Death, fear, and self-mourning

Attitudes to our own mortality are characterized by more than just fear, suggests Bob Plant

Why does Arakawa and Schubert's convective quasi-equilibrium closure not work? Mathematical analysis and implications

Arakawa and Schubert (1974) proposed convective quasi-equilibrium as a guiding principle for the closure of convection parameterization. However, empirical experiences from operational implementation efforts suggest that its strict application does not work well. The purpose of the present paper is to explain mathematically why this closure does not work in practice, and to suggest that problems stem from physically unrealistic assumptions. For this purpose, the closure hypothesis is examined in its original form, and without imposing a condition of a positiveness to the convective mass fluxes. The Jordan sounding with idealized large-scale forcing is used for diagnosis purposes. The question is addressed from several perspectives including the completeness of the entraining plume spectrum, and a singular vector decomposition of the interaction kernel matrix. The main problems with the quasi–equilibrium closure are traced to: (i) the relatively slow response of shallower convective modes to large-scale forcing; and, (ii) detrainment at convection top producing strong cooling and moistening. A strict application of the convective quasi-equilibrium principle leads to a singular response of shallow convection. An explicit coupling of convection with stratiform clouds would be crucial for preventing this unrealistic behavior, recognizing that the re-evaporation of detrained cloudy-air is a relatively slow process

Effects of stability functions in a dynamic model convective boundary layer simulation

Dynamic subgrid models are increasingly being used in simulations of the atmospheric boundary layer. We have implemented several variant forms of dynamic models in the UK Met Office Large Eddy Model (MetLEM), including a state-of-the-art Lagrangian-Averaged-Scale-Dependent (LASD) model. The implementation includes optional use of stability functions in the specification of the eddy viscosity and diffusivity, as well as optional use within the dynamic calculation of the Smagorinsky parameter. This paper reports on the behaviour of the LASD model with different choices for the inclusion and treatment of stability functions in convective boundary layer simulations at different resolutions. Results are compared against a high-resolution Large-Eddy simulation (LES) and against simulations employing the Smagorinsky-Lilly subgrid model. We conclude that the use of stability functions improves the behaviour of the LASD model in the grey zone regime. Moreover, a careful treatment of the stability functions in the calculation of the dynamic parameters, whilst attractive theoretically, is found to be unnecessary in practical terms

A physically-based stochastic boundary-layer perturbation scheme. Part II: perturbation growth within a super ensemble framework

Convection-permitting forecasts have improved the forecasts of flooding from intense rainfall. However, probabilistic forecasts, generally based upon ensemble methods, are essential to quantify forecast uncertainty. This leads to a need to understand how different aspects of the model system affect forecast behaviour. We compare the uncertainty due to initial and boundary condition (IBC) perturbations and boundary-layer turbulence using a super ensemble (SE) created to determine the influence of 12 IBC perturbations vs. 12 stochastic boundary-layer (SBL) perturbations constructed using a physically-based SBL scheme. We consider two mesoscale extreme precipitation events. For each we run a 144-member SE. The SEs are analysed to consider the growth of differences between the simulations, and the spatial structure and scales of those differences. The SBL perturbations rapidly spin-up, typically within 12 h of precipitation commencing. The SBL perturbations eventually produce spread that is not statistically different from the spread produced by the IBC perturbations, though in one case there is initially increased spread from the IBC perturbations. Spatially, the growth from IBC occurs on larger scales than that produced by the SBL perturbations (typically by an order of magnitude). However, analysis across multiple scales shows that the SBL scheme produces a random relocation of precipitation up to the scale at which the ensemble members agree with each other. This implies that statistical post-processing can be used instead of running larger ensembles. Use of these statistical post-processing techniques could lead to more reliable probabilistic forecasts of convective events and their associated hazards

