Ren Hong-Li， Wu Jie， Zhao Chong-Bo， Cheng Yan-Jie and Liu Xiang-Wen

Laboratory for Climate Studies， National Climate Center， China Meteorological Administration， Beijing 100081， China

MJO ensemble prediction in BCC-CSM1.1（m） using different initialization schemes

Ren Hong-Li， Wu Jie， Zhao Chong-Bo， Cheng Yan-Jie and Liu Xiang-Wen

Laboratory for Climate Studies， National Climate Center， China Meteorological Administration， Beijing 100081， China

The Madden-Julian Oscillation （MJO） is a dominant mode of tropical intraseasonal variability （ISV）and has prominent impacts on the climate of the tropics and extratropics. Predicting the MJO using fully coupled climate system models is an interesting and important topic. This paper reports upon a recent progress in MJO ensemble prediction using the climate system model of the Beijing Climate Center， BCC-CSM1.1（m）； specifically， the development of three different initialization schemes in the BCC ISV/MJO prediction system， IMPRESS. Three sets of 10-yr hindcasts were separately conducted with the three initialization schemes. The results showed that the IMPRESS is able to usefully predict the MJO， but is sensitive to the initialization scheme used and becomes better with the initialization of moisture. In addition， a new ensemble approach was developed by averaging the predictions generated from the different initialization schemes， helping to address the uncertainty in the initial values of the MJO. The ensemble-mean MJO prediction showed significant improvement， with a valid prediction length of about 20 days in terms of the different criteria， i.e.， a correlation score beyond 0.5， a RMSE lower than 1.414， or a mean square skill score beyond 0. This study indicates that utilizing the different initialization schemes of this climate model may be an efficient approach when forming ensemble predictions of the MJO.

ARTICLE HISTORY

Accepted 21 September 2015

MJO； initialization scheme；ensemble prediction； climate model

热带大气季节内振荡（MJO）预报是国际研究热点，我国尚处于起步阶段。近些年国际上MJO预报水平得到大幅提升，主要得益于包含海气耦合过程的气候模式的使用，这其中模式预报初始化和集合扰动生成方法至关重要。本文发展了适用于国家气候中心第二代气候预测业务模式BCC-CSM1.1（m）的MJO初始化方案，并在此基础上提出了基于不同初始化方案形成扰动的集合预报新方法，可以将MJO有技巧预报时效延长到约20天，为次季节-季节预报提供重要依据。

Introduction

The Madden-Julian Oscillation （MJO）， as a dominant mode of tropical intraseasonal variability （ISV） （Madden and Julian 1971， 1972）， is well-recognized to play a crucial role in bridging weather and climate， as an important predictability source （Zhang 2005， 2013； Li 2014）. Therefore， MJO prediction is a key part of intraseasonal and extended range predictions. In the past decade， major international scientific institutes and operational centers have achieved significant improvements in the MJO prediction level. These improvements have largely been based on the use of fully coupled global climate models （CGCMs）and high-quality assimilated data （Vitart et al. 2007； Vitart，Leroy， and Wheeler 2010； Vitart 2014； Seo et al. 2010； Kang and Kim 2010； Rashid et al. 2011； Fu et al. 2013； Hudson et al. 2013； Kang et al. 2014； Wang et al. 2014）. Indeed， MJO prediction is currently a hot topic in the global scientific community， with increasing attention being paid to developing new methods and techniques.

The prediction skill and potential predictability of the MJO in dynamical climate models have been examined in many previous studies （e.g.， Kang et al. 2014； Neena et al. 2014.）. Until now， useful MJO prediction skill， based on a large sample size of hindcasts in a number of stateof-the-art CGCMs， can extend to 20-25 days before the correlation coefficients between the observed and predicted MJO indices drop to 0.5 （Hudson et al. 2013； Kang et al. 2014； Wang et al. 2014； Vitart 2014； Ling et al. 2015）. However， only a minority of the CGCMs involved in the Coupled Model Intercomparison Project Phase 5 （CMIP5）can simulate the MJO's spectral characteristics reasonably （Hung et al. 2013）. The climate system models of theBeijing Climate Center （BCC） can reproduce the ISV/MJO signal and main features reasonably well， despite some deficiencies that still need to be resolved （Zhao et al. 2014， 2015）.

In the last two years， the BCC has been developing a prediction system for ISV/MJO based on its atmospheric/ coupled GCMs （Ren et al. 2015）. Previously， two statistical methods were used for MJO index prediction （Jia et al. 2012）. Therefore， it is important to develop adequate model initialization schemes and ensemble perturbation approaches in establishing the new prediction system. In this paper， we report upon a recent progress in MJO prediction via the development of different initialization schemes in the BCC climate system model. In addition，considering the great potential of ensemble prediction in increasing MJO prediction skill （Neena et al. 2014）， a new ensemble approach for MJO prediction， based on the different initialization schemes， is designed. This is also reported in the present paper.

