ParaCon - Representation of convection in models

Weather and climate models are critical to society's ability to reduce the impacts of hazardous weather and inform decisions regarding mitigation of and adaptation to climate change. The representation of convection remains the key error in these models, which limits our confidence in predictions and thus their value for decision-making on timescales from days to decades.

The key issue in representing convection in global models is that the resolutions of these models are too coarse to represent individual convective systems. Instead, models rely on physically based parametrization of convection. However, these parametrizations are based on paradigms developed 30-40 years ago in which convection was represented as a one dimensional, balanced problem between atmospheric instability and the convection required to remove that instability. Much more is now known about convection, how it is intimately related to the local dynamics and how it is organised on a range of space and timescales from the diurnal cycle of precipitation to synoptic scales such as tropical storms or the Madden-Julian Oscillation. These outdated paradigms have been identified as a major blockage to more skilful and reliable weather forecasts and climate predictions, in which realistic simulations of convection and the regional water cycle are of fundamental importance.

ParaCon was initiated as part of a Joint Strategic Response between NERC and the Met Office, and started in May 2016. It involves researchers from the Universities of Cambridge, Exeter, Leeds, and Reading. 

Programme phases

There are two phases to the programme:

1. A three-year exploratory phase, where new ideas in convection parametrization are investigated, and research is undertaken to understand the key elements required of a new scheme.
2. This will be followed by a two-year integration phase, where we will aim to bring together the different strands of the programme.

Project areas

The overall programme is led by Alison Stirling at the Met Office, and is divided into five project areas:

1. Triggering of convection

Led by Doug Parker, this project aims to develop a new, scale-aware genesis scheme for convective triggering and updraughts. It aims to provide sizes and spectra of triggering structures, taking organisation, temporal coherence, and stochasticity into account.

2. Fluid dynamics of convective flows

Led by Michael Herzog, this project aims to identify and quantify the dynamical processes associated with individual clouds that need to be considered in convective parametrizations.

3. Mass flux and beyond

Led by Bob Plant, this project will provide a critical examination of parametrization methods that are based around the concept of conditional averaging. This will include the traditional bulk mass flux approach, but also more general approaches, such as multi-plume, and multi-fluid formulations. The research will include analyses of how well such approaches represent a fully-resolved flow through to test-of-concept and prototype parametrizations.

4. Convection-dynamics coupling

Led by John Thuburn, this project comprises two linked strands. The first will develop and test a multi-fluid scheme, derived from ideas of conditional averaging, for representing convection in an atmospheric model. The second will use theory and numerical experimentation to improve understanding of the mechanisms by which convection couples to the larger-scale circulation, and to quantify the sensitivity of aspects of the coupled circulation to the formulation and parameters in convection schemes.

5. Turbulent approaches for the grey zone

Led by Peter Clark, this component is concerned with the development of improved cloud and turbulence schemes for convection permitting models on scales (100 m - 10 km). It will provide a critical examination of volume-averaged formulations of the Navier-Stokes equation, assessing the performance of different levels of complexity in the formulation against high-resolution simulations of convection.

These research areas are underpinned by high-resolution modelling, which is being coordinated across the programme by Steve Woolnough, and Simon Vosper to ensure consistency of modelling tools, data availability and efficient use of the HPC. This working group will also develop a joint plan for the evaluation of convection parametrization schemes, including a hierarchy of test cases.

Working groups

In addition, there will be two working groups that cut across the individual projects:

Unifying conceptual framework for the formulation of convection schemes

Led by John Thuburn, we will seek to formulate an overarching mathematical framework from which each of the proposed approaches can be derived by a clearly stated set of approximations.

Numerical methods within parametrizations

Led by Hilary Weller, the aim of this activity is to share knowledge and methods in order to improve the numerical implementation of the physical parametrizations arising from ParaCon.

Overview of programme progress

The programme has developed three distinct convection parametrisation frameworks. All are designed to be viable parametrisations in their own right, but a future vision is to combine elements from each to arrive at a better all-encompassing structure for convection parametrisation across model scales. The philosophy for each framework is that it should be flexible, enabling differing levels of complexity, and where the individual components (for example exchange terms, closures, number of updraughts) can be modified at a later point. 

