Idealized Test Cases Research Articles

Geometrically Exact Conservative Remapping (GECoRe): Regular Latitude–Longitude and Cubed-Sphere Grids

Abstract Land, ocean, and atmospheric models are often implemented on different spherical grids. As a conseqence coupling these model components requires state variables and fluxes to be regridded. For some variables, such as fluxes, it is paramount that the regridding algorithm is conservative (so that energy and water budget balances are maintained) and monotone (to prevent unphysical values). For global applications the cubed-sphere grids are gaining popularity in the atmospheric community whereas, for example, the land modeling groups are mostly using the regular latitude–longitude grid. Most existing regridding schemes fail to take advantage of geometrical symmetries between these grids and hence accuracy of the calculations can be lost. Hence, a new Geometrically Exact Conservative Remapping (GECoRe) scheme with a monotone option is proposed for remapping between regular latitude–longitude and gnomonic cubed-sphere grids. GECoRe is compared with existing remapping schemes published in the meteorological literature. It is concluded here that the geometrically exact scheme significantly improves the accuracy of the resulting remapping in idealized test cases.

Improvements of semi-implicit schemes for hyperbolic balance laws applied on open channel flow equations

In this paper, we consider a well-balanced semi-implicit one parameter family of schemes. The presented schemes are a generalization of the well-balanced upwind explicit finite volume schemes. The schemes are applied to the Saint Venant open channel flow equations. The main feature of the presented schemes is their balancing property, achieved even for the channels with the general cross section geometry. In the paper, we present the scheme algorithm and the proof of the exact conservation property when the proposed schemes are applied to the open channel flow equations. Furthermore, the schemes’ accuracy and stability are improved by using a local semi-implicit approach, which takes into account the CFL number locally. In this way, the highly efficient, robust, and unconditionally stable family of balanced numerical schemes is developed. Newly developed schemes are able to give accurate low diffusion results in stationary as well as in non-stationary test cases. Since particular attention is focused on the simulation efficiency on real engineering problems, an algorithm for treatment and precomputation of channel geometry parameters is presented. The algorithm significantly reduces the computational cost of the simulation. Behavior of new schemes is analyzed in several idealized test cases, and on a simulation of a realistic flood wave propagation in the Kupa river involving friction, non-uniform bed slopes and strong channel width variations.

Deposition and flux of sediment from the Po River, Italy: An idealized and wintertime numerical modeling study

Recent studies of sediment dynamics and clinoform development in the northern Adriatic Sea focused on winter 2002–2003 and provided the data and motivation for development of a detailed sediment-transport model for the area near the Po River delta. We used both idealized test cases and more realistic simulations to improve our understanding of seasonal sediment dynamics there. We also investigated the relationship between physical processes and the observed depositional products; e.g. the accumulation of sediment very near the Po River distributary mouths. Sediment transport near the Po River was evaluated using a three-dimensional ocean model coupled to sediment-transport calculations that included wave- and current-induced resuspension, suspended-sediment transport, multiple grain classes, and fluvial input from the Po River. High-resolution estimates from available meteorological and wave models were used to specify wind, wave, and meteorological forcing. Model results indicated that more than half of the discharged sediment remained within 15 km of the Po River distributary mouths, even after two months of intensive reworking by winter storms. During floods of the Po River, transport in the middle to upper water column dominated sediment fluxes. Otherwise, sediment fluxes from the subaqueous portion of the delta were confined to the bottom few meters of the water column, and correlated with increases in current speed and wave energy. Spatial and temporal variation in wind velocities determined depositional patterns and the directions of sediment transport. Northeasterly Bora winds produced relatively more eastward transport, while southwesterly Sirocco winds generated fluxes towards both the north and the south. Eastward transport accounted for the majority of the sediment exported from the subaqueous delta, most likely due to the frequent occurrence of Bora conditions. Progradation of the Po River delta into the Adriatic Sea may restrict the formation of the Western Adriatic Coastal Current, increasing sediment retention at the Po delta and reducing the supply of sediment to the Apennine margin. A positive morphodynamic feedback may therefore be present whereby the extension of the delta into the Adriatic increases sediment accumulation at the delta and facilitates further progradation.

