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  • View in gallery

    Observed and predicted time series of the winter-mean NAOI index (Li and Wang 2003). Refer to Table 2 to compare the respective correlation coefficients. The multisystem ensemble mean achieves a correlation of 0.85, which despite the relatively short hindcast period (1997–2011) is found to be statistically significant against the null hypothesis of nonpositive correlation at the 99% level.

  • View in gallery

    Thick solid lines show the predictive skill (correlation coefficient) of each system as a function of subensemble size (for details refer to the text). The thin solid lines indicate the ±1 standard deviation correlation limits as computed from the various member combinations. The dashed lines show the average ratio of the interannual MSLP standard deviation between the subensemble mean and the observed anomalies at the NAO centers of action. The turquoise markers correspond to the predictive skill of the multisystem mean at different effective ensemble sizes (individual members from the three systems are combined proportionally to the respective ensemble sizes, i.e., 9/24/24), while the yellow markers show the respective ratios.

  • View in gallery

    Deterministic predictive skill (ACC) for the DJF mean MSLP ensemble mean anomalies of each SPS and of MULTI. Based on a one-sided t test accounting for autocorrelation (see text), all correlations above 0.50 (dark red, brown, and yellow shading) are statistically significant at least at the 0.95 level.

  • View in gallery

    Signal-to-noise ratio for the DJF mean MSLP anomalies of each SPS and of MULTI.

  • View in gallery

    Probabilistic predictive skill (ROC score) for the DJF mean MSLP anomalies of the MULTI ensemble mean for the upper, middle, and lower terciles.

  • View in gallery

    Skill maps showing the anomaly correlation coefficient of winter-mean (left) T2M and (right) PREC anomalies for the multisystem ensemble mean: (top) actual predicted anomalies, (middle), anomalies computed using the predicted NAO index, and (bottom) the respective NAO regression patterns as defined from the observed fields (winter-mean anomalies per standard deviation of the NAO index, the zero contour is highlighted, contour intervals are 0.2 K for T2M on the left and 0.15 mm day−1 for PREC on the right). The verification is against the corresponding anomalies from ERA-Interim (T2M) and GPCP (PREC).

  • View in gallery

    Top to bottom: MSLP, T2M, and PREC Taylor diagrams for the multisystem ensemble mean. The blue and red markers correspond, respectively, to the years with the best and the worst NAO prediction. The selected years in order of decreasing prediction quality: 2010: , 2011: , 2000: , 2008: , 2003: , 1997: , 2002: , 2005: . The gray markers represent the remaining years with smaller NAO amplitudes, yet these are not classified in respect to prediction quality.

  • View in gallery

    (left) RMSE of T2M for the multisystem ensemble (averaged across all individual members). (right) The corresponding RMSE difference between the years of the least and the most successful NAO prediction–positive values indicate a reduction in RMSE as a result of NAO skill. Units: K.

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A Multisystem View of Wintertime NAO Seasonal Predictions

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  • 1 CMCC, Bologna, Italy
  • | 2 Met Office Hadley Centre, Exeter, United Kingdom
  • | 3 CMCC, Bologna, Italy
  • | 4 Met Office Hadley Centre, Exeter, United Kingdom
  • | 5 CMCC, and INGV-CMCC, Bologna, Italy
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Abstract

Significant predictive skill for the mean winter North Atlantic Oscillation (NAO) and Arctic Oscillation (AO) has been recently reported for a number of different seasonal forecasting systems. These findings are important in exploring the predictability of the natural system, but they are also important from a socioeconomic point of view, since the ability to predict the wintertime atmospheric circulation anomalies over the North Atlantic well ahead in time will have significant benefits for North American and European countries.

In contrast to the tropics, for the mid latitudes the predictive skill of many forecasting systems at the seasonal time scale has been shown to be low to moderate. The recent findings are promising in this regard, suggesting that better forecasts are possible, provided that key components of the climate system are initialized realistically and the coupled models are able to simulate adequately the dominant processes and teleconnections associated with low-frequency variability. It is shown that a multisystem approach has unprecedented high predictive skill for the NAO and AO, probably largely due to increasing the ensemble size and partly due to increasing model diversity.

Predicting successfully the winter mean NAO does not ensure that the respective climate anomalies are also well predicted. The NAO has a strong impact on Europe and North America, yet it only explains part of the interannual and low-frequency variability over these areas. Here it is shown with a number of different diagnostics that the high predictive skill for the NAO/AO indeed translates to more accurate predictions of temperature, surface pressure, and precipitation in the areas of influence of this teleconnection.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author e-mail: Panos J. Athanasiadis, panos.athanasiadis@cmcc.it

Abstract

Significant predictive skill for the mean winter North Atlantic Oscillation (NAO) and Arctic Oscillation (AO) has been recently reported for a number of different seasonal forecasting systems. These findings are important in exploring the predictability of the natural system, but they are also important from a socioeconomic point of view, since the ability to predict the wintertime atmospheric circulation anomalies over the North Atlantic well ahead in time will have significant benefits for North American and European countries.

In contrast to the tropics, for the mid latitudes the predictive skill of many forecasting systems at the seasonal time scale has been shown to be low to moderate. The recent findings are promising in this regard, suggesting that better forecasts are possible, provided that key components of the climate system are initialized realistically and the coupled models are able to simulate adequately the dominant processes and teleconnections associated with low-frequency variability. It is shown that a multisystem approach has unprecedented high predictive skill for the NAO and AO, probably largely due to increasing the ensemble size and partly due to increasing model diversity.

