In a changing climate, there is an interest in predicting how extreme rainfall events may change. Using historical records, several recent papers have evaluated whether high-intensity precipitation scales with temperature in accordance with the Clausius–Clapeyron (C–C) relationship. For varying locations in Europe, these papers have identified both super C–C relationships as well as a breakdown of the C–C relationship under dry conditions. In this paper, a similar analysis is carried out for the United States using data from 14 weather stations clustered in four different hydroclimatic regions: the coastal northeast, interior New York, the central plains, and the western plains. In all regions except interior New York state, 99th percentile 1-h precipitation generally followed the C–C relation. In interior New York, there was evidence that intensity scaled with a super C–C relationship. For the 99.9th percentile precipitation, interior New York displayed some moderate evidence of a super C–C relationship, the western plains showed little relation between precipitation and temperature, and the remainder of sites generally scaled with the C–C relationship. Also, if only July, August, and September precipitation is considered, all stations except those in interior New York have little relation between temperature and precipitation, suggesting that precipitation intensity during summer months may not be well constrained by the C–C relationship. Overall, the C–C relationship (or a variation thereof) does not appear to constrain extreme precipitation in all regions and in all seasons, and its ability to aid in constraining future predictions of extreme precipitation may only be relevant to certain locales and time periods.
An often predicted outcome of climate change is an increase in the intensity of extreme rainfall, usually at a rate of increase greater than that for mean precipitation. Such increasing precipitation intensity has been argued for on theoretical grounds (Allen and Ingram 2002; Trenberth et al. 2003), simulated in climate models (Meehl et al. 2005; Gutowski et al. 2007), and inferred from recent observable increases in intensity (Groisman et al. 2005; DeGaetano 2009). However, there remain questions on the actual magnitude of the change and the fundamental processes inducing the change.
A common explanation for an increase in intensity links precipitation to air temperature. The Clausius–Clapeyron (C–C) relation relates the atmosphere’s moisture-holding capacity to temperature, implying a roughly 7% increase in atmospheric moisture storage per degree Celsius. Since extreme rainfall events are presumed to extract nearly all available moisture from the atmosphere, extreme rainfall intensity is assumed to be most dependent on changes in atmospheric moisture content. Allen and Ingram (2002) discussed the C–C relation as a possible dominant physical constraint on precipitation intensity, but they only evaluated it against global rainfall. Pall et al. (2007) extended Allen and Ingram’s approach and considered the C–C relation for daily rainfall at a coarse regional scale (grid boxes of 2.5° latitude and 3.75° longitude). They found the greatest agreement between the C–C relation and changes in rainfall extremes at midlatitudes.
More recently there has been work to assess the C–C relation at an even finer spatial and temporal resolution. Lenderink and van Meijgaard (2008) evaluated a record of hourly and daily rainfall from a single station in De Bilt, Netherlands. They found that changes in hourly and daily precipitation intensity generally increased at the 7% °C−1 rate anticipated by the C–C at temperatures below 10°C, but that hourly precipitation exhibited a “super C–C” relation (i.e., an increase greater than 7% °C−1) at higher temperatures. This finding was repeated when they analyzed additional station data in the Netherlands, Belgium, and Switzerland (Lenderink and van Meijgaard 2010). From analysis of hourly data in Germany, Haerter et al. (2010) observed changes in precipitation intensity with temperature at greater than the C–C relation, but they did not observe a distinct temperature threshold at which this shift in relationship took place. Notably, this super C–C relationship for hourly precipitation has not been evaluated in locales outside of northern Europe. Additionally, there has been debate why this super C–C relationship has been observed. Lenderink and van Meijgaard (2009) have argued that the super C–C relationship is of physical origin and results from stronger updrafts due to greater latent heat release. Haerter and Berg (2009) have suggested that the effect results from the transition from lower intensity precipitation from large-scale systems in cool weather to higher intensity precipitation from convective systems in warm weather, even when rainfall generation by large-scale or convective systems independently adhere to the C–C relationship. Haerter and Berg (2009) have suggested that super C–C scaling may be most prevalent in regions that have a relatively balanced coexistence of both convective and large-scale rainfall events.
