Clim Dyn (2014) 42:2271–2285 DOI 10.1007/s00382-014-2119-3

The influence of stochasticism on Indian summer monsoon rainfall and its impact on prediction B. G. Hunt

Received: 28 November 2013 / Accepted: 10 March 2014 / Published online: 28 March 2014 Ó Springer-Verlag Berlin Heidelberg 2014

Abstract Output from a multi-millennial control simulation of the CSIRO Mark 2 coupled model has been used to investigate quantitatively the relation between the Indian summer monsoon rain and El Nino/Southern Oscillation events. A moving window correlation between these two features revealed marked interannual and multi-decadal variability with the correlation coefficient varying between -0.8 and ?0.2. This suggests that current observations showing a decline in this correlation are due to natural climatic variability. A scatter diagram of the anomalies of the Indian summer monsoon rainfall and NINO 3.4 surface temperature showed that in almost 40 % of the cases ENSO events were associated with rainfall anomalies opposite to those implied by the climatological correlation coefficient. Case studies and composites of global distributions of surface temperature and rainfall anomalies for El Nino (or La Nina) events highlight the opposite rainfall anomalies over India that can result from very similar ENSO surface temperature anomalies. Composite differences are used to demonstrate the unique sensitivity of Indian summer monsoon rainfall anomalies to ENSO events. The problem of predicting such anomalies is discussed in relation to the fact that time series of the monsoon rainfall, both observed and simulated, consist of white noise. Based on the scatter diagram it is concluded that in about 60 % of the cases seasonal or annual prediction of monsoon rainfall based on individual ENSO events will result in the correct outcome. Unfortunately, there is no way, a priori, of determining for a given ENSO event whether the correct or a rogue prediction will result. B. G. Hunt (&) CSIRO Marine and Atmospheric Research, Private Bag 1, Aspendale, VIC 3195, Australia e-mail: [email protected]

Analysis of the present model’s results suggest that this is an almost world-wide problem for seasonal predictions of rainfall. Keywords Indian summer rainfall
Stochastic influences
Climatic model
Multi-millennial simulation

1 Introduction The vagaries of the Indian summer monsoon have a major impact on many aspects of life on the Indian sub-continent. An immense literature now exists on this subject, and for a comprehensive review of the climatic aspects of the monsoon see Webster et al. (1998). It is the vagaries of climate that are normally of most interest. Such vagaries, or climatic perturbations, can be categorised as those attributable to anthropogenic greenhouse gas increases, termed climatic change, and those attributable to climatic variability. The latter is then subdivided into forced (or external climatic variability associated with volcanic eruptions, solar fluctuations etc.), and unforced climatic variability. Such unforced activity is termed natural or internal climatic variability and is identified with self-generating climatic processes, such as the El Nino/Southern Oscillation (ENSO), the Atlantic Multidecadal Oscillation (AMO), the North Atlantic Oscillation (NAO) etc., see for example, Collins et al. (2001), Goosse et al. (2005), Smith et al. (2007) and Deser et al. (2012). The above climatic phenomena are all intrinsic components of the climatic system and arise from the complex physical processes and non-linearities of that system. This form of variability will be referred to as Type 1 internal climatic variability. Type 2 internal climatic variability, a major topic of this paper, is far more subtle being termed weather

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noise or stochastic. It is difficult to define and hard to quantify. Weather noise can be related to small scale fluctuations associated with convection, wave breaking, orographic features etc. However, because the climatic system is inherently chaotic this can result in stochastic outcomes. As noted by Crutchfield et al. (1986) ‘‘Chaotic systems generate randomness on their own without the need for any external random inputs’’. This aspect of chaos is separate from the usual meteorological characterisation of chaos, which attributes deviations in predictive outcomes with errors in initial conditions. Type 2 internal climatic variability is presumably a dominant cause of perturbations in a number of climatic phenomena. For example, Wang et al. (1999) have attributed variations in the onset of ENSO events to stochastic influences. These would then play a significant role in false onsets of El Nino or La Nina events. Stochastic influences may likewise be important in determining the length of the various phases of the NAO or AMO. Of particular interest, is that in the absence of any external forcing, Type 2 internal climatic variability may be a major cause of some of the unexplained vagaries of climate. The issue of the causes of the inter-annual variability of the monsoon is a major subject of interest. Many possible influences have been evaluated, these include the El Nino/ Southern Oscillation (Pant and Parthasarathy 1981; Rasmusson and Carpenter 1983): Eurasion snow cover (Hahn and Shukla 1976; Fasullo 2004): the North Atlantic Oscillation (Goswami et al. 2006a): the Atlantic Multidecadal Oscillation (Chen et al. 2010): Indian Ocean sea surface temperatures (Yang et al. 2007): and the Interdecadal Pacific Oscillation (IPO) (Krishnan and Sugi 2003). See also the list of predictors used in statistical predictions (Peings et al. 2009). All the above possible influences on the Indian summer monsoon rainfall (ISMR) were systematically examined using output from the present simulation (see Hunt 2012). While most of the observed teleconnections and correlation coefficients were reproduced in this simulation, many of the relationships exhibited transient behaviour in their correlations with the ISMR based on a 20-year moving window. This diverse range of possible influences on the ISMR highlights the problem of not only understanding the vagaries of the ISMR but also predicting it. ENSO events have the greatest influence on the occurrence and subsequent evolution of the Indian monsoon, and for this reason the present study has been limited to investigating the ENSO/ISMR relationship. Nevertheless, the present model intrinsically includes the impact, where appropriate, of the above-listed climatic phenomena, and

