A GCSS Boundary-Layer Cloud Model Intercomparison Study Of The First Astex Lagrangian Experiment

Three single-column models (all with an explicit liquid water budget and compara-tively high vertical resolution) and three two-dimensional eddy-resolving models (including one with bin-resolved microphysics) are compared with observations from the first ASTEX Lagrangian experiment. This intercomparison was a part of the second GCSS boundary-layer cloud modelling workshop in August 1995.In the air column tracked during the first ASTEX Lagrangian experiment, a shallow subtropical drizzling stratocumulus-capped marine boundary layer deepens after two days into a cumulus capped boundary layer with patchy stratocumulus. The models are forced with time varying boundary conditions at the sea-surface and the capping inversion to simulate the changing environment of the air column.The models all predict the observed deepening and decoupling of the boundary layer quite well, with cumulus cloud evolution and thinning of the overlying stratocumulus. Thus these models all appear capable of predicting transitions between cloud and boundary-layer types with some skill. The models also produce realistic drizzle rates, but there are substantial quantitative differences in the cloud cover and liquid water path between models. The differences between the eddy-resolving model results are nearly as large as between the single column model results. The eddy resolving models give a more detailed picture of the boundary-layer evolution than the single-column models, but are still sensitive to the choice of microphysical and radiative parameterizations, sub-grid-scale turbulence models, and probably model resolution and dimensionality. One important example of the differences seen in these parameterizations is the absorption of solar radiation in a specified cloud layer, which varied by a factor of four between the model radiation parameterizations.     

Mixed Integer-Real Valued Adjustment (IRA) Problems: GPS Initial Cycle Ambiguity Resolution by Means of the LLL Algorithm

In order to achieve to GPS solutions of first-order accuracy and integrity, carrier phase observations as well as pseudorange observations have to be adjusted with respect to a linear/linearized model. Here the problem of mixed integer-real valued parameter adjustment (IRA) is met. Indeed, integer cycle ambiguity unknowns have to be estimated and tested. At first we review the three concepts to deal with IRA: (i) DDD or triple difference observations are produced by a properly chosen difference operator and choice of basis, namely being free of integer-valued unknowns (ii) The real-valued unknown parameters are eliminated by a Gauss elimination step while the remaining integer-valued unknown parameters (initial cycle ambiguities) are determined by Quadratic Programming and (iii) a RA substitute model is firstly implemented (real-valued estimates of initial cycle ambiguities) and secondly a minimum distance map is designed which operates on the real-valued approximation of integers with respect to the integer data in a lattice. This is the place where the integer Gram-Schmidt orthogonalization by means of the LLL algorithm (modified LLL algorithm) is applied being illustrated by four examples. In particular, we prove that in general it is impossible to transform an oblique base of a lattice to an orthogonal base by Gram-Schmidt orthogonalization where its matrix enties are integer. The volume preserving Gram-Schmidt orthogonalization operator constraint to integer entries produces “almost orthogonal” bases which, in turn, can be used to produce the integer-valued unknown parameters (initial cycle ambiguities) from the LLL algorithm (modified LLL algorithm). Systematic errors generated by “almost orthogonal” lattice bases are quantified by A. K. Lenstra et al. (1982) as well as M. Pohst (1987). The solution point of Integer Least Squares generated by the LLL algorithm is = (L')⁻¹[L'◯] ∈ ℤ ^m where L is the lower triangular Gram-Schmidt matrix rounded to nearest integers, [L], and = [L'◯] are the nearest integers of L'◯, ◯ being the real valued approximation of z ∈ ℤ ^m , the m-dimensional lattice space Λ. Indeed due to “almost orthogonality” of the integer Gram-Schmidt procedure, the solution point is only suboptimal, only close to “least squares.” ? 2000 John Wiley & Sons, Inc.     

A sensitivity study of the WRF model in offshore wind modeling over the Baltic Sea

Accurate wind modeling is important for wind resources assessment and wind power forecasting.To improve the WRF model configuration for the offshore wind modeling over the Baltic Sea,this study per-formed a sensitivity study of the WRF model to multiple model configurations,including domain setup,grid resolution,sea surface temperature,land surface data,and atmosphere-wave coupling.The simu-lated offshore wind was evaluated against LiDAR observations under different wind directions,atmo-spheric stabilities,and sea status.Generally,the simulated wind profiles matched observations,despite systematic underestimations.Strengthening the forcing from the reanalysis data through reducing the number of nested domains played the largest role in improving wind modeling.Atmosphere-wave cou-pling further improved the simulated wind,especially under the growing and mature sea conditions.Increasing the vertical resolution,and updating the sea surface temperature and the land surface infor-mation only had a slight impact,mainly visible during very stable conditions.Increasing the horizontal resolution also only had a slight impact,most visible during unstable conditions.Our study can help to improve the wind resources assessment and wind power forecasting over the Baltic Sea.