In this paper, we present a newly developed mesoscale nesting interface for the PALM model system 6.0, which enables PALM to simulate the atmospheric boundary layer under spatially heterogeneous and non-stationary synoptic conditions. The implemented nesting interface, which is currently tailored to the mesoscale model COSMO, consists of two major parts: (i) the preprocessor INIFOR (initialization and forcing), which provides initial and time-dependent boundary conditions from mesoscale model output, and (ii) PALM's internal routines for reading the provided forcing data and superimposing synthetic turbulence to accelerate the transition to a fully developed turbulent atmospheric boundary layer.

We describe in detail the conversion between the sets of prognostic variables, transformations between model coordinate systems, as well as data interpolation onto PALM's grid, which are carried out by INIFOR. Furthermore, we describe PALM's internal usage of the provided forcing data, which, besides the temporal interpolation of boundary conditions and removal of any residual divergence, includes the generation of stability-dependent synthetic turbulence at the inflow boundaries in order to accelerate the transition from the turbulence-free mesoscale solution to a resolved turbulent flow. We demonstrate and evaluate the nesting interface by means of a semi-idealized benchmark case. We carried out a large-eddy simulation (LES) of an evolving convective boundary layer on a clear-sky spring day. Besides verifying that changes in the inflow conditions enter into and successively propagate through the PALM domain, we focus our analysis on the effectiveness of the synthetic turbulence generation. By analysing various turbulence statistics, we show that the inflow in the present case is fully adjusted after having propagated for about two to three eddy-turnover times downstream, which corresponds well to other state-of-the-art methods for turbulence generation. Furthermore, we observe that numerical artefacts in the form of grid-scale convective structures in the mesoscale model enter the PALM domain, biasing the location of the turbulent up- and downdrafts in the LES.

With these findings presented, we aim to verify the mesoscale nesting approach implemented in PALM, point out specific shortcomings, and build a baseline for future improvements and developments.

The simulation of urban flows under realistic conditions poses a multiscale problem where evolving synoptic scales interact with building- and street-size scales. While the continuing growth of available computational resources enables large-eddy simulation (LES) to be applied to more and more realistic scenarios at regional scales

Both approaches face particular challenges, mainly linked to the representation of the turbulent flow at the domain boundaries, requiring large buffer zones to move boundary effects away from the region of interest. In the first approach, periodic domain boundaries allow unrealistic flow feedbacks due to re-entering flow structures caused by complex terrain, urban surfaces, or other surface heterogeneity.
Furthermore, feedbacks are not limited to the velocity field. When anthropogenic heat or chemical compounds are emitted, unrealistic thermodynamic conditions or concentrations would re-enter the model domain on the opposite boundary modifying the upstream conditions for the urban environment, which in turn may bias the distribution of heat and mass concentrations.
Here, buffer zones help to move the affected flow region outwards

Alternatively, grid-nesting approaches can be employed, which realize a one-way coupling via time-dependent inflow and outflow boundary conditions derived from a larger-scale parent model. In mesoscale models with horizontal grid spacings on the order of

To reduce the required fetch length, various approaches to generate turbulent inflow conditions exist; for a comprehensive overview about existing methods, we refer to

In contrast to recycling methods, volume-forcing approaches do not necessarily require homogeneous inflow conditions.
To accelerate the spatial development of a turbulent flow,

Alternatives to volume-forcing approaches are so-called filtering approaches, where spatially and temporally correlated perturbations are imposed only onto the velocity components at the lateral boundaries

Beside the necessity to add perturbations at the boundaries, modellers should also be aware that numerical artefacts from the mesoscale model may propagate into the LES; e.g.

Another issue that emerges when nesting LES in mesoscale models concerns the representation of the atmospheric boundary layer. Due to different treatment of turbulent transport, i.e. boundary-layer parameterizations in the mesoscale model vs. an explicit representation of turbulent eddies in the LES model, the vertical transport of energy, water, and momentum may differ considerably. In situations where this is the case, the mean state of the LES solution, which is generally more credible due to a wider range of explicitly resolved turbulent scales, will be pushed towards the mesoscale solution including any possible model biases.