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these may also influence the ISMR in any given year. The correlation between the NINO3 sea surface temperatures and Indian region rainfall for June to September (JJAS) is r = -0.6 (Krishnamurthy and Goswami 2000; Webster et al. 1998). This correlation is not particularly stable, Kumar et al. (1999) using a 21-year sliding window found the correlation declined to r = -0.4 in the 1980s, while Kinter et al. (2002) claim the correlation has changed from r = -0.49 to -0.29 since 1979. Thus, at best, ENSO events explain less than 40 % of the variance associated with the ISMR. There have been numerous simulations of the relationship between ENSO and the ISMR, in particular, multimodel intercomparisons (Annamalai et al. 2007; Kim et al. 2008; Lin et al. 2008; Zhou et al. 2009; Kucharski et al. 2009; amongst many others). While such simulations show the general improvement in the ability of models to replicate monsoonal climatology, these also highlight the still considerable variability in the performance of individual models. Perhaps, more importantly, there have been studies designed specifically to analyse monsoon outcomes. For example, Goswami et al. (2006b) made a very detailed analyses of a variety of factors influencing the summer monsoon and the resulting limitations on its predictability. They concluded: ‘‘The fact that the predictable ‘signal’ of the Asian monsoon is comparable to the unpredictable internal variability (noise) makes it a most difficult system to predict’’. On the other hand, Ihara et al. (2008) suggest that it is the timing of the onset of ENSO events that decides whether an expected or rogue outcome for the ISMR is obtained. A further detailed study by Neena et al. (2011) identified a role for monsoon intraseasonal oscillations as a cause for a long break in the 2009 monsoon, and suggest that this mechanism may have been operative in other years. See also the more broadly based report of Hoyos and Webster (2007). Despite the restrictive conclusion of Goswami et al. (2006b) concerning the role of internal climatic variability, investigations continue to be made regarding the possible impact of discrete climatic phenomena on the ISMR. Thus Kucharski et al. (2008) identified a role for SST anomalies in the South Atlantic Ocean, while Gadgil et al. (2004) suggest that the Indian Ocean Oscillation may be important. In support of such studies is the possibility that some of these mechanisms may help to identify part of the variance noted above that is not explicable by the ENSO/ISMR correlation in any given year. However, there is no way of knowing a priori whether any given mechanism is going to be influential in a particular year. Fortunately, current climatic models should automatically generate these

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mechanisms, subject to an adequate initialisation procedure, so that they would be an intrinsic part of a comprehensive prediction or simulation scheme. The consensus seems to be that at least 50 % of the interannual variability of the ISMR is attributable to internal climatic variability (Goswami 1998; Kang et al. 2004; Goswami et al. 2006b; Kucharski et al. 2007). More generally, Deser et al. (2012) estimated that at least half of the inter-model spread in climatic trends for the period 2005-2060 in the CMIP 3 multi-model ensemble was due to internal climatic variability. The objective of the present paper is to use results from the same multi-millennial simulation as employed by Hunt (2012), in an investigation of Indian megadroughts and megafloods, in order to quantify the range of ENSO/ISMR relationships. In particular, the fact that anomalous results are a consistent feature of the climatic system will be highlighted. The extended timescale of the simulation provides a much broader insight into the ENSO/ISMR relationships than is possible from the limited observations. The consequences for the prediction of the ISMR are then discussed. The ability of the present model to replicate a very wide range of climatic phenomena has been documented in a considerable number of papers. These include the timeinvariance of the global mean climate (Hunt 2004), climatic trends (Hunt and Elliott 2006), the Medieval Warm Period and the Little Ice Age (Hunt 2006), a climatology of heat waves (Hunt 2007), Norse settlements in Greenland (Hunt 2009), surrogate tropical cyclones (Hunt and Watterson 2010) and extreme winters (Hunt 2011) amongst others.