Predicting successfully the winter mean NAO does not ensure that the respective climate anomalies are also well predicted. The NAO has a strong impact on Europe and North America, yet it only explains part of the interannual and low-frequency variability over these areas. Here it is shown with a number of different diagnostics that the high predictive skill for the NAO/AO indeed translates to more accurate predictions of temperature, surface pressure, and precipitation in the areas of influence of this teleconnection.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author e-mail: Panos J. Athanasiadis, panos.athanasiadis@cmcc.it

1. Introduction

The scope of seasonal forecasting is to predict the climate anomalies of the coming season one or more months ahead. For each seasonal forecasting system, the accuracy of the predicted anomalies, assessed in a probabilistic sense, fundamentally depends on the following: 1) the initial states provided to the model components, 2) the model climate, since climate variability depends on the mean state, and 3) the representation by the model of the physical processes associated with teleconnections and seasonal predictability.

Only recently has seasonal forecasting matured to the point of making skillful predictions of the extratropical atmospheric circulation anomalies. In particular, Riddle et al. (2013), Scaife et al. (2014), Athanasiadis et al. (2014), Kang et al. (2014), and Stockdale et al. (2015) have reported significant skill in predicting the mean-winter state of the North Atlantic Oscillation (NAO) and the Arctic Oscillation (AO). This was indicated to be possible by a number of earlier studies (e.g., Johansson et al. 1998; Folland et al. 2012) that explored the predictability of the atmospheric low-frequency variability in the extended North Atlantic domain. It is widely accepted that the NAO variability is driven by a number of different mechanisms acting simultaneously at various time scales. For interannual variability of winter mean fields, the role of internal tropospheric dynamics in driving the NAO-associated variability is relatively less important than when examining the intraseasonal variability. At longer time scales, other dynamical processes—all related to boundary forcings—come into play and constrain the internal tropospheric dynamics. These include interaction with the upper ocean (e.g., Czaja and Frankignoul 1999; Saunders and Qian 2002; Losada et al. 2007), the stratosphere (e.g., Baldwin et al. 2003; Scaife et al. 2005; Sigmond et al. 2013; Kidston et al. 2015), the snow cover and sea ice extent (e.g., Saunders et al. 2003; Douville 2010; Cohen and Jones 2011), and the soil moisture content (e.g., Douville 2010; Materia et al. 2014). The role of each of these components has been examined separately and reported to be nonnegligible to significant. Therefore, when a seasonal forecast is initialized realistically, the state of each of these components is expected to affect the seasonal mean state of the NAO. In addition, realistic representation of the associated physical processes and teleconnections by the model is key for getting the correct signal in the forecasts (e.g., Scaife et al. 2016). Currently, rapid progress is being made by most operational centers in both the representation of processes and the initialization strategies.

Higher resolution generally allows for a better representation of eddy fluxes both in the ocean and in the atmosphere. This may lead to a reduction of some model systematic biases (e.g., location and gradient of SST fronts; Minobe et al. 2008). Also, some of the processes governing the low-frequency variability of the extratropical eddy-driven jets, such as the eddy–mean flow interaction (Hartmann 2007), are expected to be better represented in a high-resolution model. Model improvements due to increased resolution have already been reported (e.g., Scaife et al. 2011), and most operational centers, including the Centro Euro-Mediterraneo sui Cambiamenti Climatici (CMCC), are moving to higher-resolution models.

The concept of having an ensemble of forecasts is key in seasonal forecasting (Palmer and Anderson 1994; Kumar et al. 2001). First introduced in weather prediction, the use of an ensemble of perturbed forecasts is a way to account for the uncertainty associated with the initial conditions or model parameter uncertainty in perturbed physics ensembles. However, in seasonal prediction the rationale behind the use of ensembles is slightly different in the sense that one is no longer trying to predict the exact state of the atmosphere at any given time (deterministic prediction) but the weather statistics over a given future period. Particularly in the extratropics, the chaotic atmospheric variability can mask any predictable component of climate variability, and thus—even for a perfect model—any individual forecast (also referred to as realization) is not sufficient for determining the predictable signal. Averaging across a large ensemble eliminates significantly the inherently unpredictable noise and so allows the predictable signal to be detected. Of course, for any nonperfect, real model this signal is not free of errors. Conceptually, for a sufficiently large ensemble, the ensemble mean anomaly represents the predictable component that supposedly is common in all realizations and masked by the superimposed chaotic noise.

The above considerations explain in a simplified way 1) why ensemble mean forecasts are more skillful than individual realizations in predicting the observed seasonal anomalies and 2) why larger ensembles are generally better in the same respect. A number of studies have clearly demonstrated the important role of a large ensemble size for skillful predictions, particularly in the extratropics. Riddle et al. (2013) have shown that for lead 0 (first month) predictions of the AO, a small ensemble size (~10) is generally quite skillful, but when considering lead 1 and longer lead predictions, larger ensemble sizes are necessary for robust skill. Saha et al. (2014) documenting the CFSv2 system show a clear increase in the lead 1 skill of predicting near-surface air temperatures over the United States for an ensemble of 25 members versus a smaller 15-member ensemble. Scaife et al. (2014) summarize the importance of the ensemble size by analyzing winter-mean forecasts of the NAO. In their study it is demonstrated that the predictive skill (anomaly correlation coefficient) increases monotonically with the ensemble size, approaching asymptotically for very large ensemble sizes (by extrapolation to ~100) an upper threshold dictated by theoretical predictability and the limitations of the prediction system. Finally, considering time-mean anomalies across a whole season (typically a period of three months, here DJF) is fundamental for canceling out a large fraction of the variability component that is inherently unpredictable.

Beyond the above considerations related to the ensemble size, in a multisystem ensemble the signal contributed by each individual system is not correct at all instances as all models are imperfect, and given that each individual system may excel in the representation of a different physical process contributing to predictability, averaging the signal of different systems generally tends to enhance the predictive skill as several studies have demonstrated in the context of seasonal to decadal predictability. As discussed below, this effect appears to be present also in this study.

