Large-eddy simulation (LES) studies have usually focused on a specific atmospheric boundary layer type, often with the purpose of addressing a specific theoretical question. Many early atmospheric LESs initially focused on cloud-free, convective boundary layers e.g.,. Later, various studies additionally investigated the effects of wind shear on the convective boundary layer e.g.,. The role of clouds in the dynamics of the boundary layer has motivated more sophisticated LESs of cloud-topped boundary layers. Stratus and stratocumulus clouds have been considered in numerous works e.g., and shallow-cumulus clouds have also been successfully simulated e.g.,. Less attention has been paid to stably stratified boundary layers because their simulation requires even higher resolutions and computer resources (compared to LESs of convective situations) as the stable boundary layers are usually very shallow. Furthermore, turbulence in the stable layers is usually intermittent and coupled to waves. Nonetheless, there are several LESs and direct numerical simulation studies of the stable boundary layer e.g.,. There are other studies investigating the diurnal transition between different boundary layer types e.g.,.

In reality, however, different types of the atmospheric boundary layer occur consecutively if longer time periods spanning weeks to months and even years are considered. LESs of these longer time periods (called long-term LESs in the following) became computationally tractable through massively parallel codes and advances in computing . What benefits and new insights can be gained from the long-term LES approach compared to previous studies? First of all, LES models can be regarded as virtual laboratories, in which the characteristics of atmospheric microscale flows can be studied and understood under controlled conditions . One major practical benefit from LES is the development and improvement of boundary layer parameterization schemes e.g.,. By testing parameterization schemes with a multitude of different boundary layer situations (including transitions), the tuning towards special atmospheric conditions, which might not even be representative, can be avoided . Furthermore, realistic long-term turbulence data sets are also of great interest in other fields of study, especially those with a high practical orientation (e.g., studies concerning wind energy or air quality and ventilation effects in urban environments).

When focusing on LESs longer than several hours, the importance of including synoptic-scale meteorological conditions in LESs increases. Larger-scale forcing in terms of time-varying horizontal and vertical advective tendencies as well as larger-scale pressure gradients (geostrophic wind) should be prescribed to account for the overall larger-scale conditions. The strategy to prescribe larger-scale forcing terms has been applied in various single-column and LES studies e.g.,. Even early LES case studies e.g., included synoptic-scale forcing. For idealized LES case studies focusing on a specific boundary layer type, the larger-scale forcing is usually constructed based on observations from measurement campaigns e.g.,. Synoptic-scale forcing can also be obtained from larger-scale models e.g., or a combination of observations and models e.g.,. Regarding long-term simulations in the semi-idealized setup, relaxation towards a reference state given by a larger-scale model or observations can be used in combination with advective forcing to prevent model drift in time .

In this study LESs covering almost 3 weeks (19 days) of the HD(CP)2 (High-Definition Clouds and Precipitation for advancing Climate Prediction) Observational Prototype Experiment HOPE; are evaluated by comparing the results with the multi-sensor HOPE data set specifically designed with this purpose in mind. Particularly, the simultaneous operation of several new lidar systems during HOPE provided the unique opportunity to study planetary boundary layer characteristics with unprecedented detail. The importance of high-resolution thermodynamic profiling for model evaluation is also outlined in . Results of a year-long LES centered at a meteorological observational supersite were presented by . They followed a statistical approach to assessing the quality of their long-term LES by comparing yearly-averaged diurnal cycles and climatologies with those from observations and concluded that the semi-idealized approach is stable enough to simulate a whole year of varying conditions. The present study focuses on a day-to-day comparison with observations from a measurement campaign, which also accounts for spatial variability by providing measurements at three different principal measurement sites. Here, we want to tackle the question of if the long-term LES approach is able to deliver a realistic boundary layer representation. In this regard, the study is one of the first approaches to allow for a direct comparison of LESs to measurements for a period longer than several days. Furthermore, the study can serve as a basis for understanding the role of the mesoscale by comparing results of LES in a limited-area setup (where, for example, orography and surface heterogeneity are considered, as in ) with the LESs in the semi-idealized setup presented here.