2 Model description and experimental details The Mark 2 version of the CSIRO coupled global climatic model was used in this study. The model has been described in detail by Gordon and O’Farrell (1997), who also give a description of some aspects of the model’s performance. The model consists of atmospheric, oceanic, biospheric and dynamic sea-ice components. A flux correction scheme is used to couple the atmospheric and oceanic components. The flux corrections vary monthly but are invariant from year-to-year. The atmospheric model has nine vertical levels and R21 spectral resolution (3.25° latitude 9 5.625° longitude) giving 3,584 model grid boxes per vertical level. Diurnal and seasonal variabilities are included, along with a mass flux convection scheme, a cloud parameterization based on relative humidity, gravity wave drag and semilagrangian water vapour transport. The oceanic component is based on Version 2 of the Modular Ocean Model, of the

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Geophysical Fluid Dynamics Laboratory. This component has twenty-one vertical levels and realistic bottom topography. The eddy-induced advection scheme of Gent and McWilliams (1990) was implemented, permitting the horizontal background diffusivity to be set to zero. The land surface scheme consisted of separate soil moisture and temperature formulations. A two-layer representation was used for soil moisture based on Deardorff (1977). Three soil types were specified as well as 11 plant types, with the latter having monthly varying characteristics. A three-layer scheme was used for soil temperature, with the bottom of the lowest layer being assumed to be insulated. Full technical specifications are available in the report by McGregor et al. (1993). The present simulation was commenced from a previous 1,000-year simulation, hence all climatic fields were initially balanced. The model was set up to simulate ‘‘present’’ climatic conditions; once initiated no changes were permitted to forcing agents such as CO2 content, volcanic eruptions or solar variability. Thus all of the climatic fluctuations in the simulation arose from internally generated climatic variability, attributable to physical processes and nonlinear interactions within the model. This simulation does not therefore represent a progression through the Holocene, as the latter experienced numerous changes to boundary conditions via external forcing agents. A fixed atmospheric CO2 concentration of 330 ppm was used in the simulation. The simulation was time invariant at the global mean level, thus time series of basic variables such as surface temperature, cloud amount, and rainfall were constant within 1–2 % over the 10,000 years of the simulation, as are the limited observations (see Hunt 2004). At the regional or local level, climatic time series were also stationary, while exhibiting considerable interannual variability. Marked regional climatic anomalies, such as those associated with the Medieval Warm Period or Little Ice Age, occur in this simulation within the constraint of this global mean time invariance (Hunt 2006). As a consequence of this invariance no detrending of climatic variables was necessary. Although the simulation extends over 10,000 years only the last 5,000 years are used here. In the original run of the model an instability occurred late in the 4th millennium associated with a need for additional smoothing of model variables at high northern latitudes. This fault was rectified and the model was restarted from year 4000 and the simulation was completed without further intervention in the model. In this paper the ISMR is defined as the rainfall for the standard summer period of June, July, August and September (JJAS), calculated over the region 10–25°N, 72–85°E.

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Fig. 1 Global correlation plots for the last 5,000 years of the simulation for JJAS conditions. a Correlation between the ISMR and global surface temperature, b correlation between Nino 3.4 surface temperature and global rainfall, c correlation between Nino 3.4 surface temperature and global surface temperature. The colour bars below the panel give the value of the correlation coefficient

3 Climatological characteristics The multi-millennial simulation of the present model permits the quantitative documentation of a number of climatic relationships relevant to the Indian summer monsoon. Previously, the ability of this model to simulate the basic characteristics of global rainfall and the Indian monsoonal rainfall has been shown in Hunt (2012). Of particular relevance was the advance and retreat of the

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seasonal rainfall over the Indian region and the active and break rainfall outcomes for both drought and flood conditions. Figure 1 illustrates some basic relationships of rainfall and temperature to demonstrate the model’s ability to replicate essential climatic characteristics. Thus, Fig. 1a shows the correlation of rainfall for JJAS conditions, for the Indian region identified above, with global surface temperature for the last 5,000 years of the simulation. A similar ensemble model outcome has been presented by Rajeevan et al. (2012). A more spatially restricted correlation plot in Kinter et al. (2002) for an observed 43-year period reveals many of the features in Fig. 1a. The dominant feature of Fig. 1a is the well-known negative correlation between the ISMR and surface temperature over the tropical Pacific Ocean. For the Nino 3.4 region r = 0.395, compared with the observed r = -0.6 of Webster et al. (1998). The lower simulated value is attributable to the very large number of events replicated in the model compared to the short observed time series. The high positive correlation over Indonesia (r * ?0.5) is noteworthy, see also Kinter et al. (2002), and is consistent with a negative correlation (r * -0.6) between the ISMR and rainfall over this region. This feature was not simulated by Rajeevan et al. (2012). The very high correlation over India is consistent with high/low rainfalls corresponding to low/high local surface temperatures. Figure 1b shows the corresponding correlation between Nino 3.4 surface temperature and JJAS global rainfall. This replicates the well-known observations (Ropeleweki and Halpert 1987) of drought conditions over India, southeast Australia and northeast Brazil associated with El Nino events, and above average rainfall for southeastern USA. The final panel, Fig. 1c, illustrates the correlation between Nino 3.4 surface temperatures and global surface temperature for JJAS conditions. This corresponds fairly well with the regression figures of Kucharski et al. (2007) for two separate periods based on observations, except over parts of the Indian Ocean. The results in Fig. 1c suggest that the northern part of the Indian Ocean, where r * 0.6, may be a slave to ENSO events. If so, then interactions between this region and the ISMR do not provide any additional insights compared to just considering ENSO events. Another climatic characteristic of particular interest is the recent weakening of the observed ENSO/ISMR relationship, noted above by Kumar et al. (1999) and Kinter et al. (2002), based on a sliding window correlation. Figure 2a shows the variation of this correlation for the last 5,000 years of the simulation using a 20-year sliding correlation. Considerable decadal and longer term variability is apparent in the figure, with the correlation coefficient ranging from about -0.8 to ?0.2. Positive values, while infrequent, are a consistent feature of this plot.

