Trends in joint quantiles of temperature and precipitation in Europe since 1901 and projected for 2100



[1] This study assesses the changes in the exceedances of joint extremes of temperature and precipitation quantiles for a number of sites in Europe. The combination of cool/dry, cool/wet, warm/dry and warm/wet modes reveals a systematic change at all locations investigated in the course of the 20th century, with significant declines in the frequency of occurrence of the “cold” modes and a sharp rise in that of the “warm” modes. The changing behavior of these four modes is also accompanied by changes in the particular conditions of temperature and precipitation associated with each mode; for example, the average amount of precipitation during cool/wet events decreases while that during warm/wet events increases, even though mean precipitation at most locations shows no significant trend. In a “greenhouse climate”, the “cool” modes are almost totally absent by 2100 whereas the warm/dry and warm/wet modes pursue the progression already observed in the 20th century.

1. Introduction

[2] Investigations of the behavior of weather extremes in a changing climate tend to focus on the tails of the probability density function (PDF) of a particular atmospheric variable, in order to assess whether there are clear relations between shifts in extremes of temperature or precipitation and changes in mean climate [e.g., Klein Tank and Können, 2003; Beniston, 2007]. Many studies have yielded mixed results, in part because it is often difficult to relate in a statistically-meaningful manner a climate that is changing on the long term (i.e., years to decades) and rare and/or intense events that, with few exceptions, occur on short time scales (i.e., hours to days).

[3] This paper reports on the trends of combined temperature and precipitation statistics in several European locations, using a concept that was described in a paper by Beniston and Goyette [2007] and more recently applied to Switzerland by Beniston [2009]. The use of joint PDFs, in this instance, those of temperature and precipitation, provides insight into the behavior of particular modes of heat and moisture that the analysis of the statistics of each variable taken individually does not. For example, while in some cases the precipitation record may show no particular trends, new insights on statistics that integrate mutual feedbacks between temperature and moisture are found when temperature and precipitation records are combined.

[4] The paper makes use of 25% and 75% quantile thresholds in order to define particular modes of heat and moisture. Four modes are investigated here, defined by joint exceedances above or below these thresholds that serve to define “cool/dry”, “cool/wet”, “warm/dry” and “warm/wet” regimes. The paper will show that there have been substantial changes in these modes at all sites investigated and, interestingly, these changes are synchronous independently of whether the location is in a Mediterranean, continental or maritime climate regime. It will be further shown that even though the moist modes are less frequent than the dry modes, the quantities of precipitation also exhibit marked changes, signaling a probable feedback effect between surface processes, soil moisture and precipitation intensity.

[5] In a final section of the paper, an insight into possible changes of these four modes will be conducted for the latter part of the 21st century, based on regional climate model projections for a “greenhouse” climate.

2. Data and Methods

[6] Nine European sites have been selected for the statistical interpretation of temperature and precipitation data; they have been chosen as a function of the availability of data over long time scales and their distribution within different climatic zones. The stations fit into each of three climatic zones that can be broadly described as Mediterranean (Lisbon, Portugal; Lugano, Switzerland; and Madrid, Spain), maritime (Copenhagen, Denmark; Dublin, Eire; and Paris, France), and continental (Hannover, Germany; Vienna, Austria; and Zurich, Switzerland). The data for the European stations is taken from the European Climate Assessment and Data website ( and from the digital database of the Swiss Office for Meteorology and Climatology (MeteoSwiss). The data sets used have been quality-checked for homogeneity in the records [Begert et al., 2005; Klein Tank et al., 2002]. Data for six of the stations spans back to 1901; for Hannover, Lisbon and Madrid, the data is only available from 1951.

