Internal variability and temperature scaling of future sub-daily rainfall return levels over Europe

The second generation Canadian Earth System Model (CanESM2) is run for 50 times with slightly different initial-conditions following RCP 8.5 for transient runs from 1950 to 2099 (Arora et al 2011, Fyfe et al 2017). These global climate projections were dynamically downscaled with the regional climate model (RCM) CRCM5 at a horizontal resolution of 0.11° following the EURO-CORDEX grid specifications (Leduc et al 2019). This large ensemble is called CRCM5-LE. The size and location of its European domain is shown in section 3 within figure 1. The detailed climate model setup and applied schemes are given in Martynov et al (2012) and its general performance at the European climate is evaluated in Leduc et al (2019). Furthermore, Von Trentini et al (2019) compare the CRCM5-LE with the multi-model EURO-CORDEX ensemble and investigate the spread of the 50 members compared to the variations of the 22 different EURO-CORDEX climate model combinations.

Zoom In Zoom Out Reset image size

As sub-daily rainfall extremes are partly governed by convectional processes, it has to be mentioned that convection is parametrized in the CRCM5. The spatial resolution of climate models has to be higher than 4 km in order to represent convectional processes (Langhans et al 2012, 2013, Tabari et al 2016), whereby unresolved processes and sources for biases still remain (Hirt et al 2019). Therefore, in the CRCM5-LE, deep convection is described with the Kain and Fritsch (1990) scheme, while shallow convection is parametrized using the Kuo-transient scheme (Kuo 1965, Bélair et al 2005). Even though convection is parameterized, the CRCM5-LE has proven to be able to sufficiently recreate the spatial pattern of sub-daily extreme precipitation over Europe (Poschlod et al 2021). Furthermore, the intensity of extreme precipitation is well reproduced for durations of three hours and longer. A comparison of extreme precipitation within a single realization of a convection-permitting RCM and the CRCM5-LE is given in Hodnebrog et al (2019) for different sub-regions in Europe.

To calculate the 10 year return levels, the approach of Poschlod et al (2021) is applied. Therefore, annual block maxima are extracted for moving windows of 3-hourly, 6-hourly, 12-hourly and 24-hourly precipitation for each of the 50 CRCM5-LE members. For the hourly time scale, maxima are constrained to fixed windows at the full hour, as the precipitation data are stored in hourly resolution. Three future 30 year time periods are investigated, namely the near (2010–2039), mid (2040–2069) and far future (2070–2099). The whole course of the year is included as data base for the extreme value analysis, as rainfall extremes in Europe do not only occur during an extended summer season (Berthou et al 2018). Furthermore, in Europe their occurrence is found to shift with a changing climate towards later in the year (Mareille et al 2018 for daily rainfall).

According to Coles (2001), block maxima samples are well represented by the generalized extreme value (GEV) distribution G (equation (1)):

$$\begin{align}G\left( {x;\xi } \right) = \left\{ {\begin{array}{*{20}{c}} {\exp \left( { - {{\left[ {1 + \xi \left( {\frac{{x - \mu }}{\sigma }} \right)} \right]}^{\frac{-1}{\xi}}}} \right),{\text{ }}\xi \ne 0} \\ {\exp \left( { - \exp \left( { - \frac{{x - \mu }}{\sigma }} \right)} \right),{\text{ }}\xi = 0} \end{array}} \right.,\end{align} \tag{ 1 }$$

with µ, σ and ξ as location, scale and shape parameters of the distribution. The GEV parameters are optimized for each of the 50 differing 30 year block maxima and three future periods applying the method of L-moments (Hosking et al 1985, Gilleland and Katz 2016). We apply this GEV approach with the simplifying assumption of stationarity within the 30 year periods. Trends within the annual maxima of the 30 year periods of all durations are investigated using the Mann-Kendall test with 5% significance level. As the test is carried out for many grid cells, we adjust the critical p-value controlling the false discovery rate (Benjamini and Hochberg 1995) following the approach of Wilks (2016).

We find no significant trends for all periods and durations, thus we can proceed with this simplifying assumption.

In order to check the goodness-of-fit of the GEV distribution, the Anderson–Darling test is applied with 5% significance level, where the critical p-value is also adjusted following Wilks (2016).This leads to a rejection of only 0.1%–0.3% of all fits for the different durations. The 10 year return levels are then derived by inverting the GEV equation (equation (1)). The median of the 50 return levels represents the estimation of 10year rainfall, where the 5th and 95th quantiles quantify the range of uncertainty related to the spread of the 50 members.

