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    Occurrence rates of summer heat waves for the (left) Northern Hemisphere (JJA) and (right) Southern Hemisphere (JFM). For each hemisphere the corresponding winter “heat waves” are also shown. The heat waves have mean intensities over the whole summer period of (top) 3, (middle) 4, and (bottom) 5 K. The color bars give the occurrence rates for the 10 000 yr of the simulation.

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    The frequency of occurrence of mean summer temperature anomalies above specified thresholds for selected model grid boxes over the 10 000 yr of the simulation. The grid boxes are located as follows: United States (35°N, 91°W), India (20°N, 80°E), Europe (50°N, 10.5°E), and Australia (25°S, 150°E).

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    Global distributions of summer mean surface temperature anomalies (K) for selected years. Individual years were selected to highlight heat waves in four separate regions.

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    Probability density functions of summer surface temperature anomalies for all 10 000 yr of the simulation are shown for the same four grid boxes as used in Fig. 2. Superimposed on each pdf is the corresponding Gaussian distribution.

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    Surface temperature (K) and rainfall (mm day−1) anomalies over Europe for the extreme heat wave year 5190 of the simulation (See Fig. 2). (left) The temperature anomalies and (right) the rainfall anomalies. Results for (top) June, (middle) July, and (bottom) August are given.

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    Monthly mean surface temperature anomalies over the North American region for January–August for the extreme U.S. heat wave year 1457 of the simulation (see Fig. 2). The color bars below the panels are in K.

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    Time series of monthly surface temperature and rainfall anomalies for the U.S. grid box (35°N, 91°W) for years 1456–1458, which encompass the extreme heat wave year of 1457. The rainfall anomalies have been shifted 0.5 months to the right of the surface temperature anomalies for clarity.

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    Monthly surface temperature anomalies (K) for Australia for an extreme heat wave situation. Results are shown for summer of year 9618 of the simulation, for January, February, and March.

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    Time series of daily maximum surface temperature anomalies for the U.S. grid box (35°N, 91°W) for the 100-yr period of 4401–4500 from the simulation. Values less than 4 K have been omitted. Results shown are for June, July, and August only.

  • View in gallery

    Time series of daily temperature anomalies (K) for the U.S. grid box (35°N, 91°W). Results are shown for arbitrarily selected years. (top) The model maximum temperature anomalies are plotted for year 4401 from the simulation; (bottom) the reanalysis results for daily mean surface air temperature anomalies are plotted for 2000 a.d.

  • View in gallery

    Occurrence rates of summer heat waves for the (left) Northern Hemisphere (JJA) and (right) Southern Hemisphere (JFM) are illustrated. Heat waves having daily maximum temperature anomalies greater than 4 K for (top) 5, (middle) 10, and (bottom) 15 successive days. The color bars give the occurrence rates for the 100-yr period of years 4401–4500 from the simulation.

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    Sequence of daily maximum surface temperature anomalies (K) for 8 days in June and July of year 4498 of the simulation during which a heat wave occurred in the United States.

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    Surface pressure distribution (mb) corresponding to 30 June of year 4498, one of the days used in Fig. 12.

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    Time series of extreme temperature anomalies for the U.S. grid box (35°N, 91°W). (top) The model values are given for the 500-yr period of years 4001–4500 from the simulation. Daily maximum surface temperature anomalies are shown for June, July, and August conditions and for magnitudes above 10 K. (bottom) The ERA-40 t2 anomalies, as the average of four values over each day, are shown for the same months but for magnitudes above 4 K.

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    Monthly time series for anomalies of selected climatic variables for year 4103 from the simulation for the U.S. grid box (35°N, 91°W).

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    Time series for the 25-yr period of years 4100–4124 from the simulation. Shown are monthly anomalies of surface temperature at the U.S. grid box (35°N, 91°W) as well as Niño-3.4 sea surface temperature.

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A Climatology of Heat Waves from a Multimillennial Simulation

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  • 1 CSIRO Marine and Atmospheric Research, Aspendale, Victoria, Australia
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Abstract

A 10 000-yr unforced simulation with the Commonwealth Scientific and Industrial Research Organisation (CSIRO) Mark 2 coupled global climatic model has been used to investigate the occurrence of heat waves over the globe. Results are presented for both seasonal (summer mean) and daily heat waves. Geographical distributions of the occurrence rates of these heat waves are shown for various magnitudes of surface temperature anomalies. The heat waves have specific geographical preferences with regions where relatively frequent, intense, and long-lasting heat waves occur. Time series over all 10 000 yr of the heat waves for the selected model grid boxes illustrate the differing temporal variabilities at these locations, as well as identifying the occurrences of extreme heat waves. To this end, the observed European heat wave of 2003 was simulated remarkably well in its overall characteristics; it occurs once in this simulation. Heat waves for various continental locations are shown to occur as isolated spatial and temporal events, and not as part of larger-scale systems over continental-size domains, suggesting stochastic forcing as a contributor to the initiation of the heat waves. Regional plots of selected heat waves at monthly intervals illustrated the considerable spatial variability, progression, and variation in the intensity of the heat waves. Comparison of year-long daily surface temperature anomalies for heat-wave years for simulated and observed conditions at individual model grid boxes indicated substantial agreement, while spatial plots permitted the progress of a short-term heat wave over the United States to be followed. Multidecadal time series plots of intense heat waves also showed basic similarities between the simulation and observations, despite the brevity of the latter. The simulated time series suggest that more extreme heat waves than currently are observed, owing to the brevity of the observations, may be a possibility as a consequence solely of natural variability. An examination of the physical processes associated with a heat wave showed mutually consistent climatic relationships, such that a heat wave was associated with reduced rainfall and consequently reduced soil moisture content, evaporation, and cloud cover, and increased insolation at the surface. These combined changes created the surface temperature increase intrinsic to the heat wave. All heat waves examined for different regions experienced negative rainfall anomalies prior to a heat wave. The cause of these rainfall anomalies was not readily apparent. While an ENSO influence on heat waves is shown to exist in the simulation, not all ENSO events produce heat waves, suggesting that stochastic influences may determine when a major heat wave occurs in conjunction with these events. The limitations of the adequacy of the model ENSO may, however, have had an influence in this regard.