To asses how representative and robust the results of the present study are, two strategies are followed. One strategy is to use two well-established LES models instead of just one. Applying two LES models provides a measure for the variability among the LESs – comparable to assessing observations of one quantity from multiple sensors. The other strategy is to study how the results depend on details of the setup. As the long-term LES approach relies on prescribing larger-scale forcing it is important to know how sensitive the LES results are with respect to details of the forcing like the calculation of the larger-scale advective tendencies from the mesoscale model or the relaxation (nudging) to the mesoscale model. Furthermore, this gives us the opportunity to assess the extent to which mesoscale variability plays a role in determining boundary layer characteristics.

This study also has some relevance for using 3-D LESs in the form of a superparameterization in large-scale (global) models as proposed by . In this approach, an LES model is embedded in each column of the large-scale model with horizontal grid lengths of the order of 10–50 km to account for an improved representation of small-scale processes in global models. In each global model grid box, one LES runs on a separate core of a massive parallel computer and communicates with the global model by exchanging only mean profiles during the simulation. The long-term LES approach under investigation would be representative for the superparameterization of one global model grid box.

Note that the LES statistics in this semi-idealized setup with prescribed forcing can only provide a mean over a certain representative area. The measurements, however, are exposed to spatial variability, and a point measurement at a certain location is only a local sample. As measurements from all available HOPE-sites are used for the comparison between the LESs and observations, a certain degree of variability can be expected in the measurements and compared to LESs. In this sense we expect that a fair comparison between observations and the LESs is possible and that the measurements inform what should be expected to be seen in the representative LESs.

The paper is organized as follows. Section  provides a description of the LES models applied and of the setup. The relative importance of the larger-scale forcing terms is also assessed. Section  gives an overview of the measurement campaign HOPE and of the observations used in this study. In Sect.  the 19-day reference simulation is analyzed. First (Sect. ), the temporal evolution of key boundary layer quantities is discussed. Next (Sect. ), vertical profiles of second-moment turbulent quantities for a cloud-free and a shallow-cumulus case are compared with profiles obtained from lidar. In Sect. , the results of various sensitivity runs are presented. Summary and conclusions are presented in Sect. .

HOPE took place near Jülich (located in the western part of Germany) in April and May 2013. The agricultural area around the permanent observational site JOYCE Jülich Observatory for Cloud Evolution (JO) at 50.907∘ N, 6.414∘ E, 111 m a.m.a.l.; was chosen to employ various in situ and remote sensing instruments to capture a most complete set of atmospheric parameters at a high temporal and spatial resolution. JOYCE was complemented by two additional measurement sites, LACROS Leipzig Aerosol and Cloud Remote Observations System (LA) at 50.880∘ N, 6.415∘ E, 99 m a.m.s.l.; and the KITcube Karlsruhe advanced mobile observation platform (Kc) at 50.897∘ N, 6.464∘ N, 110 m a.m.s.l.; during the HOPE period. The locations of the three sites and Jülich are shown in Fig. . Additional surface flux measurements used in this study were obtained at the Kc site Wasserwerk and the three TERENO TERrestrial Network of Observations, TER; sites Selhausen, Ruraue and Niederzier (see Fig. b), where energy balance stations were located. Within a 50 km × 50 km domain centered around JOYCE, the Eifel mountain range is located southwest of the HOPE domain (see Fig. a). The most significant orographic element in the area around the HOPE sites is the Sophienhöhe (which can be seen in the upper right part of Fig. b) with a maximum altitude of 301 m a.m.s.l. This element results from an open-pit mine located east of Sophienhöhe. The measurements during HOPE were taken by a multitude of instruments, such as Doppler lidars, Raman lidars, differential absorption lidar, ceilometers, microwave radiometers, cloud Doppler radars, meteorological towers, eddy-covariance stations and radiosondes. However, only a selection of these measurements are actually used in this study, as the main emphasis is put on boundary layer characteristics and turbulence.

