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 Deficiencies of the nesting technique for regional models and their internal variability represent a significant source of uncertainties in regional model outputs. Presented numerical experiments on four different-size domains, two of them being midlatitude channel domains, show that the spatial structure and magnitude of uncertainties strongly depend on the domain size. The experiments are performed by using the Weather Research and Forecasting (WRF) model nested into the operational European Centre for Medium-Range Weather Forecasts (ECMWF) analyses on the same horizontal resolution 0.25°× 0.25° and by nesting WRF into a larger WRF domain with the same resolution. Uncertainties are quantified by the root-mean-square differences (rmsd) between the WRF results and their driving lateral boundary fields. The results from the midlatitude channel domain show that uncertainties in the tropospheric wind associated with the imperfect nesting method are amplified in the baroclinically active regions of the Atlantic and Pacific. The zonal wind rmsd have a dipole structure in the Atlantic in both the midlatitude channel and the half-channel simulations nested into ECMWF. The dipole is absent when WRF is nested into itself. On the contrary, the maximal rmsd for the meridional wind are always located in the domain center. When the domain centered on Europe excludes the western Atlantic and North America, the simulated uncertainties become spatially nearly homogeneous, and the magnitude of rmsd due to the imperfect nesting technique greatly reduces.
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 The need for much finer scales than currently affordable by global ensemble prediction systems and global climate models (GCM) drives numerous applications of regional models (RMs), and this is likely to continue in the coming years. For example, the recent European project ENSEMBLES (http://ensembles-eu.metoffice.com, van der Linden and Mitchell ) involved about 15 regional climate models (RCMs) and almost 100 European partner and affiliated institutes. Similar projects are carried out for North America (North American Regional Climate Change Assessment Program, NARCCAP, Mearns et al. ) and for the multiple domains worldwide (Coordinated Regional Climate Downscaling Experiment, CORDEX, http://wcrp.ipsl.jussieu.fr/SF_RCD_CORDEX.html, Giorgi et al. ). A majority of RCMs uses one-way nesting approach in which the solution of an RCM is driven at the lateral boundaries (LBs) by time-dependent fields from a coarse resolution global climate model [e.g., Giorgi and Mearns, 1999]. Results of RCMs contain all uncertainties that characterize GCMs, such as model errors, the internal variability and the emission scenarios, and additional uncertainties coming from the lateral boundary forcing. In addition, different sources of uncertainty interact and their impacts are not additive.
 The fundamental tenets involved in downscaling have been discussed by Laprise et al. . The most important assumption deals with the generation and properties of the small-scale features that are absent in the lateral boundary conditions (LBCs) from the global model. The validity of this tenet has been demonstrated by numerous studies with RCMs. For example, Denis et al.  designed a perfect-model framework, called the Big-Brother experiment, to validate the downscaling ability of an RCM in the case without model error. A similar approach was used in several follow-on studies to isolate the uncertainties in an RCM due to imperfect LBCs [e.g., Diaconescu et al., 2007; see Laprise et al., 2008, and references therein]. On the other hand, a recent paper by Diaconescu and Laprise  investigated the effect of domain size with focus on the larger scales and questioned whether an RCM can actually improve the large scales compared to those of the driving data. Their results showed that when an RCM is driven by perfect LBCs, its skill at reproducing the large scales decreases with increasing the domain of integration, but the errors remain small. If the LBCs contain errors, RCMs can bring some reduction of errors in large scales.
 The present study differs from most of the other studies with RCMs in the most important aspect of downscaling—generation of scales absent in LBCs. Namely, in our numerical experiments, the horizontal resolution of an RCM is equal to the resolution of the driving LB fields. We apply the operational analyses of the European Centre for Medium-Range Weather Forecasts (ECMWF), available at 0.25°× 0.25° resolution, as forcing fields of an RCM with the same horizontal grid. The goal of this approach is to isolate uncertainties in an RCM due to the nesting methodology, independently from uncertainties due to different scales represented by a global model, which provides LBC, and a nested model.
