Skill of monthly rainfall forecasts over India using multi-model ensemble schemes

Transcription

1 INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 32: (2012) Published online 7 April 2011 in Wiley Online Library (wileyonlinelibrary.com) DOI: /joc.2334 Skill of monthly rainfall forecasts over India using multi-model ensemble schemes Sarat C. Kar, a * Nachiketa Acharya, b U. C. Mohanty b and Makarand A. Kulkarni b a National Centre for Medium Range Weather Forecasting, A-50, Sector-62, Noida, India b Centre for Atmospheric Sciences, IIT, New Delhi, India ABSTRACT: Rainfall in the month of July in India is decided by large-scale monsoon pattern in seasonal to interannual timescales as well as intraseasonal oscillations. India receives maximum rainfall during July and August. Global dynamic models (either atmosphere only or coupled models) have varying skills in predicting the monthly rainfall over India during July. Multi-model ensemble (MME) methods have been utilized to evaluate the skills of five global model predictions for The objective has been to develop a prediction system to be used in real time to derive the mean of the forecast distribution of monthly rainfall. It has been found that the weighted multi-model ensemble (MME) schemes have higher skill in predicting July rainfall compared to individual models. Through the MME methods, skill of rainfall predictions improved significantly over eastern parts of India. However, there is a region over India where none of the models or the MME scheme has any useful skill. Similarly, there are few typical years in which the mean distribution of July rainfall cannot be predicted with higher skill using the available statistical post-processing methods. A simple MME probabilistic scheme has been utilized to show that skill of probabilistic predictions improved when the representation of mean of forecast distribution has better skill. Copyright 2011 Royal Meteorological Society KEY WORDS monthly; rainfall; skill; forecast; distribution; MME Received 6 March 2010; Revised 7 September 2010; Accepted 7 March Introduction India receives maximum rainfall during July and August of the Indian summer monsoon season. Rainfall in July over India is crucially important for the agricultural crop production in India, because in this month, the rice crops over most of the rainfed cultivated land need large amounts of water for growth. Deficit of rainfall in July not only brings down the total seasonal rainfall over India during monsoon season, it also affects the total crop yield. After onset of the Indian summer monsoon over Kerala by the end of May or early June, the monsoon system progresses northward to cover most of the country by the end of June. Rainfall in the month of July in India is decided by large-scale monsoon variability in seasonal to interannual timescales as well as due to intraseasonal oscillations. The equatorial intraseasonal oscillations (ISOs) in its active phase create a conducive environment for enhanced convective activity when these are over the Indian Ocean. These convective regions then move northward over to the Indian landmass and affect the monsoon activity over India. Monsoon lows and depressions form over the Bay of Bengal and move towards northwest and bring a lot of rainfall activity along the monsoon trough region. Therefore, total monthly rainfall over India in the month of July varies from one * Correspondence to: Sarat C. Kar, NCMRWF, A-50, Sector-62, Noida, India. sckar@ncmrwf.gov.in year to another due to large-scale strength of the monsoon in a given year as well as due to the variability of the monsoon in intraseasonal timescales. India Meteorological Department (IMD) is responsible for providing operational seasonal and monthly monsoon predictions to the public. In addition, there are several other government agencies which work on various aspects of monsoon prediction and provide valuable input to the Government and to the public as well. Extensive studies on monsoon variability of different components of the Indian monsoon have led to better understanding of physical mechanisms responsible for this variability of the monsoon rainfall. Since the pioneering work of Sir Gilbert Walker (Walker, 1924), influence of the El Nino- Southern Oscillation (ENSO) on the Indian monsoon rainfall has been investigated (Sikka, 1980; Rasmusson and Carpenter, 1983; Shukla, 1987). The ENSO-monsoon interaction is considered to be primarily through the change in the equatorial Walker circulation influencing the regional Hadley circulation associated with the Asian monsoon (Goswami, 1998; Webster et al., 1998). While statistical models, e.g. Rajeevan et al. (2006a) and Sahai et al. (2008), offer reasonable skill in predicting Indian monsoon rainfall, they fail to predict the extreme monsoons and their skill is limited in providing the evolution of the Indian monsoon in temporal and spatial scales. Xavier and Goswami (2007) have developed an OLRbased model to predict the monsoon activity (active and dry spells) over India up to three weeks. Copyright 2011 Royal Meteorological Society

