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 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.     

ON THE SENSITIVITY OF PRECIPITATION FORECASTS TO THE MOIST PHYSICS AND THE HORIZONTAL RESOLUTION OF NUMERICAL MODEL*

The impacts of the enhanced model's moist physics and horizontal resolution upon the QPFs(quantitative precipitation forecasts) are investigated by applying the HIRLAM(high resolution limited area model) to the summer heavy-rain cases in China.The performance of the control run,for which a 0.5°×0.5°grid spacing and a traditional "grid-box supersaturation removal+Kuo type convective paramerization" are used as the moist physics,is compared with that of the sensitivity runs with an enhanced model's moist physics(Sundqvist scheme) and an increased horizontal resolution(0.25°×0.25°),respectively.The results show:(1) The enhanced moist physics scheme(Sundqvist scheme),by introducing the cloud water content as an additional prognostic variable and taking into account briefly of the microphysics involved in the cloud-rain conversion,does bring improvements in the model's QPFs.Although the deteriorated QPFs also occur occasionally,the improvements are found in the majority of the cases,indicating the great potential for the improvement of QPFs by enhancing the model's moist physics.(2) By increasing the model's horizontal resolution from 0.5°×0.5°,which is already quite high compared with that of the conventional atmospheric soundings,to 0.25°×0.25°without the simultaneous enhancement in model physics and objective analysis,the improvements in QPFs are very limited.With higher resolution,although slight amelioration in locating the rainfall centers and in resolving some finer structures of precipitation pattern are made,the number of the mis-predicted fine structures in rainfall field increases with the enhanced model resolution as well.     

Behaviour of Fe-oxides relevant to contaminant uptake in the environment

The behaviour of Fe-oxides was investigated during precipitation and co-precipitation, phase transformation and dissolution, while their ability to adsorb and incorporate trace components was examined. Some samples were synthesised and studied under controlled laboratory conditions and other samples were taken from experiments designed to test the effectiveness of waste treatment strategies using iron. Surface-sensitive and high-resolution techniques were used to complement information gathered from classical, macroscopic methods.

Adsorption isotherms for Ni²⁺ uptake on synthetic ferrihydrite (Fe₅HO₈·4H₂O, often written simply Fe(OH)₃), goethite (-FeOOH), hematite (-Fe₂O₃) and magnetite (Fe₃O₄) were all similar, increasing as expected at higher pH. Desorption behaviour was also similar, but one third or more of the Ni²⁺ failed to return to solution. In the past, “irreversible sorption” has been blamed on uptake into micro-fractures or pores, but during examination (using Atomic force microscopy, AFM) of hundreds of Fe-oxide particles, no evidence for such features could be found, leading to the conclusion that Ni²⁺ must become incorporated onto or into the solids. When solutions of Fe(II) are oxidised in controlled laboratory conditions or during treatment of ash from municipal waste incinerators, two-line ferrihydrite forms rapidly and on never-dried samples, AFM shows abundant individual particles with diameter ranging from 0.5 to several tens of nanometers. Aging in solution at 70°C promotes growth of the particles into hematite and goethite and their identification (by X-ray powder diffraction, XRPD, with Rietveld refinement) becomes possible at the same aging stage as mineral morphology becomes recognisable by AFM. In other experiments that were designed to mimic natural attack by organic acids, colloidal lepidocrocite (γ-FeOOH) was observed in situ by AFM, while reductive dissolution removed material on specific crystal faces. Lath ends are eroded fastest while basal planes are more stable.

In order to help elucidate mechanisms of contaminant immobilisation by Fe-oxides, we examined samples from a reactive barrier made with 90% quartz sand, 5% bentonite and 5% zero-valent iron filings that had reacted with a solution typical of leachate from coal-burning fly ash using time-of-flight secondary ion mass spectroscopy (TOF-SIMS). Fe(0) oxidised to Fe(III), while soluble and toxic Cr(VI) was reduced to insoluble Cr(III). Chemical maps show Fe-oxide coatings on bentonite; Cr is associated with Fe-oxides to some extent but its association with Ca in a previously undescribed phase is much stronger. Other samples taken from municipal waste incinerator ash that had been treated by aeration in Fe(II) solutions were examined with transmission electron microscopy (TEM), selected area electron diffraction (SAED) and energy dispersive X-ray spectroscopy (EDS). Pb and some Zn are seen to be dispersed throughout two-line ferrihydrite aggregates, whereas Sn and some Zn are incorporated simply as a result of entrainment of individual ZnSn-oxide crystallites.

Geochemical speciation models that fail to account for contaminant uptake in solid solutions within major phases or as thin coatings or entrained crystals of uncommon phases such as those described here risk to underestimate contaminant retardation or immobilisation.     

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.     

Experimental and numerical modelling of sedimentation in a rectangular shallow basin

Numerical simulation of flows in shallow reservoirs has to be checked for its consistency in predicting real flow conditions and sedimentation patterns. Typical flow patterns may exhibit flow separation at the inlet, accompanied by several recirculation and stagnation areas all over the reservoir surface. The aim of the present research project is to study the influence of the geometry of a reservoir on sediment transport and deposition numerically and experimentally, focusing on a prototype reservoir depth between 5 and 15 m as well as suspended sediment transport.
A series of numerical simulations is presented and compared with scaled laboratory experiments, with the objective of testing the sensitivity to different flow and sediment parameters and different turbulence closure schemes. Different scenarios are analyzed and a detailed comparison of preliminary laboratory tests and some selected simulations are presented.
The laboratory experiments show that suspended sediment transport and deposition are determined by the initial flow pattern and by the upstream and downstream boundary conditions. In the experiments, deposition in the rectangular basin systematically developed along the left bank, although inflow and outflow were positioned symmetrically along the centre of the basin. Three major horizontal eddies developed influencing the sediment deposition pattern. Although asymmetric flow patterns are privileged, a symmetric pattern can appear from time to time. This particular behaviour could also be reproduced by a two-dimensional depth-averaged flow and sediment transport model （CCHE2D）. The paper presents numerical simulations using different turbulence closure schemes （k-ε and eddy viscosity models）. In spite of the symmetric setup, these generally produced an asymmetric flow pattern that can easily switch sides depending on the assumptions made for the initial and boundary conditions. When using the laboratory experiment as a reference, the most reliable numerical results have been obtai