 Many regional models used for climate simulations have developed from models used for the operational numerical weather prediction (NWP). Thus, the RCMs share problems related to the treatment of the lateral boundary conditions that are common to NWP applications [e.g., Warner et al., 1997]. As discussed by Warner et al. , the method which introduces the LBCs by replacing the boundary values of prognostic variables of a nested model with the same variables from the driving model can alone be a source of significant errors. There is no perfect technique for the formulation of LBCs for 3-D primitive equation models [Oliger and Sundström, 1978]. A method for the formulation of LBC, used in most of NWP and regional climate models, is the boundary relaxation scheme introduced by Davies [1976, 1983]. In that scheme, a Newtonian relaxation term is added to the prognostic equations over the boundary zone, which gradually replaces the interior domain solution by the solution from the coupling model at the outer edge of the boundary zone. Such a relaxation method is applied also in the Weather Research and Forecasting model (WRF-ARW, Skamarock et al., 2008), which is used in the present study. The imperfect formulation of LBC introduces uncertainties in the interior domain even in the case of a perfect-model framework [e.g., Marbaix et al., 2003; Diaconescu and Laprise, 2013]. We wish to quantify these uncertainties in relationship to the domain size for a typical resolution regional model in the Northern hemisphere midlatitudes. This is contrary to most of the other studies with RCMs, in which uncertainties due to imperfect formulation of LBCs are an integral part of other nesting errors.
 In climate downscaling, the choice of domain size and a location of the boundaries affect the simulated regional climate, and this has been the subject of numerous studies [e.g., Seth and Giorgi, 1998; Miguez-Macho et al., 2004; Leduc and Laprise, 2009]. There is no precise algorithm for the optimal choice of the domain size and the location of boundaries for an RCM. In general, the area of interest should be set well within the domain interior and should not cause inconsistencies at the outflow boundaries due to different large-scale structure developed in an RM and LBs [e.g., Rinke and Dethloff, 2000; Alexandru et al., 2007; Laprise et al., 2008, and references therein]. A typical domain for NWP and regional climate modeling for Europe covers Europe, Mediterranean, and a part of the northern Atlantic. In a limited-area domain, the errors associated with lateral boundaries propagate into the domain interior at different speeds. In addition to fast-propagating inertio-gravity waves associated with geostrophic imbalance, there is a slowly moving component of error which is propagating toward the domain interior at rates of 20°–30° per day (Baumhefner and Perkey ; see also discussion in Warner et al. ). Furthermore, the quality of LB forcing plays a critical role for the modeling results, as demonstrated in several studies [e.g., Wu et al., 2005, and references therein]. In the present study, results are verified against the fields which provide LB forcing in the perfect and imperfect-model framework. In the perfect-model framework, uncertainties of an RCM, which has the same resolution like the LBCs, are due to deficiencies of the nesting technique including spatial and temporal interpolation of lateral boundaries, internal dynamics on a limited area, and interaction of these factors. Reference numerical experiments are carried out on a midlatitude channel domain in order to avoid the component of the LB error associated with the western and eastern boundaries in the middle and high latitudes. The domain is then gradually reduced in the longitudinal direction to study the varying influence of the domain size.
 In response to a given set of LBCs, results of an RCM experiment are not unique, a property known as internal variability [e.g., Seth and Giorgi, 1998; Giorgi and Bi, 2000; Christensen et al., 2001; Alexandru et al., 2007]. The internal variability is addressed by a minimal ensemble of experiments in each domain. The experiments and methodology for their evaluation are described in details in section 2. Section 3 presents results by comparing outputs of numerical experiments on various domains. It is shown how RM uncertainties, defined as differences between dynamical variables of an RM and the driving LB fields, diminish as the domain size is reduced. Discussion and conclusions are provided in section 4.
2 Numerical Experiments
 Numerical experiments with the WRF model are carried out over the 3 month period in January–March 2009. The summary of numerical experiments performed is provided in Table 1, while the horizontal domains can be seen in Figure 1. All simulations have the same numerical grid horizontally equal to that of the driving ECMWF analysis fields. The ECMWF analyses on the 0.25°× 0.25° resolution grid are retrieved from the meteorological archive system at ECMWF, and they are a product of the ECMWF 4D-Var assimilation system. It includes a forecasting system with T799 resolution and a 4D-Var assimilation with the inner loops carried out on lower resolutions than the forecasting model [Andersson and Thepaut, 2008].
Listed are domains longitude and latitude limits, the coupling model, and experiment label.
