Abstract

The “gray zone” of convection is defined as the range of horizontal grid-space resolutions at which convective processes are partially but not fully resolved explicitly by the model dynamics (typically estimated from a few kilometers to a few hundred meters). The representation of convection at these scales is challenging, as both parameterizing convective processes or relying on the model dynamics to resolve them might cause systematic model biases. Here, a regional climate model over a large European domain is used to study model biases when either using parameterizations of deep and shallow convection or representing convection explicitly. For this purpose, year-long simulations at horizontal resolutions between 50- and 2.2-km grid spacing are performed and evaluated with datasets of precipitation, surface temperature, and top-of-the-atmosphere radiation over Europe. While simulations with parameterized convection seem more favorable than using explicit convection at around 50-km resolution, at higher resolutions (grid spacing ≤ 25 km) models tend to perform similarly or even better for certain model skills when deep convection is turned off. At these finer scales, the representation of deep convection has a larger effect in model performance than changes in resolution when looking at hourly precipitation statistics and the representation of the diurnal cycle, especially over nonorographic regions. The shortwave net radiative balance at the top of the atmosphere is the variable most strongly affected by resolution changes, due to the better representation of cloud dynamical processes at higher resolutions. These results suggest that an explicit representation of convection may be beneficial in representing some aspects of climate over Europe at much coarser resolutions than previously thought, thereby reducing some of the uncertainties derived from parameterizing deep convection.

1. Introduction

As computational capabilities increase in time, so does the resolution of climate models (Schulthess et al. 2019; Satoh et al. 2019). In the future, the increase in computer resources will likely allow us to simulate the climate of Earth at so-called convection-resolving scales (Schneider et al. 2017), in which some of the atmospheric convective processes are resolved explicitly by numerical integration of the governing equations of fluid dynamics. Convection by cumulus clouds is one of the most important processes that, at the current resolution of global climate models, is considered necessary to be parameterized in order to represent its effects in climate due to the small scales at which these processes happen. These convective processes interact with the larger-scale flow, modulating the vertical structure of the atmosphere by diabatic heating and moistening. Nowadays, it is typically considered that a model can permit deep convection if it has a horizontal grid spacing smaller than about 4 km (Weisman et al. 1997; Hohenegger et al. 2008, Kendon et al. 2017; Prein et al. 2015). At these “kilometer-scale” resolutions (often referred to as “convection-permitting” or “convection-resolving” scales), the need for parameterizations of deep convection is accepted to be no longer a requirement, reducing greatly model uncertainties and parameter sensitivities. The resolution sensitivity of model variables tends to decrease with resolution, as the models approach convergence close to those scales. For example, Langhans et al. (2012) and Panosetti et al. (2018) demonstrated that domain-averaged and integrated quantities related to large ensembles of convective cells converge at the kilometer scale in real-case simulations of summertime thermally driven convection over the Alps. Similar results were obtained in simulations of a cold front over the United Kingdom (Harvey et al. 2017). Pauluis and Garner (2006) showed that the sensitivity of horizontally averaged quantities related to deep convective clouds decreases with resolution in simulations of idealized radiative convective equilibrium. However, several studies showed that cloud-scale and updraft statistics do not converge until resolutions of a few hundred meters or lower (Jeevanjee 2017; Panosetti et al. 2018, 2019) and storm morphology is greatly affected by resolution even at resolutions below 1 km (Hanley et al. 2015). Several studies have performed climate simulations at kilometer-scale resolutions over regional domains, showing the added value that using high-resolution simulations produce in representing orographic regions, producing high-order statistics, predicting events with small temporal and spatial scales, and representing convective organization (White et al. 2018; Ban et al. 2014, 2015; Berthou et al. 2018; Leutwyler et al. 2017; Kendon et al. 2017; Prein et al. 2015; Fosser et al. 2015; Kendon et al. 2012). However, these studies usually compare runs at a coarse resolution (>10-km horizontal grid spacing) using parameterized convection against higher-resolution simulations (<4 km) with no parameterization of deep convection. From this type of comparison, it is difficult to determine which improvements are due to the increased resolution of the model and which to the different treatment of convection.

Whereas developing models to run using a higher resolution is always favorable due to the better dynamical representation of atmospheric processes, high resolution is costly, and the limited computational resources make it difficult and expensive to simulate large domains at kilometer-scale resolution over long periods (Fuhrer et al. 2018). This will make climate simulations in the gray zone a necessary step for simulating the present and future Earth climate. Therefore, there is a need to study how the representations of different phenomena evolve across resolutions to quantify the optimal resolution at which to switch from parameterized to explicit convection.

Parameterizing deep convection is known to produce several characteristic model biases such as a diurnal cycle of precipitation over land that peaks too early in the day (Yang and Slingo 2001; Pearson et al. 2014; Dirmeyer et al. 2012) and too much light intensity precipitation (Stephens et al. 2010; Sun et al. 2006). Hence there is a great interest in the community to be able to represent convection explicitly from the model dynamics without relying on semiempirical parameterizations. On the other hand, studies performed with explicit convection at scales finer than 4 km show that using an explicit representation of convection, despite systematic improvements in the precipitation statistics, tends to produce too little light rain, and to have too much extreme precipitation compared with observations (Berthou et al. 2018). We should note that even at grid spacings of 1 km, convective processes will not be fully resolved as updrafts will not be simulated at the correct intensity due to the coarse grid size (Kendon et al. 2012; Panosetti et al. 2018; Jeevanjee 2017), which might help explaining the overestimation in extreme precipitation intensities at high resolutions. Also, biases in the observed intensities of heavy rain events due to rain gauge undercatch (up to 58% of in worst-case scenarios; Chubb et al. 2015) might explain some of the differences between observed and simulated precipitation intensity.

