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Eugenia Kalnay and Amnon Dalcher

Abstract

We have shown that it is possible to predict the skill of numerical weather forecasts—a quantity which is variable from day to day and region to region. This has been accomplished using as predictor the dispersion (measured by the average correlation) between members of an ensemble of forecasts started from five different analyses. The analyses had been previously derived for satellite data impact studies and included, in the Northern Hemisphere, moderate perturbations associated with the use of different observing systems.

When the Northern Hemisphere was used as a verification region, the prediction of skill was rather poor. This is due to the fact that such large area usually contains regions with excellent forecasts as well as regions with poor forecasts, and does not allow for discrimination between them. However, when we used regional verifications, the ensemble forecast dispersion provided a very good prediction of the quality of the individual forecasts.

Although the period covered in this study is only one month long, it includes cases with wide variation of skill in each of the four regions considered. The method could be tested in an operational context using ensembles of lagged forecasts and longer time periods in order to test its applicability to different arms and weather regimes.

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Eugenia Kálnay De Rivas

Abstract

The deep circulation of the atmosphere of Venus is simulated by means of two-dimensional numerical models. Two extreme cases are considered: first, rotation is neglected and the subsolar point is assumed to be fixed; second (and more realistically), the solar heating is averaged over a Venus solar day and rotation is included. For each case a Boussinesq model, in which density variations are neglected except when coupled with gravity, and a quasi-Boussinesq model which includes a basic stratification of density and a semi-gray treatment of radiation, are developed. The results obtained with the Boussinesq models are similar to those obtained by Goody and Robinson and by Stone. However, when the stratification of density is included and most of the solar radiation is absorbed near the top, the large-scale circulation is confined to the upper layers of the atmosphere during the 4×107 sec of simulated time. We cannot be sure that on a much longer time scale (109 sec) the circulation will not penetrate the interior, but our results suggest that radiation will tend to make the lower atmosphere highly stable. When solar radiation is allowed to penetrate the atmosphere, so that at the equator 6% of the incoming solar radiation reaches the surface, then the combination of a more deeply driven circulation and a partial greenhouse effect is able to maintain an adiabatic stratification.

The effect of symmetrical solar heating is to produce direct Hadley cells in each hemisphere with small reverse cells near the poles. Poleward angular momentum transport in the upper atmosphere produces a shear in the zonal motion with a maximum retrograde velocity of the order of 10 m sec−1 at the top of the atmosphere.

The numerical integrations were performed using non-uniform grids to allow adequate resolution of the boundary layers.

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Eugenia Kálnay-Rivas

Abstract

Although.there is some ambiguity in the description of the U.S. Navy Fleet fourth-order primitive-equation model developed by Mihok and Kaitala (1976), the finite differences used for the continuity equation and pressure gradient term appear to contain second-order errors comparable to those of the original second-order model, and larger fourth-order errors. In the thermodynamics, moisture and momentum equations, there is partial cancellation of second-order errors, leading to a better approximation of the phase speed. However, in regions with strong horizontal variations of wind, the second-order errors in these equations are serious. These errors are due to the neglect of the truncation errors introduced by horizontal averaging in the staggered grid.

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Eugenia Kalnay and Masao Kanamitsu

Abstract

In atmospheric models that include vertical diffusion and surface fluxes of heat and moisture it is common to observe large amplitude “fibrillations” associated with these noniinear damping terms. In this paper this phenomenon is studied through the analysis of a simple nonlinear damping equation, ∂X/∂t = −(KXP)X + S. It is concluded that the behavior of several time schemes for the strongly nonlinear damping equations currently used can be quite pathological, with either large amplitude oscillations, or even nonoscillatory but incorrect solutions. Also presented are new simple schemes, which are easy to implement and have a much wider range of stability. These schemes are applied in the new National Meteorological Center (NMC) spectral model.

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Eugenia Kálnay de Rivas

Abstract

The results of two-dimensional simulations of the deep circulation of Venus are presented. They prove that the high surface temperature can only be explained by the greenhouse effect, and that Goody and Robinson's dynamical model is not valid. Very long time integrations, up to a time comparable with the radiative relaxation time, confirm these results. Analytical radiative equilibrium solutions for a semi-grey atmosphere, both with and without an internal heat source, are presented. It is shown that the green-house effect is sufficient to produce the high surface temperature if τT * ≫ 100 and S = τS *T * ≲ 0.005. This result is still valid in the presence of an internal heat source of intensity compatible with observations.

