Improvements in SINTEX‐F2 seasonal prediction by implementing an atmospheric nudging scheme

Improvements in the seasonal prediction system Scale Interaction Experiment‐Frontier version 2 (SINTEX‐F2) achieved via atmospheric initialisation were evaluated using hindcast experiments. The atmospheric initialisation in the system was implemented using an atmospheric nudging scheme. The prediction skill of SINTEX‐F2 with and without initialisation (new and original systems) for nine climate indices that represent the interannual variability were evaluated against the observational data. It was found that the prediction skill for some climate indices in the Tropics and most of the climate indices in the midlatitude including subtropics was improved by the atmospheric initialisation. The skills for El Niño–Southern Oscillation (ENSO) and ENSO Modoki, however, remained comparable with the original system. Further investigation for the prediction skill revealed that the sea level pressure (SLP) in the midlatitude was predicted better by the new system than in the original system. The 2‐m temperature was better predicted by the new system, due to the improved SLP prediction. The precipitation prediction was improved in regions where the improved interannual variability had an influence on the variability of precipitation. The difference in air–sea coupling regimes was found to be effective for improving the prediction skill in different latitudes. The atmospheric nudging enhances correct atmospheric feedback on the ocean in midlatitude leading to better subsurface ocean properties; thus, it can improve the prediction skill there. However, by neglecting the ocean side feedback, it deteriorates the prediction skill in Tropics where the sea surface temperature (SST) feedback on the atmosphere is dominant. The finding for the prediction skill is general and can be used for other prediction systems to increase their prediction skill using an atmospheric nudging scheme.

Along with the progression of global warming, the climate variability is also changing drastically, and this is causing larger variability in the occurrence and strength of extreme weather events (Cai et al., 2015;Collins et al., 2010;Yoon et al., 2015).Therefore, more accurate prediction techniques are required to reduce the climaterelated risks.Seasonal prediction is a useful technique for identifying the risks of climate variability and extreme weather events.The seasonal prediction system, which consists of a coupled general circulation model (GCM), is normally used to predict these events with a lead time of several months.In general, an atmosphere-only GCM is known to be inappropriate for seasonal prediction because the seasonal variability is closely related to the interannual variability, the development of which involves a coupled atmosphere-ocean mechanism.
The most influential source of variability in global circulation is known to be El Niño-Southern Oscillation (ENSO), which modifies the Walker circulation in the Tropics and causes various effects on the global climate via teleconnections.Other instances of interannual variability exist in the Tropics, such as the Indian Ocean Dipole (IOD; Saji et al., 1999), ENSO Modoki (Ashok et al., 2007) and Atlantic Niño (and Niña;Zebiak, 1993).The tropical variability has a great impact on global climate variability, and therefore a seasonal prediction system consisting of a coupled GCM has been used to predict their development and termination.Such interannual variability exists not only in the Tropics (23 S-23 N) but also in the midlatitude (outside the Tropics and 66 S-66 N, including subtropics defined by 35 -23 S and 23 -35 N).The coastal Niños (and Niñas;Feng et al., 2013;Shannon et al., 1986;Yuan & Yamagata, 2014) and subtropical dipoles (Behera & Yamagata, 2001;Morioka et al., 2011) are types of interannual variability that appears in the midlatitude.In those regions, the sea surface temperature (SST) is relatively lower than that in the Tropics, and so the influence of atmospheric variability on the development of the interannual variability is considered more dominant than that of the ocean.Therefore, precise prediction of atmospheric behaviour rather than that of ocean behaviour is more important for improving seasonal prediction.
To achieve precise prediction, accurate simulations of atmospheric and oceanic circulations, including the atmosphere-ocean interaction, are necessary.Scale Interaction Experiment-Frontier version 2 (SINTEX-F2) is a seasonal prediction system that has relatively high prediction skill for the interannual variability (Masson et al., 2012).Although SINTEX-F2 shows improvements in its prediction skill compared to its predecessor by updating its atmospheric and oceanic models, the system still cannot predict certain events well (Doi et al., 2016).One area in which SINTEX-F2 could improve its prediction skill is through initialisation.In SINTEX-F2, the initialisation of the atmosphere and ocean has been only conducted via a simple SST nudging scheme using observed SST.This method of initialisation appears unable to correct the bias derived from the atmospheric model since there is no direct initialisation of the atmosphere.The atmospheric model originally has a large degree of uncertainty derived from the cumulus parameterisation (Baba, 2019), and therefore advanced initialisation methods to reduce the model's uncertainty are necessary.
Recent prediction systems that consist of a coupled model employ various initialisation methods for the atmosphere and ocean.Several studies reported the impacts of changing the atmospheric initialisation method on the prediction results.Balmaseda and Anderson (2009) reported that the atmospheric initialisation reduced the forecast error for the interannual variability in the Pacific.Hudson et al. (2011) showed that the prediction of El Niño was improved by introducing atmospheric initialisation that uses realistic data compared with the initialisation using the results of an atmosphere-only model run.Several other studies employed the atmospheric initialisation and also reported that this could improve seasonal and decadal prediction (Baehr et al., 2015;Lu et al., 2020;Paolino et al., 2012;Yang et al., 2021).These results suggest that the incorporation of atmospheric initialisation into SINTEX-F2 is expected to improve its prediction skill for the interannual variability.However, since the above preceding studies focused on tropical variability, the skill improvement for interannual variability which is originated from both tropical and subtropical SST due to the initialisation scheme remains unknown.Although impact of atmospheric initialisation on seasonal prediction of midlatitude surface temperature has been studied (Paolino et al., 2012), the impact and related improvement mechanism on the midlatitude SST prediction which are important for estimating climate variability have not been clarified yet.
The purpose of this study is to examine the improvements in seasonal prediction realized by SINTEX-F2 incorporating atmospheric initialisation by a nudging scheme.Here, the seasonal prediction means the SST prediction.To examine the improvements, hindcast experiments are conducted with and without the atmospheric initialisation that uses the reanalysis datasets.The atmospheric variability is assumed to have a larger impact on the interannual variability in the midlatitude than that on that in the Tropics.Therefore, the expected change in the prediction skill for the midlatitude interannual variability and mechanism of the skill improvement will be the focus of this paper.The change in such SST prediction skill by the atmospheric initialisation has not been analysed yet, and only few findings have been known for the predictability (e.g., Doi et al., 2013Doi et al., , 2015Doi et al., , 2016)).The remainder of this manuscript is structured as follows.Section 2 presents the details of the model, experimental setup and analysis methods.The results and discussion are presented in section 3. Section 4 provides summary and conclusions.

