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J. Sela and S. J. Jacobs

Abstract

Ageostrophic effects on the stability properties of a frictionless adiabatic atmosphere are investigated. The neutral stability boundary is found to consist of the range of variation in the basic state zonal speed. It is found that fast moving waves are not marginal to the neutral boundary. A numerical study shows that the introduction of lateral dependence results in a selective ageostrophic influence on the growth rates of unstable modes. This result is in contrast to the purely distortive modification in the three-dimensional quasi-geostrophic corresponding case.

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J. Sela and S. J. Jacobs

Abstract

A two-layer Gulf Stream model is considered. We assume no motion in the lower layer and a basic state zonal jet in the upper. The purpose of the study is to examine numerically the validity of hydrodynamic stability investigations of the Gulf Stream.

It is found that the ageostrophic influence depends on the basic state velocity profile and on the inverse radius of deformation, γ. In the case of a basic velocity profile without countercurrent, an increase in the Rossby number results in a more stable flow. When a countercurrent is included, the results depend on the radius of deformation and wavelength. For a realistic value of γ, short zonal waves are destabilized while long ones are stabilized. It is also found that an increase in γ stabilizes the flow for both profiles.

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JOSEPH SELA and WILLIAM J. BOSTELMAN

Abstract

The primitive equations are integrated with respect to the vertical coordinate, sigma. The resulting equations contain vertical eddy terms arising from non-linearities. These eddies are parameterized using a standard-atmosphere temperature distribution and a linear jet wind profile independent of horizontal position.

The model includes topography and is capable of responding to diabatic heating. Experiments with and without the continuity equation are carried out, and a comparison is made with barotropic forecasts. Exclusion of the mass continuity condition results in superior forecasts, especially near high terrain.

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X. Zou, I. M. Navon, and J. Sela

Abstract

Variational four-dimensional data assimilation, combined with a penalty method constraining time derivatives of the surface pressure, the divergence, and the gravity-wave components is implemented on an adiabatic version of the National Meteorological Center's 18-level primitive equation spectral model with surface drag and horizontal diffusion. Experiments combining the Machenhauer nonlinear normal-mode initialization procedure and its adjoint with the variational data assimilation are also presented. The modified variational data-assimilation schemes are tested to assess how well they control gravity-wave oscillations.

The gradient of a penalized cost function can be obtained by a single integration of the adjoint model. A detailed derivation of the gradient calculation of different penalized cost functions is presented, which is not restricted to a specific model.

Numerical results indicate that the inclusion of penalty terms into the cost function will change the model solution as desired. The advantages of the use of simple penalty terms over penalty terms including the model normal modes results in a simplification of the procedure, allowing a more direct control over the model variables and the possibility of using weak constraints to eliminate the high-frequency gravity-wave oscillations. This approach does not require direct information about the model normal modes. One of the encouraging results obtained is that the introduction of the penalty terms does not slow the convergence rate of the minimization process.

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I. M. Navon, X. Zou, J. Derber, and J. Sela

Abstract

Variational four-dimensional (4D) data assimilation is performed using an adiabatic version of the National Meteorological Center (NMC) baroclinic spectral primitive equation model with operationally analyzed fields as well as simulated datasets. Two limited-memory quasi-Newton minimization techniques were used to iteratively find the minimum of a cost function, with the NMC forecast as a constraint. The cost function consists of a weighted square sum of the differences between the model forecast and observations over a time interval. In all the experiments described in this paper, observations are available for all degrees of freedom of the model. The derivation of the adjoint of the discretized adiabatic NMC spectral model is presented. The creation of this adjoint model allows the gradient of the cost function with respect to the initial conditions to be computed using a single backward-in-time integration of the adjoint equations.