Corresponding author address: B. G. Hunt, CSIRO Marine and Atmospheric Research, PMB1, Aspendale VIC 3195, Australia. Email: barrie.hunt@csiro.au

Abstract

A 10 000-yr unforced simulation with the Commonwealth Scientific and Industrial Research Organisation (CSIRO) Mark 2 coupled global climatic model has been used to investigate the occurrence of heat waves over the globe. Results are presented for both seasonal (summer mean) and daily heat waves. Geographical distributions of the occurrence rates of these heat waves are shown for various magnitudes of surface temperature anomalies. The heat waves have specific geographical preferences with regions where relatively frequent, intense, and long-lasting heat waves occur. Time series over all 10 000 yr of the heat waves for the selected model grid boxes illustrate the differing temporal variabilities at these locations, as well as identifying the occurrences of extreme heat waves. To this end, the observed European heat wave of 2003 was simulated remarkably well in its overall characteristics; it occurs once in this simulation. Heat waves for various continental locations are shown to occur as isolated spatial and temporal events, and not as part of larger-scale systems over continental-size domains, suggesting stochastic forcing as a contributor to the initiation of the heat waves. Regional plots of selected heat waves at monthly intervals illustrated the considerable spatial variability, progression, and variation in the intensity of the heat waves. Comparison of year-long daily surface temperature anomalies for heat-wave years for simulated and observed conditions at individual model grid boxes indicated substantial agreement, while spatial plots permitted the progress of a short-term heat wave over the United States to be followed. Multidecadal time series plots of intense heat waves also showed basic similarities between the simulation and observations, despite the brevity of the latter. The simulated time series suggest that more extreme heat waves than currently are observed, owing to the brevity of the observations, may be a possibility as a consequence solely of natural variability. An examination of the physical processes associated with a heat wave showed mutually consistent climatic relationships, such that a heat wave was associated with reduced rainfall and consequently reduced soil moisture content, evaporation, and cloud cover, and increased insolation at the surface. These combined changes created the surface temperature increase intrinsic to the heat wave. All heat waves examined for different regions experienced negative rainfall anomalies prior to a heat wave. The cause of these rainfall anomalies was not readily apparent. While an ENSO influence on heat waves is shown to exist in the simulation, not all ENSO events produce heat waves, suggesting that stochastic influences may determine when a major heat wave occurs in conjunction with these events. The limitations of the adequacy of the model ENSO may, however, have had an influence in this regard.

Corresponding author address: B. G. Hunt, CSIRO Marine and Atmospheric Research, PMB1, Aspendale VIC 3195, Australia. Email: barrie.hunt@csiro.au

1. Introduction

Heat waves are a fact of life. They are also a factor in death, with some thousands of fatalities attributed to the European heat wave in 2003 (WMO 2003), and over a thousand deaths associated with the U.S. heat wave of 1995 (Palecki et al. 2001).

Although there is no agreed definition of a heat wave, such an event consists of a period of several days or more with temperatures sufficiently enough above normal to cause stress resulting in increased human mortality and damage to vegetation.

The impact of a heat wave varies considerably from region to region. For example, a multiday temperature anomaly of 5 K in summer in central Europe would be expected to create more problems and loss of life than a similar heat wave in Iceland, simply because the latter has much lower mean temperatures. The characteristics of heat waves also vary considerably. The European heat wave of 2003 was sustained over June, July, and August (Schär et al. 2004; Fink et al. 2004), while the U.S. heat waves of 1995 and 1999 were confined to a few extreme days in July (Kunkel et al. 1996; Palecki et al. 2001). Most heat waves seem to be in the latter category; see, for example, Burt (2004), Khaliq et al. (2005), and Founda et al. (2004).

Because of the loss of life, damage to crops and vegetation in general and the impact on water supplies, these recent heat waves have stimulated much interest in their climatological features, recurrence times, and, especially, whether they are a portent of greenhouse-induced climatic change. For example, Trigo et al. (2005) state that the hot summer of 2003 in Europe exceeded any over the past 500 yr, and Schär et al. (2004) claim that this event was statistically very unlikely, and was also consistent with results from climatic change simulations. Stott et al. (2004) estimate that past anthropogenic influences doubled the probability of the occurrence of the 2003 heat wave. More intense and frequent heat waves are also predicted by Meehl and Tebaldi (2004) and Beniston (2004) on the basis of greenhouse simulations.

The difficulty of estimating the return periods for current observations is well illustrated by Karl and Knight (1997), who obtained a value of about 100 yr for the so-called Chicago heat wave of 1995. Four years later in 1999 Chicago again experienced a heat wave very similar to that of 1995 (Palecki et al. 2001). Benestad (2003) has also discussed the problem of estimating return periods for rare climatological events.

Regional and global estimates of observed heat wave characteristics are limited by the availability of suitable data. Frich et al. (2002) have produced a heat wave duration index that was able to cover only North America, Europe, parts of Asia, and Australia. This index is defined as the maximum period with more than 5 days with a maximum temperature anomaly 5 K above the 1961–90 daily temperature maximum norm. For the second half of the twentieth century they showed increases in the index values, except for eastern North America and parts of southern Asia. Thus, their analysis suggests an increase in heat-wave frequency over the past few decades, which is presumably consistent with a greenhouse influence. Choi and Meentemeyer (2002) have devised a climatology of persistent positive temperature anomalies for the United States for 1850–1995. They present a variety of outcomes showing spatial patterns of such anomalies for various durations and intensities.

The potential (or actual?) impact of the greenhouse effect creates problems in determining the characteristics of severe climatic events, such as heat waves, owing to the nonstationarity of the climate. There is obviously a need to quantify pregreenhouse climate in order to differentiate it from greenhouse influences. In particular, the U.S. heat waves of 1995 and 1999 and the European heat wave of 2003, being very recent, need to be placed in an appropriate historical perspective.

Unfortunately, the lack of surface temperature observations extending back over many centuries prevents such a perspective from being obtained. However, some insight into the location, duration, intensity, etc. of heat waves can be deduced from multimillennial simulations with coupled global climatic models. While these models have limitations, they do provide consistent and comprehensive datasets for all climatic variables of interest, and can be applied to a wide range of issues.

To this end, a 10 000-yr simulation with the Commonwealth Scientific and Industrial Research Organisation (CSIRO) Mark 2 coupled global climatic model has been analyzed to investigate the characteristics of heat waves across the globe. The simulation was not undertaken simply to examine heat waves, but also to consider a wide range of climatic features generated by natural climatic variability. The analysis includes the identification of the spatial patterns at seasonal and monthly intervals; time series illustrating the temporal variability of heat waves for specific locations; the intensity and duration of heat waves, including daily variability; and related hydrological, radiative, and dynamic processes.

