Interannual variations of the boreal summer intraseasonal variability predicted by ten atmosphere–ocean coupled models Hye-Mi Kim ? In-Sik Kang ? Bin Wang ? June-Yi Lee Received: 9 January 2007 / Accepted: 19 June 2007 / Published online: 18 July 2007 ? Springer-Verlag 2007 Abstract The reproducibility of boreal summer intra- seasonal variability (ISV) and its interannual variation by dynamical models are assessed through diagnosing 21-year retrospective forecasts from ten state-of-the-art ocean– atmosphere coupled prediction models. To facilitate the assessment, we have de?ned the strength of ISV activity by the standard deviation of 20–90 days ?ltered precipitation during the boreal summer of each year. The observed cli- matological ISV activity exhibits its largest values over the western North Paci?c and Indian monsoon regions. The notable interannual variation of ISV activity is found pri- marily over the western North Paci?c in observation while most models have the largest variability over the central tropical Paci?c and exhibit a wide range of variability in spatial patterns that are different from observation. Al- though the models have large systematic biases in spatial pattern of dominant variability, the leading EOF modes of the ISV activity in the models are closely linked to the models' El Nino-Southern Oscillation (ENSO), which is a feature that resembles the observed ISV and ENSO rela- tionship. The ENSO-induced easterly vertical shear anomalies in the western and central tropical Paci?c, where the summer mean vertical wind shear is weak, result in ENSO-related changes of ISV activity in both observation and models. It is found that the principal components of the predicted dominant modes of ISV activity ?uctuate in a very similar way with observed ones. The model biases in the dominant modes are systematic and related to the external SST forcing. Thus the statistical correction method of this study based on singular value decomposition is capable of removing a large portion of the systematic errors in the predicted spatial patterns. The 21-year-averaged pattern correlation skill increases from 0.25 to 0.65 over the entire Asian monsoon region after applying the bias correction method to the multi-model ensemble mean prediction. Keywords Intraseasonal variability ? ISV activity ? ENSO ? Predictability ? Statistical correction 1 Introduction Interannual variability of the Asian monsoon has been considered an important issue because of its social and economic impact on populations and its in?uence on global circulation. Therefore monsoon seasonal prediction has been a goal of forecasters for a long time. Monsoon climate prediction has been attempted in several studies using state-of-the-art dynamic prediction models (Sperber and Palmer 1996; Kang et al. 2002, 2004; Kang and Shukla 2006; Wang et al. 2004, 2005a, b, 2007). However, the dynamical prediction is mainly limited by the nonlinear characteristics of the atmosphere and by the inaccurate performance of current climate models (Kang et al. 2004). The contribution of the internal component to the seasonal mean is larger than that of the external component in monsoon regions where the internal variability arises partly from year-to-year change of intraseasonal variability (ISV) (Sperber et al. 2000; Goswami et al. 2006). H.-M. Kim ? I.-S. Kang (&) School of Earth and Environmental Sciences, Seoul National University, Seoul 151-742, South Korea e-mail: kang@climate.snu.ac.kr B. Wang ? J.-Y. Lee Department of Meteorology and International Paci?c Research Center, University of Hawaii at Manoa, Honolulu, HI, USA 123 Clim Dyn (2008) 30:485–496 DOI 10.1007/s00382-007-0292-3 The ISV is one of the most prominent large-scale vari- ability in the tropics (known as Madden–Julian oscillation (MJO), Madden and Julian 1994). In particular, boreal summer ISV plays a crucial role in the evolution of the Asian summer monsoon, including its onset and break through northward propagation over the Indian monsoon region, its northwestward movement over the western Pa- ci?c, and its eastward movement along the equator (Yasunari 1979; Lau and Chan 1986; Kang et al. 1989, 1999). It has been well documented that ISV exhibits a con- siderable interannual variation (Salby and Hendon 1994; Hendon et al. 1999; Slingo et al. 1999; Sperber et al. 2000; Goswami et al. 2006). The interannual variation of ISV has a practical importance because of its in?uence on various phenomena like monsoon onset and break in the Asian monsoon regions and because of a close relationship with mean monsoon changes (Yasunari 1979; Lau and Chan 1986; Kang et al. 1989, 1999; Sperber et al. 2000; Gosw- ami and Mohan 2001; Webster and Hoyos 2004; Hoyos and Webster 2006). Observational studies have shown that a strong (weak) monsoon is associated with a higher probability of the occurrence of active (break) conditions (Sperber et al. 2000; Goswami and Mohan 2001; Goswami et al. 2006). Especially, recent studies show that the sea- sonal mean is highly correlated with the amplitude of ISV activity from observational (Goswami et al. 2006) and modeling studies (Waliser et al. 2004). Moreover, they are closely linked to each other from the viewpoint of pre- dictability as well. Waliser et al. (2003) found that active ISV is related to large intra-ensemble variance (internal variability) which leads to low predictability of the sea- sonal mean. Therefore, it is noted that the nonlinearity of the ISV is related to the seasonal mean to some degree and the proper simulation of ISV has the potential to improve monsoon predictability. Because the seasonal mean monsoon is governed by a slowly varying external component of forcing (e.g., ENSO) (Philander 1990; Kang et al. 2004), the interannual varia- tion of ISV may have ENSO-related variability as well. There are a few studies on the interannual variation of ISV and its relationship with SST variations, particularly the ENSO, but the results have remained controversial. Most of the studies demonstrate that overall ISV activity is uncor- related with SST variations (Salby and Hendon 1994; Hendon et al. 1999; Slingo et al. 1999; Lawrence and Webster 2001). Salby and Hendon (1994) examined the Madden–Julian Oscillation (MJO, Madden and Julian 1994) activity based on wavenumber–frequency ?ltering and could not ?nd any relationship with ENSO. Hendon et al. (1999) focused on the boreal winter MJO and found the year-to-year variation of MJO intensity to be uncorre- lated with ENSO. Slingo et al. (1999) used the variance of the intraseasonally ?ltered zonal mean wind at 200 mb as a measure of MJO activity and found no signi?cant rela- tionship between the MJO intensity and ENSO. In contrast to these studies for boreal winter, the linkage between ISV activity and ENSO has been explained in term of an ENSO-induced easterly vertical wind shear mechanism in Teng and Wang (2003) for boreal summer. They found that the strongest interannual variations of ISV are found in the western North Paci?c where the westward and northward propagating waves are enhanced based on an increased easterly vertical shear in developing El Nino years. However, there is no model-based study to examine whether the above relationship can be represented in GCMs and exploited in predictions. Therefore, we need to examine if a model can demonstrate interannual ISV pre- dictability that could be traced to interannual SST anom- alies, and thus has potential for prediction. Moreover, the predictability can be improved if the model errors are systematic and related to the external SST forcing (Kang et al. 2004). If the interannual variation of ISV is closely linked to external forcing and therefore predictable, it has the potential to in?uence the seasonal prediction as well. Based on the aforementioned consideration, the objec- tive of this study is to address the following questions: Is the interannual variation of ISV purely chaotic or is it re- lated to a slowly varying external forcing like ENSO? In the latter case, could the predictability of the interannual variation of ISV be improved by statistical correction methods? To address these questions, we used historical prediction data from ten state-of-the-art climate prediction models. This study has two signi?cant differences from previous intercomparison studies. One is the use of retrospective forecasts (hindcasts), and the other is the use of coupled models. There are many intercomparison studies that have used AMIP-type simulation only to examine the perfor- mance of ISV simulation and cannot relate to real fore- casting directly (Slingo et al. 1996; Kang et al. 2002; Waliser et al. 2003). In contrast, this study uses retro- spective forecasts from ten state-of-the-art coupled climate prediction models for the 21 years of 1981–2001. More- over, most of the previous intercomparison studies use atmospheric-only GCMs. However, recent observational and modeling studies suggest that air–sea coupling on intraseasonal timescales is important for the maintenance of ISV and incorporating the coupled processes improves ISV simulation in terms of its intensity, propagation, seasonality and predictability (Wang and Xie 1998; Wal- iser et al. 1999; Woolnough et al. 2000; Kemball-Cook et al. 2002; Webster et al. 2002; Fu et al. 2003, 2006; Fu and Wang 2004; Zheng et al. 2004; Wang et al. 2005a, b). Based on the need for a reassessment of the ISV character- istics in coupled models, this study uses ten state-of-the-art 486 H.