We use five years of data from the Atmospheric Infrared Sounder (AIRS) to develop a correlation between the frequency of Deep Convective Clouds (DCC) and the zonal mean tropical surface temperature. AIRS data show that the frequency of DCC in the tropical oceans is very temperature sensitive, increasing 45% per 1 K increase of the zonal mean surface temperature. The combination of the sensitivity of the DCC frequency to temperature indicates that the frequency of DCC, and as a consequence the frequency of severe storms, increases at the rate of 6%/decade with the current +0.13 K/decade rate of global warming. This result is only qualitatively consistent with state-of-the-art climate models, where the frequency of the most intense rain events increases with global warming.
 The expectation that the hydrologic cycle will accelerate with global warming is largely based on the Clausius Clapeyron (CC) equation. With the observed multi-decadal global warming at the rate of 0.13 K/decade [Trenberth et al., 2007] and a 7%/K increase of water vapor following the CC relation, the expected increase in water vapor is 7%/K * 0.13 K/decade = 1%/decade. This expected rate is qualitatively consistent with recent re-analysis of SSMI data [Wentz et al., 2007], which found that precipitation over the oceans has increased by 1.5%/decade during the past 19 years. Changes at such low levels are difficult to measure directly. The combination of higher temperatures and higher water vapor may produce larger and more easily measured increases in the frequency of high clouds. This reasoning was one motivation for the analysis of 22 years of data from a long sequence of HIRS instruments in the NOAA/ATOVS weather satellites between 1978 and 2003. However, this analysis revealed no significant trend in the high cloud fraction, defined as cloud tops above 400 hP [Wylie et al., 2005]. The frequency and/or intensity of severe storms, including hurricanes and typhoons, may be much more sensitive to global warming. This question was first raised in the literature in 1987 [Emanuel, 1987], with articles as recent as 2005 [Knutson and Tuleya, 2004; Webster et al., 2005], but its resolution has been hampered by the rarity of hurricanes, only of the order of one hundred per year, and observational biases. We address a similar question with the analysis of the frequency of Deep Convective Clouds (DCC), which correspond to large cumulus towers associated with severe storms.
 We use the first five years of Atmospheric Infrared Sounder (AIRS) [Chahine et al., 2006] data to analyze the frequency of DCC in the tropical oceans for temperature sensitivity and trend. AIRS is an infrared hyperspectral cross-track scanning sounder on the EOS Aqua spacecraft, which covers the 3.7–15.4 micron infrared spectral region with spatial resolution of 13 km at nadir. AIRS was launched into a 705 km altitude orbit on May 4, 2002 and has been in routine data gathering mode essentially uninterrupted since September 2002. The 1:30 PM ascending node and orbital altitude of the EOS Aqua orbit are accurately maintained to minimize confusion of diurnal variability with climate trends. Essentially global coverage is achieved twice per day from the ascending (day) and descending (night) orbits. The AIRS absolute radiometric calibration accuracy at the 200 mK level, milli-Kelvin per year radiometric stability and frequency stability at the 1 part per million level have been documented in the literature [Strow et al., 2006; Aumann et al., 2006a].
 We defines a DCC as any AIRS footprint over non-frozen land or ocean where the brightness temperature in the 1231 cm−1 atmospheric window channel is less than 210 K. The frequency of DCC is highly correlated with the zonal mean temperatures of the tropical oceans [Aumann et al., 2007]. This correlation can be used to estimate the sensitivity of DCC frequency to a change in the zonal mean surface temperature, TSurf. The established long term trend in TSurf due to global warming can then be used to estimate the change of frequency of DCC with time.
 On average about six thousand DCC are identified globally each day with the 210 K threshold, almost all within 30 degrees of the equator. Twenty five percent of the DCC identified with this threshold have cloud top temperatures colder than 200 K. While six thousand DCC seems like a large number, it corresponds to a little less than one percent of all spectra in the tropical ocean latitudes. Figure 1 shows the daily count of DCC observed in the 0–30 N zone from the descending orbits between September 2002 and August 2008. The continuous trace is a 32 day smoothing average.