Previous analyses from this simulation have demonstrated the ability of the model to replicate many observed climatic features. These include a demonstration of the stationarity of the global mean climate over all 10 000 yr of the simulation (Hunt 2004), a necessary outcome given the fixed boundary conditions used in the simulation, and the lack of any climatic drift in the simulation. Hunt (2004) also provides a selected comparison of surface temperature and rainfall variability with observations. The simulation has also been used to demonstrate that critical observed drought events could be reproduced by the model, attributable solely to natural variability (Hunt and Elliott 2002, 2005). It has also been shown that the present simulation can reproduce many features of the Medieval Warm Period and Little Ice Age (Hunt 2006c), as well as the characteristics of extreme rainfall events (Hunt 2006b) and climatic outliers (Hunt 2006a). An earlier simulation was used to demonstrate that many aspects of ENSO events were reproduced by the model (Hunt and Elliott 2003), while the model has been shown to perform well in international comparisons of these events (AchutaRao and Sperber 2000).

Previous studies of heat waves using models have been rather restricted and have been primarily concerned with future, greenhouse-induced impacts (Schär et al. 2004; Meehl and Tebaldi 2004). Huth et al. (2000) investigated the occurrence of heat waves and dry spells over the Czech Republic for control and greenhouse conditions. They noted a number of discrepancies with observations for the control, including too high peak temperatures and too long duration heat waves.

2. Model description

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 adjustment scheme is used to couple the atmospheric and oceanic components. The flux adjustments vary monthly but are invariant from year to year. The atmospheric model has nine vertical levels and R21 spectral resolution (3.25° latitude × 5.625° longitude) giving 3584 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 semi-Lagrangian water vapor transport. The oceanic component is based on version 2 of the Modular Ocean Model, of the Geophysical Fluid Dynamics Laboratory. This component has 21 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 limited resolution of the model inevitably means that small-scale features, a few hundred kilometers in extent, cannot be adequately resolved in this simulation. There is also the question of the representativeness of results at individual model grid boxes compared to observed station data. These issues arise in all simulations, but the case studies presented here suggest that for these specific examples credible outcomes have been achieved.

The present simulation was commenced from a previous 1000-yr 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 generated in the simulation arose from naturally occurring climatic variability.

This simulation does not therefore represent a progression through the Holocene, as the latter experienced numerous changes to boundary conditions via external forcings such as volcanic eruptions, compositional changes, etc. A fixed atmospheric CO2 concentration of 330 ppm was used in the simulation.

As mentioned above, 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 yr 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 2006c). As a consequence of this invariance, no detrending of climatic variables was necessary.

3. Seasonal heat waves

Although most heat waves are defined in terms of days, they can have extended durations. The European heat wave of 2003 is such an example, while Chang and Wallace (1987) list heat waves with durations up to 3 months for the United States.

An indication of the frequency of occurrence of summer heat waves [June–August (JJA) for the Northern Hemisphere; January–March (JFM) for the Southern Hemisphere] over all 10 000 yr of the simulation is presented in Fig. 1. Results are given for three ranges of intensity of the heat waves—those having average anomalies of 3, 4, or 5 K sustained over these summer periods. In each set of panels in Fig. 1, results are also shown for the corresponding winter hemisphere. The latter represents positive temperature anomalies occurring within winter conditions and, thus, are indicative of mild winter states rather than heat wave conditions.

Dealing with the Northern Hemisphere first in Fig. 1, it can be seen that apart from a few restricted locations in this hemisphere heat waves are not experienced over the oceans. This is a consequence of the large heat capacity of the mixed layer ocean. Even over the tropical Pacific Ocean no heat waves are recorded in the region where El Niño events occur. This is because the model produces El Niño warmings of only about one-half to two-thirds of the observed value (Hunt and Elliott 2003), but also because even the lowest range of intensity in Fig. 1 would appear to be observationally exceptional [see sea surface temperature anomaly maps in Allan et al. (1996)]. Summer heat waves of these magnitudes also do not occur in southeast Asia, parts of North America, and over the Arctic Ocean; see Fig. 1. At other regions in the Northern Hemisphere, summer heat waves with a magnitude of 3 K are restricted to about 20 occurrences over the 10 000 yr of the simulation, except for high northern latitudes, the south-central United States, and parts of the Middle East and India. In these latter regions some hundreds of heat waves occur, highlighting the susceptibility of these regions to these extreme climatic conditions.

All of these regions have high standard deviations of summer temperature (not shown). Over high northern land areas any heat wave conditions would, of course, be based on relatively low surface temperatures.

The occurrence rates of mean summer anomalies of 4 and 5 K in the Northern Hemisphere in Fig. 1 decline very rapidly compared to those for 3 K. For 5-K anomalies they are restricted to small regions in the central United States, India, and the Middle East, together with large areas of northern Asia. Given the extreme nature of such heat waves, this outcome is to be expected.

The occurrence rates of 3-K summer heat waves for the Southern Hemisphere in Fig. 1 are noticeably lower than those for the Northern Hemisphere, and are restricted to regions in southeast Africa, Australia, and South America and most of Antarctica. These rates decline very rapidly for the higher-intensity cases, so that for 5-K heat waves occurrences are restricted to northeast Australia and sea ice regions.

In summary, for middle- to high-latitude land areas summer heat waves with an average intensity of 3 K have a probability of occurrence of about 1 in 500 yr.

The results for the winter hemisphere in Fig. 1 reveal contrasting outcomes for the Southern and Northern Hemispheres. In the Southern Hemisphere the relatively small area of sea ice and the limited land areas means that it does not experience the climatic impacts associated with continentality so apparent in the Northern Hemisphere. Given the greater climatic variability occurring in winter, there is also an expectation that thresholds would be exceeded more frequently than in summer, as Fig. 1 confirms. These outcomes are also consistent with the view that it is easier to obtain positive temperature anomalies from a low temperature base (i.e., winter) than a high temperature base (i.e., summer), and that the greater atmospheric stability in winter means any thermal anomaly is restricted to the lower troposphere, whereas in summer anomalies attain much higher levels owing to convection.

Figure 2 shows time series of mean summer temperature anomalies for selected grid boxes in the model where high occurrence rates are identified in Fig. 1. In this and a number of subsequent figures, results are presented for selected case studies. Although, unlike Fig. 1, they are not necessarily representative of global conditions or long-term statistics, such case studies provide a perspective of outcomes that potentially can be experienced by individuals. Different thresholds are used in the various panels in Fig. 2 in order to have roughly the same number of events for each panel. For the selected thresholds, it can be seen that century-long periods, and occasionally millennial periods, exist where no heat waves of the specified intensity occur. In addition, there are periods of relatively frequent heat waves, interspersed with much lower occurrence rates; see especially the U.S. panel in Fig. 2. The India panel in Fig. 2 had the largest number of extreme heat waves (>6 K) and Europe the lowest. In all four panels outliers can be identified.