-M. Kim et al.: Interannual variations of the boreal summer intraseasonal variability 123 climate prediction models that include fully coupled atmosphere–ocean processes. The aim of this study is to investigate whether the in- terannual ISV is related to the external forcing component, particularly ENSO, and is thus predictable. It begins with a description of the datasets in Sect. 2. The relationship be- tween interannual variations of ISV and ENSO is examined in Sect. 3. Section 4[k1] describes the method for statisti- cal correction and compares the predictability before and after correction. Section 5 summarizes and discusses the results. 2 Experimental framework and data sources The analysis is based on historical prediction data of fully coupled atmosphere–ocean-land seasonal prediction sys- tems from the following two international projects: The Asia-Paci?c Economic Cooperation Climate Center/Cli- mate Prediction and its Application to Society (APCC/ CliPAS) (Wang et al. 2007) and ''Development of a European Multi-Model Ensemble System for Seasonal to Inter-Annual Prediction'' (DEMETER) (Palmer et al. 2004). DEMETER is known to offer better prediction skills over the globe compared with the uncoupled systems (Kang and Shukla 2006). A description of the experiments is shown in Table 1. The hindcasts for the period 1981–2001 will be discussed in this paper, because it is the common period for which the participating coupled models have generated hindcasts. All models have hindcast with 6- to 9-month integrations for 3–15 different initial conditions. In order to assess seasonal dependence on skill, the hindcasts were started from the initial conditions on 1 February, 1 May, 1 August, and 1 November except for the CFS model, in which the 15 atmospheric initial conditions were taken on the 9, 10, 11, 12, 13, 19, 20, 21, 22, and 23 of the month prior to the target month, and on the last 2 days of the previous month, as well as the ?rst-to-third days of the target month (Saha et al. 2006). We focus on the boreal summer that is de?ned as May through August with 25 pentads per year. In order to extract the ISV component, a 20–90 days band-pass ?lter is applied to each pentad anomaly that has been computed from the 1981 to 2001 pentad cli- matology for reanalysis and each simulation, respectively. The ?lter is a symmetric, four-pole, low-pass, tangent Butterworth ?lter (Oppenheim and Schafer 1975). The ?lter is applied, ?rst retaining timescales longer than 20 days and then retaining timescales longer than 90 days. The bandpass data are obtained by subtracting the two ?ltered datasets. The end-point effect is reduced by extending the ends of the series by duplicating the beginning and ending values. Table 1 Description of atmosphere and ocean models Acronym names Institute AGCM Resolution OGCM Resolution Period Integration (months) Ensembles References CERF CERFACS ARPEGE T63 L31 OPA 8.2 2.0 · 2.0 L30 1980–2001 6 9 Palmer et al. (2004) ECMW ECMWF IFS T95 L40 HOPE-E 1.4 · 0.3–1.4 L29 1958–2001 6 9 INGV INGV ECHAM-4 T42 L19 OPA 8.1 2.0 · 0.5–1.5 L31 1973–2001 6 9 LODY LODYC IFS T95 L40 OPA 8.2 2.0 · 2.0 L31 1974–2001 6 9 METF Meteo France ARPEGE T63 L31 OPA 8.0 182 · 152 GP L31 1958–2001 6 9 MAXP MPI ECHAM-5 T42 L19 MPI-OM1 2.5 · 0.5–2.5 L23 1969–2001 6 9 UKMO UK Met Of?ce HadAM3 2.5 · 3.75 L19 GloSea OGCM 1.25 · 0.3–1.25 L40 1959–2001 6 9 SNU SNU SNU T42 L21 MOM2.2 1/3 ° · 1 ° L32 1960–2004 7 5 Kug et al. (2007) NCEP NCEP GFS T62 L64 MOM3 1/3 ° · 1 ° L40 1981–2003 8 15 Saha et al. (2006) NASA NASA NSIPP1 2 ° · 2.5 ° L34 Poseidon V4 1/3 ° · 5/8 ° L27 1980–2004 6 3 Vintzileos et al. (2003) H.-M. Kim et al.: Interannual variations of the boreal summer intraseasonal variability 487 123 All data were interpolated to a spatial resolution of 2.5° latitude · 2.5° longitude. The observational datasets for veri?cation are obtained from the Climate Prediction Center Merged Analysis of Precipitation (CMAP) (Xie and Arkin 1997). Zonal winds at 850 and 200 hPa are from the National Center for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reana- lysis (Kalnay et al. 1996) and SST data were obtained from NCEP (Reynolds and Smith 1994). 3 Interannual variations of ISV and its relationship with ENSO To examine the interannual variation of ISV, the ISV activity (ry) is de?ned as: r2 y ? 1 P?E ? 1? X P p?1 X E e?1 ?xype ? xe?2 ; where xype is precipitation anomaly, y year, p pentad number relative to the initial forecast date (P = 25), and e ensemble member. Overbar denotes the climatological (21 years) mean of ?ltered precipitation anomalies. Therefore, ISV activity indicates the ensemble mean intensity of ISV, which varies from year to year. To reduce the errors associated with the uncertainties in model physical parameterization and to make an effective way to aggregate and synthesize the model outputs, the model composite ry ? ? is calculated as: r2 y ? 1 M X M m?1 ?r2 ym?; where m number of the model (M = 10). Figure 1 shows the distribution of climatological ISV activity which is obtained by 21-year averaged ISV activity (ry), from observation and the model composite, respec- tively. The largest amplitude of the observed ISV activity exists around the Philippine Sea, the Bay of Bengal, and over the eastern Arabian Sea. The model composite shows a pattern broadly similar to observation. However, it underestimates the variability in the equatorial eastern Indian Ocean and the western Paci?c considerably, which has been one of the main problems for GCMs (Slingo et al. 1996; Kang et al. 2002; Waliser et al. 2003). The interannual variation of ISV activity is examined by the standard deviation of the ISV activity anomalies during each summer for 21 years. Although the climatological ISV activity is strong in the Bay of Bengal, its interannual variation is weaker than in the western North Paci?c (WNP) (Fig. 2a). The WNP shows the most pronounced interannual variations. Teng and Wang (2003) showed similar results and have demonstrated that the strongest interannual variations in ISV activity found in the WNP result from enhanced westward and northward propagating waves in the ENSO developing summer. Figure 2b is the corresponding pattern of the model composite. In the model composite, the interannual variation is limited in the central equatorial Paci?c and has no signi?cant value over the Indian monsoon region or over the WNP where the dominant interannual change is exhibited in the observa- tional ?eld. The performance of each model in simulating the interannual variation of ISV activity is examined and shows a variety of spatial patterns (Fig. 2c–l). Although there are some differences between the models, most of them simulate excessive variation in the central tropical Paci?c and fail to reproduce the largest variability in the WNP region. We note that there are dif?culties in simu- lating the interannual changes of ISV using recent climate prediction models even though the atmosphere–ocean coupled process is included in them. To know the systematic bias in model simulations and to understand the main factor that controls interannual vari- ations in ISV, EOF analysis was applied to the observed and simulated ISV activity anomaly. Compared to the large standard deviation of ISV activity that is located over the WNP in observation (Fig. 2a), the ?rst EOF mode of ISV activity that explains 14.47% of the total variance is characterized by large positive components over the central a) b) Fig. 1 Distributions of the climatological ISV activity for the a observation and b model composite. The unit is mm day–1 488 H.-M. Kim et al.: Interannual variations of the boreal summer intraseasonal variability 123 western Paci?c with maxima between 10°S and 10°N (Fig. 3a). The ?rst mode of the model composite (Fig. 3c), that accounts for 47.61% of the total variance, produces the large variability over the central western Paci?c that cor- responds with its standard deviation reasonably well (Fig. 2b). Figure 4 exhibits the eigenvector of the ?rst EOF for individual models, indicating a large variability of systematic error in simulated spatial patterns among mod- els. The second eigenvectors of the observation and model composite explain 11.18 and 24.40% of total variance, respectively (Fig. 3b, d). In observation (Fig. 3b), the spatial pattern is characterized by large variations in the WNP, which is similar to the standard deviation of ISV activity (Fig. 2a). For the ?rst and second mode, the spatial patterns of the model counterpart show a great difference from observa- tion. However, the time series of principal components (PC) associated with the eigenvectors, shown in Fig. 3e and f, vary in a similar way to observation. In particular, the PC time series of the ?rst mode is well correlated to the Nino3.4 index. Therefore, it is noted that the ?rst mode is related to ENSO SST anomalies. The similarity between the observed and predicted PC time series provides possi- bilities for model error correction using a statistical ap- proach. To examine how well individual models simulate the ENSO-related variability, the pattern correlation of the ?rst EOF eigenvector (Fig. 4) over the ENSO-monsoon region (40°–300°E and 20°S–30°N) and the temporal correlation of the ?rst PC time series between observation and the model were computed (Fig. 5). The most of model have some dif?culties in capturing the spatial distribution of the observed ?rst mode showing the pattern correlation coef- ?cients ranging from 0.32 (for INGV model) to 0.67 (Met France model) (Fig. 5, black shading). Although EOF spatial patterns in the models are somewhat different from observation (Fig. 4), a similarity exists between the PC time series of observed and predicted modes (Fig. 5, diagonal shading). Therefore, prediction models have the ability to capture the prominent mode of ISV activity corresponding to ENSO even if the spatial pattern is slightly different from observation. To investigate the relationship between ISV activity and forced SST variation, the correlation coef?cient between the ?rst EOF time series and the Nino 3.4 index from its own model output was computed (Fig. 5, gray shading). In a) b) c) d) e) f) g) h) i) j) k) l) Fig. 2 Interannual standard deviations of the boreal summer ISV activity in a observation, b model composite, and c–l various models. Contour interval is 0.8 mm day–1 and shadings indicate the standard deviation more than 0.6 mm day–1 H.