Data， model， and experiments

The daily observed outgoing longwave radiation data were from the NOAA （Liebmann and Smith 1996）， and the daily wind， moisture， and temperature data were from ERA-Interim （Dee et al. 2011）. These data were used to generate model initial values and evaluate the model results. In the ISV/MJO monitoring and prediction system （IMPRESS） being developed at the BCC， the dynamic model used for prediction is BCC-CSM1.1（m） which atmospheric component has been used in the operational MJO prediction at the BCC （Ren et al. 2015）. This model includes four basic components （atmosphere， ocean， land-use，and sea ice）， and has been applied in research on climate change projection and climate prediction at the BCC （Wu et al. 2014）. Evaluation has shown that this model can simulate the features of the ISV/MJO reasonably well，albeit with a relatively shorter period and weaker eastward propagation compared to observations （Zhao et al. 2014， 2015）. This deficiency may influence the predictability of the MJO.

To better predict the MJO using this model in IMPRESS，we sought to develop adequate initialization schemes that are able to introduce realistic MJO signals into the model，as well as make initial values dynamically consistent with model behaviors. Three experiments were designed，adopting three different initialization schemes， as follows:（1） Nudging experiment I （NDG.RPLC）， in which the model variables were completely replaced with observations， as a special kind of explicit nudging in which the relaxation time was set to a double time step （Krishnamurti et al. 1991）； （2） Nudging experiment II （NDG.UVT）， which used an implicit nudging scheme that only allowed an adequate part of the values of model variables （including zonal and meridional wind as well as air temperature） to be replaced by observations； （3） Nudging experiment III （NDG.UVTQ），which was the same as NDG.UVT but with the addition of specific humidity into the nudging process. The nudging relaxation time scale was set to one hour for the latter two schemes， consistent with Subramanian and Zhang （2014）. The experiments were conducted at 0000 UTC on the first day of each month， covering 2000-10， with a two-month initialization period before each initial time， followed by a one-month prediction. In addition to the three experiments， the ensemble mean of the three prediction results was taken， referred to as ENSEMBLE.

To verify the MJO prediction results， we first calculated the real-time multivariate MJO （RMM） indices for both the observation and model predictions， following the definition of Wheeler and Hendon （2004）. The prediction skillscores used for verification included the bivariate anomaly correlation coefficient （COR）， bivariate root-mean-square error （RMSE）， and mean square skill score （MSSS）， following Lin et al. （2008）.

Figure 3. COR skill scores of ENSEMBLE as a function of the eight initial MJO phases （x-axis） and different lead days （y-axis）.

Results

The skill scores of RMM index prediction for all of the initialization schemes and their ensemble mean are shown in Figure 1. As can clearly be seen in Figure 1a， prediction of the MJO using any initialization scheme has a valid prediction length of around 15-16 days， during which the COR is beyond 0.5. The NDG.UVTQ scheme gives a slightly longer predictable length （16 days）， compared to the other two，but its corresponding COR is the smallest within the first 10 days. These results indicates that while on one hand the initialization schemes that partly nudge the model states towards the observations are more effective in improving the prediction of the MJO than the scheme that directly replaces the model variables with observations， on the other hand it is fairly important to involve moisture in the initialization process besides the dynamic and thermodynamic variables， although model adjustment could take more time than with the other two schemes. Also， marked improvement in MJO prediction using the model is apparent compared to the skill generated through using the previous statistical methods （Jia et al. 2012）.

The ensemble mean of the three individual MJO predictions shows a considerable improvement in skill， with a valid prediction length reaching 19 days. Also， the COR skill scores of ENSEMBLE are higher than the three ensemble members for all the forecast lead days， particularly after the first week of weather range forecasting. This clearly indicates that such a new ensemble approach， based on averaging the predictions generated from the different initialization schemes of the same climate model， is able to effectively reduce the uncertainty induced by the model initial values and reasonably capture the MJO signal that dominates in the extended range predictability.

The skill scores defined from the quantification of prediction errors， i.e.， the RMSE and MSSS， were also examined， even though they are not often employed to measure the duration of useful MJO prediction. Overall， both the RMSE and MSSS results indicate the same conclusions as the COR. As seen in Figures 1b and 1c， the times at which the RMSE becomes 1.414 when using the NDG.UVT， NDG. RPLC， and NDG.UVTQ schemes are 13， 15， and 16 days，respectively， which are exactly the same as the times at which the corresponding MSSS scores are beyond 0. Among the three schemes， NDG.UVTQ always produces the best prediction during the valid prediction period，while NDG.UVT produces the worst. These results indicate that losing the moisture information in the model initialization may cause inconsistency or an imbalance between the model's dry and moist variables， and hence cause the prediction error to increase.

It is also reasonably clear that the ensemble mean of the three individual predictions can significantly reduce the prediction error and increase the prediction skill， compared to any single ensemble member， as shown in Figures 1b and 1c. Even more encouraging is that the time length of useful prediction is 20 （22） days in terms of the criterion defined by the RMSE （MSSS）， which is slightly greater than the time length of the COR definition. Recently， Neena et al. （2014） estimated MJO predictability at 20-30 and 35-45 days， based on a single member and the ensemble mean， respectively. Our results reflect their conclusion well and demonstrate further that a well-perturbed ensemble can greatly improve the prediction skill of the MJO.

