The parameterised description of subgrid-scale processes in the clear and cloudy boundary layer has a strong impact on the performance skill in any numerical weather prediction (NWP) or climate model and is still a prime source of uncertainty. Yet, improvement of this parameterised description is hard because operational models are highly optimised and contain numerous compensating errors. Therefore, improvement of a single parameterised aspect of the boundary layer often results in an overall deterioration of the model as a whole. In this paper, we will describe a comprehensive integral revision of three parameterisation schemes in the High Resolution Local Area Modelling – Aire Limitée Adaptation dynamique Développement InterNational (HIRLAM-ALADIN) Research on Mesoscale Operational NWP In Europe – Applications of Research to Operations at Mesoscale (HARMONIE-AROME) model that together parameterise the boundary layer processes: the cloud scheme, the turbulence scheme, and the shallow cumulus convection scheme. One of the major motivations for this revision is the poor representation of low clouds in the current model cycle. The newly revised parametric descriptions provide an improved prediction not only of low clouds but also of precipitation. Both improvements can be related to a stronger accumulation of moisture under the atmospheric inversion. The three improved parameterisation schemes are included in a recent update of the HARMONIE-AROME configuration, but its description and the insights in the underlying physical processes are of more general interest as the schemes are based on commonly applied frameworks. Moreover, this work offers an interesting look behind the scenes of how parameterisation development requires an integral approach and a delicate balance between physical realism and pragmatism.

Due to ever-growing computer resources, numerical resolution of weather and climate models is steadily refined. Presently, limited area models operate routinely at resolutions of around 1 km and the first global intercomparison project for global storm-resolving models at resolutions of 5 km demonstrates that deep convective overturning processes are at least partly resolved by the new generation of weather and climate models

Prime atmospheric processes that remain to be parameterised at these scales are turbulent transport in the boundary layer, shallow cumulus convection, radiation, and cloud micro- and macrophysical processes of unresolved clouds. Traditionally, parameterisation of these processes has been developed as independent building blocks. The turbulence scheme describes the transport of heat, moisture, and momentum by the small-scale turbulent eddies in the boundary layer, whereas the convection scheme represents the transport by the larger-scale organised convective plumes. The cloud scheme aims to estimate the cloud fraction and the amount of condensed water.

Nowadays, it is recognised that the latter three parameterisation schemes need to be tightly coupled, as illustrated in Fig.

As stated by

The here-investigated parameterisations are part of the convection-permitting High Resolution Local Area Modelling – Aire Limitée Adaptation dynamique Développement InterNational (HIRLAM-ALADIN) Research on Mesoscale Operational NWP In Europe – Applications of Research to Operations at Mesoscale (HARMONIE-AROME) numerical weather prediction

The primary goal of these adjustments is to improve on what is considered one of the most important model deficiencies of HARMONIE-AROME cy40: a substantial underestimation of low cloud amount and overestimation of cloud base height.

The presented changes in the parameterisation schemes are primarily based on process studies and theoretical considerations. For example, long-term single-column model (SCM) runs are used to evaluate the turbulence scheme in terms of theoretical flux–gradient relationships, following the procedure of

This paper can be considered a description of a substantial model update concerning several parameterisation schemes. Although the parameterisations are embedded in the HARMONIE-AROME model, we believe that our findings are more generally applicable in numerical weather prediction (NWP) and climate models. Even though the schemes in other models may differ in details, the parameterisations in HARMONIE-AROME are based on widely applied frameworks: a statistical cloud scheme, a (bulk) mass flux convection scheme, and a turbulence kinetic energy (TKE)-based turbulence scheme. Hence, the here-described modifications and the impact of certain parameters, or combinations of them, are useful for any atmospheric model that requires a parameterised representation of the clear and cloudy boundary layer.

We start with a description of the convection, turbulence, and cloud scheme in Sect.

Before giving a more detailed description of the involved parameterisations in the next sections, we start by introducing the general parameterisation framework of the clear and cloud-topped boundary layer. The grid-box-averaged prognostic equations for the liquid water potential temperature

The turbulent fluxes are parameterised using the eddy-diffusivity mass flux (EDMF) framework

The remaining small-scale local turbulence is approximated by vertical diffusion by means of an eddy diffusivity (ED) approach:

There is a strong interplay between turbulence and convection (see Fig.

The last parameterisation involved in the modifications is the cloud scheme. The task of the cloud scheme is to estimate the subgrid-scale cloud fraction and the condensed water.
A common approach to calculate cloud cover and condensed water is to assume a subgrid-scale distribution of humidity and temperature and to determine the cloud cover as the fraction of the distribution above saturation. A key element in such a statistical cloud scheme is the estimate of the subgrid-scale variance of the relative humidity. Important contributions to this variance are the convective (Eq.