An interesting feature of the summer heat waves is illustrated in Fig. 3, where global distributions of summer surface temperature anomalies are displayed for individual years selected from each of the panels in Fig. 2. The most extreme years in Fig. 2 were not used; hence, the results in Fig. 3 are more representative of “typical” heat wave situations. With the exception of the panel for Europe in Fig. 3, these individual summer heat waves occurred as isolated, localized events, and not as “hotspots” associated with much larger-scale systems. In particular, for the U.S. and Australian examples, the heat waves were restricted to modest areas of their respective continents, with opposite-signed temperature anomalies in adjacent regions. These outcomes suggest that the heat waves were stochastically generated.

To determine the representativeness of the heat wave characteristics in the individual panels in Fig. 3, composite plots were made for the years with the largest values in Fig. 2. A minimum of 10 yr was used for each composite. Results (not shown) for the heat wave regions of the United States, India, and Europe were very similar to those displayed in Fig. 3, both in magnitude and spatial extent. Thus, the individual heat waves shown in Fig. 3 are characteristic of those to be expected in other years. As can be seen from Fig. 1, heat waves are endemic to these regions; hence, the occurrence of systematic patterns. For these three case studies the composites did not contain any other areas with heat waves, indicating that any other substantial positive temperature anomalies in the individual panels in Fig. 3 were transient events, and not systematic features associated with the heat waves. In the case of Australia the composite heat wave pattern was more extensive than that shown in Fig. 3, extending over about 75% of the continent but with the maximum amplitude still located on the east coast. A number of regions in the Northern (winter) Hemisphere had positive or negative anomalies of up to 3 K in the Australian composite. Note that since we experience the impact of individual, rather than composite, heat waves, it is considered that the results displayed in Fig. 3 are the more relevant outcomes.

The statistical distribution of the surface temperature anomalies for summer conditions for the four grid boxes in Fig. 2 is shown in the form of probability density functions (pdf’s) in Fig. 4. Superimposed on each of the individual pdf’s is a Gaussian distribution. Considerable differences are apparent between the grid boxes. In the case of the European panel in Fig. 4c, the temperature pdf corresponds very closely to the Gaussian distribution, indicating a normal distribution of anomalies. For the other panels in Fig. 4, there was a notable departure from normality in the form of an extended positive tail to the pdf’s, as might be expected from the time series plots in Fig. 2, and a lower count of events for small positive anomalies. The U.S. and India grid boxes also had fewer extreme cold anomalies than expected.

The pdf distributions for individual grid boxes varied considerably with location. For example, a grid box to the north and west of the Australian grid box in Fig. 4d produced an almost Gaussian outcome, as did a grid box over the south-central Pacific Ocean. When a spatial average of the surface temperature anomalies was made for the region of the Australian grid box in Fig. 4d, the resulting pdf retained the basic shape of the pdf in that figure, but the “noise” apparent in that distribution was removed. The pdf distribution for a single grid box is preferred in the present analysis, even allowing for the implied spatial smoothing compared to observed station data, as it is again considered to be more representative of outcomes experienced by individuals.

Returning to Fig. 2, the most exceptional outlier, in terms of relative anomalies, is that for Europe, where a sustained summer temperature anomaly of 4 K occurred for year 5190. According to Fink et al. (2004) a surface temperature anomaly >5 K occurred across large parts of Europe in June and August of 2003, while small regions with anomalies >3 K existed during July. Thus, the simulated outcome is plausible. Nevertheless, there was only one such event in the simulation, highlighting the extreme rarity of this heat wave. This outcome reinforces the conclusions of Trigo et al. (2005) and Schär et al. (2004) concerning the infrequency of the observed 2003 European heat wave. A recurrence of heat wave conditions similar to those of 2003 in the next few decades would support the contention of Stott et al. (2004) that the 2003 event was partially anthropogenically influenced, but in the meantime this event may be attributable to naturally occurring climatic variability. Meehl and Tebaldi (2004) have suggested that greenhouse-induced heat waves will not only be more intense and longer lasting but also more frequent, thus distinguishing them from the naturally occurring heat wave simulated here.

The spatial patterns of surface temperature and rainfall anomalies over the European region for June, July, and August individually are illustrated in Fig. 5 for the extreme year 5190. The heat wave in the model commenced in June, as in May there were regional positive surface temperature anomalies only over parts of the United Kingdom, Poland, and eastern Russia. The heat wave contracted in magnitude and intensity in July, expanded again in August, and was reduced to anomalies of +1 to +2 K over the United Kingdom, France, and Germany in September (not shown). The June and August surface temperature anomalies in Fig. 5 are very similar to the observed values; see Fink et al. (2004). Large parts of Europe experienced above average rainfall in July 2003 (Fink et al. 2004); hence, observed surface temperature anomalies were mainly <3 K. In the simulation (Fig. 5), below average rainfall was recorded for June, July, and August, amplifying and perpetuating the heat wave. The simulated anomalous rainfall patterns for June and August were quite similar to the observed values (Fink et al. 2004). Thus, fortuitously the simulation replicated the main characteristics of the European 2003 heat wave—a remarkable outcome given the rarity of this event.

Although recent heat waves in the United States (1995 and 1999) have been restricted to days, as opposed to months as was the case for Europe in 2003, Chang and Wallace (1987) have presented observations that indicate longer-duration heat waves do occur frequently. Thus, their Table 1 records heat waves for June, July, and August 1934; July and August 1936; and month-long heat waves in the summers of some years in all decades from 1930 to 1980. While their analysis was based on Kansas City, Missouri, they show that this was representative of a much larger area. Temperature anomalies ranging from 2.5 to 5 K were associated with these heat waves.

The U.S. panel in Fig. 2 is restricted to mean summer temperature anomalies over 4 K, but the numerous occasions with anomalies below that limit would correspond more closely to the observations reported by Chang and Wallace (1987). Individual years taken from the U.S. panel in Fig. 2 normally revealed simulated surface temperature anomaly patterns centered over the south-central United States, with some movement from month to month, and maximum anomalies >4 K for at least three summer months. Given this broad agreement with the observed temperature anomalies for 1934 (Chang and Wallace 1987), results for the most extreme U.S. case in model year 1457 (see Fig. 2) will be presented as a possible indication of an outcome over the United States that would correspond to the 2003 European heat wave in relative severity.