In this paper, we present the mesoscale nesting interface of the PALM 6.0 model system. It provides time-dependent spatially heterogeneous boundary conditions for PALM obtained from the mesoscale model COSMO

This approach provides a one-way nesting capability of PALM into a mesoscale simulation, where boundary conditions are only set for child model. At this point, we want to distinguish the mesoscale nesting interface from PALM's self nesting capabilities

This paper is structured as follows. We describe the mesoscale nesting approach in Sect.

INIFOR's input and output variables. INIFOR supplies initial and boundary conditions for the variables marked with

Simulation workflow using PALM's mesoscale nesting interface.

Model differences between COSMO and PALM. PBL is the planetary boundary layer. RANS stands for Reynolds-averaged Navier–Stokes equations.

The PALM model is nested into the mesoscale model by prescribing initial conditions and time-dependent Dirichlet boundary conditions derived from output of the parent mesoscale model. Boundary conditions for PALM are given for the top and lateral domain boundaries. The boundary conditions at the surface are provided by PALM's urban- and land-surface model, which are initialized from the mesoscale data.

The boundary conditions enter PALM via the mesoscale nesting interface, which consists of two major components: (i) the preprocessor INIFOR and (ii) PALM's internal boundary condition routines. The workflow of a model run using the mesoscale nesting interface is illustrated in Fig.

The required prognostic variables for which the dynamic driver provides initial and boundary conditions are listed in Table

Hence, we recommend to run the soil-model spinup mechanism as described in

In addition to the initial state, the dynamic driver provides the time-dependent boundary conditions for PALM's atmospheric prognostic variables

The velocity boundary conditions and the associated mass-flux fields obtained from a compressible mesoscale model such as COSMO do not generally satisfy the divergence-free condition of incompressible models such as PALM.
To overcome this, we correct the velocity

We do not currently use any damping zones near the lateral boundaries to relax the solution towards the boundary conditions as is done, for instance, in the WRF model. There, a relaxation term according to

Example PALM domain (blue) for Berlin nested within the DWD COSMO configurations (green). Panel

Coordinate systems and grid indices.

In the following, we describe the relevant model properties and point out the relevant differences, which yield the conceptual steps that need to be carried out by INIFOR. Here, we omit in-depth descriptions of both models and refer the reader to additional publications. In particular, more information about the formulation and numerics of COSMO can be found in the model documentation by

PALM and COSMO differ in a number of ways, between which INIFOR needs to translate in order to derive PALM forcing data. The first difference lies in the physical formulation of the models. COSMO is a non-hydrostatic limited-area atmospheric model. It is based on fully compressible equations, which are formulated in terms of the three spherical wind components, absolute temperature and pressure, density, and multiple water phases. PALM, on the other hand, solves incompressible equations for the moist atmosphere, where either the Boussinesq or an anelastic limit of the Navier–Stokes equations may be used. The model is formulated in terms of the three Cartesian wind components, the potential temperature, and the water vapour mixing ratio. The continuity equation in the anelastic and Boussinesq approximations reduces to divergence constraint

Secondly, due to their different domain extents, both models use different approximations of Earth's surface and, as a result, use different coordinate systems. COSMO represents the planet as a perfect sphere with radius

Lastly, COSMO and PALM use different numerical grids which require interpolation. Both models discretize their respective governing equations on structured grids aligned with their respective coordinate axes and equidistant horizontal spacings – in the case of COSMO equidistant in rotated latitudes and longitudes, and in the case of PALM equidistant in Euclidean length. Both are based on the Arakawa-C-type grid structure, where scalars are defined at the mass points at the cell centre and velocity components are staggered one half grid cell. In the vertical, both models allow for grid stretching. COSMO uses a hybrid

Coordinate systems used in INIFOR. The PALM grid coordinates are first projected onto the PALM rotated-pole system (see Eq.