| SINTEX-F2
SINTEX-F2 seasonal prediction system (Masson et al., 2012) consists of a coupled GCM (CGCM).The CGCM itself comprises of atmospheric and oceanic GCMs.The atmospheric GCM (AGCM) is ECHAM5 (Roeckner et al., 2003(Roeckner et al., , 2006) ) which has a 1.125 (T106) horizontal resolution and 31 layers in the vertical hybrid sigma-pressure coordinates.Recently, a new convection scheme based on spectral cumulus parameterisation was introduced into this part of the model (Baba, 2019(Baba, , 2021)), but this scheme is not used here, and the original scheme (Tiedtke, 1989) is instead used for simplicity.The oceanic GCM (OGCM) is Nucleus for European Modelling of the Ocean (NEMO) version 3.2 (Madec and NEMO team, 2008).The OGCM employs the ORCA05 grid (with approximately 0.5 resolution) in the horizontal direction, and employs 31 vertical levels in the vertical direction which is given by z-coordinate.The AGCM and OGCM are coupled by the Ocean Atmosphere Sea Ice Soil (OASIS) version 3 coupler (Valcke, 2013).Fluxes from each model components are exchanged by the coupler every 2 h and no flux correction is used for the coupling of the models.

| Initialisation
The original system employs a simple SST nudging scheme to initialise the atmosphere and ocean (Masson et al., 2012), utilizing weekly and daily data based on Optimum Interpolation SST (OISST; Reynolds et al., 2002Reynolds et al., , 2007)).Three different restoring times are used by setting the value of negative feedback to be −2400, −1200 and −600 WÁm −2 .These values correspond to 1, 2 and 3 day restoring times for the SST, whose mixed layer depth is assumed to be 50 m.In addition to this initialisation scheme, another atmospheric initialisation scheme is introduced for the new system.This is realized using the nudging scheme of ECHAM5 for surface pressure, horizontal winds and temperature (Eden et al., 2012).It is possible to reduce the number of variables to be nudged to just surface pressure; however, this is not done here because this would result in a worse result (e.g., Yang et al., 2021).The atmospheric nudging data were created using daily ERA5 reanalysis (Hersbach et al., 2020) by interpolating the data to the vertical coordinates of the model (Roeckner et al., 2003).The high wavenumber components of the nudging data were cut off to T63 and used for T106 resolution.This cut off operation was performed in order to avoid having to enforce fine scale variability in the model with the nudging data.The restoring time of the atmospheric nudging was set to 1 day and the nudging within the boundary layer was omitted to avoid initialisation shock in the hindcast run (Baehr et al., 2015).

| Experimental setup
Initialisation runs using SST nudging with and without atmospheric initialisation schemes were first performed for 24 years starting in 1982.Then, the hindcast was started from the first or second day of each month during 1990-2005, and the prediction was continued for 5 months.Therefore, the hindcast results were obtained as hindcast with up to a 5-month lead time for 16 years since 1990.The hindcast was conducted as an ensemble hindcast.The ensemble members were generated using two nudging SST datasets and three restoring times for the SST nudging.The original system increased the ensemble members using an ocean mixing perturbation, but this was not used for the present study, as it results in a small ensemble spread (Baba, 2021;Doi et al., 2016).Instead, the number of ensemble members was doubled by using a time-lagging ensemble, that is, the hindcast was performed not only from the first day but also from the second day of each month.The resulting number of ensemble members was 12 for each experiment.The daily atmospheric and monthly ocean fields were recorded.The hindcast experiments without and with the atmospheric initialisation (original and new systems) are referred to as RUN-CTL and RUN-NDG, respectively, hereafter.