 The initial and LB conditions from the operational ECMWF analyses are prepared every 6 h.The operational ECMWF model has 91 vertical levels. On average, 15 levels are located in the planetary boundary layer (below 850 hPa), 28 levels is between 850 and 200 hPa, while the remaining 48 levels are distributed between 200 hPa and 0.01 hPa. On the other hand, most of the RMs including the WRF model derive their ICs from the standard-pressure level data (21 levels currently), which include only 11 levels up to 100 hPa. For comparison, the ECMWF model contains 53 model levels below 100 hPa. In order to reduce the amount of applied interpolations to a minimum and to make good use of the available ECMWF model-level data, we have performed the interpolation from the ECMWF hybrid σ−pressure levels directly to the WRF σ−pressure levels. Among other advantages, this ensures that initial conditions for the WRF simulations are nearly identical to the driving ECMWF data.
 WRF Model physics used in the present study includes the Kain-Fritch convection [Kain, 2004], the Single-Moment three-class scheme of mycrophysical processes (WSM; Hong et al. ), and the planetary boundary layer scheme of Hong et al. . For calculations of surface heat and moisture fluxes, the Noah land surface model is used [Chen and Dudhia, 2001]. The Rapid Radiative Transfer Model (RRTM; Mlawer et al. ) is chosen for longwave radiation, whereas the MM5 radiation scheme [Dudhia, 1989] is used for solar radiation. Nonhydrostatic computations are carried out with a time step for the Runge-Kutta third-order integration of 50 s. The number of WRF levels was 32 levels distributed between the surface and 10 hPa level, where ω=0 condition applies. As we focus on the impact of imperfect coupling on dynamical variables in the troposphere, there are five levels above 100 hPa, five levels between 200 hPa and 100 hPa, the remaining levels being distributed in the boundary layer (six levels below 850 hPa), the lower troposphere (eight levels between 850 hPa and 500 hPa) and the upper troposphere (eight levels between 500 hPa and 200 hPa).
 The method for LBCs includes both Newtonian relaxation and the diffusive relaxation. The default profile for the Newtonian relaxation in WRF, used in vast majority of WRF applications, is the linear relaxation over five grid points. This is a default option also in our study. It is compared with the linear relaxation over nine points and with the exponential relaxation profile to show that a wider relaxation zone provides better results. The linear profile of the boundary relaxation function is applied also in some other RCMs [e.g., Jones et al., 1995]. In all experiments the LBCs are updated with 6 h frequency with the linear interpolation in between which is a typical approach in regional modeling as well as in NWP.
 The reference experiment is a midlatitude channel extending between 35°N and 70°N and it is denoted as “Ch”. It includes 1440×140 grid points on a 0.25°× 0.25° resolution grid, which is the same grid as that of the applied initial conditions (ICs) and LBCs, which are the operational ECMWF analyses. The channel domain has been used before for the regional climate simulations in the tropics [e.g., Coppola et al., 2012], but not in the midlatitudes. Another two domains nested directly into ECMWF occupy a half and a quarter of the channel domain and they are denoted as“HCh” and “QCh”, respectively. “HCh” extends between 100°W and 60°E, whereas the longitude limits of “QCh” are 45°W and 35°E. Experiments on the three domains, “Ch”, “HCh,” and “QCh”, provide results that differ from the ECMWF fields due to differences between the two models, the imperfect nesting method, and the internal variability within WRF. The internal variability is addressed by carrying out three simulations on the same domain, each starting on a different date with a 6 day shift; experiments start on 1, 7 and 13 January. All experiments last until 31 March 2009.
 In order to eliminate the model differences as a cause of errors, another set of WRF experiments is carried out in which the “Ch”, “HCh,” and “QCh” domains are nested into a larger channel domain, which is extended 5° to the south and 10° northward in comparison with “Ch” (Figure 1). This experiment is denoted as “LCh,” and it is prepared in the same way as the other experiments including a set of three simulations. Experiments “Ch2”, “HCh2,” and “QCh2” are the same as “Ch”, “HCh,” and “QCh,” respectively, except that they are nested into the “LCh” simulation. This is a perfect-model framework, which ensures that differences between “LCh” on one side and “Ch2”, “HCh2,” and “QCh2” simulations on the other side are due to deficiencies of the nesting technique and the internal variability. Again, the internal variability is addressed by carrying out three simulations starting on different days just like in the case of “Ch”, “HCh,” and “QCh” experiments. No spatial interpolation of LBCs is involved between LCh and Ch2, HCh2, and QCh2 except for the temporal interpolation and the relaxation methodology.
