Shorter cyclone clusters modulate changes in European wintertime precipitation extremes

We employ simulations [22] from models of the Coupled Model Intercomparison Project Phase 5 (CMIP5), i.e. BCC-CSM1-1, BCC-CSM1-1-m, CCSM4, CMCC-CM , GFDL-CM3, GFDL-ESM2G, GFDL-ESM2M, INMCM4, IPSL-CM5A-LR IPSL-CM5A-MR, MIROC5, MIROC-ESM, MIROC-ESM-CHEM, MRI-CGCM3, NorESM1-M (r1i1p1 for all models, but r6i1p1 for CCSM4). We also use data from ERA-Interim reanalysis [23] to evaluate the fidelity of the CMIP5 models for the purpose of the study. The precipitation rate associated with the 6-hourly time steps of the cyclone tracks was derived from the 3-hourly precipitation rate averaged over the three hours before and after the cyclone time step of interest. For CMIP5 models, precipitation is obtained for the past during 1975–2004, and for the future during 2081-2098; the latter period is shorter because of the limited data availability of CMIP5 output for 3-hourly precipitation [19]. For ERA-Interim, we analyse the period 1979–2008, given that this dataset is available from 1979 onward.

Cyclones were identified and tracked based on the objective feature tracking algorithm TRACK [24–26]. The algorithm identifies and tracks cyclones based on the 850 hPa relative vorticity field, which is obtained from the 6-hourly zonal and meridional wind fields. To filter the small-scale noise and the large-scale background field, the 850 hPa relative vorticity field is smoothed on a T42 grid by removing the spectral components of total wavenumbers larger than 42 and smaller than 6 [19, 27]. After identifying cyclones as relative maxima (exceeding 10⁻⁵ s⁻¹) of the obtained vorticity field, tracks are determined through the minimisation of a cost function for the smoothness of the track [19, 24]. Only cyclone tracks that have a lifetime greater than 2 days and propagation greater than 1112.6 km (corresponding to 10° latitude) are retained to avoid including potential unrealistic stationary and short-lived features. Finally, a cyclone track is characterised by a sequence of 6-hourly time steps, each associated with time and geographical coordinates.

The analyses are performed on the original grids of each model and then the resulting fields are regridded to a common 1$^{\circ} \times\,1^{{\circ}}$ grid to compute multimodel statistics. For graphical purposes, the multimodel statistics are then interpolated to a finer grid.

We employ population data [28] for the future, which is available every 10 years; hence we use data for 2090. Future data are based on projected populations and gross domestic products under the three shared socioeconomic pathways (SSP): SSP1; SSP2; and SSP3. Uncertainties associated with differences among climate model projections are substantially larger than those due to different population in SSP scenarios, therefore we report results based on the intermediate SSP2 future scenario only.

To define cyclone clusters and the associated precipitation, we first identify the cyclones transiting within a radius of influence R of any location of interest; here, we select and employ R = 1112.6 km (corresponding to 10° latitude) as discussed in the appendix (therein, we also show that the results of the study are insensitive to the chosen radius).

Secondly, we attribute to each identified cyclone j the precipitation accumulated at the location ($P_{\mathrm{cyclone\,j}}$) while the cyclone is within such radius of influence R [1, 29]. (If more than one cyclone at the same time is present within the radius R, the 6-hourly precipitation is divided among the cyclones proportionally to the inverse of the distance between the cyclone centre and the location.)

Thirdly, we define a cluster of cyclones as a sequence of $N_{\mathrm{cyclones}}$ consecutive cyclones transiting within the 1112.6 km radius of the location of interest with an elapsed time between them smaller than 24 h.

Finally, the sum of the precipitation attributed to each cyclone within the cluster gives the accumulated precipitation associated with the cluster, i.e. $P_{\mathrm{accum}} = \sum_j P_{\mathrm{cyclone\,j}}$. The mean precipitation per cyclone within the cluster is defined as $P_{\mathrm{cyclone}}^{\mathrm{mean}} = (\sum_j P_{\mathrm{cyclone\,j}}) / N_{\mathrm{cyclones}}$.

