAO_{Best}, that is
sharper and considerably less biased that the raw ECMWF System 5 ensemble
mean one (Fig. 2a).

In Table 2 some deterministic (RMSE, correlation coefficient with ERAI)
verification scores of the raw uncorrected ECMWF System 5 ensemble mean of
the NAO index, the mean of bias corrected ECMWF NAO Gaussian pdf
(NAO_{BC_ECMWF-S5}), and the mean of the Best NAO Gaussian
pdf estimate (NAO_{Best}) are displayed. RMSE is slightly reduced and
correlation with ERAI is maintained in the Best NAO Gaussian estimate.
Probabilistic verification scores for the NAO pdf forecast by the same
systems are also provided in Table 2: Brier Skill Score (BSS), and Relative
Operating Characteristic (ROC) area for NAO index anomalies below/above the
lower/upper tercile (Wilks, 2006). In short, the Relative Operating
Characteristic ROC area can be considered a summary of the performance of a
probabilistic forecasting system with respect to its ability to discriminate
the occurrence or not of a certain event (e.g. to be below the lower
tercile). Notice that an upper/lower tercile event corresponds to a
positive/negative NAO. BSS measures the relative skill of the forecast of a
certain event compared to the climatology, in relation to reliability and
resolution of the probabilistic forecast. In general, a ROC/BSS score above
0.5∕0.0 indicates skill better than climatological probabilities. Columns
2–4 of Table 2 show marginal prediction skill for both positive and negative
phases of NAO by probabilistic forecasts of the three systems. Spread/RMSE
ratio has been also obtained for the Best NAO Gaussian pdf estimate
(NAO_{Best}) and shows to be close to 1 (0.94).

This section presents the results obtained in the second step of the
methodology here proposed. The outcome compares the use of the two obtained
Gaussian functions representing enhanced NAO pdf forecasts to weight ECMWF
System 5 ensemble members. These two Gaussian functions correspond to
NAO_{BC_ECMWF-S5}, the bias corrected ECMWF System 5 NAO
pdf described in Sect. 3.1, and to NAO_{Best}, the Best NAO pdf obtained
in Sect. 3.2, respectively. Extended winter (NDJFM) is the season
considered for precipitation and hindcast period covers 1997 to 2016. For
each year of the hindcast period, these two Gaussian weighting functions
have been obtained leaving the current year NAO index errors predicted by
ECMWF System 5 and S-ClimWaRe out in the procedure to calculate the bias
correction coefficient and NAO index error standard deviation or RMSE values
employed as width of the a priori Gaussian estimates. Notice that in an
operational context, weights assigned to ensemble members each year of the
hindcast period are not static. They must be re-initialized when additional
information on NAO forecast errors of the past winter becomes available in
order to better train bias correction coefficient and NAO index RMSE values.
This implies that also SFS climatology might change due to the update of the
member's weighting function for each year of the hindcast period. Member's
weighting of the seasonal forecast initialized in October for the next
winter would also benefit of longer hindcast period and then time series of
NAO forecast errors.

The outcome of the ensemble member's weighting has been assessed using
gridded observational precipitation from E-OBSv16 dataset (Cornes et al., 2018) over the Iberian Peninsula. Figure 4 shows a selection of the
verification scores employed: anomaly correlation coefficient (ACC) of the
ensemble mean precipitation, and Relative Operating Characteristic area for
precipitation anomalies above/below the upper/lower terciles (upper ROC
area/lower ROC area). They have been computed for the extended winter
forecasted precipitation using three strategies for ECMSF S5 ensemble:
equally weighted members, weighted members with the bias corrected NAO
Gaussian pdf (NAO_{BC_ECMWF-S5}) and weighted members using
the Best NAO pdf estimate (NAO_{Best}). ACC provides skill information of
the SFS deterministic precipitation forecast. Relative Operating
Characteristic (ROC) area score has been used to assess the performance of
the SFS probabilistic precipitation forecasts. Maps in Fig. 4 show that
the procedure for the bias correction of ECMWF System 5 and adoption of a
Gaussian NAO pdf here described and its application for weighting ensemble
members produces an improvement over the precipitation pdf based on equally
weighted members. Both deterministic (for ensemble mean) and probabilistic
scores demonstrate the benefit obtained. The prediction skill is further
enhanced by applying the Best NAO pdf estimate for member's weighting.

The effect of ECMWF System 5 ensemble member's weighting on winter NAO index
forecasts has been also assessed. Corresponding verification scores are
displayed in the last two columns of Table 2. Ensemble members weighting
with NAO_{BC_ECMWF-S5} and NAO_{Best} decrease RMSE of
the ensemble mean of NAO index with respect to consider equiprobable members
(see column 2 of Table 2). The usage of NAO_{Best} as weighting function
decreases RMSE of the ensemble mean of NAO index the most. Correlation of
the ensemble mean of NAO index with that derived from ERAI also increases by
ensemble member's weighting. Verification scores for probabilistic forecasts
of NAO index presented in Table 2 show a clear improvement in case of NAO
index anomalies in the upper tercile (positive NAO) when ensemble members
are weighted with the two NAO Gaussian pdfs forecasts. Again the usage of
NAO_{Best} produces the larger forecast skill improvement. So, the
methodology proposed consistently enhance both winter NAO prediction, and
precipitation forecasts over the Iberian Peninsula.