2 1272 S. C. KAR et al. Dynamical prediction of monsoon rainfall using stateof-the-art general circulation models (GCMs), especially, coupled GCMs, provide an alternative over the statistical models (Kang et al., 2004; Kang and Shukla, 2005). Dynamical prediction is limited by the nonlinearity of the monsoon system as well as systematic biases. Recently, dynamical models have been introduced for monsoon forecast (Krishnamurti et al., 2002; Palmer et al., 2004; Kumar et al., 2005; Wang et al., 2005; Krishnamurti et al., 2006, and Kar, 2007). Joseph et al. (2009) have analysed summer-time intraseasonal oscillations and seasonal Indian monsoon predictions in DEMETER-coupled models and found that the very long break (VLB) drought relationship is poorly captured by almost all the models. However, there has not been any systematic study towards development of a prediction system for the Indian monsoon rainfall in monthly timescale. With the availability of climate predictions produced by several dynamical models, multi-model ensemble (MME) forecasting has drawn some attention recently. Several approaches were attempted to combine MME forecasts to a single reliable forecast that carries higher skills when compared to the individual member models. These include the simple ensemble mean (Doblas-Reyes et al., 2000; Pavan and Doblas-Reyes 2000; Stephenson and Doblas-Reyes, 2000; Peng et al., 2002; Palmer et al., 2004), regression-improved ensemble mean (Peng et al., 2002; Kharin and Zwiers, 2003), bias-removed ensemble mean (Kharin and Zwiers, 2002). The multi-model super ensemble technique showed higher skill for short-range and seasonal forecasting compared with member model forecasts (Krishnamurti et al., 2000a, 2000b; Yun et al., 2003, 2005). Kar et al. (2006) have used several multimodel approaches to estimate the economic values of the forecasts and have found that the MME schemes improve the value of the forecasts over the single model. Kug et al. (2008) is a comprehensive paper describing skills of many MME methods for seasonal prediction. The paper also provides improvements on the existing methods and proposes a step-wise pattern projection scheme for MME. Performance of multi-model techniques for precipitation forecast over India have been examined in some recent studies (Chakraborty and Krishnamurti 2009; Krishnamurti et al., 2009). Skill of MME techniques for both deterministic and probabilistic forecasts have been reported in the literature. Compared to a single control forecast, an ensemble forecast not only provides a more accurate estimate of the first moment (the mean) of the probability density function (PDF) of future atmospheric states, but also provides higher-order-moment estimations such as the forecast error variance. However, no such studies exist for the monthly prediction of monsoon rainfall over India. The existing system of weather and climate forecasting in India is geared up for providing forecast services in the short- and medium-range time scales as well as the long-range time scale. However, there exists a gap in respect of forecast service in the intraseasonal time scales or monthly time scales. This deficiency in the Indian forecast system was noticeable during the severe drought episode of The drought of 2002 was unique in respect of its climate anomalies and impact on society, particularly in respect of the farm production. The deficiency of rainfall in July turned out to be the severest in recorded history since 1877 at 49%; the earlier record was 48% in Equally dramatic was the revival of monsoon in August. The drought of 2002 brought to the forefront an extreme situation of the adverse impacts of the active and break cycles of sub-seasonal time scales in the Indian summer monsoon. It was realized that advance knowledge of a break in monsoon of July and monsoon revival in August with a lead time of days could have minimized the losses significantly by appropriate corrective farm operations. The 2002 drought event thus threw up an urgent requirement for developing methodologies for providing advance weather and climate information in extended range (monthly) time scales on the one hand and, on the other, for refining and improving the approaches to anticipate and manage the weather-associated crop production losses by treating monsoon aberrations as an intrinsic risk to agriculture. This motivated the need to undertake a concerted research effort via a multi-institutional approach, for development and application of extended range forecast system (ERFS) for climate risk management in agriculture, in order to fill the existing gap in this area in the Indian weather and climate forecast system. The MME schemes such as in Yun et al. (2003, 2005) and Chakraborty and Krishnamurti (2009), aim at providing the mean of the prediction distribution required for probabilistic schemes. The ensemble spread or the error in predictions during the hindcast period can then be used to describe the PDF. The aim of the present work is to examine monthly forecasts of July rainfall from few GCMs whose predictions could be readily available, examine the strengths and weaknesses of these model predictions, and to develop a MME system for the mean forecast distribution of monthly rainfall over India using schemes such as those described in Yun et al. (2003, 2005). This study also aims at examining the skill of such MME schemes and attempts to answer if statistical post-processing schemes can provide improved monthly predictions over all the regions of India and for all the extreme cases. Section 2 of this paper briefly describes the models and data used for this study. Skill of individual models are presented in Section 3. In the same section, the MME schemes used in this study as well as results from these schemes are discussed. Section 4 has the conclusion and summary. 2. Models and datasets Hindcast runs (lead 0 for July of 1982 to 2004, forecasts prepared in early July) from five global models have been used in this study. These models were selected since they have a long series of hindcast runs. Also, the