Turbulence characteristics across a range of idealized urban canopy geometries

Good representation of turbulence in urban canopy models is necessary for accurate prediction of momentum and scalar distribution in and above urban canopies. To develop and improve turbulence closure schemes for one-dimensional multi-layer urban canopy models, turbulence characteristics are investigated here by analyzing existing large-eddy simulation and direct numerical simulation data. A range of geometries and flow regimes are analyzed that span packing densities of 0.0625 to 0.44, different building array configurations (cubes and cuboids, aligned and staggered arrays, and variable building height), and different incident wind directions (0 degrees and 45 degrees with regards to the building face). Momentum mixing-length profiles share similar characteristics across the range of geometries, making a first-order momentum mixing-length turbulence closure a promising approach. In vegetation canopies turbulence is dominated by mixing-layer eddies of a scale determined by the canopy top shear length scale. No relationship was found between the depth-averaged momentum mixing length within the canopy and the canopy top shear length scale in the present study. By careful specification of the intrinsic averaging operator in the canopy, an often-overlooked term that accounts for changes in plan area density with height, is included in a first-order momentum mixing-length turbulence closure model. For an array of variable-height buildings, its omission leads to velocity overestimation of up to 17%. Additionally, we observe that the von Karman coefficient varies between 0.20 and 0.51 across simulations, which is the first time such a range of values has been documented. When driving flow is oblique to the building faces, the ratio of dispersive to turbulent momentum flux is larger than unity in the lower half of the canopy, and wake production becomes significant compared to shear production of turbulent momentum flux. It is probable that dispersive momentum fluxes are more significant than previously thought in real urban settings, where the wind direction is almost always oblique

Working group 3: What are and how do we measure the pros and cons of existing approaches?

WG3 discussed both the pros and cons of existing schemes as well as metrics to measure relative advantages and disadvantages. We first provide a list of the current operational techniques and their respective advantages and disadvantages that were discussed in the WG. We do not claim that the list is complete, and we note that the pros and cons are neither exhaustive nor quantitative. Nevertheless, it may be useful to note the WG’s consensus on the general advantages and disadvantages of the most commonly-used schemes. We then list our recommendations for evaluating model uncertainty schemes. At the end is a short list pertaining to recommendations for further development of methods to represent model uncertainty

Summary and Recommendations from Working Group 1: model uncertainty representations in convection-permitting / shorter lead-time / limited-area ensembles

WG3 discussed both the pros and cons of existing schemes as Working group 1 considered the treatment of model uncertainty (MU) in high-resolution ensembles, at grid spacings of order 1-5 km. These systems are often run for regional weather forecasting, perhaps over a single country, and for lead times of up to 5 days. Looking ahead, ECMWF’s strategy seeks to deliver global medium-range ensemble forecasts with 3-4 km grid spacings by 2030. It is questionable for what grid spacing we should dispense with a deep convection parameterization, but it will be either switched off or damped in these systems, such that deep convection can be assumed to be dominated by explicit motions. One of the problems with limited-area ensemble systems at this scale is that spread depends not only on the modelling system itself but also on the variability inherited from the large-scale boundary conditions. There is often thought to be a lack of spread in our high-resolution EPS (ensemble prediction systems), but this could reflect a lack of diversity on larger scales. The relative importance of lateral-boundary diversity and the model uncertainty mechanisms is regime dependent. The lateral boundaries will generally be more important in midlatitude winter but less so for summertime convection in relatively weak synoptic flow

On being (not quite) dead with Derrida

Thanks to Gerry Hough for helpful comments on an earlier draft of this article.Peer reviewedPostprin

Interaction of the convective energy cycle and large-scale dynamics

The importance of the convective life cycle in tropical large-scale dynamics has long been emphasized, but without explicit analysis. The present work provides it by coupling the convective energy cycle under the framework of Arakawa and Schubert's (1974) convection parameterization with a shallow-water analogue atmosphere. The square frequency of linear convectively-coupled waves is given by a squared sum of the dry gravity-wave and the convective energy-cycle frequencies, shortening the period of the convective cycle through the large-scale coupling. In a weakly nonlinear regime, the system follows an equation analogous to the Kortweg-de Vries equation, which exhibits a solitary-wave solution, with behavior reminiscent of observed tropical westerly-wind bursts