I. Michael Navon

Improved Skill for the Anomaly Correlation of Geopotential Heights at 500 hPa

This paper addresses the anomaly correlation of the 500-hPa geopotential heights from a suite of global multimodels and from a model-weighted ensemble mean called the superensemble. This procedure follows a number of current studies on weather and seasonal climate forecasting that are being pursued. This study includes a slightly different procedure from that used in other current experimental forecasts for other variables. Here a superensemble for the „ 2 of the geopotential based on the daily forecasts of the geopotential fields at the 500hPa level is constructed. The geopotential of the superensemble is recovered from the solution of the Poisson equation. This procedure appears to improve the skill for those scales where the variance of the geopotential is large and contributes to a marked improvement in the skill of the anomaly correlation. Especially large improvements over the Southern Hemisphere are noted. Consistent day-6 forecast skill above 0.80 is achieved on a day to day basis. The superensemble skills are higher than those of the best model and the ensemble mean. For days 1‐6 the percent improvement in anomaly correlations of the superensemble over the best model are 0.3, 0.8, 2.25, 4.75, 8.6, and 14.6, respectively, for the Northern Hemisphere. The corresponding numbers for the Southern Hemisphere are 1.12, 1.66, 2.69, 4.48, 7.11, and 12.17. Major improvement of anomaly correlation skills is realized by the superensemble at days 5 and 6 of forecasts. The collective regional strengths of the member models, which is reflected in the proposed superensemble, provide a useful consensus product that may be useful for future operational guidance.

The analysis of an ill-posed problem using multi-scale resolution and second-order adjoint techniques

Abstract A wavelet regularization approach is presented for dealing with an ill-posed problem of adjoint parameter estimation applied to estimating inflow parameters from down-flow data in an inverse convection case applied to the two-dimensional parabolized Navier–Stokes equations. The wavelet method provides a decomposition into two subspaces, by identifying both a well-posed as well as an ill-posed subspace, the scale of which is determined by finding the minimal eigenvalues of the Hessian of a cost functional measuring the lack of fit between model prediction and observed parameters. The control space is transformed into a wavelet space. The Hessian of the cost is obtained either by a discrete differentiation of the gradients of the cost derived from the first-order adjoint or by using the full second-order adjoint. The minimum eigenvalues of the Hessian are obtained either by employing a shifted iteration method [X. Zou, I.M. Navon, F.X. Le Dimet., Tellus 44A (4) (1992) 273] or by using the Rayleigh quotient. The numerical results obtained show the usefulness and applicability of this algorithm if the Hessian minimal eigenvalue is greater or equal to the square of the data error dispersion, in which case the problem can be considered as well-posed (i.e., regularized). If the regularization fails, i.e., the minimal Hessian eigenvalue is less than the square of the data error dispersion of the problem, the following wavelet scale should be neglected, followed by another algorithm iteration. The use of wavelets also allowed computational efficiency due to reduction of the control dimension obtained by neglecting the small-scale wavelet coefficients.

On Estimation of Temperature Uncertainty Using the Second Order Adjoint Problem

The uncertainty of temperature prediction from the heat flux error is estimated using first and second order adjoint equations. The adjoint codes developed for the inverse heat transfer problems provide the uncertainty estimation for the corresponding forward problems. Numerical tests corroborate the feasibility of fast uncertainty estimation using Hessian maximum eigenvalue obtained via second order adjoint equations.

Four-Dimensional Variational Data Assimilation Experiments with a Multilevel Semi-Lagrangian Semi-Implicit General Circulation Model

Abstract Four-dimensional variational data assimilation (VDA) experiments have been carded out using the adiabatic version of the NASA/Goddard Laboratory for Atmospheres semi-Lagrangian semi-implicit (SLSI) multilevel general circulation model. The limited-memory quasi-Newton minimization technique was used to find the minimum of the cost friction. With model-generated observations, different first-guess initial conditions were used to carry out the experiments. The experiments included randomly perturbed initial conditions, as well as different weight matrices in the cost function. The results show that 4D VDA works well with various initial conditions as control variables. Scaling the gradient of the cost function proves to be an effective method of improving the convergence rate of the VDA minimization process. The impacts of the length of the assimilation interval and the time density of the observations on the convergence rate of the minimization have also been investigated. An improved assimilation ...

Determination of the structure of mixed argon–xenon clusters using a finite‐temperature, lattice‐based Monte Carlo method

The energy‐optimized structures of all mixed Ar–Xe clusters containing 7, 13, and 19 atoms have been determined using a finite‐temperature, lattice‐based Monte Carlo procedure, which incorporates a highly efficient, memoryless, quasi‐Newton‐like conjugate gradient algorithm. This involves locating the global minima on the corresponding potential energy surfaces constructed from pairwise‐additive Lennard‐Jones potentials. For these systems, this optimization procedure has been found to be much more efficient than the more generally applicable simulated annealing method. Based on these energy‐optimized structures, substitution sequences have been presented and discussed.

The impact of background error on incomplete observations for 4d-var data assimilation with the FSU GSM

To assess the impact of incomplete observations on the 4D-Var data assimilation, twin experiments were carried out with the dynamical core of the new FSU GSM consisting of a T126L14 global spectral model in a MPI parallel environment. Results and qualitative aspects are presented for incomplete data in the spatial dimension and for incomplete data in time, with and without inclusion of the background term into the cost functional. The importance of the background estimate on the 4D-Var analysis in the presence of small Gaussian errors in incomplete data is also investigated.

Non-parametric calibration of the local volatility surface for European options using a second-order Tikhonov regularization

We calibrate the local volatility surface for European options across all strikes and maturities of the same underlying. There is no interpolation or extrapolation of either the option prices or the volatility surface. We do not make any assumption regarding the shape of the volatility surface except to assume that it is smooth. Due to the smoothness assumption, we apply a second-order Tikhonov regularization. We choose the Tikhonov regularization parameter as one of the singular values of the Jacobian matrix of the Dupire model. Finally we perform extensive numerical tests to assess and verify the aforementioned techniques for both volatility models with known analytical solutions of European option prices and real market option data.