| Analysis methods
In this study, nine climate indices used by Doi et al. (2016) were selected to evaluate the prediction skill of the system for interannual variability, except for the Niño3.4.Niño3 was used instead of Niño3.4.The climate indices and definitions estimated from SST anomaly (SSTA) are shown in Table 1.
The locations of each climate index are shown in Figure 1.To exclude short-term variability, a 3-month running mean was taken for all climate indices.The monthly mean of daily OISST was used to evaluate the predicted SST against the observational data.Climate drift was estimated using the observational data, and the drifting component was removed from the hindcast results to compute the anomaly of each field.Monthly mean ERA5 reanalysis was used as the observed sea level pressure, 10-m winds and 2-m temperature, and the CPC Merged Analysis of Precipitation (CMAP; Xie & Arkin, 1997) was used as the observed precipitation.The ensemble means of SST and other variables obtained from the 12 ensemble members are used for the analyses.
Statistical analysis of the prediction skill followed Doi et al. (2016).For the deterministic skill scores, the anomaly correlation coefficient (ACC) and normalized rootmean-square error normalized by standard deviation of observed value (nRMSE) were calculated for the ensemble mean of the predicted SST.The ACC and nRMSE represent phase and amplitude prediction skill, respectively.For the skilful prediction, the ACC (estimated from hindcast and observation) should exceed a persistence (lagautocorrelation of the observed value; e.g., Jin et al., 2008; ENSO is the most significant interannual variability in the Tropics, and thus the change in prediction skill by atmospheric initialisation is first reviewed (Figure 3).Both cases captured major Niño3 peaks, such as those that occurred in 1997-1998, but RUN-NDG sometimes overestimated or underestimated them (Figure 3a).The ACC of both systems exceeded the persistence across MAM (Figure 3b,g), meaning that they are skilful even with the spring barrier (Balmaseda et al., 1995).The ACC of RUN-NDG, however, decreased more than that of RUN-CTL during Jul-Sep with a 5-month lead time.
Likewise, the nRMSE of RUN-NDG worsened compared with RUN-CTL (Figure 3c,h).These degradations may have derived from the overestimation of Niño3 seen in 1992 and 1993.The ROCS indicates that the probabilistic skill of RUN-NDG was improved compared to RUN-CTL, except for ROCS-p during SON.It is apparent that the climate drift of RUN-NDG improved compared with RUN-CTL for many seasons (Figure 3f,k).
(a) Niño 3 time series ENSO Modoki is another type of ENSO in the tropical Pacific that forms a tripolar SSTA pattern rather than a bipolar SSTA pattern (Ashok et al., 2007).A similar analysis for EMI is shown in Figure S1, Supporting Information.Both cases present a similar time series of EMI and there is no clear difference between them.Similar to Niño3, the ACC and nRMSE do not indicate improvement but rather slight degradation, especially for the 4and 5-month lead times.This implies that the present atmospheric initialisation may not work well in improving the deterministic prediction skill for ENSO and ENSO Modoki, especially with a longer lead time.The ROCS indicates that RUN-NDG improved the probabilistic skill for EMI, whereas a cold climate drift is slightly magnified in RUN-NDG.Unlike Niño3 and EMI, DMI for IOD shows apparent improvements in the prediction skill of RUN-NDG (Figure 4).The time series of DMI indicates that both cases predicted the peaks of IODs well during the targeted period.Furthermore, RUN-NDG suppressed the overestimated or underestimated DMI in RUN-CTL as in 1993, 2001and 2003.Similarly, unrealistic DMI was seen in the predictions of the original system during different period and its predecessor (Doi et al., 2016).Therefore, these unrealistic predictions may be derived from the SST nudging-only initialisation, and the atmospheric initialisation could suppress the unrealistic DMI.The ACC and nRMSE indicate apparent improvements in RUN-NDG during SON, which correspond to the peak season of IOD, whereas ROCS shows that improvements appeared for JJA (only ROCS-p) and SON.Similar to the other indices, RUN-NDG showed the improved climate drift, as the warm drift was suppressed compared with RUN-CTL.
To understand why RUN-NDG improved the prediction of DMI compared with RUN-CTL, seasonally averaged anomalies of SST, sea level pressure (SLP) and 10-m winds were compared for JJA in 2001 and SON in 2003 (Figure 5).In 2001, SST formed a negative IOD pattern (Baba, 2020;Guo et al., 2015), and there was a negative SLP anomaly (SLPA) off the west coast of Sumatra.This negative SLPA pattern enhanced the ocean Ekman downwelling via cyclonic circulation, causing a positive SSTA there (Figure 5a).RUN-CTL, however, predicted positive SLPA there, leading to upwelling that decreased SSTA, similar to the positive IOD pattern.Meantime, an easterly wind anomaly appeared in the western tropical Indian Ocean, which enhanced the downwelling Rossby waves and caused positive SSTA in the western pole (Xie et al., 2002) (Figure 5b).In contrast to the case in 2001, there was a positive SLPA off the west coast of Sumatra in 2003, and the positive SLPA enhanced the ocean upwelling, leading to a positive IOD pattern via anticyclonic circulation (Figure 5d).RUN-CTL failed to predict this positive SLPA but rather predicted negative SLPA there (Figure 5e).In both cases, RUN-NDG predicted the correct sign of the SLPA off the west coast of Sumatra, and this could have suppressed the unrealistic DMI (Figure 5c,f).Focusing on the SLPA pattern around IOD, the SLPA was found to be a part of the subtropical high which centre location is in the southern Indian Ocean.Therefore, prediction of the SLPA in the subtropics is important for DMI prediction.Indeed, the difference in  ACC of SLP during JJA and SON also indicates that SLP prediction in RUN-NDG was improved there (Figure 5g,h).RUN-NDG showed improved prediction skill for ATL3 compared with RUN-CTL, but the degree of improvement was smaller than for DMI (Figure S2).RUN-NDG showed similar time series for ATL3 compared with RUN-CTL.The ACC and nRMSE indicate that RUN-NDG has improved phase and amplitude prediction skills during SON-DJF, which seasons are different from the peak season of the Atlantic Niño.Differing from the ACC and nRMSE, ROCS-n indicates improvements but ROCS-p indicates degradation.The climate drift of RUN-NDG was almost the same as that of RUN-CTL, but the warm drift was slightly improved for all seasons.