Currently, INIFOR is designed to process model output of DWD's current operational configuration COSMO-D2

PALM and COSMO differ in their physical formulation, i.e. their prognostic and available output variables, the representation of Earth's surface, the coordinate systems, and the structure and resolution of the numerical grids used. To translate those differences, INIFOR needs to carry out the following conceptual steps:

convert between the sets of prognostic variables (see Table

project PALM's Cartesian domain onto COSMO's spherical Earth,

transform PALM's projected Cartesian coordinates to COSMO's rotated-pole system, and

interpolate COSMO data onto PALM's grid in the COSMO rotated-pole system.

Note that the data interpolation could be carried out in different coordinate systems. With INIFOR, we decided to interpolate in COSMO's rotated-pole system where the required interpolation neighbours are located on a rectangular grid leading to simple and efficient interpolation rules. We obtain the COSMO coordinates for the PALM grid points using a two-step transformation as shown in Fig.

Schematic comparison of direct spherical-to-Cartesian transformation

Horizontal

Diagram of INIFOR's program flow.

Differences in the model formulations require conversions between the sets of prognostic equations. In our case, this includes the computation of the potential temperature and the volumetric soil moisture. INIFOR converts both quantities before interpolating them onto the PALM grid.

As for the air temperature preprocessing, INIFOR replaces the absolute temperature

For soil data, preprocessing is slightly more involved because on sea or inland water cells, COSMO's soil data are not defined. Due to the coarser grid resolution, shorelines or inland lakes do not necessarily correspond to the high-resolution surface input required by PALM. In order to provide soil data at each PALM grid point, the missing information is iteratively generated by horizontal averaging of soil data from neighbouring land cells. Every iteration of this procedure generates new virtual land cells. By repeating this procedure using both the original and newly generated virtual cells, the virtual shoreline moves one COSMO cell per iteration. This procedure is currently repeated five times, before the field is used for interpolation.
After the data extrapolation on the COSMO grid, the units of COSMO's soil moisture are converted to PALM's formulation. COSMO provides soil moisture as vertically integrated water density, while PALM requires the volumetric water content. The conversion is given by

There are multiple ways as to how the differences in the representation of Earth's surface can be resolved. Two options are illustrated in Fig.

In particular, we use an inverse plate carrée projection which linearly maps between the Cartesian coordinates

When transforming the PALM to the COSMO rotated-pole coordinates, we consider the PALM system a rotated-pole system relative to the COSMO rotated-pole system, the same way the COSMO system is a rotated-pole system relative to the geographical system. Because, as we discuss below, the definition and evaluation of the transformation from PALM's to COSMO's coordinates involves forward and backward transformations between rotated systems, we begin with the general forward and backward transformations. The forward transformation from a geographical (

The definition of the PALM rotated-pole system starts with the specification of its origin in terms of its geographical coordinates (

Finally, the PALM domain may generally be shifted a.s.l. by specifying a non-zero domain base

Having the COSMO rotated-pole coordinates for each PALM grid point available, we can interpolate COSMO fields by locating the appropriate interpolation neighbours and by computing the corresponding interpolation weights. We use the coordinate symbols laid out in Table

Using this convention, a general interpolation scheme for an arbitrary scalar

In the case of bilinear interpolation, Eq. (

Using the location of the neighbour grid points, we can compute the corresponding bilinear interpolation weights based on the nondimensional coordinates:

The interpolation in three dimensions is split in two steps in INIFOR: (i) a bilinear horizontal interpolation onto an intermediate grid and (ii) a linear vertical interpolation in each of its columns. The intermediate grid, hereafter indicated by an overbar, shares PALM's fine horizontal grid but features COSMO's coarser vertical levels
(see Fig.

