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Vertical Coordinate (vertical + coordinate)

Distribution by Scientific Domains

Earth and Environmental Science	85%

Selected Abstracts

The effect of the electrical anisotropy on the response of helicopter-borne frequency-domain electromagnetic systems

GEOPHYSICAL PROSPECTING, Issue 5 2004
Changchun Yin
ABSTRACT Helicopter electromagnetic (HEM) systems are commonly used for conductivity mapping and the data are often interpreted using an isotropic horizontally layered earth model. However, in regions with distinct dipping stratification, it is useful to extend the model to a layered earth with general anisotropy by assigning each layer a symmetrical 3 × 3 resistivity tensor. The electromagnetic (EM) field is represented by two scalar potentials, which describe the poloidal and toroidal parts of the magnetic field. Via a 2D Fourier transform, we obtain two coupled ordinary differential equations in the vertical coordinate. To stabilize the numerical calculation, the wavenumber domain is divided into two parts associated with small and large wavenumbers. The EM field for small wavenumbers is continued from layer to layer with the continuity conditions. For large wavenumbers, the EM field behaves like a DC field and therefore cannot be sensed by airborne EM systems. Thus, the contribution from the large wavenumbers is simply ignored. The magnetic fields are calculated for the vertical coaxial (VCX), horizontal coplanar (HCP) and vertical coplanar (VCP) coil configurations for a helicopter EM system. The apparent resistivities defined from the VCX, VCP and HCP coil responses, when plotted in polar coordinates, clearly identify the principal anisotropic axes of an anisotropic earth. The field example from the Edwards Aquifer recharge area in Texas confirms that the polar plots of the apparent resistivities identify the principal anisotropic axes that coincide well with the direction of the underground structures. [source]

Jacobian mapping between vertical coordinate systems in data assimilation

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 627 2007
Y. J. Rochon
Abstract Radiances measured by remote-sensing instruments are now the largest component of the atmospheric observation network. The assimilation of radiances from nadir sounders involves fast radiative transfer (RT) models which project profiles provided by forecast models onto the observation space for direct comparison with the measurements. One of the features typically characterizing fast RT models is the use of a fixed vertical coordinate. If the vertical coordinate of the RT model is not identical to that used by the forecast model, an interpolation of forecast profiles to the RT model coordinate is necessary. In variational data assimilation, the mapping of the Jacobians (derivatives of the RT model output with respect to its inputs) from the RT model coordinate to the forecast model coordinate is also required. This mapping of Jacobians is accomplished through the adjoint of the forecast profile interpolator. As shown, the nearest-neighbour log-linear interpolator commonly used operationally can lead to incorrect mapping of Jacobians and, consequently, to incorrect assimilation. This incorrect mapping occurs as a result of leaving out intermediate levels in the interpolation. This problem has been previously masked in part through the smoothing effect of forecast-error vertical correlations on the analysis increments. To solve this problem, two simple versions of an interpolator relying on piecewise log-linear weighted averaging over the layers are investigated. Both markedly improve Jacobian mappings in the assimilation of observations, with one being slightly favoured over the other. This interpolator is being incorporated into the RTTOV model used by several operational weather forecasting centres. Copyright © 2007 Crown in the right of Canada. Published by John Wiley & Sons, Ltd. [source]

Vertical discretizations giving optimal representation of normal modes: Sensitivity to the form of the pressure-gradient term

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 621 2006
J. Thuburn
Abstract The normal-mode dispersion properties and structures of some vertical discretizations of the compressible Euler equations are re-examined. It is shown that the dispersion properties can be sensitive to the form in which the pressure-gradient term is expressed. For a height coordinate and for an isentropic vertical coordinate, discretizations are identified that have optimal dispersion properties and, at the same time, lend themselves to mass conservation by predicting the relevant density variable. Copyright © 2006 Royal Meteorological Society [source]

A consistent vertical Bowen ratio profile in the planetary boundary layer

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 620 2006
M. Hantel
Abstract It has recently been suggested that the integrand b=,,,,, of the subgrid-scale conversion rate between available and kinetic energy has a measurable impact upon the Lorenz energy cycle. Here we discuss a technique to estimate this quantity within the lower part of an atmospheric column by relating b to the subgrid-scale fluxes of sensible and latent heat in form of their sum (the total convective heat flux, c, to be diagnosed from the pertinent energy law) and their ratio (a generalized Bowen ratio, ,, to be specified a priori). We focus on the frequently observed case that c vanishes at or above the top of the boundary layer, which implies that , must be minus unity at the same level (referred to as ,critical pressure'). , at the earth's surface is taken as measured. Observations suggest that the vertical curvature of the , profile is negative in the boundary layer. We specify an analytic vertical profile ,(,) that interpolates these pieces of information; , is a non-dimensional vertical coordinate. The pertinent thermodynamic energy law from which the column profile c(,) is gained (referred to here as convection equation) is driven by the (observed) grid-scale budget; the solution c is over most of the boundary layer quite insensitive to ,. It is only in the immediate vicinity of the critical pressure that c(,) becomes sensitively dependent upon ,(,); it actually turns infinite at this level (a ,pole' of the convection equation). We remove the pole through adjusting the critical pressure by a uniquely determined (and actually quite small) amount. This makes the , profile consistent with the convection equation and with the other convective flux profiles, across the entire boundary layer. The remaining open parameter that cannot be fixed by our method is the curvature of the Bowen ratio profile. This exercise has implications for about a third of all atmospheric columns over the globe and thus may be relevant for the quantification of the global energy cycle. Copyright © 2006 Royal Meteorological Society [source]

Flavours of pseudo-height

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 606 2005
A. A. White
Various functions of pressure have been used as vertical coordinate in atmospheric dynamics. Some of these are called pseudo-heights, or described as height-like, although they could equally well be called pseudo-thicknesses and described as thickness-like. Three pseudo-heights are reviewed here, and a unified treatment is presented in which two appear as specializations of the third. The common feature is a standard temperature profile which is a function only of pressure, and the two specializations arise when that function is chosen to represent either an isothermal atmosphere or an isentropic atmosphere. Neither of these choices,or any other reasonable function of pressure,itself introduces approximation. Under quasi-geostrophic approximation, the need for a non-zero mean-state stratification means that a second reference-temperature profile must be introduced if isentropic pseudo-height is used as vertical coordinate. © Crown copyright 2005. [source]

On the dynamics of a spherical scaffold in rotating bioreactors

BIOTECHNOLOGY & BIOENGINEERING, Issue 3 2003
L. E. S. Ramirez
Abstract We analyze the dynamics of a spherical scaffold in rotating bioreactors (or clinostats). The idealized clinostat environment consists of a purely rotational flow that is perpendicular to a gravitational field. We confirm through a detailed analytical study that lift effects considerably alter the position of the equilibrium point reached by the scaffolds in the (vertical) direction collinear to the gravitational field. This result holds for small particle and shear Reynolds numbers. Our analysis shows that the inertial lift effect is negligible in the horizontal direction. We show that for all rotations of practical interest, and for the range of particle Reynolds number smaller than unity, the vertical coordinate of the equilibrium point is strongly affected by consideration of lift effects. For light (heavy) particles, inclusion of lift in the formation forces the equilibrium position to be below (above) the horizontal plane that contains the axis of rotation. The equilibrium point for light particles is stable and therefore is observable experimentally. The equilibrium point for heavy particles is unstable. We also estimate the stress level applied to the scaffold and derive an algebraic expression that indicates that the stress level acting on the scaffold decreases with increasing shear Reynolds number. © 2003 Wiley Periodicals, Inc. Biotechnol Bioeng 84: 382,389, 2003. [source]