SUMMARYA computational scheme suitable for numerical weather prediction and climate modelling over a wide range of length scales is described. Its formulation is non-hydrostatic and fully compressible, and shallow atmosphere approximations are not made. Semi-implicit, semi-Lagrangian time-integration methods are used. The scheme forms the dynamical core of the unified model used at the Met Office for all its operational numerical weather prediction and in its climate studies.

Practical experience in developing and using the U.K. Met Office Unified Model for both weather and climate prediction provides lessons about both the benefits and challenges of seamless prediction.T he concept of a unified or seamless framework for weather and climate prediction has attracted a lot of attention in the last few years (Hurrell et al. 2009;Brunet et al. 2010;Shapiro et al. 2010;Nobre et al. 2010;Hazeleger et al. 2010;Senior et al. 2011). Traditionally the weather and climate prediction problems have been seen as different disciplines. Numerical weather prediction (NWP) is crucially dependent on defining an accurate initial state and running at the highest possible resolutions, while climate prediction has sought to incorporate the full complexity of the Earth system in order to accurately capture long time-scale variations and feedbacks determining the current climate and potential climate change. Unifying modeling and prediction across time scales stems from a recognition that the evolution of the weather and climate are linked by the same physical processes in the atmosphereocean-land-cryosphere system operating across multiple space and time scales. In addition, there is an increasing requirement to include Earth system complexity in NWP models (e.g., atmospheric chemistry for air quality predictions) and growing evidence that improvements to the resolution and initialization of coupled climate models are required to accurately capture important modes of atmospheric and oceanic variability on monthly to decadal time scales (e.g., Scaife et al. 2011).What does seamless prediction look like in practice? The aim of this paper is to discuss the Met Office experiences over the last 25 years as we have moved toward a fully unified framework for our global and regional atmospheric, land, and ocean prediction systems, highlighting the clear benefits but also the potential drawbacks and pitfalls encountered along the way. We will also discuss the current status of our unified prediction systems and vision for the future. historiCAl deVelopMent of the Met offiCe WeAther And CliMAte Models. Phase 1 (1960-90): Separate NWP and climate models. As in most other modeling centers, the Met Office initial development of numerical models for weather forecasting and climate was entirely 1865 december 2012 AmerIcAN meTeOrOLOGIcAL SOcIeTY |

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A warm bias in tropical tropopause temperature is found in the Met Office Unified Model (MetUM), in common with most models from phase 5 of CMIP (CMIP5). Key dynamical, microphysical, and radiative processes influencing the tropical tropopause temperature and lower-stratospheric water vapor concentrations in climate models are investigated using the MetUM. A series of sensitivity experiments are run to separate the effects of vertical advection, ice optical and microphysical properties, convection, cirrus clouds, and atmospheric composition on simulated tropopause temperature and lower-stratospheric water vapor concentrations in the tropics. The numerical accuracy of the vertical advection, determined in the MetUM by the choice of interpolation and conservation schemes used, is found to be particularly important. Microphysical and radiative processes are found to influence stratospheric water vapor both through modifying the tropical tropopause temperature and through modifying upper-tropospheric water vapor concentrations, allowing more water vapor to be advected into the stratosphere. The representation of any of the processes discussed can act to significantly reduce biases in tropical tropopause temperature and stratospheric water vapor in a physical way, thereby improving climate simulations.

After extensive efforts over the course of a decade, convective-scale weather forecasts with horizontal grid spacings of 1–5 km are now operational at national weather services around the world, accompanied by ensemble prediction systems (EPSs). However, though already operational, the capacity of forecasts for this scale is still to be fully exploited by overcoming the fundamental difficulty in prediction: the fully three-dimensional and turbulent nature of the atmosphere. The prediction of this scale is totally different from that of the synoptic scale (103 km), with slowly evolving semigeostrophic dynamics and relatively long predictability on the order of a few days. Even theoretically, very little is understood about the convective scale compared to our extensive knowledge of the synoptic-scale weather regime as a partial differential equation system, as well as in terms of the fluid mechanics, predictability, uncertainties, and stochasticity. Furthermore, there is a requirement for a drastic modification of data assimilation methodologies, physics (e.g., microphysics), and parameterizations, as well as the numerics for use at the convective scale. We need to focus on more fundamental theoretical issues—the Liouville principle and Bayesian probability for probabilistic forecasts—and more fundamental turbulence research to provide robust numerics for the full variety of turbulent flows. The present essay reviews those basic theoretical challenges as comprehensibly as possible. The breadth of the problems that we face is a challenge in itself: an attempt to reduce these into a single critical agenda should be avoided.

This article demonstrates how numerical methods for atmospheric models can be validated by showing that they give the theoretically predicted rate of convergence to relevant asymptotic limit solutions. This procedure is necessary because the exact solution of the Navier-Stokes equations cannot be resolved by production models. The limit solutions chosen are those most important for weather and climate prediction. While the best numerical algorithms for this purpose largely reflect current practice, some important limit solutions cannot be captured by existing methods. The use of Lagrangian rather than Eulerian averaging may be required in these cases.

Numerical weather, climate, or Earth system models involve the coupling of components. At a broad level, these components can be classified as the resolved fluid dynamics, unresolved fluid dynamical aspects (i.e., those represented by physical parameterizations such as subgrid-scale mixing), and nonfluid dynamical aspects such as radiation and microphysical processes. Typically, each component is developed, at least initially, independently. Once development is mature, the components are coupled to deliver a model of the required complexity. The implementation of the coupling can have a significant impact on the model. As the error associated with each component decreases, the errors introduced by the coupling will eventually dominate. Hence, any improvement in one of the components is unlikely to improve the performance of the overall system. The challenges associated with combining the components to create a coherent model are here termed physics–dynamics coupling. The issue goes beyond the coupling between the parameterizations and the resolved fluid dynamics. This paper highlights recent progress and some of the current challenges. It focuses on three objectives: to illustrate the phenomenology of the coupling problem with references to examples in the literature, to show how the problem can be analyzed, and to create awareness of the issue across the disciplines and specializations. The topics addressed are different ways of advancing full models in time, approaches to understanding the role of the coupling and evaluation of approaches, coupling ocean and atmosphere models, thermodynamic compatibility between model components, and emerging issues such as those that arise as model resolutions increase and/or models use variable resolutions.

Operational weather forecasting requires the accurate simulation of atmospheric motions on scales ranging from the synoptic down to tens of kilometres. Weather fronts, characteristic of midlatitude weather systems, are generated through baroclinic instability on the large scale but are anisotropic features in which temperature and winds can vary rapidly on the short scale. We present a framework for evaluating model error in terms of asymptotic convergence using the Eady model. Through rescaling the problem, we are able to approach solutions of a balanced model, given by the semi‐geostrophic equations, using the non‐hydrostatic, incompressible Euler–Boussinesq Eady equations. Using this approach, we are able to validate the numerical implementation and assess the long‐term performance in terms of solution lifecycles. We present results using a finite‐difference method with semi‐implicit time‐stepping and semi‐Lagrangian transport, and show that we are able to proceed past the point of frontal collapse and recover the theoretical convergence rate. We propose that numerical diffusion of potential vorticity after collapse, as a result of insufficient Lagrangian conservation, is detrimental to the long‐term evolution of the solution.