The specific parameterisation implementations in HARMONIE-AROME are described in more detail in the upcoming subsections. The parameterisations of the convective mass flux

Schematic diagram illustrating the direct (thick arrows) and indirect (thin arrows) dependencies of parameterisation schemes with a focus on the schemes involved in the modifications.

The mass flux description is based on a dual mass flux approach (see, e.g.

Schematic diagrams of the convective boundary layer regimes and the corresponding entrainment formulations (Eq.

The updraft profiles

The updrafts are initialised at the lowest model level with a temperature and humidity that exceed the mean values at that level. The excess values are determined by assuming that the temperature and humidity are Gaussian distributed with a variance estimated from the turbulent surface fluxes following the standard surface layer scaling of

Updraft area fractions per PBL regime in cy40NEW. Constants

In addition to the updraft model for heat and moisture, a similar updraft equation is used for the vertical velocity

Applied

Fractional entrainment is not only applied in determining the updraft dilution in Eq. (

Previously, the entrainment coefficients of the HARMONIE-AROME convection scheme have been discussed only briefly (B17). Here, they are described in detail. Further motivation for the parameter settings and adjustments is provided in Sect.

We need to specify the fractional entrainment factors,

The entrainment formulations for the non-cloudy layers are based on existing LES-based formulations with the inversion height,

Schematic diagram of the subsequent steps in the shallow convection scheme to determine the ultimate inversion heights and corresponding entrainment formulations and the diagnosed regimes. After the test parcel (yellow), two iteration steps are done per entrainment formulation (red refers to dry and green to moist). Although the test parcel might have diagnosed a cloudy regime, it is possible that the ultimate moist updraft could not reach the lcl. In this case, no moist updraft is active (left panel of Fig.

Apart from estimating

After diagnosing the PBL regime and the inversion height with the test updraft, the updraft rise is again calculated but this time with the area fractions from Table

In the event of an ultimately cloudy PBL, the cloud layer depth is diagnosed, and if it exceeds a threshold (currently set to 4000 m), the model is supposed to resolve moist convection, and only dry convection remains parameterised. Note that this threshold value should decrease with increased spatial resolution.

For any convective PBL regime, we need an entrainment formulation for the dry updraft. Based on LES results for a dry CBL,

Also for the entrainment of the moist updraft in the subcloud layer (Eq.

As argued in Appendix

Similar to Eq. (

The final entrainment profile to be defined is

The counterpart of entrainment is detrainment,

Equation (

For the moist updraft, we use the commonly applied mass flux closure at cloud base

In the cloud layer, variations in the mass flux profile from case to case and hour to hour can be almost exclusively related to variations in the fractional detrainment as first pointed out by

With

In cycle 36 and older versions, HARMONIE-AROME made use of the CBR (Cuxart–Bougeault–Redelsperger) turbulence scheme

A full description of the turbulence scheme can be found in LH04 and B17 but for convenience here we introduce the components and parameters involved in the adjustments. In our turbulence scheme, the eddy diffusivity (see Eq.

To get the final length scale

For most parameters in the length scale formulation, there is some theory that provides a reasonable range of values (LH04), but

The last aspect of the turbulence scheme we discuss concerns the subcloud cloud interaction. The mass flux contribution to the total vertical transport results in a stable stratification in the upper part of the subcloud layer. Consequently, mixing by the TKE scheme will be strongly diminished in this area. These feedbacks between the mass flux and the turbulence scheme generally lead to an unrealistically strong inversion at cloud base. In many mass flux schemes, this runaway process is prevented by numerical diffusion which is dependent on the vertical resolution, and results of these schemes therefore tend to break down at very high resolution

Let us briefly discuss the underlying ideas of the energy cascade term. Its formulation is inspired by the prognostic equation of the mass flux vertical velocity variance (

Profile of

Next to the usual dissipation, transport, buoyancies and shear terms,

Accurate predictions of clouds, liquid water, and ice are important because they have a large impact on radiation and therewith on several components of the model. This applies in particular to low boundary layer clouds such as stratocumulus and cumulus. In HARMONIE-AROME, high (ice) clouds are parameterised separately in a relative humidity scheme (B17) and are outside the scope of this paper. The here-presented derivations, ideas, and modifications concerning parameterisation of low clouds in HARMONIE-AROME are valuable for statistical cloud schemes in general.