Investigating the impact of surface wave breaking on modeling the trajectories of drifters in the northern Adriatic Sea during a wind-storm event

An accurate numerical prediction of the oceanic upper layer velocity is a demanding requirement for many applications at sea and is a function of several near-surface processes that need to be incorporated in a numerical model. Among them, we assess the effects of vertical resolution, different vertical mixing parameterization (the so-called Generic Length Scale –GLS– set of k– ε, k– ω, gen, and the Mellor–Yamada), and surface roughness values on turbulent kinetic energy ( k) injection from breaking waves. First, we modified the GLS turbulence closure formulation in the Regional Ocean Modeling System (ROMS) to incorporate the surface flux of turbulent kinetic energy due to wave breaking. Then, we applied the model to idealized test cases, exploring the sensitivity to the above mentioned factors. Last, the model was applied to a realistic situation in the Adriatic Sea driven by numerical meteorological forcings and river discharges. In this case, numerical drifters were released during an intense episode of Bora winds that occurred in mid-February 2003, and their trajectories compared to the displacement of satellite-tracked drifters deployed during the ADRIA02-03 sea-truth campaign. Results indicted that the inclusion of the wave breaking process helps improve the accuracy of the numerical simulations, subject to an increase in the typical value of the surface roughness z 0. Specifically, the best performance was obtained using α CH = 56,000 in the Charnok formula, the wave breaking parameterization activated, k– ε as the turbulence closure model. With these options, the relative error with respect to the average distance of the drifter was about 25% (5.5 km/day). The most sensitive factors in the model were found to be the value of α CH enhanced with respect to a standard value, followed by the adoption of wave breaking parameterization and the particular turbulence closure model selected.

Ensemble Held–Suarez Test with a Spectral Transform Model: Variability, Sensitivity, and Convergence

Abstract The idealized test case proposed by Held and Suarez is carried out with the atmospheric general circulation model ECHAM5 of the Max Planck Institute for Meteorology. The aim is to investigate the sensitivity of the solutions of the spectral dynamical core to spatial and temporal resolution, and to evaluate the numerical convergence of the solutions. Low-frequency fluctuations at time scales as long as thousands of days are found in ultralong integrations. To distinguish the effect of changed resolution from the fluctuations caused by the internal variability, the ensemble method is employed in experiments at resolutions ranging from T31 to T159 with 16 to 81 vertical levels. Significance of the differences between ensembles is assessed by three different statistical tests. Convergence property of the numerical solution is concisely summarized by a ratio index. Results show that the simulated climate state in the Held–Suarez test is sensitive to spatial resolution. Increase of horizontal resolution leads to slight weakening and poleward shift of the westerly jets. Significant warming is detected in high latitudes, especially near the polar tropopause, while the tropical tropopause becomes cooler. The baroclinic wave activity intensifies considerably with increased horizontal resolution. Higher vertical resolution also leads to stronger eddy variances and cooling near the tropical tropopause, but equatorward shift of the westerly jets. The solutions show an indication of convergence at T85L31 resolution according to all the three statistical tests applied. Differences between integrations with various time steps are judged to be within the noise level induced by the inherent low-frequency variability.

Assimilation Experiment of Lidar Measurements for Wake Turbulence

Numerical simulation of wake turbulence was performed by integrating the lidar measurements using four-dimensional variational method. A bogus vortex technique was adopted to ensure the existence of wake vortices in the flow field. The validation of the method was performed by an idealized test case using virtual lidar measurement which was produced by the reference simulation of a vortex pair. The results of the validation showed the convergence of a vortex parameter such as a circulation to the parameter of reference simulation case. It was also confirmed that the velocity distribution on a measurement plane agreed with reference one.

Thermodynamics of Atomic Clusters Using Variational Quantum Hydrodynamics

Small clusters of rare-gas atoms are ideal test cases for studying how quantum delocalization affects both the thermodynamics and the structure of molecular scale systems. In this paper, we use a variational quantum hydrodynamic approach to examine the structure and dynamics of (Ne)n clusters, with n up to 100 atoms, at both T = 0 K and for temperatures spanning the solid-to-liquid transition in bulk Ne. Finite temperature contributions are introduced to the grand potential in the form of an "entropy" potential. One surprising result is the prediction of a negative heat capacity for very small clusters that we attribute to the nonadditive nature of the total free-energy for very small systems.