The 19-day period from 24 April to 12 May 2013 was chosen for the following reasons. This period contains different weather regimes (clear-sky, convective, cloudy, frontal and post-frontal situations). Furthermore, during this time span 7 of the 18 conducted intensive observation periods (IOPs) in which the temporal coverage of measurements was higher (e.g., radiosondes were launched every 2 h during the daytime) took place. Moreover, it covers the passage of a frontal system, i.e., an event that is strongly controlled by fast-changing larger-scale flow conditions. The frontal passage allows the study of how the LES models react to such forcings. The selected period is too short for a feasible statistical analysis as conducted by , but it is long enough to showcase and analyze the general capability of performing long-term LESs.

The synoptic conditions during the 19-day period can be grouped into four different periods. During the first 2 days (24–25 April) high pressure dominated the HOPE area, resulting in a calm, clear sky (24 April) and a shallow-cumulus (25 April) day. On 26 April the situation changed noticeably as a frontal system passed from the northwest over the HOPE domain, accompanied by an overcast, rainy situation and followed by 3 days (27–29 April) under post-frontal, overcast conditions where temperatures were significantly lower than before. The third period covering 30 April to 6 May was characterized by a calm, high-pressure period with mostly low- to mid-level convective clouds (where 3 and 4 May were even clear-sky days). The last period began on 7 May with strong convective events (local thunderstorms). The following days were determined by local troughs of low-pressure systems forming over England, resulting in a rough and predominantly wet period with westerly gusts up to 14 m s-1. In terms of clouds, this evolution is also apparent in Fig. a, which displays the Cloudnet target classifications at the LACROS site.

To obtain a first visual impression of the LES data sets, snapshots of 4 different days (one out of each of the four weather periods previously described) of the PALM reference simulation RP are compared with images from the total sky imager TSI-880 at the JOYCE site. Additionally, horizontally averaged mean profiles of potential temperature θ, mixing ratio qv from PALM and radiosondes launched at 11:00 UTC at the KITcube site, together with simulated cloud (qc) and rain (qr) water mixing ratios (if present), are shown in Fig. . The snapshots were taken at 11:00 UTC on each day corresponding to the launch time of the radiosondes. The visualization of simulated cloud fields, which was performed with the Visualization and Analysis Platform for Ocean, Atmosphere, and Solar Researchers VAPOR;, allows for a first impression about the diversity of weather conditions encountered in the simulations.

Visually comparing sky imager and volume-rendered cloud fields of the 4 days (left and middle columns of Fig. ), it can be noted that the simulated cloud types agree qualitatively with the observed ones. The three-layer vertical structure in the boundary layer on 24 April is principally reproduced by PALM (Fig. c). However, the potential temperature is about 2 K lower than measured in the well-mixed layer and up to 1 K lower above. On 26 April, the day when the front passes the HOPE region, a significant number of clouds and amount of precipitation are simulated at 11:00 UTC (Fig. f). The temperature profile of PALM is reproduced very well. However, PALM simulates a well-mixed humidity layer below 1.5 km, which is not seen in the sounding. Similar to 24 April, the boundary layer and lower tropospheric layer are about 1 to 2 K colder than observed on 5 May (Fig. i) and also on 10 May (Fig. l). The vertical structure is reproduced well on both later days.

To study how robust the previously discussed results are with respect to the chosen setup, the reference simulations RP and RU were complemented by 14 additional simulations with PALM. Table  lists the simulations with their differences in the setups relative to the setup RP and RU, which was described in Sect. . Most of these additional simulations were run on a smaller horizontal domain (4.8 × 4.8 km2 instead of 48 × 48 km2, denoted with a capital S in Table ) and for the first 3 days only (24–26 April) for the sake of computational resources. Note that RP and RU ran on 2000 cores for around 7 and 10 days, respectively. The period 24–26 April was chosen as it contains three different boundary layer states (clear sky, shallow clouds and frontal passage) in a row, being a condensed representative of the longer period.

