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Performance of Multimodel Schemes for Seasonal Precipitation over Indian Region

Performance of Multimodel Schemes for Seasonal Precipitation over Indian Region Hindawi Advances in Meteorology Volume 2018, Article ID 5874270, 14 pages https://doi.org/10.1155/2018/5874270 Research Article Performance of Multimodel Schemes for Seasonal Precipitation over Indian Region 1 2 Vinay Kumar and Tirthankar Ghosh Department of Physical and Environmental Sciences, Texas A&M University, Corpus Christi, TX 78412, USA Department of Statistics, Visva Bharati University, Bolpur Santiniketan, West Bengal 731235, India Correspondence should be addressed to Vinay Kumar; vinay.kumar@tamucc.edu Received 5 July 2017; Revised 15 October 2017; Accepted 8 November 2017; Published 3 January 2018 Academic Editor: Takashi Mochizuki Copyright © 2018 Vinay Kumar and Tirthankar Ghosh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This study uses downscaled rainfall datasets from 16 coupled climate models at high resolution of 25 km from 1987 to 2001. The multimodel superensemble scheme is widely tested for rainfall forecast over mid-latitude, subtropical, and, especially, various regions of the monsoonal belt. A well-known statistical estimation theoretic approach, namely, Best Linear Unbiased Estimator (BLUE), is examined on 16 member models. eTh results are compared with superensemble methodology based on various skill scores. Results show that BLUE is providing promising forecasts. As far as comparative studies are concerned BLUE and superensemble schemes compete and show their importance from normal years to extreme rainfall years. BLUE methodology is capable of predicting draughts very well compared with other multimodel schemes. One basic advantage of BLUE is computationally less expensive than superensemble scheme. These statistical schemes like downscaling, BLUE, and superensemble can improve rainfall forecasts further, if a dense rain gauge data is provided. 1. Introduction models and postprocessing statistical techniques in pre- dicting seasonal rainfall [1, 10]. The successes of statistical Several multimodel schemes are being listed in the literature methods depend on the long-time series of data for training of the climate and weather for rainfall prediction. eTh se period to calculate better-quality coefficients. If the training commonly used multimodel rainfall forecast schemes are datasets consist in many new information pieces on flood ensemble scheme, biased removed ensemble mean, clustering and drought events, then their obtained coefficients do better techniques, and superensemble method. The superensemble in forecast period. On the other hand, dynamical models scheme from Florida State University (FSU) is being tested have problems with their parametrization schemes and some since 1999 by various researchers [1–4]. Nowadays a good simplification of various schemes used in them. In these quality of rainfall dataset is available from satellites (e.g., models, systematic error grows with time. Worldwide more Global Precipitation Measurement, GPM/Tropical Rainfall than 20 climate prediction centers are engaged in the monthly Measuring Mission, TRMM), reanalysis (e.g., MERRA), and to seasonal predation with their home grown global models. rain gauge (e.g., APHRODITE) at high resolution. Somehow Multimodel schemes were suggested to bring consensus climate global models still have a coarse resolution of 100 km. forecast for a season [11–13]. Such gap of resolution calls for downscaling of the climate India Meteorological Department has used statistical global models. All the acronyms are mentioned in Acronyms models and modified them over a period to provide an forModels, Institutes,orOtherNames. improved Indian summer monsoon rainfall prediction [14– Statistical downscaling procedures have been used to improve the horizontal resolution of the member models [4– 17]. Some of the limitations of statistical and dynamical 9]. By doing so, the regional details of the dry and wet patches models used for Indian rainfall prediction are noted by Nan- of rainfall bulge out. er Th e are limitations of dynamical jundiah [18] and Gadgil et al. [10]. Various new multimodel 2 Advances in Meteorology schemes were tested on the Indian region for rainfall forecast of detection)andfalsepositiverate(hereFARratioorFalse [19–21]. On examination of 5-multimodel schemes they Alarm Ratio) for the forecasts. A curve closer towards the realized that the accuracy of the rainfall forecasts can be 𝑦-axis indicates more accurate test. us, Th the area under the increased over Indian region. Furthermore, they worked curve is the measure of the ROC score. upon probabilistic prediction of the Indian region and found the probabilistic forecasts are superior to multimodel 2. Dataset Used ensemble mean. This group has numerous research works on the prediction of rainfall using various techniques. In mid- Downscaled rainfall datasets (for 15 years, 1987–2001) from latitude,thesealevelpressure,wind,andrainfallhaveastrong sixteen coupled models [33] are included in this study. All tieand thuscanbeusedinmultipleregressionmethodto the models were integrated from May 1 to September 30 for downscale the rainfall. In a recent study, canonical correlation the summer season (JJAS). Here we analyzed only summer analysis is used to downscale rainfall over Indian region season of monsoon (June to September) datasets in this study. and other [22, 23]. They found some improvements in the Table 1 contains some details for atmospheric and oceanic forecastsskillsoversomepartsof northeastandpeninsular components of each model, namely, model name, model India. eTh re is no strong relationship between rainfall and resolution, initial conditions for simulation, and numbers of other variables like sea surface temperature, winds, and ensemble predictions. The ensemble mean forecasts from a outgoing long wave radiation over tropical region. In another single model’s several runs are also included in this study. study using stepwise regression, Salvi et al. [24] showed that These model forecasts are cast at a common horizontal their method could capture the rainfall over mountainous resolution of 2.5-degree latitude by 2.5-degree longitude for regions of India. eTh y evaluated the future projection of the construction of multimodel ensembles. APHRODITE rainfall over Indian region. eTh group is engaged in the Rainfall [34] dataset was used as observed rainfall. This data various kinds of downscaling methods for rainfall over Indian is based on thousands of rain gauges over a large region of region. monsoon Asia. The spatial resolution of the datasets is 0.25 In this study, we used liner regression method to down- × 0.25 lat-lon grid while the time interval of data is daily to scale the rainfall over the Indian region. It is known that, even monthly. To interpolate model’s data from coarse resolution in hindcast mode, none of the models provide correct forecast to fine resolution of observational dataset, we used 4-point forarangeofyears.Perhaps,thatwas oneofthenecessitiesof Bessel interpolation method. the multimodel based prediction techniques. In a better way postprocessing datasets and statistical techniques can work 3. Downscaling and Multimodel Schemes together to ren fi e the forecast further. Answers on various issues, for example, minimum number of member models Linerregressionschemeisapplied fordownscaling andto to construct superensemble, length of datasets, and other construct downscaled datasets from each member model sensitivity issues can be found in Kumar and Krishnamurti against APHRODITE Rainfall datasets. [25]. eTh rainfall product is being improved rfi st by down- Chakraborty and Krishnamurti [26] have shown the scaled methodology and then by superensemble method. improved rainfall forecasts with downscaling and without In some of the studies, the prediction of Indian summer downscaling from member models, ensemble mean, and monsoon rainfall is being improved by superensemble and superensemble scheme. They illustrated that the downscaled downscale method [25–28]. In the present study, we worked superensemble scheme shows higher correlation and reduced with rainfall anomalies and the skills were compared among RMSE over Indian summer monsoon rainfall. During mul- the best models (ECMWF model comes out best among 16 timodel ensemble, we considered entire duration of datasets suites of models for Indian region, Kumar and Krishnamurti of 15 years (15 years × 4 months = 60 values) of monthly [25]), ensemble mean (EM), and two multimodel schemes. rainfall. Next, we constructed multimodel schemes based on One of the important aspects here we tried to bring out is, downscaled datasets. It is shown that the data of 15 years how, accurately, can we forecast the extreme events? A new were sufficient to carry out the downscaling as the