Conservative Split-Explicit Time Integration Methods for the Compressible Nonhydrostatic Equations

Abstract Historically, time-split schemes for numerically integrating the nonhydrostatic compressible equations of motion have not formally conserved mass and other first-order flux quantities. In this paper, split-explicit integration techniques are developed that numerically conserve these properties by integrating prognostic equations for conserved quantities represented in flux form. These procedures are presented for both terrain-following height and hydrostatic pressure (mass) vertical coordinates, two potentially attractive frameworks for which the equation sets and integration techniques differ significantly. For each set of equations, the linear dispersion equation for acoustic/gravity waves is derived and analyzed to determine which terms must be solved in the small (acoustic) time steps and how these terms are represented in the time integration to achieve stability. Efficient techniques for including numerical filters for acoustic and external modes are also presented. Simulations for several idealized test cases in both the height and mass coordinates are presented to demonstrate that these integration techniques appear robust over a wide range of scales, from subcloud to synoptic.

The groundwater–land-surface–atmosphere connection: Soil moisture effects on the atmospheric boundary layer in fully-coupled simulations

This study combines a variably-saturated groundwater flow model and a mesoscale atmospheric model to examine the effects of soil moisture heterogeneity on atmospheric boundary layer processes. This parallel, integrated model can simulate spatial variations in land-surface forcing driven by three-dimensional (3D) atmospheric and subsurface components. The development of atmospheric flow is studied in a series of idealized test cases with different initial soil moisture distributions generated by an offline spin-up procedure or interpolated from a coarse-resolution dataset. These test cases are performed with both the fully-coupled model (which includes 3D groundwater flow and surface water routing) and the uncoupled atmospheric model. The effects of the different soil moisture initializations and lateral subsurface and surface water flow are seen in the differences in atmospheric evolution over a 36-h period. The fully-coupled model maintains a realistic topographically-driven soil moisture distribution, while the uncoupled atmospheric model does not. Furthermore, the coupled model shows spatial and temporal correlations between surface and lower atmospheric variables and water table depth. These correlations are particularly strong during times when the land-surface temperatures trigger shifts in wind behavior, such as during early morning surface heating.

Petascale atmospheric general circulation models

The High-Order Method Modeling Environment (HOMME) is a framework to investigate using high-order element-based methods to build conservative and accurate atmospheric general circulation models. Currently, HOMME employs the discontinuous Galerkin and spectral element methods on a cubed-sphere tiled with quadrilateral elements to solve the primitive equations, and has been shown to scale to \U0001d4aa(10K) processors of a Cray XT 3/4 and \U0001d4aa(32K) processors of an IBM Blue Gene/L. Here we briefly describe the development of a baroclinic model using the discontinuous Galerkin option in the HOMME framework, present idealized test case results, and provide preliminary performance data.

Lagrangian modelling of multi-dimensional advection-diffusion with space-varying diffusivities: theory and idealized test cases

To efficiently simulate the advection-diffusion processes along and across density surfaces, we need to deal with a diffusivity tensor containing off-diagonal elements (Redi, J Phys Oceanogr, 12:1154–1158, 1982). In the present paper, the Lagrangian model, in case of a space-varying diffusivity tensor, is developed. This random walk model is applied for two idealized test cases for which the analytical solutions are known. Results of the testing show that the Lagrangian approach provides accurate and effective solutions of advection-diffusion problems for general diffusivity tensor.