-M. Kim et al.: Interannual variations of the boreal summer intraseasonal variability 489 123 general, most models simulate well the relationship be- tween the ?rst mode of ISV activity and the model Nino 3.4 SST. Even the models that have dif?culty in repre- senting the leading vectors exhibit a close relationship between ISV activity and their own SST variability. In the second mode that is supposed to have a much more sig- ni?cant effect on the monsoon region in observation, the spatial patterns of the predicted eigenvectors are different from observation but the interannual variation of the pre- dicted PC timeseries are similar to the observed counterpart like the ?rst mode (not shown). The linkage between ISV activity and ENSO can be explained by the ENSO-induced easterly vertical wind shear mechanism (Teng and Wang 2003). Previous studies have shown that the easterly vertical shear can enhance Rossby waves in the lower troposphere and the enhanced low-level perturbation increases moisture convergence at the boundary layer and ampli?es the moist equatorial Rossby waves (Wang and Xie 1996; Xie and Wang 1996). The enhanced shear in the western Paci?c enhances the development and northwestward emanation of Rossby waves in the lower troposphere effectively, and then the ISV is reinforced in the western Paci?c. On the other hand, in the Indian Ocean, the ENSO-induced wind shear is too weak to affect the mean circulation. Therefore, ISV activity is insensitive to ENSO in the Indian monsoon region. To examine the robust relationship between the ISV activity and ENSO-induced wind shear in individual models, we applied the regression analysis. Before the regression analysis, we made the summer mean easterly vertical wind shear (u850–u200) for each individual year in observation and model composite, respectively. Then, we obtained the regression coef?cient for ISV activity and mean vertical wind shear by a linear regression method with respect to the observed and simulated Nino 3.4 SST, respectively. Figure 6a and b show the regression coef?- cients of ISV activity and Fig. 6c and d the wind shear. The western Paci?c, which is a climatologically transi- tion region of wind shear has a pronounced interannual variation associated with ENSO—a strong easterly vertical shear—both in observation and in the model composite (Fig. 6c, d). Because of the weak vertical shear in the mean state (not shown) over the western Paci?c, it is easier to reverse the sign of the vertical wind shear in the ENSO season. It is noted that the enhanced vertical shear region is similar to the ENSO-induced ISV active region (Fig. 6a, b). The enhanced waves promote the northward and north- westward propagating waves and reinforce the ISV in the WNP. Although this study offers explanations on ENSO-in- duced ISV activity over the WNP region, a number of issues remain to be addressed. In some models (ECMWF, LODYC, UKMO, and NCEP), there is a strong interannual a) b) c) d) e) f) Fig. 3 The ?rst and second EOF modes of the observed and model composite ISV activity. a, b The observed ?rst and second eigenvectors; c, d the simulated counterparts. Shading indicates positive value and contour interval is 0.02. e, f The time series associated with the eigenvectors. Solid and dashed lines indicate the observed and simulated time series, respectively 490 H.-M. Kim et al.: Interannual variations of the boreal summer intraseasonal variability 123 modulation of ISV activity over the Indian Ocean (Fig. 2). Moreover, the spatial pattern of the ?rst EOF eigenvector (Fig. 4) and strong correlation between ?rst PCs and Nino 3.4 time series (Fig. 5) would mean a strong interannual modulation of ISV by ENSO over the eastern Indian Ocean. Note that over the eastern Indian Ocean, the anomalous anti-Walker circulation during El Nino events tends to suppress the convection over the eastern equatorial Indian Ocean, thus the ISV there should be signi?cantly affected. The ISV in the off-equatorial Indian monsoon region is different. In the off-equatorial Indian monsoon region, the change of vertical shear is relatively small during ENSO—less than 10% of the climatological value. Thus, the changes in vertical shear cannot signi?cantly a) b) c) d) e) f) g) h) i) j) k) l) Fig. 4 The ?rst EOF mode of the ISV activity in a observation, b model composite, and c–l various models. Shading indicates positive value and contour interval is 0.02 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 CERF ECMW INGV LODY MAXP METF UKMO SNU NCEP NASA COMP EVmod & EVobs PCmod & PCobs PCmod & NINO3.4mod Fig. 5 Pattern correlation coef?cients of the ?rst EOF eigenvectors between the observed and associated model ISV activity over the ENSO-monsoon region (40°–300°E and 20°S–30°N; black shaded bar), correlation coef?cients of the ?rst EOF time series between observation individual model (diagonal shaded bar), and correlation coef?cients between the ?rst EOF time series of each model and its own Nino 3.4 index (gray shaded bar) H.-M. Kim et al.: Interannual variations of the boreal summer intraseasonal variability 491 123 affect the interannual variability of ISV there. Moreover, even though these models reproduce more realistic ampli- tude of interannual variability in ISV, they have a model- dependent systematic bias in their spatial pattern of vari- ability (Fig. 4). Especially, ECMWF and LODYC show opposite sign of ISV variation compared to observation over equatorial western Indian Ocean. Although some models show signi?cant amplitude as observed value in Indian Ocean, the spatial pattern has systematic bias, and therefore statistical correction plays important role. 4 Predictability of ISV activity after systematic bias correction Models still have problems in simulating the ISV activity in monsoon regions even when they include the atmo- sphere–ocean coupled process. Although the models have dif?culty in simulating the spatial variability of ISV activity, they have the ability to capture the temporal var- iability, which is related to the SST boundary forcing. Therefore, the predictability can be improved by statistical correction since the model errors are systematic and related to external forcing. In previous studies these errors were shown to be correctable by a close statistical relationship between observation and model prediction (Kang et al. 2004). In spite of the poor simulation of the EOF spatial pattern, the similarity between the time series of observed and predicted modes offers the possibility of error correc- tion (Fig. 3e, f). The difference in spatial patterns can be corrected by replacing the model eigenmodes with the corresponding observed modes. A statistical correction method is applied to reduce the systematic error for individual models based on the SVD method (Feddersen et al. 1999; Kang et al. 2004). The correction is performed by replacing the coupled pattern of forecasts with that of observations which are temporarily correlated. Because the normalized principal component of forecasts and observations is used in construction of the covariance matrix to be solved by SVD, it is the same as the Canonical Correlation Analysis (CCA) (Bretherton et al. 1992). The spatial pattern of leading CCA modes is used, and the transfer function for the replacement is as follows: F?x; t? ? X m i?1 aiYi?t?Ri?x?; where F(x,t) is corrected ?eld, Yi(t) time coef?cient of the CCA mode of forecast and Ri(x) CCA pattern of observa- tion. i is the number of the mode and ten leading modes are used (m = 10) because the sum of the ?rst ten modes ex- plains more than 90% of the total variance. ai is weighting coef?cient based on the correlation coef?cient between the CCA time series of observation and forecast. Therefore, the leading modes have more weight. Once the CCA patterns and weighting coef?cients are determined by the training dataset, the time coef?cient Yi(t) of the target forecast is obtained by projecting the CCA pattern of the forecast onto the model forecast ?led. A detailed description of statistical correction can be found in Kang et al. (2004). A cross- validation method is applied to each year. The prediction skill of ISV activity can be measured by the anomaly correlation between predictions and the cor- responding observations for 21 years. The predictability of the model composite is computed by averaging the pre- dicted ?eld after correction for ten models. Figure 7 shows the prediction skill of the model composite before and after error correction. ISV activity is predictable only in the Tropics before correction but is improved across the whole a) b) c) d) Fig. 6 Regression coef?cients of ISV activity (left) for the a observation and b model composite, and coef?cients of summer mean u850–u200 vertical wind shear (right) for the c observation and d model composite 492 H.