G. J. Shutts

A Spectral Stochastic Kinetic Energy Backscatter Scheme and Its Impact on Flow-Dependent Predictability in the ECMWF Ensemble Prediction System

Understanding model error in state-of-the-art numerical weather prediction models and representing its impact on flow-dependent predictability remains a complex and mostly unsolved problem. Here, a spectral stochastic kinetic energy backscatter scheme is used to simulate upscale-propagating errors caused by unresolved subgrid-scale processes. For this purpose, stochastic streamfunction perturbations are generated by autoregressive processes in spectral space and injected into regions where numerical integration schemes and parameterizations in the model lead to excessive systematic kinetic energy loss. It is demonstrated how output from coarse-grained high-resolution models can be used to inform the parameters of such a scheme. The performance of the spectral backscatter scheme is evaluated in the ensemble prediction system of the European Centre for Medium-Range Weather Forecasts. Its implementation in conjunction with reduced initial perturbations results in a better spread‐error relationship, more realistic kinetic-energy spectra, a better representation of forecast-error growth, improved flow-dependent predictability, improved rainfall forecasts, and better probabilistic skill. The improvement is most pronounced in the tropics and for largeanomaly events. It is found that whereas a simplified scheme assuming a constant dissipation rate already has some positive impact, the best results are obtained for flow-dependent formulations of the unresolved processes.

Impact of a quasi-stochastic cellular automaton backscatter scheme on the systematic error and seasonal prediction skill of a global climate model

The impact of a nonlinear dynamic cellular automaton (CA) model, as a representation of the partially stochastic aspects of unresolved scales in global climate models, is studied in the European Centre for Medium Range Weather Forecasts coupled ocean–atmosphere model. Two separate aspects are discussed: impact on the systematic error of the model, and impact on the skill of seasonal forecasts. Significant reductions of systematic error are found both in the tropics and in the extratropics. Such reductions can be understood in terms of the inherently nonlinear nature of climate, in particular how energy injected by the CA at the near-grid scale can backscatter nonlinearly to larger scales. In addition, significant improvements in the probabilistic skill of seasonal forecasts are found in terms of a number of different variables such as temperature, precipitation and sea-level pressure. Such increases in skill can be understood both in terms of the reduction of systematic error as mentioned above, and in terms of the impact on ensemble spread of the CAs representation of inherent model uncertainty.

Using a Stochastic Kinetic Energy Backscatter Scheme to Improve MOGREPS Probabilistic Forecast Skill

AbstractAn improved stochastic kinetic energy backscatter scheme, version 2 (SKEB2) has been developed for the Met Office Global and Regional Ensemble Prediction System (MOGREPS). Wind increments at each model time step are derived from a streamfunction forcing pattern that is modulated by a locally diagnosed field of likely energy loss due to numerical smoothing and unrepresented convective sources of kinetic energy near the grid scale. The scheme has a positive impact on the root-mean-square error of the ensemble mean and spread of the ensemble. An improved growth rate of spread results in a better match with ensemble-mean forecast error at all forecast lead times, with a corresponding improvement in probabilistic forecast skill from a more realistic representation of model error. Other examples of positive impact include improved forecast blocking frequency and reduced forecast jumpiness. The paper describes the formulation of the SKEB2 and its assessment in various experiments.

Operational lee wave forecasting

An operational lee wave forecasting code is described and tested on a number of actual cases. Although the solution procedure involves a well-known numerical algorithm, its implementation for operational purposes needs to be intelligent and flexible. The technique involves an eigenvalue problem based on the vertical structure equation for stationary, internal gravity waves. Since the orientation of the trapped lee waves is not known a priori, the code solves the eigenvalue problem for a range of wind directions centred on the low-level wind direction and makes a decision as to which direction will have the largest amplitude and most highly trapped lee wave. The amplitude of the lee wave motion depends on the intensity of orographic forcing in a spectral band centred on the resonant wavelength. For complex terrain this is difficult to quantify. Here, it is assumed that the Fourier spectrum of the orography follows a power law in wavenumber and that the wave amplitude is attributed with a ‘wave launching-height’ condition. One of the test cases considered is the notorious ‘Sheffield gale’ of 16 February 1962, and in that case the lee wave code does predict an unusually large-amplitude wave. Copyright

Stably stratified flows in meteorology

Abstract It is generally believed by those undertaking research in the fundamental aspects of geophysical fluid dynamics and meteorology that their results contribute to the improvements to numerical weather prediction and in practical weather forecasting. However, the techniques whereby the appropriate research results are selected and incorporated into the numerical models are not widely known, particularly the methods for representing the phenomena whose horizontal scale is less than that of the grid boxes.(say, 50 km). Some accounts of numerical weather prediction imply that the representation of subgrid-scale phenomena is formally similar to classical physics. In fact, atmospheric motions on these scales are not like molecular motions in an ideal gas, but show considerable structure, approximating to combinations of various idealized states. Great skill and experience in this specialized activity has been applied to deciding on these states, finding physical criteria for defining them and then modelling the relevant phenomena occurring on this scale. In this paper, we focus on a restricted range of phenomena associated with stably stratified flows, notably mountain waves, convection and clouds, and boundary layer phenomena. This category provides many examples of structures which need to be considered in detail to reconstruct the large-scale picture accurately, as well as in local forecasting.

