In a recent effort to address this question within the Three Gorges area of China, which comprises the Chongqing Municipality and the western part of Hubei Province, including the reservoir region of the Three Gorges Dam, Deng et al. (2012) used daily mean, maximum and minimum temperatures for the period 1958-2007 that they obtained from ten meteorological stations within this region to determine the number of hot days (HDs, at or above 35°C), very hot days (VHDs, at or above 38°C) and extremely hot days (EHDs, at or above 40°C). And defining a heat wave (HW) as a period with no fewer than three consecutive HDs, they defined a short heat wave (SHW) as being at least six days long, and a long heat wave (LHW) as a heat wave exceeding six days.

Based on the criteria above, the three Chinese researchers report that over the course of their study period (1958-2007), their study area did indeed experience a mean annual warming trend, but with slight decreasing trends in spring and summer temperatures. They also say that extreme high temperature events showed a U-shaped temporal variation, decreasing in the 1970s and remaining low in the 1980s, followed by an increase in the 1990s and the 21st century, such that "the frequencies of HWs and LHWs in the recent yeas were no larger than the late 1950s and early 1960s." In fact, they indicate that "coupled with the extreme low frequency in the 1980s, HWs and LHWs showed a slight linear decreasing trend in the past 50 years." Put another way, they say that the most recent frequency of heat waves "does not outnumber 1959 or 1961," and that "none of the longest heat waves recorded by the meteorological stations occurs in the period after 2003."

In concluding their discussion of their findings, Deng et al. write that "compared with the1950s and 1960s, SHWs instead of LHWs have taken place more often," which change, as they describe it, "is desirable, as longer duration leads to higher mortality," citing Tan et al. (2007). And so it is that for the Three Gorges area of China, even a mean annual warming trend over the past half-century, has not led to an increase in the frequency of extremely long heat waves.

Writing as background for their study of the subject, Redner and Petersen (2006) note that "almost every summer, there is a heat wave somewhere in the United States that garners popular media attention," and that it is only natural to wonder if global warming played a role in producing it. Driven by this same curiosity, Redner and Petersen set out to investigate "how systematic climatic changes, such as global warming, affect the magnitude and frequency of record-breaking temperatures," after which they assessed the potential of global warming to produce such temperatures by comparing their predictions to a set of Monte Carlo simulation results and to 126 years of real-world temperature data from the city of Philadelphia.

The results of their mathematical analysis led the two researchers to conclude that "the current warming rate is insufficient to measurably influence the frequency of record temperature events, a conclusion that is supported by numerical simulations and by the Philadelphia data." Hence, they state that they "cannot yet distinguish between the effects of random fluctuations and long-term systematic trends on the frequency of record-breaking temperatures," even with 126 years of real-world data. In other words, confident attribution of record-breaking temperatures in Philadelphia to generic global warming over the past 126 years cannot yet be made, suggesting that the attribution of such temperature extremes to CO2-induced global warming is a difficult task that is far from being achieved.

With respect to why the models may have gotten it wrong when it comes to projecting heat waves, some insight may be gained from the studies of Fischer et al. (2007) and Robock et al. (2000), as explained below.

Fischer et al. conducted regional climate simulations, both with and without land-atmosphere coupling, for the major European summer heat waves of 1976, 1994, 2003 and 2005, seeking to understand what conditions led to their occurrence. In doing so, the authors found that during all simulated heat wave events, "soil moisture-temperature interactions increase the heat wave duration and account for typically 50-80% of the number of hot summer days," noting that "the largest impact is found for daily maximum temperatures," which were amplified by as much as 2-3°C in response to observed soil moisture deficits in their study.

For their part, Robock et al. developed a massive collection of soil moisture data from over 600 stations spread across a variety of climatic regimes (including the former Soviet Union, China, Mongolia, India and the United States), finding that, "for the stations with the longest records, summer soil moisture in the top 1 m has increased [italics added] while temperatures have risen." This counter-intuitive finding was confirmed by Robock et al. (2005) and Li et al. (2007), the latter of whom note that when exposed to elevated concentrations of atmospheric CO2, "many plant species reduce their stomatal openings, leading to a reduction in evaporation to the atmosphere," so that "more water is likely to be stored in the soil or [diverted to] runoff," which latter phenomenon has in turn been confirmed by the work of Gedney et al. (2006), the senior author of whom was quoted by Pearce (2006) as saying that "climate change on its own would have slightly reduced runoff, whereas the carbon dioxide effect on plants would have increased global runoff by about 5%," with the combined effect of the two competing phenomena leading to the 3-4% flow increase actually observed.