To compare all the experiments, a metric based on the boundary layer depth (see Fig. ) is constructed. As zi is a central quantity for evaluating mean boundary layer characteristics, it is chosen as a basis for the metric. For each available value, the absolute difference in boundary layer depth of PALM between the host model COSMO, the aerosol lidar Polly and the wind lidar HALO, respectively, are calculated. Then, an average over the number of available daily time spans from 12:00 to 14:00 UTC (either 19 or 3 depending on the case) is taken and the standard deviation is provided accordingly. This metric is called mean peak difference to PALM in the following. A daily averaging time span of 2 h (12:00–14:00 UTC) was chosen to consider the state of a well-developed boundary layer in a quasi-steady period. Figure  shows the mean peak difference in boundary layer depth to PALM for all the additional simulations. At a first glance it can be noted that the mean peak differences to PALM of COSMO, Polly and HALO show the same behavior in most cases. The metric based on the wind lidar HALO usually shows the highest and positive values, meaning that the peak boundary layer depth of PALM is usually higher than the one measured by HALO.

Comparing the 19-day reference simulation RP with the 19-day simulation RPS, which was conducted on the small horizontal domain, we note that the domain size has virtually no effect on the mean peak difference to PALM (Fig. a, comparing cases RP and RPS , 19d). Thus, robust first-order statistics are gained even in case the domain size is significantly smaller than in the reference case. This finding suggests that the mesoscale circulations that can develop internally on a 50 km × 50 km domain without orography and surface heterogeneity are not particularly important.

A fundamental parameter of the larger-scale forcing method is the averaging domain size for the applied forcing data LCOSMO, specified in degrees on the geographical grid (see also Appendix ). For the reference runs RP and RU, a size of LCOSMO = 2.0∘ was used. To evaluate whether the size of the averaging box is appropriate to represent larger-scale processes, the simulations F0.25, F0.5, F1.0, F3.0 and F4.0 (see Table ) were conducted, where the COSMO averaging domain sizes varied from 0.25 to 4.0∘, which corresponds to horizontal extensions Dx × Dy of 17.5 × 27.8 to 280 × 444 km2 being equivalent to averaging over 10 × 10 to 160 × 160 COSMO grid points. The averaging domain size of the COSMO forcing has a large impact on the boundary layer depth as can be seen in Fig. b. Especially the two smallest averaging domain sizes produce large discrepancies in peak boundary layer depth to the estimates of zi stemming from Polly and HALO lidar. Thus, as the averaging area gets small, more mesoscale flows, which COSMO does not necessarily represent well, are sampled. Nonetheless, mean boundary layer characteristics become less sensitive if a 2.0∘ or larger averaging domain size is used. Cloud structures and precipitation depend more strongly on the averaging domain size of the forcing (not shown). Overall, the averaging domain should have a size that is large enough to not include mesoscale fluctuations on the one side and that is small enough to still account for a localized, representative area like the HOPE region.

The temporal resolution of the forcing data is 3 h, which also includes the prescribed surface temperature and humidity and via Monin–Obukhov similarity theory the surface fluxes. However, boundary layer timescales are usually much shorter (the turnover timescale is about 10 min around noon for the presented period). As the simulations are strongly determined by the imposed surface fluxes, the question of whether prescribing new surface values every 3 h is too infrequent to impose the signal of a proper diurnal cycle was posed. Thus, the simulation TR1 was performed, where forcing data with a temporal resolution of 1 h were used. As the larger-scale horizontal and vertical advective forcing act on larger timescales than the surface forcing, a higher temporal resolution should affect the surface fluxes most. Comparing the cases RPS (3d) and TR1 shown in Fig. a, it can be noticed that the metrics are nearly identical. The higher temporal resolution seems to bring no additional value. Hence, it is concluded that a 3-hourly forcing data set is sufficient to impose a proper diurnal cycle in the simulations.