The increase in saturation specific humidity is governed by the CC relation, yielding an increase of approximately 6%–8% per warming degree. However, present-day precipitation–temperature scaling relations indicate that hourly precipitation extremes may have a response to warming exceeding the CC relation (Lenderink et al 2017). When scaling the increasing precipitation with temperature, there are differing approaches for the choice of the relevant location and time scale. Westra et al (2013) use a world-wide climatological approach applying the global mean temperature to scale global precipitation increases, whereas Berg et al (2013) conducted an event-based analysis focusing on the local temperatures during the rainfall event. Here, the average temperature of the whole European domain is taken following the argumentation of Keune and Miralles (2019), who attribute the sources of European precipitation mostly to regional moisture transfers. Hence, for each of the 50 CRCM5-LE members, the increase of 10year rainfall at the grid cell is scaled with the increase of temperature in the whole European domain. Thereby, the changes for the three future periods are calculated in comparison to the reference period. As extreme precipitation is spatially highly variable (Aalbers et al 2018, Poschlod et al 2021), the CC scaling is not only shown for each grid cell, but also provided as areal average for eight European sub-regions.

The 10 year return levels are openly available for the reference period (Poschlod 2020) and the future periods (Poschlod 2021). The change of 10 year return levels of sub-daily precipitation is shown in figure 1 for the 3-hourly aggregation. It is found to increase by 7.0% until 2010–2039, by 13.9% until 2040–2069, and by 20.3% until 2070–2099. Thereby, areas are identified, where the future extreme precipitation levels leave the inter-quantile range between the 5th and 95th quantiles of the reference period, which is induced by internal variability. Exceedance of the 95th quantile is found for 2.5%, 35.5% and 57.5% of the study area during the near, mid and far future, respectively. The corresponding areas refer to Scandinavia, the British Isles, the Baltic States, central Europe, Portugal and parts of the Mediterranean. In contrast, 0.52% of the area is projected to stay below the 5th quantile of the reference period during the far future. These grid cells are located in Morocco. For the other temporal aggregations, figures S1–S4 (available online at stacks.iop.org/ERL/16/064097/mmedia) are given in the supporting information. Changes are quantified in table 1 for all durations.

We assign the resulting spatial patterns mainly to the moisture availability and the increasing contribution of convective events. In Scandinavia, the British Isles, the Baltic States, and central Europe extreme precipitation events occur mostly during the summer season. There, future extreme rainfall can strongly increase with rising temperatures due to no or low limitations related to moisture availability (see figures S5(g)–(i)). Furthermore, convective processes can increasingly contribute to extreme events (see figure 2). In the central and eastern parts of the Mediterranean, extreme precipitation occurs mainly during the fall season (Berthou et al 2018, Wood and Ludwig 2020). While mean precipitation is projected to decrease slightly also during fall (Wood and Ludwig 2020), the available moisture (figures S5(j)–(l)) still allows for intensifying extreme rainfall events, whereas in southern Spain and North Africa extreme precipitation is projected to decrease due to limited moisture availability. Similar patterns are also found for the EURO-CORDEX ensemble (Tramblay and Somot 2018). In the northwestern parts of the Iberian Peninsula, extreme precipitation events are simulated during fall and winter (Wood and Ludwig 2020), where future mean precipitation during this season is projected to increase. The intensity of extreme events can also increase without major limitations due to moisture availability (figures S5(a)–(c), (j)–(l)).

Zoom In Zoom Out Reset image size

Shorter-duration rainfall is projected to increase stronger than longer-duration rainfall, whereby the spatial patterns of the changes remain similar for all durations. Also the averaged increase per 30 year period is quite stable for each of the three investigated future periods. For hourly (3-hourly, 6-hourly, 12-hourly, 24-hourly) duration, the increase amounts to roughly 8% (7%, 6%, 5%, 4%) per 30 year period, respectively. However, between the mid and far future, the change is slightly lower than during the former periods.

As the CRCM5 does not include an implementation of a three-dimensional ocean model, the ocean conditions are governed by the lateral boundary conditions of the driving global climate model (GCM) CanESM2. This is a common feature of RCMs, even though atmosphere-ocean coupling can also improve the reproduction of regional climate characteristics over Europe (Somot et al 2008, Giorgi and Gao 2018). Furthermore, the simulation of extreme rainfall over the oceans could not be evaluated within Poschlod et al (2021) due to the lack of observational sub-daily data. Hence, these return level estimations are excluded from the analysis.