[7] A suite of regional climate models (RCMs) was applied to simulate conditions in Europe for the last 30 years of the 21st century during the EU “PRUDENCE” project; (,. The inter-model variability and the quality of model simulations have been reported in a special issue of Climatic Change [PRUDENCE, 2007] and elsewhere. In the present investigation, the HIRHAM regional climate model (RCM) of the Danish Meteorological Institute has been used because of its skill in reproducing contemporary climate [Beniston et al., 2007]. The model has been applied to Europe at a 50-km resolution for both baseline climate (1961–1990), and a “greenhouse climate” for (2071–2100), using the IPCC SRES A2 scenario [Nakicenović et al., 2000] that leads to CO2 levels of about 800 ppmv by 2100. Climate response by 2100 to these emission levels is close to the upper range of possible global warming published by the Intergovernmental Panel on Climate Change (IPCC) [2007].

[8] Quantile thresholds are calculated using the daily mean temperature and precipitation (24-hour precipitation totals) for each month of the 30-year baseline period 1961–1990. The thresholds calculated in this manner then serve to define the exceedances for all the time periods considered in this paper and defined in the next section. The joint exceedance of the PDFs of mean temperature and precipitation is obtained by counting the frequency of exceedance, for each month, season or year, below or above the four combinations of heat and moisture quantiles, i.e., T25/ p25, T25/ p75, T75/ p25, and T75/ p75, that define respectively the cool/dry (CD), cool/wet (CW), warm/dry (WD), and warm/wet (WW) modes. Subscripts 25 and 75 refer to the respective quantile level for temperature and precipitation.

3. Results and Discussion

[9] The discussion here focuses on the exceedances of the joint quantiles of temperature and precipitation using the 25% and 75% quantile levels as an intermediary threshold between using just the median as a separation of modes and more constraining or “extreme” quantiles. While there is a consensus view that the 10% and 90% quantiles define an extreme in the PDF of, say, temperature [e.g., IPCC, 2007], the values are set here at 25% and 75% in order to capture a larger number of events. The chosen thresholds enable to focus on particular modes of variability that can have perceptible impacts on environmental (e.g., hydrology) and managed systems (e.g., agriculture) that the use of the 50% quantile would not. The use of joint quantiles allows an exploration of climate statistics that in many instances would be overlooked by simply analyzing single quantile thresholds of temperature or precipitation.

[10] Figure 1 provides an example of the changes in threshold exceedances for the four precipitation modes (CD; CW, WD; and WW), expressed in days per year, that have occurred since the beginning of the 20th century in Paris. For each mode, the 95% limits of climate variability computed on the basis of the 1961–1990 baseline have been included in the form of solid or dashed lines associated with the corresponding solid or dashed curves. The frequency of occurrence of each mode is statistically different to that of the baseline period prior to the 1930s, where the “cool” modes were dominant, and since the mid-1980s where the “warm” modes have become more commonplace. While the exceedances of the two “wet” modes are far less frequent, it will be shown later that the shifts in these modes are accompanied by substantial changes in precipitation amounts that the threshold exceedance per se does not reveal. The example for Paris is repeated at all the other sites considered, with the interannual fluctuations of threshold exceedance well in phase, irrespective of the geographical location and climatic zone considered.

Figure 1.

Threshold exceedance of the four joint temperature and precipitation modes (CD; CW; WD; WW) for Paris, France. Horizontal solid and dashed lines indicate the lower and upper bounds of the 95% limits of variability for the 1961–1990 baseline.

[11] Figure 2 shows the evolution in the threshold exceedances of the CD (Figure 2, top) and WD (Figure 2, bottom) combinations since 1901 for the 9 selected stations, expressed as annual averages for each decade in order to remove the interannual noise from the data and thereby facilitate the comparison between curves. The changes are manifest over the course of the past century in both modes, with decreases from a large spread of 60–120 days per year for the CD mode at the beginning of the 20th century, depending on the location, to a much tighter spread of 40–60 days per year in the past 10–20 years. Conversely, the frequency of occurrence of the WD mode has increased from a range of 20–40 days per year in the early part of the record to 60–120 days per year in the latter years of the time series, i.e., a 2 to 4-fold rise since the early 20th century. Even if the behavior of the joint quantile exceedances is broadly similar, the rate of change of each mode differs according to the climatic zone in which the observing station is located. On average, the slowest decrease in the exceedance of the CD mode occurs for the three “maritime climate” stations, closely followed by the “continental climate” sites and, with a rate almost three times that of the other two zones, the “Mediterranean climate” locations. The same change of trend by climatic zone is observed for the WD mode, with the Mediterranean stations exhibiting a rate of change that is twice as fast as that of the continental or maritime locations.