Indian summer monsoon rainfall 0.4

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Fig. 2 Twenty year moving window correlation between the ISMR and JJAS Nino 3.4 surface temperature. a 5,000year time series, b sample time series for years 5600–5700, c sample time series for years 7400–7500

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Fig. 3 Scatter plot of the relationship between the anomalies for ISMR and Nino 3.4 surface temperature for JJAS conditions. The number of points in each quadrant is listed in that quadrant. Note points in the bottom right hand quadrant and top left hand quadrant,

El Nino and La Nina events respectively, are those associated with the negative sign of the climatological correlation coefficients. The points in the other two quadrants are associated with rogue events

More detailed aspects of the correlation are shown in the lower panels of Fig. 2. Thus, Fig. 2b reveals that after a fairly constant negative correlation between years 5600 and 5640, the correlation declined from about -0.6 to -0.3,

returned to large negative values before rapidly attaining a value of almost -0.1 around year 5700. In Fig. 2c a rapid decrease in the correlation occurs around year 7430, followed by a period of about 30 years with low values,

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b Fig. 4 Probability density functions for the ISMR. a The red curve is

for the last 5,000 years of the simulation, the blue curve is a Gaussian fit and the green curve is based on observations, b–d are subsets of the simulated values in a

before returning to a stable period of high negative values. A range of other perturbations is apparent Fig. 2a. Annamalai et al. (2007) have produced a similar analysis to that in Fig. 2 for a range of models used in the IPCC AR4 simulation between 1850 and 2000 AD. In general, the agreement with observation was poor, and noticeable variability was apparent between the various members of the ensemble. They suggest that the observed weakening of the ENSO/ISMR relationship is due to interdecadal vacillations of the associated teleconnection rather than global warming. More specifically, the results from the present study suggest that this weakening is caused by internal climatic variability, however defined, and should not be attributed to global warming unless specific mechanisms prove otherwise. The implications of a weakening of the correlation coefficient is that Type 2 internal climatic variability has increased, and thus diminished the impact of Type 1 variability (essentially ENSO events). This would suggest that for such periods the predictability of the ISMR will be reduced, whereas periods with a high negative correlation would have enhanced predictability. The variable behaviour of the correlation coefficient in Fig. 2 agrees with a comment of Ramage (1983), who noted that large correlation coefficients can not only diminish with time, but can also change sign. Similarly, Gershunov et al. (2001) reported that two stochastic time series can exhibit low-frequency evolution. They concluded that decadal modulation of the ENSO/ISMR relationship could be due solely to stochastic processes. Thus the observed correlation based on relatively short time series is presumably not representative of the overall relationship. Certainly, the extended time series in Fig. 2 provides a salutary perspective of the possible long term variability of the observed ENSO/ISMR relationship, and may give a useful context for assessing current and future variations in this relationship. Figure 3 provides a quantification of the vagaries of the ENSO/ISMR relationship, where the JJAS Nino 3.4 surface temperature anomaly is plotted against the ISMR anomaly, for the last 5,000 years of the simulation. Kumar et al. (2006) have produced a similar diagram, for the very much more limited observations, which has the same characteristics as Fig. 3. Importantly their diagram shows that anomalous outcomes, termed ‘‘rogue’’ results here, where La Nina events are associated with droughts and El Nino events with above average rainfall, are a common feature of the Indian summer monsoon climatology. It is these rogue results that reduce the ENSO/ISMR correlation coefficient.