3 SKILL OF MONTHLY RAINFALL FORECASTS OVER INDIA 1273 Table I. Resolution of the models and number of ensemble members of each model. Model Resolution Number of ensemble member NCEP-CFS (T62) ECHAM4p5 (ca sst) (T42) ECHAM5 (ca sst) (T42) Echam4p5-GML (T42) Echam4p5-MOM3 (anomaly coupled) (T42) models products are available in real time to the ERPS project on operational basis through a special understanding between the ERPS project in India and International Research Institute for Climate and Society (IRI), USA. Brief descriptions of the models used in the present study are provided here. The Climate Forecast System (CFS) of the National Centre for Environmental Prediction (NCEP) is a single-tier-coupled ocean atmosphere model (Saha et al., 2006) with a 15-member ensemble. ECHAM4.5 and ECHAM5 are two different version of European Centre-Hamburg Model and these are atmosphere-only GCMs developed at the Max Planck Institute for Meteorology, Roeckner et al., 1996, These models have been run by forcing them with prescribed SST anomalies prepared using Constructed Analogue method at IRI. Both the models have 24 ensemble members. ECHAM4.5-GML is a hybrid single-tier semi-coupled model where ECHAM4.5 has been coupled to slab-ocean mixed layer model, with CFS-predicted SSTs prescribed over the tropical Pacific basin (Roeckner et al., 1996; Lee and De Witt, 2009). ECHAM4.5-MOM3 is a single-tier coupled model (anomaly coupling) where ECHAM4.5 is coupled with the 3rd version of Modular Ocean Model (MOM) (Roeckner et al., 1996; Pacanowski et al., 1998). All model data have been downloaded from IRI These five models are referred to as CFS, E4P5, E5, GML, and MOM3 in our study. Table I shows the resolution of the model and number of ensemble members of each model. High-resolution (1 1 ) gridded daily rainfall data from India Meteorological Department (IMD; Rajeevan et al., 2006b) is used in this study. The observed sea surface temperature (SST) datasets used in the study are based on Reynolds and Smith (1994) and have been downloaded from (ftp://ftp.emc.ncep.noaa.gov/cmb/sst/ oimonth v2/ ). For this study, all data are taken from 1982 to 2004, and low-resolution models data are linearly interpolated to a grid. 3. Results and discussion 3.1. Individual models Figure 1 shows the climatology of rainfall over India in the month of July from IMD observed data and the model hindcast runs for the study period. During the month of July, most parts of India get more than 2 mm/day rainfall. The zones of maxima of rainfall in July are the Western Ghat region and the northeastern part of India. Some parts of northern and eastern India also receive more than 10 mm/day rainfall. While most models simulate the zones of maxima in rainfall reasonably well, the amount and spatial distribution vary. The CFS models simulate more than 10 mm/day over a smaller region in the eastern parts of India compared to observations. The E5 model simulates very high amounts of rainfall along the foothills of the Himalayas, which is absent in observations. It may be noted that the rainfall climatological patterns from E4P5, GML, and MOM3 models are very similar due to their similar origin. The models used in this study have coarse horizontal resolution (e.g. resolution of all the ECHAM-based models is T42 and that of CFS model is T62). Therefore, it is expected that much of the details of rainfall structure over India may not come out well from these models. Interannual variability (IAV) of rainfall from observations (IMD data) and from model runs are shown in Figure 2. It is seen from observations that the regions with maximum rainfall during July have also maximum interannual variability. The west coast of India, the northeastern region, the central parts, as well as the regions along the foothills of the Himalayas in northern India have IAV of about 4 mm/day. Eastern and central regions of the country have higher rainfall variability due to IAV in low pressure systems passing through these regions in the month of July. These are the regions where the paddy crops need higher amount of rainfall in July. Any deficit in the rainfall in this month shall crucially define the rice yield in the region. Moreover, higher amount of rainfall will lead to floods and affect the lives and economy in the region. The models have very similar IAV pattern over India. However, the magnitude of IAV is much less than that observed. None of the models have IAV more than 4 mm/day over most parts of India. Since we have used ensemble mean for each GCM, the IAV from a model could be smaller than observed IAV. The conclusions drawn from a comparison of coefficients of variation (CV) between observed data and model date are the same as that of the IAV. The temporal correlation between the observed rainfall and the model results are shown in Figure 3. The temporal correlations are computed grid point by grid point (following leave-one-out cross-validation procedure) for the 23 years of hindcast runs. It is seen that the CFS model rainfall has the best correlation over India in July. The correlations are positive and more than 0.3 over most parts of northern India and some parts of eastern India. In peninsular India, the correlations are mostly negative. For all other models, the correlation values between observation and model runs are less compared to the CFS model. There are few regions here and there, where the correlations have positive values and more than 0.3. It may be noted that for statistically significant correlation (95% confidence interval) for 23 years of study, it