In order to represent convective processes at gray zone resolutions, studies generally make use of scale-unaware parameterizations for deep convection, or switch them off completely. However, some approaches also attempt to represent convective processes with scale-aware parameterizations of convection (Gerard et al. 2009; Grell and Freitas 2014). These parameterizations attempt to provide a smooth transition across scales, becoming less active at higher resolutions. While these approaches are an advantage when it comes to represent convection, they are not available for all parameterization schemes. Therefore, some studies have investigated the performance of atmospheric models using explicit convection at coarser resolutions than 4 km. Dirmeyer et al. (2012) showed that using explicit convection at 7-km resolution greatly improves the timing of the diurnal cycle of rain over tropical and extratropical regions when compared with coarser-resolution simulations with parameterized convection. Looking at the West African region, Pearson et al. (2014) showed that even at 12-km resolution the diurnal cycle of convection is better represented when explicit convection is used. Similarly, Hohenegger et al. (2015) and Birch et al. (2015) showed improvements in representing sea-breeze circulations when using explicit convection at coarse resolutions. Vellinga et al. (2016) showed large improvements in representing precipitation intensities over the Sahel when using a 12-km model with no parameterization of deep convection in contrast to coarser-resolution convection parameterized models. Studying the Indian monsoon, Willetts et al. (2017) found improvements using explicit convection at 8 km when simulating water vapor advection over land during the monsoon period. This was produced by a better represented land–sea temperature contrast as the diurnal cycle of precipitation is improved. Using simulations of the West African monsoon, White et al. (2018) found a much better organization of convective cells when switching off parameterized convection at 12- and 4-km grid sizes. Crook et al. (2019) showed that the spatial distribution and direction of propagation of convective cells in West Africa is much better represented when convection is turned off at resolutions much coarser than 4 km. In a model intercomparison study of a cold air outbreak within gray zone resolutions, Field et al. (2017) found that the spread in model result was larger in models with convection parameterized than when explicit convection was used. They also found that intermodel differences were larger than the changes obtained by single models when increasing the resolution, suggesting that different physical parameterizations and dynamical cores are important to explain the model differences. It is also likely that these results might depend upon the choice of the time step. Some large-scale models with semi-implicit dynamical cores use large time steps (often corresponding to a Courant number around 5), while split-explicit dynamical cores commonly used in mesoscale models use much smaller time stepping; Fuhrer et al. 2018) [for a description of different time-stepping methods see Mengaldo et al. (2019)].

In this study we address the question of which choice of representation for convective processes performs better by simulating the European climate for a year-long period with a regional model at various resolutions in the gray zone of deep convection. The simulations are performed by systematically decreasing the resolution of our model and testing model performance with either parameterized deep convection, shallow convection or not using any parameterization of convective processes (referred as explicit convection). We then make use of observational datasets of precipitation, temperature, and radiation to quantify model performance, focusing on phenomena produced by convective processes (diurnal cycle of summer precipitation, precipitation intensities, and clouds). Making use of a regional model allows us to simulate longer time periods at resolutions as high as 2.2 km and compare them with coarser-resolution simulations. The choice of the European region for our simulations gives us the possibility to use several high-quality verified products for evaluating the simulations. Our analysis will focus mainly on the summer season as it is characterized by strong convection, therefore making the differences between simulations more visible. We refer to the online supplemental information for the results over different seasons.

2. Methods

a. Model description

For our simulations, we use the Consortium for Small-Scale Modeling Weather and Climate Model (COSMO; Steppeler et al. 2003) in its graphics processing unit (GPU) enabled version (Fuhrer et al. 2014; Leutwyler et al. 2016). The model is a nonhydrostatic limited-area model that solves the fully compressible governing equations of fluid dynamics on a structured grid using finite difference methods (Förstner and Doms 2004). Horizontal advection is calculated using a fifth-order upwind scheme. Vertical advection is computed with an implicit Crank–Nicholson scheme (Baldauf et al. 2011). Time integration is performed with a split-explicit third-order Runge–Kutta discretization (Wicker and Skamarock 2002). Cloud microphysics are represented with a single-moment scheme using five hydrometeors (cloud water, rain, ice crystals, snow, and graupel) (Reinhardt and Seifert 2006). The representation of soil moisture is performed using a 10-layer soil model (TERRA_ML) with a new formulation for water runoff dependent on orography (Schlemmer et al. 2018). The radiation scheme is based on a δ-two-stream approach as described in Ritter and Geleyn (1992). Turbulent fluxes within the planetary boundary layer are parameterized with a 1.5-order turbulent kinetic energy (TKE)-based scheme (Mellor and Yamada 1982; Raschendorfer 2001). We use stationary aerosol fields updated monthly from the Aerocom climatology (Kinne et al. 2006).

The standard parameterization of convection used in the model is based on Tiedtke (1989). This scheme is a mass-flux closure approach used to parameterize modifications to the vertical structure of the atmosphere due to deep, midlevel and shallow convection. Deep convection is activated when there is low-level moisture convergence due to gridscale flow. The parameterization assumes that the atmospheric moisture content below cloud stays unperturbed in a quasi-steady state to calculate the vertical convective transports. The magnitude of the gridscale moisture convergence is used to determine the cloud-base convective mass flux. Shallow convection works with a similar assumption of constant moisture content below cloud base. Shallow convection is restricted to have a maximum depth of 250 hPa and does not produce any precipitation, so its role is only to redistribute heat and moisture in small updrafts. Midlevel convection is maintained by large-scale moisture converge as well as deep convection; however, midlevel convection does not have its origin in the boundary layer, but rather can originate from higher levels in the atmosphere.

b. Simulation setup

We perform an ensemble of simulations at seven different horizontal grid spacings ranging from 0.44° (~50 km) to 0.02° (~2.2 km). Each of these domains is nested to a 12-km domain driven by ERA-Interim fields updated every 6 h [similar to that presented in Leutwyler et al. (2017)]. The nesting from the 12-km domain is a one-way nesting with boundary conditions updated every hour. We should note that for the simulations at 25 and 50 km the boundary conditions are upscaled from 12 km to those coarser resolutions, consistently with treating all resolutions similarly. This does not seem to affect the results as the large-scale features are propagated similarly across all the model resolutions (see section 3d). The domain configuration can be seen in the supplemental material (Fig. S9). For each of the resolutions over the inner domain, we perform three different simulations with a different representation of convective processes:

  • One set of simulations uses the full scheme presented in Tiedtke (1989) to represent deep, midlevel, and shallow convective processes (named DEEP). This setup is similar to those commonly used for running simulations at horizontal resolutions coarser than about ~10 km.

  • Another set of simulations is performed by allowing the convection scheme to act only when shallow convective motions should be produced, therefore switching off deep and midlevel convection (named SHALLOW). This type of representation has been used in previous simulations using the same model at resolutions of 2.2 km (Ban et al. 2014, 2015; Leutwyler et al. 2017; Hentgen et al. 2019).