This simulated U.S. heat wave appears to have commenced in Alaska, and northern Canada, where >6 K surface temperature anomalies were simulated in January; see Fig. 6. As far as these regions are concerned, this would imply a mild winter rather than a heat wave. The “heat wave” conditions over North America in February expanded and intensified, and subsequently moved southeastward into the United States. In May the heat wave pattern had bifurcated into lobes over the northeast and southeast, but subsequently it contracted throughout June, July, and August, while remaining fairly stationary over the south-central United States; see Fig. 6. Given the movement of the heat wave pattern, no single location experienced the maximum temperature anomalies of 4 K for several months continuously. Extreme temperature anomalies of 7 K occurred in a number of months. If such a summer heat wave is ever experienced over the United States, and the results in Fig. 2 suggest that this is not implausible, then a death rate similar to that of Europe in 2003 might be expected. As was shown for the European heat wave in Fig. 5, below average rainfall was associated with the summer heat wave conditions in Fig. 6. The sequence of temperature and rainfall anomalies for the extreme heat wave in model year 1457 is shown in Fig. 7 for the U.S. grid box (35°N, 91°W) used in Fig. 2. The figure clearly illustrates the intensity of the heat wave at this grid box, with temperatures anomalies above 4 K from April to August and a peak anomaly of 7.7 K in June. Below average rainfall occurred for most of the previous year (1456), thus preconditioning the surface for a heat wave by reducing the evaporative cooling. The negative rainfall anomalies peak during the heat wave year as expected. In year 1458 conditions returned to “normal,” with no residual influences from the heat wave in the previous year.

Examination of Niño-3.4 sea surface temperature anomalies revealed a modest La Niña event in model year 1456 (maximum anomalies of −0.55 K), thus accounting for the below average rainfall in that year. After weakening in late 1456 to mid-1457, the La Niña event strengthened and retained anomalies less than −0.4 K from mid-1457 to mid-1458. Subsequently, anomalies of about −0.1 K prevailed for the remainder of 1458. Thus, this particularly extreme heat wave was associated with a persistent, but moderate intensity, La Niña event. The relationship between such events and U.S. heat waves is examined in more detail below.

An examination of heat waves over India was also made; see Figs. 2 and 3 for background details. Spatial plots of surface temperature anomalies over India (not shown) revealed a fairly constant location of the maximum anomaly over the center of India in any given month. The maximum anomaly was usually 6–7 K, and the heat waves almost invariably commenced in June and were finished by September. Examination of years adjacent to extreme years revealed no indication of a heat wave, with normal, or in some months below normal surface temperatures in such years. As expected, the heat wave years had below average rainfall, usually over all of India, during the summer monsoon season.

Heat waves over Australia exhibited a wide range of spatial patterns, for months within a given year, and also from one event to another. This situation is illustrated in Fig. 8 for the most extreme case, model year 9618, depicted in the Australia panel in Fig. 2. As shown in Fig. 8, the heat wave in January was restricted to central eastern Australia, but expanded rapidly in February to a bipolar pattern covering the whole country and then weakening noticeably in March. In general, most of these summer heat waves commenced in December and had terminated by April. For extreme years, the maximum surface temperature anomalies reached 6–7 K in February or March, and for less extreme years these were normally 4–5 K. The Australian heat waves were also associated with negative rainfall anomalies (not shown), although a clear spatial correspondence between temperature and rainfall anomalies was not always apparent.

4. Daily heat waves

The most commonly experienced type of heat waves are those that occur over a number of consecutive days; see for example Kunkel et al. (1996), Huth et al. (2000), Palecki et al. (2001), Burt (2004), and Khaliq et al. (2005). More than one such heat wave can occur in a given summer (Khaliq et al. 2005) and the intensity of the heat waves can be higher, given their short duration, than that for seasonal heat waves.

A comprehensive analysis of heat waves in the United States for the period 1950–95 has been presented by Choi and Meentemeyer (2002). They plot the frequency of occurrence of heat wave characteristics for various durations and intensities, and, in view of this documentation, much of the detailed model analysis in this section will be based on events occurring over the United States.

For convenience, results will be presented as anomalies of daily maximum temperature for the simulated period of years 4401–4500. These anomalies are departures from the mean of years 4001–5000 over which daily data were saved. The 100-yr period used here was arbitrarily chosen, but other centennial-long periods produced very similar results. The analysis was primarily confined to 100 yr simply because of the voluminous nature of the daily data.

In Fig. 9 anomalies of the daily maximum temperature, restricted to values greater than 4 K, are plotted for the U.S. grid box, 35°N, 91°W. Results are for the summer months of June, July, and August only. A considerable range of variability is apparent in Fig. 9, with extreme anomalies of up to 12 K. For this particular example the largest number of successive days meeting the 4-K criterion was 20, which occurred in model year 4470 in Fig. 9. In their observational analysis, Choi and Meentemeyer (2002) note a maximum duration heat wave occurrence of 41 days in Texas, where values were one standard deviation (∼4 K) above normal. What appear as single lines in Fig. 9 usually involve several individual days; hence, any implied heat wave conditions may be longer lasting than they seem. The most intense series of events occurred in year 4470 where there was a sequence of runs of consecutive days, separated by days that did not meet the criterion. This situation appears to be comparable to conditions prevailing in the summer of 1934 at Kansas City, Missouri; see Table 1 of Chang and Wallace (1987). Overall, Fig. 9 indicates a range of situations, from relatively quiescent states, the first 20 yr, a number of individual years where the heat wave criterion was not attained, and episodes of marked anomalies occurring over multiple days; see years 4443, 4470, etc.

As a further indication of the model’s performance, Fig. 10 compares daily temperature anomalies over a year for the model and reanalysis results [taken from the European Centre for Medium-Range Weather Forecasts (ECMWF) 40-yr reanalysis (ERA-40) dataset] for the same U.S. point as was used in Fig. 9. The model anomalies are for the maximum daily temperature; the observations are the mean of four daily values for a height of 2 m. Given that both years used in Fig. 10 were arbitrarily selected (but were heat wave years), there is no reason why they should closely agree. Nevertheless, both time series display similar characteristics with both positive and negative anomalies throughout the year, and with similar ranges of anomaly values, although the model had more positive anomalies. This comparison indicates that the model simulated the basic features of the observations, providing confidence in the results to be presented below.

A global perspective of daily heat waves is now illustrated in Fig. 11. This figure shows the occurrence rate of heat waves with daily anomalies greater than 4 K for three different durations. For each hemisphere the corresponding winter anomalies for the opposite hemisphere are also displayed. Not surprisingly, there are virtually no oceanic grid boxes recording heat-wave conditions by these definitions in Fig. 11. In addition, no heat waves occur over jungle-covered land regions.