The frameworks are:

• A flexible mass-flux scheme called CoMorph

• A 3D second-order turbulence scheme designed as a replacement for the Smagorinsky scheme, and targeting km and sub-km scales. 

• A multi-fluid approach, in which convection is treated directly as a problem of mass transfer. The fluid elements are discretely partitioned in much the same way as a mass flux scheme, but these then use the same dynamical equations as the parent grid to move (and be moved) around. 

Three cross-cutting themes of process studies, evaluation, and unification have complemented the building of the frameworks. Each area of research is described in more detail below.

CoMorph: A new mass flux scheme 

A version ‘A’ of CoMorph (Whitall, 2021) within the UM has now been developed, which performs well compared with previous global model releases. Particular strengths are its smooth operation across timesteps, and its ability to couple well to the large-scale circulation, enabling emergent features such as the MJO to develop. Development of a version ‘B’ is underway, which is designed to enable cold-pool forced initiation to be included, with a view to improving the representation of the diurnal cycle. An accompanying cold pool scheme, C-Pool (Rooney et al, 2021), has been developed that will eventually be coupled to the revised version ‘B’ of CoMorph. A more scale-aware, third version, ‘C’, is planned in the coming year that enables CoMorph to operate at km scales by reducing the sub-grid mass flux as the convective activity approaches the resolvable scale. A CoMorph Working Group has been set up to enable UM partners to test and evaluate the different versions as they are shared.

As well as global-model tests, CoMorph has been tested extensively in an idealised framework, in which the results are compared to companion MONC LES simulations. Tests have included diagnosing its linear response characteristics (Hwong et al, 2021), its memory properties (in the context of the diurnal cycle) and its response to large-scale couplings (formulated via weak-temperature gradient or damped gravity wave methods). The last of these has been particularly valuable, and quickly identified issues to resolve with early CoMorph prototypes. 

A number of extensions to CoMorph are planned. One that is ongoing is to use the framework to represent a spectrum of cloud sizes, by embedding the concepts of the convective cloud field model, CCFM, into CoMorph’s framework.

A new turbulence scheme for km and sub-km scales

We have developed a 3D Turbulence Energy scheme within the UM based upon second order closure of space/time filtered equations using prognostic Turbulent Kinetic Energy (TKE) and cloud-conserved variables that relate to the Turbulent Potential Energy. Solution of the closed equation results in turbulent fluxes expressed as a sum of local, down-gradient fluxes, non-local buoyancy-driven fluxes and fluxes resulting from the tilting and gradient-production terms that have identical form (in the vertical direction) to the Leonard terms proposed by Moeng et al (2010) and already implemented in the UM (thus providing an alternative, and arguably stronger, theoretical basis for the terms (Hanley et al., 2019). 

The scheme is scale-aware through blending of the mixing length between filter-scale (as used in the Smagorinsky scheme) and relevant outer-length scales. In the absence of the tilting/Leonard term, this scheme has asymptotic behaviour that approaches the Smagorinsky scheme at very high (true LES) resolution but it is well-known that even at this resolution there is no theoretical justification for ignoring tilting of fluxes; future work will include evaluating the importance of this term. It has already been shown to have significant positive impact in more ‘grey-zone’ resolution models (Hanley et al., 2019). At the other end of the resolution scale, the scheme as a whole asymptotes to the existing Nakanishi and Niino 1D boundary-layer scheme, and testing so far shows encouraging behaviour at intermediate scales (i.e. horizontal grid-length of a few 100 m).  

A more flexible version of the scheme is being implemented within MONC as a research tool; this includes different choices of prognostic up to a fully prognostic second-order scheme. This will be used to test both alternative prognostic choices and, in particular, closures. The latter, in particular, is being pursued as a mechanism to unify the scheme with CoMorph.

Future work will also focus on replacing the mixing-length formulation with one based on the Germano dynamic approach that has already shown benefit in the ‘near-LES’ turbulence grey zone. (Efstathiou and Plant, 2018; Efstathiou et al 2018).