coefficients multimodel scheme, based on estimation theory, namely, Best stabilizeaeft r10yearsof datasets [25]. Linear Unbiased Estimator (BLUE), has been examined [29]. We believe that a data processing method improves the Furthermore, this study compares two operational schemes model datasets and adds some error as well. However, this which have been used in hurricane prediction in the Atlantic can be reduced in some situations. er Th e is a major difference basin. between the mathematical strategy for downscaling and for The present study illustrates performance of the best the construction of the multimodel superensemble scheme. model, ensemble mean, synthetic superensemble (SSE) tech- The former downscales each model separately with respect to nique,andBLUEschemeon16state-of-the-artcoupled the observed estimates, whereas the multimodel superensem- climate models for 15 summer seasons for the Indian region. ble calculates a single forecast considering forecasts from This paper deals with the application of multimodel statistical the member models all together. It performs a multiple methods. The skill scores used in this work are spatial linerregressiontoremovethe collective biasof thesuite correlation coefficient, RMSE, chi-square values for measure of models. eTh two methods are mutually independent. of association, ETS, BIAS, Heidke Skill Score [30], and ROC Over all, first downscaling helps in sprouting the regional (Relative Operating Characteristic [30, 31]). ROC is the plot features in the rainfall forecasts from each member model betweentruepositiverates(herehitsscoreratioorprobability and then superensemble scheme is improving the forecast Advances in Meteorology 3 Table 1: Details of sixteen global coupled models used in this study. Name Atmospheric component Oceanic component Ensemble size (institute) and reference Model Resolution Initial condition Model Resolution Initial condition FSUGSM with Coupled Arakawa-Schubert ECMWF with 5 longitude, AOR (FSU) assimilation ∘ ∘ convection and new T63L14 physical HOPE global 0.5 –5 latitude, 1 Cocke and LaRow (2000) relaxed to observed radiation initialization 17 levels SST (band model) FSUGSM with Kuo Coupled convection and new ECMWF with 5 longitude, assimilation ∘ ∘ KNR (FSU) radiation T63L14 physical HOPE global 0.5 –5 latitude, 1 relaxed to observed (emissivity-absorptivity initialization 17 levels SST model) FSUGSM with Kuo Coupled convection and old ECMWF with 5 longitude, assimilation ∘ ∘ KOR (FSU) radiation T63L14 physical HOPE global 0.5 –5 latitude, 1 relaxed to observed (emissivity-absorptivity initialization 17 levels SST model) ∘ ∘ CFS (NCEP) 1 × 1/3 , Ocean data GFS T62L64 CFS SST forecast MOM3 15 Saha et al. (2006) 40 levels assimilation From latest From ocean Bureau of Meteorology atmosphere and assimilation that Australian Community ∘ ∘ ∘ POAMA 1.5 (Australia) Research Center ocean conditions 2 × 0.5 –1.5 , was based on T47L17 Ocean Model 2 10 Zhong et al. (2005) (BMRC) Atmospheric From Global 31 levels optimum (ACOM2) model (BAM3) Atmospheric interpolation (OI) Sampling Program technique ECMWF 40 yr ∘ ∘ 2 × 2 , CERFACS (France) ARPEGE T63L31 Reanalysis OPA 8.2 Forced by ERA-40 9 31 levels (ERA-40) ∘ ∘ ∘ 1.4 × 0.3 –1.4 , ECMWF (Europe) IFS T95L40 ERA-40 HOPE-E Forced by ERA-40 9 29 levels 4 Advances in Meteorology Table 1: Continued. Name Atmospheric component Oceanic component Ensemble size (institute) and reference Model Resolution Initial condition Model Resolution Initial condition 2 (lon) × FRCGC (SINTEX-F) NCEP/DOE SST nudging ECHAM-4 T106L19 OPA 8.2 2 cos (lat), 9 Luo et al. (2005) Reanalysis-2 scheme 31 levels ∘ ∘ ∘ ∘ GFDL 2.5 × 2 ,34 NCEP/DOE 1 × 1/3 , Ocean data AM2.1 OM3.1 (MOM4) 10 Delworth et al. (2006) levels Reanalysis-2 50 levels assimilation ∘ ∘ ∘ 2 × 0.5 –1.5 , INGV (Italy) ECHAM-4 T42L19 AMIP type OPA 8.1 Forced by ERA-40 9 31 levels ∘ ∘ 2 × 2 , LODYC (France) IFS T95L40 ERA-40 OPA 8.2 Forced by ERA-40 9 31 levels Coupled run Coupled run ∘ ∘ ∘ MPI Open Model Interface 2.5 × 0.5 –2.5 , MPI (Germany) ECHAM-5 T42L19 relaxed to observed relaxed to observed 9 (MPI-OMI) 23 levels SST SST 182 × 152 GP, MetFr (France) ARPEGE T63L31 ERA-40 OPA 8.0 Forced by ERA-40 9 31 levels SNU (Seoul National ∘ ∘ NCEP/DOE 1 × 1/3 , SST nudging University) SNU T42L21 MOM2.2 6 Reanalysis-2 32 levels scheme Kug et al. (2007) Thermocline- ∘ ∘ UH (University of Hawaii) NCEP/DOE 2 × 1 , ECHAM4 T31L19 UH Ocean Depth 10 Fu and Wang [32] Reanalysis-2 2levels nudging GloSea OGCM Third ∘ ∘ 2.5 × 3.75 ,19 Hadley Center Coupled UKMO (United Kingdom) HadAM3 ERA-40 Forced by ERA-40 9 levels Ocean-Atmosphere GCM (HadCM3) based Advances in Meteorology 5 basedonmultimodel.Crossvalidationmethodisusedduring are shown in the first, second, third, fourth, and h rows, superensemble and BLUE methodology. In this method, a respectively. eTh rainfall anomalies from APHRODITE, year, which was forecasted, was not taken, while calculating ECMWF model, EM, superensemble scheme, and BLUE cap- the downscaling or superensemble weights. turedarangeofvariability from droughttofloodyearrainfall over Indian region. Year 1987 was considered as one of the 3.1. Downscaled Methodology. APHRODITE Rainfall [34] is worst droughts in the history of Indian summer monsoonal used to downscale the rainfall forecast from member models rainfall variability, which, remotely, had an influence from over the Indian region. El-Nino ˜ event in Eastern Pacific Ocean. The central Indian region was badly affected by very low rainfall while eastern 𝑅 =𝑎𝑅 +𝑏+𝜀, (1) obs mdl India received a good rainfall. Rainfall deficient over central India was simulated by most of the models, while the patches where 𝑅 and 𝑅 are the observed and interpolated model obs mdl of extreme rainfall were not captured by any one. Year 1991 forecasts of rainfall (at the same resolution), respectively; was affected by low rainfall over northern and northeastern 𝑎 and 𝑏 are regression coefficients known as the slope and India. Interestingly ECMWF captured it fully, as well as intercept of the least square tt fi ing; and 𝜀 is the error term. superensemble scheme, but EM and BLUE failed here. Year 1995 was witnessed with drought over southcentral India 𝑅 =𝑎𝑅 +𝑏, (2) dscl mdl while flood kinds of situations prevailed over northern India. where 𝑅 is the downscaled rainfall forecast of the model; ECMWF model was best to simulate the rainfall variability dscl over the Indian region, but it failed to simulate the rainfall here 𝑎 and 𝑏 are calculated using (2) at each grid point and over the eastern parts of India. SSE tried to simulate the separatelyforevery monthoftheyear.Weleft outtheyear to be downscaled from the calculation to calculate 𝑎 and 𝑏 rainfall variability but missed deficient rainfall patches over central India. Some of the patches of dry region over Odisha following the method of cross validation. There are many more downscaling methods, for example, canonical analysis (20.95N, 85.05E) were remarkably captured. It is to be noted and stepwise pattern projection. eTh linear downscaling that BLUE did better than other models in case of year 2000, which was almost a monsoon drought (rainfall was −9% of methods perform well as compared to other methods [35]. We choose a linear downscaling method here. the climatological normal) over Indian region. Tables 2 and 3 show the year by year spatial correlation and RMSE numbers 3.2. Synthetic Superensemble Technique. The superensemble for all the member models, EM, superensemble scheme, and methodology [1, 36] produces a single forecast based on BLUE.FromTables2and3,wefound thatthecorrelation multimodel forecasts. Multimodel superensemble forecasts varies from −0.31 to 0.59 for all the models. The ranges of based on downscaled datasets from member models were correlation coefficients are varying from negative to positive constructed as well [37]. We expressed that as follows: values which is why we cannot talk about signicfi ance of the correlations. For some of the years (e.g., 1991, 1995) the mdl correlation has significance of 0.02 (two-tailed probabilities). (3) 𝑆= 𝑂+ ∑ 𝑤 (𝐹 − 𝐹 ), 𝑖 𝑖 𝑖 It may be noted that the highest correlation for a year 𝑖=1 varies from model to model, yet multimodel schemes (BLUE and superensemble) perform better than any member model where 𝑆 is the superensemble prediction, 𝑂 is the observed andEM. We observethatfor theyear1999 none ofthe time mean (climatology),𝑤 are the weights for the individual models and schemes has a positive correlation except CERF, models 𝑖, 𝐹 and 𝐹 are the forecast and forecast mean for 𝑖 𝑖 KORAM, MAXP, and NCEP. Table 2 has the RMSE range amodel 𝑖 for training period, and 𝑁 is the number of mdl from 1.34 to 3.82. Here multimodel schemes tried to minimize models. Here weights are obtained by minimizing error using the RMSE but the margin between them and member models least square method. The sum of the weights needs not be one are not