  • Finally, we perform one last set of simulations switching off the Tiedtke scheme completely, and therefore relying on the model dynamics to represent convective processes explicitly (named EXPLICIT). This type of representation is also being used in simulations at convection resolving scales (Kendon et al. 2017; Prein et al. 2017).

The simulations are named “X_Y” where X corresponds to the resolution in degrees and Y to the representation of convection used (e.g., 0.22_DEEP means a model resolution of 0.22° and using the DEEP setup for convection). Table 1 shows the setup and characteristic of each simulation. The 0.02° domain is slightly larger than that presented in Leutwyler et al. (2017). We do so in order to make the domain size of all the inner domains to be exactly the same across all tested resolutions. Therefore, all our simulations are being fed with the same lateral boundary conditions.

Table 1.

Description of the nested domains used in this study. For each of the domains three simulations are conducted, one with deep and shallow convection parameterizations on (DEEP), one with shallow convection on (SHALLOW), and one with both schemes off (EXPLICIT).

Description of the nested domains used in this study. For each of the domains three simulations are conducted, one with deep and shallow convection parameterizations on (DEEP), one with shallow convection on (SHALLOW), and one with both schemes off (EXPLICIT).
Description of the nested domains used in this study. For each of the domains three simulations are conducted, one with deep and shallow convection parameterizations on (DEEP), one with shallow convection on (SHALLOW), and one with both schemes off (EXPLICIT).

For every simulation, we perform a model integration of 16 months starting in September 2005 until December 2006. We initialized the soil moisture of our driving 12-km simulation with that of a previous simulation with a similar version of the model (Leutwyler et al. 2017). Then, we use the first 4 months of the simulations to spin up the soil in the inner nests. These months (September 2005–December 2005) are not included in the analysis. We choose to simulate the year 2006 as it is characterized by a very convective summer season over Europe (Hohenegger et al. 2009; Langhans et al. 2012; Panosetti et al. 2018), therefore making the differences between model simulations with different convective representations more visible.

To imitate as closely as possible the processes performed when increasing the resolution of a model, we perform the following modifications: To account for the increase in turbulent fluxes resolved by the model as the resolution increases, we decrease linearly the Blackadar asymptotic length scale l of the turbulence scheme as a function of resolution. This modification affects the amount of vertical mixing in the turbulent boundary layer by limiting the maximum value of the characteristic length scale lυ as defined in Blackadar (1962). This treatment is consistent with several previous studies (Leutwyler et al. 2016; Ban et al. 2014), and it is a common practice when reducing the grid size of a model. The time step of the model is also modified between resolutions by linearly interpolating between the finest (using 20 s) and the coarsest resolution (360 s), thereby maintaining the Courant number. The representation of orography is also modified across the different resolutions, to allow for the model to better resolve orographic features as the resolution increases.

Usually when increasing model resolution, one last modification is performed: the model “tuning,” in which several uncertain model parameters are modified within their uncertainty range to achieve a better agreement between model results and observations (Bellprat et al. 2012; Hourdin et al. 2017). In the current study, we do not perform any model tuning in any of the setups. Instead, we simply use the set of tuning parameters used in the 12-km simulation presented in Leutwyler et al. (2017) for all the model simulations (equivalent to simulation 0.11_DEEP in this study). We should note therefore that increases in model performance could probably be achieved if model tuning was performed for each model setup; however, that would also obscure the effect of solely changing the convection parameterization and would make the comparison between model resolutions more complicated. Therefore, we choose not to apply any tuning in our model. As a result, the performance ranking of the different simulations should be considered with care, as likely it could be changed by model tuning. We should also note that the interplay between the convective scheme and the turbulence is not trivial and some improvements could be also obtained if a more careful selection of the turbulence length scale is chosen for each simulation.

c. Validation data and methods

1) E-OBS dataset

To evaluate the skill of each simulation to represent the mean summer condition of the year considered, we use a gridded dataset of daily temperature and precipitation over Europe (E-OBS version 19.0e; Haylock et al. 2008). The dataset provides gridded temperature and precipitation fields at a daily resolution over a large European domain. When compared with other regional datasets at a higher spatial resolution, the mean absolute errors of this dataset were estimated to be of the order 0.8°C in temperature. For the precipitation fields the mean absolute errors can be about 1 mm in most areas reaching up to 2.5 mm over strongly orographic regions such as Switzerland (Hofstra et al. 2009). The E-OBS precipitation product is also subject to biases in the frequency distribution of rain in areas with poor data coverage (Isotta et al. 2015; Prein and Gobiet 2017).

The model evaluation is performed in the following manner. First, the 2-m temperature simulated by the models is regridded into the E-OBS grid, and then seasonal mean values are calculated for each simulation. The model results over land are then compared against the seasonal mean values from E-OBS (year 2006) and the bias and absolute errors at each grid box are calculated and averaged across all valid land grid points [Eqs. (1) and (2)] excluding the grid boxes corresponding to the relaxation zone of the models (defined as 2.64° from each boundary). We should note that differences in the topography used in the dataset and in the model might produce some temperature biases.

2) Hourly precipitation

We use two precipitation datasets with high temporal and spatial resolutions, one corresponding to a region with strong orographic forcing (Switzerland; Wüest et al. 2009) and another in a more plain region (Germany; Paulat et al. 2008).

The Swiss dataset (RdisaggH) provides hourly precipitation data at a 2-km resolution using the so-called disaggregation technique in which the temporal evolution of rain is determined by radar but the absolute amount is constrained to rain gauge measurements. Errors in this dataset are considered to be lower than 25% in intensity over the Swiss plateau, but probably larger in mountainous areas due to the lower number of rain gauges at high altitude (Wüest et al. 2009). One should notice that measuring precipitation intensities is a challenging task, as rain gauge measurements can be subject to systematic biases due to undercatch of hydrometers deflected by strong winds (Frei et al. 2003) leading to potential biases in precipitation observations. Also extreme precipitation intensities might be underestimated in the dataset due to the smoothing process performed while gridding the data (O and Foelsche 2019; Schroeer et al. 2018).

Over Germany, the dataset employed for the precipitation evaluation (DisaggDE) is composed of gridded values of hourly precipitation at a horizontal resolution of 7 km and it was derived following a similar disaggregation technique, so it will likely be subject of similar uncertainties as previously mentioned.

