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Martin Leutbecher

Abstract

The effect of partial reflections on surface pressure drag is investigated for hydrostatic gravity waves in two-layer flow with piecewise constant buoyancy frequency. The variation of normalized surface pressure drag with interface height is analyzed for axisymmetric mountains. The results are compared with the familiar solution for infinitely long ridges. The drag for the two-layer flow is normalized with the drag of one-layer flow. An analytical expression for the normalized drag of axisymmetric mountains is derived from linear theory of steady flow. Additionally, two-layer flow over finite-height axisymmetric mountains is simulated numerically for flow with higher stability in the upper layer. The temporal evolution of the surface pressure drag is examined in a series of experiments with different interface and mountain heights. The focus is on the linear regime and the nonlinear regime of nonbreaking gravity waves.

The entire spectrum of gravity waves can be in resonance in hydrostatic flow over infinitely long ridges. This cannot occur in 3D flow over isolated mountains due to the dispersion of gravity waves. In consequence, the oscillation of the normalized drag with interface height is smaller for axisymmetric mountains than for infinitely long ridges. However, even for a reflection coefficient as low as ⅓ the drag of an axisymmetric mountain can be amplified by 50% and reduced by 40%.

The nonlinear drag becomes steady in the numerical experiments in which no wave breaking occurs. The steady-state nonlinear drag agrees quite well with the prediction of linear theory if the linear drag is computed for a slightly lowered interface.

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Martin Leutbecher

Abstract

The impact on the ECMWF Ensemble Prediction System of using singular vectors computed from 12-h forecasts instead of analyses has been studied. Results are based on 34 cases in November–December 1999 and 28 cases in September 2003. The similarity between singular vectors started from a 12-h forecast and singular vectors started from an analysis is very high for the extratropical singular vectors in each of the 62 cases and for both hemispheres. Consistently, ensemble scores and spread measures show close to neutral impact on geopotential height in the extratropics. The sensitivity of the singular vectors to the choice of trajectory is larger in the Tropics than in the extratropics. However, the spread in tropical cyclone tracks is not significantly decreased if singular vectors computed from 12-h forecasts are used.

The computation of singular vectors from forecasts could be used to disseminate the ensemble forecasts earlier or to allocate more resources to the nonlinear forecasts. Furthermore, it greatly facilitates the implementation of computationally more demanding configurations for the singular-vector-based initial perturbations.

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Martin Leutbecher

Abstract

A new tool for planning adaptive observations is introduced. Different modifications of the observing network can be compared prior to the time of modification. The method predicts the variance of forecast errors projected into a low-dimensional subspace. Tangent-linear error evolution is assumed and the contribution of model errors to the forecast error is neglected. Singular vectors of the propagator of the tangent-linear version of the forecast model are used to define a relevant subspace. The method employs the Hessian of the cost function of a variational assimilation scheme to obtain information on the distribution of initial errors. Thus, this technique for planning adaptive observations can be made consistent with operational variational assimilation schemes. The application of the method is currently limited to intermittent modifications of the observing network as changes of the background error distribution due to modifications of the network in previous assimilation cycles are not accounted for. The predicted changes of forecast error variance are identical to those that the ensemble transform Kalman filter method would yield if applied to a set of Hessian singular vectors.

The reduced rank estimate has been implemented in the Integrated Forecasting System of the European Centre for Medium-Range Weather Forecasts. To illustrate the scope of the method, it is applied to the 2-day forecast of an extratropical cyclone. The expected reduction of the total energy of forecast error is computed for various hypothetical adaptive networks that differ by spatial coverage, observation density, and the type of observation.

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Martin Leutbecher and Hans Volkert

Abstract

On 6 January 1992 measurements of a mountain wave with significant amplitude were taken over the southern tip of Greenland during an ER-2 flight at an altitude of about 20 km. This work focuses on 3D numerical simulations of the wave generation and its propagation into the stratosphere during this event. The sensitivity of the simulated mountain wave to surface friction and horizontal resolution is explored. A nonhydrostatic model is used for experiments with horizontal resolutions of 12, 4, and 1.3 km.