4 1274 S. C. KAR et al. (a) (b) (c) (d) (e) (f) Figure 1. Climatology of rainfall over India in July from IMD observed data and the model hindcast runs from 1982 to Rainfall areas with >8 mm/day have been shaded. This figure is available in colour online at wileyonlinelibrary.com/journal/joc is expected that the correlation magnitude should be at least Interannual variability in rainfall in model simulations is due to response of the model to interannually varying SSTs and variability due to internal dynamics. The ocean and atmosphere are strongly coupled in the Indian Ocean and western Pacific basin. All-India averaged rainfall in July is related to remote response from the eastern Pacific SSTs as well as response from local SSTs in the north Indian Ocean. The correlation plot for all-india July rainfall with observed SST is shown in Figure 4(a). The equatorial eastern and central Pacific SSTs are negatively correlated to rainfall over India in July. The correlation value is more than 0.4, and is statistically significant. The reason why the individual models do not have any good skill in hindcasting July rainfall over India is seen in Figure 4(b f). The observed pattern is not well brought out from the model simulations. The negative relationship between the eastern and central Pacific SST with July rainfall over India is represented only in E5 model. For all other models, correlation values are not at all significant. For the MOM3 model runs, the relationship is opposite. As far as the Indian Ocean SST impacts on the rainfall over India, the models, to some extent, bring out observed relationship. Deficiencies of the models to predict SSTs as well as the inability of the atmospheric component of the coupled models to respond to SST forcing correctly have led to poor

5 SKILL OF MONTHLY RAINFALL FORECASTS OVER INDIA 1275 (a) (b) (c) (d) (e) (f) Figure 2. Interannual variability (IAV) of rainfall over India in July from IMD observed data and the model results. Rainfall areas with >4 mm/day have been shaded. This figure is available in colour online at wileyonlinelibrary.com/journal/joc skills in rainfall prediction over India. The remote impact of the Pacific SST on the Indian monsoon during July could be different in GCMs as compared to observations due to dominance of internally generated variability in the GCMs. A detailed study on this aspect is being carried out MME schemes MME using simple arithmetic mean In this study, MME techniques have been used to estimate mean forecast distribution monthly mean precipitation anomalies over India. Simplest of all the MME schemes in literature has been the method based on simple averaging of all the individual models. Hagedorn et al. (2005) have described the rationale behind the success of such MME techniques for seasonal prediction. In the present study, the method of carrying out MME by simple arithmetic mean of individual models is being referred to as MME1. In this method, all the individual member models have been assigned same weight while carrying out ensemble average Point by point multiple regression For carrying out weighted MME mean, point-by-point multiple regression method has been employed following Yun et al. (2003). Singular value decomposition (SVD) has been employed for the computation of the regression coefficients (referred to as MME2 scheme in the following text). Cross-validation technique has been used in which each year has been successively withheld from the training dataset, and the remaining 22 years have been used for calculation of the model and observed