The most noticeable feature in Fig. 11 is the high occurrence rate of “heat waves” for winter conditions in both hemispheres. This response can be clearly discerned in the ERA-40 reanalysis in Fig. 10 and is indicative of mild spells during winter. These are associated with synoptic conditions producing intrusions of warmer air from oceanic or midlatitude regions. The noticeable drop in the occurrence rate for 10- and 15-day periods again can be attributed to the time scale of the synoptic events.

For summer conditions in both hemispheres in Fig. 11 the occurrence rate of the specified heat waves declines rapidly as the duration of the heat waves is extended (top to bottom panels in Fig. 11). Given the vagaries of the weather and the frequency of synoptic systems, the difficulties of maintaining long-duration heat waves can be readily appreciated. In the Northern Hemisphere, the heat waves mainly occur at high latitudes, where they represent enhancements of relatively low temperatures, but persistent heat waves are also noted over India and the central and southern United States. For the Southern Hemisphere, the heat waves are principally located over Australia.

The high occurrence rates in the two upper panels in Fig. 11, that is, those for heat waves with durations of 5 successive days, indicate that in some years more than one event lasting 5 days was identified.

Finally, in Fig. 12 a daily sequence of anomalies for the daily maximum temperature is shown for a heat wave over the United States encompassing late June–early July of year 4498 of the simulation. This heat wave commenced and terminated after the days shown in Fig. 12, but the most intense phase is given in the figure. This heat wave slowly progressed southeastward across the United States, with peak temperature anomalies of about 8 K being maintained during this progression. In the early stages of the heat wave, temperatures below average occurred to the region north and west of the heat wave zone; thus, the continent was not under the influence of a single synoptic system. In fact, the spatial scale of this heat wave emphasizes its isolated nature and the lack of any connection to large-scale systems. For the duration of the U.S. heat wave, a large negative temperature anomaly was sustained over northern Asia, together with another sustained negative anomaly over Australia. These anomalies were associated with low insolation at the surface, implying high cloud amounts (daily cloud amounts were not saved); in contrast, high insolation was incident over the U.S. region experiencing the heat wave.

The temperature anomaly pattern over the United States for late June in Fig. 12 was similar to a composite observed anomaly pattern presented by Chang and Wallace (1987) for the hottest summer months in the 1930s. The amplitude of their anomalies was smaller than that simulated, but this would be expected owing to the averaging involved in generating the composite. They also reported negative temperature anomalies over the western third of the United States in their composite figure, similar to those shown in Fig. 12.

Chang and Wallace (1987) also reproduced the observed composite surface pressure chart corresponding to their temperature anomaly composite. This had high pressure systems situated off the west and east coasts of the United States and a low pressure system over North America. Figure 13 shows the surface pressure distribution for 30 June of year 4498 of the simulation. This reveals a similar situation to that of Chang and Wallace (1987), indicating again that the model replicated the observed synoptic systems. The pressure patterns over the North American region shown in Fig. 13 were representative of other days of the simulated heat wave, but with small sequential changes corresponding to the movement of the heat wave across the United States.

Given the apparent reasonable agreement of the simulation with observations over the United States, it is of interest to explore some of the more extreme simulated heat waves. Because of the very limited duration of the observational record, it is plausible to assume that only a limited sample of potential heat waves has been experienced to date. Even without any contribution from a greenhouse warming, more extreme heat waves than presently recorded should occur, simply as a consequence of natural variability; see for example Fig. 2.

In Fig. 14 simulated and reanalysis (ERA-40) temperature anomalies for the U.S. point (35°N, 91°W) are shown, for JJA values only, with the objective of comparing the frequency of occurrence and the magnitude of extreme daily temperature anomalies at this specific location. The simulated anomalies are for the maximum daily surface temperature, for values exceeding 10 K, and are for the 500-yr period 4001–4500. The ERA-40 anomalies are for the mean daily temperature at a height of 2 m (denominated t2), for values exceeding 4 K only, and are for the 44-yr period 1958–2001. Thus, there is a tenfold difference in the two timeframes.

The use of mean daily t2 data from the ERA-40 dataset (daily maximum values were not available) acts to restrict the magnitude of the resulting anomalies; hence, the ERA-40 magnitudes peak out between 7 and 8 K compared to 12 and 13 K for the simulation. The brevity of the ERA-40 dataset also limits the extreme amplitudes that might be expected.

Considerable secular variability is apparent in the simulation in Fig. 14, with a 90-yr period between years 4340 and 4430 with no anomalies reaching the set criterion, while at other times these events occur at multiannual intervals. The brevity of the observations limits the possibility of secular variability, while illustrating the relatively high frequency of the occurrence rate of extreme temperature anomalies. Each of the results in Fig. 14 normally involved multiple-day events reaching the set criteria, as well as other adjacent days with smaller-amplitude temperature anomalies. As such, these results are indicative of local heat wave conditions.

5. Mechanistic processes

A related series of physical processes is involved in the generation of a heat wave; see, for example, Manabe and Wetherald (1987) and Wetherald and Manabe (1999). In Fig. 15 monthly anomalies for year 4103 of the simulation for the U.S. grid box (35°N, 91°W) are compared for six climatic variables. As shown in Fig. 14, a heat wave occurred at this location, and this is also clearly indicated by the monthly surface temperature anomalies in Fig. 15. The precursor to this heat wave was the below average rainfall that commenced in January of year 4103 (Fig. 15b); above average rainfall occurred for most of year 4102. This below average rainfall was accompanied by below average cloud amount (not shown), resulting in an above average net surface short wave flux (Fig. 15f). This enhanced solar heating was the primary generator of the related heat wave. Because of the below average rainfall, negative soil moisture anomalies resulted (Fig. 15d), and this reduced the surface evaporation (Fig. 15c). Since the surface evaporative flux is the primary cooling agency in determining the surface temperature, the reduced evaporation rate also contributed to the maintenance of the heat wave. As shown in Fig. 15e, the sensible heat flux at the surface increased, to partially compensate for the reduced evaporation rate, but such an increase usually requires higher surface temperatures.

Thus, a very consistent set of physical processes was associated with this heat wave. A similar analysis for an Indian heat wave in year 9661 of the simulation, resulted in the same related physical processes as are shown in Fig. 15. This, together with the results in Fig. 7, indicate that the relationships shown in Fig. 15 are a robust characteristic of heat waves.