so much. It may be mentioned that rainfall variability and they vary from negative values to positive values. over Sri Lanka was very well captured by superensemble (correlation coecffi ient (CC) = 0.44). eTh skills of rainfall 3.3. BLUE Technique. In this study, we introduce another variability from year to year are explained in Figures 2(a) multimodel construction technique based on estimation and 2(b) in terms of spatial correlation coefficient and RMSE. theory. Individual model is downscaled to sprout the regional BLUE and EM keep their spatial correlation coefficient features of the rainfall. Next, superensemble scheme and positive for most of the time except for 1999. In Figure 2, BLUE acted on multimodels to remove the model biases. In we considered the target region slightly smaller than the case of BLUE the coefficients are inversely proportional to the bigger region displayed in Figure 1, because many of the errors of the models and the sum of coefficients is one. The northern regions especially north of 30N are rain gauges methodology is described in the Appendix. sparse. Chakraborty and Krishnamurti [38] found the neg- ative anomaly correlation for year 1999 for a bigger monsoon 4. The Spatial Variability of Rainfall region.IncaseofECMWFandsuperensembleschemespatial Spatial patterns of rainfall anomalies for 1987, 1991, 1995, correlation is not higher for all years. It is varying from and 2000 are being shown in Figure 1. Rainfall anomalies positive to negative from 0.5 to −0.24. Figure 2(b) shows RMSE, which is lowest in case of BLUE. Here superensemble from APHRODITE Rainfall datasets, coupled model from ECMWF, ensemble mean, superensemble scheme, and BLUE scheme comes out distinct in many years with lowest RMSE. fift 6 Advances in Meteorology 1987 1991 1995 2000 35 ． 30 ． 25 ． 2.2 20 ． 15 ． 1.6 10 ． 35 ． 30 ． 1.1 25 ． 20 ． 0.7 15 ． 10 ． 0.4 35 ． 30 ． 25 ． 0.2 20 ． 15 ． −0.2 10 ． 35 ． −0.4 30 ． 25 ． ∘ −0.7 20 ． 15 ． −1.1 10 ． 35 ． 30 ． −1.6 25 ． 20 ． −2.2 15 ． 10 ． ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ 70 ％ 80 ％90 ％ 70 ％ 80 ％90 ％ 70 ％ 80 ％90 ％ 70 ％ 80 ％90 ％ Figure 1: June to September rainfall anomalies (mm/day) for 1987, 1991, 1995, and 2000 from APHRODITE, ECMWF (abbreviated in caption as ECMW), EM, SE, and BLUE. A rectangular box (69–92E, 8–30) is shown in the first panel (top right corner). This is the target region of Figures 2 and 3. 2.5 0.7 0.6 0.5 0.4 0.3 1.5 0.2 0.1 0 1 −0.1 −0.2 −0.3 Year Year −0.4 ECMW BLUE ECMW BLUE EM EM SSE SSE (a) (b) Figure 2: (a) CC and (b) RMSE for ECMWF, EM, superensemble scheme, and BLUE for JJAS seasonal rainfall anomaly predictions. Area averaged over Indian region (69–92E, 8–30N). Correlation coeffieient BLUE SSE EM ECMW APHRODITE Root mean square error 2001 Advances in Meteorology 7 Table 2: CC for all the member models, EM, superensemble scheme, and BLUE for JJAS seasonal rainfall anomaly predictions. CC more than 0.5, statistica lly significant at 95% level, is italicized. ANRM BMRC CERF ECMW GFDL INGV KNRM KORM LODY MAXP METF NCEP SINT SUT1 UHT1 UKMO EM SSE BLUE 1987 −0.01 0.5 0.05 0.22 0.38 0.35 0 0.1 0.41 0.21 0.03 0.08 0.12 0.24 0.43 −0.02 0.42 0.45 0.47 1988 −0.05 0.08 −0.21 0.34 0.06 0.08 0.27 0.05 0.01 −0.03 −0.18 0.17 0.04 −0.33 −0.14 0.42 0.13 −0.25 0.24 1989 0.49 0.04 −0.18 0.22 −0.02 0 0.13 0.02 0.06 0.06 −0.18 0.13 −0.15 −0.06 0.01 −0.03 0.16 0.37 0.21 1990 −0.1 −0.15 0.21 −0.06 0.16 −0.08 0.26 0.03 −0.07 −0.04 0.21 0.26 0.01 −0.08 −0.09 0.28 0.12 0.38 0.27 1991 0.22 −0.1 −0.29 0.29 0.23 −0.03 0.27 0.32 0.03 0.29 0.32 0.46 −0.12 −0.14 −0.12 0.11 0.45 0.48 0.53 1992 0.18 0.07 0.31 0.33 0.34 0.15 0.34 0.45 0.25 −0.2 −0.42 −0.06 0.39 0.4 −0.31 0.51 0.47 −0.15 0.5 1993 −0.1 0.02 0.14 −0.23 −0.19 −0.04 0.03 0.11 −0.07 −0.05 0.13 0.28 0 0.39 0.22 −0.1 0.11 0.09 0.16 1994 −0.09 0.21 −0.28 −0.18 −0.02 −0.03 0.23 0.27 −0.28 0.21 0.12 0.23 −0.12 −0.08 0.02 0.45 0.36 0.52 0.47 1995 0.11 0.19 0.47 0.49 0.29 −0.32 0.12 −0.27 0.37 −0.25 0.34 0.25 0.23 0.2 −0.14 0.42 0.51 0.17 0.59 1996 0.41 −0.1 0.02 0.03 0.05 −0.14 0.02 −0.09 −0.17 −0.02 0.11 0.12 0.39 0.06 0.2 0.12 0.1 −0.09 0.13 1997 0.14 −0.14 0.31 −0.35 −0.08 −0.11 0.19 0.18 0.11 0.22 0 0.27 −0.16 0.22 0.03 0.13 0.04 0.29 0.13 1998 0.18 −0.04 0.04 0.22 0.22 −0.1 −0.31 0.14 −0.02 0.12 0.23 0.51 0.21 −0.03 0.1 0.25 0.21 0.33 0.36 1999 −0.16 −0.15 0.18 −0.22 −0.24 −0.37 −0.17 0.17 −0.2 0.12 −0.12 0.03 −0.33 −0.31 −0.26 −0.01 −0.28 −0.13 −0.16 2000 −0.04 0.22 −0.22 −0.03 0.01 0.21 0.22 0.29 0.38 0.22 0.02 0.34 0.06 0.05 0.2 0.19 0.49 0.39 0.6 2001 0.22 −0.17 −0.33 0.36 0.06 0.24 0.18 0.41 0.18 0.58 −0.23 0.17 −0.06 0.01 −0.1 0.13 0.31 0.19 0.39 8 Advances in Meteorology Table 3: RMSE (mm/day) for all the member models, EM, superensemble scheme, a nd BLURE BLUE for JJAS seasonal rainfall anomaly predictions. Smallest value of RMSE in each year is italicized. ANRM BMRC CERF ECMW GFDL INGV KNRM KORM LODY MAXP METF NCEP SINT SUT1 UHT1 UKMO EM SSE BLUE 1987 3.13 2.6 2.55 2.57 2.56 2.5 3.16 2.61 2.46 2.38 2.69 2.58 2.64 2.36 2.36 3.11 2.48 2 2.43 1988 1.9 2.65 1.93 1.78 1.8 2.6 2.02 2.78 1.82 1.86 2.02 1.83 1.93 1.97 1.97 1.74 1.75 1.89 1.72 1989 1.41 2.31 1.72 1.52 1.65 2.23 2.08 1.97 1.67 1.55 1.66 1.59 1.67 1.69 1.69 2.06 1.54 1.5 1.53 1990 1.98 2.5 1.86 1.98 1.87 2.22 1.84 3.04 2.09 1.96 1.79 1.77 1.9 1.94 1.94 1.78 1.87 1.78 1.82 1991 1.92 2.11 2.16 1.83 1.77 2.48 1.87 2.4 2.05 1.72 1.83 1.64 2.31 2 2 1.97 1.89 1.65 1.85 1992 1.64 1.73 1.56 1.47 1.49 1.75 1.43 1.41 1.6 1.61 1.7 1.7 1.39 1.41 1.41 1.39 1.38 1.85 1.36 1993 1.59 1.96 1.42 1.9 1.53 1.43 2.14 1.87 1.67 1.51 1.43 1.39 1.46 1.34 1.34 1.72 1.41 1.48 1.41 1994 2.83 2.99 2.94 2.97 2.95 2.77 2.7 2.85 2.9 2.97 2.94 2.65 3.02 2.97 2.97 2.48 2.77 2.3 2.72 1995 1.6 1.82 1.41 1.39 1.48 1.91 2.22 2.92 1.48 1.73 1.5 1.48 1.52 1.66 1.66 1.5 1.55 1.57 1.48 1996 1.58 2.24 1.8 1.72 1.81 2.13 1.78 2.56 1.89 1.8 1.77 1.89 1.64 1.91 1.91 2.02 1.75 2.05 1.73 1997 1.93 2.56 2 2.54 2.69 3.82 2 2.1 2.26 1.91 2.2 1.9 2.88 1.88 1.88 2.28 2.14 1.87 2.13 1998 2.6 3.01 2.83 2.69 2.84 3.08 2.96 2.72 2.9 2.63 2.6 2.49 2.66 2.73 2.73 3.1 2.65 2.66 2.6 1999 2.74 3.12 2.58 2.97 2.87 3.39 2.93 3.06 2.99 2.57 2.64 3.04 2.88 2.96 2.96 3.23 2.78 2.79 2.75 2000 1.8 1.96 1.72 1.73 1.82 2.3 1.79 1.76 1.52 1.64 1.76 1.55 1.78 1.77 1.77 1.81 1.55 1.61 1.53 2001 2.01 2.79 2.32 1.97 2.28 1.92 2.04 2.05 2.09 1.82 2.2 2.02 2.01 1.99 1.99 2.29 1.93 1.96 1.92 Advances in Meteorology 9 Table 4: Contingency table for year 1987 corresponding to the rainfall anomaly threshold of −0.1 mm/day for BLUE. 2500 Prediction Yes No Total Observation a b Yes 2894 1913 4807 c d No 1690 8543 10233 Total 4584 10456 15040 a b c d Hits. Misses. False alarm. Correct negatives. ECMW BLUE the Indian region. Next in case of BIAS (Figure 4(b)) BLUE EM shows least BIAS for positive thresholds while superensemble SSE scheme shows least BIAS for negative thresholds. BLUE has Figure 3: 𝜒 values for measuring association between observed the range of BIAS from 0.1 to 1.67 while superensemble rainfall and rainfall over Indian region (69–92E, 8–30N) from scheme has 0.1 to 0.4. ECMWF and EM are not performing ECMWF, EM, superensemble scheme, and BLUE for JJAS seasonal well with BIAS as compared to multimodel schemes. Some of rainfall anomaly predictions for threshold of −1 mm/day. the incompatibility has been discussed regarding ETS while scoring about extreme events [40]. Heidke Skill Score (HSS) has been presented for various It is interesting to note that BLUE is almost following the EM. years (Figure 5) including flood and drought years of Indian Furthermore, in case of year 1995 all the models have lowest summer monsoon. BLUE is doing better for 1995 and 1998, RMSE andhighestcorrelation, whilefor theyear1999 RMSE while superensemble scheme does better for 1988 and 1989. reached the highest value and correlation became lowest. Still, their response becomes mixed if we pin down their In this study, we also used measure of association of superiorities for all the thresholds. For example, in 1995, attributes to judge the extent of closeness between a model BLUE does well with ETS for the threshold range of −3to1.5 forecast and observed rainfall. Qualitative variables whose but skill degraded for 1.5 to 3. In case of 1988 superensemble outcomes are expressed as “yes” or “no” or by some cate- scheme does good for −0.5to3butstumbledfor −3to −1 gories, namely, “Good” or “Bad,” are referred to as attributes thresholds. Overall, these two multimodel schemes come out in the statistics literature. whether two attributes are associ- finer and doing better for all the threshold and years except ated or not is tested using the chi-square test of independence. for few. Hogan et al. [40] recommended HSS over ETS to Figure 3 displays the chi-square values for comparing express skill from multimodels. In Table 4, we explained the association between observed and different model forecasts numbers of hits, misses, false alarm, and