The present study involves three operational seasonal prediction systems (UKMO, CFSv2, and CMCC; see section 2) that have recently been reported to have improved NAO prediction skill as described above.1 It principally aims to answer two questions: first, whether the recently reported high skill of a number of individual systems in predicting the wintertime NAO can be further enhanced by combining the ensembles of these systems into a larger multisystem ensemble, and second, whether the skillful NAO predictions truly impact the quality of the seasonal forecasts in the domain of influence of the NAO. The first question is tackled in section 3 and the second one is discussed in section 4. Section 2 provides an introduction to the characteristics of the three seasonal prediction systems that have been used, plus a description of the datasets and the methods. Conclusions are given in section 5.

2. Data and methods

As stated in the previous section, three operational seasonal prediction systems (SPSs) are analyzed (UKMO, CFSv2, and CMCC, defined below) in this study. The basic characteristics of the three seasonal prediction systems are summarized in Table 1. For each of these systems, only winter hindcasts initialized near the beginning of November or in this calendar month have been used. The hindcast period, the ensemble size, and the initialization strategy (among other aspects) are different for each system. Thus, some choices had to be made in dealing with these differences so as to allow for as fair as possible a comparison. The evaluation is performed for the winter period (DJF). Some additional facts for each system are provided below. It should be noted, between other differences, that unlike UKMO and CFSv2 the CMCC system is not stratosphere resolving.

  • The hindcasts of the UK Met Office Global Seasonal Prediction System 5 (GloSea5, referred to as UKMO) cover the period 1997–2011 with an ensemble of 24 members. Three initialization dates centered on 1 November (25 October, 1 November, and 9 November) are used, each contributing eight members to the ensemble. This system undergoes continuous development. The version used here is documented in detail by MacLachlan et al. (2015). The respective monthly data are available online at http://chfps.cima.fcen.uba.ar.
  • The Climate Forecast System version 2 (CFSv2) of the National Centers for Environmental Prediction (NCEP) is described in detail in Saha et al. (2014). The hindcasts of this system (referred to as “reforecasts” by NCEP) cover the period 1983–2011, referring to the year of initialization. The data from these runs are available online at http://nomads.ncdc.noaa.gov/data.php. Our criterion in forming an ensemble from the plethora of CFSv2 runs (4 runs every 5th day year-round) was to utilize all those runs initialized in November that allow—from an operational point of view—a winter (DJF) forecast to be issued by the end of this same month. Thus, the runs initialized on 2, 7, 12, 17, 22, and 27 November at 0000, 0600, 1200, and 1800 UTC have been chosen, forming an ensemble of 24 members. Of course, the last of these runs are initialized very close to the evaluation period (DJF) and thus marginally benefit from deterministic medium-range predictability. Therefore, alternatively, and for a fair comparison with the UKMO system, a different 24-member ensemble has been used utilizing the runs initialized on 23 and 28 October and 2, 7, 12, and 17 November. The latter is referred to as CFSv2oct.
  • The hindcasts of the CMCC Seasonal Prediction System version 1.5 (referred to as CMCC) consist of nine members covering the period 1983–2011. These are all initialized on 1 November. To account for the uncertainty in the exact initial state, past atmospheric states (with a 12-h interval, thus going back to 28 October), representing perturbed initial states, are assigned to the model as the initial condition on 1 November. Further details of this system can be found in Materia et al. (2014), while the respective monthly data can be found online at ftp://downloads.cmcc.bo.it/p_spsv15/.
Table 1.

Basic characteristics of the three seasonal forecasting systems.

Table 1.

The above seasonal prediction systems (UKMO, CFSv2, and CMCC) are combined to form a multisystem prediction, hereafter referred to as MULTI. The multisystem ensemble mean is defined as the average of the three individual ensemble means, thus giving equal weight to each SPS. Alternatively, one can define the multisystem ensemble mean with the pooling method, that is, by weighing the individual ensemble means proportionally to the corresponding ensemble sizes. Kharin and Zwiers (2002) and other studies have proposed more elaborate methods. However, as Kirtman and Pirani (2009) put it: “the use of multimodel ensembles techniques improves skill, though the optimal way to combine models has yet to be established” (p. 457). In this study, as mentioned in section 3, the corresponding differences in skill were found to be insignificant.

The verification of seasonal predictions is performed against ERA-Interim reanalysis (Dee et al. 2011) data. For this purpose, monthly mean fields are used from the period December 1982 to February 2011 (29 DJF seasons). In particular, mean sea level pressure (MSLP) is used to compute the NAO and the AO indices, and 2-m air temperature (T2M) for assessing climatic impacts. For precipitation verification, the dataset of the Global Precipitation Climatology Project (GPCP) is used. Prior to further processing, all the fields (model and observational) have been interpolated to a common regular 2.5° × 2.5° grid.

A number of different ways have been used in the literature to define an index for the NAO. Along with the traditional definition of Wallace and Gutzler (1981), in this study an alternative definition is adopted for comparison, yielding higher predictive skill for each of the examined systems. This alternative index was introduced by Li and Wang (2003) and is referred to as the NAOI. The latter study discusses some advantages that the NAOI has over the traditional definition due to the zonal averaging that involves. These indices are computed using monthly MSLP anomalies averaged across winter (DJF). The AO pattern is defined as the leading EOF of ERA-Interim MSLP winter-mean anomalies (focusing on interannual variability) in the circumpolar region 20°–90°N for the period December 1982 to February 2011. Then, as in Stockdale et al. (2015), the respective AO model and observed time series are computed by projecting the respective MSLP winter-mean fields (from individual model runs, ensemble-mean fields, and ERA-Interim) onto this fixed pattern. For the EOF analysis, as well as for computing the projections, area weighting has been used to account for the varying area represented by grid points at different latitudes.

3. Predicting the NAO–AO teleconnection

The NAO/AO skill for some individual state-of-the-art seasonal prediction systems has already been examined and documented in detail (Kim et al. 2012; Riddle et al. 2013; Scaife et al. 2014; Athanasiadis et al. 2014; Kang et al. 2014; Stockdale et al. 2015). Here we also show that even better predictions are currently possible by utilizing a multisystem approach.