A two-dimensional version of a three-dimensional model is used to test the validity of the new mechanism proposed by Gierasch to explain the 4-day circulation. Numerical experiments with horizontal viscosities vH = 1011 – 1012 cm2 s−1 failed to show strong zonal velocities even for the case of large Prandtl numbers. It is observed that the dissipation of angular momentum introduced by the strong horizontal diffusion more than compensates for the upward transport of angular momentum due to the Hadley cell.

Preliminary three-dimensional calculations show a tendency to develop strong small-scale circulations.

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Zoltan Toth and Eugenia Kalnay

Abstract

The breeding method has been used to generate perturbations for ensemble forecasting at the National Centers for Environmental Prediction (formerly known as the National Meteorological Center) since December 1992. At that time a single breeding cycle with a pair of bred forecasts was implemented. In March 1994, the ensemble was expanded to seven independent breeding cycles on the Cray C90 supercomputer, and the forecasts were extended to 16 days. This provides 17 independent global forecasts valid for two weeks every day.

For efficient ensemble forecasting, the initial perturbations to the control analysis should adequately sample the space of possible analysis errors. It is shown that the analysis cycle is like a breeding cycle: it acts as a nonlinear perturbation model upon the evolution of the real atmosphere. The perturbation (i.e., the analysis error), carried forward in the first-guess forecasts, is “scaled down” at regular intervals by the use of observations. Because of this, growing errors associated with the evolving state of the atmosphere develop within the analysis cycle and dominate subsequent forecast error growth.

The breeding method simulates the development of growing errors in the analysis cycle. A difference field between two nonlinear forecasts is carried forward (and scaled down at regular intervals) upon the evolving atmospheric analysis fields. By construction, the bred vectors are superpositions of the leading local (time-dependent) Lyapunov vectors (LLVs) of the atmosphere. An important property is that all random perturbations assume the structure of the leading LLVs after a transient period, which for large-scale atmospheric processes is about 3 days. When several independent breeding cycles are performed, the phases and amplitudes of individual (and regional) leading LLVs are random, which ensures quasi-orthogonality among the global bred vectors from independent breeding cycles.

Experimental runs with a 10-member ensemble (five independent breeding cycles) show that the ensemble mean is superior to an optimally smoothed control and to randomly generated ensemble forecasts, and compares favorably with the medium-range double horizontal resolution control. Moreover, a potentially useful relationship between ensemble spread and forecast error is also found both in the spatial and time domain. The improvement in skill of 0.04–0.11 in pattern anomaly correlation for forecasts at and beyond 7 days, together with the potential for estimation of the skill, indicate that this system is a useful operational forecast tool.

The two methods used so far to produce operational ensemble forecasts—that is, breeding and the adjoint (or “optimal perturbations”) technique applied at the European Centre for Medium-Range Weather Forecasts—have several significant differences, but they both attempt to estimate the subspace of fast growing perturbations. The bred vectors provide estimates of fastest sustainable growth and thus represent probable growing analysis errors. The optimal perturbations, on the other hand, estimate vectors with fastest transient growth in the future. A practical difference between the two methods for ensemble forecasting is that breeding is simpler and less expensive than the adjoint technique.

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Takuma Yoshida and Eugenia Kalnay

Abstract

Strongly coupled data assimilation (SCDA), where observations of one component of a coupled model are allowed to directly impact the analysis of other components, sometimes fails to improve the analysis accuracy with an ensemble Kalman filter (EnKF) as compared with weakly coupled data assimilation (WCDA). It is well known that an observation’s area of influence should be localized in EnKFs since the assimilation of distant observations often degrades the analysis because of spurious correlations. This study derives a method to estimate the reduction of the analysis error variance by using estimates of the cross covariances between the background errors of the state variables in an idealized situation. It is shown that the reduction of analysis error variance is proportional to the squared background error correlation between the analyzed and observed variables. From this, the authors propose an offline method to systematically select which observations should be assimilated into which model state variable by cutting off the assimilation of observations when the squared background error correlation between the observed and analyzed variables is small. The proposed method is tested with the local ensemble transform Kalman filter (LETKF) and a nine-variable coupled model, in which three Lorenz models with different time scales are coupled with each other. The covariance localization with the correlation-cutoff method achieves an analysis more accurate than either the full SCDA or the WCDA methods, especially with smaller ensemble sizes.

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Eugenia Kálnay-Rivas

Abstract

The “box-type” finite-difference method includes a weighted average of the pressure gradient with weights proportional to the surface of the grid walls. It is shown that this averaging introduces first-order truncation errors near the poles. An example is shown in which the relative error is of zero order and the scheme produces large distortions in the solution at high latitudes.

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Eugenia Kálnay de Rivas

Abstract

No abstract available.

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Eugenia Kalnay and Roy Jenne
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