The transformation in Eqs. (

INIFOR provides the option to initialize and force PALM with three-dimensional atmospheric data (LOD

Concretely, this is done carrying out the following steps. We first define the averaging region as a horizontal box bounded by the minimum and maximum rotated longitude and latitude of the PALM domain. Once all COSMO columns in the region are identified, we compute the average vertical grid levels of the terrain-following COSMO grid and then compute the vertical neighbours and weights for every PALM level relative to the averaged COSMO levels. The average profile (denoted in the following by the double bar) is then formed by scanning through the

INIFOR's program structure is organized around the set of netCDF variables that are to be computed for the dynamic driver. The dynamic driver contains individual netCDF variables for each combination of prognostic variable and model boundary, e.g. netCDF variables for the

This is reflected in INIFOR's program flow, which is depicted in Fig.

As input data, INIFOR reads hourly netCDF files containing COSMO analyses. Each hourly input is processed separately and translated into one instantaneous boundary condition in the dynamic driver. Input data are not interpolated temporally in INIFOR but rather in PALM during the simulation as described in Sect.

With the generation of time-dependent boundary conditions from mesoscale model output in a preprocessing step and online processing of the boundary data, PALM is enabled to simulate more realistic scenarios considering time-evolving synoptic conditions. However, due to the nature of RANS models, turbulence is parameterized and thus the boundary values are free of any turbulent fluctuations.

To obtain turbulent flow components

Depending on characteristic length scales

From a mathematical point of view, the imposed fluctuations should have zero mean.
Due to a finite sample of random numbers and the finite number of discrete grid points, however, the fluctuations have mean values slightly different from zero in practice.
In order to overcome this,

For non-stationary flows, an inflow boundary can become an outflow boundary, and vice versa.
Hence, the turbulence generator is applied at each lateral boundary simultaneously, while at opposite boundaries (west and east, as well as north and south) we use the same

From Eq. (

The random numbers

In order to create time- and height-dependent synthetic turbulence, respective information about the Reynolds stresses, as well as turbulent length scales and timescales for the velocity components are required. For stationary flows, this information can be deduced from observations or from cyclic precursor simulations

In contrast to

Note that Eqs. (

Further, the synthetic turbulence generation requires information about the turbulent length scales and timescales.
The turbulent timescale of the flow is estimated according to

Assuming that turbulence is only present within the boundary layer,

In the case of non-stationary flows, the turbulence parameters

COSMO-derived vertical profiles of

Variances of the velocity components:

Vertical profiles of potential temperature prescribed at the inflow boundary as well as within the inner part of the domain where the flow has been spatially fully developed. Profiles are shown for simulation REF (green) as well as for a test simulation PSF (grey) with prescribed surface heat fluxes obtain from COSMO. Profiles are shown for

In order to test the implemented mesoscale nesting approach, we selected a particular weather scenario with a developing daytime convective boundary layer (CBL) that features advective conditions with moderate wind speeds and changing mean-wind direction. Moreover, the scenario is characterized by little to no cloud cover which is attributed to the fact that PALM cannot capture high-altitude clouds yet (due to missing ice-phase physics, planned) and thus cannot realistically reproduce the prevailing radiative forcing.
We simulated one diurnal cycle of the evolving CBL starting at 00:00

The simulated domain is located at 52.5

We performed two simulations with different lateral boundary conditions.
In the first simulation, hereafter referred to as REF, the boundary conditions were given as LOD

Hence, we calculated resolved-scale variances of the velocity components by

Please note that in this study we will mainly focus on convective conditions, especially with respect to the spatial development of the flow. The nighttime stable flow is only poorly resolved at the given grid spacing, making it difficult to make reliable conclusions concerning the flow adjustment. Here, we will refer to follow-up studies.