Figure 1 shows the interannual observed and predicted winter-mean NAO time series based on ERA-Interim reanalysis and the model hindcasts. The anomaly correlation coefficient (ACC) between the observed and the predicted multisystem mean (MULTI) NAOI index is 0.85. This is also the case for the AO index (see Table 2), while for all systems and all hindcast periods the traditional NAO index yields relatively lower correlations of 0.6 to 0.75. All the correlations shown in Table 2 have passed a t test of statistical significance at the 0.99 level against the null hypothesis of nonpositive correlation. To account for interannual autocorrelation, the effective ensemble size was calculated separately for each model according to Bretherton et al. (1999). Although one can argue that due to sampling variations any system may be found exhibiting a very high correlation for a short hindcast period, here there are some common features across all systems that add to the typical statistical significance testing.

Fig. 1.
Fig. 1.

Observed and predicted time series of the winter-mean NAOI index (Li and Wang 2003). Refer to Table 2 to compare the respective correlation coefficients. The multisystem ensemble mean achieves a correlation of 0.85, which despite the relatively short hindcast period (1997–2011) is found to be statistically significant against the null hypothesis of nonpositive correlation at the 99% level.

Citation: Journal of Climate 30, 4; 10.1175/JCLI-D-16-0153.1

Table 2.

The predictive skill (correlation coefficient) of each system and the multisystem mean for different teleconnection indices and hindcast periods. The subscript “oct” indicates a different CFSv2 ensemble including the 24 runs initialized from 23 October to 17 November. NAO refers to the traditional Wallace and Gutzler (1981) index, while NAOI stands for an alternative NAO index involving some zonal averaging of MSLP anomalies (Li and Wang 2003). The computation of the Arctic Oscillation index (AO) is described in the text. The observed indices are computed from ERA-Interim reanalysis.

Table 2.

The correlation coefficient of each system for each teleconnection index (NAO, NAOI, AO) and for each of the two different hindcast periods (1997–2011 and 1983–2011, where applicable) are summarized in Table 2, including the respective correlations for MULTI. As mentioned above, the correlations for the traditional NAO index are generally lower, something that may be understood considering that this index is based on two single points (centers of action, where teleconnectivity takes a maximum) that 1) are not identical for all calendar months and 2) may differ slightly for each system compared to the observed pattern. It should be noted that using the pooling method for defining the multisystem mean (by averaging all 57 ensemble members) gave correlations for the NAOI that differ from the value quoted in Table 2 only at the third decimal.

Also, in Table 2 it is seen that compared with the extended 1983–2011 period, the CMCC and the CFSv2 systems exhibit higher correlations for the most recent period (1997–2011). In fact, this difference is more pronounced if one compares the skill between the first and the second half of the 29-yr hindcast period (results not shown), and a one-tailed paired t test shows that the former difference is statistically significant at the 95% level. These findings corroborate a similar result by Kang et al. (2014). Seasonal forecasts are not equally successful every year, and therefore for relatively short hindcast periods sampling fluctuations may explain part of the previous difference. Kumar (2009) provide an interesting discussion of the uncertainty associated to sampling. Obviously, there exist year-to-year differences in the skill of seasonal forecasts (assessed by forecast verification for individual years) and these may be understood, at least in part, by considering that predictability itself may vary from one year to another. In fact, from a theoretical perspective it is rather expected that some climatic states (i.e., initial conditions, and therefore years) may have a more predictable evolution than others. Shi et al. (2015) have shown that the correlation/skill for the wintertime NAO may vary significantly between different hindcast periods, and our analysis does not contradict this finding. On the other hand, the correlations for both hindcast periods, for all teleconnection indices and for all individual systems remain statistically significant at the 95% level (also to the 99% level with few exceptions) and the multisystem predictions consistently outperform each individual system.

As discussed above, all systems exhibit higher skill in the more recent period.2 Stockdale et al. (2015) show that this is also the case for the ECMWF-S4 predictions, and they argue that the difference arises due to the actual stratospheric initial states allowing for higher predictability in the recent years. However, one should not forget that oceanic reanalyses have become more realistic after the introduction of Argo floats (e.g., Balmaseda et al. 2015) and other components of the climate system are also more accurately observed in the most recent period likely contributing to better skill in the recent years. Furthermore, the CMCC system does not resolve the stratosphere (sponge layer at 10 hPa) but still exhibits this behavior. With the relatively short hindcast periods available and with a number of different mechanisms simultaneously in play affecting the Northern Hemisphere extratropical wintertime circulation, it is difficult to draw statistically robust conclusions regarding variations in skill from one period to another.

The CFSv2 correlation drops fast with lead time (comparing skill for December to January and February; results not shown). This is not the case for CMCC and UKMO, which exhibit comparable (if not even higher) skill for January and February compared to December. It should be noticed also that the CFSv2 with only the last 12 runs of November (17, 22, and 27 November) achieves +0.72 for DJF-mean NAO, while with its 20 earlier runs (23 and 28 October and 2, 7, and 12 November) it manages only +0.31, and +0.42 if the runs of 17 November are also included. The fact that the CFSv2 skill drops fast with lead time may be taken as an indication that a major part of the predictive skill of this system is related to the realistic initialization of the atmosphere—which is the component of the climate system with the least persistence—and the associated shorter range predictability. It is worth mentioning that for the CMCC and the UKMO systems the skill for individual calendar months is minimum for December (then increasing; results not shown) in contrast to the CFSv2 system that exhibits maximum skill for December (then decreasing). Supposing that these differences are statistically robust and significant, a possible interpretation could involve the fact that certain physical mechanisms, such as El Niño–Southern Oscillation (ENSO), influence the atmospheric circulation in the North Atlantic (Zhang et al. 2015; Toniazzo and Scaife 2006), leading to higher predictability in late winter.