 Results are evaluated by the root-mean-square differences (rmsd), , between results of WRF simulations and verifying fields which provided LBCs. Values of σ2 are computed during the integration period for each ensemble member as
Here the prognostic WRF variables at standard pressure levels are denoted by xw, whereas xbc stands for variables from the driving fields. The parameters i, j, p, and t have their usual meaning of indices in the zonal direction, meridional direction, pressure level, and time. The operator − denotes a spatial, temporal or ensemble averaging. As the driving LB fields in our case represent the truth, we call the σ fields errors. This is not an appropriate name as a temporally evolving solution in the interior of an RCM domain does not follow the simulated truth, which is driving it at the lateral boundaries. The averaged differences in equation (1) represent uncertainties, which have the same meaning as errors throughout our paper. The error variances σ2 are averaged for each level and domain. In particular, we are interested in the ensemble-averaged and time-averaged errors over the “QCh” domain. The experiments “LCh,” “Ch,” “HCh,” and “QCh” are verified against ECMWF, whereas the experiments “Ch2,” “HCh2,” and “QCh2” are verified against “LCh”. In addition, “Ch2,” “HCh2,” and “QCh2” are verified also with ECMWF, and this is explicitly mentioned as “Ch2E,” “HCh2E,” and “QCh2E” results. The experiments which are nested into “LCh” quantify uncertainties due to imperfect nesting procedure commonly used in downscaling experiments in the midlatitudes.
 We note that our rmsd measure is different from measures used to evaluate the internal variability [e.g., Christensen et al., 2001; Alexandru et al., 2007; Lucas-Picher et al., 2008]. For example, Lucas-Picher et al.  normalized the rmsd between the ensemble members and the mean by the variability of the field to get the relative internal variability as a better measure of the RCM internal variability. We compute spread among the ensemble members during the integration as the standard deviation between the three ensemble members for various experiments as it is commonly done [e.g., Alexandru et al., 2007]. In our small ensemble, the estimated spread can be regarded as a minimalistic illustration of the internal variability. We have a too-small ensemble for an in-depth study of the internal variability, and our focus is on the interaction of the LB errors with the model internal dynamics.
3.1 Temporal Evolution of RMSD
 In Figure 2, we compare the temporal evolution of rmsd of the meridional wind (v) at 700 hPa level in the three simulations nested directly into the ECMWF analyses. The errors for the three ensemble members are averaged over the “QCh” domain every 6 h. There are two main features in this figure. First, we notice that the rmsd reduces as the domain size becomes longitudinally smaller. The time-averaged rmsd in the “QCh” experiment is about 4 ms−1(Figure 2c) whereas in the “HCh” (Figure 2b) and “Ch” (Figure 2a) experiments, the average rmsd varies around 6 ms−1and 8 ms−1, respectively. In “LCh”, the average magnitude of rmsd is about 11 ms−1 (not shown).
 Second, Figure 2 shows that the temporal variability of rmsd over the “QCh” domain varies among the experiments. In the “QCh” experiment, there is little difference among the three simulations after the first 3 weeks (Figure 2c). We can discuss this result in relation to the spread among the ensemble members during the integration period. In Figure 3, we compare the temporal evolution of the ensemble spread averaged over the “QCh” domain. It shows that the internal variability as well as its temporal changes reduce as the model domain becomes smaller in the same manner as rmsd. On the other hand, if we compare various simulations over the “HCh” domain, the rmsd and the ensemble spread are comparable in the “Ch” and “HCh” experiments (figure not shown). The described reduction of rmsd and the internal variability in the “QCh” domain applies also to the zonal wind (u) and temperature (T) variables and to other levels (figures not shown).
 In the simulations nested in “LCh”, the rmsd magnitudes are on average 10% to 30% smaller than in the experiments nested into ECMWF (not shown). In the “Ch2” and “HCh2” experiments, the internal variability and temporal variations in rmsd are about the same as in “Ch” and “HCh,” respectively (figures not shown). A significant reduction of the rmsd in the “QCh” domain in comparison to larger domains is present also in these simulations.
 It can also be seen in Figures 2 and 3 that it takes 7–8 days for a simulation to forget its initial conditions. Thus, we compute the time-averaged statistics for a 70 day period between 21 January and 31 March 2009, and we perform the averaging of rmsd over the three experiments.