Multi-fluid  

Governing equations for turbulent second-moment quantities have been derived in the multi-fluid framework. In addition to the terms appearing in the single-fluid case (or their analogues), additional terms arise to account for relabelling (i.e. entrainment and detrainment) and for certain subfilter-scale pressure fluctuations. This derivation is a necessary step towards a possible unification of the multi-fluid and higher-order turbulence approaches.

A new multi-fluid single-column model has been developed (Thuburn et al, 2018). It is based on new numerical methods giving better conservation and stability, and it includes (equilibrium) moist processes and background wind shear. The model includes prognostic equations for TKE and diagnostic equations for entropy and moisture variances, thus approximating a multi-fluid level 2.5 Mellor-Yamada scheme. The turbulent second moments are used in computing subfilter-scale fluxes, entrainment and detrainment, and the effects of subfilter-scale condensation. The model is able to capture the leading-order behaviour in the ARM and BOMEX test cases. Three papers documenting this work are in preparation.

In the short term, we are investigating what lessons learnt from the multi-fluid model development might be transferred to a mass flux scheme such as CoMorph. In the longer term we are working towards developing and evaluating a three-dimensional multi-fluid model.

A second multi-fluid model has also been developed in parallel. This is a three-dimensional multi-fluid model of dry convection that simulates unresolved, partially resolved and fully resolved convection using two or three fluids. This model is able to capture aspects of Rayleigh-Benard convection over a range of Rayleigh numbers and resolutions and a warm rising bubble. Next steps are to include a prognostic equation for sub-filter-scale TKE and moisture. (Weller & McIntyre, 2019; McIntyre et al, 2020; Weller et al, 2020; Shipley et al, 2021)

Process research

Crucial to CoMorph is specifying the inputs into the plume model.Using large eddy simulations and novel analysis techniques we are identifying which boundary layer structures feed into the convective clouds and produce statistics on the size and properties of these structures in order to constrain the inputs to CoMorph. Such statistics will also underpin development of a stochastic version of CoMorph, with a spectrum of plumes to represent the real-world variability in convective clouds. (Denby et al, 2021)

We have studied convective memory as a function of scale and forcing strength in idealised simulations of a diurnal cycle of deep convection. Following a period of suppression after prior convection, we identified a secondary enhancement phase. The old convection scheme fails to capture the lifetime of convection and the suppression phase. CoMorph improves on this significantly but does not have the secondary enhancement. We believe that this can be addressed through suitable coupling to a cold pool representation. (Daleu et al, 2020)

The above study has been extended to consider the convective response to surface heterogeneity, which has allowed us to investigate the interplay between boundary-layer circulations, convective initiation, and convective circulations. (Harvey et al, 2022)

We have studied the accuracy of the mass flux approach for the representation of sub-filter fluxes, focussing on the potential improvements in accuracy for multiple partitions of the flow. For shallow, deep and aggregated convection, we show that two types of updraft/downdraft offer a considerable improvement over a single type but 3+ types have little further to offer. These results have helped to motivate the use of “core” and “mean” properties in CoMorph as being representative of two “types”. (Gu et al, 2020)

We have studied the internal structure of shallow cumulus, showing that internal distributions are better represented by a quadratic form rather than a top hat, and emphasising the importance of the region near cloud edge for the total fluxes. The latter point is consistent with the identification of the second type in the above study. (Gu et al, 2021)

We further studied the processes near the cloud edge by investigating the size of the cloud halo (region adjacent to the cloud where the RH exceeds the environment) showing that it does not scale with cloud size, as had been suggested in the literature. This may have implications for cloud-radiation interactions.

We have studied the role of pressure drag in the vertical momentum equation for shallow cumulus, explaining the different character of the budget between individual clouds and the cloud ensemble. We expect this analysis to prove valuable as and when CoMorph is extended to incorporate a separate w equation. (Gu et al, 2020)

Using a trajectory analysis we have studied the physical mechanisms of the entrainment / detrainment process. Our analysis casts doubt on the “buoyancy sorting” paradigm and suggests that “acceleration sorting” may be able to provide a better paradigm. The study has considered shallow cumulus only, but is currently being extended to deep convection. 