Figure 2.

(top) Threshold exceedance of the CD mode for all 9 stations (decadal averages); (bottom) WD mode; CPH, Copenhagen; DBN, Dublin; HAN, Hannover; LIS, Lisbon; LUG, Lugano; MAD, Madrid; PAR, Paris; VIE, Vienna; ZRH, Zurich.

[12] It could be argued that temperature trends alone explain the shifts in CD and WD modes; while it is true that these two modes closely mimic the trends of average temperature, not all the variance can be explained by temperature alone. However, as will be shown hereafter, the joint mode highlights statistical features that the single quantiles alone do not, essentially because additional degrees of freedom are enabled by the joint quantiles methodology. Temperature and its evolution is not the exclusive driver of change, even if for the “dry modes”, it is certainly a key driver The correlation between mean temperature trends and those of the CD and CW modes changes over time, as seen in Table 1, that compares the rates of change in mean annual temperature (expressed in °C/century) with the temperatures that occur when each of the four modes is exceeded in Zurich. Linear trends are calculated for the entire series (1901–2007) and for four 30-year time slices (1901–1930; 1931–1960; 1961–1990; and the most recent 30-year period 1978–2007). The data in Table 1 shows that, for the entire period, mean temperatures have risen at a rate of 1.15°C per century, while the “warm” modes, on the other hand, exhibit even stronger increases (1.50°C/century for WD and 1.35°C/century for the WW mode). The latter part of the record, from the 1960s and for the last 30 years, show even greater contrasts between the change in mean annual temperature and those averaged for the 4 modes. If the trends for the most recent period were to be sustained, then the increases in temperature for each of the 4 modes would be between 0.1 and 0.2°C per decade greater than the mean annual temperature rise. The more modest and sometimes negative, trends seen during the mid-20th century are related to the consequences of the rise in temperatures during the 1940s and subsequent fall in the 1950s. The differential behavior between mean temperature trends and temperature trends per joint quantile mode reported for Zurich is common to all the climate stations investigated here, albeit with differences in the rates of change.

Table 1. Comparisons of the Trends in Mean Annual Temperature (°C/Century), and Mean Temperatures Computed for the CD, CW, WD, and WW Modes for Zurich
 Mean TempTemp for CDTemp for CWTemp for WDTemp for WW

[13] An additional feature that has changed over time within the “moist” combinations of temperature and precipitation quantiles is related to the average quantities of precipitation that fall when the CW and WW quantiles are exceeded. The average amount of precipitation during CW modes has decreased by 10–30% according to location since the beginning of the 20th century, while in contrast there has been an increase in the average quantities of precipitation during WW modes, sometimes double the amount in the early 2000s compared to the early 1900s, as illustrated for Copenhagen (Figure 3). Average annual precipitation at this location has remained essentially unchanged over the past century. The crossover from high to low precipitation within the CW mode between the early 1900s and the early 2000s, and the reverse for the WW mode, is common to all 9 sites investigated here. Mean annual precipitation, on the other hand, exhibits no statistically-significant trend (very slightly positive in the maritime locations, slightly negative in the Mediterranean locations); the redistribution of precipitation, while significant within the two moist modes, has no measureable influence on the mean precipitation record.

Figure 3.

Comparisons between time series of mean annual precipitation and mean precipitation that occurs during CW and WW events at Copenhagen. Equations are given for the linear regressions over the entire record.

