Climatological Extremes of Simulated Annual Mean Rainfall

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Oct 15, 2006 - tral United States has been presented by Woodhouse and Overpeck (1998). ...... house and Overpeck 1998; Trenberth et al. 1988; Ting.
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Climatological Extremes of Simulated Annual Mean Rainfall B. G. HUNT CSIRO Atmospheric Research, Aspendale, Australia (Manuscript received 13 May 2005, in final form 25 January 2006) ABSTRACT The Commonwealth Scientific and Industrial Research Organisation (CSIRO) Mark 2 global coupled climatic model has been used to generate a 10 000-yr simulation of “present” climate. The resultant dataset has been used to investigate a number of aspects of extremes associated with annual mean rainfall. Multimillennial time series of normalized rainfall amounts for selected points are used to highlight secular variability, spatial variations, and the differences between pluvial and drought conditions. Global distributions are also presented for selected rainfall characteristics, including the frequency of occurrence of specified rainfall anomalies with annual durations, the frequency of occurrence of 5-yr sequences of specified rainfall anomalies, and the maximum and minimum normalized rainfall amounts attained in the simulation. Such features cannot be obtained from observations because of their limited duration. A case study is also made of a megadrought over the southwestern United States, together with an analysis of the associated causal mechanisms. Given the exclusion of all external forcing from the model, it is concluded that the extreme annual mean rainfall extremes presented in the paper are attributable to stochastic events.

1. Introduction Climatic extremes, be they rainfall, temperature, or wind, can have a major impact on life. Such extremes are defined here as being greater than ⫾2 standard deviations (SDs) from the climatic mean. Exceptionally, extremes may even have resulted in the demise of civilizations, as the Maya dynasty, for example, is thought to have succumbed to a succession of severe droughts (Hodell et al. 1995; Haug et al. 2003; Hunt and Elliott 2005). Observational studies are limited by the difficulties of obtaining lengthy time series that are capable of recording the infrequent occurrence of extremes. Any such time series are, of necessity, based on proxies that introduce uncertainties into the analysis. Although proxy rainfall time series exist for many regions of the globe, the most comprehensive datasets, particularly as regards numbers, appear to be those for the United States (see, e.g., Fye et al. 2003). In particular, a very extensive, multisource analysis extending over a period of 2000 yr documenting drought conditions in the central United States has been presented by Woodhouse

Corresponding author address: B. G. Hunt, CSIRO Atmospheric Research, PMB1, Aspendale, VIC 3195, Australia. E-mail: [email protected]

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and Overpeck (1998). An interesting feature of their analysis is the spatial variability of drought implied by the individual time series they show. The occurrence of megadrought in the United States has been demonstrated by Stahle et al. (2000), who identify a particularly severe event in the late sixteenth century, although their use of decadally smoothed results exaggerates the duration of this event in their Fig. 3. A difficult observation to understand is that of Laird et al. (1996), who, on the basis of inferred salinity from Moon Lake, North Dakota, suggest that for almost all of the first millennium A.D. below-average rainfall occurred in this region. Naturally occurring climatic variability from model simulations (Hunt 2001) indicates that only decadal-length runs of below-average rainfall are to be expected, although time smoothing can enhance the apparent duration of such runs. Proxy data for East Africa (Verschuren et al. 2000) also imply the existence of lengthy dry periods between about A.D. 900 and 1300. The derivation of such proxies is of considerable importance as it helps to identify the location and frequency of occurrence of extreme annual mean rainfall events and thus their statistical occurrence rate. The identification of the causes of such events is of critical concern, as this may lead to some predictive capacity. El Niño–Southern Oscillation (ENSO) events (Cole et al. 2002) and the Pacific decadal oscillation (PDO; Ged-

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alof and Smith 2001) are potential sources of the generation of extreme events, as are other sources of teleconnections. For example, Cole et al. (2002) suggest that multiyear droughts in the United States are associated with prolonged La Niña events whose impact is then extended by additional feedbacks. Similarly, Hunt and Elliott (2002) identified El Niño events supplemented by stochastic processes as the cause of megadrought in Mexico simulated with the present climatic model. Vital as proxy datasets are for climatic studies, they do have a number of limitations. Amongst these are the existence of a single proxy dataset for a region in many cases, the limited variance explained by the proxy when compared with concurrent observations (see, e.g., Table 3 of Woodhouse and Overpeck 1998), the lack of datasets for other relevant climatic variables, and the inability to obtain a global perspective of climatic anomalies. These limitations can, however, be overcome by using output from millennial-length simulations of coupled global climatic models. These models provide coherent, interrelated datasets that can be interrogated to not only explore a very wide range of questions concerning climatic extremes, but can also be used to probe the underlying mechanisms associated with these extremes. Nevertheless, current models are not without their own problems. By definition, all simulated variables are averages over quite large areas, corresponding to the model grid boxes used. Thus small-scale features such as thunderstorms, which can produce extremely high localized rainfall, are not resolved. Any extreme event is also subject to spatial averaging over the model grid box, which could be expected to reduce both the frequency and intensity of such events. More subtly, model parameterizations of subgrid-scale physical processes are tuned for stability rather than extremes, which are associated with the “tails” of the Gaussian distribution of climatic variables. In general, climatic extremes are a feature of model simulations that have not been greatly explored outside the context of climatic change (Haylock and Nicholls 2000, Frich et al. 2002; Klein Tank and Konnen 2003). An indication of the capabilities and limitations of climatic models is provided by Gates et al. (1999), who compared a set run of most of the current models against a number of basic, observed climatic variables, including rainfall. A more detailed examination of simulation errors has recently been given by Jung (2005) for the European Centre for Medium-Range Weather Forecasts (ECMWF) model, but such errors would be fairly typical of most current models. The present study is based upon a 10 000-yr simula-