3) Top-of-the-atmosphere radiation

To evaluate our simulations against top-of-the-atmosphere (TOA) radiation, we use data from the Satellite Application Facility on Climate Monitoring (CM-SAF) (Urbain et al. 2017). The dataset is created by continuously monitoring the TOA reflected solar radiation [hereafter shortwave radiation (SW)] and emitted thermal radiation [hereafter longwave radiation (LW)]. It combines data from the Meteosat Visible InfraRed Imager (MVIRI) and Spinning Enhanced Visible and Infrared Imager (SEVIRI) instruments on board Meteosat, following a geostationary orbit. The data used in this study correspond to monthly mean observations of TOA net SW and LW radiation at a resolution of 0.05°.

4) Validation metrics

As standard metrics to evaluate model performance we focus on mean absolute errors (MAE) and mean biases (MB) between a set n of model data xi and observation data yi:

 
MAE=i=1n|yixi|n,
(1)
 
MB=i=1nyixin.
(2)

For the comparisons against the E-OBS and CM-SAF datasets the model data are first regridded to the observational grid before calculating the averaged metrics.

5) Bin normalization

We calculate precipitation frequency (see Figs. 3 and 4 below) by using the precipitation bins bn presented in (Klingaman et al. 2017) as used in previous studies with high-resolution simulations (Berthou et al. 2018):

 
bn=eln(0.005)+{n[ln(120)ln(0.005)]259}1/2(mmh1).
(3)

Then the contribution of each intensity to the mean rain amount ci is assessed by multiplying each frequency fi by the intensity of the middle of the corresponding bin Ii:

 
ci=fi×Ii.
(4)

After the frequency and the contribution to the mean precipitation are calculated, we then normalize the values by dividing them by the logarithm of the bin size [Eqs. (5) and (6)], so the area under the curve when plotted in logarithmic scale becomes proportional to the precipitation frequency and the mean precipitation. Therefore, the fractional contribution between two different intensities can be assessed by integrating the area under the curve “by eye,” thereby making the plots “visually correct.” This technique also makes the values independent on the bins used, therefore making the plots comparable with other studies using different bins.

 
Freqnormi=filog10bi+1log10bi.
(5)
 
Contnormi=cilog10bi+1log10bi.
(6)

3. Results

a. Evaluation versus E-OBS observations

Figure 1 presents the mean bias and mean absolute error for each model in the summer [June–August (JJA)] and winter [December–February (DJF)] seasons following the method presented in section 2c(1). All the mean absolute errors in season mean temperature produced by the various simulations averaged across the domain are comparable with the mean absolute errors of the dataset (0.8°C) and the mean biases are mainly within the dataset uncertainty (Figs. 1a,c). Therefore, all the simulations, including the very coarse-resolution simulations with explicit convection perform similarly in reproducing the mean seasonal temperature. One of the most notable features, however, is that models using explicit convection tend to produce slightly colder temperatures both in winter and summer than models with parameterized deep and/or shallow convection, which might be related to differences in radiative fluxes (see section 3e). The errors and biases in precipitation are also within the uncertainties of the dataset across all the simulations, therefore making it impossible to conclude which of the models actually perform better. However, it is noticeable that there is a clear increase in wet precipitation biases in summer as the resolution of the models increase. This increase in precipitation with resolution could be happening as smaller grid boxes are easier to reach saturation or because the distribution of vertical velocities becomes broader at higher resolution, therefore giving more moisture available for precipitation when this is triggered. We should also note that these biases are affected by rain gauge under catch and due to the model being tuned to represent precipitation at a 12-km resolution.

Fig. 1.

Evaluation of all the simulations performed against the E-OBS dataset for (a),(c) seasonal mean temperature and (b),(d) seasonal mean precipitation. The model fields are regridded into the E-OBS grid and then mean absolute errors and mean biases are calculated as averages across all E-OBS grid boxes [Eqs. (1) and (2)].

Fig. 1.

Evaluation of all the simulations performed against the E-OBS dataset for (a),(c) seasonal mean temperature and (b),(d) seasonal mean precipitation. The model fields are regridded into the E-OBS grid and then mean absolute errors and mean biases are calculated as averages across all E-OBS grid boxes [Eqs. (1) and (2)].

Figure 2 shows the precipitation biases over the European domain during summer for a selection of resolutions (0.22, 0.08, 0.02) with the three representations of convection used. Generally, all the simulations have similar bias patterns such as a slight dry bias over the northern part of France and over the Balkan area. The wet biases over mountainous areas are also consistent across simulations, similarly to previous simulations (Leutwyler et al. 2017; Ban et al. 2014), and might be simply an observational artifact due to rain gauge undercatch. One should note that the observations over these areas are subject to large biases that might explain the differences between the simulated and observed precipitation fields. Also, these mountainous areas tend to have larger values of mean precipitation, therefore making any fractional error seem larger than the surroundings when presented in absolute terms. The biases of the models in representing mean winter precipitation are presented in the supplemental material (see Figs. S1–S3) and also follow similar patterns across all the simulations. They show slightly wet biases over the domain with an increased magnitude over the Adriatic region. Surface temperature biases (Figs. S2 and S3) show also consistent patterns of biases very lightly influenced by the resolution used or the representation of convection. It is interesting to note that increasing resolution alone does not affect substantially the patterns of model biases.

Fig. 2.

Map of mean precipitation biases over the summer season against the E-OBS dataset for a selected set of simulations regridded onto the E-OBS grid. The values of spatial correlation (R), mean bias (MB; mm day−1), and mean absolute error (MAE; mm day−1) are shown below each plot. Similar figures for an evaluation on winter precipitation and summer and winter temperature can be found in the supplemental material (Figs. S1–S3).

Fig. 2.

Map of mean precipitation biases over the summer season against the E-OBS dataset for a selected set of simulations regridded onto the E-OBS grid. The values of spatial correlation (R), mean bias (MB; mm day−1), and mean absolute error (MAE; mm day−1) are shown below each plot. Similar figures for an evaluation on winter precipitation and summer and winter temperature can be found in the supplemental material (Figs. S1–S3).