Assessing parametrization uncertainty associated with horizontal resolution in numerical weather prediction models

The need to represent uncertainty resulting from model error in ensemble weather prediction systems has spawned a variety of ad hoc stochastic algorithms based on plausible assumptions about sub-grid-scale variability. Currently, few studies have been carried out to prove the veracity of such schemes and it seems likely that some implementations of stochastic parametrization are misrepresentations of the true source of model uncertainty. This paper describes an attempt to quantify the uncertainty in physical parametrization tendencies in the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecasting System with respect to horizontal resolution deficiency. High-resolution truth forecasts are compared with matching target forecasts at much lower resolution after coarse-graining to a common spatial and temporal resolution. In this way, model error is defined and its probability distribution function is examined as a function of tendency magnitude. It is found that the temperature tendency error associated with convection parametrization and explicit water phase changes behaves like a Poisson process for which the variance grows in proportion to the mean, which suggests that the assumptions underpinning the Craig and Cohen statistical model of convection might also apply to parametrized convection. By contrast, radiation temperature tendency errors have a very different relationship to their mean value. These findings suggest that the ECMWF stochastic perturbed parametrization tendency scheme could be improved since it assumes that the standard deviation of the tendency error is proportional to the mean. Using our finding that the variance error is proportional to the mean, a prototype stochastic parametrization scheme is devised for convective and large-scale condensation temperature tendencies and tested within the ECMWF Ensemble Prediction System. Significant impact on forecast skill is shown, implying its potential for further development.

The relation of moist symmetric instability and upper‐level potential‐vorticity anomalies to the observed evolution of cloud heads

The cloud-head phenomenon has been known for some time as a precursor of rapid cyclogenesis. Based upon satellite imagery, two stages of cloud-head development are identified in this study that can be related to early and late stages of the associated cyclone. Weakly convex cloud heads emerge from the baroclinic zone at an early stage in cyclogenesis and strongly convex cloud heads develop in association with the rapid deepening of the cyclone. Trajectories are used to highlight the role of an upper-level potential-vorticity (PV) anomaly in the growth of the strongly convex cloud head and the main flow associated with the growth of the strongly convex cloud head is viewed using isentropic analysis. The possible role of moist symmetric instability in the development of both weakly and strongly convex cloud heads is discussed and a new diagnostic for measuring the vertically integrated extent of realizable symmetric (VRS) instability, based on the moist geostrophic PV, is introduced.

Some exact solutions to the semi-geostrophic equations for uniform potential vorticity flows

Abstract Some exact, nonlinear solutions to the unapproximated semi-geostrophic invertibility problem are noted for flows with uniform potential vorticity. One class of these solutions corresponds to an isolated homogeneous intrusion of fluid in a stratified background flow; the other represents a baroclinic point vortex analogous to the singular solution of the Laplacian which arises in the related quasi-geostrophic problem. The isolated intrusion solution is the formal, axisymmetric extension of the two-dimensional case given by Gill(1981). Using the conformal mapping method introduced by Gill, a two-dimensional, barotropic solution to the semi-geostrophic equations is obtained. This can be interpreted as an exact solution corresponding to uniform barotropic flow around an obstacle.

Stochastic parametrization of multiscale processes using a dual-grid approach

Some speculative proposals are made for extending current stochastic sub-gridscale parametrization methods using the techniques adopted from the field of computer graphics and flow visualization. The idea is to emulate sub-filter-scale physical process organization and time evolution on a fine grid and couple the implied coarse-grained tendencies with a forecast model. A two-way interaction is envisaged so that fine-grid physics (e.g. deep convective clouds) responds to forecast model fields. The fine-grid model may be as simple as a two-dimensional cellular automaton or as computationally demanding as a cloud-resolving model similar to the coupling strategy envisaged in ‘super-parametrization’. Computer codes used in computer games and visualization software illustrate the potential for cheap but realistic simulation where emphasis is placed on algorithmic stability and visual realism rather than pointwise accuracy in a predictive sense. In an ensemble prediction context, a computationally cheap technique would be essential and some possibilities are outlined. An idealized proof-of-concept simulation is described, which highlights technical problems such as the nature of the coupling.

An analytical model of the balanced flow created by localized convective mass transfer in a rotating fluid

Abstract A class of exact analytic solutions is presented which represent the steady flow which persists after a finite region of stratified fluid is displaced vertically under the action of non-entraining, moist convection. In this process, the absolute momentum and equivalent potential temperature are imagined to mix within the convecting fluid so that the end state has constant absolute momentum and (dry) static stability. The balanced flow that remains consists of a vertical shear-line front in the region from which the fluid was withdrawn and a lenticular region characterized by zero absolute vorticity with adiabatic warming below and cooling above. The form of this lens-front configuration changes depending on the amount of mass that is assumed to convect. A contour integration technique for evaluating the total energy of this class of solution is presented. Simple asymptotic expressions for the energy may be obtained for large lens-front separation and if the initial convective available potential energy is known, an upper bound can be deduced for the total amount of mass that can convect through a single plume. This limit, together with the Rossby radius of deformation based on the depth of the convection, defines two fundamental length scales.