Low-resolution Grid Research Articles

A Low-Dispersion 3-D Second-Order in Time Fourth-Order in Space FDTD Scheme (<tex>$ M3d_24 $</tex>)

A second-order in time fourth-order in space modified finite-difference time-domain (FDTD) scheme for three dimensional electromagnetic problems M3d/sub 24/ is presented. The algorithm enables the numerical phase error to be minimized, so that it leads to high accuracy with low resolution grids. The advantage of this method is demonstrated by considering the long distance propagation of the wave radiated from a time harmonic elementary dipole using a low resolution grid, and comparing the results with other FDTD schemes.

Implementation of direct and iterative methods for a class of Helmholtz wave problems

In this article, the applicability and the performance of two direct (DirCSR and DirSkyline) and one iterative (IterCG_CSR) methods for solving large linear systems of equations are analyzed. Alternative ways of storing the coefficient matrix K generated by the application of the finite element method (FEM) to the Helmholtz equation for wave propagation in coastal regions are considered. The two direct methods are based on a Crout variant, the LDL t factorization, but they are implemented with two different sparse storage modes, one being the standard skyline, and the other being the compressed sparse row. The preconditioner of the conjugate gradients iterative method is the above DirCSR, with a minor parameter adjustment. These methods are compared in terms of CPU time, size of the matrices and number of iterations, for the same systems of equations with complex symmetric and indefinite matrices. Their behavior in low resolution grids is also investigated because this is a critical issue in practical applications. All these methods were implemented in a wave propagation model (DREAMS) for harbours and sheltered zones, which is used to generate the FEM systems of equations to be solved.

Implementation of direct and iterative methods for a class of Helmholtz wave problems

In this article, the applicability and the performance of two direct (DirCSR and DirSkyline) and one iterative (IterCG_CSR) methods for solving large linear systems of equations are analyzed. Alternative ways of storing the coefficient matrix K generated by the application of the finite element method (FEM) to the Helmholtz equation for wave propagation in coastal regions are considered. The two direct methods are based on a Crout variant, the LDLt factorization, but they are implemented with two different sparse storage modes, one being the standard skyline, and the other being the compressed sparse row. The preconditioner of the conjugate gradients iterative method is the above DirCSR, with a minor parameter adjustment. These methods are compared in terms of CPU time, size of the matrices and number of iterations, for the same systems of equations with complex symmetric and indefinite matrices. Their behavior in low resolution grids is also investigated because this is a critical issue in practical applications. All these methods were implemented in a wave propagation model (DREAMS) for harbours and sheltered zones, which is used to generate the FEM systems of equations to be solved.

Anomalous Rayleigh scattering with dilute concentrations of elements of biological importance

The anomalous scattering factor (ASF) correction to the relativistic form-factor approximation for Rayleigh scattering is examined in support of its utilization in radiographic imaging. ASF corrected total cross-section data have been generated for a low resolution grid for the Monte Carlo code EGS4 for the biologically important elements, K, Ca, Mn, Fe, Cu and Zn. Points in the fixed energy grid used by EGS4 as well as 8 other points in the vicinity of the K-edge have been chosen to achieve an uncertainty in the ASF component of 20% according to the Thomas–Reiche–Kuhn sum rule and an energy resolution of 20 eV. Such data is useful for analysis of imaging with a quasi-monoenergetic source. Corrections to the sampled distribution of outgoing photons, due to ASF, are given and new total cross-section data including that of the photoelectric effect have been computed using the Slater exchange self-consistent potential with the Latter tail. A measurement of Rayleigh scattering in a dilute aqueous solution of manganese (II) was performed, this system enabling determination of the absolute cross-section, although background subtraction was necessary to remove K β fluorescence and resonant Raman scattering occurring within several 100 eV of the edge. Measurements confirm the presence of below edge bound–bound structure and variation in the structure due to the ionic state that are not currently included in tabulations.

