1. Introduction
Korea is located in East Asia and its climate is under the influence of the East Asia monsoon (EAM). In summer (June–August), the major rain-producing system is the monsoon subtropical front known as changma in Korea. More than 60% of the annual precipitation is concentrated during the changma period. The EAM often leads to severe disasters such as flooding or drought, which makes the forecast of the interannual variation of EAM important for the management of water resources and power allocation.
Current general circulation models (GCMs), however, show quite low skill in predicting the EAM precipitation owing to the systematic biases in their simulation of regional features such as the Changma front (Kang et al. 2002; Wang et al. 2004; Kang et al. 2007a). In the past decade, the multimodel ensemble (MME) technique has been developed, to improve the seasonal prediction skill by reducing the uncertainties associated with individual models. It has been demonstrated that MME forecasts in general have better skills relative to forecasts from individual models (Krishnamurti et al. 1999; Palmer and Shukla 2000). With timely contributions of GCM hindcasts and forecasts from 15 institutes in the Asia–Pacific Economic Cooperation (APEC) regions, APEC Climate Center (APCC) has been providing operational MME seasonal forecasts since 2004. The MME prediction skill, however, is still poor over the EAM region, including Korea (Kang and Shukla 2006). In addition, the current operational GCMs are still far from providing station-based information for users. For example, MME uses a 2.5° × 2.5° latitude–longitude grid system with only two grid points located over Korea.
One approach that can provide valuable station-based precipitation prediction information is statistical downscaling. It is widely accepted that GCMs are able to reasonably simulate the large-scale atmospheric variables, such as geopotential height at 500 hPa (Z500) or sea level pressure (SLP; von Storch et al. 1993; Kang et al. 2004). Different downscaling techniques have been developed as tools for interpolating large-scale information into a local or regional scale (Zorita and von Storch 1999). Statistical downscaling methods establish an empirical statistical relationship between one or several large-scale meteorological variables, commonly atmospheric circulation, and local-scale variables (predictand), and then infer local changes by projecting the large-scale information on the local scale (Zorita and von Storch 1999). A statistical downscaling scheme can also use GCM output as predictor data to make predictions, which is known as model output statistics (MOS; Glahn and Lowry 1972; Wilks 1995). Thus, local precipitation can be specified by well-predicted large-scale circulation based on derived statistical relationships during the training period. MOS requires long series of data that are produced from the same dynamical model prediction system. Every time the dynamical model undergoes a major upgrade, the long series of hindcasts must be recomputed in order to derive new MOS relations that take into account possibly altered systematic errors of the dynamical model.
The GCM hindcast data series, collected for MME seasonal forecasts at APCC, are also well suited for MOS-based downscaling. Some of these data have been used in the downscaling predictions of summer precipitation in the Philippines and Thailand; Z500 and SLP are used as predictors, separately (Kang et al. 2007b). Some of them have been used in the downscaling prediction of summer rainfall in Taiwan, where a method of combination of empirical orthogonal function (EOF) truncation and singular value decomposition analysis (SVDA) was developed for downscaling; both Z500 and SLP are used as predictors (Chu et al. 2008). The above research domains are located in tropical or subtropical regions where the rainfall is much affected by low-frequency tropical variability. In this study, our target area is located in extratropics where the precipitation is influenced by more complicated factors. Therefore, a synthesized downscaling strategy using the multipredictor optimal selection method and the MME technique is adopted to predict precipitation at the 60 stations over Korea. Section 2 describes the datasets used in this study and introduces the downscaling methodology. Section 3, first, demonstrates the skills of downscaling prediction, and goes on to analyze how the prediction skills are improved in the downscaling procedures. A summary is presented in section 4.
2. Data and methodology
a. Data
The predictand is summer precipitation at 60 stations over Korea, whose locations are shown in Fig. 1. Station-based observed monthly rainfall data series from 1983 to 2003 were obtained from the Korea Meteorological Administration (KMA). The observed data were used not only for the development of a statistical downscaling technique, but also for validating the prediction scheme using a cross-validation framework.