correct negatives for for domain under study. It is based on every grid point over year 1987. It is same as Table 5, but for a year with values. India. The target region is India (69–92E, 8–30N). BLUE Rainfall over Indian region shows high rainfall variability, is showing highest categorical association for 1996, 1997, due to large variations in orographic lands, vegetation cover, 2000, and 2001, while superensemble scheme shows highest and soil texture. Probabilistic forecasts are based on the categorical association for 1987, 1990, 1998, and 1999. Next yes/no proposition. Over a grid, for a threshold, this yes/no ECMWF shows highest categorical association for 1988, 1989, proposition decides the hits (both observation and model 1992, and 1994, while EM comes out with highest association show nonzero rainfall values), misses (where observation for 1991, 1993, and 1995. Both BLUE and superensemble shows nonzero while model shows zero rainfall values), scheme are doing well with respect to this measure. One and false alarm (where observation shows zero while model contingency table, Table 3, is provided for year 1987 for the shows nonzero rainfall values) as basic variables for the threshold of −0.1 rainfall anomalies for BLUE. This table has probabilistic forecasts. Figure 6 shows the ROC plots between a significance to calculate the skill scores for the categorical hit ratio and false ratio for JJAS seasonal rainfall anomalies, rainfall. ETS and BIAS were calculated for rainfall anomalies for the threshold of −3 to 3 mm/day (Figures 4(a) and 4(b)) forfouryears.Ifthe ROCcurve foramodelisfaraway for the Indian region (lon = 69.0, lon = 92.0E; lat = 8.0, lat from the 45-degree line that model performs better than = 30.0N). Interestingly, BLUE is commanding for negative others. eTh pink dotted line indicates exact matches of the threshold while superensemble scheme is commanding for observed and forecast cases, that is, ideal forecast cases. all positive rainfall thresholds for 15 years of period. BLUE For 1998 BLUE comes out as the best one while for 2000 had ETS range between 0 and 0.28, while superensemble superensemble comes out as the best. For the two remaining scheme had ETS range from 0.04 to 0.18. That indicates years 1987 and 1998 their responses are mixed. Acharya et BLUE has remarkable potential to predict droughts. An ETS al. [41] showed results for three categories of rainfall from of 0.3 is considered a good one in case of rainfall [38]. For multimodel schemes over Indian region. They found better the various categories of rainfall (light, moderate, and heavy skills of ROC for the wet and dry years as compared to normal rains) Dash et al. [39] get ETS values of 0.24 to 0.03 over monsoon years. Chi-square 2001 10 Advances in Meteorology 0.35 2.5 0.3 0.25 1.5 0.2 0.15 0.1 0.5 0.05 −3 −2.5 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2.5 3 −3 −2.5 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2.5 3 Threshold (mm/day) Threshold (mm/day) ECMW BLUE ECMW BLUE EM EM SSE SSE (a) (b) Figure 4: (a) ETS and (b) BIAS for ECMWF, EM, superensemble scheme, and BLUE for JJAS seasonal rainfall anomaly predictions for Indian region. 0.47 0.47 0.37 0.37 0.27 0.27 0.17 0.17 0.07 0.07 −0.03 −3 −2.5 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2.5 3 −0.03 −3 −2.5 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2.5 3 Threshold (mm/day) −0.13 Threshold (mm/day) ECMW BLUE ECMW BLUE EM EM SSE SSE 0.47 0.47 1995 1998 0.42 0.37 0.37 0.32 0.27 0.27 0.22 0.17 0.17 0.12 0.07 0.07 −0.03 0.02 −3 −2.5 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2.5 3 −0.03 −3 −2.5 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2.5 3 Threshold (mm/day) −0.13 Threshold (mm/day) ECMW BLUE ECMW BLUE EM EM SSE SSE Figure 5: Heidke Skill Score plots for ECMWF, EM, superensemble scheme, and BLUE for JJAS seasonal rainfall anomaly predictions for many years over Indian region. 5. Conclusions and Discussion APHRODTE. Year by year, the superiority of four models hasbeencitedbasedonchi-squarewhichindicatesthe All the results based on commonly used skill metrics are dependency of model on skill matrix. eTh maximum values performed on downscaled datasets for 15 years (1987–2001), of correlation coefficient obtained from the multimodel 16 member models, and observed rainfall datasets from schemes EM, SSE, and BLUE are −0.28 to 0.51, −0.16 to ETS Heidke Skill Score Heidke Skill Score Heidke Skill Score Heidke Skill Score BIAS Advances in Meteorology 11 Table 5 Model Yes No Total Observed Yes a (hits) b (misses) a + b (observed yes) No c (false alarms) d (correct negatives) c + d (observed no) Total a +c(forecastyes) b +d(forecastno) 𝑛 =a+b+c+d(total) ROC curve ROC curve 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 1987 1990 0.3 0.3 0.2 0.2 0.1 0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 FAR ratio FAR ratio ECMW BLUE ECMW BLUE EM EM SSE SSE ROC curve ROC curve 1 1 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 1998 2000 2000 0.3 0.3 0.2 0.2 0.1 0.1 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 FAR ratio FAR ratio ECMW BLUE ECMW BLUE EM EM SSE SSE Figure 6: ROC plots for ECMWF, EM, superensemble scheme, and BLUE for JJAS seasonal rainfall anomaly predictions over Indian region. 0.59, and −0.25 to 0.52. On the other hand, ECMWF has the 1.36 to 2.75. Categorical association attained by ECMWF is range from −0.35 to 0.49 only. Clearly the improvement is 0.39,EMis0.42, SSEis0.48,andBLUEis0.45. In case not much, but for rainfall anomalies, surely it is appreciable. of ETS, ECMWF attained 0.27. The ETS for EM is 0.28, While, in case of RMSE, EM has a range from 1.41 to 2.78, SSE SSE is 0.18, and BLUE is 0.29. BIAS is reduced to 0.35 in hasthe rangefrom1.48to2.79and BLUE hasthe rangefrom case of ECMWF, 0.15 for EM, and 0.05 for SSE and BLUE. Hit score ratio Hit score ratio Hit score ratio Hit score ratio 12 Advances in Meteorology OverallSSEandBLUEimprovedonbestmodel(ECMWF) We consider andensemblemean(EM)onthe metricsskillusedinthis study for the Indian region. Sometime BLUE does better than (A.5) 𝑇= ∑ 𝛼 𝑇 𝑖 𝑖 superensemble scheme and sometime superensemble scheme 𝑖=1 does better than BLUE method. It is worth mentioning that the BLUE methodology has the simplicity in computing as the estimator of 𝜇 such that model weights for constructing the multimodel forecast. So, 𝐸 𝑇 =𝜇. this method can be explored more for other events as well. ( ) (A.6) One of the challenges is the prediction of rainfall anomalies Clearly, 𝑇 will be unbiased for 𝜇 if (e.g., extreme events of floods). Multiple regression schemescan beappliedtoimprove therainfallforecasts,astheperformanceoftheGCMare ∑ 𝛼 =1. (A.7) very poor for rainfall forecasts. In the multiple regressions, 𝑖=1 one can use winds, temperature, geopotential height, and specific humidity to predict rainfall. Some of the studies have Now, shown the use of other variable, for example, SST and OLR for downscaling the rainfall. Somehow, linear regression is a 2 2 var(𝑇 ) = ∑ 𝛼 𝜎 . (A.8) 𝑖 𝑖 crude method while canonical correlation analysis and step- 𝑖=1 wise pattern projection methods are considered an advanced one for downscaling. Furthermore, other sophisticated meth- Since 𝑇 ’s are independent, we are in search of 𝛼 ’s such that 𝑖 𝑖 ods like statistical-dynamical Kalman Filter method [42], var(𝑇) is minimum. hyperensemble method [43], and Artificial Neural Network Den fi e method can be used for multimodel ensemble prediction of rainfall in our next study. 𝑤= var (𝑇 )−2𝜑( ∑ 𝛼 −1), (A.9) 𝑖=1 Appendix where 𝜑 is Lagrange’s multiplier. The data are expressed in 2 × 2contingency tableasshownin Taking partial derivative of 𝑤 with respect to 𝛼 and Table 5. equating it to zero for minimizing 𝑤 subject to condition us Th the Chi-square statistics is given by (A.7) we have 𝑛 (ad − bc) (A.1) 𝜒 = . 𝜑= . (A.10) (a + c)(b + d)(a + b)(c + d) ∑ 1/𝜎 𝑖=1 𝑖 This follows chi-square distribution with 1 degree of freedom This leads to [44]. Comparing the two contingency tables for two different 1/𝜎 models the chi-square value gives the guidance about the 𝛼 = . (A.11) ∑ 1/𝜎 strength of the relationship between observed and model 𝑖=1 forecast values. eTh larger chi-square value indicates a We propose estimating 𝜎 from the past performances of the stronger relationship. Here we are getting different categories 𝑖 model 𝑖 and using 𝛼 to n fi d out 𝑇,the multimodel output corresponding to different threshold values of rainfall anoma- comprising 𝑘 models. 𝑇 wouldbeanoptimum multimodel lies. output [29]. If 𝑇 ,𝑇 ,...,𝑇 are 𝑘 unbiased independent estimators of 1 2 𝑘 2 𝑘 the parameter 𝜇 and variances 𝜎 then𝑇= ∑ 𝛼 𝑇 will be 𝑖 𝑖=1 𝑖 𝑖 theBestLinearUnbiasedEstimator of 𝜇,if BIAS =[ ∑ (𝑓 −𝑂 )] 𝑚 𝑚 𝑚=1 1/𝜎 𝛼 = , 𝑖 = 1,2,...,𝑘 (A.12) (A.2) 𝐻− 𝑂/𝑀 𝑖 ( ( )) ETS = ∑ (1/𝜎 ) 𝑖=1 𝑖 𝐹+𝑂−𝐻− ( (𝑂/𝑀 )) Proof. 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Performance of Multimodel Schemes for Seasonal Precipitation over Indian Region