| Indian Ocean and southern Atlantic subtropical dipoles
The Indian Ocean subtropical dipole (IOSD) is a source of interannual variability that occurs in the subtropical region in the Indian Ocean (Behera & Yamagata, 2001).The prediction skill for IOSD is summarized in Figure S3.The time series of IOSDI indicates that RUN-NDG partly succeeded in predicting some peaks of IOSDI better than RUN-CTL (e.g., 1997-1998and 2004-2005), but shows worse prediction than RUN-CTL in other cases (e.g., 1992-1993 and 1995-1996).The ACC for IOSDI did not become significantly higher by implementing atmospheric initialisation, but became higher during SON and DJF.The nRMSE was slightly improved during DJF.The ROCS-p in RUN-NDG showed improvement but the ROCS-n did not.The climate drift for both cases was similar.These facts suggest that RUN-NDG improved the IOSD prediction skill but only to a small degree.
The southern Atlantic subtropical dipole (SASD) is the dominant source of interannual variability in the South Atlantic (Morioka et al., 2011).Remarkable prediction skill changes in RUN-NDG are observed in SASDI (Figure 6).The time series of SASDI shows that both cases captured their peaks well but that RUN-NDG outperformed RUN-CTL for some peak seasons.The ACC indicates that the phase prediction skill increased substantially during SON and DJF and that RUN-NDG was more skilful, especially during SON.The nRMSE was also improved during SON and DJF.The ROCS-n in RUN-NDG became worse but the ROCS-p improved especially during DJF.A cold climate drift throughout the seasons was improved by RUN-NDG.
The reason for the improvement in the prediction skill was investigated by the composite anomalies of SST, SLP and 10-m wind (Figure 7).SASD is normally triggered by the SLPA in the subtropics that warms (cools) the mixed layer by solar radiation, and the SLPA makes the mixed layer thinner (thicker) than the normal condition, leading to further warming (cooling) in each pole (Morioka et al., 2011).When a positive (negative) SASD F I G U R E 7 (a-f) Composite anomalies of SST (shading, C), SLP (contour line, hPa) and 10-m winds (vector, mÁs −1 ) for positive and negative phases of SASD.The SST and atmospheric conditions in 1999SST and atmospheric conditions in , 2000SST and atmospheric conditions in and 2002SST and atmospheric conditions in (1994SST and atmospheric conditions in , 1995SST and atmospheric conditions in and 1998) )  occurs, its western pole is covered by the positive (negative) SLPA.RUN-CTL, however, could not predict a sufficiently strong SLPA in this region, and thus the mixed layer warming (cooling) was insignificant, resulting in its failure to predict the SASD.RUN-NDG predicted stronger SLPA compared with RUN-CTL, and the mixed layer correctly responded to the SLPA.Thus, a sufficiently strong SASD was predicted.The ACC difference reflected these features regardless of the cases, as RUN-NDG predicted better SLPA in each pole than RUN-CTL during SON (Figure 7g,h).

| Coastal Niños
Ningaloo Niño is one of the coastal Niños that occurs off the west coast of Australia (Feng et al., 2013;Kataoka et al., 2014).The prediction skill for NNI of Ningaloo Niño is summarized in Figure 8.The time series of NNI indicates that both cases partly captured the trends of NNI, but neither could capture the NNI peaks well.The ACC indicates that both cases were not skilful at predicting the peak season but RUN-NDG largely extended skilful prediction for JJA and SON.The nRMSE indicates that amplitude prediction was improved, especially during SON.RUN-NDG showed improved ROCS-p and ROCS-n, and the improvement was remarkable for ROCS-n.The climate drift showed that RUN-NDG suppressed a warm bias for all seasons.
To analyse the reason behind the improved skill, composite anomalies of the SLP and 10-m winds are compared for SON (Figure 9).In the observation, there is a negative (positive) SLPA in the southwestern ocean region off Australia for the positive (negative) phase of NNI.Along with the SLPA pattern, downwelling (upwelling) winds appear due to the cyclonic (anticyclonic) circulation.These patterns are close to the SLPA pattern that appears in the locally amplified Ningaloo Niño (Kataoka et al., 2014).RUN-CTL predicted downwelling (upwelling) winds along with a SLPA similar to the observation, but the centre of the SLPA was located in the northwestern region off Australia, and the SLPA was much weaker than the observation.RUN-NDG could not improve the location of SLPA, but improved its amplitude.Due to the more accurate SLPA amplitude, the surface winds were magnified as per the observation, so that RUN-NDG is considered to have a better prediction skill.
The ACC difference of SLP apparently indicates that RUN-NDG predicted better SLPA than RUN-CTL in the southwestern ocean during JJA and SON which fact is consistent with the above features (Figure 9g,h).
The California Niño is a coastal Niño that occurs off Baja California (Yuan & Yamagata, 2014).The prediction skill for CNI of California Niño is summarized in Figure 10.Unlike NNI, both cases predicted CNI, capturing its peak in the time series.RUN-NDG outperformed RUN-CTL in predicting some CNI peaks.Although RUN-NDG failed to increase the ACC to more than the persistence during the peak season (Jul-Aug-Sep), RUN-NDG increased ACC for all seasons compared with RUN-CTL.The nRMSE shows that RUN-NDG extended predictable seasons.RUN-NDG exhibited increased ROCS, especially ROCS-p for almost all seasons.The warm climate drift of CNI was also improved in RUN-NDG, especially during SON and DJF.
The anomalies of the SLP, SST and 10-winds are compared for situations when RUN-NDG outperformed RUN-CTL (Figure 11).In 1992, the California Niño  occurred, due to the presence of a negative SLPA off west coast of California that enhanced the ocean downwelling via cyclonic circulation (Figure 11a).RUN-CTL predicted a negative SLPA far from the west coast, and downwelling winds were not well developed.On the other hand, RUN-NDG predicted a negative SLPA close to the west coast, and thus downwelling winds were generated, leading to a higher SSTA (Figure 11b,c).In 2005, the observed California Niño was suppressed because there was a positive SLPA off the west coast of California that worked to suppress further ocean downwelling (Figure 11d).RUN-CTL predicted a negative SLPA close to the west coast, resulting in a higher SSTA, whereas RUN-NDG predicted a positive SLPA over the west coast, similar to the observation (Figure 11e,f).When focusing on the ACC difference of SLP before peak season of CNI, RUN-NDG predicted better SLPA around the region of CNI than RUN-CTL (Figure 11g,h).Similar to IOD, SASD and NNI, these facts imply that predicting the SLPA in the midlatitude is important for CNI prediction.Prediction of the Benguela Niño was difficult using the original system (Doi et al., 2016).In the time series of ABA, both cases partly captured its variability (Figure S4); however, the ACC indicates that both cases were not skilful at predicting many seasons, that is, the ACC is lower than the persistence.RUN-NDG slightly improved the ACC and nRMSE, but the skill difference between the cases is relatively small compared with the other climate indices.The ROCS-p of RUN-NDG is similar but the ROCS-n during DJF-JJA was better 3.5 | Global maps