We decompose the wintertime precipitation extremes from clustered cyclones into the number of clustered cyclones and the mean precipitation of the cyclones within the clusters. In particular, for any given location, we decompose the mean of the annual maxima (indicated with the operator $\lt\cdot\gt$) of the wintertime precipitation from clustered cyclones $P_{\mathrm{accum}}$ as:

$$\begin{equation} \lt\,P_{\mathrm{accum}}\gt \; \sim \; \lt\,N_{\mathrm{cyclones}}\gt \cdot \lt\,P_{\mathrm{cyclone}}^{\mathrm{mean}}\gt \end{equation} \tag{ 1 }$$

where $N_{\mathrm{cyclones}}$ and $P_{\mathrm{cyclone}}^{\mathrm{mean}}$ are the number and the mean precipitation of the cyclones within the clusters associated with the annual maxima of $P_{\mathrm{accum}}$ (figure 2; figure B1 in appendix shows the same quantities based on reanalysis data, confirming the fidelity of the CMIP5 models for this purpose). Precipitation extremes from cyclone clusters are largest in Western Europe, due to the potential for very long and populated cyclone clusters (figure 2(a) and (c)); and in the Northern Mediterranean area, where clustered cyclones are fewer but their precipitation intensity is higher (figure 2), consistent with the higher temperatures and atmospheric moisture content. The scaling, i.e. the right-hand side of the equation (1), describes to good approximation the precipitation extremes $\lt\,P_{\mathrm{accum}}\gt$ (figure 2(a) and (b)) both for individual models and for the multimodel mean. Over the analysed area, the scaling only slightly overestimates the magnitude of the precipitation with an average present-day absolute value of the bias of 9 mm (18% in relative terms) in the multimodel mean ($\lt$11 mm (22%) for individual models). The spatial pattern of $\lt\,P_{\mathrm{accum}}\gt$ is very well represented by the scaling (spatial correlation $\gt0.98$ for individual models and 0.99 for the multimodel mean).

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At the end of the century, under a high emissions scenario (RCP8.5)[22] accumulated precipitation extremes are projected to increase at latitudes above 45° north, and to decrease over the regions of the Mediterranean Basin (figure 3(a)). The scaling also describes remarkably well these future changes (figure B2(a) and (b)). The correlation of the spatial pattern between changes in the accumulated precipitation and in the scaling is high (0.99 in the multimodel mean and $\gt0.83$ for individual models). The percentage change per degree of future warming in the scaling can be decomposed exactly as

$$\begin{align*} & \Delta_{\mathrm{\%/K}} (\lt\,N_{\mathrm{cyclones}}\gt \cdot \lt\,P_{\mathrm{cyclone}}^{\mathrm{mean}}\gt )\nonumber\\ & = \Delta_{\mathrm{\%/K}} \lt\,N_{\mathrm{cyclones}}\gt + \Delta_{\mathrm{\%/K}} \lt\,P_{\mathrm{cyclone}}^{\mathrm{mean}}\gt \nonumber\\ & + (\Delta_{\mathrm{\%/K}} \lt\,P_{\mathrm{cyclone}}^{\mathrm{mean}}\gt)\nonumber\\ & \cdot (\Delta_{\mathrm{\%/K}} \lt\,N_{\mathrm{cyclones}}\gt) \cdot \Delta T/100, \end{align*}$$

where ΔT represents the magnitude of the future warming (see appendix); but the last, second-order, term is much smaller than the first two, and only plays a role where the first two largely cancel (figure B2(c) in the appendix). Hence, the percentage changes in the accumulated precipitation $\Delta_{\mathrm{\%/K}} \lt\,P_{\mathrm{accum}}\gt$ can be decomposed to good approximation into the sum of percentage changes in the number of cyclones within the cluster and in the mean precipitation of the individual cyclones (compare figures 3(a) and (b)), i.e.:

$$\begin{equation} \begin{aligned} \Delta_{\mathrm{\%/K}} \lt\,P_{\mathrm{accum}}\gt \; \sim &\Delta_{\mathrm{\%/K}} \lt\,N_{\mathrm{cyclones}}\gt\\ +&\Delta_{\mathrm{\%/K}} \lt\,P_{\mathrm{cyclone}}^{\mathrm{mean}}\gt. \end{aligned} \end{equation} \tag{ 2 }$$

The first term on the right-hand side can be considered as a dynamical contribution to the change in accumulated precipitation extremes, and the second term as a combination of dynamic and thermodynamic effects. We now employ the scaling to decompose the change in accumulated precipitation extremes into the individual contributions from the changes of its drivers, i.e. $\Delta_{\mathrm{\%/K}} \lt\,N_{\mathrm{cyclones}}\gt$ and $\Delta_{\mathrm{\%/K}} \lt\,P_{\mathrm{cyclone}}^{\mathrm{mean}}\gt$.