There have been other direct assessments of the C–C relationship at relatively fine spatial scales (0.44° gridded cells), but they have been done for daily precipitation values (Berg et al. 2009). In such assessments, Berg et al. (2009) found that the ability of the C–C relationship to predict changes in rainfall intensity is dependent on season. On hot summer days, precipitation intensity was negatively correlated to temperature because the availability of moisture (both at the land surface as well as in condensed form in the atmosphere) was most important to determining intensity, not the capacity of the atmosphere to hold moisture. In winter, Berg et al. (2009) did find that the C–C relationship set a limit to increases in daily large-scale precipitation with increasing temperature.
In this paper, our objective is to assess the ability of the C–C relationship to explain hourly precipitation intensity in varying hydrometeorological regions of the midlatitudes in North America. We focus on the midlatitudes since previous modeling work has suggested this is where the C–C relation should best constrain extreme rainfall (i.e., Pall et al. 2007). We focus on hourly rainfall because the magnitude of these high intensity events are directly relevant to changes in the frequency of infiltration excess runoff generation as well as soil erosion. Since infiltration excess runoff and rain-driven soil erosion are nonlinear, threshold-dependent processes, they are often not well explained by daily rainfall.
This article will provide a further check on the universality of earlier findings. In particular it will assess the presence of a “super C–C” relationship (Lenderink and van Meijgaard 2008; Lenderink and van Meijgaard 2010) and the dependency of rainfall intensity on moisture availability (Berg et al. 2009). Because this study analyzes historical records of climate, past relationships between extreme precipitation and temperature at a given location are not necessarily indicative of future relationships in a changing climate, especially if there is a fundamental shift in types of weather in a certain region. However, if a C–C relationship does not apply to the current climate, it will unlikely apply to future climates.
Meteorological stations with data archived at the National Climatic Data Center (NCDC) were identified in each of four distinct regions of the United States: coastal northeast, interior northeast, central plains, and western plains. Regions were selected to represent a range in atmospheric moisture availability, as indicated by total annual precipitation (Fig. 1). In Fig. 1, the original source of the mean annual precipitation data was Owensby and Ezell (1992). Table 1 lists the station name, NCDC Co-op number, and period of record. For each of the stations, we related hourly precipitation (P) and daily surface air temperature (T). Daily T is used since we are interested in the temperature of the air mass and not fluctuation due to varying radiation intensity or boundary layer processes. The relationship between P and T is assessed separately for two time periods: the complete annual record and the three-month period from July through September. This July–September period was intended to highlight any possible limits to extreme rainfall due to moisture limitations as was previously found by Berg et al. (2009).
For days on which greater than trace precipitation occurred, P was segregated by T into bins of size 2°C (with the exception of periods with T < 6°C when 4° bins were used). Within each bin, the 99.9th and 99th percentile P value were determined directly. For a subset of the stations, the 99.9th and 99th percentile P values were also determined by fitting a Generalized Pareto Distribution (GPD) to the upper 5% of each binned dataset. Note, given that only 5% of the raw data was used, the 98th and 80th percentile values (corresponding to the 99.9th and 99th percentiles of the raw data) were extracted from the GPD. The T versus P relationships determined from the GPD were virtually identical to those from directly determined P values, so we just used the directly determined percentile values. In wetter, eastern regions, the number of hourly P values in each bin was around 1500 while in the dryer western plains region, bins had approximately 500 values. Bins with less than 300 values were not used to assess the relationship between T and P.