Overall, for all the resolution tested, including the very coarse ones (>10 km), the performance skills over Europe (Fig. 1) when not parameterizing deep convection are comparable to those obtained with deep convection parameterized. Therefore, from this comparison against observed seasonal mean temperature and precipitation, it appears that explicit convection produces similar seasonal mean values of European temperature and precipitation as parameterized convection although they might happen due to different underlying daily and hourly distributions. In other words, we can not find so far any evident model bias in these simple metrics that would suggest that explicit convection at coarse resolutions should not be used. To continue assessing the performance of the models to simulate the characteristics of precipitation, a more detailed comparison is necessary and it is carried out in the following sections.

b. Evaluation versus hourly precipitation datasets

Over Europe, isolated convective events tend to appear more commonly during the summer season. Some of these events are triggered by orographic circulation (e.g., the Alps), but more generally they develop and organize along (sometimes weak) large-scale forcing such as associated with trailing cold fronts. Convective rain, which produces strong and intense peaks on precipitation, is driven by small deep convective systems and plays a principal role in the European summer precipitation distribution. Large-scale driven precipitation, in contrast, tends to be much more continuous and is responsible for the majority of rain during the winter season. Therefore, an interesting way to look at the performance of the models in representing convective processes is to evaluate the distribution and timing of hourly precipitation in summer. For that purpose, we use the two hourly intensity datasets mentioned above (RdisaggH and DisaggDE).

Figures 3 and 4 show the hourly precipitation distribution over Switzerland and Germany in each simulation using the DEEP (Figs. 3a,b and 4a,b) or EXPLICIT (Figs. 3c,d and 4c,d) convective representations and the observations from the two hourly datasets over the their respective countries. The values have been calculated using the bin distribution defined in section 2c(5). For the figure presented here we have used the native resolutions of the models and datasets to avoid smoothing out extreme intensities when regridding the data into a common grid. We also performed the same analysis with the simulations and observations regridded into a common grid with a horizontal resolution of 50 km. This process did not substantially change the results (Figs. S13 and S14). The frequency and contribution of extreme hourly precipitation events are shown by plotting the values of the 99% (i99) and 99.9% (i99.9) strongest hourly intensities, including dry hours (Schär et al. 2016).

Fig. 3.

(a),(c) Distribution of summer precipitation intensities over Switzerland and (b),(d) contribution of each precipitation intensity to the season mean precipitation; (a) and (b) show the frequency distribution and contributions to the mean for the DEEP simulations, while (c) and (d) are equivalent, but for the EXPLICIT simulations. The values are normalized by the logarithm of the bin size with the method presented in section 2c(5), making therefore the surface under the curves equivalent to the total frequency and total mean precipitation. The vertical lines denote the intensity of the 99th and 99.9th all-hour percentiles.

Fig. 3.

(a),(c) Distribution of summer precipitation intensities over Switzerland and (b),(d) contribution of each precipitation intensity to the season mean precipitation; (a) and (b) show the frequency distribution and contributions to the mean for the DEEP simulations, while (c) and (d) are equivalent, but for the EXPLICIT simulations. The values are normalized by the logarithm of the bin size with the method presented in section 2c(5), making therefore the surface under the curves equivalent to the total frequency and total mean precipitation. The vertical lines denote the intensity of the 99th and 99.9th all-hour percentiles.

Fig. 4.

As in Fig. 3, but for Germany.

Fig. 4.

As in Fig. 3, but for Germany.

For all the resolutions tested and in both domains, when parameterizing deep convection, the frequency of low-intensity rain events is overestimated (Figs. 3a and 4a), and so is the contribution of these low intensities to the mean precipitation amount (Figs. 3b and 4b). This is in agreement with previous studied that showed that parameterized convection simulations typically overestimate the frequency of low-intensity rain events (Stephens et al. 2010). When explicit convection is used (Figs. 3c,d and 4c,d), an underestimation of low-intensity rain events and an overestimation of extreme precipitation happen for all the resolutions studied and both the orographic and low-lying domain. However, the datasets might suffer from biases in heavy precipitation intensities due to rain gauge undercatch, and because they do not have the same effective spatial resolution as the simulation data. Therefore, the comparison of these extreme intensities with model results might be potentially misleading. This behavior of too much low-intensity rain when deep convection is parameterized and too little when explicit convection is used has been observed previously by several studies (Ban et al. 2014; Kendon et al. 2017; Han and Hong 2018). However, it is surprising that even at resolutions as coarse as 50 km this trade-off between the ability of the models to represent light and heavy precipitation events can be observed, which makes the choice of using or not a parameterization and not the resolution employed the main factor affecting the distribution of precipitation intensities. The coarser models tend to perform worse, even when convection is parameterized, especially over the Swiss domain, which is likely caused at least in part by the coarse representation of the orography. Parameterizing only shallow convection produces a similar behavior as representing convection explicitly when simulating hourly rain intensities (Figs. S4 and S5).

To perform a more quantitative comparison, for each simulation we calculate the mean absolute errors between the simulated distribution of intensities and the observed across each distribution bin defined in section 2c(5). Over Germany (Figs. 5c,d) the mean absolute errors when looking at the distribution of frequencies and the contribution to mean precipitation depend more strongly on the representation of convection used rather than on the resolution of the simulations, being slightly lower for the simulations using deep convection parameterized. These skill values, however, do not change substantially with resolution. Over Switzerland, in contrast, the mean absolute errors decrease as the resolution of the model increases, potentially due to a better resolved orography (Figs. 5a,b). However, modifying the representation of convection in the model still has a big effect on model performance skill over this strongly orographic region (Fig. 5a). When looking at mean absolute errors of the contribution of each intensity to the mean, they tend to be lower when deep convection is parameterized. However, the MAE of the distribution of frequencies over Switzerland produces lower values when deep convection is switched off. This happens because of the importance of light precipitation events when looking at the overall frequency in contrast to their lower importance for mean precipitation. We should note that the datasets employed might underestimate extreme precipitation intensities, as mentioned previously, and therefore we should be cautious when interpreting model performance at the most extreme percentiles.

Fig. 5.

Mean absolute errors of the different simulations to represent the distribution of frequencies and the contribution of each intensity to the seasonal mean precipitation. MAEs are calculated between the predicted model contributions and the observed from Figs. 3 and 4 using the bins presented in section 2c(5). (a),(c) The performance in reproducing the frequency distribution over Switzerland and Germany respectively. (b),(d) The performance in reproducing the contribution of the different intensities to mean summer precipitation.