The classical Rayleigh–Bénard model of dry convection has been extended to include the effects of condensation and latent heating, providing some basic understanding of moist convection in a simplified setting (Vallis et al., 2019).

A robust mechanism providing a possible explanation for the MJO has been identified in a moist shallow water model, addressing a long-standing problem in convection-circulation coupling (Vallis and Penn 2020, Vallis 2021). The region of convective heating gives rise to a Gill-type circulation pattern, which, in turn, is responsible for the moisture flux convergence that enables the convective heating and its eastward propagation.

Evaluation

A highly configurable version of the UM, known as Flex-UM, has been developed to bridge the gap between the most idealized configurations, such as dry-physics Held-Suarez, and the full physics version (Maher and Earnshaw, 2021). Flex-UM includes optional simplified schemes for convection, large-scale precipitation, radiation, boundary layer, and the sea surface temperature boundary condition.  Flex-UM broadens the climate model hierarchy capabilities of the UM, facilitating the evaluation of new parameterization schemes such as CoMorph.

As part of the evaluation of CoMorph, Paracon is working with other major projects, including the EUREC4A and CloudSense programmes, to leverage additional value from these projects. We are using new field observations and high resolution LES and convection permitting Met Office simulations to evaluate CoMorph over a range of convection regimes to help constrain the physical parameters used in CoMorph.

PhD theses

ParaCon has supported a number of ph.D. students during the programme, these have resulted in the following theses: 

McIntyre, W. (2020) Multi-fluid modelling of dry convection. PhD thesis, University of Reading. doi: https://doi.org/10.48683/1926.00095351 

Shipley, D. 2021 Multi-fluid modelling of idealized convection. PhD thesis, University of Reading.

C. C. Chui, 2021. On the Parameterisation of Convection in the Grey Zone. 114pp 

M. Johnston, 2019. Island Convection and its Representation in Numerical Weather Prediction Models. 235pp 

M. Muetzelfeldt, 2019. Designs for Representing Shear-Induced Cloud Field Organization in a Convection Parametrization Scheme. 245pp

References

Daleu C. L., Plant R.S., Woolnough S.J., Stirling A.J. Harvey N.J., (2020) Memory properties in cloud-resolving simulations of the diurnal cycle of deep convection. Journal of Advances in Modeling Earth Systems.  https://doi.org/10.1029/2019MS001897

Denby L., Boeing, S.J., Parker, D.J., Ross, A.N., Tobias, S.M. (2021) Characterising the shape, size, and orientation of cloud-feeding coherent boundary-layer structures. Quarterly Journal of the Royal Meteorological Society, https://doi.org/10.1002/qj.4217

Efstathiou G, Plant RS. (2018) A dynamic extension of the pragmatic blending scheme for scale‐dependent sub‐grid mixing, Quarterly Journal of the Royal Meteorological Society, DOI:10.1002/qj.3445. [PDF] 

Efstathiou G, Plant R, Bopape M-J. (2018) Simulation of an evolving convective boundary layer using a scale-dependent dynamic Smagorinsky model at near-grey-zone resolutions, Journal of Applied Meteorology and Climatology, volume 57, pages 2197-2214, DOI:10.1175/JAMC-D-17-0318.1. [PDF] 

Gu J.F., R. S. Plant, C. E. Holloway, T. R. Jones, A. Stirling, P. A. Clark, S. J. Woolnough, and T. L. Webb. Evaluation of the bulk mass flux formulation using large eddy simulations. J. Atmos. Sci., 77:2115-2137, 2020.

Gu J.-F., R. S. Plant, C. E. Holloway, and T. R. Jones. Composited structure of non-precipitating shallow cumulus clouds. Q. J. R. Meteorol. Soc., 147:2818-2833, 2021

Gu J.F., R. S. Plant, C. E. Holloway, and M. R. Muetzelfeldt. Pressure drag for shallow cumulus clouds: from thermals to the cloud ensemble. Geophys. Res. Lett., 47:e2020GL090460, 2020.