A Godunov-Type Scheme for Atmospheric Flows on Unstructured Grids: Euler and Navier-Stokes Equations

In recent years there has been a growing interest in using Godunov-type methods for atmospheric flow problems. Godunov's unique approach to numerical modeling of fluid flow is characterized by introducing physical reasoning in the development of the numerical scheme (van Leer, 1999). The construction of the scheme itself is based upon the physical phenomenon described by the equation sets. These finite volume discretizations are conservative and have the ability to resolve regions of steep gradients accurately, thus avoiding dispersion errors in the solution. Positivity of scalars (an important factor when considering the transport of microphysical quantities) is also guaranteed by applying the total variation diminishing condition appropriately. This paper describes the implementation of a Godunov-type finite volume scheme based on unstructured adaptive grids for simulating flows on the meso-, micro- and urban-scales. The Harten-Lax-van Leer-Contact (HLLC) approximate Riemann solver used to calculate the Godunov fluxes is described in detail. The higher-order spatial accuracy is achieved via gradient reconstruction techniques after van Leer and the total variation diminishing condition is enforced with the aid of slope-limiters. A multi-stage explicit Runge-Kutta time marching scheme is used for maintaining higher-order accuracy in time. The scheme is conservative and exhibits minimal numerical dispersion and diffusion. The subgrid scale diffusion in the model is parameterized via the Smagorinsky-Lilly turbulence closure. The scheme uses a non-staggered mesh arrangement of variables (all quantities are cell-centered) and requires no explicit filtering for stability. A comparison with exact solutions shows that the scheme can resolve the different types of wave structures admitted by the atmospheric flow equation set. A qualitative evaluation for an idealized test case of convection in a neutral atmosphere is also presented. The scheme was able to simulate the onset of Kelvin-Helmholtz type instability and shows promise in simulating atmospheric flows characterized by sharp gradients without using explicit filtering for numerical stability.

A new parametrization for the radiative properties of ice crystals: Comparison with existing schemes and impact in a GCM

A new parametrization of the single scattering properties of ice crystals suitable for use in general circulation models of the atmosphere is presented. The parametrization is developed from a recent treatment of the scattering properties of an ensemble of ice crystals, which has been validated against observational data and is based on a more rigorous treatment of ice optics than has been possible until recently. The new parametrization is compared with existing schemes in idealized test cases and its impact in a climate model is assessed.

Application of the multidimensional positive definite advection transport algorithm (MPDATA) to environmental modelling on adaptive unstructured grids

AbstractTwenty years ago, the multidimensional, positive definite, advection transport algorithm was introduced by Smolarkiewicz. Over the two decades since, it has been applied countless times to numerous problems, however almost always on rectilinear grids. One of the few exceptions is the Operational Multiscale Environment model with Grid Adaptivity (OMEGA), an atmospheric simulation system originally designed to simulate atmospheric dispersion in the planetary boundary layer, but since then used for both mesoscale (from meso‐α to meso‐γ) dispersion and weather forecasting. One of the unique aspects of OMEGA is the triangular unstructured grid geometry which leads in a natural way to the creation of a global grid with continuously variable resolution from roughly 100 km over the oceans to less than 10 km over regions of interest. Another unique aspect is the concept of dynamically adapting grid resolution—sometimes also called solution‐adaptive grid resolution. A central element of the modelling system, however, is its advection solver—MPDATA. This paper presents the implementation of MPDATA on an unstructured grid and demonstrates its accuracy and efficiency using analytic and idealized test cases. Copyright © 2005 John Wiley & Sons, Ltd.

FEMSECT: An inverse section model based on the finite element method

A new inverse model is presented for the analysis of hydrographic section data in conjunction with velocity measurements. The model offers advantages over commonly applied interpolation techniques because it combines data and physical assumptions such as geostrophic balance in the framework of a finite element discretization. Specifically, a quadratic objective function of model‐data misfits is minimized to give estimates of transports together with formal error estimates. The finite element method allows the accurate representation of highly irregular bottom topography and ensures consistent interpolation of model variables to measurement points. The model is called Finite Element Method Section model (FEMSECT). FEMSECT also gives improved flexibility and performance over standard box models by allowing dynamic adjustment of the model variables temperature and salinity. Idealized test cases illustrate that the finite element methods solve the thermal wind equations far more accurately than standard finite difference methods, especially in the presence of steep topography. For a more realistic test, FEMSECT is applied to hydrographic conductivity‐temperature‐depth section data and moored instrument current meter measurements from an array in the Fram Strait. Transport estimates by FEMSECT prove to be more robust and less sensitive to the spatial data resolution than estimates by a conventional interpolation method that only uses information from moored instruments. FEMSECT is available as a highly portable Matlab code and can be run on an ordinary desktop computer.