Three-dimensional coarse large-eddy simulations of the flow above two-dimensional sinusoidal waves

Large-eddy simulations (LES) of the flow over two-dimensional sinusoidal waves with a very low grid resolution are presented. A dynamic two-parameter subgrid scale (SGS) model is employed. A configuration characterized by a wave length of 0.6096 m, a maximum slope of 0.497, and a bulk velocity of 10 m s -1 is initially considered. Comparisons with experimental data, and with the results of a previous LES show that, in spite of the very low grid resolution, the mean flow and both the viscous and the pressure drag forces are well predicted. Some details of the flow, such as the presence of a secondary flow, are also captured. Thus, additional LES are carried out to investigate the effect of the Reynolds number (Re), and of the wave amplitude. In particular, the dependence of viscous and pressure drag on these parameters is studied and compared with the results of similar analyses in the literature.

Comparison between Wavenumber Truncation and Horizontal Diffusion Methods in Spectral Models

Abstract Commonly used horizontal diffusion and wavenumber truncation dealiasing methods in spectral models are verified using the National Center for Atmospheric Research Community Climate Model version 3. For the same horizontal grid resolution, time step, physical processes, boundary conditions, and initial conditions, the simulated climate, using the horizontal diffusion alone model, is better than that using the wavenumber truncation method. In comparison with the observed climate data, the global root-mean-square of simulated January monthly mean 500-hPa geopotential using the horizontal diffusion alone model is 25% less than that using the wavenumber truncation model. However, for the same spectral resolution, the wavenumber truncation model (high horizontal grid resolution) leads to more accurate solutions than the horizontal diffusion model (low horizontal grid resolution).

Finite element analysis and ray tracing modeling of petroleum migration

Separate phase flow is the dominant transport mechanism for secondary migration of petroleum phases. Commonly two different methods are used for the modeling of separate phase flow: full 3D modeling (finite element analysis) which leads to the physically best description but can only be performed on low resolution grids, and flowpath modeling (ray tracing) which can be performed on high resolution grids but is based on simplified physical assumptions. A new approach that integrates both methods allows a physically realistic description without losing any of the original geometric information. This new approach cuts processing times considerably.

Sensitivity studies with the North Atlantic sigma coordinate Princeton Ocean Model

The sigma coordinate, Princeton Ocean Model (POM) has been configured for the North Atlantic Ocean between 5°N and 50°N as part of data assimilation, model predictability and intercomparison studies. The model uses a curvilinear orthogonal grid with higher resolution in the western North Atlantic and lower resolution in the eastern North Atlantic. A series of experiments, each one of a 10-year duration, are performed to evaluate the sensitivity of the ocean mean state and variability to model parameters and model configuration; these experiments include open vs. closed boundary conditions, low vs. high resolution grids, and different choices of diffusion and viscosity. The results show that the use of closed boundaries together with near-boundary buffer zones where temperature and salinity are relaxed towards the observed values give less realistic flows, weaker recirculation gyres and less realistic Gulf Stream separation than do open boundary conditions. The experiments show that the sensitivity of the ocean variability in the model to the choice of the Smagorinsky diffusion and viscosity coefficients significantly differs from one region to another and largely depends on other attributes such as the mean position of the Gulf Stream in each simulation. A 50% change in model resolution in the Gulf Stream region has a larger effect on ocean variability than a change of diffusivity by a factor of 10. In areas where either the high or the low resolution models have sufficient resolution, as in the Gulf of Mexico, they are able to produce variability comparable to that observed from altimeter data; elsewhere, model variability is underestimated.