3.2 Distribution of Uncertainties in the Midlatitude Channel
 Figure 4 shows the spatial properties of average rmsd at 250 hPa and 850 hPa for both wind components in the “LCh” experiment. A common feature of rmsd for both velocity components is the dominance of errors in the Atlantic and Pacific regions. The values of rmsd over the Atlantic and the Pacific are on average twice greater than over the Northern America and Eurasia. The most important difference between the u and v rmsd is their meridional structure. The zonal wind errors have a dipole structure, while the meridional rmsd are centered between 50°N and 60°N. The three maxima of rmsd for v, the Atlantic, the eastern, and the western Pacific maximum, have almost the same amplitude (Figure 4c). On the contrary, the global maximum in rmsd for u is located in the north Atlantic (Figure 4a).
 The vertical structure of rmsd is nearly barotropic; the location of error maxima in the Atlantic and the Pacific remains the same throughout the troposphere although the intensity varies. In the Atlantic, the dipole structure of the zonal wind rmsd is clearly seen throughout the troposphere, while in the Pacific, the dipole structure is absent in the lower troposphere (Figure 4b).
 Figure 5 shows that the dipole structure of rmsd in the zonal wind is not related to the impact of the latitudinal channel boundaries. As illustrated in Figure 5a, a well-defined dipole structure of the rmsd in the Atlantic is found also in the “Ch” simulation. Similarly, the spatial structure of rmsd for v in “Ch” resembles that from “LCh” (Figure 5b). The difference between the “LCh” and “Ch” experiments is in the rmsd magnitude, which is in some areas 50% and greater in “LCh” than in “Ch” (Figure 5 versus Figures 4a and 4c). In the lower troposphere in “Ch,” the Atlantic dipole is weaker with respect to “LCh,” and the maximal rmsd is placed in the northern Atlantic at the tip of Greenland (figure not shown). The spatial structure of time-averaged rmsd is similar among the ensemble members. This especially applies to the v errors. The well-defined dipole structure for u is found in all three ensemble members in the Atlantic, although its shape is somewhat different.
 The rmsd maxima in the Atlantic and Pacific are associated with the jet stream and the storm tracks locations in these two regions. In these baroclinically sensitive areas, small differences in the thermal wind can cause significant amplitude and phase differences in the development of weather systems in the ECMWF and WRF models. It is reflected in rmsd at individual times and in various ensemble members. In other words, the rmsd are largest here because these are the regions with greater natural variability. Every ensemble member is showing the same signal.
 A major change in the rmsd structure for u occurs when differences between the driving model and the regional model are removed. These are our simulations nested into a larger WRF channel. In the “Ch2” simulation, the rmsd result from deficiencies of the nesting technique and the internal model dynamics, which amplifies the errors propagating from the boundaries and the initial state. The largest difference between the rmsd in the zonal wind in “Ch” and “Ch2” experiments is the absence of the dipole structure in the latter case (Figures 6a and 6c).
 In “Ch2,” the dominant u error is over the Greenland area close to the domain edge, which illustrates an enhancement of nesting deficiencies in orographic regions sensitive to the baroclinic development (Figure 6a). Like in “Ch,” the rmsd in “Ch2” in the upper troposphere are greater in the Atlantic than in the Pacific. Contrary to the u wind, the spatial distribution of rmsd for the v wind in “Ch2” is significantly less changed with respect to “Ch”. The main modification is seen in a greater dominance of the Atlantic error maximum throughout the troposphere. The Eurasia and the continental Northern America remain regions of smaller uncertainties in the wind field, especially Asia. In general, when the model differences are removed, the uncertainties associated with an imperfect nesting coupled with the internal variability are reduced more in the Pacific than in the Atlantic, especially in the western Pacific. The smallest rmsd in “Ch2” are found over the south Asia. The differences between the Atlantic and the Pacific must be related to the propagation of the lateral and bottom boundary impact in the forecasts coupled with the dynamics. A strong influencing factor may be a different impact of the ECMWF LBs in “LCh” in the Pacific and in the Atlantic, especially the southern boundary located in the subtropics. In each case, downstream baroclinic development plays a major role in propagating and amplifying the influences eastward, just like in the NWP case [e.g., Szunyogh et al., 2002].