| Sea level pressure
The improvement in prediction skill achieved by atmospheric initialisation was realized by improving the prediction of the SLPA in the midlatitude for most of the climate indices.To understand this feature in more detail, the seasonally averaged ACC of SLP was analysed in a global map (Figure 12).A remarkable difference in the predictability between the cases is seen in the polar regions for DJF, MAM and SON.In particular, higher ACC in RUN-NDG was observed in the southern polar regions.Other differences are also seen in the subtropical region of the southern hemisphere, especially during DJF and SON.
The ACC of RUN-NDG shows an increase in the subtropical and tropical Indian Ocean during DJF, JJA and SON, compared with RUN-CTL.These higher ACCs correspond to the prediction skill increase for DMI, which is derived from the SLPA pattern (see also Figure 5).According to the skill statistics, RUN-NDG increased the ACC and nRMSE of ATL3 during DJF.However, both cases show a similar ACC during DJF at the region of ATL3.The ACC of RUN-NDG is also high during SON in this region.This implies that better predicted SLPA during SON contributed to the improved ATL3 prediction.
In the region of IOSD, the ACC in RUN-NDG was slightly higher than that of RUN-CTL, especially in the region of the western pole of IOSD during SON and DJF.This slightly higher ACC in the western pole explains the slight prediction skill improvement.In the southern Atlantic, RUN-NDG shows higher ACC than RUN-CTL during SON in the subtropical regions.The high ACC corresponds well with the prediction skill increase for SASD (see also Figure 7).The ACC regarding NNI showed a small difference around the west coast of Australia during SON; however, the ACC in RUN-NDG around the area was higher than that of RUN-CTL during JJA (see also Figure 9).RUN-NDG showed higher ACC over the west coast of California during MAM (over land), DJF and JJA (over ocean).The high ACC corresponds well to the better CNI prediction of RUN-NDG, since SLPA patterns in both land and ocean areas are important for the formation of the California Niño (see also Figure 11).
In summary, the higher ACC of SLP is related to the improved prediction skill for almost all the climate indices.In addition, the results show that the better predicted SLPA one season before corresponds to the skill increase for many climate indices.In other words, this suggests that the skill increases when the system can better predict the SLPA in advance.Considering these points, the detailed mechanism for the relation between the SLPA and the prediction skill can be explained as follows.The SLPA generates wind or radiative forcing over the ocean through cyclonic and anticyclonic circulations, and the forcing induces interannual variability.For the tropical variability and coastal Niños, the important forcing relating to the SLPA appeared to be coastal downwelling (upwelling) wind forcing.For the subtropical dipoles, the forcing appeared to be winds that enhance evaporative cooling for IOSD (Behera & Yamagata, 2001) or divergent F I G U R E 1 2 Seasonally averaged global map for the ACC of SLP (first and second columns) and the ACC difference between RUN-CTL and RUN-NDG (third column, RUN-NDG minus RUN-CTL).The ACC was given by the ACCs from hindcast with 2-to 5-month lead times.
The region with grey shading indicates where the persistence of reanalysis SLPA exceeds the ACC.The regions for climate indices are indicated by rectangles using solid black (DMI), dashed black (ATL3), solid red (NNI), dashed red (CNI), solid blue (IOSDI) and dashed blue (SASDI) coloured lines.The SLPA from ERA5 was used as the reference [Colour figure can be viewed at wileyonlinelibrary.com] (convergent) winds that enhance warming (cooling) by solar radiation for SASD.Therefore, when the SLPA was better predicted by the system, better forcing on the ocean was assumed to be given, resulting in a better prediction skill.
To analyse the mean state error of SLP which is derived from climate drift, their distributions are compared between cases (Figure 13).The climate drift of RUN-NDG indicates that RUN-NDG does not predict large drift in the Tropics, but negative and positive drifts remain in the subtropical and subpolar regions (left column of Figure 13).Comparing the magnitude of the climate drift, both cases indicate small and similar drifts in the Tropics (right column of Figure 13).However, the magnitudes in the midlatitude and subpolar regions are different.RUN-NDG shows decreased climate drifts in the subtropics to subpolar regions of the southern Indian Ocean, south of Australia, and in the subtropics of the south Atlantic.In addition, RUN-NDG shows decreased climate drifts in the northern part of Indian Ocean (DJF and SON) and in the northeastern Pacific (DJF, MAM and SON).The regions where RUN-NDG shows decreased climate drifts correspond to the regions where the ACC of SLP is high and the regions of interannual variability for which RUN-NDG demonstrates better prediction skill.