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tion of “present” climate derived from the Commonwealth Scientific and Industrial Research Organisation (CSIRO) Mark 2 coupled global climatic model. No changes in the external forcing, such as solar perturbations, volcanic eruptions, or increases in greenhouse gases, were permitted during the simulation, hence the results obtained are solely attributable to naturally occurring climatic variability produced by the complex physical mechanisms and nonlinear processes incorporated in the model. Inclusion of external forcing might be expected to create additional extreme events especially in the case of volcanic eruptions or increases in greenhouse gases. As shown in Hunt (2003), the global mean, annually averaged climate of the model is time invariant to within 1% to 2% over the 10 000 yr. Thus the various examples of climatic anomalies and extremes presented below all occur within this global mean constraint. A further aspect of climatic variability within this simulation, which is not discussed further here, is that distinct climatic trends also exist (Hunt and Elliott 2006), some with millennial duration. Hence, the climate for a given region or point may be changing subtly because of such a trend, while also experiencing sporadic extremes.

2. Model description and data The CSIRO Mark 2 global coupled climatic model was used for the simulation. This model has been described in detail by Gordon and O’Farrell (1997). The model has an R21 horizontal spectral resolution (3.25° latitude ⫻ 5.625° longitude) with 9 atmospheric levels and 21 oceanic levels. The atmospheric and oceanic components are flux-corrected to prevent climatic drift, with the corrections varying monthly but being invariant from year to year. The model has dynamical sea ice and a static biosphere, with a number of different soil and plant types. Diurnal and seasonal variability are included in the model and the usual range of subgridscale parameterizations [see Gordon and O’Farrell (1997) for more information and model performance]. The present simulation commenced from a previous 1000-yr simulation. Model outputs were stored at monthly intervals for a wide range of climatic (both atmospheric and oceanic) variables. A very limited number of climatic variables were saved at daily intervals for one millennium only. A number of climatic characteristics and extremes are presented below for annual mean rainfall. Some of these have never been derived previously. For succinctness, the analysis has been limited to annual mean values, but it could readily be extended to seasonal or monthly values. Such an extension requires a considerable increase in data manipulation, while one also tends

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FIG. 1. (top) Simulated and observed total rainfall amounts are compared for annual mean conditions (mm day⫺1). (bottom) The corresponding SDs. The simulated results used all 10 000 yr of the model run. The observations are for the period 1979–1995 only.

to become overwhelmed with the resultant detail. For reasons explained above regarding the availability of proxy datasets, preference has been given to analysis of the simulation for the North American region where case studies have been investigated. Similar analyses can readily be made for any region of the globe. The outputs presented here provide a useful illustration of the enormous potential that exists for describing, quantifying, and interpreting climatic variability from millennial-length climatic simulations. The annual mean climatic extremes shown below are generally in the form of normalized anomalies, that is, the individual annual mean anomalies from the 10 000yr mean divided by the 10 000-yr standard deviation.

3. Annual mean climatology In Fig. 1 annual mean total rainfall and its standard deviation are compared for the model and observation.

The model values are based on all 10 000 yr of the simulation, while the observations are for 1979 to 1995 only (Xie and Arkin 1996). The annual mean totals in Fig. 1 agree extremely well. The observations are somewhat noisier, probably owing to the brevity of the dataset. While the spatial patterns of the standard deviations in Fig. 1 are quite similar, the observations are again noisier and have larger magnitudes over the lowlatitude oceans. The latter may be attributable to lower activity levels in the model, as the sea surface temperature anomalies in the Pacific Ocean associated with El Niño–Southern Oscillation events are only about twothirds of observed values, and this would be expected to have an impact also on some of the statistics presented in this paper. Equally important is the brevity of the observations, as this period encompasses a time of above-average ENSO variability, and a much longerterm average might produce somewhat less activity in rainfall variability.

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FIG. 2. PDFs of simulated annual mean rainfall for a grid box in the United States (40°N, 90°W). The heavy line shows the PDF for the millennium 9001 to 10 000 yr, the dotted line that for years 9001 to 9053, and the dashed line that for years 9301 to 9353.

