Physics-Dynamics Coupling: Understanding Tropical Processes and Process Interactions in Weather and Climate Models

The tropics are an important area of uncertainty in weather and climate models with variation between models in the tropics often being larger than in the extra-tropics for example due to a lack of strong geostrophic balance. In this thesis, we consider atmospheric behaviour in the tropics with a focus on understanding the long-term balance regimes that arise when drag and heating interact in the tropical atmosphere. We will look at the dry and moist case as well as considering the adjustment to balance process. We outline a number of long-term balance regimes for the 2D dry and moist tropical atmosphere in the absence of Coriolis acceleration with heating and drag physics, deriving scalings for horizontal velocity, vertical velocity, potential temperature, Exner pressure, and where appropriate buoyancy frequency and total water. We then investigate the ability of a model to achieve or not achieve our hypothesised balances. We find in the dry case that the four regimes we outline are achievable within the model and produce distinct behaviours with scaling relationships that mostly match the theory. In the moist case however, only one balance regime can be achieved by the model, but the existence or not of long-term balance in the moist case has a notable effect on the triggering, sustaining and organisation of moist plumes. We also look at numerical constraints affecting the development of long-term balance regimes and we find that the horizontal gridlength has a strong effect on which long-term balance regime the model finds itself in and whether the model can achieve balance at all. We also consider the effect of horizontal gridlength on adjustment processes such as gravity waves

Simulation of all-scale atmospheric dynamics on unstructured meshes

The advance of massively parallel computing in the nineteen nineties and beyond encouraged finer grid intervals in numerical weather-prediction models. This has improved resolution of weather systems and enhanced the accuracy of forecasts, while setting the trend for development of unified all-scale atmospheric models. This paper first outlines the historical background to a wide range of numerical methods advanced in the process. Next, the trend is illustrated with a technical review of a versatile nonoscillatory forward-in-time finite-volume (NFTFV) approach, proven effective in simulations of atmospheric flows from small-scale dynamics to global circulations and climate. The outlined approach exploits the synergy of two specific ingredients: the MPDATA methods for the simulation of fluid flows based on the sign-preserving properties of upstream differencing; and the flexible finite-volume median-dual unstructured-mesh discretisation of the spatial differential operators comprising PDEs of atmospheric dynamics. The paper consolidates the concepts leading to a family of generalised nonhydrostatic NFTFV flow solvers that include soundproof PDEs of incompressible Boussinesq, anelastic and pseudo-incompressible systems, common in large-eddy simulation of small- and meso-scale dynamics, as well as all-scale compressible Euler equations. Such a framework naturally extends predictive skills of large-eddy simulation to the global atmosphere, providing a bottom-up alternative to the reverse approach pursued in the weather-prediction models. Theoretical considerations are substantiated by calculations attesting to the versatility and efficacy of the NFTFV approach. Some prospective developments are also discussed

Stochastic parameterization of shallow cumulus convection estimated from high-resolution data

In this paper, we report on the development of a methodology for stochastic parameterization of convective transport by shallow cumulus convection in weather and climate models. We construct a parameterization based on Large-Eddy Simulation (LES) data. These simulations resolve the turbulent fluxes of heat and moisture and are based on a typical case of non-precipitating shallow cumulus convection above sea in the trade-wind region. Using clustering, we determine a finite number of turbulent flux pairs for heat and moisture that are representative for the pairs of flux profiles observed in these simulations. In the stochastic parameterization scheme proposed here, the convection scheme jumps randomly between these pre-computed pairs of turbulent flux profiles. The transition probabilities are estimated from the LES data, and they are conditioned on the resolved-scale state in the model column. Hence, the stochastic parameterization is formulated as a data-inferred conditional Markov chain (CMC), where each state of the Markov chain corresponds to a pair of turbulent heat and moisture fluxes. The CMC parameterization is designed to emulate, in a statistical sense, the convective behaviour observed in the LES data. The CMC is tested in single-column model (SCM) experiments. The SCM is able to reproduce the ensemble spread of the temperature and humidity that was observed in the LES data. Furthermore, there is a good similarity between time series of the fractions of the discretized fluxes produced by SCM and observed in LES

Dynamics of an Idealized Fluid Model for Investigating Convective-scale Data Assimilation

An idealized fluid model of convective-scale numerical weather prediction, intended for use in inexpensive data assimilation experiments, is described here and its distinctive dynamics are investigated. The model modifies the rotating shallow water equations to include some simplified dynamics of cumulus convection and associated precipitation, extending and improving the model of Würsch and Craig. Changes to this original model are the removal of ad hoc diffusive terms and the addition of Coriolis rotation terms, leading to a so-called 1.5-dimensional model. Despite the non-trivial modifications to the parent equations, it is shown that this shallow water type model remains hyperbolic in character and can be integrated accordingly using a discontinuous Galerkin finite element method for nonconservative hyperbolic systems of partial differential equations. Combined with methods to ensure well-balancedness and non-negativity, the resulting numerical solver is novel, efficient and robust. Classical numerical experiments in the shallow water theory, such as the Rossby geostrophic adjustment and flow over topography, are reproduced for the standard shallow water model and used to highlight the modified dynamics of the new model. In particular, it exhibits important aspects of convective-scale dynamics relating to the disruption of large-scale balance and is able to simulate other features related to convecting and precipitating weather systems. Our analysis here and preliminary results suggest that the model is well suited for efficiently and robustly investigating data assimilation schemes in an idealized ‘convective-scale’ forecast assimilation framework

Mathematical Theory and Modelling in Atmosphere-Ocean Science

Mathematical theory and modelling in atmosphere-ocean science combines a broad range of advanced mathematical and numerical techniques and research directions. This includes the asymptotic analysis of multiscale systems, the deterministic and stochastic modelling of sub-grid-scale processes, and the numerical analysis of nonlinear PDEs over a broad range of spatial and temporal scales. This workshop brought together applied mathematicians and experts in the disciplinary fields of meteorology and oceanography for a wide-ranging exchange of ideas and results in this area with the aim of fostering fundamental interdisciplinary work in this important science area