Nissen and Ulbrich (2017) calculated 3-hourly and 24-hourly 10 year return levels as mean of the EURO-CORDEX ensemble. They identified similar regions, where the multi-model ensemble shows a significant increase of probability for extreme precipitation under RCP 8.5. Though, multi-model ensembles do not allow for the quantification of model uncertainty only, as the differences between the simulations are caused by model differences of the GCM and RCM, mixed with internal variability (Von Trentini et al 2019). In order to disentangle internal variability from model uncertainty, Aalbers et al (2018) analysed the 16-member SMILE of the RCM RACMO2 driven by the GCM EC-EARTH 2.3 under RCP 8.5, which is run for a smaller domain than the CRCM5-LE centred over the Netherlands with the same spatial resolution of 0.11°. They found an increase of 14.5% for the daily 10 year return level during summer until the far future, where the change of +11.8% for the 24-hourly aggregation in this study is slightly lower but generally ties in with their result. Furthermore, they emphasize the large role of internal variability for the ranges of extreme precipitation, whereas its role on 30 year means is found to be secondary (Addor and Fischer 2015). In this study, the inter-quantile ranges between the 5th and 95th quantiles around the median amount to −14.9%–18.5%, −15.5%–19.4%, and −16.0%–20.4% for the near, mid and far future of 3-hourly extreme precipitation, respectively (see table 1). Shorter-duration rainfall shows a higher percentage of variability than longer-duration rainfall. The future percentage range of 10 year return levels is projected to increase slightly for all durations and future periods. It has to be emphasized that the percentage range of variability is calculated in relation to the median of the respective 30 year period. As the median is found to increase and the percentual variability slightly rises as well, the absolute range of projected extreme rainfall increases even stronger. The increasing variability is also represented by the gradually rising standard deviations of the ensemble (see table 1). In order to visualize these numbers, which are aggregated for the whole domain, figure 3 shows the 50-member variability at six locations with differing local climates. This illustrates the uncertainty range at local scales. Generally, larger absolute variability is projected for locations with higher absolute return levels. For short durations of one or three hours, the range is larger in the southern cities, where rainfall extremes are dominated by convective processes. Coppola et al (2018) also expect higher impacts of internal variability in convective events and convection-permitting model simulations, which is why they recommend the use of ensembles in order to produce robust findings.

Zoom In Zoom Out Reset image size

For Europe, Berg et al (2019) have investigated the increase of 10 year rainfall return levels for a changing climate under RCP 4.5 and RCP 8.5. They explored the projections for present and future rainfall within nine selected RCMs of the EURO-CORDEX framework, and they evaluated the present rainfall levels with observations of five European countries. While they reported reasonable biases at country-wide aggregations, big deviations are shown at the reproduction of spatial patterns and gradients for the hourly duration. Poschlod et al (2021) evaluated the 10 year return levels of the CRCM5-LE during 1980–2009 at 16 European countries, where return levels and spatial patterns were well reproduced, especially for durations of 3 h and above. Topographically complex areas, such as the Alps or the Norwegian coast could not be resolved due to the spatial resolution of the RCM. Hence, they concluded that the CRCM5-LE is able to recreate the features of extreme sub-daily rainfall over Europe, even though convectional processes are parametrized.

Most studies within climate science analyse high quantiles of precipitation (e.g. 99.7% for annual maxima) or indices as the RX1h. Here, the impact-oriented 10 year return level is calculated, which has already been found to be relevant by Nissen and Ulbrich (2017) based on legislation and stakeholder interviews. Therefore, the analysis in this study gives a valid insight to the variability of projected alterations of future extreme sub-daily precipitation due to a changing climate, with the same restrictions as reported by Poschlod et al (2021) and governed by the scenario uncertainty.

The scaling of the 3-hourly return levels by the temperature increase is presented in figure 4 for the land area of the whole domain. These scalings are given in figures S6–S9 for the other durations. Superadiabatic scaling is found for central Europe, the British Isles and Scandinavia. Generally, many studies discuss the origin of superadiabatic scaling. Haerter and Berg (2009) argue that it can be caused by a shift of the rainfall-generating processes from less large-scale precipitation to more frequent convective events. They found that this behaviour emerges for sub-daily rainfall extremes but disappears for daily rainfall. This ties in with our results for the scaling of the 10 year return levels at different durations (see figures S6–S9). For the 24-hourly duration, only 2% of the area shows superadiabatic scalings for the mid and far future.