Fig. 5.

Mean absolute errors of the different simulations to represent the distribution of frequencies and the contribution of each intensity to the seasonal mean precipitation. MAEs are calculated between the predicted model contributions and the observed from Figs. 3 and 4 using the bins presented in section 2c(5). (a),(c) The performance in reproducing the frequency distribution over Switzerland and Germany respectively. (b),(d) The performance in reproducing the contribution of the different intensities to mean summer precipitation.

c. Diurnal cycles

The diurnal cycle (DC) of European summer precipitation over land is characterized by a peak on the late afternoon produced by convective precipitation. This peak is produced by the strong radiative heating at the surface during the day, which generates vertical instability, making convective processes grow and organize during the day, and forming stronger precipitation during the afternoon. Therefore, a way to test if the convective processes in our simulations interact correctly with the climate system and develop correctly to produce convective rain is to look at the performance of the models to reproduce the observed diurnal cycle of precipitation. In Fig. 6 we show the observations of summer precipitation for the year 2006 over the two countries studied using the previously mentioned hourly datasets and the results from the different model runs. Parameterizing deep convection (Figs. 6a,d) produces a peak in precipitation too early in the day across all the resolutions studied, in agreement with several previous studies (Yang and Slingo 2001; Dirmeyer et al. 2012; Brockhaus et al. 2008). This bias in the timing of summer precipitation produces clouds that interact with radiation at the wrong moment of the day, affects mountain flows, sea-breeze dynamics, and the organization of convection (Hohenegger et al. 2015; Birch et al. 2015). When the parameterization for deep convection is switched off (the SHALLOW and EXPLICIT runs), the diurnal cycle peak greatly improves both in Switzerland and Germany even for resolutions as coarse as 25 km (0.22°). In Fig. 7 we quantify mean absolute errors and the correlation between the simulated summer diurnal cycles and the observed in both countries. At 50 km the model struggles to represent the diurnal cycle of precipitation producing very low correlation values with either parameterized or explicit deep convection (Figs. 7a,c). When using explicit convection at 50 km, the diurnal cycle peak gets delayed about 4–5 h as the model needs to generate greater instabilities before deep convection can be initiated. At 25 km, the diurnal cycle peak is slightly delayed; however, the performance skills are substantially higher than when convection is parameterized (Figs. 7a,c). At resolutions below 25 km, the mean absolute errors depend more strongly on the representation of convection rather than on the resolution employed over the German domain. Over the Swiss domain, in contrast, we observe similar improvements in the diurnal cycle of precipitation (Figs. 7a,b) as those observed for precipitation intensities when the resolution is increased (Fig. 5a), which might be related to an improved representation of orography.

Fig. 6.

Observed and simulated diurnal cycle of summer precipitation over (a)–(c) Switzerland and (d)–(f) Germany; (a) and (d) correspond to the DEEP simulations, (b) and (e) to the SHALLOW runs, and (c) and (f) to the EXPLICIT setup.

Fig. 6.

Observed and simulated diurnal cycle of summer precipitation over (a)–(c) Switzerland and (d)–(f) Germany; (a) and (d) correspond to the DEEP simulations, (b) and (e) to the SHALLOW runs, and (c) and (f) to the EXPLICIT setup.

Fig. 7.

Performance metrics for the different model setups to represent the observed diurnal cycle of summer precipitation. The first row corresponds to the performances to represent the diurnal cycle over Switzerland and the second row over Germany. (a),(c) The coefficient of determination (R2) between models and observations. (b),(d) The mean absolute error of the different simulations. The values are calculated with the precipitation binned every hour.

Fig. 7.

Performance metrics for the different model setups to represent the observed diurnal cycle of summer precipitation. The first row corresponds to the performances to represent the diurnal cycle over Switzerland and the second row over Germany. (a),(c) The coefficient of determination (R2) between models and observations. (b),(d) The mean absolute error of the different simulations. The values are calculated with the precipitation binned every hour.

d. Visual evolution of precipitation and clouds during summer

To have a direct visualization of the behavior and geographical distribution of convection during summer, we present a video attached to this manuscript (available in the online supplemental material; Vergara-Temprado 2019). The time series presented show the evolution of the precipitation and cloud fields during two weeks of intense summer similarly as Leutwyler et al. (2015). The upper panels show the evolution of the models when deep convection and shallow convection is parameterized (DEEP) at three different resolutions (0.22, 0.08, and 0.02) and the lower panels show the behavior of the model when both parameterizations are switched off (EXPLICIT). The video presented does not attempt to be an objective evaluation of the simulations against real data, but rather a qualitative comparison of the different behaviors of the model focusing on the effects presented quantitatively in the previous sections. From the video, it can be seen how the largest differences in precipitation fields between models arise mainly from the choice of the representation of convective processes. Moving toward high-resolution models gives a more detailed representation of precipitation and clouds, but the organization and appearance of convection appears qualitatively similar as at coarser resolutions. The simulations with parameterized deep convection tend to produce much more light precipitation compared with their explicit counterparts as presented in section 3b. They also tend to produce precipitation much earlier in the day as it has been shown in section 3c. Convective cells in the coarse model with explicit convection (0.22_EXPLICIT) tend to group into larger clusters than in the finescale model, which is an effect partly caused by the coarse resolution employed. The evolution of the cells in the coarse model also tends to be slightly delayed from the cells in the finescale models as shown in Figs. 6c and 6f. These effects, however, do not seem to strongly influence the state of the simulations, as several of the performance skills presented are similar to those of the finer-resolution simulations. A more intensive study of the characteristics of the precipitation cells such as that presented by Crook et al. (2019) would be very beneficial for the analysis, but it is beyond the scope of this study.

e. Evaluation versus satellite-measured radiative fields

Convective processes are closely related to cloud formation. Its model representation therefore affects the way clouds are formed in the atmosphere and their properties. The timing and height at which clouds are formed affects their temperature and microphysical composition, therefore affecting their interaction with infrared emitted radiation from Earth (longwave radiation) and solar radiation (shortwave radiation). Implicitly, this interaction affects the amount of radiation at the Earth surface available to evaporate soil moisture, affecting the water cycle on a large scale. A good way to assess changes in cloud processes is therefore to look at the effect on the radiative balance at the TOA. For that purpose, we use the radiation observations from the CM-SAF dataset. The results are qualitatively consistent with Hentgen et al. (2019), who compared cloud and radiation biases in explicit 2-km and parameterized 12-km simulations, using a simulation period of 10 years.