For the NAO the years of successful and poor predictions do not seem to follow a common pattern among the three systems (see Fig. 1). This becomes more obvious by comparing to the corresponding Pacific–North American (PNA) time series (not shown) in which the impact of strong positive ENSO events on the predictive skill is quite clear. The authors searched for evidence of a dominant source of predictability3 common between these systems, yet did not reach conclusive results. Here it should be clarified that although the effect of ENSO on the wintertime North Atlantic circulation has been demonstrated in various studies [Folland et al. (2012) provide a number of references], this effect is often masked by other processes that are less well simulated by seasonal prediction systems. Knowing that the low-frequency NAO variability is driven by various mechanisms in combination (e.g., strong anomalies in the initial state of the polar vortex, upper ocean heat content, snow cover, and sea ice extent can influence the subsequent evolution of the NAO), and considering the fact that each of these components and the associated dynamical processes impacting on the NAO is represented by each system with varying fidelity, it can be argued that the contribution to NAO predictability by the various sources/mechanisms may vary from year to year and from one system to another. Following this argument, it is expected that a multisystem mean prediction may benefit more robustly from the abovementioned natural sources of predictability, since averaging across systems would tend to retain the signal of the skillful ones and cancel the differences among the remaining systems. Currently, dynamical predictions just match statistical predictions based on single predictors, such as the Snow Advance Index of Cohen and Jones (2011) and the October Z500 anomalies of Kryjov and Min (2016). However, when all important processes are adequately represented by models, multisystem dynamical predictions are expected to surpass statistical predictions based on single predictors as the former can—in principle—benefit from various sources of predictability, while the latter arguably capture a sole mechanism contributing to predictability.

The high predictive skill of the multisystem mean (0.85) for the wintertime NAO is unprecedented in dynamical forecast systems initialized in November. In addition, the significance of this high correlation (interpreted as skill) is backed up by some other findings presented in the next section. In view of some comparably high correlations presented in Kang et al. (2014), it should be emphasized that in the latter study all individual seasonal prediction systems exhibiting correlations higher than 0.55 for the wintertime AO included runs initialized in December (up to 50% of the corresponding ensemble total). For the CFSv2 in particular, Kang et al. (2014) have used 28 forecast runs, four of which initialized on 27 November and another four on 2 December. Instead, in our multisystem ensemble (UKMO, CMCC, CFSv2) there are no forecasts initialized in December, and those initialized after 22 November represent only 7% of the total. Moreover, excluding completely CFSv2 from the multisystem ensemble (i.e., for UKMO and CMCC alone, with all forecasts initialized before 10 November) gives a correlation of 0.78, which is unprecedented in its own right for dynamical predictions.

Regarding the actual lead time of the MULTI reforecasts, it should be considered that the center of the DJF period is about two and a half months ahead in lead time for the CMCC (last runs initialized on 1 November), more than two months ahead for the UKMO (last runs initialized on 9 November) and a month and a half ahead for the CFSv2 (last runs initialized on 27 November). However, strictly speaking and according to the terminology suggested by the World Meteorological Organization (WMO), the here discussed MULTI reforecasts are lead 0 forecasts. From an operational viewpoint, they could be issued just before the start of December.

To put our analysis in the context of some previous findings demonstrating the importance of the ensemble size (e.g., Scaife et al. 2014; Riddle et al. 2013), in Fig. 2 we present the correlation of each system for different subensemble sizes (averaged across all possible combinations of single members). In the same figure we present also the average ratio of the interannual MSLP standard deviation between the subensemble mean and the observed anomalies at the NAO centers of action. The correlations and the ratios for any given ensemble size n (with 1 < nN, where N is the size of the actual ensemble) are averaged across all different combinations of ensemble members. For example, for n = 3 and for N = 9 (CMCC), there are 84 distinct three-member combinations out of the available nine members. For each value of n, the ratios and the correlations shown in Fig. 2 are the averages across the respective combinations. In fact, it is the most likely correlation—not the average correlation—that is of interest here. From a theoretical view point, the correlation mean does not coincide with the mode, although the authors have found their difference here to be negligible. In the same figure, the thin lines show the spread of the correlation coefficient (±1 standard deviation around the mean). In interpreting these results one must keep in mind that subsampling from a limited actual sample (the available ensemble) is different than sampling from the entire “population” of possible perturbed runs. Nevertheless, the latter is indicative of how the predictive skill changes with the ensemble size. Interestingly, comparing to Fig. 3 in Scaife et al. (2014), the correlation for our multisystem mean (collective ensemble size of 57, correlation 0.74 for the NAO index) seems to fit with what one would expect from a single system with the same ensemble size. Nevertheless, this expectation is based solely on a certain extrapolation. Moreover, in Fig. 2 it appears that the skill of each individual system would saturate at a different ensemble size.

Fig. 2.
Fig. 2.

Thick solid lines show the predictive skill (correlation coefficient) of each system as a function of subensemble size (for details refer to the text). The thin solid lines indicate the ±1 standard deviation correlation limits as computed from the various member combinations. The dashed lines show the average ratio of the interannual MSLP standard deviation between the subensemble mean and the observed anomalies at the NAO centers of action. The turquoise markers correspond to the predictive skill of the multisystem mean at different effective ensemble sizes (individual members from the three systems are combined proportionally to the respective ensemble sizes, i.e., 9/24/24), while the yellow markers show the respective ratios.

Citation: Journal of Climate 30, 4; 10.1175/JCLI-D-16-0153.1

It is interesting to see that the interannual standard deviation of the subensemble mean decreases with the subensemble size (as an effect of “noise” cancellation between different members) but seems to tend asymptotically to a low-threshold value representing a common “signal.” On the other hand, this signal may, or may not, match the observed interannual variability (a signal may well be wrong) thus leading to different predictive skill (correlation). Mapping of the abovementioned ratio for the complete-ensemble mean of each system (not shown) interestingly revealed the NAO centers of action as areas where this ratio takes a minimum, in contrast, for instance, to the tropics and the areas dominated by ENSO-related variability where individual member predictions tend to agree with each other, and little noise cancellation occurs. These findings were found consistent with the detailed analysis of Eade et al. (2014) that highlighted the North Atlantic as an area where the predictable component of the MSLP variability is potentially high compared to the total local variance.