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A robust reduction in the number of cyclones within the clusters contributes to a decrease in the accumulated precipitation amounts over 83% of the European region (figure 3(c); IPCC regions are shown in figure B3 in appendix). This corresponds to shorter-duration clusters in the future over most of the analysed area, given that less populated clusters last shorter (figure B4 in appendix). The mean change of the number of clustered cyclones over Europe is −2.9% per degree of warming which, given an average warming of about 4.3°K under the considered RCP8.5 scenario, corresponds to a reduction of about 12.5% in the number of clustered cyclones by the end of the century. This reduction is particularly large south of 55° latitude, with projected values of about −3.4  and −5.2 %/K in Central Europe and in the Mediterranean, respectively.

We find that such a reduction in the number of clustered cyclones (figure 3(c)) is consistent with a general decrease of the total number of wintertime cyclones (figure B5(a) in appendix), while no association with changes in the statistical metric φ is apparent (figure 1(d)). This decrease occurs north of Iceland, over the southern flank of the Atlantic storm-track, and in the Mediterranean (figure B5(a) in appendix). Only a negligible change in the number of clustered cyclones is found in Northern Europe (−0.1 %/K) (figure 3(c)); this is consistent with the fact that the regional change in cyclone frequencies is small compared to the climatology (figure B5(a) in appendix).

The relation found between the reduction of wintertime clustered and total cyclones is confirmed by the fact that in Central Europe and in the Mediterranean, i.e. where most of the reduction in the number of cyclones occurs, models with a stronger/weaker reduction in the number of wintertime cyclones tend to also project a stronger/weaker reduction in the number of clustered cyclones (figure B5(b)–(d) in appendix). In particular, the strong association found across the model ensemble between changes in the number of wintertime total and clustered cyclones ($\rho$ = 0.93; figure B5(b) in appendix) indicates that even in the individual climate realisations, the influence of changes in the statistical metric φ on changes in the number of clustered cyclones tends to be small. Hence, less frequent cyclones are projected to lead to less populated cyclone clusters across large parts of Europe regardless of the tendency towards higher/lower statistical clustering in time depicted by the metric φ.

The changes in the mean precipitation per cyclone within the clusters drive an increase in accumulated precipitation extremes over 86% of the European region (mean of +4.7 %/K), especially in Central (+8.2 %/K) and Northern Europe (+5.9 %/K) and to a lesser extent in the Mediterranean (+1.5 %/K) (figure 3(d)). To first-order, these increases can be explained by an average thermodynamic effect, i.e. a warmer atmosphere will allow storms to carry more moisture and result in higher precipitation intensities [8, 30–32]. However, other thermodynamic and dynamic factors will further modulate precipitation intensities [33–35]. For example, weaker upward motion during precipitation events (reducing the condensation rate) would offset the thermodynamic increase around Iceland [33]. In central Europe, the thermodynamic increase is modulated by competing effects such as higher cyclone intensities and a speed-up of cyclone translation speeds [36, 37] (figure B6 in appendix). The former favours higher moisture flows within the cyclone leading to higher precipitation rates and accumulations [38], while cyclones translating faster lead to shorter local precipitation events and therefore lower accumulations [39–44]. Along the southern flank of the North Atlantic storm-track region, e.g. in Northern Africa, the weakening of the cyclone intensities [38] and an associated decrease in upward velocities during precipitation extremes [33] can even reverse the first-order thermodynamic increase (figure 3(d)), contributing to the relatively weak increase (+1.5 %/K) of mean precipitation from cyclones across the Mediterranean region.

The magnitude of the changes in the drivers of accumulated precipitation from cyclone clustering, i.e. $N_{\mathrm{cyclones}}$ and $P_{\mathrm{cyclone}}^{\mathrm{mean}}$, are comparable over many populated land areas (figure 4). Hence, both changes should be considered together to quantify and understand the overall trends in the accumulated precipitation extremes and avoid biased assessments that could be misleading for policy-making and engineering practices. Over the European region, the decreased number of clustered cyclones is responsible for a northward shift of the dry-wet boundary seen in the multimodel mean of $\Delta_{\mathrm{\%/K}} \lt\,P_{\mathrm{accum}}\gt$ of about, on average, 1200 km, compared to that seen in the mean precipitation per cyclone (figure 3(a), (d) and light orange area in figure 4). Note that the approximated change of the scaling given on the right-hand side of equation (2) underestimates the extent of this northward shift, as the second-order term is negative over the region where the approximated change of the scaling transitions from wetting to drying.