The predictor data are taken from six operational seasonal prediction model outputs. The hindcast data, of 1-month lead predictions, are outputs from (Seasonal Prediction Model Intercomparison Project) SMIP-type experiments (Kobayashi et al. 2000). Table 1 shows the basic descriptions of the six models and their hindcast datasets. The National Centers for Environmental Prediction (NCEP) model is a coupled model (tier 1) while other models are tier 2 systems. The predictors are taken from eight variables of GCM outputs: Z500, SLP, 850-hPa temperature (T850), 2-m air temperature (T2M), 850-hPa zonal and meridional velocity (U850 and V850), and 200-hPa zonal and meridional velocity (U200 and V200). The hindcast data also span the 21-yr period from 1983 to 2003 and have a spatial resolution of 2.5° in latitude and longitude.
b. Methodology
The downscaling prediction includes three steps as follows: coupled pattern selection and projection, multipredictor optimal selection, and the multimodel ensemble.
1) Coupled pattern selection and projection
One important step in the downscaling procedure is the selection of the optimal window. It has been documented that GCM predictions, whose large-scale circulation variables are used as predictors in downscaling, commonly suffer from substantial drifts away from the observed climate, and these drifts are quite different for each model (Kang et al. 2002). To avoid these model biases, a movable window with a size of 15 × 10 latitude–longitude grid points is set to scan over the globe. The optimal window is the most sensible area in which the sum of correlation coefficients of a predictor in the window with the precipitation at target station reaches its maximum. Through this step, the large-scale signals related to the variability of local precipitation may be captured, and the precipitation at the target station is ultimately specified by the large-scale information in the optimal window.
2) Multipredictor optimal selection
There are two main mountains in Korea: Taeback Mountain is along the eastern coastline and Soback Mountain is in the southern region (see the shading in Fig. 1). The figure also shows the rainfall climatology in contours. In Korea, summer precipitation is mainly due to the changma front; however, it is also obviously influenced by local terrain, which results in two centers of maximum rainfall in two mountain areas. Figure 2 shows the spatial patterns and time coefficients of the four leading modes of the EOF analysis of the observed summer precipitation during the 21 years from 1983 to 2003. It is found that the first leading mode, which has the same sign over Korea, explains 45.9% of the total variance. This suggests that only less than half of total precipitation variance may be due to the same large-scale system. Moreover, Fig. 2 shows that other three leading modes can explain a sum of 36.3% of the total variance and each mode has a dipole structure. Compared to the locations of the two mountains, these dipole structures imply the influence of the two mountains on rainfall. From the EOF analysis, it can be found that the precipitation at 60 stations, owing to the influence of local terrain, show quite different interannual variations with each other. Consequently, using only one predictor to specify the variation of rainfall at 60 stations is not enough, one needs to search for more signal-bearing predictors and select the best one for different stations. In this study, the eight model output variables are used for downscaling and the predictor is the one with the best downscaling prediction skill; therefore, the predictor for one station may be different from another.
3) Multimodel ensemble
The uncertainties for MOS forecasts, in general, are caused by internal variability of the climate system, GCMs, and statistical downscaling models (Benestad 2001; Chen et al. 2006). Benestad (2002) found that uncertainties in monthly and annual precipitation scenarios associated with GCM realizations tended to be greater than those associated with the downscaling strategies. To reduce the uncertainties associated with GCMs, a MME prediction is performed using the average of the precipitation downscaled from the best predictor of the GCMs (hereafter referred to as DMME). For comparison, we created another MME using the average of the precipitation predicted from these GCMs (hereafter referred to as RMME). RMME precipitation, which has the same resolution of 2.5° × 2.5° as the GCMs, is interpolated to station points. As a result, the precipitation from both DMME and RMME can be verified against the observation at 60 stations; moreover, both MME prediction skills can be compared with each other.
Figure 3 shows the flowchart of the downscaling strategy. For each model, the downscaling is first carried out using each of the eight variables as predictors, separately. The downscaling procedure is tested within a leave-one-out cross-validation framework, where 1 yr used as a forecast year is removed, leaving the other 20 yr as the training period for developing the statistical relation (WMO 2002). In this way, the downscaling forecast is performed in turn for 21 yr. Then, DMME is generated by averaging the downscaled rainfall from the best predictor of GCMs. Finally, both DMME and RMME predictions are compared with the observed precipitation at each station.