For the three systems employed in this analysis, the multisystem mean exhibits clearly higher skill compared to each individual system, as one would expect. In this case, however, as it emerges from Fig. 2, the benefit seems to come mainly from the increased collective ensemble size (24 + 24 + 9 = 57), which currently cannot be matched by any single seasonal prediction center. This means that for the time being, and until operational centers arrive at a point of having such large ensembles that they exploit almost all their (system dependent) potential skill, combining a number of systems together to make a larger ensemble is clearly beneficial, yielding an unmatched predictive capability. In the future, even when the skill of individual systems gets saturated by virtue of large ensemble sizes, a superensemble consisting of many different systems is envisaged that will still provide more reliable seasonal forecasts thanks to the error cancellation across systems (consider the uncertainties related to imperfect models) accomplished by averaging. In fact, indications of this effect are present in this study. For instance, the positive effect of averaging across systems can be seen for individual years in Fig. 1, while if all the skill improvement came solely from increasing the ensemble size one should not see in Fig. 2 any individual system outperforming the multisystem for the same ensemble size.

4. Predicting surface pressure, temperature, and precipitation anomalies

The NAO and AO indices computed in this study are based on MSLP, so any predictability and predictive skill associated with these teleconnections originate from this field. Figure 3 shows the anomaly correlation coefficient (ACC) for the DJF mean MSLP ensemble mean anomalies of each SPS and of MULTI. Based on a one-sided t test accounting for autocorrelation [the effective ensemble size was calculated separately for each model and for MULTI, according to Bretherton et al. (1999)], all correlations above 0.50 (dark red, brown, and yellow shading) are statistically significant at least at the 0.95 level. At first view, it is rather an encouraging result that all three individual models exhibit similar large-scale features in the skill distribution. Considering the significant differences in the formulation of these SPSs (dynamical models, parameterizations, perturbation methods, reanalyses for initialization, etc.), this similarity indicates that such a distribution of predictive skill may be a property of the natural climate system. For instance, an area of reduced skill around 55°N, 25°W, largely coinciding with the primary center of action of the eastern Atlantic pattern (Wallace and Gutzler 1981), may indicate low predictability for this teleconnection, in contrast to the NAO. Although the former teleconnection is defined at 500 hPa, like the NAO, it is closely related to the variability of the North Atlantic eddy-driven jet and particularly to the occurrence of the northern jet position, as this is defined in Woollings et al. (2010). On the other hand, some similar features in the distribution of the predictive skill (Fig. 3), particularly some areas of low skill, may just indicate common problems across the analyzed SPSs. In contrast, all three SPSs and MULTI exhibit two lobes of high predictive skill in the North Atlantic, which are clearly associated with the NAO/AO skill.

Fig. 3.
Fig. 3.

Deterministic predictive skill (ACC) for the DJF mean MSLP ensemble mean anomalies of each SPS and of MULTI. Based on a one-sided t test accounting for autocorrelation (see text), all correlations above 0.50 (dark red, brown, and yellow shading) are statistically significant at least at the 0.95 level.

Citation: Journal of Climate 30, 4; 10.1175/JCLI-D-16-0153.1

Having seen, in Fig. 2, that the ACC increases with the ensemble size while the ensemble mean standard deviation decreases, it seems constructive to examine also the direct relationship between these two. In Peng et al. (2011), Kumar and Chen (2014), and various other studies on ensemble prediction, it has been shown that an inverse relationship is generally expected between ensemble spread and predictability, yet a small ensemble spread does not guarantee skill. In fact, overconfidence (i.e., small spread without adequate skill) has been acknowledged as a typical problem in seasonal forecasts. On the other hand, the ensemble spread relates closely to the so-called signal-to-noise ratio (StN ratio; e.g., Kumar 2009). Different definitions for the StN ratio can be formulated, involving the average standard deviation of the ensemble members (noise) and the standard deviation of the ensemble mean or the observed time series (signal). This terminology may be slightly misleading in the sense that what is referred to as “noise” above apparently includes the “signal” and hence the StN ratio is found in the range [0, 1]. A low StN ratio indicates strong cancellation across the ensemble members, which is consequently indicative of a large ensemble spread. Figure 4 shows the StN ratio for the DJF mean MSLP anomalies of each SPS and MULTI. Comparing these maps with the respective skill maps (Fig. 3), one can see that the high predictive skill in the tropics is accompanied by high StN ratios. Dividing these two quantities gives the ratio of predictable components (RPC; as in Eade et al. 2014). It should be noted, though, that because of the different ensemble sizes (9, 24, 24, and 57, corresponding to CMCC, UKMO, CFSv2, and MULTI), neither the StN ratio maps nor the ACC maps are directly comparable to each other. The message to be taken from Fig. 4 is that the StN ratio patterns of the individual SPSs are quite different (much less alike, compared to the skill patterns), indicating different representation of the natural variability and imprints of predictability.

Fig. 4.
Fig. 4.

Signal-to-noise ratio for the DJF mean MSLP anomalies of each SPS and of MULTI.