A further examination of the rainfall characteristics was made by calculating probability density functions (PDF). For this purpose, the recently generated, observed global rainfall dataset of Alexander et al. (2006) was used as this notionally extends from 1901 to 2003 compared with the much shorter dataset of Xie and Arkin (1996). In reality, the rainfall values of Alexander et al. (2006) are available for only the principal land areas, with noticeable gaps even for some of these areas. An important question is whether a stable PDF can be generated from only 53 yr of rainfall data. This was explored by calculating PDFs for a model grid box in the United States (40°N, 90°W) for the last millennium of the simulation, and two arbitrarily selected 53-yr periods (9001 to 9053 and 9301 to 9353) within that millennium (see Fig. 2). The 1000-yr PDF in Fig. 2 is stable and has Gaussian characteristics, apart from a positive skewness caused by the heaviest rainfall amounts. In comparison, the two 53-yr PDFs exhibit remarkable surpluses and deficits compared to the 1000-yr PDF, and also one another, especially for values near 2 mm day⫺1. Clearly a stable PDF cannot be produced within the limitations of only 53 yr of data. Despite the limitation of having only 53 yr of observations, PDFs are compared in Fig. 3 for grid boxes for three different countries for the observations, and the 53-yr period 9001 to 9053 of the simulation. In the case of Russia only 51 yr of observations were available. The three locations in Fig. 3 exhibit widely different results. For the United States, (Fig. 3a) the simulation underestimates the rainfall intensities, although the 1000-yr PDF in Fig. 2 shows that the model is capable of simulating higher rainfall intensities in better agreement

FIG. 3. PDFs for three model grid boxes [(a) United States: 40°N, 90°W; (b) Australia: 30°S, 150°E; and (c) Russia: 60°N, 45°E]. Observed results are depicted by the heavy line (for years 1951 to 2003), while the dotted lines are for the simulation (for years 9001 to 9053).

with the observations. For Australia, (Fig. 3b) reasonable agreement was obtained between model and observation, while for Russia (Fig. 3c), the model overestimates the rainfall intensities. Of course, a choice of

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other 53-yr periods of the simulation could have resulted in better agreement with the observations. The comparison in Fig. 1 and Fig. 3 clearly indicates that there are differences between the model and observations. While any climatic model has deficiencies, particularly as regards rainfall, the results in Fig. 3 suggest that the limited length of current observed “global” rainfall datasets cannot provide an adequate description of the possible range of rainfall variability. In this situation the present simulation may provide a useful indication of possible outcomes as regards rainfall characteristics, particularly the extremes of annual mean rainfall, which is the subject of this paper. In the absence of millennial or multimillennial observed or reconstructed rainfall datasets, the present simulation provides valuable insight into aspects of potential rainfall variability otherwise unobtainable.

4. Extreme annual mean rainfall events To provide a general perspective of the characteristics of the annual mean rainfall anomalies, Fig. 4 shows such anomalies for a drought-prone model grid box in northeastern Australia for years 8001 to 9000 of the simulation. In the lower panel of Fig. 4 this time series has been smoothed with a 10-point running mean filter to highlight the underlying temporal variations. The time series in Fig. 4 is fairly typical of other regions and illustrates the predominant nature of interannual variability in annual mean rainfall within the simulated climatic system. A comparison of 53-yr time series of rainfall anomalies from the observed dataset of Alexander et al. (2006) and the model for a number of different regions produced very similar outcomes. The maximum duration of runs of positive or negative anomalies in these limited samples was typically 4 to 6 yr. An important feature is that extensive (say, multidecadal) runs of positive or negative anomalies do not occur, a feature discussed in detail in Hunt (2001), who found that runs of same signed rainfall anomalies tend to be limited to about a 15-yr duration at most. Longer duration runs can be achieved if one or two anomalies with the opposite sign are permitted to be present in a given run. Such implied, extended runs are readily identifiable by time smoothing the original time series (see Fig. 4, bottom). These smoothed time series highlight the presence of, apparent, multidecadal runs of anomalies of a given sign. The oversimplification of time series of climatic fluctuations that can occur owing to time smoothing is well illustrated by superimposed smoothed and unsmoothed reconstructed time series presented by Fye et al. (2003). Unfortunately, there are many occasions when only time-smoothed results are given, and

FIG. 4. Time series of annual mean rainfall anomalies for years 8001 to 9000 of the 10 000-yr simulation for a point in northeast Australia: (top) the raw values; (bottom) time-smoothed series with a 10-point running mean.