-M. Kim et al.: Interannual variations of the boreal summer intraseasonal variability 123 globe after correction. The predictability is also examined through the 21-year-averaged spatial pattern correlation averaged over the Asian monsoon regions (60°–180°E and 10°S–30°N) for each model (Fig. 8). All models exhibit enhanced predictabilities and the model composite changes from 0.25 to 0.65 after correction. To examine more clearly the enhancement of predictability after correction, the ISV activity index is de?ned by the area-averaged ISV activity anomaly over the WNP (100°–150°E and 10°–30°N) where the interannual variation of ISV activity is dominant. Fig- ure 9 shows the time correlation coef?cient of the ISV activity index, before and after error correction. The pre- dictability of ISV activity index is enhanced except in INGV. Negative correlations change to positive in some models (e.g., CERF, MAXP, UKMO, and NCEP), and low correlations have relatively large positive values after correction (e.g., ECMW, SNU, and NASA). The predict- ability of the model composite ISV activity index changes from 0.03 to 0.48 after correction. In this study, a cross-validation method is applied to each year. However, when a statistical forecast or correc- tion methodology is to be applied to real time forecasts or correction of anomalies, adequate cross-validation becomes essential as no information of future values exists for performing the real time training. The de-correlation time scale de?nes a suf?ciently large window for the cross- validation process. For interannual variability this window is of the order of 2–3 years. Therefore, we re-compute Fig. 8 by cross-validation with removal of 1 year prior, the year in consideration, and one year after. By comparison between Fig. 8 and re-computed results (not shown), we notice that improvements accomplished by the proposed statistical correction technique are very dependent on the cross-validation window. For example, for the model composite, the corrected correlation drops from 0.65 to 0.44 when the 3-year cross-validation window is used. Therefore, the sensitivity of the cross-validation window should be considered for applying the statistical correction method. 5 Summary and discussion Reproducibility of the boreal summer (MJJA) intraseasonal variability (ISV) and its interannual variation related to ENSO in coupled climate prediction models are evaluated by diagnosing 21-year hindcast outputs from ten state-of- the-art prediction models that participated in the APCC/ CliPAS and DEMETER projects. There are two sensitivity tests with the dataset. One is about the choice of cut-off frequency. To extract the ISV component, a 20–90 days ?lter is applied to pentad pre- cipitation anomalies. Through an examination of the sen- sitivity of the cut-off frequency with daily data that is available in hindcasts, it is concluded that the interannual variability of ISV related to ENSO is not sensitive to the choice of cut-off frequency if the frequency range is within a) b) Fig. 7 Distribution of the correlation coef?cient between the observed and the predicted ISV activity of the model composite for a before and b after correction. Contour interval is 0.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 CERF ECMW INGV LODY MAXP METF UKMO SNU NCEP NASA COMP Before Correction After Correction Fig. 8 21-year-averaged pattern correlation coef?cients between the observed and predicted ISV activity before (open bar) and after (shaded bar) the correction over the Asian monsoon regions (60°– 180°E and 10°S–30°N) H.-M. Kim et al.: Interannual variations of the boreal summer intraseasonal variability 493 123 10–100 days. The other is the sensitivity of the period de?ned as ''summer''. With increasing lead time, the mean state of each model drifts towards its own climatology and we stated the interannual variation of ISV is linked with the mean state. As a result, the characteristics of the ISV may be lead time dependant. However, the difference in the variance characteristics (Figs. 1, 2, 3) is not distinctive over the MJJ or JJA periods instead of the MJJA period. The observed climatological ISV activity for the MJJA period exhibits its largest values over the western North Paci?c and Indian monsoon regions. The interannual var- iation of ISV activity is primarily found over the western North Paci?c in observation, while most models have the largest variability over the central tropical Paci?c and ex- hibit a large range of spatial patterns that are different from observation. However, the leading EOF modes of ISV activity in the models are closely linked to the model's El Nino-Southern Oscillation (ENSO). This feature resembles the observed ISV and ENSO relationship. The ENSO-in- duced easterly vertical shear anomalies in the western and central tropical Paci?c, where the summer mean vertical wind shear is weak, result in ENSO-related changes in ISV activity in both the observation and the models. In the Indian monsoon region, ENSO-induced wind shear is too weak to affect the mean circulation and thus the ISV activity is insensitive to ENSO. A close relationship in the temporal variations of the dominant modes of ISV activity exists between the observation and models. Thus, a statistical correction method based on singular value decomposition is designed. It is shown that this method is able to remove a large portion of the systematic errors. After the bias correction, the predictability is enhanced, especially in the western Paci?c. The 21-year-averaged pattern correlation skill changes from 0.25 to 0.65 over the entire Asian monsoon region after applying the bias correction to the multi-model ensemble mean prediction. The improved predictability of the ISV activity offers a possibility of an improvement in seasonal prediction be- cause of the close relationship between the ISV and sea- sonal mean state, as mentioned in the introduction. Figure 10 exhibits the relationship between the mean state and ISV activity in terms of predictability. The predict- ability can be measured by the spatial correlation between the predicted ISV activity anomaly and the corresponding observation over the Asian monsoon region (40°–180°E and 20°S–30°N) and then averaged for 21 years (the ver- tical axis in Fig. 10). The predictability is generally low compared to the predictability of the summer mean obtained in the same way (the horizontal axis in Fig. 10). The ?gure shows a very close relationship between the predictability of the mean ?eld and the ISV activity which is correlated at a level of 0.92. Most of the state-of-the-art climate prediction models still have dif?culty in simulating even the seasonal mean state and its interannual variations (Sperber and Palmer 1996; Kang et al. 2002; Kang and Shukla 2006). The results of this study suggest that this can be partly overcome by the improvement in the predict- ability of ISV activity. The way to link these two variables remains as a subject for further study. It has been emphasized that the air–sea interactions are important for ISV simulation, and especially for ISV pre- diction (Fu et al. 2006). In order to fully understand the importance of air–sea coupling in ISV prediction, not only on an interannual timescale but also on a daily timescale, a Corr = 0.92 0 0.1 0.2 0.3 0.4 0.2 0.3 0.4 0 Predictability of Interannual Summer Mean PRCP .5 Predictability of Internnual ISO activity CERF ECMW INGV LODY MAXP METF UKMO SNU NCEP NASA COMP Fig. 10 Scatter plot of predictability on summer mean precipitation (horizontal axis) and ISV activity (vertical axis) over the Asian monsoon region (40°–180°E and 20°S–30°N). The correlation is 0.92 Fig. 9 Correlation coef?cients between the observed and predicted ISV activity index before (open bar) and after (shaded bar) the bias correction 494 H.-M. Kim et al.: Interannual variations of the boreal summer intraseasonal variability 123 comparison study with coupled and uncoupled models will be carried out in further work. Acknowledgments This research has been supported by the SRC program of Korea Science and Engineering Foundation, and the Ministry of Environment as ''The Ecotechonopia 21 Project'', and the second stage of the Brain Korea 21 Project. The third and fourth authors were supported by APEC Climate Center (APCC) as a part of APCC International research project. References Bretherton CS, Smith C, Wallace JM (1992) An intercomparison of methods for ?nding coupled pattern in climate data. J Clim 5:541–560 Feddersen H, Navarra A, Ward MN (1999) Reduction of model systematic error by statistical correction for dynamical seasonal prediction. J Clim 12:1974–1989 Fu X, Wang B, Li T, McCreary JP (2003) Coupling between northward propagation, intraseasonal oscillations and sea surface temperature in the Indian Ocean. J Atmos Sci 60:1733–1753 Fu X, Wang B (2004) Differences of boreal summer intraseasonal oscillations simulated in an atmosphere–ocean coupled model and an atmosphere-only model. 