To perform the evaluation, we first regrid all the model output into the CM-SAF grid and exclude the first 2.64° at each boundary of the domain in order to avoid contamination from the relaxation zone of the models. Then, seasonal mean values of outgoing LW and net SW radiation are calculated for all the simulations and compared against the satellite observations. In Figs. 8 and 9 we show the seasonal model biases in LW and SW radiation during the summer season of three of the resolutions tested (0.22°, 0.08°, and 0.02°). Similar figures for the winter season are given in the supplemental material (Figs. S6 and S7). In our analysis, the downward direction is treated as positive, so that net SW fluxes are positive and net LW fluxes are negative.

Fig. 8.

(a) LW net downward radiation at TOA from CM-SAF during the summer season. Model radiative biases (model − observations) for the (b),(f),(j) 0.22°, (c),(g),(k) 0.08°, and (d),(h),(l) 0.02° degrees, using DEEP in (b)–(d), SHALLOW in (f)–(h), and EXPLICIT in (j)–(l) as convective representations. All model results have been regridded to the CM-SAF grid. The domain averaged (e) mean bias and (i) mean absolute error for all the simulations tested in this study. A similar figure for the winter season can be found in the supplemental material (Fig. S6).

Fig. 8.

(a) LW net downward radiation at TOA from CM-SAF during the summer season. Model radiative biases (model − observations) for the (b),(f),(j) 0.22°, (c),(g),(k) 0.08°, and (d),(h),(l) 0.02° degrees, using DEEP in (b)–(d), SHALLOW in (f)–(h), and EXPLICIT in (j)–(l) as convective representations. All model results have been regridded to the CM-SAF grid. The domain averaged (e) mean bias and (i) mean absolute error for all the simulations tested in this study. A similar figure for the winter season can be found in the supplemental material (Fig. S6).

Fig. 9.

As in Fig. 8, but for net downward SW radiation at TOA. A similar figure for the winter season can be found in the supplemental material (Fig. S7).

Fig. 9.

As in Fig. 8, but for net downward SW radiation at TOA. A similar figure for the winter season can be found in the supplemental material (Fig. S7).

Figure 8e shows that across all the resolutions tested, the models tend to produce large LW radiative biases at TOA when parameterizing deep convection, especially over the Alps and the Mediterranean coast. The observed bias is greatly reduced during the other seasons, suggesting the important role of convective processes in producing it (Fig. S6). This bias is caused by a too intense transport of moisture to the higher levels of the atmosphere, which favors the formation of cold high clouds (Fig. S8) having a thermal emissivity much lower than that of the surface. Therefore, they reduce the loss of energy to space. Recalling that the downward direction is treated as positive, a positive LW radiation bias results (see Figs. 8b–d), implicitly in warming the atmosphere. This effect is consistent with the results presented in Hentgen et al. (2019). Switching off the deep convection parameterization significantly reduces the bias. It is interesting to note that increasing the resolution increases the magnitude of the LW bias when deep convection is parameterized. In contrast, when an explicit representation of deep convection is used, the evaluation with LW radiation is unaffected by changes in model resolution. This suggests that the vertical transport of water by deep convective systems does not change substantially when increasing resolution if deep convection is produced explicitly by the model dynamics.

The evaluation of net incoming SW radiation, on the other hand, shows a very different picture (Fig. 9). Across all our simulations, there is a clear and strong SW bias in the Atlantic region, produced by the models reflecting too much sunlight back to space. This feature intensifies when explicit convection is used due to a large increase in low-level cloud cover, especially over the oceans (Fig. S8). Increasing the model resolution diminishes the magnitude of this bias, suggesting that the model is starting to simulate the evolution of marine clouds in a more realistic way (Figs. 9e,i). The use of a shallow convection parameterization (the SHALLOW and DEEP simulations) reduces the magnitude of the bias strongly compared with the EXPLICIT simulations at coarse and intermediate resolutions, as it helps reducing the amount of low clouds by eliminating instabilities and producing upward mass fluxes. Over land regions, a bias of opposite sign appears at finer resolutions due to a substantial decrease in low cloud cover. This bias of too little reflected solar radiation is consistent with the surface radiative bias presented in Leutwyler et al. (2017) and Hentgen et al. (2019), who considered 10-yr-long simulations (equivalent to run 0.02_SHALLOW in this study). At the finest resolution (0.02°), both the SHALLOW and EXPLICIT representations show very similar performance skills, which suggest that either option could be chosen to represent clouds at this resolution, although both representations might suffer from biases in midlevel clouds as presented by Keller et al. (2016). The strong decreases in mean bias and mean absolute errors as resolution increases are shown in Fig. 9e. The large sensitivity of these low-level clouds to resolution changes demonstrates that the model is not fully able to resolve explicitly some of the important motions affecting cloud properties and their evolution at the studied resolutions, and therefore it is a clear demonstration of the added value that can be obtained by using high-resolution simulations to represent cloud processes and its interaction with radiation.

However, it should be noted that improvements in simulated biases could be obtained by using selective tuning of model parameters at each resolution. We also note that improvements in the microphysics and boundary layer schemes can lead to a much better representation of the evolution and radiative properties of clouds that could potentially overcome the improvements obtained by simply increasing resolution (Keller et al. 2016; Field et al. 2017; Vergara-Temprado et al. 2018).