We graphically assess the relation between observed extreme P versus T and that suggested by the C–C relationship. We use an approximation to the C–C relationship of the form: es = A exp[BT/(C + T)], where es is the saturated vapor pressure (kPa) and the constants A, B, and C have the values 0.6108, 17.27, and 237.3 (Shuttleworth 1993). Since we are only presenting the slope of the relationship between es and T and not the absolute value of es in Figs. 2 and 3, we arbitrarily modify A to fit the C–C curve on the figures. Notably, this approximation of the C–C relationship is not linear in semilog space and differs slightly from the linear C–C reference lines presented in Lenderink and van Meijgaard (2008, 2010) and Berg et al. (2009).
For each site, the log of the 99.9th and 99th percentile hourly precipitation amounts are plotted against T. Sites are grouped by region (Fig. 2). The 99th percentile precipitation intensity generally scales with the C–C relationship of approximately 7% °C−1. One notable exception is at Hyannis, Massachusetts; this discrepancy is presumably due to the strong coastal influence relative to the other stations used in this study. Knoxville and Ames, Iowa, also appear to have higher P at low T than would be expected given a C–C relationship. However, given the log scale of P, this perceived discrepancy is caused by only a 2–3-mm increase in P and could very likely be related to errors in measuring snowfall (i.e., Yang et al. 1998). In interior New York, when considered across the full range of T, P appears to scale with the C–C relationship. However, at temperatures above 15°C, the interior New York sites appear to scale at greater than the C–C relationship. If the slope of the relationship between log P and T is determined by linear regression, for the 99th percentile P, slopes above 15°C are consistently larger than slopes below 15°C, and the slopes differ by more than the sum of their standard errors (see Table 2). For the 99.9th percentile P, regression slopes above 15°C are consistently larger than slopes below 15°C, but the slopes do not consistently differ by more than their standard errors. Notably, while there does seem to be evidence of a super C–C relationship, it is not a doubling of the C–C relationship as observed by Lenderink and van Meijgaard (2008, 2010). The C–C relationship has a slope of approximately 0.026 (in log mm hr−1 °C−1) near 15°C. In Table 2, we observe slopes greater than 0.026, but not double that.
For the 99.9th percentile P, Hyannis, Knoxville, and Ames diverge from the C–C relation (consistent with the 99th percentile P) but so do the three western plain stations. Knoxville and Ames appear to correspond to the C–C relation at temperatures above 10°C, but not below. Hyannis and the three western plains have only a weak upward trend with high intensity rainfall and the curves suggest that large P values are apparently possible at nearly any daily T value. The interior New York sites again appear to display some deviation from the C–C relationship above 15°C, but this deviation is weaker than that observed at the 99th percentile (see Table 2). For the 99.9th percentile P, the remainder of the stations generally adhere to the C–C relationship.
The P versus T relationships for the months of July, August, and September (Fig. 3) can be used to evaluate Berg et al.’s (2009) observation of an inverse relationship between T and P in the dry summer months. It is apparent that no inverse relationship is present at the hourly temporal resolution for any of the regions studied here. Additionally, for the central and western plains there is little relationship between P and T at both the 99th and 99.9th percentile P while the coastal northeast sites have little relationship at the 99.9th percentile P.
The findings differ somewhat from those of both Berg et al. (2009) and Lenderink and van Meijgaard (2008, 2010). Unlike Lenderink and van Meijgaard (2008, 2010), with the possible exception of the interior New York sites, there was no super C–C relation between T and P. This suggests that a super C–C relationship may only be seen in select regions with unique features. For instance, Lenderink and van Meijgaard’s (2008, 2010) study areas were dominated by the coastal plain (Belgian and Dutch sites) and mountain (Swiss sites) features and characterized by a mean daily T always below 22°C (all the U.S. sites had maximum mean T of at least 28°C). Different from other sites in this study, the interior New York sites are relatively unaffected by either tropical cyclones (Villarini and Smith 2010) or the most intense of extratropical cyclonic activity; thus, high-intensity rainfall in interior New York is primarily dependent only on local and mesoscale convective events that occur during warm weather. The seemingly strong correlation among temperature, season, and weather-system type in interior New York may support Haerter and Berg’s (2009) suggestion that regions with the coexistence of both convective and large-scale extreme rainfall (albeit with each dominating in different seasons) are likely to display a super C–C relationship.