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Interannual variations of the boreal summer intraseasonal variability predicted by ten atmosphere–ocean coupled models Hye-Mi Kim ? In-Sik Kang ? Bin Wang ? June-Yi Lee Received: 9 January 2007 / Accepted: 19 June 2007 / Published online: 18 July 2007 ? Springer-Verlag 2007 Abstract The reproducibility of boreal summer intra- seasonal variability (ISV) and its interannual variation by dynamical models are assessed through diagnosing 21-year retrospective forecasts from ten state-of-the-art ocean– atmosphere coupled prediction models. To facilitate the assessment, we have de?ned the strength of ISV activity by the standard deviation of 20–90 days ?ltered precipitation during the boreal summer of each year. The observed cli- matological ISV activity exhibits its largest values over the western North Paci?c and Indian monsoon regions. The notable interannual variation of ISV activity is found pri- marily over the western North Paci?c in observation while most models have the largest variability over the central tropical Paci?c and exhibit a wide range of variability in spatial patterns that are different from observation. Al- though the models have large systematic biases in spatial pattern of dominant variability, the leading EOF modes of the ISV activity in the models are closely linked to the models' El Nino-Southern Oscillation (ENSO), which is a feature that resembles the observed ISV and ENSO rela- tionship. The ENSO-induced easterly vertical shear anomalies in the western and central tropical Paci?c, where the summer mean vertical wind shear is weak, result in ENSO-related changes of ISV activity in both observation and models. It is found that the principal components of the predicted dominant modes of ISV activity ?uctuate in a very similar way with observed ones. The model biases in the dominant modes are systematic and related to the external SST forcing. Thus the statistical correction method of this study based on singular value decomposition is capable of removing a large portion of the systematic errors in the predicted spatial patterns. The 21-year-averaged pattern correlation skill increases from 0.25 to 0.65 over the entire Asian monsoon region after applying the bias correction method to the multi-model ensemble mean prediction. Keywords Intraseasonal variability ? ISV activity ? ENSO ? Predictability ? Statistical correction 1 Introduction Interannual variability of the Asian monsoon has been considered an important issue because of its social and economic impact on populations and its in?uence on global circulation. Therefore monsoon seasonal prediction has been a goal of forecasters for a long time. Monsoon climate prediction has been attempted in several studies using state-of-the-art dynamic prediction models (Sperber and Palmer 1996; Kang et al. 2002, 2004; Kang and Shukla 2006; Wang et al. 2004, 2005a, b, 2007). However, the dynamical prediction is mainly limited by the nonlinear characteristics of the atmosphere and by the inaccurate performance of current climate models (Kang et al. 2004). The contribution of the internal component to the seasonal mean is larger than that of the external component in monsoon regions where the internal variability arises partly from year-to-year change of intraseasonal variability (ISV) (Sperber et al. 2000; Goswami et al. 2006). H.-M. Kim ? I.-S. Kang (&) School of Earth and Environmental Sciences, Seoul National University, Seoul 151-742, South Korea e-mail: kang@climate.snu.ac.kr B. Wang ? J.-Y. Lee Department of Meteorology and International Paci?c Research Center, University of Hawaii at Manoa, Honolulu, HI, USA 123 Clim Dyn (2008) 30:485–496 DOI 10.1007/s00382-007-0292-3 The ISV is one of the most prominent large-scale vari- ability in the tropics (known as Madden–Julian oscillation (MJO), Madden and Julian 1994). In particular, boreal summer ISV plays a crucial role in the evolution of the Asian summer monsoon, including its onset and break through northward propagation over the Indian monsoon region, its northwestward movement over the western Pa- ci?c, and its eastward movement along the equator (Yasunari 1979; Lau and Chan 1986; Kang et al. 1989, 1999). It has been well documented that ISV exhibits a con- siderable interannual variation (Salby and Hendon 1994; Hendon et al. 1999; Slingo et al. 1999; Sperber et al. 2000; Goswami et al. 2006). The interannual variation of ISV has a practical importance because of its in?uence on various phenomena like monsoon onset and break in the Asian monsoon regions and because of a close relationship with mean monsoon changes (Yasunari 1979; Lau and Chan 1986; Kang et al. 1989, 1999; Sperber et al. 2000; Gosw- ami and Mohan 2001; Webster and Hoyos 2004; Hoyos and Webster 2006). Observational studies have shown that a strong (weak) monsoon is associated with a higher probability of the occurrence of active (break) conditions (Sperber et al. 2000; Goswami and Mohan 2001; Goswami et al. 2006). Especially, recent studies show that the sea- sonal mean is highly correlated with the amplitude of ISV activity from observational (Goswami et al. 2006) and modeling studies (Waliser et al. 2004). Moreover, they are closely linked to each other from the viewpoint of pre- dictability as well. Waliser et al. (2003) found that active ISV is related to large intra-ensemble variance (internal variability) which leads to low predictability of the sea- sonal mean. Therefore, it is noted that the nonlinearity of the ISV is related to the seasonal mean to some degree and the proper simulation of ISV has the potential to improve monsoon predictability. Because the seasonal mean monsoon is governed by a slowly varying external component of forcing (e.g., ENSO) (Philander 1990; Kang et al. 2004), the interannual varia- tion of ISV may have ENSO-related variability as well. There are a few studies on the interannual variation of ISV and its relationship with SST variations, particularly the ENSO, but the results have remained controversial. Most of the studies demonstrate that overall ISV activity is uncor- related with SST variations (Salby and Hendon 1994; Hendon et al. 1999; Slingo et al. 1999; Lawrence and Webster 2001). Salby and Hendon (1994) examined the Madden–Julian Oscillation (MJO, Madden and Julian 1994) activity based on wavenumber–frequency ?ltering and could not ?nd any relationship with ENSO. Hendon et al. (1999) focused on the boreal winter MJO and found the year-to-year variation of MJO intensity to be uncorre- lated with ENSO. Slingo et al. (1999) used the variance of the intraseasonally ?ltered zonal mean wind at 200 mb as a measure of MJO activity and found no signi?cant rela- tionship between the MJO intensity and ENSO. In contrast to these studies for boreal winter, the linkage between ISV activity and ENSO has been explained in term of an ENSO-induced easterly vertical wind shear mechanism in Teng and Wang (2003) for boreal summer. They found that the strongest interannual variations of ISV are found in the western North Paci?c where the westward and northward propagating waves are enhanced based on an increased easterly vertical shear in developing El Nino years. However, there is no model-based study to examine whether the above relationship can be represented in GCMs and exploited in predictions. Therefore, we need to examine if a model can demonstrate interannual ISV pre- dictability that could be traced to interannual SST anom- alies, and thus has potential for prediction. Moreover, the predictability can be improved if the model errors are systematic and related to the external SST forcing (Kang et al. 2004). If the interannual variation of ISV is closely linked to external forcing and therefore predictable, it has the potential to in?uence the seasonal prediction as well. Based on the aforementioned consideration, the objec- tive of this study is to address the following questions: Is the interannual variation of ISV purely chaotic or is it re- lated to a slowly varying external forcing like ENSO? In the latter case, could the predictability of the interannual variation of ISV be improved by statistical correction methods? To address these questions, we used historical prediction data from ten state-of-the-art climate prediction models. This study has two signi?cant differences from previous intercomparison studies. One is the use of retrospective forecasts (hindcasts), and the other is the use of coupled models. There are many intercomparison studies that have used AMIP-type simulation only to examine the perfor- mance of ISV simulation and cannot relate to real fore- casting directly (Slingo et al. 1996; Kang et al. 2002; Waliser et al. 2003). In contrast, this study uses retro- spective forecasts from ten state-of-the-art coupled climate prediction models for the 21 years of 1981–2001. More- over, most of the previous intercomparison studies use atmospheric-only GCMs. However, recent observational and modeling studies suggest that air–sea coupling on intraseasonal timescales is important for the maintenance of ISV and incorporating the coupled processes improves ISV simulation in terms of its intensity, propagation, seasonality and predictability (Wang and Xie 1998; Wal- iser et al. 1999; Woolnough et al. 2000; Kemball-Cook et al. 2002; Webster et al. 2002; Fu et al. 2003, 2006; Fu and Wang 2004; Zheng et al. 2004; Wang et al. 2005a, b). Based on the need for a reassessment of the ISV character- istics in coupled models, this study uses ten state-of-the-art 486 H.