3. Results
In this section, we first compare the skills of DMME and RMME in predicting interannual variations of rainfall over 60 stations in Korea. We then demonstrate how DMME achieves these skills through two steps of multipredictor optimal selection and MME.
a. Downscaling prediction skills
Figure 4 compares the temporal correlation coefficients (Wilks 1995; WMO 2002) of the predicted summer precipitations by both DMME and RMME with observations at 60 stations, during the period from 1983 to 2003. It can be seen that RMME shows very poor prediction skills; DMME, however, substantially improved the prediction skills with the correlation skill significant at the 95% confidence level at 59 stations. The striking contrast of the prediction skills indicates that RMME currently lacks the predictability for Korean rainfall, but DMME can provide valuable prediction of station rainfall for users.
Figure 5 presents three time series of station-averaged precipitation anomalies: observation, DMME, and RMME during the period of 1983–2003. Compared with the observation, RMME predicts the opposite sign of anomalies in 12 yr. On the other hand, DMME predicts the same sign of rainfall anomalies as the observations in 17 yr, especially in the heavy rainfall years of 1987, 1998, 2002, and 2003 and in the drought years of 1983, 1988, 1992, and 1994. This indicates that the large-scale variables, which are output from the current operational dynamical models, are useful in predicting local rainfall, particularly in extreme years, by means of the downscaling strategy.
b. Prediction skill improved by multipredictor optimal selection
In this subsection, we take the Japan Meteorological Agency (JMA) and NCEP models as examples to show how prediction skills are improved through multipredictor selection procedure.
Figure 6 shows the distributions of correlation skills for the JMA model. The verification period is 21 yr from 1983 to 2003. Figure 6a shows the correlation coefficients of the JMA predicted precipitation with observations. Figures 6c–j show the correlation coefficients of JMA-downscaled precipitation by using eight output variables as predictors with observations, separately. The best prediction skill among these predictors at each station forms a “composite” skill map for all stations, as shown in Fig. 6b. It can be seen that a different predictor improves the prediction skill at different stations: Z500 as a predictor mainly improve the skills in the western part of Korea, SLP mainly in the central part, and T850 mainly in the northern part. It should be noted that some variables such as V850 and U200 contribute less skill. Moreover, no predictor can improve prediction skill at all stations on Jeju Island. This indicates that JMA cannot provide effective associated large-scale circulation information in predicting the precipitation variation on Jeju Island. Nevertheless, compared with the raw JMA prediction skills in Fig. 6a, Fig. 6b shows that multiple predictor selection significantly improves prediction skills at most stations, especially in the northern part of Korea.
As in Fig. 6, Fig. 7 demonstrates the distributions of the correlation skills, but for the NCEP model. It is found that most of the predictors, such as Z500, SLP, V850, U200, and V200, obviously improve the prediction skills in the southern part of Korea. This suggests that in many fields of the large-scale variables predicted by the NCEP model, there are some areas where the NCEP model output is highly correlated with the rainfall variations in the southern part of Korea. It is also noted that in the northern part of Korea, only a few predictors contribute skills marginally in a few stations. As a composite map of best skills, however, Fig. 7b still shows that downscaling performs much better than the NCEP model over all of Korea, especially in its southern part.
From the above two examples, it is found that JMA T850 is a good predictor for the northwestern area of Korea and the NCEP SLP is good for the southwestern part. Next, through taking Seoul in the northwestern area and Gwangju in the southwestern area as examples, we will illustrate the impact of optimal window selection and demonstrate how the stability of optimal window is related to prediction skill for different predictors.
Figures 8a,b show the correlation coefficients between the precipitation at Seoul and JMA T850/SLP separately. Figures 7c,d show the correlation coefficients between the precipitation at Gwangju and NCEP T850/SLP separately. It is found that Seoul’s rainfall has good correlation with JMA T850 in an extensive region of tropical South America and northern Africa; however, it has less correlation with JMA SLP. Consequently, JMA T850 is a better signal-bearing predictor for Seoul’s rainfall compared with JMA SLP. The result is consistent with Fig. 6, where T850 has the best prediction skill at the Seoul station among the eight variables. For the NCEP model, it is found that Gwangju’s rainfall has good correlation with SLP over broad regions of Africa, southern Australia and the ocean to its east, and the southern Atlantic Ocean; but it has only marginal correlations in some areas with NCEP T850. Hence, NCEP SLP is a better predictor for Gwangju’s rainfall compared with T850. Figure 6 suggests that downscaling prediction skills in the southern part of Korea mainly result from using SLP as a predictor other than T850. Figure 8 reveals that a variable, owing to its prediction uncertainties associated with different GCMs, may be a good predictor for one model but not for another. Therefore, it is necessary, at each station, to choose the best predictor for each model.