| 2-m temperature and precipitation
Along with the SLPA and interannual variability, the prediction for the atmospheric variability was expected to be improved.To clarify this point, the ACC difference for 2-m temperature for each season are compared (Figure 14).The ACC difference of temperature indicates that the prediction was improved over many regions, for example, the Southeast Asia, northsouth America, and central and south Africa during DJF.The remarkable  high ACC over the area of Europe for RUN-NDG did not appear during DJF and SON, but rather during MAM and JJA.The ACC of RUN-NDG over Australia was higher than RUN-CTL for all seasons.The ACC over the south Atlantic was also higher during JJA-DJF.These higher ACCs partly correspond to the improved climate drift, for example, over North America and northeastern Pacific during DJF.However, other high ACCs in RUN-NDG corresponds to the high ACC of SLP (Figure 12), meaning that improved SLP properties contributed to the improvement of 2-m temperature prediction.The improvements in precipitation prediction achieved by RUN-NDG are more obscure compared with those in 2-m temperature (Figure 15).Although the improvements are unclear, several improvements are seen over the land areas.The ACC of precipitation slightly increased over east and south Africa during JJA and DJF, west coast of North America during DJF-MAM, the northern part of South America during MAM-JJA, western coast of Australia during JJA and SON, and around the Maritime Continent (MC) except for JJA.In some regions over the MC, RUN-NDG shows lower ACC than RUN-CTL, but the ACC is originally higher than those of other subtropical regions and the ACC exceeds 0.5 (second column in Figure 15).These higher ACCs appeared close to the regions of interannual variability for which RUN-NDG showed better prediction skill.The high ACC of precipitation corresponds to the mitigated climate drift in the Tropics, but it does not correspond to that in the midlatitude (Figure S5).The higher ACC in some land areas is neither related to the high ACC of SLP nor to the improved climate drift.Therefore, the improvements are considered to have originated from the remote influence of the each interannual variability, such as through a precipitation response due to IOD (over MC and eastern Africa), California Niño (western coast of North America) and Ningaloo Niño (western coast of Australia).Note that the ACC difference presented here may be valid only during the period of the hindcast, since the difference was estimated using the precipitation only during 16 years.

| Atmosphere-ocean feedback
The better predicted SLPA seems to have a relation with the better predicted SSTA especially in the midlatitude.
This stems from the atmosphere-ocean feedback, which relationship is shown by air-sea coupling regime (Figure 16).In Tropics, SST has a large influence on the atmosphere via latent heat flux since the mean SST is high (Figure 16a).In this regime, SST controls convection above the ocean, and so the SLPA, that is, higher (lower) SSTA, enhances lower (higher) SLPA.
On the other hand, in midlatitude, the atmosphere has a large influence on the SST via a cyclone (an anticyclone) since the mean SST is low (Figure 16b).In this regime, the cyclone (anticyclone) controls solar radiation into the ocean, and so the SST, that is, lower (higher) SLPA enhances lower (higher) SSTA.It should be noted that Kumar et al. (2013) presented a similar mechanism, but they did not present the change of SLPA in the air-sea coupling regime that plays an important role to change the ocean properties.
Figure 17 shows global map for correlation coefficient between SLPA and SSTA.It is apparent that atmospheric feedback is dominant in the midlatitude (the correlation is positive), while SST feedback is dominant in the Tropics (the correlation is negative).Also, SLPA before 3-month is found to have more significantly and positively correlated with the SSTA of each climate indices than the simultaneous SLPA in midlatitude.These facts indicate that the prediction skill for the climate indices where the atmospheric feedback is originally dominant can be improved by the atmospheric nudging initialisation since one season before.However, the SST feedback is dominant in Tropics, so the initialisation enhances incorrect atmospheric feedback with neglecting the feedback from the ocean, then resulting in a skill decline in Tropics.
The above results presented a possibility that atmospheric nudging initialisation improved the seasonal prediction.However, it is generally believed that influence of the initialised atmospheric condition does not remain over seasonal timescale in midlatitude (e.g., Kumar et al., 2013), and so the ACC increase of SLP in 2-to 5-month lead time hindcast normally does not occur.
Considering the present results and known findings, the influence of atmospheric forcing may remain in the deeper ocean, and the influence is assumed to provide better SLP prediction via air-sea coupling.This idea is based on the finding of Rosati et al. (1997) who revealed that better ocean subsurface properties improved seasonal prediction by working as memory of the ocean.
To evaluate this hypothesis, ACC difference for subsurface ocean temperature is estimated (Figure 18).The ACC difference apparently shows that RUN-NDG predicted better subsurface temperature than RUN-CTL especially in the midlatitude and higher latitudes.This clearly indicated the fact that the present atmospheric nudging helped to initialise the subsurface ocean properties, leading to better prediction skill in the midlatitude.Furthermore, this fact gives a speculation for the reason why the lagged SLPA is better correlated with SSTA than the simultaneous SLPA in Figure 17.The ocean subsurface requires a longer time to change it properties, so the earlier atmospheric variability is more important than the simultaneous variability for determining the ocean properties.
Finally, using additional analysis, the skill decline by the initialisation in the topics is further detailed.RUN-NDG shows slightly worse prediction skill than RUN-CTL for ENSO (and ENSO Modoki) which appears in the SSTfeedback-dominant region.If the above hypothesis for the skill decline is reasonable, RUN-NDG must have predicted worse atmospheric variability for ENSO, even though the atmosphere was nudged to the observed condition.This was confirmed by investigating predicted zonal wind anomaly which is known to be an important forcing for development of ENSO (McPhaden, 2015).Indeed, RUN-NDG predicted worse phase and amplitude of the zonal wind anomaly in troposphere especially during JJA-SON that coincides with the skill decline period (Figure S6).The results suggest that the nudged atmosphere caused incorrect atmosphere-ocean feedback in the ENSO development by neglecting SST feedback on the atmosphere during the initialisation, and the influence is considered to remain in the ENSO prediction.