this has consequently created a false impression of the duration of drought or pluvial events. The ability of the model to simulate quantitatively time-smoothed, past rainfall anomalies is shown in Fig. 5. A time series of normalized annual mean rainfall anomalies for years 8001 to 9000 of the simulation for a grid box centered on Vaughan, New Mexico, is compared with the corresponding reconstructed proxy rainfall dataset for El Malpais, New Mexico (Stahle et al. 2000), for a period of approximately two millennia. Many features of the two time series are remarkably similar, such as the dominant multidecadal variability, the growth and decay of trends over multidecadal time spans associated with longer-term changes, and the existence of quiescent periods with low variability. The magnitude of the maximum and minimum anomalies is larger in the reconstructed time series, particularly for the former. This outcome might be expected given the PDF discrepancies noted in Fig. 3a. The apparent

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FIG. 5. Time series of normalized annual mean rainfall anomalies for the (top) simulation and (bottom) observation for points in New Mexico. Both time series have been time smoothed. The lower panel has been redrawn from Stahle et al. (2000).

higher frequency of variability in the reconstructed time series is partially attributed to the longer duration of this time series compared to that used for the model. In the reconstructed time series an “epic” drought around A.D. 1600 is highlighted, which is not only sustained in time but is also large in peak magnitude. The simulated time series also has a corresponding feature around year 8715 with similar magnitude, almost 1.5 SDs below normal, but with slightly shorter duration. Examination of the unsmoothed simulated time series revealed a sequence of only 12 years with belowaverage rainfall, but with peak departures of about ⫺2.8 SDs below normal. Note that substantial pluvial events are also recorded in both the proxy record and the simulation. Thus the model, in an unforced simulation, replicated many of the characteristics of this reconstructed time series in the United States. For any selected point or region it is usually possible to readily identify the years having extremes of annual mean rainfall by generating time series in the format used in the top panel of Fig. 4. Examination of the global distribution of rainfall anomalies for such years reveals that on many occasions these extremes occur as isolated features within an otherwise unremarkable large-scale circulatory system. Taken in conjunction with the major drought identified in Fig. 5, which is

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discussed in detail below, this suggests that stochastic processes are important influences in these phenomena (see also Hunt and Elliott 2005). A matter of considerable interest is the tabulation of the occurrence rate of extreme events, however specified. Results for three locations in the United States, for both positive and negative annual mean rainfall extremes, are given in Fig. 6 where time series of normalized annual mean rainfall anomalies above a specified threshold are illustrated. Different cutoff values were used for the three locations, and for the positive and negative ranges, in order to produce roughly the same number of events in each panel. The results in Fig. 6 are designed to identify the years with the largest SD. Those shown in the individual panels represent, at most, only 1% of the 10 000-yr time series, hence they are exceptional events in the simulation. For any given grid box there are, of course, numerous years with smaller SD associated with less extreme rainfall anomalies. For example, while only three droughts are shown for Kansas in Fig. 6 between 4000 and 7000 yr, reducing the cutoff criterion used in this panel from ⫺3 to ⫺2.5 SDs reveals scores of additional droughts in this interval. Substantial differences are apparent in anomaly characteristics for both drought and pluvial conditions for the three grid boxes in Fig. 6. For the drought years in Fig. 6 (left), it can be seen that the magnitude of the SD increases from Tucson, Arizona, to Kansas, implying larger rainfall variations. In contract, Tucson has more extreme pluvials (Fig. 6, right). Not all the events identified for the drought or pluvial situations in Fig. 6 are necessarily simultaneous. This can arise from two causes. The first may be actual spatial variability of rainfall anomalies, where a given anomaly pattern may not embrace all three points. The second may occur for situations where all three points are part of the same anomaly pattern but with quite different rainfall anomaly magnitudes; an example of this situation is illustrated below. In some of the panels in Fig. 6 noticeable outliers can be seen. The characteristics of the extreme negative outlier for Kansas in Fig. 6, having an SD of ⫺4.3, were examined and compared with the major drought that occurred in the United States in 1952. Between 1951 and 1956 a continuous series of widespread droughts occurred across the United States, sometimes even extending into Canada and Mexico. These and other American droughts, together with reconstructed case studies, have been discussed by Fye et al. (2003). The simulated drought for year 6963 and the observed drought for 1952 are shown in Fig. 7 for annual

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FIG. 6. Time series of normalized annual mean rainfall anomalies for three points in the United States, nominally Tucson, Arizona; Pittsburgh, Pennsylvania; and southwest Kansas. (left) The individual years with normalized values below ⫺2 SDs (⫺2 for Tucson, ⫺2.5 for Pittsburgh, and ⫺3 for Kansas). (right) The individual years with normalized values above 2.5 SDs (3 for Tucson and 2.5 for Pittsburgh and Kansas).

mean conditions. The limitations of the observed rainfall dataset (Alexander et al. 2006) are readily apparent in Fig. 7, with results available for only North America, and no data shown for the oceans or the portion of South America in the figure. In contrast, results are

available for the whole of the region shown for the simulation, and these suggest that the negative rainfall anomalies over the United States are part of a more extensive spatial system. In the simulation a large region of the central United

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FIG. 8. Global distributions of the occurrence rates (10 000yr)⫺1 of individual normalized annual mean rainfall anomalies (a) below ⫺3 SDs and (b) above ⫹3 SDs. FIG. 7. Annual mean rainfall anomalies for the North American region are shown for the (top) simulation (year 6963, mm day⫺1) and (bottom) observations (1952, mm yr⫺1).