4. Conclusions

We performed a set of simulations at grid scales from 50 to 2.2 km to study the role of switching off the different parameterizations of convective processes in our model. Across the majority of resolutions studied (from 25 to 2.2 km), seasonal mean values of precipitation and temperature can be simulated with similar performance skills, irrespective of whether deep convection is parameterized or not, while the biases in the diurnal cycle of summer precipitation are smaller for EXPLICIT and SHALLOW for resolutions from 25 to 2.2 km. Overall the results are thus consistent with the idea that explicit convection is useful and overall performs better than parameterized convection for resolutions up to 25 km. This result is perhaps surprising given the large agreement currently in the community toward using parameterized convection until the simulations are performed at a scale of a few kilometers. By looking at hourly precipitation statistics, we observe that the model behavior is more dependent on the treatment of convection rather than the resolution employed, at least for the measures considered. Improvements of skill scores are observed as the resolution increases over orographic regions. Parameterizing deep convection creates too much light rain, whereas using an explicit representation produces the opposite effect in agreement with several previous studies. This behavior is observed to happen also across all resolutions studied, pointing out that it is mainly created by the representation of convection rather than the resolution employed. At 50-km resolution, the diurnal cycle of summer precipitation when using explicit convection is substantially delayed in the day, making the use of a convective parameterization helpful in this context. However, the peak in the diurnal cycle over land can be adequately represented at resolutions as coarse as 25 km in a more accurate way with explicit than with parameterized deep convection. These results suggest that some of the credit given in the past to “convection-permitting” models for improving the representation of precipitation is solely produced by switching off the parameterization of deep convection and not due to the increase in resolution. The radiative balance of the model at TOA is the variable, of the ones we evaluated, that is most strongly affected by changes in resolution and parameterizations. Parameterizing deep convection in our model produces a large bias in outgoing LW radiation that is greatly reduced when the parameterization is switched off independently of the grid spacing. The net SW component, in contrast, strongly depends on the resolution employed, clearly showing the added value of using high-resolution simulations to improve the dynamical evolution of clouds and its interaction with radiation. From resolutions coarser than 4-km grid spacing, the models perform the best in top-of-the-atmosphere radiative fluxes when only a parameterization of shallow convection is used. At the finest resolution (2.2 km) explicit convection and parameterized shallow convection performs similarly when looking at TOA radiative fluxes, suggesting that either option is equally valid at this resolution.

5. Discussion

Overall, our results suggest that the regional climate of Europe can be simulated without the need for a parameterization of deep convection at much coarser resolutions than previously thought. For resolutions below or equal to 25 km, switching off the parameterization of deep convection might be considered as an option for model simulations as deep convection starts to be partly resolved in a way that makes the use of a parameterization not necessary. We observe that switching the parameterization off does not lead to an overall degradation of model skills but rather to a trade-off for some model skills (precipitation distribution, SW radiation) or to a clear improvement for some others (LW radiation, diurnal cycle of precipitation). The term “convection-permitting resolution” that is currently used for referring to “kilometer-scale” simulations should therefore be expanded to much coarser resolutions than previously considered. We note that for any of the resolutions studied shallow and deep convective processes will not be totally resolved, although the results presented here suggest that the majority of the beneficial effects of explicit convection in climate simulations emerge at surprisingly low resolutions. We should also note that the term “convection-permitting” does not imply that convection is fully and accurately represented, but rather that the models do not intrinsically block convection from occurring due to their resolution. The validity of these results in different climate regions and longer simulation periods should be validated further. Specifically, for any global model simulation, the behavior in the tropics when an explicit representation of deep convection at these scales is used should be studied carefully due to the strong impact of tropical deep convection on the global climate and where convection is particularly essential in defining the larger-scale circulations such as the Hadley cell and the ITCZ. We should note that we only tested a parameterization of convection with no scale dependency. The added value in model performance that could be obtained when using scale-aware convective parameterizations should also be studied and considered in future studies.

A puzzling result of our study that merits further consideration is the evident insensitivity of the overall results with respect to a range of resolutions that covers hydrostatic and nonhydrostatic scales. The presence of convective updrafts in hydrostatic models is common, even when convective parameterizations are on (Herrington and Reed 2017), but the vertical motions are weak. At kilometer-scale resolution, Weisman et al. (1997, see their section 5a and Figs. 16 and 17) and Jeevanjee (2017) show that idealized hydrostatic and nonhydrostatic simulations of deep convection are similar at 8 km, start to diverge at 4 km, and differ in terms of vertical motion at 2 km by a factor > 2. They also find that hydrostatic models overestimate (and not underestimate) vertical motion when used at nonhydrostatic resolutions. This result is consistent with the real-case study of Jang and Hong (2016, see their Fig. 9). They conducted simulations at 3 km using two models, both available in hydrostatic and nonhydrostatic versions. With the WRF model, the hydrostatic simulations strongly overestimate vertical motion and precipitation, while with the Regional Model Program (RMP) model the differences are much smaller (they argue because the RMP is much more diffusive). Our model simulations are nonhydrostatic, but for resolutions > 4 km the flow will essentially be hydrostatic. Our results indicate that even on those coarser scales, explicit convection behaves qualitatively realistic although the vertical velocities will be smaller than those at higher resolutions. It appears that—irrespective of the role of nonhydrostatic motions—explicit simulations enable the flow to stabilize the vertical atmospheric structure, in a way that is driven by and consistent with the evolution of the large-scale flow. Overall this might pinpoint a resolution around 4 km as particularly attractive for large-scale or global models, as the hydrostatic approximation is still approximately valid, and as idealized and real-case studies have demonstrated signs of bulk convergence (Panosetti et al. 2018, 2019; Pauluis and Garner 2006), and as the computational costs are substantially smaller than at fully nonhydrostatic resolutions.

One of the most significant limitations of the current study is the use of the same model version throughout all simulations (i.e., without retuning the model when changing resolution or the parameterization setup). In climate modeling, it is common practice to conduct a substantial amount of subjective tuning or objective calibration, whenever the configuration is changed, with the intent to optimally select semiempirical parameters within their range of uncertainty (Hourdin et al. 2017; Bellprat et al. 2012, 2016). Conducting such a tuning process would help to improve model scores, but we do not think that it would fundamentally change the model behavior. Nevertheless, conducting a systematic set of numerical experiments including some objective model calibration would be of considerable interest.

Acknowledgments

We thank the three anonymous reviewers of this paper for their detailed and constructive comments. This work was supported by the European Union’s Horizon 2020 research and innovation programme under Grant Agreement 776613 (EUCP) and by the Swiss National Science Foundation under Sinergia Grant CRSII2_154486/1 crCLIM. The authors would like to acknowledge the Center for Climate Systems Modeling (C2SM), the Federal Office of Meteorology and Climatology MeteoSwiss, and the Swiss National Supercomputing Center (CSCS). We acknowledge PRACE for awarding us access to Piz Daint at CSCS, Switzerland. We would also like to acknowledge the E-OBS data set from the EU-FP6 project ENSEMBLES (http://ensembles-eu.metoffice.com). We acknowledge the use of data from EUMETSAT’s Satellite Application Facility on Climate Monitoring (CM-SAF).

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