-M. Kim et al.: Interannual variations of the boreal summer intraseasonal variability 123 climate prediction models that include fully coupled atmosphere–ocean processes. The aim of this study is to investigate whether the in- terannual ISV is related to the external forcing component, particularly ENSO, and is thus predictable. It begins with a description of the datasets in Sect. 2. The relationship be- tween interannual variations of ISV and ENSO is examined in Sect. 3. Section 4[k1] describes the method for statisti- cal correction and compares the predictability before and after correction. Section 5 summarizes and discusses the results. 2 Experimental framework and data sources The analysis is based on historical prediction data of fully coupled atmosphere–ocean-land seasonal prediction sys- tems from the following two international projects: The Asia-Paci?c Economic Cooperation Climate Center/Cli- mate Prediction and its Application to Society (APCC/ CliPAS) (Wang et al. 2007) and ''Development of a European Multi-Model Ensemble System for Seasonal to Inter-Annual Prediction'' (DEMETER) (Palmer et al. 2004). DEMETER is known to offer better prediction skills over the globe compared with the uncoupled systems (Kang and Shukla 2006). A description of the experiments is shown in Table 1. The hindcasts for the period 1981–2001 will be discussed in this paper, because it is the common period for which the participating coupled models have generated hindcasts. All models have hindcast with 6- to 9-month integrations for 3–15 different initial conditions. In order to assess seasonal dependence on skill, the hindcasts were started from the initial conditions on 1 February, 1 May, 1 August, and 1 November except for the CFS model, in which the 15 atmospheric initial conditions were taken on the 9, 10, 11, 12, 13, 19, 20, 21, 22, and 23 of the month prior to the target month, and on the last 2 days of the previous month, as well as the ?rst-to-third days of the target month (Saha et al. 2006). We focus on the boreal summer that is de?ned as May through August with 25 pentads per year. In order to extract the ISV component, a 20–90 days band-pass ?lter is applied to each pentad anomaly that has been computed from the 1981 to 2001 pentad cli- matology for reanalysis and each simulation, respectively. The ?lter is a symmetric, four-pole, low-pass, tangent Butterworth ?lter (Oppenheim and Schafer 1975). The ?lter is applied, ?rst retaining timescales longer than 20 days and then retaining timescales longer than 90 days. The bandpass data are obtained by subtracting the two ?ltered datasets. The end-point effect is reduced by extending the ends of the series by duplicating the beginning and ending values. Table 1 Description of atmosphere and ocean models Acronym names Institute AGCM Resolution OGCM Resolution Period Integration (months) Ensembles References CERF CERFACS ARPEGE T63 L31 OPA 8.2 2.0 · 2.0 L30 1980–2001 6 9 Palmer et al. (2004) ECMW ECMWF IFS T95 L40 HOPE-E 1.4 · 0.3–1.4 L29 1958–2001 6 9 INGV INGV ECHAM-4 T42 L19 OPA 8.1 2.0 · 0.5–1.5 L31 1973–2001 6 9 LODY LODYC IFS T95 L40 OPA 8.2 2.0 · 2.0 L31 1974–2001 6 9 METF Meteo France ARPEGE T63 L31 OPA 8.0 182 · 152 GP L31 1958–2001 6 9 MAXP MPI ECHAM-5 T42 L19 MPI-OM1 2.5 · 0.5–2.5 L23 1969–2001 6 9 UKMO UK Met Of?ce HadAM3 2.5 · 3.75 L19 GloSea OGCM 1.25 · 0.3–1.25 L40 1959–2001 6 9 SNU SNU SNU T42 L21 MOM2.2 1/3 ° · 1 ° L32 1960–2004 7 5 Kug et al. (2007) NCEP NCEP GFS T62 L64 MOM3 1/3 ° · 1 ° L40 1981–2003 8 15 Saha et al. (2006) NASA NASA NSIPP1 2 ° · 2.5 ° L34 Poseidon V4 1/3 ° · 5/8 ° L27 1980–2004 6 3 Vintzileos et al. (2003) H.-M. Kim et al.: Interannual variations of the boreal summer intraseasonal variability 487 123 All data were interpolated to a spatial resolution of 2.5° latitude · 2.5° longitude. The observational datasets for veri?cation are obtained from the Climate Prediction Center Merged Analysis of Precipitation (CMAP) (Xie and Arkin 1997). Zonal winds at 850 and 200 hPa are from the National Center for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reana- lysis (Kalnay et al. 1996) and SST data were obtained from NCEP (Reynolds and Smith 1994). 3 Interannual variations of ISV and its relationship with ENSO To examine the interannual variation of ISV, the ISV activity (ry) is de?ned as: r2 y ? 1 P?E ? 1? X P p?1 X E e?1 ?xype ? xe?2 ; where xype is precipitation anomaly, y year, p pentad number relative to the initial forecast date (P = 25), and e ensemble member. Overbar denotes the climatological (21 years) mean of ?ltered precipitation anomalies. Therefore, ISV activity indicates the ensemble mean intensity of ISV, which varies from year to year. To reduce the errors associated with the uncertainties in model physical parameterization and to make an effective way to aggregate and synthesize the model outputs, the model composite ry ? ? is calculated as: r2 y ? 1 M X M m?1 ?r2 ym?; where m number of the model (M = 10). Figure 1 shows the distribution of climatological ISV activity which is obtained by 21-year averaged ISV activity (ry), from observation and the model composite, respec- tively. The largest amplitude of the observed ISV activity exists around the Philippine Sea, the Bay of Bengal, and over the eastern Arabian Sea. The model composite shows a pattern broadly similar to observation. However, it underestimates the variability in the equatorial eastern Indian Ocean and the western Paci?c considerably, which has been one of the main problems for GCMs (Slingo et al. 1996; Kang et al. 2002; Waliser et al. 2003). The interannual variation of ISV activity is examined by the standard deviation of the ISV activity anomalies during each summer for 21 years. Although the climatological ISV activity is strong in the Bay of Bengal, its interannual variation is weaker than in the western North Paci?c (WNP) (Fig. 2a). The WNP shows the most pronounced interannual variations. Teng and Wang (2003) showed similar results and have demonstrated that the strongest interannual variations in ISV activity found in the WNP result from enhanced westward and northward propagating waves in the ENSO developing summer. Figure 2b is the corresponding pattern of the model composite. In the model composite, the interannual variation is limited in the central equatorial Paci?c and has no signi?cant value over the Indian monsoon region or over the WNP where the dominant interannual change is exhibited in the observa- tional ?eld. The performance of each model in simulating the interannual variation of ISV activity is examined and shows a variety of spatial patterns (Fig. 2c–l). Although there are some differences between the models, most of them simulate excessive variation in the central tropical Paci?c and fail to reproduce the largest variability in the WNP region. We note that there are dif?culties in simu- lating the interannual changes of ISV using recent climate prediction models even though the atmosphere–ocean coupled process is included in them. To know the systematic bias in model simulations and to understand the main factor that controls interannual vari- ations in ISV, EOF analysis was applied to the observed and simulated ISV activity anomaly. Compared to the large standard deviation of ISV activity that is located over the WNP in observation (Fig. 2a), the ?rst EOF mode of ISV activity that explains 14.47% of the total variance is characterized by large positive components over the central a) b) Fig. 1 Distributions of the climatological ISV activity for the a observation and b model composite. The unit is mm day–1 488 H.