So what do the results of these two studies have to do with heat waves? Quite a lot. In light of the complementary global soil moisture and river runoff observations, it would appear that, in general, the anti-transpiration effect of the historical rise in the air's CO2 content has more than compensated for the soil-drying effect of concomitant global warming; and based upon (1) the findings of Fischer et al. (2007) that soil moisture depletion greatly augments both the intensity and duration of summer heat waves, plus (2) the findings of Robock et al. (2000, 2005) and Li et al. (2007) that global soil moisture has actually increased over the past half century, likely as a result of the anti-transpiration effect of atmospheric CO2 enrichment - as Gedney et al. (2006) have also found to be the case with closely associated river runoff - it directly follows that the increase in soil moisture caused by rising atmospheric CO2 concentrations will tend to decrease both the intensity and duration of summer heat waves as time progresses, which may explain why historic heat waves in locations such as Philadelphia and the Three Gorges area of China have not increased in response to what climate alarmists refer to as the unprecedented warming of the late 20th and early 21st century.

Another reason why the models may have it all wrong is elucidated in the study of Jeong et al. (2010). Writing as background for their work, the authors state that modeling studies in the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) suggest that future heat waves over Europe will be more severe, longer lasting and more frequent than those of the recent past, due largely to an intensification of quasi-stationary anticyclone anomalies accompanying future warming, citing in support of this statement the publications of Meehl and Tebaldi (2004) and Della-Marta et al. (2007). Against this backdrop, Jeong et al. investigated "the impact of vegetation-climate feedback on the changes in temperature and the frequency and duration of heat waves in Europe under the condition of doubled atmospheric CO2 concentration in a series of global climate model experiments," where land surface processes were calculated by the Community Land Model (version 3) described by Oleson et al. (2004), which includes a modified version of the Lund-Potsdam-Jena scheme for computing vegetation establishment and phenology for specified climate variables. So what did they learn?

In the words of the authors, their calculations reveal that "the projected warming of 4°C over most of Europe with static vegetation has been reduced by 1°C as the dynamic vegetation feedback effects are included," and that "examination of the simulated surface energy fluxes suggests that additional greening in the presence of vegetation feedback effects enhances evapotranspiration and precipitation, thereby limiting the warming, particularly in the daily maximum temperature." And, pertinent to the subject at hand, they state that "the greening also tends to reduce the frequency and duration of heat waves."

Although the above findings by no means constitute the final word on the subject of the ultimate climatic consequences of a doubling of the air's CO2 content on heat waves, they indicate just how easily the incorporation of a new suite of knowledge, in even the best climate models of the day, can dramatically alter what the IPCC and others purport to be reality.

References
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Deng, H., Zhao, F. and Zhao, X. 2012. Changes of extreme temperature events in Three Gorges area, China. Environmental and Earth Sciences 66: 1783-1790.

Fischer, E.M., Seneviratne, S.I., Luthi, D. and Schar, C. 2007. Contribution of land-atmosphere coupling to recent European summer heat waves. Geophysical Research Letters 34: 10.1029/2006GL029068.

Gedney, N., Cox, P.M., Betts, R.A., Boucher, O., Huntingford, C. and Stott, P.A. 2006. Detection of a direct carbon dioxide effect in continental river runoff records. Nature 439: 835-838.

Jeong, S.-J., Ho, C.-H., Kim, K.-Y., Kim, J., Jeong, J.-H. and Park, T.-W. 2010. Potential impact of vegetation feedback on European heat waves in a 2 x CO2 climate. Climatic Change 99: 625-635.

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Pearce, F. 2006. Increased CO2 may cause plant life to raise rivers. NewScientist.com.

Redner, S. and Petersen, M.R. 2006. Role of global warming on the statistics of record-breaking temperatures. Physical Review E 74: 061114.

Robock, A., Mu, M., Vinnikov, K., Trofimova, I.V. and Adamenko, T.I. 2005. Forty-five years of observed soil moisture in the Ukraine: No summer desiccation (yet). Geophysical Research Letters 32: 10.1029/2004GL021914.

Robock, A., Vinnikov, K.Y., Srinivasan, G., Entin, J.K., Hollinger, S.E., Speranskaya, N.A., Liu, S. and Namkhai, A. 2000. The global soil moisture data bank. Bulletin of the American Meteorological Society 81: 1281-1299.

Tan, J., Zheng, Y. Song, G., Kalkstein, L.S., Kalkstein, A.J. and Tang, ZX. 2007. Heat wave impacts on mortality in Shanghai, 1998 and 2003. International Journal of Biometeorology 51: 193-200.