Kumar, Vinay; Ghosh, Tirthankar
Advances in Meteorology , Volume 2018: 14 – Jan 3, 2018
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Copyright © 2018 Vinay Kumar and Tirthankar Ghosh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Hindawi Advances in Meteorology Volume 2018, Article ID 5874270, 14 pages https://doi.org/10.1155/2018/5874270 Research Article Performance of Multimodel Schemes for Seasonal Precipitation over Indian Region 1 2 Vinay Kumar and Tirthankar Ghosh Department of Physical and Environmental Sciences, Texas A&M University, Corpus Christi, TX 78412, USA Department of Statistics, Visva Bharati University, Bolpur Santiniketan, West Bengal 731235, India Correspondence should be addressed to Vinay Kumar; vinay.kumar@tamucc.edu Received 5 July 2017; Revised 15 October 2017; Accepted 8 November 2017; Published 3 January 2018 Academic Editor: Takashi Mochizuki Copyright © 2018 Vinay Kumar and Tirthankar Ghosh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This study uses downscaled rainfall datasets from 16 coupled climate models at high resolution of 25 km from 1987 to 2001. The multimodel superensemble scheme is widely tested for rainfall forecast over mid-latitude, subtropical, and, especially, various regions of the monsoonal belt. A well-known statistical estimation theoretic approach, namely, Best Linear Unbiased Estimator (BLUE), is examined on 16 member models. eTh results are compared with superensemble methodology based on various skill scores. Results show that BLUE is providing promising forecasts. As far as comparative studies are concerned BLUE and superensemble schemes compete and show their importance from normal years to extreme rainfall years. BLUE methodology is capable of predicting draughts very well compared with other multimodel schemes. One basic advantage of BLUE is computationally less expensive than superensemble scheme. These statistical schemes like downscaling, BLUE, and superensemble can improve rainfall forecasts further, if a dense rain gauge data is provided. 1. Introduction models and postprocessing statistical techniques in pre- dicting seasonal rainfall [1, 10]. The successes of statistical Several multimodel schemes are being listed in the literature methods depend on the long-time series of data for training of the climate and weather for rainfall prediction. eTh se period to calculate better-quality coefficients. If the training commonly used multimodel rainfall forecast schemes are datasets consist in many new information pieces on flood ensemble scheme, biased removed ensemble mean, clustering and drought events, then their obtained coefficients do better techniques, and superensemble method. The superensemble in forecast period. On the other hand, dynamical models scheme from Florida State University (FSU) is being tested have problems with their parametrization schemes and some since 1999 by various researchers [1–4]. Nowadays a good simplification of various schemes used in them. In these quality of rainfall dataset is available from satellites (e.g., models, systematic error grows with time. Worldwide more Global Precipitation Measurement, GPM/Tropical Rainfall than 20 climate prediction centers are engaged in the monthly Measuring Mission, TRMM), reanalysis (e.g., MERRA), and to seasonal predation with their home grown global models. rain gauge (e.g., APHRODITE) at high resolution. Somehow Multimodel schemes were suggested to bring consensus climate global models still have a coarse resolution of 100 km. forecast for a season [11–13]. Such gap of resolution calls for downscaling of the climate India Meteorological Department has used statistical global models. All the acronyms are mentioned in Acronyms models and modified them over a period to provide an forModels, Institutes,orOtherNames. improved Indian summer monsoon rainfall prediction [14– Statistical downscaling procedures have been used to improve the horizontal resolution of the member models [4– 17]. Some of the limitations of statistical and dynamical 9]. By doing so, the regional details of the dry and wet patches models used for Indian rainfall prediction are noted by Nan- of rainfall bulge out. er Th e are limitations of dynamical jundiah [18] and Gadgil et al. [10]. Various new multimodel 2 Advances in Meteorology schemes were tested on the Indian region for rainfall forecast of detection)andfalsepositiverate(hereFARratioorFalse [19–21]. On examination of 5-multimodel schemes they Alarm Ratio) for the forecasts. A curve closer towards the realized that the accuracy of the rainfall forecasts can be 𝑦-axis indicates more accurate test. us, Th the area under the increased over Indian region. Furthermore, they worked curve is the measure of the ROC score. upon probabilistic prediction of the Indian region and found the probabilistic forecasts are superior to multimodel 2. Dataset Used ensemble mean. This group has numerous research works on the prediction of rainfall using various techniques. In mid- Downscaled rainfall datasets (for 15 years, 1987–2001) from latitude,thesealevelpressure,wind,andrainfallhaveastrong sixteen coupled models [33] are included in this study. All tieand thuscanbeusedinmultipleregressionmethodto the models were integrated from May 1 to September 30 for downscale the rainfall. In a recent study, canonical correlation the summer season (JJAS). Here we analyzed only summer analysis is used to downscale rainfall over Indian region season of monsoon (June to September) datasets in this study. and other [22, 23]. They found some improvements in the Table 1 contains some details for atmospheric and oceanic forecastsskillsoversomepartsof northeastandpeninsular components of each model, namely, model name, model India. eTh re is no strong relationship between rainfall and resolution, initial conditions for simulation, and numbers of other variables like sea surface temperature, winds, and ensemble predictions. The ensemble mean forecasts from a outgoing long wave radiation over tropical region. In another single model’s several runs are also included in this study. study using stepwise regression, Salvi et al. [24] showed that These model forecasts are cast at a common horizontal their method could capture the rainfall over mountainous resolution of 2.5-degree latitude by 2.5-degree longitude for regions of India. eTh y evaluated the future projection of the construction of multimodel ensembles. APHRODITE rainfall over Indian region. eTh group is engaged in the Rainfall [34] dataset was used as observed rainfall. This data various kinds of downscaling methods for rainfall over Indian is based on thousands of rain gauges over a large region of region. monsoon Asia. The spatial resolution of the datasets is 0.25 In this study, we used liner regression method to down- × 0.25 lat-lon grid while the time interval of data is daily to scale the rainfall over the Indian region. It is known that, even monthly. To interpolate model’s data from coarse resolution in hindcast mode, none of the models provide correct forecast to fine resolution of observational dataset, we used 4-point forarangeofyears.Perhaps,thatwas oneofthenecessitiesof Bessel interpolation method. the multimodel based prediction techniques. In a better way postprocessing datasets and statistical techniques can work 3. Downscaling and Multimodel Schemes together to ren fi e the forecast further. Answers on various issues, for example, minimum number of member models Linerregressionschemeisapplied fordownscaling andto to construct superensemble, length of datasets, and other construct downscaled datasets from each member model sensitivity issues can be found in Kumar and Krishnamurti against APHRODITE Rainfall datasets. [25]. eTh rainfall product is being improved rfi st by down- Chakraborty and Krishnamurti [26] have shown the scaled methodology and then by superensemble method. improved rainfall forecasts with downscaling and without In some of the studies, the prediction of Indian summer downscaling from member models, ensemble mean, and monsoon rainfall is being improved by superensemble and superensemble scheme. They illustrated that the downscaled downscale method [25–28]. In the present study, we worked superensemble scheme shows higher correlation and reduced with rainfall anomalies and the skills were compared among RMSE over Indian summer monsoon rainfall. During mul- the best models (ECMWF model comes out best among 16 timodel ensemble, we considered entire duration of datasets suites of models for Indian region, Kumar and Krishnamurti of 15 years (15 years × 4 months = 60 values) of monthly [25]), ensemble mean (EM), and two multimodel schemes. rainfall. Next, we constructed multimodel schemes based on One of the important aspects here we tried to bring out is, downscaled datasets. It is shown that the data of 15 years how, accurately, can we forecast the extreme events? A