The concept of parameterising clouds with a statistical cloud scheme was already pioneered by

The base of statistical cloud schemes is an expression of variance in

In the literature, several approaches exist to estimate

If we neglect advection, precipitation, and radiation terms, the budget equations for (co)variances are (see, e.g.

Similar to dissipation, the turbulent fluxes in Eq. (

In the absence of convection and no noticeable amount of turbulent activity, variance will still be non-zero. In nature, other sources of variance exist like surface heterogeneity, horizontal large-scale advection, mesoscale circulations, and gravity waves. Instead of imposing a minimum value to variance to cover these sources, we apply an extra variance term with the characteristics of a relative humidity scheme. This additional term was already introduced in

Let us assume a statistical cloud scheme with a uniform distribution of a fixed width

From the description above and Appendix

This paper describes a large variety of modifications to the current reference cloud, turbulence, and convection parameterisations. Argumentation of these adjustments is diverse. For example, part of the changes to the cloud and turbulence scheme have a theoretical basis, namely thermodynamics and surface layer similarity, respectively. Other modifications are substantiated by an in-depth comparison of 1-D model results with LES for several idealised intercomparison cases. Lastly, optimisation of some more uncertain model parameters is based upon evaluation of full 3-D model runs. Considering the large number of modifications and mutual influences, it is impossible to discuss the separate and incremental impact of them all. Instead, we focus on the performance of two HARMONIE-AROME configurations: firstly, the reference HARMONIE-AROME setup as described in B17, cy40REF, and, secondly, the new configuration, cy40NEW, as proposed in this paper. Nevertheless, all adjustments are substantiated and the isolated impact of several of them is demonstrated. An overview of all modifications is presented in Table D1 in Appendix

Total turbulent transport and transport by the dry and moist updraft (m s

The kinematic total turbulent transport (m s

ARM case specific humidity profile after 12 h of simulation. These profiles can be seen as the accumulated impact of the total turbulent humidity transport during the ARM case.

Many of the proposed adaptations are the result of a comparison of 1-D model with LES results as obtained with the DALES model

The ARM case

LES results around the cloud base inversion height for the ARM case at the ninth simulation hour. Panel

The eddy diffusivity (ED) turbulent moisture transport for ARM at the ninth simulation hour with three different model versions: cy40REF (blue), cy40REF but without

With the current operational resolution of HARMONIE-AROME, turbulent transport in the ARM case is fully unresolved and is presented as the sum of parameterised convective and diffusive turbulent transport. In LES, however, shallow convection and the bulk part of the diffusive transport is resolved. By sampling LES data in the cloud layer, we can estimate that part of the total turbulent transport that should be described by a convection scheme. Although the convective transport by LES should be interpreted as a rather crude estimate, it is also the best available way to study the performance of our mass flux convection scheme in the cloud layer. A detailed description of such an evaluation is provided in Appendix

However, the ultimate goal of a convection and turbulence scheme is to provide an accurate estimate of the total turbulent transport. After all, the vertical divergence of the total turbulent transport determines the tendencies of the prognostic model variables. Whereas LES convective transport should be interpreted as an estimate, depending on the sampling method, LES total turbulent transport during the ARM case will be close to observed values. Besides, in contrast to convective transport, LES provides the total turbulent transport for the complete atmosphere, including the subcloud layer. Figure

Contour plot of cloud fraction for the ARM case.

Total cloud cover for the ARM case. Plotted are observations (blue crosses), LES (blue), cy40REF (orange), cy40NEW with

ARM case, 10th simulation hour. Panel

ARM case, 10th simulation hour. The convective contribution to the variance in

A closer examination of Figs.

Additionally, the decomposition is used to look specifically into the turbulent transport around the cloud base inversion height in relation to the energy cascade term (Eq.

Based on this shallow cumulus case, it is evident that the physical basis of our parameterisation is a strong simplification of reality. Moreover, the rather good approximation of the total turbulent transport during the ARM case is partly caused by a compensating error (Appendix

A contour plot of cloud fraction during the ARM case (Fig.

Observed differences in cloud fraction and cover between cy40REF and cy40NEW (Figs.

As illustrated in Figs.

Humidity near cloud base is also influenced by the dry updraft. In the reference formulation, Eq. (

Another contribution to the different results stems from the removal of bugs in the reference cloud scheme. Most notable are erroneous thermodynamic coefficient

The largest impact is related to the choice of parameter

Apart from the (too)-high cloud fractions at cloud base, also the underestimation of low values of cloud fraction in the upper part of the cloud layer by both model versions stands out in Fig.