States had an annual mean rainfall deficit above –1 mm day⫺1, with this outlier case involving rainfall deficits across the whole of the United States. In contrast, the observations in Fig. 7 indicate a maximum rainfall deficit region of less than ⫺1.0 mm day⫺1, highlighting the relative modesty of this drought compared to the simulated outlier. Even though the 1950 droughts in the United States were, in fact, quite severe, the comparison to Fig. 5 emphasizes how extreme drought could be, assuming that the simulation is plausible. While both the drought patterns in Fig. 7 show maximum rainfall anomalies toward the southeastern United States, other patterns do occur. Fye et al. (2003) found that another preferred pattern has maximum rainfall anomalies more toward the central and northwestern United States for the 1930 Dust Bowl droughts and other reconstructed cases. Although there are a number of similarities between the two rainfall anomaly

patterns in Fig. 7, as well as differences, there is no reason why they should exhibit a closer correspondence. The simulated pattern is for an outlier situation, while the observed pattern is only one example of the patterns that occurred during the 1950 drought sequence. Nevertheless, the comparison suggests that this simulated extreme drought is plausible and highlights the potential for the occurrence of actual droughts substantially more devastating than those documented in the recent observed rainfall record. The utility of the simulation is highlighted by the global perspective of the frequency of occurrence of extreme annual mean rainfall events given in Fig. 8. This shows the number of occurrences, over the 10 000 yr of the simulation, of normalized annual mean rainfall anomalies either below ⫺3 or above ⫹3 standard deviations for individual years (as opposed to sequences of years). These would presumably represent extreme droughts or pluvials. As can be seen in Fig. 8, the pattern in one panel is almost the reverse of the other. An ENSO-like spatial pattern is evident over the low-

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latitude Pacific Ocean in both periods, although the magnitudes in Fig. 8 may be underestimated, as indicated by the lower simulated SD in Fig. 1. Given the 10 000 yr of the simulation, the relative infrequency of the occurrence of these simulated extreme events across the globe is especially noteworthy. In particular, Fig. 8a reveals that no events within the specified range occurred over most of the semitropical oceans and the major desert regions of the globe. All these regions have low rainfall (see Fig. 1) so that marked negative anomalies are hardly to be expected. Apart from the Amazon and Congo, the highest occurrence rates were over the oceans, especially at high latitudes. Even so, only three events per millennium was the maximum occurrence rate in Fig. 8a, indicating the rarity of such extreme droughts. Whether this rarity is attributable to model deficiencies or is a realistic outcome is difficult to determine precisely as reconstructed rainfall time series of sufficient duration and global coverage are totally lacking. Reconstructed values of the Palmer Drought Severity Index (PDSI) for various regions in the United States (Fye et al. 2003; Woodhouse and Overpeck 1998) for the last 500 yr reveal rather few extreme negative values, the largest being for the sixteenth-century megadrought. According to the reconstructed time series shown in Fig. 5 this megadrought had an SD of about ⫺1.5. The analysis of Fye et al. (2003) reveals that reconstructions underestimate the true value of the observed PDSI, thus more extreme droughts may have occurred in reality. Nevertheless, the limited reconstructed data available do not seem to be at great variance with the frequency of occurrence shown in Fig. 8. In the absence of any alternative information, Fig. 8 provides a useful indication of the likely occurrence rate and geographical distribution of extreme annual mean rainfall anomalies. While Fig. 8b has essentially the reverse pattern of activity to Fig. 8a, there is a further asymmetry in that there were almost no grid boxes where no extremes events were recorded. A further difference is the large area of the globe in Fig. 8b where 30 or more events occurred. The highest occurrence rates were in regions of both low rainfall amount and low standard deviation (see Fig. 1). This is presumably because it is relatively easier to obtain positive rainfall anomalies in low rainfall regions. In contrast, locations with high rainfall amounts, the Congo, Indonesia, and the Amazon, had relatively low counts in Fig. 8b. As the severity of the threshold used in Fig. 8 is increased the number of locations attaining the given threshold drops very fast. For a threshold of ⫺4 SD activity was primarily restricted to the Congo, Indone-