Physical aspects of the weather generator

One task in B ahc is to develop a physical understanding of the weather generator (WG). The core of the WG concept is scale interaction, represented by upscaling and downscaling, between the gridscale atmospheric fields and the subgrid-scale hydrological and ecosystem patterns. This paper considers scale interaction in terms of the convective (=latent plus sensible heat) and rain fluxes. Earth's surface and atmosphere are coupled through these fluxes. However, horizontal scale interaction in the free atmosphere is physically different from that at the surface. Upscaling atmospheric fluxes generates new sub-gridscale fluxes at the lower grid resolution, caused by the gridscale fluxes resolved at the higher grid resolution. Downscaling has to recover these secondary circulations, usually through mesoscale submodels. The same gridscale eddy effect is zero for surface fluxes because there is no cross-surface mass flux of air. The atmospheric fluxes on the various scales are quantified here with an atmospheric diagnostic model (D iamod) coupled to a surface flux model (S urfmod). Two convectively active periods over Europe (one disturbed, one undisturbed) are considered. Upscaling from 100 to 1000 km horizontal resolution generates additional grid-scale eddy fluxes. However, these amount, in both cases, to just 10% of the diagnosed fluxes that are sub-gridscale at 100 km; this suggests that the additional gridscale eddy effect may be negligible in convective situations. We further apply a simple downscaling recipe for disturbed periods (scale the rain flux profiles with the observed surface rain) and for undisturbed periods (scale the convective flux profiles with the observed surface latent plus sensible heat flux). At the Earth's surface, we study the upscaling–downscaling mechanism, not with diagnosed, but with modeled latent and sensible heat fluxes. With a simplified version of S urfmod, plus the probability density function of soil moisture, we reproduce the fatal impact of taking mean soil moisture for calculating mean evaporation: evaporation can be underestimated by 25% in dry situations and overestimated by 10% in moist situations. We demonstrate how to completely remove this bias. The technique presented here can be generalized to a wide class of deterministic and statistical models and offers a rational framework for the aggregation problem and the WG problem in general.

Real-time modal control implementation for adaptive optics

The electronics, computing hardware, and computing used to provide real-time modal control for a laser guide-star adaptive optics system are presented. This approach offers advantages in the control of unobserved modes, the elimination of unwanted modes (e.g., tip and tilt), and automatic handling of the case of low-resolution lens arrays. In our two-step modal implementation, the input vector of gradients is first decomposed into a Zernike polynomial mode by a least-squares estimate. The number of modes is assumed to be less than or equal to the number of actuators. The mode coefficients are then available for collection and analysis or for the application of modal weights. Thus the modal weights may be changed quickly without recalculating the full matrix. The control-loop integrators are at this point in the algorithm. To calculate the deformable-mirror drive signals, the mode coefficients are converted to the zonal signals by a matrix multiply. When the number of gradients measured is less than the number of actuators, the integration in the control loop will be done on the lower-resolution grid to avoid growth of unobserved modes. These low-resolution data will then be effectively interpolated to yield the deformable-mirror drive signals.

A modified FDTD (2, 4) scheme for modeling electrically large structures with high-phase accuracy

A new fourth-order finite-difference time-domain (FDTD) scheme has been developed that exhibits extremely low-phase errors at low-grid resolutions compared to the conventional FDTD scheme. Moreover, this new scheme is capable of combining with the standard Yee (1966) scheme to produce a stable hybrid algorithm. The problem of wave propagation through a building is simulated using this new hybrid algorithm to demonstrate the large savings in computing resources it could afford. With this new development, the FDTD method can now be used to successfully model structures that are thousands of wavelengths large, using the present day computer technology.

Issues related to low resolution modeling of soil moisture: experience with the PLACE model

This study documents the new PLACE soil hydrology model, and examines the effects of various parameterization schemes on the solution of the Richards equation. Richards equation is the basis upon which many of the land surface schemes participating in the PILPS experiments model soil water transport. Generally, the integration is carried out using a coarse model grid, which makes the solution more sensitive to particulars of the parameterization scheme. Parameterization schemes for the lower boundary condition, lateral interflow, and for moisture fluxes between model layers are tested in PLACE using both high and low resolution grids. Simulations were made using PILPS-HAPEX forcing data and soil and vegetation parameters. The soil hydrology model is validated against the annual observed HAPEX soil moisture profiles. The predicted evapotranspiration is also compared to a value computed from the PILPS-HAPEX forcing data using the Penman-Monteith equation. When testing a low-resolution soil grid typical of land surface schemes, predicted soil moisture was found to be highly sensitive to the interpolation method for computing vertical moisture fluxes between model layers. A new interpolation method for low resolution models is proposed and tested. It reproduces the high resolution model results more faithfully, over the entire range of soil moisture, than two methods commonly applied in the literature. Further tests demonstrate that by varying the parameterizations for lower boundary condition and the treatment of lateral flow (collectively called drainage), the predicted total annual evapotranspiration may range between 74% and 97% of the incident precipitation in this case. Both of these parameterizations involve one free parameter, and both are largely unconstrained by the available observations. Good overall agreement between the PLACE predicted and HAPEX observed soil moisture profiles was attained by varying these two PLACE drainage parameters over their respective ranges for a series of model simulations. Root-mean square error tests were then used to determine the set of parameters which corresponded to the best predicted soil moisture profile. However, the best predicted soil moisture profiles do not correspond with the best predicted evapotranspiration. This inconsistency occurs not only for PLACE, but, to varying degrees, for all of the land-surface schemes participating in PILPS-HAPEX.