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Based on the multimodel mean, accumulated precipitation extremes increase over 60% of the European region. In Central Europe, despite a large regional increase in the mean precipitation per cyclone (+8.2 %/K), accumulated precipitation extremes are projected to grow by only +2.7 %/K due to the reduction in the number of clustered cyclones (figure 4). In the Mediterranean, the substantial decrease in the number of clustered cyclones is projected to more than offset the increase seen in the mean precipitation per cyclone (+1.5 %/K), resulting in a reduction of –4.3 %/K in accumulated precipitation extremes. Only in Northern Europe is the regional increase in accumulated precipitation extremes (+5.5 %/K) described to good approximation by considering the changes in mean precipitation per cyclone alone. Changes at sub-regional level are shown in table B1 in appendix.

Taking a probabilistic interpretation of the CMIP ensemble, the uncertainties in the changes of mean precipitation per cyclone and of the number of clustered cyclones contribute similarly to the overall uncertainty in the changes of accumulated precipitation (see error bars of orange and blue histograms in figure 4). The uncertainty in the change of accumulated precipitation is generally smaller than what would be expected based on the uncertainty in the changes of the two individual drivers (see error bars in figure 4). This occurs because the changes of the drivers tend to be negatively correlated across models at the grid point scale. The above highlights the importance of considering the local uncertainties in the evolution of both drivers together, rather than focusing on the uncertainties of the individual drivers alone/independently, to avoid potentially under-confident, and therefore misleading, projections of the local future risk [45].

Such correlations can arise, e.g. from atmospheric circulation, which exerts a strong control on regional climate [46]; therefore, the regional uncertainties in the future dynamics of accumulated precipitation extremes can be physically understood through exploring different plausible storylines [18, 47] of atmospheric circulation change. This is shown for the Mediterranean, where the regional changes in the precipitation extremes from clustered cyclones depend on the magnitude of the changes in the storminess across the Mediterranean storm-track (figure 5(a)). In particular, a relatively strong weakening of the wintertime cyclone frequency would favour a pronounced reduction in the number of clustered cyclones, resulting in a widespread decrease of precipitation extremes in Southern Europe, by −7 %/K on average (figures 5(b) and (c)). Alternatively, an equally plausible weaker storminess reduction would result in a relatively small decrease in precipitation extremes (−0.9 %/K) (figure 5(e) and (f)). The two storylines highlight that an evolution of the regional precipitation extremes deviating from the multi model mean scenario is quite plausible [18, 47] as a result of well-known uncertainties in the future dynamics of the atmospheric circulation [48]. Notably, the two storylines differ in the position of the dry-wet boundary in precipitation extremes (figures 5(b) and (e)), which appears to be mainly controlled by underlying differences in the regional reduction of clustered cyclones (figures 5(c) and (f)), rather than in the mean precipitation changes (figure 5(d) and (g)). This is reflected in the model agreement on the sign of the accumulated precipitation changes, which, although widespread across Europe, is lacking around the dry-wet boundary (stippling in figure 3(a)) (a feature also observed in changes of typical IPCC precipitation metrics; figure 1(a)–(b)).

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If cyclones were to occur randomly in time at a given location, the distribution of the occurrences in any time interval could be described via an homogeneous Poisson process [13, 15, 52] with constant intensity λ. This implies that the distribution of the number of cyclones occurring in any time interval of length T would be Poisson with mean (µ) and variance (σ²) equal to λ · T (hence, σ²/µ = 1). Deviations from such a Poisson distribution indicates that cyclone occurrences are either regular ($\sigma^2/ \mu \lt 1$) or clustered in time ($\sigma^2/ \mu \gt 1$). Hence, different values of a dispersion statistic defined [15] as $\phi = \sigma^2/\mu -1$ indicates that cyclone occurrences at a given location tend to be regular ($\phi\lt0$), random (φ = 0) or clustered in time ($\phi\gt0$). Following previous studies [13, 14] of cyclone clustering projections, we estimate φ based on the sample mean and variance of the wintertime (December–February) total number of cyclones transiting in a radius R of a given location. Here, we employ a radius R of 1112.6 km (10° latitude) for consistency with the analysis of the accumulated precipitation from cyclone clusters.

