In this study, we assess the role of soil moisture for heat wave persistence using simulations with a regional climate model. Several studies have investigated changes in the frequency of hot summer days but very few investigated changes in their persistence. We use two different heat wave thresholds, either defined by the 90th percentile of the control run or by the 90th percentile of the respective sensitivity experiment. We identify that simulations in which soil moisture is fixed to a constant value or prescribed seasonal cycle, even with prescribed constant dry conditions, present a lower intrinsic heat wave persistence than simulations with interactive soil moisture. This effect is related to the impact of soil moisture persistence in the interactive simulations and amounts to ca. 5–10% of the spell lengths of the 10% hottest days in the respective simulations. Our results highlight the key role of soil moisture memory for the persistence of heat wave events, beside the known effect of soil moisture on heat wave intensity.
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 The land energy and water balances are coupled via the latent heat flux associated with evapotranspiration (ET). In SM-limited regions, the partitioning of the surface energy into sensible (H) and latent heat (LE) fluxes is strongly determined by SM. If SM is lacking, all the energy from surface net radiation is used by H and, consequently, air temperature is strongly enhanced. Regions where SM most impacts the atmosphere are transitional zones between dry and wet climates [Koster et al., 2004]. In Central Europe, similar effects were found to play a central role during heat wave summers [Fischer et al., 2007]. More recently, Jaeger and Seneviratne  showed that SM effects on temperature are asymmetric and mostly affect hot extremes.
 In addition, SM is an important memory component within the climate system [Koster and Suarez, 2001; Seneviratne et al., 2006b]. Because SM is a slowly varying variable, the associated seasonal storage of water in the soils leads to long-term memory effects with time scales of several weeks to months [e.g. Koster and Suarez, 2001; Seneviratne et al., 2006b]. The role of SM in this respect is similar to that of other slowly varying components causing climate persistence, such as ice, snow, or sea surface temperatures.
 In this study we investigate the role of SM for heat wave persistence using regional climate model (RCM) experiments performed with the CLM model (see section 2.1). While previous studies such as those by Durre et al.  and Fischer et al.  focus on the impact of SM on the intensity of hot days (which depending on the chosen threshold, may lead to changes in heat wave persistence, see hereafter), here we look here specifically at the impact of SM persistence for intrinsic heat wave persistence, and disentangle these two effects. Effects of SM on predicted spells of extreme temperature have been, for example, investigated by Brabson et al.  for Global Climate Model (GCM) simulations, but did not distinguish between the impacts of these effects.
2.1. Model Description
 The numerical experiments are performed with the CLM RCM, which is the climate version of the COSMO-model (Consortium for Small-scale Modeling). We use CLM version 2.4.11 with 0.44° (≈50 km) horizontal grid resolution, 32 vertical layers, 10 soil layers and a model time step of 240 seconds. Lateral boundary conditions are derived from ERA40 re-analysis data (1958–2001) [Uppala et al., 2005] and from the ECMWF operational analysis dataset (2002–2006), whereas the initial conditions correspond to the climatological values of a long-term ERA40-driven CLM simulation.
 The experimental set-up includes a control run (CTL) and three sensitivity experiments. The CTL simulation covers 49 years for the period 1958–2006 and has an interactive SM. For the sensitivity experiments, the CTL simulation was repeated with the same model set-up but uncoupling SM from the atmospheric evolution (using the same method as, e.g., Koster et al.  and Seneviratne et al. [2006a]). In these uncoupled simulations, SM is prescribed at each time step for each grid point separately, according to soil type. In “IAV” SM is prescribed to a smoothed annual cycle without interannual variability [Jaeger and Seneviratne, 2010]. In “PWP” and “FCAP”, SM is fixed over the whole length of the simulations to the permanent plant wilting point (PWP) and the field capacity (FCAP), respectively, which correspond to the minimum and maximum SM values from the point of view of plant transpiration. These values were chosen in order to assess the impacts of extreme values of SM on climate (see auxiliary material for an illustration of SM evolution in all experiments). Prescribing SM in this way removes the possibility for spells with anomalous soil moisture, effectively eliminating persistence associated with SM.
2.3. Measures of Heat Waves
 The analysis focuses on different heat wave duration indices (hwdi, hwdi☆). A heat wave is defined here as the number of consecutive days (at least two) where the daily maximum temperature (Tmax) exceeds a given threshold. Hereafter, we use the long-term 90th percentile (90p) based on the empirical PDFs as threshold, either calculated from the control run (hwdi) or the actual model run (hwdi☆). The indices are based on Tmax values over the 92-day period June-July-August (JJA) for the analysed 48 years (1959–2006). For each summer day, 90p is calculated for a 5-day window centered on the respective calendar day over the same analysis period (1959–2006). Then, indices are computed by calculating the mean length of the 90p exceedances.