Zoom In Zoom Out Reset image size

Lenderink et al (2017) assume a physical origin resulting from the dynamics of convective clouds, which show stronger updrafts due to increased latent heat release with rising temperature (Lenderink and van Mejgaard 2009). However, in the CRCM5-LE the relevant processes are parametrized due to the spatial resolution of the model. We argue that shifts of the rainfall-generating processes from stratiform to convective precipitation contribute to the superadiabatic scaling in the CRCM5-LE. The contribution of convective rainfall to extreme precipitation is projected to increase in Scandinavia, the Baltic states, the British Isles, the Alps, and parts of the Mediterranean coastal areas due to the temperature rise (see figure 2). Moreover, apart from the Mediterranean, there is enough moisture available in these regions to exceed the CC scaling (figure S5). Below CC scaling is projected for large parts of the Mediterranean and eastern Europe. This reduced intensity results from limited moisture availability and changes of the atmospheric large-scale patterns (Westra et al 2014, Wood and Ludwig 2020). The decreasing moisture availability indicated by the change of relative humidity in the CRCM5-LE is given in figure S5, where especially the Mediterranean shows the strongest decline of relative humidity. Furthermore, these areas will be affected by a northward expansion of the subtropical dry zone due to alterations of large-scale patterns (Levine and Schneider 2015, Kröner et al 2017, Pfahl et al 2017, Grise et al 2019). The Hadley circulation is projected to expand polewards and, therefore, subsidence in the descending branch of the Hadley cells is found to lower the frequency and intensity of precipitation (Kröner et al 2017). However, Seager et al (2014) argue that an increase in the opposing mean flow moisture divergence leads to the drying tendency in the Mediterranean. Generally, figure 4(a) shows a patchy spatial pattern, even though the median of the 50 members at each grid cell is presented. In order to give a regionally aggregated overview of the CC scaling, eight sub-regions are introduced (see figure 5). These sub-regions are defined by the boundaries of Christensen and Christensen (2007) and often called 'PRUDENCE regions'. Water bodies are again removed from the investigated sub-regions due to their limited representation within the RCM.

Zoom In Zoom Out Reset image size

Figure 6 displays the ranges of the CC scaling averaged for the sub-regions within the 50 RCM members, which are induced by internal variability. The CC scaling is found to be higher for shorter durations, as the contribution of the shift from stratiform to convective rainfall decreases for longer durations. For the 24-hourly aggregation, no super-CC-scaling is reported by the medians of the ensemble for the sub-regions.

Zoom In Zoom Out Reset image size

The patchiness of the spatial patterns (figures 4(a)–(c)) as well as the ranges of CC scaling (figure 6) are found to decrease for future periods. This is due to the dependence of the CC scaling on the temperature forcing, as the scaling is expressed relatively to the warming. The internal variability of the temperature also contributes to the overall variability of the CC scaling. Annual mean temperature generally shows less variability than precipitation (Von Trentini et al 2019) and averaging for the whole RCM domain smoothes the effect of local internal variability. Here, the range of the temperature increase within the 50 members amounts to 0.6 K for all future periods, where the median increase amounts to 1.2 K (2.6 K, 4.3 K) for the near (mid, far) future, respectively. Therefore, the variability of precipitation and temperature in relation to the warming decreases for each future 30 year period, whereas the absolute variability of precipitation slightly rises (see section 3.1). To disentangle the contribution of precipitation variability and temperature variability to the overall variability of the CC scaling, figure 6 is replicated in the supporting information in two different ways: The 50-member range of extreme precipitation changes is scaled by the median change in temperature (figure S10) and the median change in extreme precipitation is scaled by the 50-member range of temperature changes (figure S11), respectively. This comparison illustrates the larger contribution of precipitation variability to the overall variability of the CC scaling.

Even though averaging for large sub-regions, the CC scaling shows high variability. For central Europe (MID), the hourly scaling shows a range of 3.5% K⁻¹%–10% K⁻¹ for 2070–2099, which illustrates that the same climate model configuration simulates subadiabatic, adiabatic and superadiabatic scalings only due to slightly perturbed initial conditions of the driving GCM in 1950. Additional uncertainty is induced as annual mean temperatures are used to scale the changes of extreme precipitation, while the increase in temperature varies within the seasons. Also, the timing of extreme precipitation events in the domain is different for varying sub-regions (see section 3.1). The effect of seasonal scaling is given in Wood and Ludwig (2020).

In sum, our findings show that any results of a single climate model member should be carefully interpreted. Such results should not be misinterpreted as model-specific as long as no ensemble with a sufficient number of members quantifies the uncertainty from internal variability (Milinski et al 2020).

In recent studies, there have been different results, whether super-CC-scaling is simulated for Europe or not. Some studies found superadiabatic scalings (e.g. Lenderink and Van Meijgaard 2008, Kendon et al 2014, 2019), whereas some studies did not (e.g. Ban et al 2015). Again it should be emphasized that internal variability is a major source of uncertainty when investigating CC scaling, which has not been quantified within the forementioned studies. Considering internal variability as uncertainty source, Hodnebrog et al (2019) found that the CRCM5 shows a relatively pronounced scaling when compared to other RCM configurations. Furthermore, in this study, the projected superadiabatic scalings can be attributed to the extreme level of 10 year return periods, as rarer events lead to higher scalings (Hodnebrog et al 2019).