new were sufficient to carry out the downscaling as the coefficients multimodel scheme, based on estimation theory, namely, Best stabilizeaeft r10yearsof datasets [25]. Linear Unbiased Estimator (BLUE), has been examined [29]. We believe that a data processing method improves the Furthermore, this study compares two operational schemes model datasets and adds some error as well. However, this which have been used in hurricane prediction in the Atlantic can be reduced in some situations. er Th e is a major difference basin. between the mathematical strategy for downscaling and for The present study illustrates performance of the best the construction of the multimodel superensemble scheme. model, ensemble mean, synthetic superensemble (SSE) tech- The former downscales each model separately with respect to nique,andBLUEschemeon16state-of-the-artcoupled the observed estimates, whereas the multimodel superensem- climate models for 15 summer seasons for the Indian region. ble calculates a single forecast considering forecasts from This paper deals with the application of multimodel statistical the member models all together. It performs a multiple methods. The skill scores used in this work are spatial linerregressiontoremovethe collective biasof thesuite correlation coefficient, RMSE, chi-square values for measure of models. eTh two methods are mutually independent. of association, ETS, BIAS, Heidke Skill Score [30], and ROC Over all, first downscaling helps in sprouting the regional (Relative Operating Characteristic [30, 31]). ROC is the plot features in the rainfall forecasts from each member model betweentruepositiverates(herehitsscoreratioorprobability and then superensemble scheme is improving the forecast Advances in Meteorology 3 Table 1: Details of sixteen global coupled models used in this study. Name Atmospheric component Oceanic component Ensemble size (institute) and reference Model Resolution Initial condition Model Resolution Initial condition FSUGSM with Coupled Arakawa-Schubert ECMWF with 5 longitude, AOR (FSU) assimilation ∘ ∘ convection and new T63L14 physical HOPE global 0.5 –5 latitude, 1 Cocke and LaRow (2000) relaxed to observed radiation initialization 17 levels SST (band model) FSUGSM with Kuo Coupled convection and new ECMWF with 5 longitude, assimilation ∘ ∘ KNR (FSU) radiation T63L14 physical HOPE global 0.5 –5 latitude, 1 relaxed to observed (emissivity-absorptivity initialization 17 levels SST model) FSUGSM with Kuo Coupled convection and old ECMWF with 5 longitude, assimilation ∘ ∘ KOR (FSU) radiation T63L14 physical HOPE global 0.5 –5 latitude, 1 relaxed to observed (emissivity-absorptivity initialization 17 levels SST model) ∘ ∘ CFS (NCEP) 1 × 1/3 , Ocean data GFS T62L64 CFS SST forecast MOM3 15 Saha et al. (2006) 40 levels assimilation From latest From ocean Bureau of Meteorology atmosphere and assimilation that Australian Community ∘ ∘ ∘ POAMA 1.5 (Australia) Research Center ocean conditions 2 × 0.5 –1.5 , was based on T47L17 Ocean Model 2 10 Zhong et al. (2005) (BMRC) Atmospheric From Global 31 levels optimum (ACOM2) model (BAM3) Atmospheric interpolation (OI) Sampling Program technique ECMWF 40 yr ∘ ∘ 2 × 2 , CERFACS (France) ARPEGE T63L31 Reanalysis OPA 8.2 Forced by ERA-40 9 31 levels (ERA-40) ∘ ∘ ∘ 1.4 × 0.3 –1.4 , ECMWF (Europe) IFS T95L40 ERA-40 HOPE-E Forced by ERA-40 9 29 levels 4 Advances in Meteorology Table 1: Continued. Name Atmospheric component Oceanic component Ensemble size (institute) and reference Model Resolution Initial condition Model Resolution Initial condition 2 (lon) × FRCGC (SINTEX-F) NCEP/DOE SST nudging ECHAM-4 T106L19 OPA 8.2 2 cos (lat), 9 Luo et al. (2005) Reanalysis-2 scheme 31 levels ∘ ∘ ∘ ∘ GFDL 2.5 × 2 ,34 NCEP/DOE 1 × 1/3 , Ocean data AM2.1 OM3.1 (MOM4) 10 Delworth et al. (2006) levels Reanalysis-2 50 levels assimilation ∘ ∘ ∘ 2 × 0.5 –1.5 , INGV (Italy) ECHAM-4 T42L19 AMIP type OPA 8.1 Forced by ERA-40 9 31 levels ∘ ∘ 2 × 2 , LODYC (France) IFS T95L40 ERA-40 OPA 8.2 Forced by ERA-40 9 31 levels Coupled run Coupled run ∘ ∘ ∘ MPI Open Model Interface 2.5 × 0.5 –2.5 , MPI (Germany) ECHAM-5 T42L19 relaxed to observed relaxed to observed 9 (MPI-OMI) 23 levels SST SST 182 × 152 GP, MetFr (France) ARPEGE T63L31 ERA-40 OPA 8.0 Forced by ERA-40 9 31 levels SNU (Seoul National ∘ ∘ NCEP/DOE 1 × 1/3 , SST nudging University) SNU T42L21 MOM2.2 6 Reanalysis-2 32 levels scheme Kug et al. (2007) Thermocline- ∘ ∘ UH (University of Hawaii) NCEP/DOE 2 × 1 , ECHAM4 T31L19 UH Ocean Depth 10 Fu and Wang [32] Reanalysis-2 2levels nudging GloSea OGCM Third ∘ ∘ 2.5 × 3.75 ,19 Hadley Center Coupled UKMO (United Kingdom) HadAM3 ERA-40 Forced by ERA-40 9 levels Ocean-Atmosphere GCM (HadCM3) based Advances in Meteorology 5 basedonmultimodel.Crossvalidationmethodisusedduring are shown in the first, second, third, fourth, and h rows, superensemble and BLUE methodology. In this method, a respectively. eTh rainfall anomalies from APHRODITE, year, which was forecasted, was not taken, while calculating ECMWF model, EM, superensemble scheme, and BLUE cap- the downscaling or superensemble weights. turedarangeofvariability from droughttofloodyearrainfall over Indian region. Year 1987 was considered as one of the 3.1. Downscaled Methodology. APHRODITE Rainfall [34] is worst droughts in the history of Indian summer monsoonal used to downscale the rainfall forecast from member models rainfall variability, which, remotely, had an influence from over the Indian region. El-Nino ˜ event in Eastern Pacific Ocean. The central Indian region was badly affected by very low rainfall while eastern 𝑅 =𝑎𝑅 +𝑏+𝜀, (1) obs mdl India received a good rainfall. Rainfall deficient over central India was simulated by most of the models, while the patches where 𝑅 and 𝑅 are the observed and interpolated model obs mdl of extreme rainfall were not captured by any one. Year 1991 forecasts of rainfall (at the same resolution), respectively; was affected by low rainfall over northern and northeastern 𝑎 and 𝑏 are regression coefficients known as the slope and India. Interestingly ECMWF captured it fully, as well as intercept of the least square tt fi ing; and 𝜀 is the error term. superensemble scheme, but EM and BLUE failed here. Year 1995 was witnessed with drought over southcentral India 𝑅 =𝑎𝑅 +𝑏, (2) dscl mdl while flood kinds of situations prevailed over northern India. where 𝑅 is the downscaled rainfall forecast of the model; ECMWF model was best to simulate the rainfall variability dscl over the Indian region, but it failed to simulate the rainfall here 𝑎 and 𝑏 are calculated using (2) at each grid point and over the eastern parts of India. SSE tried to simulate the separatelyforevery monthoftheyear.Weleft outtheyear to be downscaled from the calculation to calculate 𝑎 and 𝑏 rainfall variability but missed deficient rainfall patches over central India. Some of the patches of dry region over Odisha following the method of cross validation. There are many more downscaling methods, for example, canonical analysis (20.95N, 85.05E) were remarkably captured. It is to be noted and stepwise pattern projection. eTh linear downscaling that BLUE did better than other models in case of year 2000, which was almost a monsoon drought (rainfall was −9% of methods perform well as compared to other methods [35]. We choose a linear downscaling method here. the climatological normal) over Indian region. Tables 2 and 3 show the year by year spatial correlation and RMSE numbers 3.2. Synthetic Superensemble Technique. The superensemble for all the member models, EM, superensemble scheme, and methodology [1, 36] produces a single forecast based on BLUE.FromTables2and3,wefound thatthecorrelation multimodel forecasts. Multimodel superensemble forecasts varies from −0.31 to 0.59 for all the models. The ranges of based on downscaled datasets from member models were correlation coefficients are varying from negative to positive constructed as well [37]. We expressed that as follows: values which is why we cannot talk about signicfi ance of the correlations. For some of the years (e.g., 1991, 1995) the mdl correlation has significance of 0.02 (two-tailed probabilities). (3) 𝑆= 𝑂+ ∑ 𝑤 (𝐹 − 𝐹 ), 𝑖 𝑖 𝑖 It may be noted that the highest correlation for a year 𝑖=1 varies from model to model, yet multimodel schemes (BLUE and superensemble) perform better than any member model where 𝑆 is the superensemble prediction, 𝑂 is the observed andEM. We observethatfor theyear1999 none ofthe time mean (climatology),𝑤 are the weights for the individual models and schemes has a positive correlation except CERF, models 𝑖, 𝐹 and 𝐹 are the forecast and forecast mean for 𝑖 𝑖 KORAM, MAXP, and NCEP. Table 2 has the RMSE range amodel 𝑖 for training period, and 𝑁 is the number of mdl from 1.34 to 3.82. Here multimodel schemes tried to minimize models. Here weights are obtained by minimizing error using the RMSE but the margin between them and member models least square