Entrainment and detrainment processes have been recognised for a long time as key processes for cumulus convection and have recently witnessed a regrowth of interest mainly due to the capability of large-eddy simulations (LES) to diagnose these processes in more detail. This article has a twofold purpose. Firstly, it provides a historical overview of the past research on these mixing processes, and secondly, it highlights more recent important developments. These include both fundamental process studies using LES aiming to improve our understanding of the mixing process, but also more practical studies targeted toward an improved parametrised representation of entrainment and detrainment in large-scale models. A highlight of the fundamental studies resolves a long-lasting controversy by showing that lateral entrainment is the dominant mixing mechanism in comparison with the cloud-top entrainment in shallow cumulus convection. The more practical studies provide a wide variety of new parametrisations with sometimes conflicting approaches to the way in which the effect of the free tropospheric humidity on the lateral mixing is taken into account. An important new insight that will be highlighted is that, despite the focus in the literature on entrainment, it appears that it is rather the detrainment process that determines the vertical structure of the convection in general and the mass flux especially. Finally, in order to speed up progress and stimulate convergence in future parametrisations, stronger and more systematic use of LES is advocated.

For a wide range of shallow cumulus convection cases, large-eddy simulation (LES) model results have been used to investigate lateral mixing as expressed by the fractional entrainment and fractional detrainment rates. It appears that the fractional entrainment rates show much less variation from hour to hour and case to case than the fractional detrainment rates. Therefore, in the parameterization proposed here, the fractional entrainment rates are assumed to be described as a fixed function of height, roughly following the LES results. Based on the LES results a new, more flexible parameterization for the detrainment process is developed that contains two important dependencies. First, based on cloud ensemble principles it can be understood that deeper cloud layers call for smaller detrainment rates. All current mass flux schemes ignore this cloud-height dependence, which evidently leads to large discrepancies with observed mass flux profiles. The new detrainment formulation deals with this dependence by considering the mass flux profile in a nondimensionalized way. Second, both relative humidity of the environmental air and the buoyancy excess of the updraft influence the detrainment rates and, therefore, the mass flux profiles. This influence can be taken into account by borrowing a parameter from the buoyancy-sorting concept and using it in a bulk sense. LES results show that with this bulk parameter, the effect of environmental conditions on the fractional detrainment rate can be accurately described. A simple, practical but flexible parameterization for the fractional detrainment rate is derived and evaluated in a single-column model (SCM) for three different shallow cumulus cases, which shows the clear potential of this parameterization. The proposed parameterization is an attractive and more robust alternative for existing, more complex, buoyancy-sortingbased mixing schemes, and can be easily incorporated in current mass flux schemes.

vertical velocity, new formulae for entrainment and detrainment rates can be expressed in terms of buoyancy, vertical velocity and cloud fraction. For a variety of shallow convection cases, results from large-eddy simulations show a good correspondence of these new formulae with more traditional methods to diagnose entrainment and detrainment rates. Moreover, the formulae give insight into the behaviour and the physical nature of the mixing coefficients. They explain the observed large variability of the detrainment. The formulae cannot be directly applied as a parametrization. However, it is demonstrated how they can be used to evaluate existing parametrization approaches and as a sound physical base for future parametrization developments.

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A scheme is proposed that relates surface flux densities of sensible heat, latent heat, and momentum to routine weather data. The scheme contains parameterizations concerning the radiation components and the surface energy flux densities. The parameterizations are developed and examined using observations from 1987 of a grasscovered surface at Cabauw in the Netherlands. It is shown that improvements in the parameterizations are achieved by incorporating an albedo dependence on solar elevation, a longwave downward radiation with a correction for the amount of high clouds, and a soil heat flux with a soil temperature approximated by a 24-hmean 2-m temperature. In addition, the Penman-Monteith concept for the latent heat flux is utilized with a simple one-parameter surface resistance, which depends on atmospheric moisture deficit in particular. Special attention is paid to the treatment of surface inhomogeneities. A distinction is made between stable conditions, when measurements in the lower 10 m appear to be in equilibrium with the local surface, and unstable conditions, when measurements seem to be influenced by deviating upstream surface conditions. A constant roughness length for heat above grassland of 1 mm is applied. Finally, the scheme as a whole is evaluated and compared with a previous approach by A. P. van Ulden and A. A. M. Holtslag. It appears that in particular the sensible heat flux is improved with the new scheme. This can be ascribed mostly to the replacement of the modified Priestley-Taylor by the Penman-Monteith formulation and by a better representation of the surface temperature.

Abstract. 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.

Forecasts of marine cold air outbreaks critically rely on the interplay of multiple parameterisation schemes to represent sub-grid scale processes, including shallow convection, turbulence, and microphysics. Even though such an interplay has been recognised to contribute to forecast uncertainty, a quantification of this interplay is still missing. Here, we investigate the tendencies of temperature and specific humidity contributed by individual parameterisation schemes in the operational weather prediction model AROME-Arctic. From a case study of an extensive marine cold air outbreak over the Nordic Seas, we find that the type of planetary boundary layer assigned by the model algorithm modulates the contribution of individual schemes and affects the interactions between different schemes. In addition, we demonstrate the sensitivity of these interactions to an increase or decrease in the strength of the parameterised shallow convection. The individual tendencies from several parameterisations can thereby compensate each other, sometimes resulting in a small residual. In some instances this residual remains nearly unchanged between the sensitivity experiments, even though some individual tendencies differ by up to an order of magnitude. Using the individual tendency output, we can characterise the subgrid-scale as well as grid-scale responses of the model and trace them back to their underlying causes. We thereby highlight the utility of individual tendency output for understanding process-related differences between model runs with varying physical configurations and for the continued development of numerical weather prediction models.