Citation: Journal of Climate 30, 4; 10.1175/JCLI-D-16-0153.1

To evaluate the predictive skill, so far the correlation coefficient has been used applied to the ensemble mean and the observed time series. Although it is a widely used measure of deterministic skill for forecast verification, the correlation coefficient assesses solely the behavior of the ensemble mean prediction. Valuable information enclosed by the whole ensemble of forecasts (ensemble spread, distribution, etc.) is thus being ignored. To provide a probabilistic assessment of the predictive skill (see, e.g., Kirtman and Pirani 2009; Hagedorn et al. 2005) the relative operating characteristics (ROC) score is used (Kharin and Zwiers 2003). Figure 5 shows the global distribution of this skill measure for the lower, middle, and upper terciles of the DJF mean MSLP. This is not directly comparable to the ACC maps (Fig. 3), yet the large-scale skill “topography” is largely consistent between the two skill measures considering the ROC score for the upper and lower terciles. As it is typically the case, middle tercile events (i.e., small-amplitude anomalies) are less well predicted. Peng et al. (2011) and Kim et al. (2012) clearly demonstrate this for the case of ENSO—here we have a strong indication that this is the case also for midlatitude MSLP anomalies. Therefore, in spite of a likely high ACC, one must be aware of this deficiency.

Fig. 5.
Fig. 5.

Probabilistic predictive skill (ROC score) for the DJF mean MSLP anomalies of the MULTI ensemble mean for the upper, middle, and lower terciles.

Citation: Journal of Climate 30, 4; 10.1175/JCLI-D-16-0153.1

Having seen the capacity of the multisystem ensemble in predicting the winter-mean NAO (coefficient of determination ), it is important to ask what this means for the skill of the seasonal forecasts over Europe, the east coast of North America, and the other areas influenced by the NAO. A reliable prediction of the mean circulation anomalies associated with this teleconnection is expected to have a positive effect on predicting the seasonal weather over the affected areas, for example, via the induced anomalous advection of characteristic air masses. At the same time, the NAO is known to be closely associated with storm track changes (e.g., Athanasiadis et al. 2010; Wettstein and Wallace 2010); therefore, predicting this teleconnection goes hand-in-hand with predicting storm track changes (Yang et al. 2015) and consequently the frequency of extreme weather events, such as wind storms, floods, and cold spells. However, the mean-winter NAO “explains” only a fraction of the low-frequency variability in the respective domain. The intraseasonal NAO variability, as well as other factors independent of this teleconnection, are also important in determining the winter climate. Given this, one may ask: Does the demonstrated NAO skill have a measurable impact in predicting the winter mean climate anomalies of surface temperature, wind, and precipitation?

To answer this important question, in this section we present some new findings. First, in Fig. 6, we show the ACC maps of T2M and precipitation (PREC). Comparing these with the respective maps for each individual system (not shown) it was evident that the skill maps for the multisystem ensemble mean exhibit higher skill over northern Europe for both of these variables (more clearly so for T2M). Now, in Fig. 6 it is shown that a major part of this skill can be attributed to the NAO. In particular, given the observed patterns of T2M and PREC regressed on the NAO index (presented at the bottom of Fig. 6), fields of the respective anomalies are computed for each year by multiplying these patterns with the predicted NAO index, and the corresponding ACC maps are shown in the same figure (middle row). From these it is evident that the skill distribution generally matches the areas of impact of the NAO. This holds even more strongly for MSLP (results not shown), from which the mean surface wind anomalies can be determined. The previous methodology was first used by Scaife et al. (2014), and our results for T2M are comparable to theirs (correlation patterns are very similar, although correlation values are slightly higher in the present case).

Fig. 6.
Fig. 6.

Skill maps showing the anomaly correlation coefficient of winter-mean (left) T2M and (right) PREC anomalies for the multisystem ensemble mean: (top) actual predicted anomalies, (middle), anomalies computed using the predicted NAO index, and (bottom) the respective NAO regression patterns as defined from the observed fields (winter-mean anomalies per standard deviation of the NAO index, the zero contour is highlighted, contour intervals are 0.2 K for T2M on the left and 0.15 mm day−1 for PREC on the right). The verification is against the corresponding anomalies from ERA-Interim (T2M) and GPCP (PREC).

Citation: Journal of Climate 30, 4; 10.1175/JCLI-D-16-0153.1

As the correlation coefficient between two time series assesses only their temporal coherence and is not affected by the amplitude of their anomalies (measured by the standard deviation), it is understandable that areas with lower loadings in the NAO regression maps in Fig. 6 may still exhibit strong correlation if the respective anomalies are well predicted. As an example, in the T2M regression map (bottom left in Fig. 6) the respective anomalies near Bermuda (35°N, 60°W) are quite weak, though the ACC in the same area exceeds 0.7 (middle left in Fig. 6). It should be noted that the interannual standard deviation of the winter-mean T2M in this area (not shown) is comparable to the abovementioned loadings corresponding to ±1 standard deviation of the NAO index. Therefore, it appears that the predicted NAO index explains successfully a large part of the local variability. Instead, the direct multisystem ensemble mean T2M prediction (top left in Fig. 6) has lower skill in this area indicating that the impacts of the NAO teleconnection are not well represented there by the models. As discussed in a review article by Deser et al. (2010), the large-scale structure of the sea surface temperature anomalies associated with the NAO is driven by respective anomalies in the turbulent energy fluxes. It can be argued, therefore, that presumably these fluxes are not represented correctly by the models due to insufficient spatial resolution and imperfect parameterizations.

To verify that the high NAO skill exhibited by the multisystem ensemble mean translates to better predictions for T2M and PREC, in Fig. 7 we compare the spatial match of these anomalies with the observed ones between the years of best and worst NAO predictions by means of Taylor diagrams (Taylor 2001). For the latter, in computing spatial correlations, standard deviations, and root-mean-square differences, area weighting has been used. From the 15 winter seasons of the examined hindcast period (1997–2011), the four best (worst) are defined as those that had the correct (erroneous) NAO polarity and the largest absolute NAO amplitude. The remaining 7 years corresponding to smaller NAO amplitudes are shown by gray markers. It should be noted, however, that these years do not have a clear interpretation regarding the significance of the NAO predictive skill because they are not classified as years of successful or unsuccessful NAO prediction. Figure 7 demonstrates that when the NAO is strong and is predicted correctly the predicted and the observed anomalies of T2M and PREC have a clearly better spatial match compared to the years when the polarity of the NAO is erroneously predicted. Although not a surprising finding, in view of the discussion presented in the last paragraph, the latter is not a trivial result. Regardless of what drives the interannual NAO variability, the models seem able to represent the large-scale impacts of this teleconnection adequately well.