method. The sum of the weights needs not be one are not so much. It may be mentioned that rainfall variability and they vary from negative values to positive values. over Sri Lanka was very well captured by superensemble (correlation coecffi ient (CC) = 0.44). eTh skills of rainfall 3.3. BLUE Technique. In this study, we introduce another variability from year to year are explained in Figures 2(a) multimodel construction technique based on estimation and 2(b) in terms of spatial correlation coefficient and RMSE. theory. Individual model is downscaled to sprout the regional BLUE and EM keep their spatial correlation coefficient features of the rainfall. Next, superensemble scheme and positive for most of the time except for 1999. In Figure 2, BLUE acted on multimodels to remove the model biases. In we considered the target region slightly smaller than the case of BLUE the coefficients are inversely proportional to the bigger region displayed in Figure 1, because many of the errors of the models and the sum of coefficients is one. The northern regions especially north of 30N are rain gauges methodology is described in the Appendix. sparse. Chakraborty and Krishnamurti [38] found the neg- ative anomaly correlation for year 1999 for a bigger monsoon 4. The Spatial Variability of Rainfall region.IncaseofECMWFandsuperensembleschemespatial Spatial patterns of rainfall anomalies for 1987, 1991, 1995, correlation is not higher for all years. It is varying from and 2000 are being shown in Figure 1. Rainfall anomalies positive to negative from 0.5 to −0.24. Figure 2(b) shows RMSE, which is lowest in case of BLUE. Here superensemble from APHRODITE Rainfall datasets, coupled model from ECMWF, ensemble mean, superensemble scheme, and BLUE scheme comes out distinct in many years with lowest RMSE. fift 6 Advances in Meteorology 1987 1991 1995 2000 35 ． 30 ． 25 ． 2.2 20 ． 15 ． 1.6 10 ． 35 ． 30 ． 1.1 25 ． 20 ． 0.7 15 ． 10 ． 0.4 35 ． 30 ． 25 ． 0.2 20 ． 15 ． −0.2 10 ． 35 ． −0.4 30 ． 25 ． ∘ −0.7 20 ． 15 ． −1.1 10 ． 35 ． 30 ． −1.6 25 ． 20 ． −2.2 15 ． 10 ． ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ 70 ％ 80 ％90 ％ 70 ％ 80 ％90 ％ 70 ％ 80 ％90 ％ 70 ％ 80 ％90 ％ Figure 1: June to September rainfall anomalies (mm/day) for 1987, 1991, 1995, and 2000 from APHRODITE, ECMWF (abbreviated in caption as ECMW), EM, SE, and BLUE. A rectangular box (69–92E, 8–30) is shown in the first panel (top right corner). This is the target region of Figures 2 and 3. 2.5 0.7 0.6 0.5 0.4 0.3 1.5 0.2 0.1 0 1 −0.1 −0.2 −0.3 Year Year −0.4 ECMW BLUE ECMW BLUE EM EM SSE SSE (a) (b) Figure 2: (a) CC and (b) RMSE for ECMWF, EM, superensemble scheme, and BLUE for JJAS seasonal rainfall anomaly predictions. Area averaged over Indian region (69–92E, 8–30N). Correlation coeffieient BLUE SSE EM ECMW APHRODITE Root mean square error 2001 Advances in Meteorology 7 Table 2: CC for all the member models, EM, superensemble scheme, and BLUE for JJAS seasonal rainfall anomaly predictions. CC more than 0.5, statistica lly significant at 95% level, is italicized. ANRM BMRC CERF ECMW GFDL INGV KNRM KORM LODY MAXP METF NCEP SINT SUT1 UHT1 UKMO EM SSE BLUE 1987 −0.01 0.5 0.05 0.22 0.38 0.35 0 0.1 0.41 0.21 0.03 0.08 0.12 0.24 0.43 −0.02 0.42 0.45 0.47 1988 −0.05 0.08 −0.21 0.34 0.06 0.08 0.27 0.05 0.01 −0.03 −0.18 0.17 0.04 −0.33 −0.14 0.42 0.13 −0.25 0.24 1989 0.49 0.04 −0.18 0.22 −0.02 0 0.13 0.02 0.06 0.06 −0.18 0.13 −0.15 −0.06 0.01 −0.03 0.16 0.37 0.21 1990 −0.1 −0.15 0.21 −0.06 0.16 −0.08 0.26 0.03 −0.07 −0.04 0.21 0.26 0.01 −0.08 −0.09 0.28 0.12 0.38 0.27 1991 0.22 −0.1 −0.29 0.29 0.23 −0.03 0.27 0.32 0.03 0.29 0.32 0.46 −0.12 −0.14 −0.12 0.11 0.45 0.48 0.53 1992 0.18 0.07 0.31 0.33 0.34 0.15 0.34 0.45 0.25 −0.2 −0.42 −0.06 0.39 0.4 −0.31 0.51 0.47 −0.15 0.5 1993 −0.1 0.02 0.14 −0.23 −0.19 −0.04 0.03 0.11 −0.07 −0.05 0.13 0.28 0 0.39 0.22 −0.1 0.11 0.09 0.16 1994 −0.09 0.21 −0.28 −0.18 −0.02 −0.03 0.23 0.27 −0.28 0.21 0.12 0.23 −0.12 −0.08 0.02 0.45 0.36 0.52 0.47 1995 0.11 0.19 0.47 0.49 0.29 −0.32 0.12 −0.27 0.37 −0.25 0.34 0.25 0.23 0.2 −0.14 0.42 0.51 0.17 0.59 1996 0.41 −0.1 0.02 0.03 0.05 −0.14 0.02 −0.09 −0.17 −0.02 0.11 0.12 0.39 0.06 0.2 0.12 0.1 −0.09 0.13 1997 0.14 −0.14 0.31 −0.35 −0.08 −0.11 0.19 0.18 0.11 0.22 0 0.27 −0.16 0.22 0.03 0.13 0.04 0.29 0.13 1998 0.18 −0.04 0.04 0.22 0.22 −0.1 −0.31 0.14 −0.02 0.12 0.23 0.51 0.21 −0.03 0.1 0.25 0.21 0.33 0.36 1999 −0.16 −0.15 0.18 −0.22 −0.24 −0.37 −0.17 0.17 −0.2 0.12 −0.12 0.03 −0.33 −0.31 −0.26 −0.01 −0.28 −0.13 −0.16 2000 −0.04 0.22 −0.22 −0.03 0.01 0.21 0.22 0.29 0.38 0.22 0.02 0.34 0.06 0.05 0.2 0.19 0.49 0.39 0.6 2001 0.22 −0.17 −0.33 0.36 0.06 0.24 0.18 0.41 0.18 0.58 −0.23 0.17 −0.06 0.01 −0.1 0.13 0.31 0.19 0.39 8 Advances in Meteorology Table 3: RMSE (mm/day) for all the member models, EM, superensemble scheme, a nd BLURE BLUE for JJAS seasonal rainfall anomaly predictions. Smallest value of RMSE in each year is italicized. ANRM BMRC CERF ECMW GFDL INGV KNRM KORM LODY MAXP METF NCEP SINT SUT1 UHT1 UKMO EM SSE BLUE 1987 3.13 2.6 2.55 2.57 2.56 2.5 3.16 2.61 2.46 2.38 2.69 2.58 2.64 2.36 2.36 3.11 2.48 2 2.43 1988 1.9 2.65 1.93 1.78 1.8 2.6 2.02 2.78 1.82 1.86 2.02 1.83 1.93 1.97 1.97 1.74 1.75 1.89 1.72 1989 1.41 2.31 1.72 1.52 1.65 2.23 2.08 1.97 1.67 1.55 1.66 1.59 1.67 1.69 1.69 2.06 1.54 1.5 1.53 1990 1.98 2.5 1.86 1.98 1.87 2.22 1.84 3.04 2.09 1.96 1.79 1.77 1.9 1.94 1.94 1.78 1.87 1.78 1.82 1991 1.92 2.11 2.16 1.83 1.77 2.48 1.87 2.4 2.05 1.72 1.83 1.64 2.31 2 2 1.97 1.89 1.65 1.85 1992 1.64 1.73 1.56 1.47 1.49 1.75 1.43 1.41 1.6 1.61 1.7 1.7 1.39 1.41 1.41 1.39 1.38 1.85 1.36 1993 1.59 1.96 1.42 1.9 1.53 1.43 2.14 1.87 1.67 1.51 1.43 1.39 1.46 1.34 1.34 1.72 1.41 1.48 1.41 1994 2.83 2.99 2.94 2.97 2.95 2.77 2.7 2.85 2.9 2.97 2.94 2.65 3.02 2.97 2.97 2.48 2.77 2.3 2.72 1995 1.6 1.82 1.41 1.39 1.48 1.91 2.22 2.92 1.48 1.73 1.5 1.48 1.52 1.66 1.66 1.5 1.55 1.57 1.48 1996 1.58 2.24 1.8 1.72 1.81 2.13 1.78 2.56 1.89 1.8 1.77 1.89 1.64 1.91 1.91 2.02 1.75 2.05 1.73 1997 1.93 2.56 2 2.54 2.69 3.82 2 2.1 2.26 1.91 2.2 1.9 2.88 1.88 1.88 2.28 2.14 1.87 2.13 1998 2.6 3.01 2.83 2.69 2.84 3.08 2.96 2.72 2.9 2.63 2.6 2.49 2.66 2.73 2.73 3.1 2.65 2.66 2.6 1999 2.74 3.12 2.58 2.97 2.87 3.39 2.93 3.06 2.99 2.57 2.64 3.04 2.88 2.96 2.96 3.23 2.78 2.79 2.75 2000 1.8 1.96 1.72 1.73 1.82 2.3 1.79 1.76 1.52 1.64 1.76 1.55 1.78 1.77 1.77 1.81 1.55 1.61 1.53 2001 2.01 2.79 2.32 1.97 2.28 1.92 2.04 2.05 2.09 1.82 2.2 2.02 2.01 1.99 1.99 2.29 1.93 1.96 1.92 Advances in Meteorology 9 Table 4: Contingency table for year 1987 corresponding to the rainfall anomaly threshold of −0.1 mm/day for BLUE. 2500 Prediction Yes No Total Observation a b Yes 2894 1913 4807 c d No 1690 8543 10233 Total 4584 10456 15040 a b c d Hits. Misses. False alarm. Correct negatives. ECMW BLUE the Indian region. Next in case of BIAS (Figure 4(b)) BLUE EM shows least BIAS for positive thresholds while superensemble SSE scheme shows least BIAS for negative thresholds. BLUE has Figure 3: 𝜒 values for measuring association between observed the range of BIAS from 0.1 to 1.67 while superensemble rainfall and rainfall over Indian region (69–92E, 8–30N) from scheme has 0.1 to 0.4. ECMWF and EM are not performing ECMWF, EM, superensemble scheme, and BLUE for JJAS seasonal well with BIAS as compared to multimodel schemes. Some of rainfall anomaly predictions for threshold of −1 mm/day. the incompatibility has been discussed regarding ETS while scoring about extreme events [40]. Heidke Skill Score (HSS) has been presented for various It is interesting to note that BLUE is almost following the EM. years (Figure 5) including flood and drought years of Indian Furthermore, in case of year 1995 all the models have lowest summer monsoon. BLUE is doing better for 1995 and 1998, RMSE andhighestcorrelation, whilefor theyear1999 RMSE while superensemble scheme does better for 1988 and 1989. reached the highest value and correlation became lowest. Still, their response becomes mixed if we pin down their In this study, we also used measure of association of superiorities for all the thresholds. For example, in 1995, attributes to judge the extent of closeness between a model BLUE does well with ETS for the threshold range of −3to1.5 forecast and observed rainfall. Qualitative variables whose but skill degraded for 1.5 to 3. In case of 1988 superensemble outcomes are expressed as “yes” or “no” or by some cate- scheme does good for −0.5to3butstumbledfor −3to −1 gories, namely, “Good” or “Bad,” are referred to as attributes thresholds. Overall, these two multimodel schemes come out in the statistics literature. whether two attributes are associ- finer and doing better for all the threshold and years except ated or not is tested using the chi-square test of independence. for few. Hogan et al. [40] recommended HSS over ETS to Figure 3 displays the chi-square values for comparing express skill from multimodels. In Table 4, we explained the association between observed and different