The impact of short-term rainfall on a heat wave has been described by Kunkel et al. (1996) and Palecki et al. (2001) in relation to the Chicago heat waves of 1995 and 1998, respectively. They relate such rainfall to an increase in soil moisture content and subsequently evaporation, which then ameliorated (temporarily) the heat wave conditions. Brabson et al. (2005) have also shown how the lower soil moisture content to be expected under greenhouse conditions will cause systematically higher surface temperature values.

The central question related to Fig. 15 is how the physical processes displayed in this figure were initiated, and subsequently maintained, in order to produce a heat wave. The apparent precursor is the rainfall decline, with its associated reduction in cloud amount, which then permitted enhanced solar radiation to initiate the surface warming. This warming was then enhanced by the subsequent changes to the soil moisture content and evaporation rate. Thus, the question becomes what initiated and maintained the rainfall decline? Presumably, some change in the atmospheric circulation is responsible. Choi and Meentemeyer (2002) have shown that the composite 500-mb geopotential height has an anomaly of +50 gpm for U.S. heat waves, while Chang and Wallace (1987) present various composite charts for climatological, heat wave, and cool conditions over the United States. The latter authors make the following fundamental statement: “It is virtually impossible to distinguish this composite SLP field (for heat wave conditions) from the climatological mean pattern.” A similar outcome was obtained from examining simulated monthly surface pressure patterns for heat wave and cold episode conditions over the United States. While year-to-year differences were apparent, especially external to the United States, the basic surface pressure pattern (see Fig. 13 for a daily pattern) was essentially robust.

A one-point correlation plot of surface temperature for the U.S. grid box (35°N, 91°W) and global surface pressure, for years 4001–5000 of the simulation, produced values of less than |0.1|, thus reinforcing the insensitivity of this surface temperature to surface pressure distribution.

Given the relationship between rainfall variability over the United States and ENSO (Ropelewski and Halpert 1987), an impact of ENSO on surface temperature, and thus heat waves, might be expected. La Niña conditions are associated with droughts over the U.S. southeast and pluvials over the northwest United States. Such moisture relationships then give rise to positive and negative surface temperature anomalies, respectively, as implied from Fig. 15. In fact, these outcomes are apparent in the daily surface temperature anomalies shown in Fig. 12.

In Fig. 16 plots of monthly surface temperature anomalies for the U.S. grid box (35°N, 91°W) are contrasted with Niño-3.4 sea surface temperature anomalies for a 25-yr period of the simulation. Over the millennium of years 4001–5000, the correlation between these two variables was only −0.135, indicating a modest interrelationship. While the heat waves at years 4103 and 4117 in Fig. 16 occur during La Niña years, as might be expected, every La Niña year does not have a heat wave.

In terms of climatic extremes or outliers, it has been shown for this simulation (Hunt 2006a) that Niño-3.4 outliers are not associated with other climatic outliers outside of the Niño-3.4 region.

Thus, the occurrence of ENSO events does not provide a unique predictive capability for heat waves for the southwest United States, or elsewhere globally, even allowing for the limitations of the simulated ENSO events. This conclusion is reinforced by the U.S. and Australian heat waves in Fig. 3, where neither La Niña or El Niño events are apparent. Thus, given the invariance of the model’s boundary conditions for the duration of the simulation, the only cause of heat waves, whether or not they occur during ENSO years, has to be random (stochastic) processes arising from the nonlinear interactions existing within the climatic system. Again, while the intensity of heat waves on some occasions may have been underestimated owing to the weakness of the simulated ENSOs, the earlier comparisons suggest that this does not seem to have affected the frequency of the heat waves. The essentially random nature of heat waves for the various continents illustrated in Fig. 2, and the lack of any simultaneity between occurrences at those different locations, strongly supports this attribution of stochacism.

6. Conclusions

From an analysis of a 10 000-yr simulation with the CSIRO Mark 2 coupled global climatic model, a number of insights has been obtained regarding the climatology of heat waves.

Summer heat waves, having a duration of 3 months and a magnitude of 3 K are almost totally restricted to the continents, with maximum responses over high northern latitudes, the south-central United States, India, the Middle East, and Australia. These heat waves did not occur over southeast Asia or in South America, apart from Argentina. Many parts of the latter regions are jungle covered or mountainous.

The frequency of occurrence of these heat waves declined very fast for magnitudes of 4 and 5 K. The occurrence rate of summer heat waves was considerably more spatially limited in the Southern Hemisphere, and declined even faster for more intense heat waves.

Time series of summer heat waves for selected model grid boxes revealed substantial differences between localities, with some having fairly uniform occurrence rates and others with century or longer periods with no heat waves reaching the set criterion. Marked outliers, in terms of magnitude of the heat waves, were highlighted within these time series.

Global distributions of surface temperature anomalies for selected years where a summer heat wave was identified at a specific locality revealed the spatially isolated nature of these heat waves. No relationship to other climatic events over the globe could be discerned, suggesting that the heat waves were the result of local stochastic influences.

Over the 10 000 yr of the simulation, one outstanding heat wave was identified over Europe. This heat wave had very similar magnitude and spatial occurrence to the observed heat wave of 2003, and, like the observations, was associated with below average rainfall. This outcome suggests that the 2003 European heat wave may have been a consequence of just naturally occurring climatic variability, rather than being greenhouse influenced, although Stott et al. (2004) suggest a greenhouse-enhanced probability. The occurrence of a similar heat wave within the next few decades would, however, imply a greenhouse impact.

Monthly plots of the spatial distribution of intense heat waves over the United States and Australia revealed considerable spatial variability of the heat waves, with that for the United States progressing from Alaska to northwest Canada in January to southeast United States in August. In each case these heat waves were also associated with below average rainfall over the summer months.

The spatial patterns of daily heat wave occurrence rates were, of course, very similar to those for seasonal heat waves. Rapid declines in occurrence rates were noted for magnitudes above 4 K and durations of 10 days. Time series for a selected U.S. grid box highlighted the greater magnitude of surface temperature anomalies, with values of up to 12 K. The annual cycle of temperature anomalies for this grid box agreed reasonably well with observations, having marked positive and negative anomalies in winter and rather smaller negative anomalies in summer.

An examination of the physical processes associated with heat waves emphasized the consistent relationships occurring among the various climatic variables. This revealed that reduced rainfall, and thus reduced cloud cover, permitted increased solar radiation to penetrate to the earth’s surface, providing the energy source for the subsequent heat wave. The associated reduced soil moisture content resulted in low surface evaporation, and evaporative cooling, thereby reinforcing the initial solar heating.