-M. Kim et al.: Interannual variations of the boreal summer intraseasonal variability 123 western Paci?c with maxima between 10°S and 10°N (Fig. 3a). The ?rst mode of the model composite (Fig. 3c), that accounts for 47.61% of the total variance, produces the large variability over the central western Paci?c that cor- responds with its standard deviation reasonably well (Fig. 2b). Figure 4 exhibits the eigenvector of the ?rst EOF for individual models, indicating a large variability of systematic error in simulated spatial patterns among mod- els. The second eigenvectors of the observation and model composite explain 11.18 and 24.40% of total variance, respectively (Fig. 3b, d). In observation (Fig. 3b), the spatial pattern is characterized by large variations in the WNP, which is similar to the standard deviation of ISV activity (Fig. 2a). For the ?rst and second mode, the spatial patterns of the model counterpart show a great difference from observa- tion. However, the time series of principal components (PC) associated with the eigenvectors, shown in Fig. 3e and f, vary in a similar way to observation. In particular, the PC time series of the ?rst mode is well correlated to the Nino3.4 index. Therefore, it is noted that the ?rst mode is related to ENSO SST anomalies. The similarity between the observed and predicted PC time series provides possi- bilities for model error correction using a statistical ap- proach. To examine how well individual models simulate the ENSO-related variability, the pattern correlation of the ?rst EOF eigenvector (Fig. 4) over the ENSO-monsoon region (40°–300°E and 20°S–30°N) and the temporal correlation of the ?rst PC time series between observation and the model were computed (Fig. 5). The most of model have some dif?culties in capturing the spatial distribution of the observed ?rst mode showing the pattern correlation coef- ?cients ranging from 0.32 (for INGV model) to 0.67 (Met France model) (Fig. 5, black shading). Although EOF spatial patterns in the models are somewhat different from observation (Fig. 4), a similarity exists between the PC time series of observed and predicted modes (Fig. 5, diagonal shading). Therefore, prediction models have the ability to capture the prominent mode of ISV activity corresponding to ENSO even if the spatial pattern is slightly different from observation. To investigate the relationship between ISV activity and forced SST variation, the correlation coef?cient between the ?rst EOF time series and the Nino 3.4 index from its own model output was computed (Fig. 5, gray shading). In a) b) c) d) e) f) g) h) i) j) k) l) Fig. 2 Interannual standard deviations of the boreal summer ISV activity in a observation, b model composite, and c–l various models. Contour interval is 0.8 mm day–1 and shadings indicate the standard deviation more than 0.6 mm day–1 H.-M. Kim et al.: Interannual variations of the boreal summer intraseasonal variability 489 123 general, most models simulate well the relationship be- tween the ?rst mode of ISV activity and the model Nino 3.4 SST. Even the models that have dif?culty in repre- senting the leading vectors exhibit a close relationship between ISV activity and their own SST variability. In the second mode that is supposed to have a much more sig- ni?cant effect on the monsoon region in observation, the spatial patterns of the predicted eigenvectors are different from observation but the interannual variation of the pre- dicted PC timeseries are similar to the observed counterpart like the ?rst mode (not shown). The linkage between ISV activity and ENSO can be explained by the ENSO-induced easterly vertical wind shear mechanism (Teng and Wang 2003). Previous studies have shown that the easterly vertical shear can enhance Rossby waves in the lower troposphere and the enhanced low-level perturbation increases moisture convergence at the boundary layer and ampli?es the moist equatorial Rossby waves (Wang and Xie 1996; Xie and Wang 1996). The enhanced shear in the western Paci?c enhances the development and northwestward emanation of Rossby waves in the lower troposphere effectively, and then the ISV is reinforced in the western Paci?c. On the other hand, in the Indian Ocean, the ENSO-induced wind shear is too weak to affect the mean circulation. Therefore, ISV activity is insensitive to ENSO in the Indian monsoon region. To examine the robust relationship between the ISV activity and ENSO-induced wind shear in individual models, we applied the regression analysis. Before the regression analysis, we made the summer mean easterly vertical wind shear (u850–u200) for each individual year in observation and model composite, respectively. Then, we obtained the regression coef?cient for ISV activity and mean vertical wind shear by a linear regression method with respect to the observed and simulated Nino 3.4 SST, respectively. Figure 6a and b show the regression coef?- cients of ISV activity and Fig. 6c and d the wind shear. The western Paci?c, which is a climatologically transi- tion region of wind shear has a pronounced interannual variation associated with ENSO—a strong easterly vertical shear—both in observation and in the model composite (Fig. 6c, d). Because of the weak vertical shear in the mean state (not shown) over the western Paci?c, it is easier to reverse the sign of the vertical wind shear in the ENSO season. It is noted that the enhanced vertical shear region is similar to the ENSO-induced ISV active region (Fig. 6a, b). The enhanced waves promote the northward and north- westward propagating waves and reinforce the ISV in the WNP. Although this study offers explanations on ENSO-in- duced ISV activity over the WNP region, a number of issues remain to be addressed. In some models (ECMWF, LODYC, UKMO, and NCEP), there is a strong interannual a) b) c) d) e) f) Fig. 3 The ?rst and second EOF modes of the observed and model composite ISV activity. a, b The observed ?rst and second eigenvectors; c, d the simulated counterparts. Shading indicates positive value and contour interval is 0.02. e, f The time series associated with the eigenvectors. Solid and dashed lines indicate the observed and simulated time series, respectively 490 H.-M. Kim et al.: Interannual variations of the boreal summer intraseasonal variability 123 modulation of ISV activity over the Indian Ocean (Fig. 2). Moreover, the spatial pattern of the ?rst EOF eigenvector (Fig. 4) and strong correlation between ?rst PCs and Nino 3.4 time series (Fig. 5) would mean a strong interannual modulation of ISV by ENSO over the eastern Indian Ocean. Note that over the eastern Indian Ocean, the anomalous anti-Walker circulation during El Nino events tends to suppress the convection over the eastern equatorial Indian Ocean, thus the ISV there should be signi?cantly affected. The ISV in the off-equatorial Indian monsoon region is different. In the off-equatorial Indian monsoon region, the change of vertical shear is relatively small during ENSO—less than 10% of the climatological value. Thus, the changes in vertical shear cannot signi?cantly a) b) c) d) e) f) g) h) i) j) k) l) Fig. 4 The ?rst EOF mode of the ISV activity in a observation, b model composite, and c–l various models. Shading indicates positive value and contour interval is 0.02 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 CERF ECMW INGV LODY MAXP METF UKMO SNU NCEP NASA COMP EVmod & EVobs PCmod & PCobs PCmod & NINO3.4mod Fig. 5 Pattern correlation coef?cients of the ?rst EOF eigenvectors between the observed and associated model ISV activity over the ENSO-monsoon region (40°–300°E and 20°S–30°N; black shaded bar), correlation coef?cients of the ?rst EOF time series between observation individual model (diagonal shaded bar), and correlation coef?cients between the ?rst EOF time series of each model and its own Nino 3.4 index (gray shaded bar) H.-M. Kim et al.: Interannual variations of the boreal summer intraseasonal variability 491 123 affect the interannual variability of ISV there. Moreover, even though these models reproduce more realistic ampli- tude of interannual variability in ISV, they have a model- dependent systematic bias in their spatial pattern of vari- ability (Fig. 4). Especially, ECMWF and LODYC show opposite sign of ISV variation compared to observation over equatorial western Indian Ocean. Although some models show signi?cant amplitude as observed value in Indian Ocean, the spatial pattern has systematic bias, and therefore statistical correction plays important role. 4 Predictability of ISV activity after systematic bias correction Models still have problems in simulating the ISV activity in monsoon regions even when they include the atmo- sphere–ocean coupled process. Although the models have dif?culty in simulating the spatial variability of ISV activity, they have the ability to capture the temporal var- iability, which is related to the SST boundary forcing. Therefore, the predictability can be improved by statistical correction since the model errors are systematic and related to external forcing. In previous studies these errors were shown to be correctable by a close statistical relationship between observation and model prediction (Kang et al. 2004). In spite of the poor simulation of the EOF spatial pattern, the similarity between the time series of observed and predicted modes offers the possibility of error correc- tion (Fig. 3e, f). The difference in spatial patterns can be corrected by replacing the model eigenmodes with the corresponding observed modes. A statistical correction method is applied to reduce the systematic error for individual models based on the SVD method (Feddersen et al. 1999; Kang et al. 2004). The correction is performed by replacing the coupled pattern of forecasts with that of observations which are temporarily correlated. Because the normalized principal component of forecasts and observations is used in construction of the covariance matrix to be solved by SVD, it is the same as the Canonical Correlation Analysis (CCA) (Bretherton et al. 1992). The spatial pattern of leading CCA modes is used, and the transfer function for the replacement is as follows: F?x; t? ? X m i?1 aiYi?t?Ri?x?; where F(x,t) is corrected ?eld, Yi(t) time coef?cient of the CCA mode of forecast and Ri(x) CCA pattern of observa- tion. i is the number of the mode and ten leading modes are used (m = 10) because the sum of the ?rst ten modes ex- plains more than 90% of the total variance. ai is weighting coef?cient based on the correlation coef?cient between the CCA time series of observation and forecast. Therefore, the leading modes have more weight. Once the CCA patterns and weighting coef?cients are determined by the training dataset, the time coef?cient Yi(t) of the target forecast is obtained by projecting the CCA pattern of the forecast onto the model forecast ?led. A detailed description of statistical correction can be found in Kang et al. (2004). A cross- validation method is applied to each year. The prediction skill of ISV activity can be measured by the anomaly correlation between predictions and the cor- responding observations for 21 years. The predictability of the model composite is computed by averaging the pre- dicted ?eld after correction for ten models. Figure 7 shows the prediction skill of the model composite before and after error correction. ISV activity is predictable only in the Tropics before correction but is improved across the whole a) b) c) d) Fig. 6 Regression coef?cients of ISV activity (left) for the a observation and b model composite, and coef?cients of summer mean u850–u200 vertical wind shear (right) for the c observation and d model composite 492 H.