Figure 9 is designed to reveal where the optimal window is selected in every forecast year. As stated before, the downscaling procedure in this study is under a leave-one-out cross-validation framework; the optimal window for each forecast year is selected based on its training period of 20 yr with the forecast year removed. With the forecast year changing from 1983 to 2003, the respective set of 20 training years also changes. Owing to these changes, there is a possibility that the location of the window may be unstable from one forecast year to another. Figure 9 illustrates how many times a grid point is selected for downscaling in the 21 forecast years. It is found that for the JMA model, T850 over the southern part of tropical South America is a stable information source for Seoul’s rainfall; however, SLP as a predictor is dispersed. The NCEP model is another story: SLP over southern tropical Africa is stably selected for downscaling, but T850 is not. In this study, even within an optimal window, only the grid point with an absolute value of the correlation coefficients between predictand and predictor larger than 0.3 is selected for downscaling. As compared to Figs. 6 and 7, Fig. 9 clearly demonstrates that prediction skill is proportional to the stability of optimal window. The reason is that if a predictor window locates in a high correlation area and it changes less with different sets of training years, then the predictor window is a stable information source associated with rainfall variation; therefore, the downscaling can skillfully predict the rainfall variation through the stable statistical relationship under the cross-validation framework.
c. Prediction skill improved in MME procedure
As shown in section 3b, JMA downscaling mainly improves the prediction skills over central Korea but not much in the southern part; NCEP downscaling mainly improves the prediction skills over the southern part of Korea but not much in the northern part. This is due to the prediction uncertainties associated with individual GCMs. To reduce the uncertainties of this type, we perform the ensemble mean of multimodel downscaling.
Figure 10 shows the distributions of temporal correlation coefficients between the observed precipitation and predicted precipitation: Figs. 10a–f are for six models, Fig. 10g is for RMME, Figs. 10h–m are for six downscaling models, and Fig. 10n is for DMME. It is found that the predictions from these models except for the Global Climate Prediction System (GCPS), show very poor performance at most of the stations. Even RMME performs poorly. This indicates that prediction skill cannot be improved through the MME procedure if these participating models predict poor skill. On the other hand, the downscaling prediction skills for these models have been substantially improved compared with their respective raw model predictions. Moreover, DMME prediction is not only much better than RMME prediction, but also better than any downscaling model prediction. It is noticed that downscaling predictions by these individual models commonly perform well only in parts of Korea, but the combination of these downscaling predictions (DMME) achieves quite good prediction skills at all 60 stations. Figure 10 clearly demonstrates that DMME further improves prediction skill through the MME procedure, which successfully reduces the uncertainties associated with the individual models.
Figure 11 shows the temporal correlation coefficients of the average observed rainfall over Korea with the predictions from six models and RMME and six models downscaled and DMME during 1983–2003. It is found that all the models except GCPS present negative prediction skills and that the correlation of RMME with the observation is only −0.21. After downscaling, all the prediction skills have been apparently improved compared with their respective raw model predictions and five of them reach the skills significant at the 95% confidence level. The correlation coefficient of DMME with observations even reaches 0.75; this skill is also higher than the prediction skill of any of individual model’s downscaling techniques.