The cause of the precursor reduction of rainfall and cloud cover is presumed to be stochastic. While ENSO influences have a role in creating drought conditions conducive to a heat wave, not all ENSO events produce a heat wave. It is this difference between outcomes as regards the occurrence of heat waves that is attributed to stochastic forcing. In the case of the exceptional European heat wave in the simulation, this would seem to be totally the result of stochastic forcing in the simulation.

In summary, coupled global climatic models are capable of simulating most of the observed characteristics of heat waves, and provide a unique tool for obtaining both global and temporal perspectives of the climatological features of heat waves. An important outcome is that the present simulation suggests that observed heat waves, to date, may have occurred through natural climatic variability and that recourse to external influences is not required. However, any future positive shift in the near-Gaussian temperature distributions, such as might be anticipated under global warming conditions, would make the occurrence of more extreme heat waves more likely.

Acknowledgments

The assistance of Mark Collier, Martin Dix, and Tracey Elliott in different aspects of the production of this paper is noted with thanks.

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Fig. 1.
Fig. 1.

Occurrence rates of summer heat waves for the (left) Northern Hemisphere (JJA) and (right) Southern Hemisphere (JFM). For each hemisphere the corresponding winter “heat waves” are also shown. The heat waves have mean intensities over the whole summer period of (top) 3, (middle) 4, and (bottom) 5 K. The color bars give the occurrence rates for the 10 000 yr of the simulation.

Citation: Journal of Climate 20, 15; 10.1175/JCLI4224.1

Fig. 2.
Fig. 2.

The frequency of occurrence of mean summer temperature anomalies above specified thresholds for selected model grid boxes over the 10 000 yr of the simulation. The grid boxes are located as follows: United States (35°N, 91°W), India (20°N, 80°E), Europe (50°N, 10.5°E), and Australia (25°S, 150°E).

Citation: Journal of Climate 20, 15; 10.1175/JCLI4224.1

Fig. 3.
Fig. 3.

Global distributions of summer mean surface temperature anomalies (K) for selected years. Individual years were selected to highlight heat waves in four separate regions.

Citation: Journal of Climate 20, 15; 10.1175/JCLI4224.1

Fig. 4.
Fig. 4.

Probability density functions of summer surface temperature anomalies for all 10 000 yr of the simulation are shown for the same four grid boxes as used in Fig. 2. Superimposed on each pdf is the corresponding Gaussian distribution.

Citation: Journal of Climate 20, 15; 10.1175/JCLI4224.1

Fig. 5.
Fig. 5.

Surface temperature (K) and rainfall (mm day−1) anomalies over Europe for the extreme heat wave year 5190 of the simulation (See Fig. 2). (left) The temperature anomalies and (right) the rainfall anomalies. Results for (top) June, (middle) July, and (bottom) August are given.

Citation: Journal of Climate 20, 15; 10.1175/JCLI4224.1

Fig. 6.
Fig. 6.

Monthly mean surface temperature anomalies over the North American region for January–August for the extreme U.S. heat wave year 1457 of the simulation (see Fig. 2). The color bars below the panels are in K.

Citation: Journal of Climate 20, 15; 10.1175/JCLI4224.1

Fig. 7.
Fig. 7.

Time series of monthly surface temperature and rainfall anomalies for the U.S. grid box (35°N, 91°W) for years 1456–1458, which encompass the extreme heat wave year of 1457. The rainfall anomalies have been shifted 0.5 months to the right of the surface temperature anomalies for clarity.

Citation: Journal of Climate 20, 15; 10.1175/JCLI4224.1

Fig. 8.
Fig. 8.

Monthly surface temperature anomalies (K) for Australia for an extreme heat wave situation. Results are shown for summer of year 9618 of the simulation, for January, February, and March.

Citation: Journal of Climate 20, 15; 10.1175/JCLI4224.1

Fig. 9.
Fig. 9.

Time series of daily maximum surface temperature anomalies for the U.S. grid box (35°N, 91°W) for the 100-yr period of 4401–4500 from the simulation. Values less than 4 K have been omitted. Results shown are for June, July, and August only.

Citation: Journal of Climate 20, 15; 10.1175/JCLI4224.1

Fig. 10.
Fig. 10.

Time series of daily temperature anomalies (K) for the U.S. grid box (35°N, 91°W). Results are shown for arbitrarily selected years. (top) The model maximum temperature anomalies are plotted for year 4401 from the simulation; (bottom) the reanalysis results for daily mean surface air temperature anomalies are plotted for 2000 a.d.

Citation: Journal of Climate 20, 15; 10.1175/JCLI4224.1

Fig. 11.
Fig. 11.

Occurrence rates of summer heat waves for the (left) Northern Hemisphere (JJA) and (right) Southern Hemisphere (JFM) are illustrated. Heat waves having daily maximum temperature anomalies greater than 4 K for (top) 5, (middle) 10, and (bottom) 15 successive days. The color bars give the occurrence rates for the 100-yr period of years 4401–4500 from the simulation.

Citation: Journal of Climate 20, 15; 10.1175/JCLI4224.1

Fig. 12.
Fig. 12.

Sequence of daily maximum surface temperature anomalies (K) for 8 days in June and July of year 4498 of the simulation during which a heat wave occurred in the United States.

Citation: Journal of Climate 20, 15; 10.1175/JCLI4224.1

Fig. 13.
Fig. 13.

Surface pressure distribution (mb) corresponding to 30 June of year 4498, one of the days used in Fig. 12.

Citation: Journal of Climate 20, 15; 10.1175/JCLI4224.1

Fig. 14.
Fig. 14.

Time series of extreme temperature anomalies for the U.S. grid box (35°N, 91°W). (top) The model values are given for the 500-yr period of years 4001–4500 from the simulation. Daily maximum surface temperature anomalies are shown for June, July, and August conditions and for magnitudes above 10 K. (bottom) The ERA-40 t2 anomalies, as the average of four values over each day, are shown for the same months but for magnitudes above 4 K.

Citation: Journal of Climate 20, 15; 10.1175/JCLI4224.1

Fig. 15.
Fig. 15.

Monthly time series for anomalies of selected climatic variables for year 4103 from the simulation for the U.S. grid box (35°N, 91°W).

Citation: Journal of Climate 20, 15; 10.1175/JCLI4224.1

Fig. 16.
Fig. 16.

Time series for the 25-yr period of years 4100–4124 from the simulation. Shown are monthly anomalies of surface temperature at the U.S. grid box (35°N, 91°W) as well as Niño-3.4 sea surface temperature.

Citation: Journal of Climate 20, 15; 10.1175/JCLI4224.1

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