[14] It is likely that feedback effects between heat (energy) availability and the presence or absence of moisture explain both the trends in mean temperature and temperatures associated with the CD and WD modes and the increases (decreases) of precipitation during WW (CW) modes. It is suggested here that warmer temperatures associated with little or no rainfall lead to enhanced warming in the WD mode because of the positive feedback effects of drier land-surface conditions and also to changing soil-moisture characteristics as suggested by Seneviratne et al. [2006]. Unfortunately there is no soil-moisture data for the stations used in this investigation to corroborate this hypothesis.

[15] The changes in precipitation during the warm/moist events are related to changing availability of heat close to the ground that may on occasion contribute to an amplification of convective instability and hence greater to precipitation potential. The decrease of the CW modes, on the other hand, is related to progressively drier conditions that are observed particularly in winter in many parts of Europe, and to the reduction of the cold events in all seasons during the 20th century.

[16] Use of the HIRHAM RCM data for the 9 locations shows how a much warmer climate may modify the four joint modes by 2100. Figure 4 highlights the fact that as climate warms in the course of the 21st century, the trends in quantile exceedances already noted for the observational record will accelerate by 2100. For the three representative sites shown in Figure 4, the “cold” modes essentially disappear by 2100, while the “warm” modes pursue the rise already observed during the 20th century. The increase is particularly marked in Lugano and at the other Mediterranean sites (not shown), likely due to the rapid progression of persistent summertime droughts in the Mediterranean zone. The WW mode shows sharp increases by 2071–2100 in the maritime and continental climates, but no change or even a decrease in the Mediterranean zone, again as a result of the generally lower quantities of moisture available to generate strong moist convection and hence possibly precipitation.

Figure 4.

Annual exceedances for the CD, CW, WD and WW thresholds at sites representative of maritime, continental and Mediterranean regimes, averaged for selected 30-year periods of the 20th century and projected by RCM simulations of a “greenhouse” climate by 2100.

[17] The findings illustrated in Figure 4 corroborate earlier studies on dual shifts in the extremes of precipitation in Europe [e.g., Christensen and Christensen, 2003]. Future precipitation in Europe may exhibit both an increase in drought in southern and central Europe, and an increase in short-lived but heavy precipitation events. This apparent paradox can be explained by the fact that, in a warmer climate, persistently dry summers will result in strong surface heating, thus providing the energy needed for intense convection whenever moisture convergence occurs in a given region.

4. Conclusions

[18] This paper has used joint temperature-precipitation quantile exceedances to explore the behavior of four particular modes of climate extremes that have occurred in Europe, and their possible change in frequency by 2100 in a scenario climate. Beyond the very significant changes that have taken place in the course of the 20th century, and the redistribution of precipitation and temperature within each mode as a function of time, this type of study can provide an insight into the impacts associated particularly with the “warm” modes, that have already taken place in the past, but are projected to occur increasingly in the future.

[19] The quasi-disappearance of the cold/dry and cold/wet modes by 2100 may have a number of beneficial consequences compared to today, in particular the reduction of damaging frosts for agriculture and the physiological consequences of cold and damp on humans, that often have a negative bearing on patients prone to cardio-vascular ailments. These positive impacts would, however, probably be largely offset by the projected increases in the warm/dry and warm/wet modes. These have in the past affected a number of key sectors such as human health (heat stress), agriculture (heat stress, droughts, floods, soil-moisture depletion), hydrological systems (droughts, floods, enhanced evaporation), infrastructure (floods), cryospheric systems (acceleration of glacier retreat and permafrost degradation), and slope instability events in mountain regions (associated with intense precipitation and, for higher elevations, the reduction in the cohesion of slope material by permafrost melting).

[20] Without some form of economic or technological adaptation, the types of impacts associated with the WD and WW modes will become increasingly costly. Using the information of the type discussed in this paper can help in devising a number of precautionary measures that would help avert some of the more negative consequences of the projected changes in these extreme modes of climate.


[21] This work was conducted in the context of the Swiss NCCR-Climate network project, the EU/FP6 ENSEMBLES Project and the EU/FP7 ACQWA Project.