Unlike Berg et al. (2009) (but now for hourly instead of daily precipitation), at all the stations assessed, there was no inverse relationship between T and P during the summer months. Maps of moisture recycling in different areas of the globe indicate that the Mediterranean region of Berg et al.’s (2009) European study area have a moisture recycling ratio of 25% (ratio of how much precipitation originates locally and how much advects into a region) while the U.S. sites we studied have recycling rations of about 15% (Trenberth et al. 2003). These lower recycling ratios presumably make the U.S. sites less sensitive to locally dry summer conditions, but further study is needed to confirm this. Overall, the lack of a relationship between T and P at most stations during the summer months when one did exist with data from the full year (i.e., consider differences between Figs. 2 and 3), suggests that the C–C relation may constrain P for wide-ranging T differences, but be less useful in explaining changes in P over a narrow range of T.
Besides the summer months, the C–C relationship also has limited ability to constrain the 99.9th percentile precipitation in the western plains sites and some of the central plains sites even when the complete annual data record is considered. At these sites, it is possible that mean daily T at the surface does not represent the temperature of the upper atmosphere or that storm systems move rapidly enough that daily T is not representative of temperature at the time of the precipitation event. Alternatively, it is possible that the most extreme events are constrained by factors other than moisture availability as represented by T. Characterizations of large convective systems associated with extreme precipitation in the Midwest have noted the importance of strong low-level winds for advecting moist air into the region of precipitation as well as the importance of the size, organization, and motion of the system (Schumacher and Johnson 2005), all factors not directly related to T. Additionally, of particular relevance to all the sites at higher T values (as in Fig. 3), O’Gorman and Schneider (2009) have highlighted the fact that some climate models predict a scaling of extreme rainfall at less than the C–C relationship. They suggest that the most relevant physical mechanism to dictating extreme rainfall at higher temperatures is changes in the moist-adiabatic lapse rate because this increases more slowly than the C–C relationship with temperature.
Finally, it should be noted that a lack of a clear trend between P and T at some stations could be due to the inherent nature of using a point rainfall gauge. Several studies in which C–C relationships are assessed have used model data or reanalysis data (Berg et al. 2009; Pall et al. 2007; Allen and Ingram 2002) with P and T averaged over a several hundred square mile region. However, research into the time–space distribution of rainfall has long noted that variance in rainfall depth decreases with increasing averaging area. For instance, Sivapalan and Bloschl (1998) present a nondimensional variance reduction factor which changes from near 1 at a point scale (0.1 m2 gauge scale) to near 0 six orders of magnitude larger (model grid scale). Thus, we would naturally expect more variability in the P and T relationship from station data. Furthermore, the variance reduction factor is also dependent on spatial correlation length of the rainfall fields; higher correlation length leads to lower variance. This may in part explain why Lenderink and van Meijgaard’s (2008, 2010) sites as well as some of our own stations display relatively coherent trends, while others do not. Presumably, the regions studied by Lenderink and van Meijgaard as well as locations such as in the eastern United States, have more uniform high-intensity rainfall, larger spatial correlation length, and less variability, making for more consistent trends.
The ability of the C–C relation to constrain maximum precipitation intensity appears to vary by region as well as season. This analysis suggests that one should be careful not to generalize the capacity of the C–C relationship in constraining precipitation intensity; it may prove suitable in some places or at certain times of the year but not others. Finally, it should be kept in mind that even for regions in which the C–C relationship appears to currently constrain extreme precipitation, it is not guaranteed that the dominant mechanisms will remain the same in a changing climate.
Special thanks to Christopher Berry for assisting with data compilation. Also, thanks to M. Todd Walter for organizing the discussion group that motivated this work.
Corresponding author address: Stephen B. Shaw, Dept. of Earth and Atmospheric Sciences, Cornell University, Ithaca, NY 14853. Email: email@example.com