In the following section, we show results from a mesoscale nested LES for a diurnal cycle. In order to better guide the reader through this section, we will first give a short outline of what to expect. First, we describe the boundary-layer structure and its development over the diurnal cycle in the LES as well as in COSMO. Subsequently, we discuss differences between the LES and COSMO with respect to the boundary-layer representation and its implications in a nested simulation. In the following, triggered by imposed time-dependent synthetic turbulence, we focus on the spatial development of the turbulent flow within the LES domain and determine adjustment lengths where the turbulent flow is fully developed. In addition, we present results on how roll-like structures emerging in the COSMO simulation propagate into the LES. Moreover, we discuss implications near the LES domain inflow and outflow boundaries. Finally, we look at a more technical issue and demonstrate the computational efficiency of the synthetic turbulence generation.

Time series of surface net radiation

Instantaneous

Horizontal cross-sections of the instantaneous vertical velocity component at

Parameterized components of the Reynolds-stress tensor as well as turbulent length scales at different points in time. In panels

Figure

Figure

Figure

In addition, we performed a simulation where we prescribed the diurnal cycles of

As the COSMO profiles are mapped onto the inflow boundary, the more rapid evolution or the earlier stabilization of the boundary layer at 10:00 and 16:00

The temporal change in inflow conditions can also be observed visually in the vertical velocity shown in Fig.

The parameterized Reynolds-stress components depend on the inflow profiles obtained from the mesoscale model input, i.e.

Figure

In summary, the parameterized Reynolds stresses resemble the variances profiles created by the LES itself reasonably well during the course of the day. However, we emphasize that the imposed turbulence is only considered to be a rough description to resemble the second-order statistics of a fully adjusted flow, while its spectral distribution or higher-order moments are not accounted for.

Horizontal profiles of 30

Horizontal profiles of 30

Horizontal profiles of 30

Horizontal profile of 30

Scaling parameters at 13:00

Horizontal cross-sections of the instantaneous vertical velocity component (

Horizontal cross-section of 30

Consumed CPU time by the synthetic turbulence generator for different turbulent length scales. The constantly prescribed length scale is normalized by the isotropic grid spacing. The left ordinate (black lines) shows the absolute consumed CPU time by the synthetic turbulence generator, while the right ordinate (red lines) shows the relative contribution with respect to the consumed CPU time spent for the time stepping (i.e. without initialization, data output, and finalization).

Figure

At 16:00

In order to investigate how the structure of the turbulent flow develops, Fig.

To investigate of how fast land–atmosphere interactions adjust, Fig.

Finally, we would like to note that we also simulated different scenarios with higher (2UH) and lower (05UH) wind speeds, as well as with increased (15RS) and reduced (075RS) shortwave solar radiation, in order to test the convective scaling. Even though the peak amplitudes in the horizontal TKE profile are different due to the modified forcing (see Fig.

Summarized, under convective conditions, the turbulent flow is fully developed within the boundary layer after about

Figure

In this section, we focus on the flow near the inflow and outflow boundaries.
Due to different model representations of surface processes and different surface input data, the mesoscale near-surface wind and temperature profiles can deviate from the one the LES would simulate. As an example, Fig.

With respect to the mesoscale nesting, the generation of synthetic turbulence represents the computationally most expensive part, while setting the boundary conditions and enforcing a divergence flow field is computationally much less expensive. In order to examine the efficiency of the turbulence generator implementation and estimate its computational cost, we have carried out a performance test.

The most expensive part of the turbulence generation is the computation of the filtered random numbers – see Eqs. (

Finally, we note that for the simulation covering an entire diurnal cycle, the length scales vary significantly with lower values during nighttime and larger values around noon. For these simulations, the turbulence generation consumed about 2.5

In this paper, we presented a mesoscale nesting interface for the PALM 6.0 model system that extends PALM's capabilities to simulate atmospheric boundary layers under evolving synoptic conditions.
The mesoscale nesting interface, which currently relies on output of the COSMO model, consists of two components: (i) the preprocessing interpolation tool INIFOR which provides initial and boundary conditions as a netCDF file, and (ii) PALM's internal boundary condition routines which read and process the initial and boundary conditions as well as imposed additional synthetically turbulent fluctuations. We described INIFOR's interpolation methodology in detail, beginning with the relevant model differences between PALM and COSMO, leading to the conceptual steps needed to interpolate COSMO model output onto the PALM grid.
Since the interpolated mesoscale boundary conditions are essentially free of turbulent fluctuations, the flow first needs to spatially develop before the turbulent transport of momentum, energy, and water can be analysed. In order to minimize the extent of development zones near the lateral inflow boundaries which the LES model would otherwise require to generate turbulence via shear and convective instabilities by itself