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sia, and the Amazon, together with isolated events with occurrence rates of one per ten thousand years elsewhere. Also half the surface of the globe did not record any events for a threshold of ⫹4 SD. For a threshold of ⫹6 SD activity was restricted to the Sahara, the Atacama Desert and adjacent ocean, and parts of the polar regions. Nevertheless, this indicates that extreme climatic outliers were generated in the simulation. Again, appropriate observed data are not available for comparison. Another important characteristic of climatic extremes is the frequency of occurrence of a given run of years above a specified threshold. For example, five years of severe drought in a given region may well be more damaging than a single year of extreme drought. Figure 9 presents normalized annual mean rainfall anomalies for a point in Kenya having magnitudes above ⫾1.0 standard deviation with associated runs of 3-, 4-, or 5-yr duration. The sequences in the figure appear as a single line because of the compressed horizontal scale; the largest anomaly of the sequence then sets the magnitude of the plotted signal. Even for a low magnitude of one standard deviation only one 5-yr sequence was found for negative anomalies, and two for positive anomalies, within the 10 000yr simulation (see Fig. 9, bottom). A similar result was obtained for points in Australia and the United States, suggesting that this may be a relatively common outcome. This somewhat surprising situation indicates how difficult it is for the climatic system (at least as simulated here) to maintain an anomaly of reasonable magnitude for an extended period. This limitation is mainly attributable to the spatial variability of anomaly patterns from year to year (see below). As shown in the middle panels of Fig. 9, even sequences of 4 yr for this standard deviation are not very common, especially for positive rainfall anomalies. Three-year sequences (Fig. 9, top) occur quite frequently, but periods of a 100 yr or more without such a sequence still exist. Returning to the question whether five years of severe drought is more damaging than a single year of extreme drought, an assessment was made using the Kenyan grid box of Fig. 9. The accumulated rainfall deficit for the 5-yr sequence shown in Fig. 9 was 1788.5 mm, while that for the 5-yr sequence centered on the single most extreme year in the simulation was 586.7 mm. In this particular example, the extreme year was a clear outlier in otherwise near-normal years adjacent to it. Examination of other extreme years revealed cases where some adjacent years also had drought, indicating that other situations would not have as large contrasts as the case given above. Sequences of major droughts

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FIG. 9. The occurrence frequency over all 10 000 yr of the simulation of sequences of years all with a normalized annual mean rainfall anomaly (left) below ⫺1.0 SD or (right) above ⫹1.0 SD. (top) Sequences of three successive years, (middle) four successive years, and (bottom) five successive years. All results are for a grid box in Kenya (1.6°N, 33.8°E).

would therefore seem to be more damaging than single years of extreme drought, but the issue is complicated by such aspects as the amount of rainfall falling during the cropping seasons, associated temperatures, etc.

These results do not support the existence of “megadroughts” lasting decades or longer, as reported observationally (Stine 1994; Verschuren et al. 2000; Stahle et al. 2000; deMenocal 2001). It should be noted, however,

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that the definition of a megadrought by Stahle et al. (2000) did include wet years within an overall run of dry years. Whether the difference between this simulation and observations is attributable to model deficiencies, implicit time smoothing in reconstructions of rainfall, or misinterpretations, is not clear. Certainly, the modern observational record of rainfall does not appear to support multidecadal drought, with the possible exception of the Sahel (see Nicholson 1993). If such droughts really occurred in the past, then some external forcing mechanism presumably was responsible. Relaxing the megadrought criterion to include occasional wet years (see Stahle et al. 2000) does permit “droughts” with durations of 20 or more years to be readily identified in the simulation. Figure 9 suggests a somewhat lower frequency of occurrence of runs of pluvial years compared to drought years. This outcome was also characteristic of individual Australian and American locations. Again, the model permits a global perspective to be obtained regarding the occurrence rate of sequences of dry or wet years for a specified anomaly value. Thus, Fig. 10 compares the occurrence rate of 5-yr-long sequences with normalized annual mean rainfall anomalies either below ⫺1.0 or above ⫹1.0. The outcomes are similar for both cases, with about half the globe not experiencing such sequences. Apart from activity near the poles, the major center of activity was the lowlatitude Pacific Ocean, where around five sequences occurred during the 10 000-yr simulation. Only a very few grid boxes over land had more than one 5-yr sequence of either sign, and this emphasizes the rarity of such events. Given the inherent interannual variability of climate, this result is perhaps not unexpected. As noted above, sequences of rainfall anomalies of a given sign with durations of up to 15 yr were obtained in the simulation, but these include some very small magnitude anomalies (see Fig. 4). Relaxing the ⫾1.0 standard deviation used in Fig. 10 would certainly permit many more events to be identified. Overall, one would expect rainfall fluctuations to be mainly governed by interannual variability with occasional runs of years interspersed with stochastically induced extreme rainfall anomalies. An important measure of any climatic extreme is the range between maximum and minimum normalized rainfall anomalies at any given location. Figure 11 contrasts the global distributions of such rainfall extremes. The outcome shows remarkable uniformity, with both sets of anomalies being predominantly in the range of three to four, although there is somewhat more variability for positive anomalies. The poor representation

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FIG. 10. Same as in Fig. 8, but for the occurrence rate of sequences of five successive years with normalized annual mean rainfall anomalies (10 000 yr)⫺1 (top) below ⫺1.0 SD and (bottom) above ⫹1.0 SD.