6 1276 S. C. KAR et al. (a) (b) (c) (d) (e) Figure 3. Temporal correlation between the observed rainfall and the model rainfall. Areas with correlation values with >0.3 have been shaded. This figure is available in colour online at wileyonlinelibrary.com/journal/joc statistics (i.e. the monthly means and regression coefficients). These means and regression coefficients are used for calculating the forecast for the verification year (the year that was withheld). The model weights are the most important outcome of this multiple regression method. These are shown in Figure 5 which has been computed by removing 1982 and carrying out multiple regression for the next 22 years. As expected, the model weights have similar pattern as the correlation coefficients. Over large parts of India, the weights assigned to models have less value. The plot almost remains the same when the cross-validated year is changed from 1982 to other years Empirical Orthogonal Function-based regression scheme Following the synthetic super-ensemble method as describe in Yun et al. (2005), a new dataset has been generated from the original dataset by finding a consistent spatial pattern between the observed rainfall and rainfall from each model. The newly generated set of EOF-filtered data is then used as an input multi-model dataset for grid point by grid point multiple regression. In this method, empirical orthogonal function (EOF) analysis is applied to the observed July rainfall data. The leading modes of the observed EOFs are then projected

7 SKILL OF MONTHLY RAINFALL FORECASTS OVER INDIA 1277 (a) (b) (c) (d) (e) (f) Figure 4. Correlation of the all-india July rainfall with observed SST and model predicted rainfall with model SSTs. Areas with correlation values with < 0.2 have been shaded. This figure is available in colour online at wileyonlinelibrary.com/journal/joc to each model s predictions to obtain the principal component (PC) time series of models during the training as well as the forecast period. At this stage, the observed as well as the forecast data have consistent EOF patterns, but their time variation could be different due to difference in PC time series. These model PC time series are corrected to fit the observed PCs by multiple regression technique. In our study, 16 modes are retained while reconstructing the model datasets which explain about 90% of total variance. A new set of model data are then constructed using selected number of EOF modes and the corrected time series. The MME2 method is then applied to these EOF filtered data to obtain the statistically corrected monthly predictions. This method is referred to as MME3 in the following text Skill of MME schemes Skill of individual member models in terms of temporal correlation discussed in the earlier sections showed that the member models have poor skill in simulating the monsoon IAV. The temporal correlation coefficients obtained from the simplest MME scheme (MME1) are shown in Figure 6(a). This scheme shows good skill in northern India as well as some good skill in southwest coastal India. In other words, except over the northern parts of India, and few pockets in peninsular India, the MME1 scheme does not provide any good skill. Enhanced skill in northern India is achieved due to the fact that most of the individual member models have positive skill score over the same region. In all the regions where the member models do not have any positive skill, the MME1 scheme is not able to enhance the skill over the same region. The temporal correlation coefficients obtained from the MME2 scheme are shown in Figure 6(b). This scheme maintains the positive skill over the northern parts of India which was obtained from the MME1 scheme. However, MME2 scheme provides better results over other parts of India also. Noticeably, the skill over the eastern parts of India covering Orissa, Andhra Pradesh, Chhatishgarh, and Madhya Pradesh have been increased from negative skill in MME1 scheme to positive and significant skill in MME2 scheme. The correlation of observed and predicted rainfall from the MME3 scheme shown in Figure 6(c) indicates that

8 1278 S. C. KAR et al. (a) (b) (c) (d) (e) Figure 5. Weights (regression coefficients) for each member model obtained from multiple regression analysis. Areas with weights >0.4 have been shaded light, and values < 0.4 have been shaded dark. this scheme is a marginal improvement on the MME2 scheme. Anomaly Correlation (spatial) Coefficients (ACC) has been calculated with leave-one-out cross-validation for four regions (shown in Figure 7) in India. These regions put together cover the whole country except the hilly northern part and northeast region. ACC values at different regions have been computed to examine the interannual variability of the skill of the MME schemes over different domains of interest. These domains are Region- A (20 N 30 N, 68 E 76 E), Region-B (8 N 18 N, 68 E 85 E), Region-C (14 N 24 N, 80 E 88 E), and Region-D (24 N 28 N, 72 E 88 E), covering northwest, peninsular, eastern, and central-northern India, respectively. Mean ACC for the entire period of study has been calculated for each method for each region (Figure 8(a)). In general, the MME schemes have better skill than the individual member models. However, the MME schemes have varying skill in predicting the monthly rainfall over India on regional scale. In Region-A, MME2 has higher skill than other methods, in Region-B, skill of MME1 is almost zero and skill of MME3 is higher than MME2. For Region-C, skill of MME2 is much higher than other schemes. For the Region-D, none of the MME schemes have any good skill. Rather, For the MME2, and MME3, the skill is negative. Therefore, on average,