model forecasts numbers of hits, misses, false alarm, and correct negatives for for domain under study. It is based on every grid point over year 1987. It is same as Table 5, but for a year with values. India. The target region is India (69–92E, 8–30N). BLUE Rainfall over Indian region shows high rainfall variability, is showing highest categorical association for 1996, 1997, due to large variations in orographic lands, vegetation cover, 2000, and 2001, while superensemble scheme shows highest and soil texture. Probabilistic forecasts are based on the categorical association for 1987, 1990, 1998, and 1999. Next yes/no proposition. Over a grid, for a threshold, this yes/no ECMWF shows highest categorical association for 1988, 1989, proposition decides the hits (both observation and model 1992, and 1994, while EM comes out with highest association show nonzero rainfall values), misses (where observation for 1991, 1993, and 1995. Both BLUE and superensemble shows nonzero while model shows zero rainfall values), scheme are doing well with respect to this measure. One and false alarm (where observation shows zero while model contingency table, Table 3, is provided for year 1987 for the shows nonzero rainfall values) as basic variables for the threshold of −0.1 rainfall anomalies for BLUE. This table has probabilistic forecasts. Figure 6 shows the ROC plots between a significance to calculate the skill scores for the categorical hit ratio and false ratio for JJAS seasonal rainfall anomalies, rainfall. ETS and BIAS were calculated for rainfall anomalies for the threshold of −3 to 3 mm/day (Figures 4(a) and 4(b)) forfouryears.Ifthe ROCcurve foramodelisfaraway for the Indian region (lon = 69.0, lon = 92.0E; lat = 8.0, lat from the 45-degree line that model performs better than = 30.0N). Interestingly, BLUE is commanding for negative others. eTh pink dotted line indicates exact matches of the threshold while superensemble scheme is commanding for observed and forecast cases, that is, ideal forecast cases. all positive rainfall thresholds for 15 years of period. BLUE For 1998 BLUE comes out as the best one while for 2000 had ETS range between 0 and 0.28, while superensemble superensemble comes out as the best. For the two remaining scheme had ETS range from 0.04 to 0.18. That indicates years 1987 and 1998 their responses are mixed. Acharya et BLUE has remarkable potential to predict droughts. An ETS al. [41] showed results for three categories of rainfall from of 0.3 is considered a good one in case of rainfall [38]. For multimodel schemes over Indian region. They found better the various categories of rainfall (light, moderate, and heavy skills of ROC for the wet and dry years as compared to normal rains) Dash et al. [39] get ETS values of 0.24 to 0.03 over monsoon years. Chi-square 2001 10 Advances in Meteorology 0.35 2.5 0.3 0.25 1.5 0.2 0.15 0.1 0.5 0.05 −3 −2.5 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2.5 3 −3 −2.5 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2.5 3 Threshold (mm/day) Threshold (mm/day) ECMW BLUE ECMW BLUE EM EM SSE SSE (a) (b) Figure 4: (a) ETS and (b) BIAS for ECMWF, EM, superensemble scheme, and BLUE for JJAS seasonal rainfall anomaly predictions for Indian region. 0.47 0.47 0.37 0.37 0.27 0.27 0.17 0.17 0.07 0.07 −0.03 −3 −2.5 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2.5 3 −0.03 −3 −2.5 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2.5 3 Threshold (mm/day) −0.13 Threshold (mm/day) ECMW BLUE ECMW BLUE EM EM SSE SSE 0.47 0.47 1995 1998 0.42 0.37 0.37 0.32 0.27 0.27 0.22 0.17 0.17 0.12 0.07 0.07 −0.03 0.02 −3 −2.5 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2.5 3 −0.03 −3 −2.5 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2.5 3 Threshold (mm/day) −0.13 Threshold (mm/day) ECMW BLUE ECMW BLUE EM EM SSE SSE Figure 5: Heidke Skill Score plots for ECMWF, EM, superensemble scheme, and BLUE for JJAS seasonal rainfall anomaly predictions for many years over Indian region. 5. Conclusions and Discussion APHRODTE. Year by year, the superiority of four models hasbeencitedbasedonchi-squarewhichindicatesthe All the results based on commonly used skill metrics are dependency of model on skill matrix. eTh maximum values performed on downscaled datasets for 15 years (1987–2001), of correlation coefficient obtained from the multimodel 16 member models, and observed rainfall datasets from schemes EM, SSE, and BLUE are −0.28 to 0.51, −0.16 to ETS Heidke Skill Score Heidke Skill Score Heidke Skill Score Heidke Skill Score BIAS Advances in Meteorology 11 Table 5 Model Yes No Total Observed Yes a (hits) b (misses) a + b (observed yes) No c (false alarms) d (correct negatives) c + d (observed no) Total a +c(forecastyes) b +d(forecastno) 𝑛 =a+b+c+d(total) ROC curve ROC curve 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 1987 1990 0.3 0.3 0.2 0.2 0.1 0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 FAR ratio FAR ratio ECMW BLUE ECMW BLUE EM EM SSE SSE ROC curve ROC curve 1 1 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 1998 2000 2000 0.3 0.3 0.2 0.2 0.1 0.1 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 FAR ratio FAR ratio ECMW BLUE ECMW BLUE EM EM SSE SSE Figure 6: ROC plots for ECMWF, EM, superensemble scheme, and BLUE for JJAS seasonal rainfall anomaly predictions over Indian region. 0.59, and −0.25 to 0.52. On the other hand, ECMWF has the 1.36 to 2.75. Categorical association attained by ECMWF is range from −0.35 to 0.49 only. Clearly the improvement is 0.39,EMis0.42, SSEis0.48,andBLUEis0.45. In case not much, but for rainfall anomalies, surely it is appreciable. of ETS, ECMWF attained 0.27. The ETS for EM is 0.28, While, in case of RMSE, EM has a range from 1.41 to 2.78, SSE SSE is 0.18, and BLUE is 0.29. BIAS is reduced to 0.35 in hasthe rangefrom1.48to2.79and BLUE hasthe rangefrom case of ECMWF, 0.15 for EM, and 0.05 for SSE and BLUE. Hit score ratio Hit score ratio Hit score ratio Hit score ratio 12 Advances in Meteorology OverallSSEandBLUEimprovedonbestmodel(ECMWF) We consider andensemblemean(EM)onthe metricsskillusedinthis study for the Indian region. Sometime BLUE does better than (A.5) 𝑇= ∑ 𝛼 𝑇 𝑖 𝑖 superensemble scheme and sometime superensemble scheme 𝑖=1 does better than BLUE method. It is worth mentioning that the BLUE methodology has the simplicity in computing as the estimator of 𝜇 such that model weights for constructing the multimodel forecast. So, 𝐸 𝑇 =𝜇. this method can be explored more for other events as well. ( ) (A.6) One of the challenges is the prediction of rainfall anomalies Clearly, 𝑇 will be unbiased for 𝜇 if (e.g., extreme events of floods). Multiple regression schemescan beappliedtoimprove therainfallforecasts,astheperformanceoftheGCMare ∑ 𝛼 =1. (A.7) very poor for rainfall forecasts. In the multiple regressions, 𝑖=1 one can use winds, temperature, geopotential height, and specific humidity to predict rainfall. Some of the studies have Now, shown the use of other variable, for example, SST and OLR for downscaling the rainfall. Somehow, linear regression is a 2 2 var(𝑇 ) = ∑ 𝛼 𝜎 . (A.8) 𝑖 𝑖 crude method while canonical correlation analysis and step- 𝑖=1 wise pattern projection methods are considered an advanced one for downscaling. Furthermore, other sophisticated meth- Since 𝑇 ’s are independent, we are in search of 𝛼 ’s such that 𝑖 𝑖 ods like statistical-dynamical Kalman Filter method [42], var(𝑇) is minimum. hyperensemble method [43], and Artificial Neural Network Den fi e method can be used for multimodel ensemble prediction of rainfall in our next study. 𝑤= var (𝑇 )−2𝜑( ∑ 𝛼 −1), (A.9) 𝑖=1 Appendix where 𝜑 is Lagrange’s multiplier. The data are expressed in 2 × 2contingency tableasshownin Taking partial derivative of 𝑤 with respect to 𝛼 and Table 5. equating it to zero for minimizing 𝑤 subject to condition us Th the Chi-square statistics is given by (A.7) we have 𝑛 (ad − bc) (A.1) 𝜒 = . 𝜑= . (A.10) (a + c)(b + d)(a + b)(c + d) ∑ 1/𝜎 𝑖=1 𝑖 This follows chi-square distribution with 1 degree of freedom This leads to [44]. Comparing the two contingency tables for two different 1/𝜎 models the chi-square value gives the guidance about the 𝛼 = . (A.11) ∑ 1/𝜎 strength of the relationship between observed and model 𝑖=1 forecast values. eTh larger chi-square value indicates a We propose estimating 𝜎 from the past performances of the stronger relationship. Here we are getting different categories 𝑖 model 𝑖 and using 𝛼 to n fi d out 𝑇,the multimodel output corresponding to different threshold values of rainfall anoma- comprising 𝑘 models. 𝑇 wouldbeanoptimum multimodel lies. output [29]. If 𝑇 ,𝑇 ,...,𝑇 are 𝑘 unbiased independent estimators of 1 2 𝑘 2 𝑘 the parameter 𝜇 and variances 𝜎 then𝑇= ∑ 𝛼 𝑇 will be 𝑖 𝑖=1 𝑖 𝑖 theBestLinearUnbiasedEstimator of 𝜇,if BIAS =[ ∑ (𝑓 −𝑂 )] 𝑚 𝑚 𝑚=1 1/𝜎 𝛼 = , 𝑖 = 1,2,...,𝑘 (A.12) (A.2) 𝐻− 𝑂/𝑀 𝑖 ( ( )) ETS = ∑ (1/𝜎 ) 𝑖=1 𝑖 𝐹+𝑂−𝐻− ( (𝑂/𝑀 )) Proof. 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