| SUMMARY AND CONCLUSIONS
Atmospheric initialisation was implemented in SINTEX-F2, and the improvements in the seasonal prediction skill for nine climate indices were evaluated using hindcast experiments with and without the initialisation.The initialisation was realized by employing an atmospheric nudging scheme that nudged the surface pressure, horizontal winds and temperature using reanalysis datasets.
The hindcast experiments without and with the atmospheric initialisation are referred to as RUN-CTL (original system) and RUN-NDG (new system), respectively.The ACC obtained from the hindcast experiments indicated that the phase prediction skills for ENSO and ENSO Modoki did not increase.However, the prediction skills increased for other climate indices.RUN-NDG showed a prediction skill increase for DMI, ATL3, IOSDI, SASDI, NNI, CNI and ABA.In particular, the skill increased for the peak seasons of DMI, SASDI and CNI.
When other skill statistics were estimated for the climate indices, the overall skill for ENSO and ENSO Modoki of RUN-NDG were found to be comparable with that of RUN-CTL.The statistics for DMI revealed that the prediction skill for DMI was improved especially during SON, which corresponded to its peak season.RUN-NDG also improved the large phase error of DMI that had been observed in the original system.The correctly predicted SLPA, which originated from the subtropics, was found to be the source of improving the phase error of DMI.
A similar difference in the predicted SLPA was seen in the subtropical dipoles and coastal Niños.In SASD, better predicted SLPA in subtropics contributed to the better SSTA of SASD in the south Atlantic.Although RUN-NDG could not predict the peak of NNI, it improved prediction skill for other seasons by predicting better SLPA in the subtropics and off the west coast of Australia.For the California Niño, the location of SLPA, which was in the subtropics, was identified as a key to predicting CNI.RUN-NDG predicted CNI better than RUN-CTL, as it better predicted the SLPA location and pattern.Along with all these improvements, RUN-NDG mitigated climate drift for almost all climate indices.
These facts suggest that better prediction skill for SLPA in the midlatitude including subtropics by the atmospheric initialisation may improve the prediction skill of the climate indices.The ACC of SLP showed that the ACC was higher for RUN-NDG than for RUN-CTL over or near the regions of the climate indices for which RUN-NDG showed improved prediction skill.In particular, the high ACC appeared one season before of the better predicted climate indices.This means that predicting better SLPA in advance contributes to correctly predict the interannual variability.
The ACC of 2-m temperature and precipitation also became higher by RUN-NDG.The prediction skill for 2-m temperature was improved over many land areas, and the improvement was found to be related to the regions where the SLP prediction or the climate drift of SLP was improved.The prediction for precipitation was partly improved, and the improvements appeared in the regions where the precipitation anomaly was known to be influenced by the interannual variability.
Based on the findings obtained from the above analyses, the reason for the improved prediction skill due to the incorporation of atmospheric nudging initialisation in SINTEX-F2 is explained as follows.The initialisation can provide better SLP properties in the midlatitude in the hindcast.This leads to better atmospheric forcing (e.g., upwelling or downwelling, and warming or cooling by solar radiation via the pressure patterns), which then generates better SSTA properties in the target regions.In this mechanism, influence of the atmospheric forcing reaches the deeper ocean (i.e., subsurface ocean), and this affects SST and the airsea coupling.Thus, correctly initialised atmosphere and resulting forcing which are related to the SLPA at the target region are considered the most important factor to better predict the interannual variability.
Another important finding of this study is that the prediction skill increases due to the atmospheric initialisation depending on the atmosphere-ocean feedback mechanism which can be classified into atmosphericfeedback-or SST-feedback-dominant regimes.In the midlatitude, atmospheric feedback on the SST is dominant; thus, the atmospheric nudging initialisation enhances the feedback and works well to improve the prediction skill there.It has been known that seasonal prediction skill for precipitation in midlatitude is generally low due to the air-sea coupling regime (Kumar et al., 2013), but the finding of this study suggests that the prediction skill can be improved by using the nudging initialisation.
Since the finding regarding relationship between prediction skill and the air-sea coupling regime is general, this can be used for other seasonal prediction systems to increase their prediction skill.The present new system slightly decreased prediction skill for ENSO and ENSO Modoki by incorrectly enhanced atmospheric feedback in the Tropics where SST feedback is originally dominant.To overcome this drawback with keeping the advantage of the present initialisation scheme, area-limited nudging initialisation for the atmosphere may be useful.This study presented that the atmospheric initialisation using a nudging scheme is valid for predicting midlatitude interannual variability as well as atmospheric variability which is affected by tropical and subtropical SST.Thus, the present initialisation scheme may be useful for predicting East Asian summer (winter) monsoon index (Li & Zeng, 2002;Wang et al., 2008) and relating heavy rainfall events.This feasibility will be examined in a future study.
Statistical analyses of prediction skill for Niño3.(a) Niño3 time series comparing the observation with 3-and 5-month lead time hindcast.The red crosses indicates that the deviation of RUN-CTL from the observation is greater than that of RUN-NDG for 3-month lead time.The size of the cross is proportional to the magnitude of the difference between RUN-CTL and RUN-NDG.(b, g) Seasonally stratified ACC against the persistence (ACC greater than the persistence is marked by circles, and the peak season is marked by dot-hatching).Horizontal and vertical axes indicate the lead month of the hindcast and the target month of predicted SST, respectively.(c, h) Seasonally stratified nRMSE.(d, i) Seasonally stratified ROCS for the highest 33.33% tercile (ROCS-p).(e, j) As for (d, i) but for the lowest 33.33% tercile (ROCS-n).(f, k) Climate drift for Niño3 [Colour figure can be viewed at wileyonlinelibrary.com]

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I G U R E 4 As Figure 3 but for DMI [Colour figure can be viewed at wileyonlinelibrary.com]

