Linking changes in hourly precipitation extremes to the Clausius-Clapeyron relation

Events of extreme precipitation have a huge influence on society. They are associated with flooding, erosion, water damage, and may have impacts on transport and safety.

It is commonly expected that precipitation extremes will increase as the climate warms. Changes in extreme precipitation are even often considered to be more predictable than changes in average precipitation (1,2). For example, the KNMI’06 scenarios predict increases in extreme precipitation for all scenarios, but are not conclusive about the sign of the change in mean precipitation in summer (3).

The primary reason why precipitation extremes are expected to increase is that a warmer atmosphere has a larger saturation water vapour content. The relation between “moisture-holding capacity” of the atmosphere, temperature and pressure is expressed by the Clausius-Clapeyron relation, which is based on the atmospheric thermodynamics. From this relation follows an increase in the moisture-holding capacity of the atmosphere of approximately 7 % per degree temperature rise. If the relative humidity in the future climate remains approximately the same as in the present-day climate – which is generally expected based on model results and also on physical understanding – the amount of water vapour in the atmosphere will increase also with 7% per degree temperature rise. Now, the commonly used argument is that in extreme showers all water vapour in the air (or a constant fraction of it) is converted into rain. Hence, extreme precipitation will scale with the Clausius-Clapeyron relation (see figure 1).

Figure 1. Schematic diagram of a precipitating convective cloud. Water vapour from the sub-cloud area is drawn into the base of the cloud by the convective storm dynamics and low level convergence. In the cloud water vapour condenses into cloud droplets,

There is some model evidence from Global Climate Models (GCMs) that indeed precipitation extremes increase at the rate predicted by the Clausius-Clapeyron (hereafter CC) relation (2). However, a CC scaling is not obtained in every model and there exists no observational evidence for such a scaling. Also, despite the conceptual understanding as outlined above, there is no reason why extremes should exactly follow the CC relation. For instance, changes in the dynamics of the atmosphere and the convective cloud, in the moist adiabatic temperature profile (4), and in the size of the convective cloud could cause deviations from the CC-scaling. In addition, it is not clear how robust such a scaling relation is across different time and spatial scales.

We have investigated whether a CC-scaling can be found in the observations. A relation between precipitation extremes and temperature has been derived from day-to-day variations in temperature and precipitation. We have done so for both daily and hourly extremes, but here we focus on hourly precipitation extremes since showers have a typical lifetime of one to a few hours. Finally, we examined the output from a regional climate model integration to see whether such a scaling also exists for the climate change signal. Most of the results presented here have been published in Nature Geoscience (5).


We used a long data set of hourly precipitation observed at De Bilt, starting at 1906. This data set has been homogenized and quality controlled. We divided the precipitation data based on the daily mean temperature into bins of 2 oC width. Daily mean temperatures are used, instead of hourly temperatures, because we are interested in a proxy representing the temperature of the air mass. The hourly temperatures are to a large extent controlled by boundary-layer processes and radiation. From the binned data we computed the 90th, 99th and 99.9th percentiles of the distribution of wet events (hours or days) in each bin. The 99th and 99.9th percentile are computed from a generalized Pareto distribution fitted to the upper 5 % of the data, and uncertainty bands are computed using the bootstrap. Besides the data set of De Bilt, also data from Belgium (Ukkel) and Switzerland (Bern, Basel and Zürich) has been analysed.

Figure 2a shows results from the analysis of hourly precipitation extremes for De Bilt. For temperatures below 10 oC a dependency close to 7 % per degree is found for the higher percentiles (90th percentile and higher). Thus for lower temperatures the behaviour of the extremes is close to the behaviour predicted by the Clausius-Clapeyron relation. For temperatures above 10 oC a transition is seen to a stronger temperature dependency close to 14 % per degree: a super CC scaling. For the most extreme events this super CC scaling occurs at slightly lower temperatures than for the less extreme events. For moderate events, like the 75th percentile, no clear scaling is obtained5) (not shown here).

Analysis of the other data sets confirms that the scaling relation found in the De Bilt data is robust. Data from Belgium and Switzerland reveal very similar behaviour for the most extreme events (Figures 2b,c). Differences, however, occur for the less extreme events (90th percentile and lower).

Daily precipitation extremes show less strong temperature dependencies than the hourly extremes, in general close to or below the CC relation. The scaling behaviour is also less clearly defined5).

Figure 2. Scaling of observed hourly precipitation extremes with temperature for three different data sources (De Bilt: source KNMI; Ukkel: source RMI; Bern, Basel and Zürich: source MeteoSwiss). Shown are different percentiles of the distribution (90th t

Model results

Can the scaling between temperature and extreme precipitation inferred from present-day climate observations be used as a predictor of extreme precipitation we may be confronted with in a warmer climate? To investigate this, we analysed precipitation extremes from a climate integration with the KNMI regional climate model RACMO. This high resolution run, 25 km grid spacing on a domain covering the whole of Europe, has been done in the project ENSEMBLES (6) funded by the European Union. Boundaries for this climate scenario run are taken from a global simulation with the climate model ECHAM5.

Figure 3a shows that for large parts of central Europe the change in 1-hour extremes indeed exceeds the Clausius-Clapeyron prediction significantly. In large areas typical dependencies of 10-20 % per degree are found. The increase in daily extremes is less (Figure 3b).

The model results show that changes in hourly precipitation extremes in a warmer climate could be as large as 14 % per degree temperature rise due to increases in atmospheric moisture with temperature. However, there are more factors that influence the change in the extremes, such as changes in the atmospheric circulation and soil moisture content. For example, due to severe soil drying the actual increase in water vapour in the atmosphere may not scale with temperature. In correspondence, the model results show that increases in southern Europe are much smaller, in general displaying a temperature dependency below the CC relation. Work is in progress to further clarify the relation between atmospheric circulation changes, soil drying and changes in precipitation extremes.