 When verified against ECMWF, simulations nested into “LCh” again show a strong dipole structure not only in the zonal wind rmsd in the Atlantic but also in the Pacific (Figure 7a). Figure 7 overall well compares with Figure 5 except that error magnitudes are larger and the Pacific error dipole is stronger. This applies to all levels. The dipole error structure found in our experiments is a consequence of differences between the WRF and ECMWF model systems, which affect dynamics in the baroclinic regions of the Atlantic and Pacific. In these two regions, dynamical errors concentrate as known from earlier. The effect of imperfect nesting technique is seen most in the zonal wind close to the model meridional boundaries, and it is strongly enhanced by the orography of Greenland. The northern and southern lateral boundaries exert a strong control over the meridional wind, which always has maximal errors in the domain center. The same applies to the internal variability, as will be shown later on.
 The rmsd for the mass field are most often represented in terms of geopotential height. We choose to show temperature, which is a prognostic variable, rather than geopotential height. Geopotential, being an integral, is smoother than temperature field while it has a similar large-scale structure. The temperature rmsd in the lower troposphere are largest in the lee of Rockies, while the eastern Atlantic area and west Europe are characterized by the smallest errors (Figure 8a). This result is probably associated with a larger temperature variability within continental climates than over the ocean regions. A very similar rmsd distribution and magnitudes are found in “Ch” and “Ch2” experiments. At levels in the midtroposphere and upper troposphere, the spatial rmsd distribution is different from the surface-influenced lower troposphere. At 500 hPa, which is shown in Figure 8b for the “Ch2” experiment, the temperature rmsd maxima are distributed similar to the errors in the meridional wind except that locations of maximal errors are found somewhat more northward. The pattern of rmsd in “Ch” looks similar to “Ch2” except that a single maximum in the Atlantic is found in its central area at around 55°N (not shown). The northern Atlantic is the midlatitude region with the largest temperature uncertainties in the upper troposphere.
3.3 The Impact of Meridional Lateral Boundaries
 Next, we investigate how the uncertainties over the Euro-Atlantic area in Figures 4-8 change when the domain size is reduced. The answer is illustrated in several figures showing rmsd from domains of half and quarter size of the channel domain. First we show results for the wind components in “HCh” and “HCh2” experiments (Figures 9 and 10). Figure 9 presents u and v scores for “HCh” at 250 hPa. A clear impact of the eastward-propagating signals from the western boundary is seen. There is a larger difference between the structure of u and v rmsd close to the eastern boundary than at the western edge of the domain. The structure of rmsd in both the zonal wind and meridional wind over Europe and the Atlantic in “HCh” remains similar to that found in the “Ch” experiment, but amplitudes are up to one-third smaller. Similar results are found at all levels except that the western boundary exerts a weaker impact in the lower troposphere where average westerlies are weaker. The dipole structure of the zonal wind rmsd in the Atlantic is still seen at 250 hPa (Figure 9a), while in the lower troposphere, a single error maximum is located just off the tip of Greenland (not shown). The meridional wind errors in “HCh” still contain a maximum over the northern Europe, but the maximum in the Atlantic is much weaker compared to 'Ch" due to the proximity of the western boundary (Figure 9b).
 In “HCh2,” the meridional wind scores in the upper troposphere are smaller than in “HCh,” and the maxima are shifted to the north-east (Figure 10c). For the zonal wind, the difference between “HCh2” and “HCh” is far more pronounced. The rmsd for u in the upper troposphere over the Atlantic are now smaller than over the land, and the maximum is found over the central Europe (Figure 10a). There are no errors close to the LBs over Greenland, which dominated Figure 6a. In the lower troposphere, both u and vwinds still have largest rmsd over the northern Atlantic although the errors are smaller in comparison with “Ch2”. When verified against ECMWF analyses, both zonal and meridional wind rmsd have larger amplitude than in “HCh2,” and the dipole shape of u is well defined. Overall, the rmsd gradients across the Atlantic and Europe in Figure 10 appear much smoother than in Figure 6, illustrating a strong reduction of variability exerted by the LBs in the smaller domain.