4. Summary
This study uses a multimodel output downscaling technique to predict summer rainfall at 60 stations over Korea. The hindcast datasets of six operational GCMs and station observed data, spanning a period of 21 yr from 1983 to 2003, are employed to develop the downscaling technique under a leave-one-out cross-validation framework. To search for a coupled pattern, a movable window is set to scan over a predictor field to find the area that is highly correlated with the station rainfall. Local precipitation can be specified by predicted large-scale information in the optimal window based on the derived statistical relationship during the training period. Single predictors, however, cannot capture the variations of rainfall at 60 stations because Korea’s rainfall is strongly influenced by local complex mountainous terrain. In this study, eight large-scale variables from six GCM outputs are taken as predictors to make downscaling predictions for each station separately; the best predictor for a model is the one with the best skill. The final prediction, DMME, is the average of the six downscaled rainfalls using the best predictors of GCMs. RMME, an average of six GCM-predicted rainfall, is also carried out for comparison.
This paper demonstrates that DMME predictions are superior to RMME predictions. Out of 60 stations, DMME successfully predicts rainfall with correlation coefficients significant at the 95% confidence level at 59 stations; RMME fails at all stations. Out of 21 yr, DMME predicts the same sign of the averaged precipitation anomalies as observations in 17 yr, especially in the extreme years with heavy rainfall or severe drought; RMME predicts the same sign in 12 yr, which is close to a random choice. In this study, downscaling prediction skills are first substantially improved through a coupled pattern projection procedure. Then, the skills are further improved through two steps: (i) multipredictor optimal selection and (ii) a multimodel downscaling ensemble. These skillful DMME predictions indicate that some large-scale variables, which are predicted by current operational GCMs, contain useful information on local climate variation and this information can be used to predict local precipitation variability if an appropriate downscaling strategy is applied.
In this study, DMME uses only the ensemble mean of dynamical model outputs as predictors to make a deterministic prediction. Further investigations of making probabilistic downscaling MME predictions using ensemble member information will be carried out in the near future.
Acknowledgments
The authors thank the Korea Meteorological Administration for providing the station data of precipitation in Korea. The authors also appreciate those institutes participating in the APCC multimodel ensemble operational system for providing the hindcast experiment data.
REFERENCES
Benestad, R. E., 2001: A comparison between 2 empirical downscaling strategies. Int. J. Climatol., 21 , 1645–1668.
Benestad, R. E., 2002: Empirically downscaled multimodel ensemble temperature and precipitation scenarios for Norway. J. Climate, 15 , 3008–3027.
Chen, D., C. Achberger, J. Raisanen, and C. Hellstorm, 2006: Using statistical downscaling to quantify the GCM-related uncertainty in regional climate change scenarios: A case study of Swedish precipitation. Adv. Atmos. Sci., 23 , 54–60.
Chu, J., H. Kang, C. F. Tam, C. Park, and C. Chen, 2008: Seasonal forecast for local precipitation over northern Taiwan using statistical downscaling. J. Geophys. Res., 113 , D12118. doi:10.1029/2007JD009424.
Glahn, H. R., and D. A. Lowry, 1972: The use of Model Output Statistics (MOS) in objective weather forecasting. J. Appl. Meteor., 11 , 1203–1211.
Kang, H., and C-K. Park, 2007a: Error analysis of dynamical seasonal predictions of summer precipitation over the East Asian-western Pacific region. Geophys. Res. Lett., 34 , L13706. doi:10.1029/2007GL029392.
Kang, H., K. An, C. Park, A. L. S. Solis, and K. Stitthichivapak, 2007b: Multimodel output statistical downscaling prediction of precipitation in the Philippines and Thailand. Geophys. Res. Lett., 34 , L15710. doi:10.1029/2007GL030730.
Kang, I-S., and J. Shukla, 2006: Dynamical seasonal prediction and predictability of the monsoon. The Asian Monsoon, B. Wang, Ed., Springer, 585–612.
Kang, I-S., and Coauthors, 2002: Intercomparison of the climatological variations of Asian summer monsoon precipitation simulated by 10 GCMs. Climate Dyn., 19 , 383–395.
Kang, I-S., J-Y. Lee, and C-K. Park, 2004: Potential predictability of summer mean precipitation in a dynamical seasonal prediction system with systematic error correction. J. Climate, 17 , 834–844.
Kobayashi, C., K. Takano, S. Kusunnoki, M. Sugi, and A. Kitoh, 2000: Seasonal predictability in winter over eastern Asia using the JMA global model. Quart. J. Roy. Meteor. Soc., 126 , 2111–2123.