3.1. Correlation of the DCC Frequency With TSurf
 We use the NCEP RealTime Global Sea Surface Temperature (RTGSST) [Thiébaux et al., 2003], which is available as a daily average product on a 0.5 degree grid, for TSurf. The RTGSST is based on buoys and ship reports, spatially interpolated using clear sky AVHRR SST measurements. The RTGSST has considerable predictive skill, since under clear sky conditions it agrees with the AIRS 2616 cm−1 window channel derived SST with a bias of less than 0.2 K and 0.4 K rms [Aumann et al., 2006a]. Figure 2 shows the same data as Figure 1 overlaid on to 0–30 N zonal mean NCEP TSurf as function of time. As the 0–30 N zonal mean temperature varies from 299.5 K to 301.5 K with the seasonal modulation of the incident solar radiance, the DCC count varies from about 500 to about 2500. The correlation between TSurf and the DCC count is better than 0.6. This correlation can be used to define the temperature sensitivity of the DCC count as the ratio of the seasonal change in the count and the seasonal change in the temperature. Since the count of DCC depends on the spatial coverage and the footprint size, we analyzed the data in terms of the DCC fraction, which is the DCC count divided by the mean number of DCC. Simply by inspection of Figure 2 we obtain a first order estimate of temperature sensitivity of the DCC frequency: S_dcc = (2500–500)/(301.5–299.5)/1500 = 0.7/K, i.e. in 0–30 N zone a 1K increase in TSurf increases the fraction of footprints identified as DCC by 70%. For a more quantitative estimate of the sensitivity and its uncertainty we divide the data into four independent groups and make use of scatter diagrams. The groups are 0–30 N and 0–30 S ocean, and for day and night. Figure 3 shows the same 0–30 N night daily means used for Figure 2, plotting the individual 1771 daily results of TSurf vs. the DCC frequency. The DCC frequency is defined as ratio of the DCC count to the total number of footprints. The scatter diagram shows the strong positive correlation between TSurf and the DCC frequency. Starting at about 298 K the frequency of DCC increases until about 302 K, close to the limit of the zonal mean TSurf, and is rarely reached except in the Tropical Warm Pool (TWP, defined as −10 < latitude < +10, 120 < longitude <200). Scatter plots for the four subgroups look qualitatively similar to Figure 3.
 There is no unique way of estimating the trend in the scatter diagrams, which is clearly non-linear. Since we are interested only in the sensitivity near 300 K, approximately the mean TSurf of the tropical oceans between the years 2002 and 2007, we estimate the slope using linear regression: (+0.48 ± 0.12)/K. The uncertainty in the slope is one sigma, using the auto-correlation correction from Santer et al. . Results for the four data subsets are summarized in the second to fourth columns of Table 1 in terms of the five year mean DCC frequency, the DCC frequency correlation with TSurf and the fractional DCC sensitivity to a change in TSurf. The separation of the data into four subsets results in a mean DCC sensitivity and standard deviation of (+0.43 ± 0.12)/K.
Table 1. Summary of the DCC Frequency Sensitivity Evaluation From Four Independent Data Subsetsa
Five Year Mean DCC Frequency
DCC Frequency/Tsurf Correlation
Five Year Mean DCC Frequency
DCC Frequency/Tsurf Correlation
The second to fourth columns are for the tropical oceans including the TWP and the fifth to seventh columns exclude the TWP.
0–30 N day
0–30 N night
0–30 S day
0–30 S night
 About 25% of the DCC in our data are associated with the TWP. The TWP has been the subject of considerable interest for many years [e.g., Waliser et al., 1993], although it covers only about 10% of the tropical ocean area. During the 2002–2007 period TSurf in the TWP averaged 302.1 K, with the 95%tile at 303.3 K and a maximum of 304.2K. In order to evaluate the sensitivity of the slope to the inclusion of the TWP, we repeated the analysis for the 0–30 N, 0–30 S ocean zones, excluding the TWP. Results without the TWP are listed in the fifth to seventh columns of Table 1. The results show more scatter and indications of a N/S asymmetry, but the tropical ocean mean sensitivity is (+0.45 ± 0.12)/K, consistent with the original four groups.
3.2. Five Year Trend in the DCC Frequency
 The daily measurements of the DCC frequency were used to estimate the five year anomaly trend. The anomaly is the difference between the observed data and the five year climatology generated from data. The anomaly trend is the slope of this difference with time. The numerical details of this procedure are given by Aumann et al. . The formal uncertainty of the slope deduced from the scatter in the measurements, corrected for the autocorrelation [Santer et al., 2000] of the day/night combined data, is −0.6%/yr with a one sigma uncertainty 0.4%/yr. The measured trend is not two sigma significant. As an alternative estimate of the uncertainty of the trend we subdivide the data into two independent subgroups for the tropical oceans: ascending and descending orbits. Table 2 summarizes the results in terms of the mean DCC frequency, the anomaly trend and the one sigma trend uncertainty, both in units of percent per year. The measured trend is not significant on a 95% confidence level. Table 2 also includes the analysis of the tropical TSurf anomaly, which had an anomaly trend of −23 mK/yr with an 8 mK/yr one sigma uncertainty, i.e. is significant at the 2 σ ± 95% confidence) level.
Table 2. Results of the Anomaly Trend Analysis of the DCC Frequency and the Zonal Mean Tropical TSurfa
30 S–30 N
Five Year Mean Frequency
One Sigma Trend Uncertainty
The anomaly trend uncertainty is one sigma. The DCC trend is expressed as a percentage, i.e., the trend in the frequency divided by the five year mean frequency.