We have described a methodology for ensemble member's weighting of operational seasonal forecasting systems based on an enhanced prediction of a driver of climate variability strongly affecting certain climate variables (e.g. temperature, precipitation) over a certain region. We have applied it to the North Atlantic Oscillation influence on the Iberian Peninsula winter precipitation.

The first step of our approach consists in obtaining an improved NAO index forecast. Error statistics features of forecasted NAO pattern by different SFSs have been analysed. Winter NAO index forecasted by a skilful empirical system based on a teleconnection with snow cover advance and with Gaussian errors distribution has been considered as an a priori NAO pdf estimate. Using as background the ECMWF System 5 ensemble mean of NAO index, a new a priori estimate for the pdf of NAO index encompassing a bias correction procedure and a Gaussian model for distribution of errors has been proposed. The two a priori estimates have been optimally combined to obtain an enhanced a posteriori NAO index pdf. These new NAO estimates result to be less biased and slightly improved, in terms of verification scores, to those of ECMWF System 5.

The second step of the proposed methodology is to employ the enhanced NAO index estimates for ensemble member's weighting of a SFS based on a single dynamical model. The new NAO pdfs obtained in this work have been employed to improve the ECMWF System 5 NAO index prediction and precipitation forecast skill over the Iberian Peninsula. Verification results confirm that an accurate forecast for winter NAO distribution is key to make skilful forecasts of precipitation over this region. We show noticeable improvement of winter precipitation forecasts over our region of interest when members are weighted using a NAO index Gaussian pdf based on ECMWF System 5 bias corrected errors as compared with the usual approach based on equiprobability of ensemble members. Skill of forecasted precipitation is further enhanced by weighting ensemble members making use of the Best NAO pdf estimate based on a combination of the Gaussian pdf from ECMWF System 5 and a skilful empirical relationship with near normally distributed errors. The assessment of the effect of member's weighting on ECMWF System 5 NAO index forecasts confirm that they are consistently improved with the methodology employed.

Although this procedure has been applied to the ECMWF System 5, the approach is fully general and consequently applicable to any other dynamical SFS providing a skilful NAO signal, as long as their errors are properly characterised. This work has made use of an empirical seasonal forecasting system to add new information to ECMWF System 5 forecasts, but any other SFS showing enough good performance regarding forecasted NAO might be employed. It should stressed that this method relies on a proper errors characterisation and therefore a longer hindcast period is always highly desirable. Additionally a longer hindcast period allows a more robust testing of the statistical methods described and analyzed in this work. As it has been shown by Kang et al. (2014) and other authors, the skill of AO or NAO forecasts by different SFS depends on the reforecast period considered.

The ERA Interim reanalysis data and the three operational C3S SFSs (ECMWF System 5, Met Office S12 and Météo France S5) data are available at Copernicus Climate Change Service (C3S) (https://cds.climate.copernicus.eu, Climate Data Store, 2019). The E-OBS observational data are available at European Climate Assessment & Dataset project (2019, https://www.ecad.eu/download/ensembles/download.php), implemented by ECA&D project team (Cornes et al., 2018, https://doi.org/10.1029/2017JD028200).

The S-ClimWaRe empirical model data can be requested from the authors.

ERC conceived the idea. BN developed the method of combination and weighting. ESG implemented the method and performed the analysis and assesment. JV provided the data from empirical model.

The authors declare that they have no conflict of interest.

This article is part of the special issue “18th EMS Annual Meeting: European Conference for Applied Meteorology and Climatology 2018”. It is a result of the EMS Annual Meeting: European Conference for Applied Meteorology and Climatology 2018, Budapest, Hungary, 3–7 September 2018.

The authors very much appreciate two anonymous reviewers for their valuable comments and suggestions that have helped to significantly improve the description of this work.

The research leading to these results has received funding from MEDSCOPE project. MEDSCOPE is co-funded by the European Commission as part of ERA4CS, an ERA-NET initiated by JPI Climate, grant agreement no. 690462.

This paper was edited by Silvio Gualdi and reviewed by two anonymous referees.

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- Abstract
- Introduction
- Errors of seasonal forecasting systems predicting the winter NAO
- Methodology to improve the NAO estimate
- Improved precipitation by ensemble member's weighting with enhanced NAO pdf forecast estimates
- Summary and final remarks
- Data availability
- Author contributions
- Competing interests
- Special issue statement
- Acknowledgements
- Financial support
- Review statement
- References

- Abstract
- Introduction
- Errors of seasonal forecasting systems predicting the winter NAO
- Methodology to improve the NAO estimate
- Improved precipitation by ensemble member's weighting with enhanced NAO pdf forecast estimates
- Summary and final remarks
- Data availability
- Author contributions
- Competing interests
- Special issue statement
- Acknowledgements
- Financial support
- Review statement
- References