9 SKILL OF MONTHLY RAINFALL FORECASTS OVER INDIA 1279 Figure 7. Four regions in India for which ACC and RMSE values have been computed. This figure is available in colour online at wileyonlinelibrary.com/journal/joc Figure 6. Temporal correlation between the observed rainfall and the rainfall from MME schemes. Areas with correlation values with >0.2 have been shaded Mean ACC ( ) Region A Region B Region C Region D Mean RMSE ( ) it can be said that the skill of the MME2 scheme is better than other schemes. The area average root mean square error (RMSE) with leave-one-out cross-validation of each ensemble technique has been calculated as shown in Figure 8(b). It shows that for all the regions MME2 has less RMSE than the other two schemes. Specifically in Region-C the difference of RMSE between MME2 and other two methods is large. A comparison of RMSE values for individual member models as well as of the MME schemes (figure not shown) indicate that the MME schemes are indeed able to improve the skill of mean of the forecast distribution, and are quite useful in a probabilistic scheme. Hansen and Kupier skill (HKS) score is a suitable metric for showing the skill of a deterministic prediction system for different categories, (Stanski et al., 1989). In the present study, 3-category predictions are made, namely, normal, above, and below normal. Using Region A Region B Region C Region D MME1 MME2 MME3 Figure 8. (a) Average of ACC from member models and MME schemes, and (b) average of root mean square error (RMSE) mm/day from MME schemes between the observed rainfall and the rainfall for four different regions of India. standard definitions of hit rate (h) and false alarm rate (f ) from a 2 2 contingency table (Table II), HKS score is defined as HKS = h f. The range of HKS goes from 1 to +1, the latter value corresponding to perfect forecasts (h being 1 and f being 0). In Figure 9, HKS values are shown for below normal and above normal categories for monthly rainfall predictions using various

10 1280 S. C. KAR et al. Table II. 2 2 contingency table. Observation Occurence Non-occurrence Occurrence Hit (h) False alarm (f) Forecast Non-occurence Miss (m) Correct rejection (cr) MME schemes. Negative HKS values indicate lower skill than climatology and, therefore, not usable. For clarity purpose, in the figure, the negative values are not plotted. It is clear that hit rate is more than false alarm rate over only few regions over India. For below normal rainfall category, the HKS score is better for all the MME schemes as compared to above normal category. It is seen that the weighted MME schemes such as MME2 scheme has better skill for all categories over the eastern parts of India (Region-C), northern India, as well as some parts of peninsular India. For Region-D, observed rainfall categories and MME predicted rainfall categories do not agree very well. Therefore, it is seen that in Region-D, neither individual model nor any MME scheme has any usable skill. This study suggests that only a probabilistic prediction scheme should be used for this region where probability values should be assigned to the forecasts after calibration so that proper climate risk management measures can be taken. However, for Region-C, the weighted MME schemes have quite good skill. By increasing the number of member models as well as the training period, skill of MME forecasts can be further enhanced and such (a) (d) (b) (e) (c) (f) Figure 9. HKS score for below normal and above normal rainfall categories obtained for MME schemes. Areas with positive HKS values have been shaded.

11 SKILL OF MONTHLY RAINFALL FORECASTS OVER INDIA 1281 (a) (b) (c) (d) (e) (f) Figure 10. Observed rainfall anomalies for 1987, 2002, 1988, 1994, 1997, and Regions with negative anomalies are shaded dark. Regions with positive anomalies are shaded light. forecasts may be used in the Region-C. For all other regions, improvement in models is required, as well as reasons for climate variability in monthly scale should be further examined Prediction skill in some typical years During the study period (i.e ) several July months with typical monsoon patterns were observed. While some of these are extreme monsoon months with significantly less rainfall over India (1987 and 2002), in some of the July months more than normal rainfall occurred (1988 and 1994). These years are also characterized as El Nino years (1987, 2002), La Nina year (1988), and Indian Ocean dipole (IOD) year (1994). In the July months of 1997 and 1998, normal rainfall was observed over India. These two years are special, as during , a very strong El Nino event was observed over the eastern Pacific Ocean. Contrary to expectation, near-normal monsoon rainfall was observed over India during these years. Observed rainfall anomalies for these years are shown in Figure 10. For the MME1 and MME2 schemes, predictions for these years are shown in Figures 11 and 12, respectively. Corresponding plots for MME3 have not been shown as they do not provide any additional information. For the July months with drought (1987 and 2002), the rainfall pattern from the MME1 scheme (Figure 11) do not match with the observed pattern. The multi-model