DCC frequency day
DCC frequency night
 The combination of the temperature sensitivity of the frequency of DCC of (+0.45 ± 0.12)/K and the nominal long-term global warming of 0.13 K/decade [Trenberth et al., 2007] indicates that the frequency of DCC increases at the rate of +6 ± 1.6 %/decade. The association of cloud formations with cloud tops colder than 210 K, which we refer to as DCC, with extreme convection and severe storms resulting in heavy rainfall, lightning, crop damaging hail and tornadoes goes back to infrared data from the first geosynchronous satellites [Reynolds, 1980]. The 6%/decade increase in the frequency of DCC with global warming thus pertains to severe storms. The question of how much climate change will impact the frequency of severe storms and the overall convective circulations in general, is an important topic of research and obviously still a very open question.
 In climate models used in the fourth assessment of the IPCC (AR4) the increase in water vapor, about 7%/K [e.g., Held and Soden, 2006], seems to follow the CC relation due to a relatively constant behavior of relative humidity. This corresponds to +1%/decade increase in water vapor for the nominal +0.13 K/decade global warming. However, precipitation in the models does not increase at the same rate with respect to temperature as tropospheric water vapor [Vecchi and Soden, 2007]; precipitation in the models seems to increase on the average only 2%/K, which is much less than the 7%/K C-C rate. As a consequence, as shown by Held and Soden , the mean convective mass-flux (a measure of convective intensity in climate models) must decrease for the precipitation increase to be significantly less than the water vapor increase. Assuming that precipitation is proportional to the convective mass-flux times the water vapor, a 7%/K increase in water vapor (CC) combined with a 2%/K sensitivity of precipitation (AR4 climate models) requires a 5%/K decrease in the mean tropical convective mass-flux. This is opposite to the temperature sensitivity of the frequency of DCC deduced from AIRS of +45%/K. However, it should be noted that these DCC represent the conditions in less than 1% of the tropical oceans. If the mean convective activity in the remaining 99% of the ocean indeed decreases by 5%/K as required by climate models, the global mean is hardly changed by adding 1% DCC with a strong increasing trend. Vecchi and Soden  note that the decrease in the mean strength of tropical convection in climate models should not be interpreted as a reduction in the frequency of intense precipitation events. In fact, intense precipitation events become more frequent in the GFDL CM2 model as the climate warms. Since the DCC are associated with the most intense rain events, the observed increase in the DCC frequency with warming is qualitatively consistent with a frequency increase in the most intense precipitation events in the GFDL CM2 model.
 A 6%/decade increase in the frequency of DCC with global warming may provide a long term mechanism for an increased injection of water vapor into the lower stratosphere with a seasonal dependence. The spectra of DCC are characteristic of optically thick cirrus ice [Aumann et al., 2006b]. The temperature at the tropical tropopause near 100 hPa is between 190 and 200 K [e.g., Goody, 1995; Hartmann, 1994], 10 K colder than our DCC threshold. However, as the top of a DCC approaches the tropopause from below the effective cloud top temperature decreases, then it increases again as the cloud top penetrates through the tropopause. Based on DCC model spectra [Aumann et al., 2006b], this penetration can be detected as a reversal in weak water lines near 1600 cm−1 and is present in about 50% of the DCC. Penetrative convection makes DCC potentially the major, seasonally variable contributor to cirrus ice and water vapor in the lower stratosphere. Rosenlof et al.  found that the stratospheric water vapor mixing ratio has increased steadily over the past half century at the rate of 10%/decade with a seasonal modulation, compared to the 6%/decade increase in the DCC frequency.
 The correlation between the mean SST, the frequency of DCC and stratospheric water on a shorter than multi-decadal time scale may well be more tenuous. TSurf for the tropical oceans changed by −0.023 ± 0.008 K/yr between 2002 and 2007. With the sensitivity of (+0.45 ± 0.12)/K we would expect a change of −1.0 ± 0.4 %/year in the DCC frequency. The observed trend in the frequency of DCC in the tropical oceans was (−0.6 ± 0.4) %/year, consistent with the expected change, but the agreement does not have 95% confidence. It is interesting to note that Randel et al.  found that starting in 2001 the stratospheric water mixing ratio also showed a decrease, but the change is relatively sudden, compared to a change in the SST.
 We use five years of data from the Atmospheric Infrared Sounder to study the correlation between the frequency of Deep Convective Clouds (DCC) and the zonal mean tropical surface temperature. AIRS data show that the DCC frequency in the tropical oceans is temperature sensitive, increasing by 45% per 1 K increase in the zonal mean surface temperature. The combination of the sensitivity of the DCC frequency to temperature and the +0.13 K/decade rate of global warming leads to the conclusion that the frequency of DCC, and by inference the frequency of severe storms, increases at the rate of 6%/decade. This observation is only qualitatively consistent with some state-of-the-art climate models, where the mean rain-rate decreases, but the frequency of the most intense rain event increases with global warming. The increase of the DCC frequency with global warming may also provide a mechanism for the increase in stratospheric water vapor observed over the past half century.
 We acknowledge helpful discussions with Y. Yung, Brian Kahn and W.G. Read and critical reading by Steve Broberg. Sergio DeSouza-Machado (UMBC) generated the DCC model spectra for the evaluation of tropopause penetration. This work was carried out at Caltech's Jet Propulsion Laboratory under contract with NASA.