Figure 4. Zonal-vertical structure patterns of the equatorial specific humidity averaged at （10°S， 10°N）， where the red lines in each panel are the zonal structure patterns of the equatorial precipitation averaged at （10°S， 10°N）， all regressed by the index of tropical Indian Ocean precipitation averaged over （5°S-5°N， 90-100°E） for （a） ERA-Interim， （b） NDG.RPLC， （c） NDG.UVT， and （d）NDG.UVTQ fields in 2014.

The seasonality of the skill scores of the MJO prediction is examined in Figure 2. There is a clear seasonal variation in the COR skill that is beyond 0.8， with the higher COR scores during boreal winter and the lower scores during summer. However， in contrast， the lead days of useful MJO prediction show no clear seasonality， being beyond 20 days during the months from March through October， while being much shorter in February， November， and December. Note that the variation in MJO prediction skill with the calendar months is not consistent with other studies， e.g. Raishid et al.（2011） showed higher skill scores in winter but lower ones in summer. This may imply model dependence，and requires further clarification.

Figure 3 presents the dependence of the COR skill scores on the different initial MJO phases. It is clear that the COR scores in terms of the values beyond 0.5 are much larger in phases 1， 3， 5， and 8， and relatively smaller in phases 2，4， 6， and 7， which suggests model dependence. This result indicates that the prediction is better when the MJO is initiated in the eastern Indian Ocean and western Pacific， but worse when initiated in the Maritime Continent， western Indian Ocean， and other regions.

The ensemble method is always important in improving prediction skill and reducing prediction error， particularly for MJO prediction. Comparisons of the prediction skill scores clearly show that the ensemble prediction based on the different initialization schemes is superior to the individual predictions， presenting great improvement in MJO prediction within IMPRESS. More importantly，the improvement in MJO prediction skill mostly appears after 10 forecast lead days， indicating great potential of the new ensemble approach in improving the extended-range forecasting level. Note， however， that this ensemble has only a few members. Thus， increasing the ensemble size may potentially increase the prediction skill and extend the length of useful prediction.

Summary and discussion

The MJO dominates the variability of the tropical intraseasonal timescale and prominently impacts the climate in the tropics and extratropics. At present， international efforts regarding MJO prediction are made through the use of fully coupled climate models because the air-sea coupling in these models can improve the simulation and prediction skill of the MJO through the two-way feedback between the MJO-related convection and sea surface temperature. In this paper， based on the ISV/MJO monitoring and prediction system （IMPRESS） at the BCC， significant progress in MJO prediction using BCC-CSM1.1（m）is presented； specifically， through the development of three different initialization schemes and their use in a new ensemble approach. The results show that IMPRESS is able to predict the MJO signal well and produce useful prediction skill， albeit this skill is sensitive to the initialization scheme used to some degree. In particular， the ensemble mean， based simply on the three initialization schemes， can significantly improve the MJO prediction skill. That is， the duration of useful MJO prediction can reach about 20 days， as comprehensively measured by different skill scores， i.e.， a COR score beyond 0.5， a RMSE lower than1.414， and a MSSS greater than 0. Also， the MJO prediction skill shows distinct dependences on both the initial calendar month and the initial MJO phase. However，the sample size used in this study was not large enough for clarifying such dependences.

The fact that the performance of MJO prediction was clearly sensitive to the initialization scheme in the model guided us to propose a new ensemble approach for MJO prediction in the model. We also noted the dependence of the model initial values on the different initialization schemes， as shown in Figure 4， for example. The moisture structures that are initialized in terms of the different schemes display large differences compared to each other as well as to the observation， reflecting great uncertainty in the initial values of the model. It has been shown in previous studies that moisture plays a critical role in MJO propagation （Jiang et al. 2004； Hsu and Li 2012） and initiation （Zhao et al. 2013； Hsu et al. 2014；Li et al. 2015）. Therefore， a superior approach might be to perturb the model initialization scheme for generating good perturbations of the ensemble. Compared to Neena et al. （2014.）， the valid prediction length of a single member provided in this study is quite close to their estimation （20-30 days）； whereas， that of the ensemble mean is only about 20 days， which is much shorter than their estimation （35-45 days）. This implies that further improvements in the ensemble approach for MJO prediction may contribute to more skillful MJO forecasts within IMPRESS.

Acknowledgements

This work was jointly supported by the National Basic Research Program of China （973 Program， Grant No. 2015CB453203），the China Meteorological Special Project （Grant No. GYHY201406022）， and the LCS/CMA Open Funds for Young Scholars （2014）.

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13 August 2015

CONTACT Ren Hong-Li renhl@cma.gov.cn

This article was originally published with errors. This version has been corrected. Please see Erratum （http://dx.doi.org/10.1080/16742834.2015.1132989）.

© 2015 The Author（s）. Published by Taylor & Francis.

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