Fig. 7.
Fig. 7.

Top to bottom: MSLP, T2M, and PREC Taylor diagrams for the multisystem ensemble mean. The blue and red markers correspond, respectively, to the years with the best and the worst NAO prediction. The selected years in order of decreasing prediction quality: 2010: , 2011: , 2000: , 2008: , 2003: , 1997: , 2002: , 2005: . The gray markers represent the remaining years with smaller NAO amplitudes, yet these are not classified in respect to prediction quality.

Citation: Journal of Climate 30, 4; 10.1175/JCLI-D-16-0153.1

Next, in Fig. 8 we show that between the same best and worst years there is also a difference in the root-mean-square error (RMSE) for T2M, which means that more accurate predictions are achieved for the years when the winter-mean NAO is skillfully predicted. This effect is seen in northern Europe, where the NAO teleconnection has a strong impact on surface temperature. Paradoxically, the RMSE in the Labrador Sea is not reduced by virtue of the NAO skill, a plausible explanation being that the latter is an area where models exhibit significant monthly biases in the sea ice extent and therefore when the NAO magnitude is not small, large T2M errors may occur due to erroneous temperature advection and surface fluxes. This argument points to the well-discussed need to reduce model biases in order to achieve better predictions.

Fig. 8.
Fig. 8.

(left) RMSE of T2M for the multisystem ensemble (averaged across all individual members). (right) The corresponding RMSE difference between the years of the least and the most successful NAO prediction–positive values indicate a reduction in RMSE as a result of NAO skill. Units: K.

Citation: Journal of Climate 30, 4; 10.1175/JCLI-D-16-0153.1

5. Synopsis and conclusions

Recently, significant predictive skill has been reported for the winter mean NAO and AO for a number of individual seasonal forecasting systems (Riddle et al. 2013; Scaife et al. 2014; Athanasiadis et al. 2014; Kang et al. 2014; Stockdale et al. 2015). As demonstrated by Scaife et al. (2014) this skill is limited by the ensemble sizes currently in use by most operational systems. Here we examine the benefits of a multisystem ensemble (MULTI) combining the CFSv2, UKMO, and CMCC ensemble predictions (Table 1) initialized in late autumn (cumulative ensemble size = 57). As DelSole et al. (2014) have found, here the benefits probably exceed a mere increase in the ensemble size. We also assess the impact of the associated predictive skill for the NAO in predicting near-surface air temperature and precipitation in the domain of influence of this teleconnection.

The MULTI predictions exhibit an unprecedented skill (0.85) for the winter mean NAOI (Fig. 1) and AO teleconnection indices (0.74 for the traditional NAO index). The associated hindcast period is relatively short (1997–2011) and hence these results carry some uncertainty due to sampling fluctuations; however, the abovementioned correlations were found statistically significant even at the 99.5% level (considering the effective degrees of freedom due to autocorrelation, the respective p values for a one-sided test against the null hypothesis of nonpositive correlation were smaller than 0.002).

The skill of the multisystem predictions outperforms that of each individual system for all hindcast periods and teleconnection indices considered (Table 2, Fig. 2). In general, as discussed by Hagedorn et al. (2005), multisystem ensembles are superior to single systems partly due to cancellation of errors across the different systems. Quantifying this effect was out of the scope of the present study, yet it appears that the effect of increasing the ensemble size is likely more important here. In view of the careful analysis of DelSole et al. (2014), it can be argued that in a multisystem ensemble the relative contribution of these two effects to the skill enhancement (ensemble size vs system diversity) depends on the number of systems combined, their ensemble sizes, and their signal-to-noise ratios for the particular forecasted variable. When combining few systems with skills that are far from saturation (due to limited ensemble sizes and low signal-to-noise ratios for the forecasted variable) the effect of the increased multisystem ensemble size on the skill is expected to be more pronounced compared to the case of combining several systems that are already close to skill saturation in terms of their ensemble size (as in the abovementioned study for ENSO).

Better NAO predictions translate into improved near-surface air temperature and precipitation predictions over large parts of Europe and North America (Fig. 7). Regarding winter mean precipitation in particular, but also near-surface temperatures, the skill presented here for the MULTI predictions is unprecedented (Fig. 6). Despite state-of-the-art physics and, in some cases, high resolution, predictions of near-surface air temperature and precipitation at some locations are more skillful if done via the predicted NAO index rather than taking the impacts directly from the models (Fig. 6). This is presumably due to these models having improved large-scale circulation, but not necessarily better small-scale impacts. For better seasonal predictions it is fundamentally important that the models have a realistic representation of the teleconnection patterns and their impacts. With further advances in model spatial resolution, more realistic initialization of all climatic components, increasing ensemble sizes and combining different systems together, the skill of seasonal forecasts in the extratropics can still improve significantly.

Acknowledgments

We gratefully acknowledge the support of the Italian Ministry of Education, University and Research and Ministry for Environment, Land and Sea through the project GEMINA (Grant 243888). AS, CM, and LH were supported by the joint DECC/Defra Met Office Hadley Centre Climate Programme (GA01101) and the EU SPECS project (GA308378).

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1

ECMWF-S4 (Stockdale et al. 2015) was not included due to limited data access.

2

It would be interesting to include also the most recent years 2011–14, although at the time this study was conducted the respective data were not available. Regarding the behavior of the UKMO system up to 2012, the interested reader can refer to Scaife et al. (2014).

3

For example, the upper ocean heat content at the time of initialization (late autumn) was examined stratifying between years of strong positive and negative NAO events and/or years of successful and poor NAO predictions.

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