 The spatial structure of uncertainties in temperature is similar to that found for the meridional wind. In particular, the western LBs exert a strong impact on the eastward shift of errors over Europe and the Atlantic in comparison to “Ch” (Figure 11). In comparison to the channel simulations, T errors in “HCh” over the north America have reduced and became more homogeneous at 850 hPa (Figure 11a). The Atlantic maximum of rmsd is located more eastward at 500 hPa than at 850 hPa in agreement with a stronger downstream propagation of the LB impact at higher levels. A similarity of outputs from “HCh2” and “HCh” in both amplitude and spatial distribution again suggests that differences between the driving model and the regional model become less important as the RM domain size is made smaller.
 In “QCh” and “QCh2,” rmsd become more homogeneous as can be seen in Figure 12. This is in agreement with the reduction of internal variability in relation to the domain size, which can be seen in Figures 13 and 14. In Figure 13, we choose to present the ensemble spread for the meridional wind at 700 hPa in order to allow comparison with Figures 2 and 3. In addition, Figure 14 displays the ensemble spread for the zonal wind at the same level. The zonal wind spread has the dipole structure in both “Ch” and “HCh” simulations, while the dipole is absent in the “QCh” outputs. Thus, the spatial structure of the ensemble spread is in a close agreement with the structure of rmsd defined by equation (1).
 Magnitudes of rmsd in “QCh2” are further reduced for up to about 50% in comparison with “HCh2” Under a strong LB control, there is no significant difference between “QCh” and “QCh2” in the magnitude of errors and their spatial distribution. Furthermore, the magnitudes are not significantly different at various vertical levels as could be expected when deficiencies in the nesting methodology are the primary cause of errors. In both wind components, the errors in the upper troposphere are shifted eastward with respect to the lower troposphere in agreement with the downward propagation of the LB impact. The largest rmsd in the lower troposphere in both u and v are still located in the northern Atlantic. When “QCh2” is verified by ECMWF, the maximal error in “QCh2E” is found in the north Atlantic, just like in the “Ch2E” experiment shown in Figure 7d. In particular, rmsd for v have a structure elongated toward the northeast, which is associated with the storm tracks regions as discussed before (figure not shown).
 Finally, in Figure 15 we show temperature scores in “QCh” and “QCh2” simulations, which can be compared with previous T scores for larger domains. In the lower troposphere, rmsd remain largest over the central and eastern Europe although somewhat smaller. In the upper levels where signals from LBs are propagating faster, T errors become more homogeneous, just like the wind errors.
3.4 Meridional Profiles
 If the rmsd are zonally averaged, their meridional profiles have a nearly flat shape for the zonal wind and a sinusoidal shape for the meridional wind errors (Figure 16). For v in the lower troposphere, the error profiles from “QCh” are almost the same as in “QCh2,” while in the upper troposphere, the errors in “QCh2” are somewhat smaller due to a stronger influence of LBs (not shown). The comparison of various simulations over the “QCh” domain suggests that uncertainties in RCMs over Europe are more reduced by making the domain narrower meridionally (“Ch” instead of “LCh”) than by reducing it in the zonal direction (“Ch” domain instead of “HCh”) (Figure 16). The same conclusion is valid for the zonal wind except at the northern boundary edge. This applies to all levels, and it is most likely related to the two distinct areas of the atmospheric variability in the Atlantic and Pacific storm track regions. However, the replacement of “HCh” by “QCh” domain reduces errors at all levels to a far greater extent than the replacement of “Ch” by “HCh.” This is also an expected result with regard to the impact of midlatitude dynamics in the Pacific on the Atlantic and Europe.
 The rmsd profile for the zonal wind are characterized by a zigzag shape at the rows next to the relaxation zone both at the northern and southern domain border (Figures 16a and 16c). This can be noticed also at horizontal levels shown earlier. The problem is investigated by carrying out additional “QCh” simulations using a wider relaxation zone and the linear-exponential instead of the linear relaxation profile. An example of resulting rmsd profiles is shown in Figure 17, which can be compared with Figure 16c. It shows that differences in scores from various experiments are not significant except close to the relaxation zone. Here the application of the linear-exponential relaxation provides significantly better scores, a smooth error profile with a more gradual change toward the boundary fields. This behavior is expected based on dynamical properties of the applied schemes, which are discussed in Marbaix et al. . Other authors also reported that a wider buffer zone, which applies a smooth relaxation function, provides better results [e.g., Giorgi et al., 1993; Zhong et al., 2010]. As our initial choice was to use the model default setup, we suggest to have the exponential relaxation profile and a wider buffer zone as the default option in WRF.