Krishnamurti, T. N., and Coauthors, 1999: Improved weather and seasonal climate forecasts from multi-model superensemble. Science, 285 , 1548–1550.
Kug, J-S., J-Y. Lee, and I-S. Kang, 2007: Global sea surface temperature prediction using a multimodel ensemble. Mon. Wea. Rev., 135 , 3239–3247.
Palmer, T. N., and J. Shukla, 2000: Editorial to DSP/PROVOST special issue. Quart. J. Roy. Meteor. Soc., 126 , 1989–1990.
von Storch, H., E. Zorita, and U. Cubasch, 1993: Downscaling of global climate change estimates to reigional scales: An application to Iberian rainfall in wintertime. J. Climate, 6 , 1161–1171.
Wang, B., I-S. Kang, and J-Y. Lee, 2004: Ensemble simulation of Asian-Australian monsoon variability by 11 AGCMs. J. Climate, 17 , 803–818.
Wilks, D. S., 1995: Statistical Methods in the Atmospheric Sciences. Academic Press, 467 pp.
WMO, 2002: Standardised Verification System (SVS) for Long-Range Forecasts (LRF) new attachment II-9 to the manual on the GDPS (WMO-485). Vol. I, WMO, Geneva, Switzerland, 32 pp.
Zorita, E., and H. von Storch, 1999: The analog method as a simple statistical downscaling technique: Comparison with more complicated methods. J. Climate, 12 , 2474–2489.
Korea topography map with 60 station locations and the precipitation climatology based on 21 yr from 1983 to 2003. Shading denotes the topography (m) and contours show the climatology (mm day−1). The contour interval level is 0.5 mm day−1.
Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2706.1
The spatial patterns and time coefficients of the four leading modes of the EOF analysis of the summer precipitation over Korea during the 21 years from 1983 to 2003.
Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2706.1
The flowchart of the downscaling strategy in this study.
Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2706.1
The temporal correlations of the predicted precipitation from two MMEs with observations at 60 stations, during the period from 1983 to 2003. RMME is the average of precipitation predicted from the GCMs. DMME is the average of the precipitation downscaled from the best predictor of the GCMs. The solid line indicates the critical value of correlation coefficient is significant at the 95% confidence level.
Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2706.1
The station-averaged summer precipitation anomaly time series: observation, DMME, and RMME, during 1983–2003.
Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2706.1
The correlation coefficients of predicted precipitation with the observation at each station: (a) JMA model; (b) a skill composite map with the best skill among that of above eight variables at each station; and (c)–(j) downscaling by using JMA-predicted Z500, SLP, T850, T2M, U850, V850, U200, and V200 as predictors separately. The dark shaded station indicates the correlation coefficient is significant at the 95% confidence level.
Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2706.1
As in Fig. 6, but for the NCEP model.
Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2706.1
(a),(b) The correlation coefficients between the precipitation at Seoul and the T850/SLP simulated by JMA model during the 21 years of 1983–2003 separately. (c),(d) The correlation coefficients between the precipitation at Gwangju and the T850/SLP simulated by NCEP model during the 21 yr of 1983–2003 separately. The dark shading indicates the correlation coefficient is significant at the 95% confidence level.
Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2706.1
The distributions of the number of times that a grid point is selected in the predictor area in 21 forecast years under a cross-validation framework: (a),(b) Seoul’s rainfall using JMA-predicted T850 and SLP as predictors separately, and (c),(d) Gwangju’s rainfall using NCEP-predicted T850 and SLP as predictors separately.
Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2706.1
The temporal correlation coefficients of predicted rainfall with observations at each station: (a)–(f) the six participating models, (g) RMME, (h)–(m) the six downscaling models, and (n) DMME. The dark shaded station indicates the correlation coefficient is significant at the 95% confidence level.
Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2706.1
The temporal correlations of observed precipitation of the average over Korea with the predictions from six participating models and RMME, and six downscaling models and DMME. RAW stands for the correlation skill of model prediction and DSC stands for the downscaling prediction. The solid line indicates the critical value of correlation coefficient is significant at the 95% confidence level.
Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2706.1
Description of the GCMs used in this study. Here, HFP indicates Historical Forecasting Project and GDAPS is the Global Data Assimilation and Prediction System.