Figure

Dimensionless gradients of wind

GABLS1 wind profile at the ninth simulation hour of LES model DALES (blue), cy40REF (orange), and cy40NEW (green). SCM runs use 64 levels with the lowest and highest model levels at 3 and 403 m, respectively. Note that results for GABLS1 with several LES models in

Although the cloud scheme of cy40NEW already performs satisfactorily for a wide variety of weather conditions, there are clearly several options for further optimisation. Examples of possible improvement are the introduction of a height dependence of the extra variance term, partial replacement of the extra variance term by a dry updraft contribution in the subcloud layer, increasing

Two important modifications in the turbulence scheme are based on an evaluation procedure as described by

To investigate the mixing characteristics of our turbulence scheme in terms of the similarity relations, a SCM of HARMONIE-AROME is run for 1 year at the location of super-observation site Cabauw

Due to increased mixing in near-neutral conditions with

Cloud cover ASTEX case of LES (left panel), cy40REF (middle panel), and cy40NEW (right panel).

As Fig.

As Fig.

Figures

There is one specific difference between the model versions we need to mention concerning the slow case. In the results for this case, only a moist updraft (see right panel of Fig. 4 in B17) was invoked in cy40REF because the bulk difference in potential temperature between the surface and 700 hPa exceeds the threshold of 20

As mentioned in Sect.

Cloud base height in feet (1 ft is 0.3048 m) on 19 December 2018 at 09:00 UTC as measured at discrete observation site locations in the Netherlands and part of the North Sea (left panel), forecasted by cy40REF (middle panel) and cy40NEW (right panel). Note that white in the left panel means that there is no observation available, whereas white spots in the middle and right panels mean no cloud base height was detected because all model levels have a cloud fraction

Frequency bias of the cloud base height in feet (1 ft is 0.3048 m) for December 2018 with cy40REF

Apart from the impact on low clouds, the accumulation of moisture beneath atmospheric inversions also influences the triggering of resolved deep convection and the associated (heavy) precipitation. This is illustrated in Fig.

Semi-operational, daily runs of cy40REF and cy40NEW for more than a year in parallel revealed several cases where cy40NEW did forecast resolved precipitation that was also observed but was missed in cy40REF. Moreover, 1 year of fraction skill score verification of precipitation forecasts against calibrated radar data demonstrated a significant improvement with cy40NEW (not shown).
Verification of the near-surface variables reveals that the new configuration results in a slight deterioration in the negative 2 m temperature bias but no significant impact on 2 m humidity. Wind speeds at 10 m are slightly higher but with the same diurnal amplitude, resulting in no significant change in model performance. Note that in general, near-surface variables are strongly influenced by surface processes and potential representation mismatches between observation site and model grid box (see, e.g.

Relative humidity (RH) plots (red means high RH, blue low RH) for 10 September 2011. The four columns refer to hours 12:00, 14:00, 16:00, and 18:00 UTC. The first row (cy40REF) and second row (cy40NEW) show a map of RH at approximately 500 m height that covers parts of Belgium and northwest France, as well as a black line. Along this line, a vertical atmospheric cross section for the lowest 3 km is shown in the third (cy40REF) and fourth (cy40NEW) rows. In the cross sections, the boundary layer can be recognised by relatively high RH values. The white line at 500 m in the cross sections shows the height for which the RH is plotted in the two upper rows. The rectangle in the second column of the two upper rows indicates the area used to produce the skewed

Profiles of the skewed temperature (solid red line) and dew point temperature (solid green line) against the pressure (hPa). The profiles for cy40REF

As discussed in, e.g.

Apart from being a slow and tough process, model development is often a compromise between a scientific and a pragmatic approach. In this paper, we have tried to provide an “honest” description of the development process, thus including the more pragmatic optimisations and mentioning not only the successes but also the remaining shortcomings and (over)simplifications in the parameterisations.

The model update contains substantial modifications to the cloud, turbulence, and convection schemes based on a wide variety of argumentations. On one side of the spectrum are the more theoretically based modifications to the turbulence scheme – Monin–Obukhov similarity theory, following

The adjustments to the HARMONIE-AROME model described in this paper have a substantial impact on several aspects of the model performance. The most outstanding result is the improvement on low cloud and low cloud base height forecasts. Being one of the most urgent deficiencies of HARMONIE-AROME cycle 40, increasing the quality on this aspect was also the main goal of this study. The low cloud climatology changes from a severe underestimation in the reference version to a well-balanced model. Obviously, low clouds have a large impact on radiation and therewith on several model parameters. Moreover, they are crucial for aviation safety purposes. Taking a closer look at the consequences of the model updates reveals that the better preservation of atmospheric inversion strengths plays a key role. Not only the formation of low clouds but also the triggering of deep-resolved convection and the associated (heavy) precipitation are influenced by atmospheric inversion strength. With stronger inversions, more humidity is accumulated beneath the boundary layer top, which supports the development of mesoscale resolved upward motions, ultimately leading to deep convection and rain showers.