Indian summer monsoon rainfall

The number of points in each quadrant is shown in the respective quadrants. For values of ISMR and Nino 3.4 surface temperature generating a negative correlation there are 1,725 associated with La Nina events, and 1,451 with El Nino events. For ‘‘rogue’’ outcomes producing a positive correlation both phases of ENSO events generated similar numbers, 919 for La Nina events and 905 for El Nino events. This simulation implies that rogue outcomes are a common occurrence, with approximately 36 % of monsoons being associated with them. Krishnan and Sugi (2003) identified 8 rogue outcomes in 40 years based on observations between 1884 and 2002. This amounts to 20 % of ENSO events. The lower value, compared to the simulation number given here, is due to all years being used in the present count, whereas Krishnan and Sugi (2003) limited their evaluation to only years with distinct ENSO events. While a considerable number of events in Fig. 3 are clustered around small temperature or rainfall anomalies, it is the outliers, corresponding to exceptional conditions, that are of particular interest because of their connection with economic

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impacts. For example, there are several temperature anomalies * -1.0 K that are associated with relatively small rainfall anomalies, *1–2 mm/day, while smaller temperature anomalies are associated with rainfall anomalies of 2–3 mm/day. There are observations fairly similar to the model outcomes. For example, Kumar et al. (2006) state that while the 6 leading droughts since 1871 occurred in conjunction with moderate-to-strong El Nino events, the major El Nino in 1997 did not result in a drought, but the moderate El Nino of 2002 was accompanied by the worst Indian drought of the last century. The quantification provided by Fig. 3 suggests that such anomalous outcomes may not be exceptional. The important conclusion from Fig. 3 is that stochasticism/internal climatic variability appears to be able to enhance or diminish the ISMR in any given year despite the prevailing ENSO situation. A further aspect of the ISMR is that of its probability density function (pdf). Figure 4a shows the model pdf for the last 5,000 years of the simulation. It is very close to Gaussian, which is to be expected in the absence of any external

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Fig. 5 Case studies for two El Nino events for JJAS conditions. The upper panels give the surface temperature anomalies for years 5055 and 7014, while the lower panels have the corresponding rainfall anomalies. The left hand panels are for the ‘‘expected’’ response for

the ISMR for an El Nino event, i.e. drought, the right hand panels show a ‘‘rogue’’ result with enhanced ISMR. The colour bars below the panels give the temperature anomalies in K, and the rainfall anomalies in mm/day

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forcing, but it provides additional proof of the model’s integrity. The corresponding observed pdf in Fig. 4a, based on 194 years of observations, indicates how unrepresentative such a short period is of the long term climatology. The remaining panels in Fig. 4 illustrate the variability of the simulated pdf for sample 200-year periods randomly selected from the 5,000-year time series. These samples have characteristics similar to the observed pdf in Fig. 4a, but rather broader bases. There is some secular variability between the three samples, with Fig. 4c, d having a diminished frequency of dry years. In contradistinction to this change these samples have more extreme dry years. The results in Fig. 4 may provide some guidance in evaluating future changes in the observed pdf as regards the cause being internal climatic variability versus global warming.

4 Case studies A number of case studies for individual years will now be presented to illustrate not only the capabilities of a coupled model, but also to confirm that anomalous or rogue outcomes for the ISMR, as documented in Fig. 3, are coherent

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Fig. 6 As for Fig. 5 but for two La Nina events

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climatic responses obtainable from typical ENSO events. The years selected are those with large ENSO temperature anomalies. This situation is demonstrated for El Nino events in Fig. 5 where for JJAS conditions the El Nino event in Fig. 5a for model year 5055 generated the ‘‘expected’’ drought over India, while the corresponding similar event in Fig. 5b, year 7014, produced a flood. The positive surface temperature anomalies in the tropical Pacific Ocean are constrained to the east of 180° longitude for year 7014 compared to year 5055, as noted by Kumar et al. (2006) for similar observed ISMR anomalies. Note also that the surface temperature anomalies over the Indian Ocean are quite different in these two examples, as are the rainfall anomalies over Australia, northeast Brazil, central USA and South Africa, in addition to those over India. Rajeevan et al. (2012) have also discussed the sensitivity of Indian monsoon rainfall in relation to the details of the surface temperature anomalies in the Pacific and Indian Oceans. The results in Fig. 5 show that despite a marked El Nino event in year 7014 other influences, whether sea surface temperatures outside of the Pacific or other related effects, were able to overwhelm the ability of this event to generate

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the expected rainfall anomalies, especially over India. This highlights the problem of predicting the ISMR a season or more in advance, as subtle details of the climatic system seem to be involved in generating the expected outcome. The corresponditing situation for La Nina events is shown in Fig. 6. The La Nina event in year 9393, Fig. 6a, produced the ‘‘expected’’ enhanced rainfall anomaly over India, Fig. 6c, while that for year 9808, Fig. 6b, generated a drought, Fig. 6d. The main differences in the two surface temperature patterns in Fig. 6 were positive anomalies (up to 0.5 K) over the southern Indian Ocean and South Atlantic Ocean. Apart from the disparity of the rainfall anomalies over India, there were fewer differences in the rainfall anomalies normally associated with La Nina events than for the El Nino situation in Fig. 5. Figures 5 and 6 emphasise the difficulty of predicting the ISMR outcome for any given ENSO event, as similar events can produce opposite outcomes. The sensitivity of the ISMR to JJAS ENSO conditions is further explored in Figs. 7 and 8 where composites are illustrated for El Nino and La Nina conditions respectively.