As nudging (Newtonian relaxation) does not represent a real physical process , it was analyzed how crucially the results depend on the nudging timescale and on the nudging itself. Three additional simulations were performed where a stronger nudging with τ = 1 h (case N1), a weaker nudging with τ = 12 h (case N12) and no nudging at all (τ → ∞, case Nno) compared to the reference nudging timescale of 6 h were used. The simulation without nudging can also be interpreted as a simulation where the radiative forcing is completely switched off as the effect of radiation is indirectly mimicked via the relaxation (see Sect. ). The mean peak difference to PALM (Fig. c) shows only a weak dependence for τ ≤ 12 h. In the case where Newtonian relaxation is completely turned off, the mean peak difference to PALM increases strongly. In this case PALM strongly overestimates the boundary layer depth compared to the forcing and the observations. The overall performance of the simulation becomes worse. This analysis shows that using nudging with reasonable nudging timescales of several hours is beneficial for the long-term LES framework. Furthermore, the mean boundary layer characteristics barely depend on the actual choice of the nudging timescale supporting the robustness of the setup.

To test the impact of the individual larger-scale forcing components, several tests were made in which the forcing components were mutually switched off and then added one after the other (not shown). These tests suggested that all components should be used in combination for obtaining the best results with respect to the observations. This is in agreement with the single-column model study of , where they studied the realistic simulation of clear-sky stable boundary layers over snow-covered surfaces.

In the reference setup, Dirichlet conditions are used at the surface, meaning that potential temperature and mixing ratio are prescribed at the surface. The alternative is to prescribe surface fluxes directly (using Neumann boundary conditions). The latter was used in the case of FLX. Overall, the prescribed surface fluxes are slightly smaller and show a time lag in respect to the fluxes that are calculated in the case of RPS (19d) (not shown). Comparing the cases RPS (19d) and FLX concerning the mean peak difference to PALM (Fig. a), it can be seen that the metric for COSMO changes only marginally and that the metric for Polly deteriorates, whereas the metric for HALO improves. Also taking the arguments of into account that for modeling stable boundary layers prescribing surface fluxes should be avoided, we think prescribing surface values is the better option, as during the multiple-day LES stable regimes that we conducted and simulated to a considerable fraction.

To evaluate the influence of the numerical grid spacing, the 3-day simulation RPS (3d) with an isotropic grid spacing Δ = 50 m was rerun using two finer grid spacings (Δ = 25 m called RPS25 and Δ = 12.5 m called RPS12.5) and one coarser grid spacing (Δ = 100 m called RPS100). Only minor differences were observed between the runs in the time series of the boundary layer depth, which mainly occur during nighttime. This indicates that the differences between the runs are closely linked to their different capabilities of resolving the shallow stable boundary layer at night. The influence on the better resolved nighttime stable boundary layer on the following convective day is rather small as already showed. The simulated clouds also do not show any dependence on the grid spacing. Figure d shows that the influence of the grid spacing on mean boundary layer characteristics is negligible in terms of the mean peak difference metric.

In this study long-term LESs with PALM and UCLA-LES are evaluated to assess the ability of LES in a semi-idealized setup to simulate observed characteristics of boundary layer turbulence. The semi-idealized approach consists of using periodic lateral boundary conditions and a homogeneous surface together with prescribing time-dependent larger-scale forcing and nudging deduced from the mesoscale numerical weather prediction model COSMO to account for the synoptic conditions at a specific location. A continuous period of 19 days of the HOPE measurement campaign is chosen and the simulation results are compared to the multi-sensor HOPE data set. The three principal measurement sites of HOPE enable a more representative view on the larger observational area. This circumstance facilitates the comparison to the LES, which, by construction, can only deliver a flow that is representative for the HOPE region. The analysis focuses on key boundary layer quantities like the boundary layer depth, near-surface temperatures and winds, integrated quantities like IWV and LWP, and turbulence statistics in terms of variance profiles. A metric based on the peak boundary layer depth is used to compare several sensitivity runs. With these additional simulations the robustness of the reference setup is investigated.