Verification based on more than 1 year of parallel model runs with cy40REF and cy40NEW firmly substantiates the significant improvement on low cloud and precipitation forecasts. The modifications in cy40NEW did not result in a significant improvement or deterioration of near-surface temperature, humidity, and wind speed. All modifications have recently been incorporated in the default configuration of HARMONIE-AROME cycle 43. Herewith, they will also become available in the HARMONIE-AROME climate version

An important spin-off of this project is the increased understanding of how parameter settings impact particular model output and how they influence each other via underlying physical processes. With this insight, we decided to use the proportionality constant of the stable length scale,

Here, we provide a step-by-step derivation of the variance in

Suppose we know the PDF that describes subgrid variability of

Here we present an overview of the differences between the cy40REF and cy40NEW cloud schemes. Firstly, an important difference concerns the formulation of the thermodynamic coefficients

To estimate the contribution from organised (updraft) transport, in a model represented by the convection scheme, to the total turbulent transport, LES data in the cloud layer are conditionally sampled. Different sampling methods exist (see

Kinematic convective transport (m s

Figure

Figure

Firstly, we changed

Finally, Fig.

Following

To investigate the relatively large contribution from environmental turbulence, the turbulent transport is decomposed further in three parts: cloudy updraft, cloudy downdraft, and environment

Decomposition of the turbulent fluxes for the ARM case, ninth simulation hour. Plotted are LES cloudy updraft flux (blue), small-scale subplume transport (orange), small-scale environmental transport (green), and total transport (red).

Finally, Fig.

ARM case, ninth simulation hour. Panel

ARM case, ninth simulation hour, cross section of the kinematic turbulent moisture transport at 2310 m height (with

The ALADIN and HIRLAM consortia cooperate on the development of a shared system of model codes. The HARMONIE-AROME model configuration forms part of this shared ALADIN-HIRLAM system. According to the ALADIN-HIRLAM collaboration agreement, all members of the ALADIN and HIRLAM consortia are allowed to license the shared ALADIN-HIRLAM codes to non-anonymous requests within their home country for non-commercial research. Access to the full HARMONIE-AROME codes can be obtained by contacting one of the member institutes of the HIRLAM consortium (see

The code of all routines involved in the modifications described in this paper, together with the corresponding original routines, is available in the Supplement. The Supplement retains the directory structure as in the full HARMONIE-AROME model. Directory src/arpifs/phys_dym contains four modified routines: apl_arome.F90, vdfexcuhl.F90, vdfhghtnhl.F90, and vdfparcelhl.F90 that involve changes to, respectively, the cloud scheme, the turbulence scheme, the convection and turbulence scheme, and finally the convection scheme. Corresponding original routines are always indicated by the extension _ori. Directory mpa/micro/internals includes condensation.F90 with modifications to the cloud scheme. Finally, directory mpa/turb/internals contains five routines with modifications to the cloud scheme: compute_function_thermo_mf.F90, compute_mf_cloud_stat.F90, ini_cturb.F90, turb.F90, and turb_ver_thermo_corr.F90. In the same directory, two routines include modifications related to the turbulence scheme: turb_ver_dyn_flux.F90 and turb_ver_thermo_flux.F90. With reference to this paper, all routines in the Supplement file can be freely used, e.g. in other software.

DALES full 3-D fields (divided into eight subdomains), as well as derived LES data for the ARM case, can be downloaded from Zenodo: (

The supplement related to this article is available online at:

WCdR contributed to all aspects of the paper, including writing the original draft and revisions. PS, PB, GL, and SRdR contributed to the conceptualisation. PS and PB contributed to the formal analysis. PB, ST, and BvV contributed to the visualisation. PS contributed to the writing in the form of review editing. PS, PB, GL, SRdR, HdV, EvM, and JFM commented on the paper.

The contact author has declared that neither they nor their co-authors have any competing interests.

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

This work has been done within the KNMI multi-annual strategic research (MSO) project CRIME (Cloud Representation IMprovement and Evaluation in HARMONIE-AROME) and the Norwegian Research Council (project no. 280573), “Advanced models and weather prediction in the Arctic: enhanced capacity from observations and polar process representations (ALERTNESS)”. The support of Emiel van de Plas with Python is appreciated.

The study was supported by the Norwegian Research Council (project no. 280573).

This paper was edited by Sylwester Arabas and reviewed by two anonymous referees.