 By comparing two different time series (e.g. distinct model experiments, model simulation vs. observations), differences in the heat wave duration defined with a common threshold (hwdi) can be induced by two factors: 1) A difference in a difference in the distribution functions (PDF) of Tmax which results in more (less) frequent threshold exceedances and thus a higher (lower) likelihood of 'long' heat wave events; 2) Alternatively, a difference in the temporal clustering (persistence) of high Tmax values, even independently of any differences in the PDFs. When the 90p value of the actual time series is used as threshold (hwdi☆), 10% of the data must necessarily exceed this threshold (but only if 90p and hwdi☆ are calculated for the same periods). We can thus infer from a difference in hwdi☆ between two time series that they are characterized by a different number of threshold exceedances and, hence, a different mean length of threshold exceedances. This goes along with a difference in the persistence of Tmax exceedances. Accordingly, with the joint analysis of hwdi and hwdi☆, it is possible to disentangle differences in heat wave duration caused by differences in the intrinsic persistence of Tmax (clustering of hot days) and due to differences in the PDF of Tmax.
Figures 1a and 1b display schematics with an idealized heat wave event that illustrates the implied distinctions between the hwdi and hwdi☆ indices. If there is an increase in Tmax for the experiment (T(EXP1)) compared to the control run (T(CTL)), hwdi is generally increased (Figure 1a). However, hwdi☆ is only modified if persistence itself is different, hence, if the shape of the temperature curve changes (T(EXP2) vs. T(EXP1), Figure 1b). An actual example for a case study based on the conducted experiments is provided in Figure 1c and discussed in the following sections.
 The mean climate characteristics of PWP, FCAP, and IAV compared to CTL are briefly summarized here. More details are provided by Jaeger and Seneviratne  as well as in the auxiliary material (section 2). In summary, in PWP, low SM leads to a decrease in LE and an increase in H. This causes a deeper, drier and warmer planetary boundary layer associated with decreased total cloud cover and precipitation. FCAP presents the opposite behaviour. IAV, in turn shows only a weak modification of the mean climate. In the present study we focus on the heat wave persistence characteristics of CTL, PWP, FCAP, and IAV.
3.1. Differences in Heat Wave Duration Indices
Figures 2a and 2e display hwdi and hwdi☆ for the CTL experiment (identical since for hwdi the reference threshold is set to the 90p of the CTL simulation for all experiments). The mean heat wave duration in CTL is roughly 2.5–3.5 days across Europe. Note that the values found for other RCMs (ENSEMBLES simulations, available at http://ensembles-eu.metoffice.com/) and observations (see the auxiliary material) are in the same order of magnitude. Figure 2 reveals that hwdi is statistically significant increased for PWP (Figure 2b) and decreased for FCAP (Figure 2c), as expected according to the changes in mean climate and implied differences in 90p (warmer climate in PWP and colder climate in FCAP). For IAV, hwdi is slightly decreased for the whole of Europe (2d). The differences in hwdi☆ (Figures 2f–2h) between all experiments and CTL are smaller than those for hwdi and, interestingly, of the same sign for all experiments (decrease in most of Europe). This decrease is significant at a 5%-level for 81–86% of the grid points for all three experiments.
 A detailed analysis of single heat wave events shows that pronounced heat waves occurring in CTL can also be identified in PWP, FCAP and/or IAV (see, e.g., Figure 1c). Consequently, the occurrence of heat waves is largely influenced by the large-scale circulation patterns that are not significantly perturbed in our experiments (same boundary conditions), and SM acts as an amplifying/dampening factor.
 Changes in the mean duration of heat waves defined using the 90p of the CTL (hwdi) have the same sign as changes in mean temperatures (positive for PWP; negative for FCAP and IAV), whereas the mean duration of heat waves defined based on the 90p of the actual model run (hwdi☆) show decreasing values for all simulations with prescribed SM. To shed more light on the implied decrease in persistence, the threshold exceedances of hwdi☆ are analyzed in more detail in the next sections.