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I G U R E 5 (a-f) Seasonally averaged anomalies of SST (shading, C), SLP (contour line, hPa) and 10-m winds (vector, mÁs −1 ) for IOD in JJA 2001 and SON 2003.Only surface winds with wind speed greater than 1 mÁs −1 are displayed for the observation (and those of 0.25 mÁs −1 are displayed for the hindcast).(g, h) ACC difference of SLP (shading, contour line indicates ACC of SLP in RUN-NDG) during JJA and SON for 1990-2005.The difference is defined by RUN-NDG minus RUN-CTL.The red boxes indicate the regions for which SSTA is used to compute DMI.Observational data (Obs) are given from OISST and ERA5.The results of 2-to 5-month lead time hindcast are used for the composite and ACC difference [Colour figure can be viewed at wileyonlinelibrary.com] were used for the positive (negative) phase composite.The season for the composite was chosen as SON.(g, h) ACC difference of SLP (shading, contour line indicates ACC of SLP in RUN-NDG) during JJA and SON for 1990-2005.The difference is defined by RUN-NDG minus RUN-CTL.Observational data (Obs) are given by SST of OISST and ERA5.The results of 2-to 5-month lead time hindcast are used for the composite and ACC difference [Colour figure can be viewed at wileyonlinelibrary.com] U R E 9 (a-f) Composite anomalies of SLP (shading, hPa), and 10-m wind (vector, mÁs −1 ) distributions during SON in the positive and negative phases of the Ningaloo Niño.Each composite was obtained from each field where observed NNI exceeded 1.2 standard deviations.The wind vectors in the hindcast results are stretched to twice their original size, since the values of the velocity are much smaller than the observational data.(g, h) ACC difference of SLP (shading, contour line indicates ACC of SLP in RUN-NDG) during JJA and SON for 1990-2005.The difference is defined by RUN-NDG minus RUN-CTL.The red coloured boxes indicate the regions for which SSTA was used to compute the NNI.Observational data (Obs) are given by OISST and ERA5.The results of 2-to 5-month lead time hindcast are used for the composite and ACC difference [Colour figure can be viewed at wileyonlinelibrary.com] RUN-CTL.Similar to the other climate indices, the warm climate drift was suppressed for all seasons.
U R E 1 1 (a-f) Seasonally averaged anomalies of SST (shading, C), SLP (contour line, hPa) and 10-m winds (vector, mÁs −1 ) for the California Niño in 1992 and 2005.Only surface winds with wind speed greater than 0.5 mÁs −1 are displayed.The red coloured boxes indicate the regions for which SSTA was used to compute the CNI.(g, h) ACC difference of SLP (shading, contour line indicates ACC of SLP in RUN-NDG) during DJF and MAM for 1990-2005.The difference is defined by RUN-NDG minus RUN-CTL.Observational data (Obs) are given by SST of OISST and ERA5.The results of 2-to 5-month lead time hindcast are used for the composite and ACC difference [Colour figure can be viewed at wileyonlinelibrary.com]

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I G U R E 1 3 (a, c, e, g) Seasonally averaged climate drift of SLP (hPa) for RUN-NDG.(b, d, f, h) Difference in the magnitude of the climate drift of SLP (hPa) predicted by RUN-CTL and RUN-NDG.The difference is defined as RUN-CTL minus RUN-NDG, and 2-to 5-month lead time hindcasts are used.The regions marked by rectangles are same as shown in Figure 12 [Colour figure can be viewed at wileyonlinelibrary.com] m temp ACC diff (NDG-CTL) (b) 2-m temp drift diff (NDG-CTL) , e, g) Seasonally averaged ACC difference of monthly 2 m-temperature anomaly for 3-month lead time hindcast.80% significance levels estimated from the test based on Fisher's z-transformation for the ACC difference are marked by line-hatching.(b, d, f, h) Difference in the magnitude of climate drift of 2-m temperature (×10 −2 C).The difference is defined as in Figure13, and 2-to 5-month lead time hindcasts are used.ERA5 is used as the references.The regions marked by rectangles are same as shown in Figure12[Colour figure can be viewed at wileyonlinelibrary.com] U R E 1 5 (a, c, e, g) Seasonally averaged ACC difference of monthly precipitation anomaly for 3-month lead time hindcast.The difference is defined as RUN-NDG minus RUN-CTL.80% significance levels estimated from the test based on Fisher's z-transformation are marked by line-hatching.(b, d, f, h) Seasonally averaged ACC of precipitation for RUN-NDG.CMAP is used as the references.The regions marked by rectangles are same as shown in Figure 12 [Colour figure can be viewed at wileyonlinelibrary.com] Schematic views of simultaneous air-sea coupling regimes.(a) SST-feedback-dominant regime appeared in Tropics.The red arrows indicate latent heat flux from the sea surface.(b) Atmospheric-feedback-dominant regime appeared in midlatitude (subtropics).The red arrows indicate solar incoming radiative heat flux.The black arrows above higher (lower) SST indicate convergent (divergent) winds.Large arrows with black line and white shading represent upward (downward) motion of the atmosphere that cause negative (positive) SLPA.The dominant side (SST or atmosphere) in each regime is marked by black large dashed boxes [Colour figure can be viewed at wileyonlinelibrary.com] Global map for seasonally averaged correlation coefficients between SSTA and SLPA.(a) Simultaneous correlation between SSTA and SLPA, and (b) correlation between SSTA and 3-month lagged SLPA.The SSTA and SLPA were computed for 1990-2005 using monthly OISST and ERA5, respectively.The regions marked by rectangles are same as shown in Figure 12 [Colour figure can be viewed at wileyonlinelibrary.com] Seasonally averaged ACC difference of monthly subsurface temperature anomaly for 3-month lead time hindcast.The difference is defined as RUN-NDG minus RUN-CTL.80% significance levels estimated from the test based on Fisher's z-transformation are marked by line-hatching.The subsurface temperature is defined as the temperature at 150 m depth and Global Ocean Data Assimilation System (GODAS;Behringer et al., 1998) is used as the reference [Colour figure can be viewed at wileyonlinelibrary.com]