Following previous studies [1, 29], the radius of influence of the cyclones R = 10° latitude (corresponding to 1112.6 km) was selected as that defining the area where most of the precipitation around the cyclone center falls. We analyse P(r), i.e. the average 6-hourly precipitation at distance r ± 1° latitude from the cyclone center, for the cyclones tracking on a reference box over Europe (15°W–42°E, 30°N–67°N) (figure B7). Note that the profile P(r) is obtained as the mean of the profiles of the individual cyclones (only cyclones reaching their maximum T42 vorticity at 850 hPa within the reference box are considered). The profile P(r) of an individual cyclone is defined as the average of the profiles P(r) of the cyclone at the time steps when the cyclone is within the reference box. Following previous studies [1, 29], precipitation at a high radial distance from the centre such as $r\gt$12.5° is understood as randomly sampled precipitation, i.e. not necessarily associated with the cyclones. We select a radius r = R of 10° latitude which captures most of the precipitation associated with the cyclones. Note that the results of the study, i.e. the changes in precipitation extremes from cyclone clusters and associated drivers, are insensitive to the chosen radius (figure B8 and B9 for a 7° and 13° radius, respectively).

For each model, the projected response of the investigated quantities, e.g. mean annual maximum accumulated precipitation from the cyclone clusters $\lt\,P_{\mathrm{accum}}\gt$, is defined as the percentage change $\Delta_{\mathrm{\%}} \lt\,P_{\mathrm{accum}}\gt = 100 \cdot (\lt\,P_{\mathrm{accum}}^{\mathrm{future}}\gt - \lt\,P_{\mathrm{accum}}^{\mathrm{past}}\gt)/\lt\,P_{\mathrm{accum}}^{\mathrm{past}}\gt$. The percentage change per degree of global warming $\Delta_{\mathrm{\%/K}} \lt\,P_{\mathrm{accum}}\gt$ is obtained via dividing $\Delta_{\mathrm{\%}} \lt\,P_{\mathrm{accum}}\gt$ by the winter (December–February) global warming signal in the considered model (i.e. the difference between the mean of the future and the mean of the past annual-mean near-surface temperature). Multimodel mean responses are computed as averages of the individual model responses.

For a given model, the changes Δ of the scaling between future and past climate can be decomposed [10, 29] exactly as:

$$\begin{equation*} \begin{aligned} & \Delta (\lt\,N_{\mathrm{cyclones}}\gt \cdot \lt\,P_{\mathrm{cyclone}}^{\mathrm{mean}}\gt)\\ & \quad = (\Delta \lt\,N_{\mathrm{cyclones}}\gt) \cdot \lt\,P_{\mathrm{cyclone}}^{\mathrm{mean}}\gt\\ & \quad + \lt\,N_{\mathrm{cyclones}}\gt \cdot (\Delta \lt\,P_{\mathrm{cyclone}}^{\mathrm{mean}}\gt) \\ & \quad\!\!+ (\Delta \lt\,N_{\mathrm{cyclones}}\gt) \cdot (\Delta \lt\,P_{\mathrm{cyclone}}^{\mathrm{mean}}\gt). \end{aligned} \end{equation*}$$

The percentage change $\Delta_{\mathrm{\%}}$ is obtained via dividing the change above by the scaling itself ($\lt\,N_{\mathrm{cyclones}}\gt \cdot \lt\,P_{\mathrm{cyclone}}^{\mathrm{mean}}\gt$) and multiplying it by 100:

$$\begin{align*} & \Delta_{\mathrm{\%}} (\lt\,N_{\mathrm{cyclones}}\gt \cdot \lt\,P_{\mathrm{cyclone}}^{\mathrm{mean}}\gt)\\ & \quad = \Delta_{\mathrm{\%}} \lt\,N_{\mathrm{cyclones}}\gt)\\ & \quad + \Delta_{\mathrm{\%}} \lt\,P_{\mathrm{cyclone}}^{\mathrm{mean}}\gt \\ & \quad + (\Delta_{\mathrm{\%}} \lt\,N_{\mathrm{cyclones}}\gt) \cdot (\Delta_{\mathrm{\%}} \lt\,P_{\mathrm{cyclone}}^{\mathrm{mean}}\gt)/100. \end{align*}$$

Finally, the percentage change per degree of warming ($\Delta_{\mathrm{\%/K}}$) is obtained via dividing the above by the projected global warming signal (see section above).

For individual models and considering the full geographical domain, the population that is affected by a decrease in the accumulated precipitation extremes from cyclone clustering due to a reduction in the number of clustered cyclone is quantified as that within grid points where the accumulated precipitation extremes decrease despite an increase in the mean precipitation per cyclone. This is computed based on precipitation changes regridded to the native grid of the population data (0.5$^{\circ} \times 0.5^{\circ}$).