A fully spectral solution method for parabolic equations

AbstractA comparison is made between the performance of the (aliased) Chebȳshev collocation method (CM) and the more recent Galerkin collocation method (GCM), which is a least‐squares collocation method, in solving the laminar, incompressible, steady boundary‐layer equations, which are parabolic in nature. An iterative procedure based on the preconditioned residual minimization method has been used. It is shown that the GCM is superior to the CM on several counts. Unlike the CM, the GCM minimizes the residual uniformly over the entire domain. The global accuracy of the solution is found to be higher in the GCM, at lower grid resolutions. The method also achieves much higher convergence rates. Unlike in the collocation method, the final residual values obtained in the GCM are good indicators of the level of accuracy achieved in the solution. It is highly likely that these results will be repeatable in other systems of parabolic partial differential equations.

Valley Winds and the Diurnal Circulation over Plateaus

Abstract The role of valley winds in the diurnal circulation of large-scale mountain massifs like the Tibetan Plateau is investigated. We consider a circular plateau with radial valleys leading to the surrounding lowlands. A low-resolution grid point model is used to compute the diurnal circulation above the plateau and in the valleys. The circulation is driven by the diurnal variation of the surface temperature. The model produces valley winds and a diurnal circulation above the plateau in qualitative agreement with observations. The inflow towards the plateau in the valleys is strongest in the afternoon. There is nocturnal outflow. During the day, a low pressure system with a corresponding cyclonic circulation around the massif resides at the plateau and we find high pressure well above it. At night it is the reverse. It is demonstrated that the valley winds contribute significantly to the fluxes of mass and moisture in the plateau's diurnal circulation. Linear calculations for a neutrally stratified at...

Numerical simulation of relative dispersion in two-dimensional, homogeneous, decaying turbulence

Lagrangian statistical results are presented from numerical simulations of an ensemble of fluid particles which were generated from a two-dimensional pseudospectral code. The single-particle results are in qualitative agreement with previous simulations on a lower-resolution grid. The two-particle, relative velocity correlations were found to fall off more rapidly than the single-particle correlations for short to intermediate times due to large-scale eddy advection in the single-particle case. The temporal behaviour of the mean square relative separation, 〈rl2〉, is analysed for short to intermediate times and is found to be consistent with scaling arguments based on Kraichnan's expression for the non-local strain acting in the high-wavenumber enstrophy cascade spectral range. For longer times, 〈rl2〉 exhibitstnbehaviour. The power-law region is associated with the locally determined strain rates which characterize a backward energy-cascade spectrum.

Parameterized processes in the surface boundary layer of an atmospheric circulation model

AbstractA general circulation model is modified successively by adding five new features in the lower boundary layer; namely, (i) a different roughness parameter over land and sea, (ii) a Monin‐Obukhov type treatment of the turbulent transfer process in the constant‐flux layer, (iii) a Richardson number dependent parameterization for Ekman layer process, (iv) a diurnal variation of insolation, and (v) heat conduction into the soil. To assess the effect of each, the experiments are repeated by gradually increasing the complexity of the model. The circulation model has relatively low horizontal grid resolution and 9 vertical levels, and it is applied to a winter case for 14 day predictions. The results indicate that the sophistication of the boundary layer physics does not produce a particularly large effect on the synoptic scale prediction until about 7 days. Its effect may become large after 10 days. One noteworthy result is that the effect of the diurnal variation of insolation is not great for the free atmosphere but an influence is effectively transferred in the vertical, if the Richardson number dependent parameterization for the Ekman layer process is incorporated. The entire study is a preliminary test, the purpose of which is to determine the relative magnitude of each effect. A detailed comparison with observed data was not attempted.