-M. Kim et al.: Interannual variations of the boreal summer intraseasonal variability 123 globe after correction. The predictability is also examined through the 21-year-averaged spatial pattern correlation averaged over the Asian monsoon regions (60°–180°E and 10°S–30°N) for each model (Fig. 8). All models exhibit enhanced predictabilities and the model composite changes from 0.25 to 0.65 after correction. To examine more clearly the enhancement of predictability after correction, the ISV activity index is de?ned by the area-averaged ISV activity anomaly over the WNP (100°–150°E and 10°–30°N) where the interannual variation of ISV activity is dominant. Fig- ure 9 shows the time correlation coef?cient of the ISV activity index, before and after error correction. The pre- dictability of ISV activity index is enhanced except in INGV. Negative correlations change to positive in some models (e.g., CERF, MAXP, UKMO, and NCEP), and low correlations have relatively large positive values after correction (e.g., ECMW, SNU, and NASA). The predict- ability of the model composite ISV activity index changes from 0.03 to 0.48 after correction. In this study, a cross-validation method is applied to each year. However, when a statistical forecast or correc- tion methodology is to be applied to real time forecasts or correction of anomalies, adequate cross-validation becomes essential as no information of future values exists for performing the real time training. The de-correlation time scale de?nes a suf?ciently large window for the cross- validation process. For interannual variability this window is of the order of 2–3 years. Therefore, we re-compute Fig. 8 by cross-validation with removal of 1 year prior, the year in consideration, and one year after. By comparison between Fig. 8 and re-computed results (not shown), we notice that improvements accomplished by the proposed statistical correction technique are very dependent on the cross-validation window. For example, for the model composite, the corrected correlation drops from 0.65 to 0.44 when the 3-year cross-validation window is used. Therefore, the sensitivity of the cross-validation window should be considered for applying the statistical correction method. 5 Summary and discussion Reproducibility of the boreal summer (MJJA) intraseasonal variability (ISV) and its interannual variation related to ENSO in coupled climate prediction models are evaluated by diagnosing 21-year hindcast outputs from ten state-of- the-art prediction models that participated in the APCC/ CliPAS and DEMETER projects. There are two sensitivity tests with the dataset. One is about the choice of cut-off frequency. To extract the ISV component, a 20–90 days ?lter is applied to pentad pre- cipitation anomalies. Through an examination of the sen- sitivity of the cut-off frequency with daily data that is available in hindcasts, it is concluded that the interannual variability of ISV related to ENSO is not sensitive to the choice of cut-off frequency if the frequency range is within a) b) Fig. 7 Distribution of the correlation coef?cient between the observed and the predicted ISV activity of the model composite for a before and b after correction. Contour interval is 0.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 CERF ECMW INGV LODY MAXP METF UKMO SNU NCEP NASA COMP Before Correction After Correction Fig. 8 21-year-averaged pattern correlation coef?cients between the observed and predicted ISV activity before (open bar) and after (shaded bar) the correction over the Asian monsoon regions (60°– 180°E and 10°S–30°N) H.-M. Kim et al.: Interannual variations of the boreal summer intraseasonal variability 493 123 10–100 days. The other is the sensitivity of the period de?ned as ''summer''. With increasing lead time, the mean state of each model drifts towards its own climatology and we stated the interannual variation of ISV is linked with the mean state. As a result, the characteristics of the ISV may be lead time dependant. However, the difference in the variance characteristics (Figs. 1, 2, 3) is not distinctive over the MJJ or JJA periods instead of the MJJA period. The observed climatological ISV activity for the MJJA period exhibits its largest values over the western North Paci?c and Indian monsoon regions. The interannual var- iation of ISV activity is primarily found over the western North Paci?c in observation, while most models have the largest variability over the central tropical Paci?c and ex- hibit a large range of spatial patterns that are different from observation. However, the leading EOF modes of ISV activity in the models are closely linked to the model's El Nino-Southern Oscillation (ENSO). This feature resembles the observed ISV and ENSO relationship. The ENSO-in- duced easterly vertical shear anomalies in the western and central tropical Paci?c, where the summer mean vertical wind shear is weak, result in ENSO-related changes in ISV activity in both the observation and the models. In the Indian monsoon region, ENSO-induced wind shear is too weak to affect the mean circulation and thus the ISV activity is insensitive to ENSO. A close relationship in the temporal variations of the dominant modes of ISV activity exists between the observation and models. Thus, a statistical correction method based on singular value decomposition is designed. It is shown that this method is able to remove a large portion of the systematic errors. After the bias correction, the predictability is enhanced, especially in the western Paci?c. The 21-year-averaged pattern correlation skill changes from 0.25 to 0.65 over the entire Asian monsoon region after applying the bias correction to the multi-model ensemble mean prediction. The improved predictability of the ISV activity offers a possibility of an improvement in seasonal prediction be- cause of the close relationship between the ISV and sea- sonal mean state, as mentioned in the introduction. Figure 10 exhibits the relationship between the mean state and ISV activity in terms of predictability. The predict- ability can be measured by the spatial correlation between the predicted ISV activity anomaly and the corresponding observation over the Asian monsoon region (40°–180°E and 20°S–30°N) and then averaged for 21 years (the ver- tical axis in Fig. 10). The predictability is generally low compared to the predictability of the summer mean obtained in the same way (the horizontal axis in Fig. 10). The ?gure shows a very close relationship between the predictability of the mean ?eld and the ISV activity which is correlated at a level of 0.92. Most of the state-of-the-art climate prediction models still have dif?culty in simulating even the seasonal mean state and its interannual variations (Sperber and Palmer 1996; Kang et al. 2002; Kang and Shukla 2006). The results of this study suggest that this can be partly overcome by the improvement in the predict- ability of ISV activity. The way to link these two variables remains as a subject for further study. It has been emphasized that the air–sea interactions are important for ISV simulation, and especially for ISV pre- diction (Fu et al. 2006). In order to fully understand the importance of air–sea coupling in ISV prediction, not only on an interannual timescale but also on a daily timescale, a Corr = 0.92 0 0.1 0.2 0.3 0.4 0.2 0.3 0.4 0 Predictability of Interannual Summer Mean PRCP .5 Predictability of Internnual ISO activity CERF ECMW INGV LODY MAXP METF UKMO SNU NCEP NASA COMP Fig. 10 Scatter plot of predictability on summer mean precipitation (horizontal axis) and ISV activity (vertical axis) over the Asian monsoon region (40°–180°E and 20°S–30°N). The correlation is 0.92 Fig. 9 Correlation coef?cients between the observed and predicted ISV activity index before (open bar) and after (shaded bar) the bias correction 494 H.-M. Kim et al.: Interannual variations of the boreal summer intraseasonal variability 123 comparison study with coupled and uncoupled models will be carried out in further work. 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