4 Discussion and Conclusions
 Among the various factors influencing the downscaling process, the lateral domain size plays an important role for the results of regional simulations [e.g., Leduc and Laprise, 2009]. In particular, for simulations focusing on Europe, the location of the western boundary is of a special importance, as known from NWP experience over Europe where forecast errors are traced to the impact of initial conditions over the western Atlantic and North America [e.g., Graham et al., 2000]. This has been confirmed in the present study dealing with the nesting uncertainties in a regional model in the midlatitudes. In any limited-area domain, a part of the error in the simulations is due to deficiencies of the nesting technique. These deficiencies include imperfect methods for information exchange between the driving LBCs and the regional model, differences between the driving model and a regional model, errors due to spatial and temporal interpolation of lateral boundaries, internal dynamics, as well as interactions among these error sources.
 In order to isolate uncertainties related to the nesting technique, the performed experiments used the same resolution for the regional model and LBCs. The initial and LB fields as well as the verifying data are operational analyses of ECMWF available at 0.25° horizontal resolution, which is used also for the WRF model. In addition, we have performed the interpolation from the ECMWF model levels directly to the WRF model levels in order to keep the amount of applied interpolations at minimum and to make an optimal use of the high vertical resolution of ECMWF. This approach allowed us to isolate uncertainties in the RM WRF due to the imperfect nesting and model differences. In the case when the nesting and nested models are the same, errors are only due to the nesting procedure and associated internal dynamics. Resulting uncertainties of an RCM can be considered as pure nesting uncertainties. When the RM is different from the model, which provides LBs, nesting errors combine with errors due to model differences. The comparison of the two statistics in terms of root-mean-square differences between the RM results and the driving LB fields highlights the impact of models' differences for the spatial structure of uncertainties in an RCM.
 The experiments with the midlatitude channel nested into the ECMWF analyses produced rmsd with different properties in the temperature field and the velocity components. The common property of the rmsd fields is their maximal amplitudes in the Atlantic and the Pacific. The two regions are dynamically most sensitive as they are home for the storms tracks and jet streams, and it is here where the model differences and deficiencies of the nesting methodology are resulting in greatest uncertainties of the simulated circulation. In particular, the zonal wind uncertainties in the WRF model nested into ECMWF analyses have a dipole structure in the Atlantic in both the channel and half channel simulations. The absence of the dipole structure in the case when WRF is nested into itself suggests that differences between the WRF and ECMWF model (e.g., parametrization of orographic processes) enhance uncertainties in dynamically more sensitive regions. The uncertainties associated with the imperfect nesting are greater in the Atlantic than in the Pacific. Opposite to the zonal wind, the maximal uncertainties for the meridional wind component are located around 55°N, independent of the difference between the nesting and regional model thus confirming that nesting affects the zonal much stronger than the meridional flow. The pure nesting uncertainties in the channel domain are largest for the zonal wind field in the topographically complex regions of the northern Atlantic.
 When the channel domain is made smaller and the western boundary is placed at 100°W, uncertainties over Europe and the Atlantic decrease and their maxima are found further eastward. The internal model variability over Europe is similar to that found in the channel domain. When the channel domain is further reduced by centering it over Europe with the western boundary at 45°W, the impact of the western boundary on the magnitude and structure of uncertainties over Europe becomes much stronger in comparison with the half-channel experiment. The uncertainties greatly reduce, and the dipole structure of the zonal wind rmsd in the Atlantic disappears. In this case, differences between the driving model and the regional model do not significantly influence the spatial distribution of uncertainties; in other words, the distribution of rmsd is very similar in the perfect-model experiment and in the case when LBs are provided by a different model. In the quarter-channel domain with the western boundary over the Atlantic, which is still larger than most of domains used for regional climate modeling in Europe, the strong influence of driving LBs results in spatially nearly homogeneous uncertainties throughout the free troposphere. It suggests that in such a domain, internal dynamics in the regional model can not fully develop.
 The authors would like to thank three anonymous reviewers for their constructive comments which led to the paper improvement. The Centre of Excellence for Space Sciences and Technologies SPACE-SI is an operation partly financed by the European Union, European Regional Development Fund and Republic of Slovenia, Ministry of Higher Education, Science, Sport and Culture. This research was partly carried out under the funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement 280153.