of subgrid-scale events, especially convection, may have contributed to some of this uniformity. Regions with anomalies outside the range of three to four standard deviations are primarily restricted to desert or very high rainfall areas. As such, these climatic outliers are very localized geographically according to Fig. 11. While anomalies in the range of four standard deviations can be classified as “extreme,” and therefore unlikely to be attained very frequently, it is still rather surprising that more spatial variability is not displayed in Fig. 11. The patterns in Fig. 11 were basically stable when the maximum and minimum values were computed for a single millennium (8001 to 9000 yr). As would be expected, there was a decline in the magnitude of the values overall, indicating that the most extreme values were not attainable within a single millennium at all points. The anomalously large negative values for Brazil, identified in the top panel of Fig. 11, were examined by generating a time series for this location. On about 10 occasions values below ⫺4 SDs were found over all 10 000 yr of the simulation, indicating that, while rare,

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FIG. 12. Time series of climatic variables associated with the severe drought at the Vaughan, New Mexico, grid box. The Niño3.4 sea surface temperature anomalies are indicated by the N34SST curve, the Pacific decadal oscillation by PDO, and the Vaughan rainfall by RAIN. The latter is shown by vertical lines for clarity (mm day⫺1).

FIG. 11. Global distributions of the (top) minimum and (bottom) maximum normalized annual mean rainfall anomalies attained in the 10 000-yr simulation. The color bars give the SDs obtained.

these extreme events were a persistent feature of the local climate.

5. A case study To conclude the analysis a case study was made of an extended, severe drought in New Mexico. The particular drought concerned is that which occurred around year 8715, as shown in Fig. 5 for a grid box centered on Vaughan, New Mexico. The basic aim was to establish the spatial and temporal characteristics of this drought, and, if possible, to identify causal mechanisms, even though the latter might not have general applicability to other droughts worldwide. Unsmoothed time series of simulated annual mean rainfall for Vaughan for the time period around this drought (Fig. 12) revealed 12 successive years of belowaverage values, years 8712 to 8723, and with only 2 yr of above average rainfall in the subsequent 7 yr. Six years, 8713, 8714, 8716, 8717, 8718, and 8719, had anomalies below ⫺1.0 SD. The peak negative rainfall anomaly

was ⫺2.6 SDs in year 8719. By any standard this was a period of extensive and intensive drought. There are well-known, observed relationships between North American drought and ENSO (Woodhouse and Overpeck 1998; Trenberth et al. 1988; Ting and Wang 1997; Bunkers et al. 1996), and these also existed in the simulation. Over all 10 000 yr of the simulation a correlation coefficient of 0.117 was found to exist between rainfall anomalies for Vaughan and the sea surface temperature anomalies for the Niño-3.4 region (5°S–5°N, 170°–120°W). While small, this correlation implies, as observed, that La Niña conditions were associated with drought in this region. As noted by Cole et al. (2002), persistent droughts in the United States are associated with multiyear La Niña events, modulated by the negative phase of the PDO. This situation prevailed in the model for the persistent drought centered on year 8715 as shown in Fig. 12, although the relationships illustrated are somewhat more complex. Thus the La Niña events and the negative phase of the PDO preceded the initiation of the drought and reversed sign prior to the peak drought year 8719. (Examination of the spatial distribution of annual mean sea surface anomalies for year 8719 did, however, reveal negative anomalies in the central, tropical Pacific Ocean.) The drought broke in year 8724, although only marginally, with modest El Niño events primarily prevailing during this time. Under these circumstances stochastic influences may have continued this drought episode after the termination of the La Niña events. A related situation has been suggested in the observational analysis of Cole et al.

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(2002). A similar sequence of ENSO and stochastic influences appears to have caused a megadrought in Mexico in this simulation (Hunt and Elliott 2002). Persisting land surface temperature anomalies may also have an influence. The spatial patterns of rainfall anomalies over North America for years 8715 to 8720 are shown in Fig. 13. There is no simple, continuing pattern of rainfall anomalies associated with this persistent drought, with different intensities and areas predominating from year to year (see, e.g., Fig. 7 of Woodhouse and Overpeck 1998). This suggests that a number of factors may have contributed to the variability shown in Fig. 13. A similar analysis for a sequence of wet years over northwestern North America in this simulation, not shown, also revealed varying intensities and patterns of annual mean rainfall anomalies. It is precisely these vagaries of interannual climatic variability that make it difficult to understand how century or longer droughts can be generated and maintained, as reported by Laird et al. (1996) and Stine (1994). If such droughts actually occurred then they imply some external forcing mechanisms or very unusual sequence of climatic interactions. The time average of the annual mean rainfall anomalies for years 8712 to 8723, corresponding to the drought sequence in Fig. 12, revealed a drought pattern (not shown) very similar to that identified by Fye et al. (2003) for 1950-like droughts. This simulated pattern was essentially an extension of a drought region extending northwest across the Pacific Ocean from PapuaNew Guinea to the west coast of North America, a feature unavailable in the reconstructions of Fye et al. (2003). The corresponding time-averaged sea surface temperature anomalies for this period revealed a weak La Niña situation. The drought events in Fig. 13 can be related to systematic changes in the prevailing anticyclonic surface pressure pattern that extends westward from the North Atlantic Ocean. The associated low-level inflow of moist air from the Gulf of Mexico into the New Mexico region produces the observed summer peak in rainfall. As shown in Fig. 14 for July of year 8719 (the peak drought year in Fig. 12), negative surface pressure anomalies extended over North America, thus reducing the inflow from the Gulf of Mexico and resulting in drought conditions. How these surface pressure anomalies are related to La Niña events, and the PDO, is beyond the scope of this paper, but see Hunt and Elliott (2002) for a related discussion.