The (unphysical) nudging tendency, which prevents model drift in time, is generally less important compared to larger-scale horizontal and vertical advective tendencies. The exceptions are cases with strong larger-scale forcing; then the nudging tendencies can be significant.

The reference simulation shows reasonable agreement with the HOPE measurements. The principal character of the day (weather situation) can be reproduced by the LES in about 80 % of the cases. Simulating cloud-topped boundary layers correctly is a challenge for the long-term LES. The daily development of the boundary layer depth is in principal agreement with lidar measurements. The LES surface fluxes are in a rough agreement with the weighted, averaged surface fluxes in the HOPE area showing that the surface forcing is representative for the HOPE area. Both LES models used produce very similar results.

The LES models seem to track COSMO closely and deviate from the observations in a similar fashion as COSMO does. This can be interpreted in two ways. Either deviations from the observations are inherited from the host model or they represent the signature of mesoscale forcing that the present approach is incapable of capturing. By using LES in a more realistic setup with open boundary conditions, these hypotheses might be tested.

LES turbulence statistics in terms of variance profiles are in satisfactory agreement with lidar measurements during HOPE. The peak in scalar variances at the top of the boundary layer is underestimated by LES, indicating that presumably the resolution used in the LES is rather coarse for correctly representing strong gradients and that heterogeneity is missing.

The chosen semi-idealized setup is insensitive to the horizontal domain size, the grid spacing, the temporal resolution of the forcing data and the surface boundary condition in terms of mean boundary layer characteristics. Thus, the internally generated mesoscale circulation on a larger domain is not particularly important and the character of the biases is not strongly dependent on the model or how the forcing is applied. There is a dependence on the averaging size of the forcing data. If the averaging domain is large enough and mesoscale fluctuations are sufficiently filtered out, the results converge. Using nudging itself to prevent model drift in time is important. The actual value for the relaxation timescale is of minor importance provided that it is of the order of several hours.

As the semi-idealized setup stably represents a wide range of observed weather situations, it is also applicable as superparameterization in a global model. It would be interesting to study how the overall performance of a global model with superparameterization depends on the chosen grid size, which is tied to the horizontal domain size of the imbedded LES. As the LESs obtain mean forcing profiles from the global model, the overall domain size from which the forcing is constructed might play a role as the semi-idealized setup depends on the averaging size of the forcing data.

The long-term LES approach cannot only be used to simulate periods at meteorological super sites like in but also for simulating periods of (or even whole) measurement campaigns to support the interpretation of measurement results. This approach has been adopted for the Next-generation Aircraft Remote Sensing for Validation (NARVAL) series of flight campaigns over the tropical Atlantic and is being followed in the LES ARM Symbiotic Simulation and Observation (LASSO) project (http://www.arm.gov/science/themes/lasso), where continuous LES of the southern Great Plains atmospheric radiation measurement (ARM) super site are under development.

One strength of the semi-idealized approach is that it is able to deliver robust turbulence statistics and a good representation of clouds, as is typical for LES, and that it accounts for a localized area responding to everyday weather. However, a certain variability coming from the heterogeneous surface that usually surrounds any real observational site is neglected in the LES. The semi-idealized long-term LES approach can also be seen as an intermediate step towards LES in a limited-area setup, where, for example, a land-surface model and interactive radiation are used. In the framework of HD(CP)2, these kinds of simulations are performed over Germany. They are compared to the semi-idealized simulations presented here and the HOPE data set in . Comparing LES in semi-idealized and limited-area setups also allows the quantification of the role of the mesoscale.