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These composites filter out much of the small-scale features and provide a clearer view of spatial relationships. The composites were made for the most extreme ENSO outcomes in Fig. 3 in order to enhance the signal-to-noise ratio, with each composite consisting of 10 individual years selected from the individual quadrants of Fig. 3. The El Nino composites in Fig. 7 are centred around a JJAS Nino 3.4 anomaly of ?1.0 K; the La Nina composites of Fig. 8 are centred on an anomaly of -0.7 K. Separate 10-year composites are shown for ENSO events with above or below average ISMR for both the El Nino and La Nina cases. As shown in Fig. 7a and b almost identical global surface temperature anomaly patterns existed for the two El Nino composites. In contrast, opposite rainfall anomalies are apparent over India in Fig. 7c, d. Consistent rainfall anomalies were not obtained in other ENSO-influenced regions. Very similar outcomes resulted for the two La Nina composites in Fig. 8, but with flooding conditions over India for one ensemble and drought for the other. Rather more consistent rainfall anomalies occurred in Fig. 8c and

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Fig. 7 As for Fig. 5 but for composites of the 10 most extreme El Nino events

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Fig. 8 As for Fig. 6 but for composites of the 10 most extreme La Nina events

d for ENSO-influenced regions with similar outcomes for both composites. The most consistent rainfall anomalies in Figs. 7 and 8 are clearly over India, which suggests that this region is more sensitive to ENSO events and also to influences that negate the impact of such events. The unique character of the ISMR anomalies is clearly demonstrated in Fig. 9 where, separately for El Nino and La Nina conditions, the differences in the composited global rainfall anomalies in Figs. 7 and 8, correct minus ‘rogue’, are illustrated. These difference plots show that, apart from the regions highlighted in Fig. 9, the rainfall anomalies are essentially the same for the correct and rogue composites, and thus cancel out. This outcome exists for both El Nino and La Nina states. In the highlighted regions in Fig. 9 the rainfall anomalies are of opposite sign for the correct and rogue conditions and thus sum when a difference is taken. The outcomes are exceptional over the Indian region for both El Nino and La Nina states, thus emphasising the special character of this region. Kumar

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et al. (2006) also shows a rainfall difference plot for El Nino drought minus El Nino drought-free years based on observations. Figure 9a captures most of the observed outcomes, while providing a more distinct rainfall anomaly pattern owing to the use of ‘correct’ minus ‘rogue’ results. The peculiarity of the ISMR is emphasised by comparing the rogue composite outcome for El Nino states, i.e. enhanced rainfall in Fig. 7d, with the correct composite outcome for La Nina states in Fig. 8c. The similarity of these outcomes is obtained despite totally different SST anomaly patterns in the Pacific Ocean, Figs. 7b and 8a respectively. A similar situation applies for the rogue La Nina case, Fig. 8d and the correct El Nino case, Fig. 7c. This peculiarity of the ISMR is further emphasised by examining composite surface pressure anomalies for the correct and rogue outcomes for the El Nino and La Nina states, Fig. 10. All panels in Fig. 10 show the Southern Oscillation surface pressure anomaly, with opposite anomalies for El Nino and La Nina states. For the El Nino states, Fig. 10a, c, the positive pressure anomaly is larger over the

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Fig. 9 Differences of the composite rainfall anomalies. a El Nino composite of Fig. 7, b La Nina composite of Fig. 8. For clarity rainfall anomalies less than 0.5 mm/day have been suppressed from the colour coding

Indian region for the correct composite compared to the rogue composite. For ISMR drought conditions an enhanced pressure anomaly is expected corresponding to descending air and thus reduced rainfall. Despite the enhanced ISMR anomaly for rogue El Nino states, Fig. 7d, there is still a (very) modest positive pressure anomaly over the Indian region. A similar situation exists for the La Nina composite pressure anomalies, Fig. 10b, d, but with negative values corresponding to rising air and enhanced rainfall. Thus, the overall regional pressure anomalies are only slightly different for the correct and rogue states, whether El Nino or La Nina events are considered, implying that the large scale systems are essentially similar for correct or rogue outcomes. The consistency of the model results, both in the current paper and related papers noted above, suggest that the outcomes documented in the above figures are not due to simulation errors. The similarity of Fig. 3 with Fig. 1 of Kumar et al. (2006) confirms that rogue outcomes are a real and consistent feature of the ISMR. As has been noted by others (Gershunov et al. 2001; Goswami and Xavier 2005) it appears that stochastic influences control the vagaries of the ISMR, with consequent implications for prediction.

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Although, as discussed above, there are other climatic phenomena that can impact the ISMR, viz. the AMO, NAO, Indian Ocean surface temperatures etc., it has been shown in Hunt (2012) that none of these phenomena had maxima in their individual time series occurring in conjunction with maxima in the ISMR anomaly time series in the current model. Thus, while these phenomena are intrinsic components of the climatic system, they do not appear to be instrumental in routinely causing the contrast in the ISMR outcomes displayed in Figs. 5, 6, 7, 8. This does not mean that in any individual year one or more of these phenomena may not influence the ISMR magnitude.