Hanley, K., Whitall, M., Stirling, A. and Clark, P. (2019) Modifications to the representation of subgrid mixing in kilometre‐scale versions of the Unified Model. Quarterly Journal of the Royal Meteorological Society, 145 (725). pp. 3361-3375. ISSN 1477-870X doi: https://doi.org/10.1002/qj.3624

Harvey N.J., Daleu C.L. Stratton R.A., Plant R.S., Woolnough S.J., Stirling A.J. (submitted 2022) The impact of surface heterogeneity on the diurnal cycle of deep convection. Quarterly Journal of the Royal Meteorological Society

Y. L. Hwong, S. Song, S. C. Sherwood, A. J. Stirling, C. Rio, R. Roehrig, C. L. Daleu, R. S. Plant, D. Fuchs, P. Maher, and L. Touzé-Peiffer. Characterizing Convection Schemes Using Their Responses to Imposed Tendency Perturbations. J. Adv. Model. Earth Syst., 13:e2021MS002461, 2021.

McIntyre, W. A., Weller, H. and Holloway, C. E. (2020) Numerical methods for entrainment and detrainment in the multi-fluid Euler equations for convection. Quarterly Journal of the Royal Meteorological Society, 146 (728). pp. 1106-1120. ISSN 1477-870X doi: https://doi.org/10.1002/qj.3728  

Maher, P. and Earnshaw, P. (2021) The Flexible Modelling Framework for the Met Office Unified Model (Flex-UM, part of the UM 12.1 release), Geosci. Model Dev. (accepted). https://doi.org/10.5194/gmd-2021-193

Rooney G.G., Stirling A.J., Stratton R.A., Whitall, M.J. (2021) C-POOL: a scheme for modelling convective cold pools in the Met Office Unified Model, Quarterly Journal of the Royal Meteorological Society.  https://doi.org/10.1002/qj.4241

Shipley, D., Weller, H., Clark, P. A.  and McIntyre, W. A. (2021) Two-fluid single-column modelling of Rayleigh-Bénard convection as a step towards multi-fluid modelling of atmospheric convection. Quarterly Journal of the Royal Meteorological Society. ISSN 1477-870X doi: https://doi.org/10.1002/qj.4209 

Thuburn, J., Weller, H., Vallis, G. K., Beare, R. J. and Whitall, M. (2018) A framework for convection and boundary layer parameterization derived from conditional filtering. Journal of the Atmospheric Sciences, 75 (3). pp. 965-981. ISSN 1520-0469 doi: https://doi.org/10.1175/jas-d-17-0130.1

Vallis, G.K. and Penn, J. (2020) Convective organization and eastward propagating equatorial disturbances in a simple excitable system. Quarterly Journal of the Royal Meteorological Society, 146, 2297–2314.

Vallis, G.K. (2021) Distilling the mechanism for the Madden–Julian Oscillation into a simple translating structure. Quarterly Journal of the Royal Meteorological Society, 1–16. https://doi.org/10.1002/qj.4114

G. K. Vallis, D. J. Parker, S. M. Tobias, (2019), A simple system for moist convection: the Rainy–Bénard model. Journal of Fluid Mechanics , 862 , 162-199 DOI: https://doi.org/10.1017/jfm.2018.954

Weller, H., McIntyre, W. and Shipley, D. (2020) Multi-fluids for representing sub-grid-scale convection. Journal of Advances in Modeling Earth Systems, 12 (8). e2019MS001966. ISSN 1942-2466 doi: https://doi.org/10.1029/2019MS001966  

Weller, H. and McIntyre, W. A. (2019) Numerical solution of the conditionally averaged equations for representing net mass flux due to convection. Quarterly Journal of the Royal Meteorological Society, 145 (721). pp. 1337-1353. ISSN 1477-870X doi: https://doi.org/10.1002/qj.3490  

Whitall, M (2021) UM Documentation, paper in preparation.