SUMMARYSystematic westerly biases in the northern hemisphere wintertime flow of the Meteorological Office 15-layer operational model and 11-layer general circulation model are described. Evidence that the failure to parametrize subgrid-scale orographic gravity wave drag may account for such biases is presented. This evidence is taken from aircraft studies, surface pressure drag measurements, and studies of the zonally averaged momentum budget. A parametrization scheme is described in which the surface stress is proportional to the near-surface wind speed and static stability, and to the variance of subgrid-scale orography. The stress is absorbed in the vertical by considering the influence of such gravity wave activity on static stability and vertical wind shear. A Richardson-number-dependent wave breaking formulation is devised, and the vertical stress profile determined by a saturation hypothesis whereby the breaking waves are maintained at marginal stability. It is shown that wave breaking preferentially occurs in the boundary layer and in the lower stratosphere.Results from a simple zonally symmetric model show how the adjustment to thermal wind balance with a wave drag in the stratosphere, warms polar regions by adiabatic descent, and decelerates the mean westerlies in the troposphere.The influence of the parametrization scheme on integrations of the 11-layer model is described, and found to be generally beneficial.In a discussion of the reasons why this problem has only recently emerged, it is suggested that the satisfactory northern hemisphere winter circulations of previous, coarser general circulation models were due to a compensation implied by underestimating both the surface drag, and the horizontal flux of momentum hy explicitly resolved large-scale eddies.

SUMMARYPhysical justification is provided for the use of kinetic energy backscatter in forecast models, particularly in respect of ensemble prediction systems. The rate of energy backscatter to scales near the truncation limit is controlled by a total energy dissipation function involving contributions from numerical diffusion, mountain drag and deep convection. A cellular automaton is used to generate evolving patterns that, together with the dissipation function, define a stream-function forcing field. Each member of the European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble forecast system is perturbed by a different realization of this backscatter forcing, and the resulting increase in ensemble spread, if not excessive, has a beneficial impact on probabilistic measures of forecast skill. The input of small-scale kinetic energy by the backscatter algorithm also helps to correct a known problem with the energy spectrum in the ECMWF model-the absence of the observed −5/3 spectral slope in the mesoscales.

Numerical experiments are performed with barotropic models to test a hypothesized mechanism by which barotropic eddies can, through Reynolds stresses, reinforce blocking flow patterns. Eddies propagating into a split Jetstream suffer an east‐west compression and north‐south extension of their vorticity fields and this enhanced, local enstrophy cascade is associated with energy transmission to the straining flow (i.e. the blocking flow field) and a characteristic pattern of vorticity forcing by transient motion. As a first step in demonstrating this mechanism, the barotropic vorticity equation is integrated in a form linearized about a state chosen to represent a split Jetstream with a prescribed eddy forcing function upstream. After thirty days of model integration, the time‐mean eddy kinetic energy, enstrophy and vorticity flux divergence are calculated, together with mean eddy vorticity flux vectors. The resulting eddy vorticity forcing field can be used to determine the second‐order induced flow. Experiments with the nonlinear barotropic vorticity equation show that dipole blocking patterns can be created simply by the introduction of an eddy generator into sufficiently weak, uniform westerly flow. Eddies alone are responsible for the block since the time‐mean vorticity equation has no external forcing functions such as an orographic term. Monthly mean statistics are again calculated and terms in the time‐mean vorticity equation are compared. Anticyclonic eddy vorticity forcing appears just upstream of the ‘blocking high’ in agreement with data analysed by Illari (1982) for the anomalous circulation over Europe in July 1976. Model flow fields fluctuate in a manner highly reminiscent of blocking episodes as observed in 500mb contour maps with strong bursts of southerly winds on the western flank of blocking highs during the approach and subsequent stagnation of each depression. The proposed straining mechanism and model simulations are in agreement with early observational studies of blocking.

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 large-anomaly 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.

▪ Abstract  Weather and climate predictions are uncertain, because both forecast initial conditions and the computational representation of the known equations of motion are uncertain. Ensemble prediction systems provide the means to estimate the flow-dependent growth of uncertainty during a forecast. Sources of uncertainty must therefore be represented in such systems. In this paper, methods used to represent model uncertainty are discussed. It is argued that multimodel and related ensembles are vastly superior to corresponding single-model ensembles, but do not provide a comprehensive representation of model uncertainty. A relatively new paradigm is discussed, whereby unresolved processes are represented by computationally efficient stochastic-dynamic schemes.

ABSTRACT:The Met Office has been routinely running a short-range global and regional ensemble prediction system (EPS) since the summer of 2005. This article describes a major upgrade to the global ensemble, which affected both the initial condition and model uncertainty perturbations applied in that ensemble. The change to the initial condition perturbations is to allow localization within the ensemble transform Kalman filter (ETKF). This enables better specification of the ensemble spread as a function of location around the globe. The change to the model uncertainty perturbations is the addition of a stochastic kinetic energy backscatter scheme (SKEB). This adds vorticity perturbations to the forecast in order to counteract the damping of small-scale features introduced by the semi-Lagrangian advection scheme. Verification of ensemble forecasts is presented for the global ensemble system. It is shown that the localization of the ETKF gives a distribution of the spread as a function of latitude that better matches the forecast error of the ensemble mean. The SKEB scheme has a substantial effect on the power spectrum of the kinetic energy, and with the scheme a shallowing of the spectral slope is seen in the tail. A k −5/3 slope is seen at wavelengths shorter than 1000 km and this better agrees with the observed spectrum. The local ETKF significantly improves forecasts at all lead times over a number of variables. The SKEB scheme increases the rate of growth of ensemble spread in some variables, and improves forecast skill at short lead times.

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Idealized cloud-resolving model (CRM) simulations spanning a large part of the tropical atmosphere are used to evaluate the extent to which deterministic convective parameterizations fail to capture the statistical fluctuations in deep-convective forcing, and to provide probability distribution functions that may be used in stochastic parameterization schemes for global weather and climate models. A coarse-graining methodology is employed to deduce an effective convective warming rate appropriate to the grid scale of a forecast model, and a convective parameterization scheme is used to bin these computed tendencies into different ranges of convective forcing strength. The dependence of the probability distribution functions for the coarse-grained temperature tendency on parameterized tendency is then examined.An aquaplanet simulation using a climate model, configured with similar horizontal resolution to that of the coarse-grained CRM fields, was used to compare temperature tendency variation (less the effect of advection and radiation) with that deduced as an effective forcing function from the CRM. The coarsegrained temperature tendency of the CRM is found to have a substantially broader probability distribution function than the equivalent quantity in the climate model.The CRM-based probability distribution functions of precipitation rate and convective warming are related to the statistical mechanics theory of Craig and Cohen and the "stochastic physics" scheme of Buizza et al. It is found that the standard deviation of the coarse-grained effective convective warming is an approximately linear function of its mean, thereby providing some support for the Buizza et al. scheme, used operationally by ECMWF.