An unstructured grid morphodynamic model with a discontinuous Galerkin method for bed evolution

A new unstructured grid two-dimensional, depth-integrated (2DDI), morphodynamic model is presented for the prediction of morphological evolutions in shallow water. This modelling system consists of two coupled model components: (i) a well-verified and validated continuous Galerkin (CG) finite element hydrodynamic model; and (ii) a new sediment transport/bed evolution model that uses a discontinuous Galerkin (DG) method for the solution of the sediment continuity equation. The DG method is a robust finite element method that is particularly well suited for this type of advection dominated transport equation. It incorporates upwinded numerical fluxes and slope limiters to provide sharp resolution of steep bathymetric gradients that may form in the solution, and it possesses a local conservation property that conserves sediment mass on an elemental level. In this paper, we focus specifically on the implementation and verification of the DG model. Details are given on the implementation of the method, and numerical results are presented for three idealized test cases which demonstrate the accuracy and robustness of the method and its applicability in predicting medium-term morphological changes in channels and coastal inlets.

Architecture for Combined Energy and Attitude Control System

Combining the energy and attitude control system is a feasible technology for small satellites to improve the space missions. In this Combined Energy and Attitude Control System (CEACS) a double rotating flywheel is used to replace the conventional battery for energy storage as well as to control the attitude of an earth oriented satellite. Each flywheel is to be controlled in the torque mode. The energy and attitude inputs for the flywheels' control architecture are also in the torque mode. All related mathematical representation along with the relevant transfer functions and the required numerical calculation are developed. The goals are to analyze the attitude performance with respect to the ideal and non-ideal test cases for a chosen reference mission.

A semi‐implicit method conserving mass and potential vorticity for the shallow water equations on the sphere

AbstractA semi‐implicit discretization for the shallow water equations is discussed, which uses triangular Delaunay cells on the sphere as control volumes and conserves mass and potential vorticity. The geopotential gradient, the Coriolis force terms and the divergence of the velocity field are discretized implicitly, while an explicit time discretization is used for the non‐linear advection terms. The results obtained with a preliminary implementation on some idealized test cases are presented, showing that the main features of large scale atmospheric flows are well represented by the proposed method. Copyright © 2004 John Wiley & Sons, Ltd.

A combined energy and attitude control system for small satellites

The idea of combining the satellite attitude control system and the electrical power system is investigated in this article. The combined energy and attitude control system (CEACS) concept is based on a double counter rotating flywheel assembly serving simultaneously for the satellite energy storage and attitude control tasks. In the past years, this synergistic system was proposed for larger spacecraft, but until today a comprehensive end-to-end system demonstration for small satellites still has not been performed. On this basis, the investigation is narrowed to the consideration for small satellites at the inception of the study. First, the CEACS architecture is presented along with its mathematical models. Then, numerical treatments with a sufficient magnitude are performed, which allow an assessment of the system's merits. The simulation results pertaining to the ideal and non-ideal test cases indicate that the CEACS is judiciously an attractive synergistic system for future small satellites.

Reducing Numerical Diffusion Effects with Pycnocline Filter

Numerical or artificial diffusion is the unintentional smoothing of gradients associated with the discretization of the transport equations. In lakes and reservoirs where through-flow is small, the effects of numerical diffusion of mass are cumulative, leading to a progressive weakening of vertical density stratification. This density field misrepresentation precludes accurate, long-term, three-dimensional (3D), hydrodynamic simulations on fixed grids in closed basins with an active thermocline. An ad hoc technique to limit the destratifying effects of numerical diffusion of mass is presented and tested for a 3D, hydrostatic, Z-coordinate numerical model. The technique quantifies the domain-integrated numerical diffusion by assessing the change in the background potential energy Eb. At each time step, the change in Eb associated with numerical diffusion is calculated, then removed using a sharpening filter applied to each water column. In idealized test cases, the filtering technique is effective in maintaining density stratification over one year while undergoing periodic, large-amplitude forcing by internal waves. Forty-day simulations of Lake Kinneret compared to field measurements demonstrate improved representation of density stratification using the filtering technique.