6. Conclusions A 10 000-yr climatic simulation has been used to illustrate some of the characteristics of annual mean

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rainfall extremes. The simulation was for fixed, “present” climatic conditions, hence all climatic fluctuations obtained are a consequence of naturally occurring climatic variability. These and other results from the model (Hunt 2001; Hunt and Elliott 2002, 2005) highlight the impressive range of such fluctuations that can be generated in millennial-length simulations. For example, in the present study it has been shown that not only could the model replicate the basic features of millennial-length reconstructed rainfall for New Mexico, but also the characteristics of severe, extended drought in this region. Importantly, the simulation not only confirmed the role of multiyear La Niña events in such a drought, but reinforced the contribution made by the PDO. Some insight into the associated climatic mechanism was also provided. The 10 000-yr-long time series illustrating the occurrence of severe drought or pluvial events for selected points in the United States highlighted both the temporal and spatial variability of rainfall. In general, pluvial events were more uniform in time, and had greater magnitudes, an outcome attributable to the rainfall distribution being bounded at zero. The global distribution of the frequency of occurrence of extreme drought and pluvial events (⫾3 SDs) of one year’s duration revealed almost opposite spatial patterns. Over lowlatitude oceans and desert regions no such events were found for drought, but these regions had the highest occurrence rates for pluvial events. These outcomes are readily related to the associated climatological rainfall distributions. An examination of the occurrence rate of runs of years with severe to extreme drought revealed that such runs were surprisingly rare. While 3-yr sequences of ⫾1 SD were quite common, 5-yr sequences did not occur over more than half of the globe. Over the 10 000 yr of the simulation there were very few locations that had more than five occurrences of 5-yr-long sequences for ⫾1 SD. Apart from the polar regions, most of these locations were in the low-latitude Pacific Ocean. While such an outcome seems plausible based on the vagaries of the interannual variability of climate, they are at variance with observations for some specific sites in Africa and the United States. Global distributions of the minimum and maximum normalized annual mean rainfall over the whole 10 000 yr of the simulation revealed surprising spatial uniformity. This was especially noteworthy for drought conditions where a range of ⫺3 to ⫺4 SDs was found. The major exceptions were over the Amazon and Congo river basins where far larger values were obtained. For pluvial conditions there was more spatial variability and

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FIG. 13. Annual mean rainfall anomalies for an enlarged North American region, illustrating the variations in the drought pattern over North America for a sequence of years (mm day⫺1). The color bars give the rainfall anomalies in mm day⫺1.

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an explanation for their observations may be preferable to hypothesizing external forcing. Stochastic influences, deriving from nonlinear mechanisms and physical processes, are considered to be the progenitors of the climatic fluctuations generated within the current simulation. While individual ENSO events are largely deterministic once an event has been initiated, their vagaries from one cycle to the next indicate the underlying interaction of stochastic influences on these multiannual events. Examination of the unique behavior of climatic time series, such as those in Fig. 4 and Fig. 6, provide strong support for the role of stochastic processes in climatic variability. Acknowledgments. The assistance of Martin Dix in aspects of the analysis and generation of figures is noted with thanks. REFERENCES

FIG. 14. (top) The surface pressure distribution for July of year 8719 and (bottom) the associated surface pressure anomalies (mb).

larger anomalies, typically ⫹4 to ⫹6 SDs. Exceptions were primarily over the Sahara and Atacama deserts. The global distributions illustrated in Figs. 8, 10, and 11 highlight the utility of multimillennial coupled global simulations in providing unique insights into aspects of climatic variability that cannot be obtained from observations. The spatial patterns displayed, and the magnitudes of the associated climatic outcomes, hopefully should provide some guidance to palaeoclimatologists endeavoring to interpret their much more limited datasets. This comment has to be read in conjunction with the various model deficiencies noted above. The restriction of the model to unforced climatic conditions means that the resulting variability is generated by nonlinear mechanisms and processes internal to the model. Thus the range of climatic fluctuations presented in the paper illustrates what the climatic system can produce without external forcing. It is therefore hoped that as more analyses are presented from other multimillennial simulations, palaeoclimatologists will appreciate that invoking natural climatic variability as

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