We demonstrated the nesting interface and the effectiveness of the synthetic turbulence generation using a semi-idealized benchmark case: we simulated a convective boundary layer developing near Berlin, Germany, on a clear-sky spring day using initial and boundary conditions derived from DWD's operational COSMO-DE analysis. For the sake of analysing the spatial development of the flow, the case was idealized in that we assumed flat terrain with homogeneous grassland instead of using more realistic land-surface heterogeneity, in order to disentangle turbulence built up due to the synthetic turbulence generation and convective and shear instabilities from effects of the particular surface heterogeneities of the Berlin area. We found that the flow rapidly develops up- and downdrafts, whereas the adjustment of the TKE takes a longer distance of about

In our benchmark case, the boundary layer in the mesoscale COSMO model does not develop synchronously with the boundary layer in the LES. For example, in COSMO, the boundary layer develops more rapidly before noon and the evening transition starts earlier compared to the LES simulation. As the signals due to non-synchronous boundary-layer development are imposed to the inflow boundary, these propagate through the LES domain creating a horizontally heterogeneous boundary layer during the morning and evening transition phase. Furthermore, we observed under-resolved convective rolls emerging in the mesoscale model that, similar to

Overall, especially the non-synchronous boundary-layer development and the imposed roll-like convection emphasize that the representation of the boundary layer in the LES and accompanied vertical gradients of wind velocity, potential temperature, etc. depend on the boundary-layer representation in the mesoscale model. Suppose the boundary layer is not well captured in the mesoscale model, e.g. due to misrepresented convection and turbulent mixing, cloud cover, or atmosphere–surface exchange; the boundary layer resolved in the LES will also be affected by this. In such cases, the physically more credible LES solution (with respect to the boundary-layer representation) will be continuously pushed towards the mesoscale solution. Here, further research is required to better understand the causes for such model discrepancies, under which circumstances they arise, and what the implications are for the representation of the turbulent boundary-layer flow.

Further branches of future development will be to enable INIFOR to also process WRF

The main focus of this study was to demonstrate the capability of the mesoscale nesting approach and to confirm the effectiveness of the synthetic turbulence generation to reduce the fetch length needed for the model to develop balanced turbulence characteristics. Dedicated evaluation runs of the PALM 6.0 model system including the mesoscale nesting interface are currently on their way within the project

As opposed to our comment in the PALM 6.0 overview paper

In incompressible formulations, the pressure solution is obtained by constructing and solving a Poisson-type equation which can be obtained by applying the divergence operator to the momentum equation. The equation is simplified by exploiting the incompressible continuity equation which represents a divergence constraint on the mass flux

The PALM model system 6.0 is freely available at

EK was responsible for conceptualization and development of INIFOR, writing parts of the manuscript, conceptualization of the study, analysis of the results; MS was responsible for conceptualization and implementation of mesoscale nesting into PALM, adaption of the synthetic turbulence generator, writing parts of the manuscript, conceptualization of the study, analysis of the results; TG was responsible for adaptation of synthetic turbulence generator and writing parts of the manuscript; SR was responsible for conceptualization of INIFOR and mesoscale nesting; all authors were responsible for revision of the manuscript.

The authors declare that they have no conflict of interest.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work is part of the [UC]

This research has been supported by the German Federal Ministry of Education and Research (Bundesministerium für Bildung und Forschung, BMBF) under grant no. 01LP1601.

This paper was edited by Xiaomeng Huang and reviewed by three anonymous referees.