12 1282 S. C. KAR et al. Figure 11. Same as Figure 10, but for rainfall anomalies computed using MME1 scheme. scheme provides below normal rainfall over the northern parts of India and the extreme southern peninsula. In the central zone, the scheme provides normal to above normal rainfall. However, the scheme as a whole provides indication that there is likelihood of below normal rainfall over most parts of India. For the excess months, the scheme does not provide the correct pattern of rainfall. For 1988, the scheme indicates an opposite pattern of 1987 which was not observed. For 1994, the predicted values of rainfall are too low, however, over central parts, the scheme indicates values with positive anomalies. For 1997, the MME1 scheme indicates above normal rainfall over the southern peninsula which was not observed. For 1998, there is no large-scale pattern in MME prediction as observed. Therefore, it is seen that the MME1 scheme has mixed skill in predicting rainfall in July of some typical years. The statistical post-processing scheme such as the MME2 scheme is expected to improve upon the MME1 scheme. While it does improve upon the MME1 scheme over some region for some months, the rainfall predictions from the MME2 scheme does not indicate any special characteristics which are highlighted in observations. The rainfall patterns are shown in Figure 12. It is seen that for both 1987 and 2002, the MME2 scheme indicates below normal rainfall over most parts of India. But the large-scale nature of the observed drought is missing in these plots. Similarly, it cannot be said that in 1988 or 2002, above normal rainfall occurred over most parts of India. For the normal years, the pattern predicted

13 SKILL OF MONTHLY RAINFALL FORECASTS OVER INDIA 1283 Figure 12. Same as Figure 11, but for rainfall anomalies computed using MME2 scheme. by the MME2 scheme appears to be agreeing reasonably well with observations. As expected, the MME3 scheme provides marginal improvement over the MME2 scheme, (figure not shown). However, as in other MME schemes, the special characteristics of the chosen years do not get highlighted from the MME3 predictions. It is seen that the statistical post-processing schemes do not improve rainfall prediction for these typical years. Such schemes (e.g. the point-by-point regression) uses the training period to obtain regression coefficients to be used for prediction. The objective of such post processing is to remove the statistical bias, if any, in model predictions, and to reduce mean square error so that the weighted MME predictions are closer to the observed values in the training period. The regression coefficients are then used to build the predictions as if the entire training period decides the mean bias of the model. The typical years such as the years explained above do not occur frequently. There might not be any year during the training period in which a similar situation had occurred. In a given year, the model used to predict with either prescribed boundary forcing or in a coupled mode recognizes the typical nature of the boundary forcing and responds to such forcing as per the model formulations. However, except for the MME1 scheme, no other statistical post-processing scheme has this ability

14 1284 S. C. KAR et al. to recognize this typical nature of the forcing. Therefore, MME1 scheme performs better than any other scheme for any given typical year if normalized anomalies are used. However, regression-based MME schemes (such as MME2) perform better than MME1 if an entire hindcast period is considered Multi-model ensemble probabilistic predictions Extended-range prediction is inherently probabilistic. For climate risk management, it is essential that uncertainties in predictions are communicated to user agencies. This can be achieved if probability density function (pdf) is constructed to represent the uncertainties in predictions. The mean of the forecast distribution obtained by using the MME schemes described in this study is therefore useful in developing a pdf required in a probabilistic scheme. The probabilistic monthly prediction scheme used here is a simple un-calibrated scheme. Kharin and Zwiers (2003) had proposed that probability distribution functions (PDF) can be estimated assuming that ensemble mean is the predictive signal and the deviations from ensemble mean (ensemble spread) is stochastic noise which has a Gaussian distribution. The MME probabilistic scheme used here assumes the mean of forecast distribution obtained from MME1, MME2, and MME3 schemes as the predictive signal. The ensemble spread of each model is computed as the deviation of its predictions from the MME mean. PDF is then built using these mean of forecast distribution and MME spread. Three categories of probabilistic predictions have been made for the entire hindcast period with leave-one-out cross-validation. For the probabilistic forecasts, ranked probability skill score (RPSS) is a useful skill metric. It tells about how well the probability forecast predicted the category that the observations fell into and what the relative skill of the probabilistic forecast over that of climatology was. For our probabilistic prediction, the RPSS for MME1 and MME2 are shown in Figure 13. It is seen that indeed, the MME2 has higher skill than that of MME1. It may be noted that over the eastern parts of India, the MME2 scheme had higher skill in deterministic forecasts (Figure 6). Over the same region, skill of probabilistic forecasts has also increased. It is hoped that when the representation of the stochastic noise part is further improved, skill of probabilistic predictions shall also be higher. 4. Summary and conclusion India receives maximum rainfall during July and August. Rainfall in the month of July in India is decided by large-scale monsoon pattern in seasonal to interannual timescales as well as intraseasonal oscillations. Analysis of observed data suggests that the equatorial eastern and central Pacific SST is negatively correlated to all-india rainfall in July. Hindcast runs of five global circulation models have been analysed for this month. Global Figure 13. Rank Probability Skill Score (RPSS) of probabilistic predictions using MME1 and MME2 as the mean of the forecast distribution. Areas with positive RPSS values have been shaded. dynamic models (either atmosphere only or coupled models) have varying skill in predicting the monthly rainfall over India during July. This could be due to the fact that the atmospheric models do not respond in a correct manner to the prescribed predicted SSTs used in two-tier systems, or the evolution of SSTs in coupled models do not agree with the observed SSTs. It is seen that the large-scale anomaly patterns are not brought out by these models. This may also be due to coarse resolution of the models used in our study. Multi-model ensemble methods have been utilized to evaluate skills of five global model predictions for The objective has been to develop a monthly prediction system to be used in real time. Point-bypoint multiple regression method using singular value decomposition has been utilized to determine the weights to be given to the individual models. In another method, observed and model-predicted rainfall datasets have been decomposed to identify patterns, and a new dataset has been input to point-by-point regression scheme. It has been found that the weighted MME schemes have