As an initial evaluation of the variational data-assimilation procedure, an assimilation system with a low-resolution version of the NMC spectral model was tested using fields from a Rossby-Haurwitz-wave solution as observations. The results were encouraging, with a significant reduction in the magnitudes of both the cost function and the norm of its gradient during the minimization process. In particular, the high-frequency noise exhibited in the rms of the divergence field, produced by random perturbation in the initial conditions, is largely eliminated after the variational data assimilation.

The performance of the assimilation scheme was examined in a more realistic configuration using the adiabatic NMC spectral model truncated at T40. Both operationally analyzed observations, consisting of vorticity, divergence, temperature, surface pressure and moisture fields (distributed at two time levels separated by a 6-h time interval), and model-generated data were variationally assimilated. The effect of the number of observation fields in time on the convergence rate of the minimization and the impacts due to the inclusion of the horizontal diffusion and the surface drag in the model and its adjoint on the convergence rate and the accuracy of the retrieval are addressed.

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James E. Hoke, Norman A. Phillips, Geoffrey J. Dimego, James J. Tuccillo, and Joseph G. Sela

Abstract

The three components of the Regional Analysis and Forecast System (RAFS) of the National Meteorological Center (NMC) are described. This system was implemented in March 1985 to supplement guidance from NMC's limited-area fine-mesh model (LFM), especially for precipitation forecasting. The three components of the RAFS are the regional optimum interpolation analysis, the Baer–Tribbia nonlinear normal mode initialization, and the nested grid model—a grid point, primitive-equation model in sigma coordinates. Postprocessing of model forecasts and plans for system improvement are also discussed.

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S. Zhang, X. Zou, J. Ahlquist, I. M. Navon, and J. G. Sela

Abstract

Cost functions formulated in four-dimensional variational data assimilation (4DVAR) are nonsmooth in the presence of discontinuous physical processes (i.e., the presence of “on–off” switches in NWP models). The adjoint model integration produces values of subgradients, instead of gradients, of these cost functions with respect to the model’s control variables at discontinuous points. Minimization of these cost functions using conventional differentiable optimization algorithms may encounter difficulties. In this paper an idealized discontinuous model and an actual shallow convection parameterization are used, both including on–off switches, to illustrate the performances of differentiable and nondifferentiable optimization algorithms. It was found that (i) the differentiable optimization, such as the limited memory quasi-Newton (L-BFGS) algorithm, may still work well for minimizing a nondifferentiable cost function, especially when the changes made in the forecast model at switching points to the model state are not too large; (ii) for a differentiable optimization algorithm to find the true minimum of a nonsmooth cost function, introducing a local smoothing that removes discontinuities may lead to more problems than solutions due to the insertion of artificial stationary points; and (iii) a nondifferentiable optimization algorithm is found to be able to find the true minima in cases where the differentiable minimization failed. For the case of strong smoothing, differentiable minimization performance is much improved, as compared to the weak smoothing cases.

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E. Kalnay, M. Kanamitsu, J. Pfaendtner, J. Sela, M. Suarez, J. Stackpole, J. Tuccillo, L. Umscheid, and D. Williamson
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M. Kanamitsu, J.C. Alpert, K.A. Campana, P.M. Caplan, D.G. Deaven, M. Iredell, B. Katz, H.-L. Pan, J. Sela, and G.H. White

Abstract

A number of improvements were implemented on 6 March 1991 into the National Meteorological Center's global model, which is used in the global data assimilation system (GDAS), the aviation (AVN) forecast, and the medium-range forecast (MRF):

  • The horizontal resolution of the forecast model was increased from triangular truncation T80 to T126, which corresponds to an equivalent increase in grid resolution from 160 km to 105 km.

  • The use of enhanced orography has been discontinued and replaced by mean orography.

  • A new marine-stratus parameterization was introduced.

  • A new mass-conservation constraint was implemented.

  • The horizontal diffusion in the medium scales was reduced by adopting the Leith formulation.

  • A new, more accurate sea-surface temperature analysis is now used.

In this note, we discuss each of the changes and briefly review the new model performance.

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