5 The problem of prediction The difficulty of correctly predicting the ISMR a season or year in advance is primarily attributable to the conclusion that about 50 % of the monsoon fluctuations are associated with Type 2 internal climatic variability (see, for example, Goswami 1998; Kang et al. 2004; Goswami and Xavier 2005; Kucharski et al. 2007). A consequence of this is the plaintive plea of Gadgil et al. (2005), ‘‘Monsoon prediction—why yet another failure?’’ In this respect, the scatter diagram in Fig. 3 suggests that *40 % of predictions using current approaches can be expected to generate rogue outcomes, and thus failed predictions, attributable to stochastic influences implicit in Type 2 internal climatic variability. Analysis by Goswami and Xavier (2005), based on simulations with an atmospheric climatic model, concluded that internal interannual variability of the Indian summer monsoon appears to be decoupled from Type 1 internal variability (basically ENSO). They also found that monsoon summer intraseasonal oscillations were responsible for Type 2 internal variability. Kulkarni et al. (2009, 2011) found that while faster intra-seasonal oscillations, 3–7 and 10–20 days, were favourable for monsoonal rainfall, slower modes, 30–60 days, were not. Such modal variations add another complexity to the prediction of the ISMR. A detailed study of observed intraseasonal variability and the ISMR has been presented by Hoyos and Webster (2007). A very elaborate study of the 2009 Indian summer drought by Neena et al. (2011) highlighted the complexity of the physical processes associated with active/break spells. They were able to identify the role of such processes in the major break spell in July/August, but different processes seem to have been involved in the earlier June break. Whether generic processes are involved in break spells in other drought years remains to be determined. In contrast, Ratnam et al. (2010) carried out a series of simulations of the 2009 ISMR using a very high resolution

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(a)

(c)

(b)

(d)

Fig. 10 Composites of surface pressure anomalies for JJAS conditions. These composites are for the 10 most extreme years used on Figs. 7 and 8. The left hand panels are for the El Nino events, the right hand panels for the La Nina events. The colour bars below the panels are in mbar

atmospheric model, and concluded that Pacific SST anomalies (i.e. ENSO events) had a dominant role in the ISMR outcomes, although they did not rule out the possible influence of other climatic phenomena. Their model would have been capable of resolving many of the features discussed by Neena et al. (2011). The analysis of Neena et al. (2011) suggests that Type 2 internal climatic variability is associated with specific climatic features. Thus, given the very high resolution models now available for predictions, together with a correct initialisation of the model at this fine scale, which should initialise Type 2 internal climatic variability, this would presumably permit the ISMR to be predicted for both correct and rogue years for all ENSO events. The problem with this hypothesis is that low resolution models, such as that used here, which are unable to resolve the climatic features identified by Neena et al. (2011), are able to replicate the observed range of the ISMR. This implies that large scale climatic processes dominate the ISMR evolution.

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Although correct prediction of the ISMR has proved to be difficult, the simulation of its interannual variability can be adequately replicated in a coupled model as shown in Fig. 11. The 100-year samples of observed and simulated ISMR in this figure both exhibit similar interannual variability, with occasional departures associated with extreme events. Thus, there is no inherent restriction on the ability of a coupled prediction model to generate rogue results, rather the problem is to understand the causes. A critical issue related to the prediction of the ISMR is that both the observed ISMR time series commencing in 1844 (Sontakke et al. 1993), and that commencing in 1813 (Sontakke et al. 2008), are white noise, i.e. they are stochastic. Gershunov et al. (2001) obtained an autoregression coefficient of a1 = -0.109 for a 124-year observed Indian rainfall time series, which they stated was indistinguishable from zero. They noted that their result ‘‘has grave implications for climatic predictability on seasonal-interannual timescales’’. The present 5,000-year ISMR time series returned an autoregressive coefficient of a1 = 0.072, essentially zero.

Indian summer monsoon rainfall

(a) Observed Indian region rainfall

JJAS rainfall,mm/day

8.5 8 7.5 7 6.5 6 5.5 5 1900

1920

1940

1960

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2000

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(b) Simulated Indian region rainfall

JJAS rainfall,mm/day

9 8 7 6 5 4 3 5500

5520

5540

5560

5580

5600

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JJAS rainfall,mm/day

Fig. 11 100-year time series of a the observed ISMR, b, simulated ISMR, illustrating the close relationship in their interannual variability

(a) Years 5101 to 5120 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -2.5 -0.8