15 SKILL OF MONTHLY RAINFALL FORECASTS OVER INDIA 1285 higher skill in predicting July rainfall. Through the MME methods, skill of rainfall predictions improved significantly over eastern parts of India. However, there is a region over India (Region-D in our study covering parts of central and northern India) where none of the models or the MME schemes have any useful skill. Similarly, there are few typical years in which the mean of the forecast distribution of July rainfall does not have any higher skill using the available statistical post-processing methods. Skill of probabilistic forecasts improved when the representation of the mean of the forecast distribution improved through the use of MME schemes. This study mainly deals with the monthly prediction for 0 lead time. We have also carried out skill assessment of the models as well as the MME schemes with lead 1 and lead 2. There is a significant drop in skill of the models as the lead time increases. It is seen that the higher skill observed at lead 0 over the eastern zone of India has reduced in longer lead hindcasts. No significant increase in skill is noticed in lead 1 over India except that over some parts of western India, the correlation values have become statistically significant. More or less, it is seen that the skill decreases as the lead time increases. A major component of weighted MME forecast techniques is training of a forecast dataset. The prediction skill from these techniques during the forecast phase could be degraded if the training was executed with either a poorer analysis or poorer forecasts. That means that the prediction skill is improved when a higher quality training dataset is deployed for the evaluation of the multi-model bias statistics (Yun et al., 2003). Moreover, in general, equally reliable model forecasts may not necessarily be weighted equally when combined optimally using the methods described in this study. Moreover, multi-model linear regression forecast is superior to all other linear combinations of the individual model forecasts when very large training datasets are available for estimating the regression coefficients. In practice, the coefficients depend on the estimates of covariance of model with observation and between models. In these circumstances, estimating too many regression coefficients leads to over fitting that causes a degradation in skill (Kharin and Zwiers, 2002). It may be noted that total period of data used in this study is only from 1982 to 2004 which may not be very large for estimation of regression coefficients. Limited size of the hindcasts is also a challenge for training in multiple regression schemes. However, regressions will suffer from the decadal changes associated with global warming, and associated teleconnections (Ashok et al., 2007). Therefore, it is not just the hindcast length, but other options such as improving the models, data assimilation, etc. should also be considered. Acknowledgements The authors wish to thank International Research Institute for Climate and Society (IRI), USA, for providing hindcast datasets which have been used in the study. India Meteorological Department is thanked for providing observed gridded rainfall datasets. The authors thank Dr A. Robertson, IRI, USA, for going through the draft manuscript and providing useful suggestions to improve the paper. This research has been conducted as part of the project titled Development and Application of Extended Range Weather Forecasting System for Climate Risk Management in Agriculture at IIT, Delhi, sponsored by the Department of Agriculture and Cooperation, Government of India. 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