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R. Gelaro, R. Buizza, T. N. Palmer, and E. Klinker


The sensitivity of forecast errors to initial conditions is used to examine the optimality of perturbations constructed from the singular vectors of the tangent propagator of the European Centre for Medium-Range Weather Forecasts model. Sensitivity and pseudo-inverse perturbations based on the 48-h forecast error are computed as explicit linear combinations of singular vectors optimizing total energy over the Northern Hemisphere. It is assumed that these perturbations are close to the optimal perturbation that can be constructed from a linear combination of these singular vectors. Optimality is measured primarily in terms of the medium-range forecast improvement obtained by adding the perturbations a posteriori to the initial conditions. Several issues are addressed in the context of these experiments, including the ability of singular vectors to describe forecast error growth beyond the optimization interval, the number of singular vectors required, and the implications of nonmodal error growth. Supporting evidence for the use of singular vectors based on a total energy metric for studying atmospheric predictability is also presented.

In general, less than 30 singular vectors capture a large fraction of the variance of the Northern Hemisphere sensitivity pattern obtained from a T63 adjoint model integration, especially in cases of low forecast skill. The sensitivity patterns for these cases tend to be highly localized with structures determined by the dominant singular vectors. Forecast experiments with these perturbations show significant improvements in skill in the medium range, indicating that singular vectors optimized for a short-range forecast continue to provide a useful description of error growth well beyond this time. The results suggest that ensemble perturbations based on 10–30 singular vectors should provide a reasonable description of the medium-range forecast uncertainty, although the inclusion of additional singular vectors is likely to be beneficial.

Nonmodality is a key consideration in the construction of optimal perturbations. There is virtually no projection between the contemporaneous unstable subspaces at the end of one forecast trajectory portion and the beginning of a second, consecutive portion. Sensitivity and ensemble perturbations constructed using the evolved singular vectors from a previous (day−2) forecast are suboptimal for the current (day+0) forecast initial conditions. It is argued that these results have implications for a range of issues in atmospheric predictability including ensemble weather prediction, data assimilation, and the development of adaptive observing techniques.

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L. Ferranti, T. N. Palmer, F. Molteni, and E. Klinker


An observational and modeling study is made of tropical-extratropical interactions on time scales relevant to medium and extended range forecasting. First, an empirical orthogonal function (EOF) analysis is made of outgoing longwave radiation (OLR) in the tropics over seven winters. Having removed the seasonal cycle and interannual variability, the two leading EOFs describe the 30–60 day oscillation. A composite of extratropical 500 mb geopotential height correlated simultaneously with this mode of tropical variability is constructed. In its two phase-quadrature components, this composite has significant projection onto the Pacific/North American teleconnection pattern and onto the North Atlantic oscillation pattern, respectively.

The 500 mb height composite is compared with the Simmons, Wallace and Branstator (SWB) mode of barotropic instability, which has similar periodicity and similar spatial structure in both its phase-quadrature components. A simple theoretical analysis shows that the SWB mode can be strongly excited by a periodic forcing in the tropics whose spatial structure resembles the oscillation in convective activity described by the first two EOFs of OLR. This is confirmed in a barotropic model integration, which is forced using the observed EOFs of OLR. The model response in the extratropics compares well with the observed composite oscillation in 500 mb height.

In the final phase of this study, the ECMWF model has been integrated over four wintertime 20-day periods. For each period, five integrations have been performed; a control forecast, an integration in which the tropics are relaxed towards the verifying analysis, an integration in which the tropics are relaxed towards the initial analysis, an integration in which the extratropics are relaxed towards the verifying analysis and finally an integration in which the extratropics are relaxed towards the initial analysis. The four initial dates were chosen on the basis that in the succeeding 20 days, observed OLR and extratropical height provided a reasonable realization of each separate quarter of the composite oscillation.

It was found that in the extratropics, skill scores in the range of 11–20 days were noticeably improved, particularly over the Pacific/North American region (consistent with expectations from the data analysis). The mean geopotential height error in the extratropics; i.e., the error averaged over the four experiments, was also reduced (mainly in the Pacific area) when the model tropical fields were relaxed towards the verifying analysis. Indeed, maps showing the time evolution of geopotential height from the first 5 days of the forecast were generally correlated with the differences between the integrations with tropics relaxed to the verifying analysis and to the initial analysis indicating a link between tropical and extratropical low-frequency variability.

The impact of the extratropics on the tropics was also studied where it was shown that the largest response was on the nondivergent component of the wind over the tropical east Pacific. Tropical skill scores and model systematic error in upper tropospheric streamfunction were significantly improved with the extratropics relaxed to the verifying analysis. By contrast, extratropical relaxation had a much smaller impact on the divergent component of the tropical wind.

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Christopher S. Bretherton, E. Klinker, A. K. Betts, and J. A. Coakley Jr.


Cloud fraction is a widely used parameter for estimating the effects of boundary-layer cloud on radiative transfer. During the Atlantic Stratocumulus Transition Experiment (ASTEX) during June 1992, ceilometer and satellite-based measurements of boundary-layer cloud fraction were made in the subtropical North Atlantic, a region typified by a 1–2 km deep marine boundary layer with cumulus clouds rising into a broken stratocumulus layer underneath an inversion. Both the diurnal cycle and day-to-day variations in low-cloud fraction are examined. It is shown that ECMWF low cloudiness analyses do not correlate with the observed variations in cloudiness and substantially underestimate the mean low cloudiness.

In these analyses, the parameterization of low cloud fraction is primarily based on the inversion strength. A comparison of ECMWF analyses and ASTEX soundings (most of which were assimilated into the analyses) shows that the thermodynamic structure of the boundary layer and the inversion strength are well represented (with some small but significant systematic biases) in the analyses and preserved (again with some biases) in 5-day forecasts.

However, even when applied to the actual sounding the ECMWF low cloud scheme cannot predict the observed day-to-day variations or the diurnal cycle in low cloud. Other diagnostic schemes based on lower tropospheric stability, cloud-top entrainment instability, boundary-layer depth, and vertical motion do equally poorly. The only successful predictor of low cloud frontier from sounding information is the relative humidity in the upper part of the boundary layer.

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T.N. Palmer, C. Brankovic, F. Molteni, S. Tibaldi, L. Ferranti, A. Hollingsworth, U. Cubasch, and E. Klinker

Results from a 3 1/2-yr experimental program of extended-range integrations of the European Centre for Medium-Range Weather Forecasts (ECMWF) numerical weather prediction model are summarized. The topics discussed include

Our results are broadly consistent with those from other major centers evaluating the feasibility of dynamical extended-range prediction. We believe that operational extended-range forecasting using the ECMWF model may be viable to day 20—and possibly beyond—following further research on techniques for Monte Carlo forecasting, and when model systematic error in the tropics has been reduced significantly.

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