Figure 3. The change in the 99.9th percentile of extreme precipitation on a grid scale (25x25 km) normalized by the seasonal mean local temperature change. Changes are computed from the difference between the future period 2071-2100 and the reference peri

Cause of the super Clausius-Clapeyron scaling

There is some debate about the cause of the super CC scaling in the observations (7,8). In our opinion, the explanation must be searched in the physics of deep convective clouds. For this type of precipitating clouds the strength of the upward motions in the atmosphere is (largely) determined by the latent heat release occurring in the cloud. More rainfall formation implies more latent heat release, which forces stronger updrafts and potentially a stronger rate of condensation and rainfall formation in the cloud. Thus, we argue that a positive feedback between water vapour and the dynamics of rainfall formation in a convective cloud causes the super CC scaling.

Alternatively, statistical effects potentially affect the scaling as well. Different temperature ranges are characterized by different atmospheric conditions, and these give rise to different precipitation regimes. Low temperatures mostly occur in the winter season, with the prevalence of synoptic large scale cyclones. In these large-scale systems rainfall intensities are generally low, but the rainfall duration is long (typically 4 to 6 hours). Conversely, the high temperature range is dominated by convective rainfall, with high intensities and short durations (typically 1 hour). Therefore, the change from low temperature to higher temperatures involves a change in the frequencies of both the large scale and the convective events, whereby on average less intense large scale events (with longer durati0n) are replaced by more intense convective events (with shorter duration). This statistical effect could give rise to an enhanced temperature dependency of hourly precipitation (7).

The reason why it is important to establish the cause of the super CC scaling is that this has direct consequences for how this scaling will manifest itself in the climate change signal. It is not expected that the ratio between the frequencies of large-scale and convective precipitation events will change considerably due to climate change. Therefore, if the super CC scaling is due to the proposed statistical effect, changes in precipitation extremes would likely be not larger than predicted by the CC relation (that is, 7 % per degree). However, if the super CC scaling is due to the physics of the convective precipitation process, than one would expect this scaling to hold under warmer future climate conditions. In that case, changes in precipitation extremes are likely to be larger than predicted by the CC relation.

Although the scaling relation could be influenced by the statistical effect mentioned above, we think that the primary cause of the super CC scaling is to be found in the physics of the convective events. One reason is that an almost identical scaling for higher temperatures is obtained when considering the summer season only, and rainfall in the summer season is dominated by small scale convective events. Also when taking only data that has been classified to be convective, a super CC scaling is obtained for this sub-selection of events. (This classification is based on the WW code in the SYNOP message, that contains a subjective description of the past hour weather as reported by the meteorological observer.) Another reason is that the regional model simulation indeed shows a response larger than predicted by the CC relation.


We obtained a temperature dependency of hourly precipitation extremes of approximately 14 % per degree in observations at De Bilt. This relation exceeds the well known Clausius-Clapeyron relation, which is commonly used as a predictor of the increases in precipitation extremes, by a factor of two. Similar relations are obtained from time series from Belgium and Switzerland, and the results therefore appear to be a robust feature of hourly precipitation extremes in this part of Europe.

Our hypothesis is that the relation found in the present-day climate can be used as a predictor for the climate change signal. This hypothesis is confirmed by simulations with the KNMI regional climate model RACMO. However, we also note that a recent ensemble of model simulations, which is performed in the ENSEMBLES project6), shows a very large range of predicted changes in hourly precipitation extremes. New research will focus on understanding the range of model outcomes in order to reduce the uncertainty in predictions of future changes in precipitation extremes.


Hourly precipitation data has been provided by the Swiss Federal Office of Meteorology and Climatology MeteoSwiss, and the Royal Meteorological Institute in Belgium. Financial support by the EU FP6 Integrated Project ENSEMBLES (Contract number 505539) and the Dutch programs Climate Changes Spatial Planning (CcSP) and Knowledge for Climate (KfC) is gratefully acknowledged.


  • Emori, S. and S. Brown, 2005. Dynamic and thermodynamic change in mean and extreme precipitation under climate change. Geophys. Res. Lett., 32, L177061.
  • Pall, P., M. Allen and D. Stone, 2007. Testing the Clausius-Capeyron constraint on changes in extreme precipitation under CO2 warming. Clim. Dyn., 28, 351-363.
  • Lenderink, G., A. van Ulden, B. van den Hurk and F. Keller, 2007. A study on combining global and regional climate model results for generating climate scenarios of temperature and precipitation for the Netherlands. Clim. Dyn., 29, 157-176.
  • O'Gorman, P. A. and T. Schneider, 2009. The physical basis for increases in precipitation extremes in simulations of 21st-century climate change. Proc. Nat. Acad. Sciences, 106, 14773-14777.
  • Lenderink, G. and E. van Meijgaard, 2008. Increase in hourly precipitation extremes beyond expectations from temperature changes. Nature Geosci., 1, 511-514.
  • Hewitt, C. and D. Griggs, 2004. Ensembles-Based Predictions of Climate Changes and Their Impacts (ENSEMBLES). EOS-Transactions, 85, 566.
  • Haerter, J. O. and P. Berg, 2009. Unexpected rise in extreme precipitation caused by a shift in rain type? Nature Geosci., 2, 372-373.
  • Lenderink, G. and E. van Meijgaard, 2009. Reply to: Unexpected rise in extreme precipitation caused by a shift in rain type? Nature Geosci., 2, 373.
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