3.2. Impact of Soil Moisture on Tmax Threshold Exceedances
Figures 3a and 3c display the differences in 90p threshold exceedance length between CTL and the experiments for the Iberian Peninsula and Mid-Europe, 2 of the 8 PRUDENCE subdomains defined, e.g., by Christensen and Christensen . The differences between CTL and the experiments are statistically significant (tested with a two-sided Kolmogorov-Smirnov test). In PWP, FCAP, and IAV the number of short heat waves (≈2–3 days) increases, whereas the number of longer heat waves (>3 days) is smaller. The increase in 2-day heat wave frequency amounts to up to 8%, whereas e.g. the frequency of 5-day heat waves drops on average by ≈2% (over all 8 domains). Hence, heat waves in the PWP, FCAP, and IAV experiments are in general shorter than those in CTL. This behaviour points to a decrease of heat wave persistence when SM is prescribed to a constant value or seasonal cycle (i.e. no extended spells of SM anomalies). Hence, in our experiments, temperature time series exhibit more frequent fluctuations that are dominated by components other than SM (e.g., chaotic atmospheric fluctuations) and therefore the persistence of intrinsic heat waves is likely to be decreased. In the control simulation SM persistence results in a higher persistence of heat waves. This behaviour is well illustrated for the case study presented in Figure 1c (see also Figure S4 in the auxiliary material for another example).
3.3. Impact of Soil Moisture on Amplitudes of Tmax Threshold Exceedances
 The exceedance amplitudes (Figures 3b and 3d) are smallest for FCAP, of medium size for IAV and highest for both CTL and PWP. The small amplitudes for FCAP are a result of the damping effect of SM. The similar shape of the histograms for PWP and CTL is a consistent feature in all domains (not shown). Hence, even though exceedance amplitudes are much smaller in the wet simulation (FCAP), they are not further increased for the dry simulation (PWP) compared to CTL, suggesting that heat waves in the CTL simulation occur under conditions similar to those in PWP (dry soils). This is consistent with the results of Fischer et al. , which identified heat waves in Europe to be associated with (and to a large extent caused by) anomalously dry SM conditions. Consequently, the effect of SM on exceedance amplitude is asymmetric and not further enhanced in permanently dry climate (PWP) according to our model simulations. Note that this applies to the mean climate characteristics of the simulations but not necessarily to extreme summers (see Jaeger and Seneviratne , who found even stronger heat waves in PWP for extreme summer case studies). Hence, our simulations highlight two different effects of SM on heat waves: an enhancement (dampening) of the exceedance amplitudes under dry (wet) conditions, while these effects can be asymmetric, and an increase of the longevity of the exceedances due to SM persistence.
4. Discussion and Conclusions
 To investigate the impact of SM on heat wave persistence we performed several RCM experiments with the CLM model for the period 1959–2006. A heat wave is defined here by the length of exceedance of Tmax above a certain temperature threshold, in our case for at least two consecutive days.
 Our results show that SM has an impact on the length of heat waves, which can be explained by the impact of SM persistence. Indeed, we identify a decreasing tendency of hwdi☆ in the dry run (PWP), the wet run (FCAP), as well as the experiment with removed interannual variability of SM but same mean SM (IAV), i.e., a decreasing persistence of high temperatures when SM is prescribed to a constant level or seasonal cycle. In addition, with prescribed SM, the number of short exceedances increases while longer exceedances are less frequent. This decrease in heat wave persistence is summarized in Figure 3e, which shows the difference in hwdi☆ for all experiments normalized by the heat wave lengths of the CTL for different subdomains of Europe. The decrease in intrinsic heat wave length (hwdi☆) amounts to ca. 5–10% in the mean, and in excess of 20% for certain grid points.
 This study also highlights the importance of the exact definition of the duration of heat waves using the hwdi vs hwdi☆ indices. As we illustrate, an enhancement of the heat wave duration can be diagnosed when using a common threshold (hwdi index) for cases such as when only the mean temperature is changed. However, when using relative thresholds (hwdi☆), such changes are only found in the case of changes of intrinsic persistence of hot days. Since society is better able to adapt to changes in mean climate than to the clustering of given extreme events, we argue that changes in the intrinsic heat wave persistence, as measured by hwdi☆, may be more relevant than changes induced solely by mean temperature changes only, for instance in the context of climate change. Our findings indicate that the SM persistence (or memory) is particularly relevant for this persistence measure.
 We acknowledge the EU-project CECILIA and the NCCR-Climate program for funding, the Swiss National Supercomputing Centre (CSCS) for computational resources, the COSMO and CLM community as well as ECMWF for access to models and data, D. Lüthi for technical support, and M. Hirschi and B. Orlowsky for helpful discussions.