In all simulations the flow over the southern tip of Greenland generates a mountain wave, which propagates into the stratosphere. Changes of surface friction and horizontal resolution affect mostly the amplitude of the mountain wave. Increasing surface friction on the slopes reduces the amplitude of the excited orographic gravity wave. Horizontal diffusion required for numerical stability attenuates gravity waves during their propagation into the stratosphere. Increasing the horizontal resolution permits a smaller diffusion and thereby results in larger stratospheric wave amplitudes.

The experiment with increased surface friction at 1.3-km horizontal resolution shows the best agreement with the observational data of the wave in the stratosphere. The differences between the simulated and measured amplitudes of vertical displacement and temperature anomaly are less than about 20%. The disparity in vertical velocity is larger; downward velocities were observed up to 4.8 m s−1 and simulated up to 2.7 m s−1. In the experiments with lower surface friction at 4-km resolution, the accuracy regarding the amplitude of vertical displacement and temperature anomalies is similar, but the simulated maximum downdraft is even weaker. The other experiments with increased surface friction at 4-km resolution and normal friction at 12-km resolution significantly underestimate the wave amplitude. The results of the experiments suggest that the generation of orographic gravity waves and their propagation into the stratosphere can be simulated in three dimensions in a realistic manner provided that the magnitude of the parameterized surface friction is in a realistic range and the horizontal resolution is sufficient.

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Jean-Jacques Morcrette, George Mozdzynski, and Martin Leutbecher

Abstract

A specific interface between the radiation transfer calculations and the rest of the ECMWF model was introduced in 2003, potentially providing substantial economy in computer time by reducing the spatial resolution at which radiation transfer is evaluated, without incurring some of the deficiencies produced by the sampling strategy previously used in the ECMWF model. The introduction of a new more-computer-intensive radiation package (McRad) in June 2007 has led to a differentiated use of this interface depending on the applications. The history of the interface, how it is used, and its impact when using the new radiation scheme are discussed here. For a given model resolution, the impact of a lower-resolution radiation grid on the model behavior is studied here, in the context of 10-day forecasts at high resolution (TL799L91), of medium-resolution forecasts (TL399L62) used in the Ensemble Prediction System (EPS), and of low-resolution simulations (TL159L91) as used for model development and seasonal forecasts with an interactive ocean. Results for the high-resolution forecasts are compared in terms of objective scores and of the quality of “surface” parameters (total cloud cover, 2-m temperature and specific humidity, and 10-m wind) usually verified in a meteorological context. For the medium-resolution forecasts, the impact of the radiation grid is studied in terms of the potential increase in the efficiency of the EPS system without deteriorating the probabilistic skill. The impact of changes in the radiation grid resolution on the low-resolution versions of model is discussed in terms of cloud–radiation interactions and ocean surface temperature. For these operational applications, a radiation grid with a coarsening factor even as large as 2.5 for TL799L91 and TL159L91 and 4.2 for the EPS TL399L62 is shown to give results free of any systematic differences linked to the spatial interpolation and to the coarser resolution of both the inputs to and the outputs from the radiation transfer schemes.

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Peter D. Düben, Martin Leutbecher, and Peter Bauer

Abstract

Data storage and data processing generate significant cost for weather and climate modeling centers. The volume of data that needs to be stored and data that are disseminated to end users increases with increasing model resolution and the use of larger forecast ensembles. If precision of data is reduced, cost can be reduced accordingly. In this paper, three new methods to allow a reduction in precision with minimal loss of information are suggested and tested. Two of these methods rely on the similarities between ensemble members in ensemble forecasts. Therefore, precision will be high at the beginning of forecasts when ensemble members are more similar, to provide sufficient distinction, and decrease with increasing ensemble spread. To keep precision high for predictable situations and low elsewhere appears to be a useful approach to optimize data storage in weather forecasts. All methods are tested with data of operational weather forecasts of the European Centre for Medium-Range Weather Forecasts.

Open access
Linus Magnusson, Martin Leutbecher, and Erland Källén

Abstract

In this paper a study aimed at comparing the perturbation methodologies based on the singular vector ensemble prediction system (SV-EPS) and the breeding vector ensemble prediction system (BV-EPS) in the same model environment is presented. A simple breeding system (simple BV-EPS) as well as one with regional rescaling dependent on an estimate of the analysis error variance (masked BV-EPS) were used. The ECMWF Integrated Forecast System has been used and the three experiments are compared for 46 forecast cases between 1 December 2005 and 15 January 2006. By studying the distribution of the perturbation energy it was possible to see large differences between the experiments initially, but after 48 h the distributions have converged. Using probabilistic scores, these results show that SV-EPS has a somewhat better performance for the Northern Hemisphere compared to BV-EPS. For the Southern Hemisphere masked BV-EPS and SV-EPS yield almost equal results. For the tropics the masked breeding ensemble shows the best performance during the first 6 days. One reason for this is the current setup of the singular vector ensemble at ECMWF yielding in general very low initial perturbation amplitudes in the tropics.