-0.6

-0.4

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0

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1

A succession of 150-year samples from this time series were all found to consist of white noise. Thus, the much more quantitative results from the present model confirm the stochastic nature of the observed ISMR time series. A global plot of the a1 autoregressive coefficient (not shown) for annual rainfall for the last 5,000 years of the simulation revealed most regions had values less than 0.05, exceptions were areas northeast and southeast of the Equatorial Pacific Ocean where values of up to 0.4 were obtained. For global JJAS conditions the areas with a1 above 0.05 were even more limited and centred mainly on the Equator. Outcomes for a 1,000-year subset time series were similar to those for the 5,000-year series, but for a 100-year time series few values exceeded a1 = 0.2 and the spatial distribution was extremely noisy. Thus over most of the globe these time series were essentially stochastic. Following Gershunov et al. (2001), these results do not augur well for seasonal to interannual rainfall predictions almost anywhere. However, Shukla (1998) presents a more optimistic view. A consequence of this stochasticism is shown in Fig. 12, where ISMR and Nino 3.4 temperature anomalies, abstracted from Fig. 3, are plotted for four 20-year timespans. The extreme, random variations of this relationship from year-toyear emphasise that the outcome for any given year bears no relationship to its previous year. In any 20-year period in Fig. 12 all quadrants of the four panels are accessed by the two variables, thus highlighting the problem of predicting the ISMR. Rogue outcomes presumably occur when Type 2 internal climatic variability dominate over Type 1, being

JJAS rainfall,mm/day

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(b) Years 6201 to 6220 3 2.5 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -2.5 -0.8

-0.6

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(c) Years 7501 to 7520 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -0.6

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JJAS rainfall,mm/day

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(d) Years 801 to 820 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -1

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Fig. 12 Sample scatter plots for four 20 year subsets abstracted from Fig. 3, highlighting the marked interannual variability of the relationship between the ISMR and Nino 3.4 surface temperature. The red asterisk indicates the start of the individual plots

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attributable to stochastic processes. If the relative contributions of these two Types could be quantified at the start of a prediction some confidence in the outcome might be possible. The current negligible skill in predicting ISMR using models has been noted by Goswami and Xavier (2005). Regardless of any improvement in future coupled prediction schemes, a fundamental problem remains concerning the outcome of predicted ISMR. As demonstrated in Fig. 3 in the majority of years it should be possible to predict correctly the ISMR anomaly based on the prevailing ENSO event. However, in about 40 % of the years a rogue outcome will be obtained. Unfortunately, there appears to be no way of determining at the time of the prediction, a season or more in advance, whether a correct or rogue event will prevail. Thus the situation is not quite as dire as stated by Goswami and Xavier (2005), even though forecasters will have to live with a failure rate of somewhat less than one out of two! While the Indian region appears to be particularly sensitive to fluctuations in internal climatic variability, Fig. 9, the influence of stochasticism on rainfall seems to be a worldwide problem, as noted above in relation to the discussion on autoregressive coefficients. That analysis is basically in agreement with Goswami’s (1998) estimate of potential predictability of JJA rainfall. He found that, apart from the central Pacific Ocean, there are only very small regions of the globe where any predictability can be expected. Hence the influence of stochasticism of seasonal to annual prediction of rainfall anomalies appears to be generic.

6 Conclusions The utility of using a multi-millennial climatic simulation to investigate the ISMR has been demonstrated in the present paper. The ability of the CSIRO Mark 2 coupled climatic model to replicate basic features of the ISMR and its climatic connections has been illustrated here and in Hunt (2012). Using a 20-year moving window correlation it was shown that the ENSO/ISMR relationship has multiannual to decadal variability ranging between -0.8 and ?0.2. Observed variations in this correlation can therefore be attributed to internal climatic variability rather than external forcing factors. Periods of low correlation correspond with high Type 2 internal climatic variability implying the expectation for above normal rogue outcomes for predictions. The scatter diagram in Fig. 3 greatly extends the limited observations, and implies that about 40 % of ENSO events produce ISMR outcomes at variance with the climatological correlation between these two variables. Both case studies for individual years and composites of the global

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rainfall and surface temperature anomalies clearly reproduce the expected and rogue ISMR results for both El Nino and La Nina events. They also highlight the unique sensitivity of the Indian region rainfall variability. These results emphasise the difficulty of predicting the ISMR a season or more in advance for any given ENSO events. Time series of both observed and simulated ISMR were shown to have very similar characteristics, with both consisting of white noise. Such white noise does not mean that the ISMR is unpredictable. In the majority of cases for a given ENSO event the expected ISMR anomaly will result. Unfortunately, there is no way, a priori that the correctness or otherwise of the prediction can be determined. In general, years with high Type 2 internal climatic variability will produce rogue outcomes. Thus, if some measure of this variability can be quantified at the time of a prediction it may be possible to have higher confidence in the outcome of the prediction. This is an area of research that warrants special attention. Finally, the autoregressive analysis of the global distribution of rainfall from the present model does not indicate an encouraging prospect for seasonal prediction of rainfall outside of the Pacific subtropics. Acknowledgments It is a particular pleasure to thank Martin Dix for his assistance with technical aspects of the figures and analysis.

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