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André Walser, Marco Arpagaus, Christof Appenzeller, and Martin Leutbecher

Abstract

This paper studies the impact of different initial condition perturbation methods and horizontal resolutions on short-range limited-area ensemble predictions for two severe winter storms. The methodology consists of 51-member ensembles generated with the global ensemble prediction system (EPS) of the European Centre for Medium-Range Weather Forecasts, which are downscaled with the nonhydrostatic limited-area model Lokal Modell. The resolution dependency is studied by comparing three different limited-area ensembles: (a) 80-km grid spacing, (b) 10-km grid spacing, and (c) 10-km grid spacing with a topography coarse grained to 80-km resolution. The initial condition perturbations of the global ensembles are based on singular vectors (SVs), and the tendencies are not perturbed (i.e., no stochastic physics). Two configurations are considered for the initial condition perturbations: (i) the operational SV configuration: T42 truncation, 48-h optimization time, and dry tangent-linear model, and (ii) the “moist SV” configuration: TL95 truncation, 24-h optimization time, and moist tangent-linear model.

Lokal Modell ensembles are analyzed for the European winter storms Lothar and Martin, both occurring in December 1999, with particular attention paid to near-surface wind gusts. It is shown that forecasts using the moist SV configuration predict higher probabilities for strong wind gusts during the storm period compared to forecasts with the operational SV configuration. Similarly, the forecasts with increased horizontal resolution—even with coarse topography—lead to higher probabilities compared with the low-resolution forecasts. Overall, the two case studies suggest that currently developed operational high-resolution limited-area EPSs have a great potential to improve early warnings for severe winter storms, particularly when the driving global EPS employs moist SVs.

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Tsz Yan Leung, Martin Leutbecher, Sebastian Reich, and Theodore G. Shepherd

Abstract

Global numerical weather prediction (NWP) models have begun to resolve the mesoscale k −5/3 range of the energy spectrum, which is known to impose an inherently finite range of deterministic predictability per se as errors develop more rapidly on these scales than on the larger scales. However, the dynamics of these errors under the influence of the synoptic-scale k −3 range is little studied. Within a perfect-model context, the present work examines the error growth behavior under such a hybrid spectrum in Lorenz’s original model of 1969, and in a series of identical-twin perturbation experiments using an idealized two-dimensional barotropic turbulence model at a range of resolutions. With the typical resolution of today’s global NWP ensembles, error growth remains largely uniform across scales. The theoretically expected fast error growth characteristic of a k −5/3 spectrum is seen to be largely suppressed in the first decade of the mesoscale range by the synoptic-scale k −3 range. However, it emerges once models become fully able to resolve features on something like a 20-km scale, which corresponds to a grid resolution on the order of a few kilometers.

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Tsz Yan Leung, Martin Leutbecher, Sebastian Reich, and Theodore G. Shepherd

Abstract

The accepted idea that there exists an inherent finite-time barrier in deterministically predicting atmospheric flows originates from Edward N. Lorenz’s 1969 work based on two-dimensional (2D) turbulence. Yet, known analytic results on the 2D Navier–Stokes (N-S) equations suggest that one can skillfully predict the 2D N-S system indefinitely far ahead should the initial-condition error become sufficiently small, thereby presenting a potential conflict with Lorenz’s theory. Aided by numerical simulations, the present work reexamines Lorenz’s model and reviews both sides of the argument, paying particular attention to the roles played by the slope of the kinetic energy spectrum. It is found that when this slope is shallower than −3, the Lipschitz continuity of analytic solutions (with respect to initial conditions) breaks down as the model resolution increases, unless the viscous range of the real system is resolved—which remains practically impossible. This breakdown leads to the inherent finite-time limit. If, on the other hand, the spectral slope is steeper than −3, then the breakdown does not occur. In this way, the apparent contradiction between the analytic results and Lorenz’s theory is reconciled.

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