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    Tellus. 03/2010; 29(6):588 - 592.
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    ABSTRACT: ABSTRACTA two-level, quasi-geostrophic, β-plane, general circulation model is developed, incorporating a time-dependent surface energy balance equation and a time-dependent heating function at the 500 mb level, with an associated feedback relationship. This system enables the surface temperature distribution to be evaluated as a function of time in the model, and so allows an associated variable spatial distribution of surface albedo to be carried in the model, including a simulated “snow and ice” edge. The effect on the model of successive small changes in solar radiation (of 1/2% up to a total of 3%) are then studied by carrying out numerical experiments over long time periods, these being sufficiently long (involving a total time of integration of 1800 model days) to produce oscillations in model heating and albedo distributions about asymptotic mean values. The successive latitudinal positions of the, zonally averaged, “snow and ice” edge agree approximately with those calculated by Gordon and Davies (1974) using a modified form of the statical energy balance method of Budyko (1969). However, the experiments also showed that the greater the reduction made in solar radiation the greater was the ensuing amplitude of spatial movement of the associated albedo distribution, implying a strong tendency towards instability of the simulated edge as the reduction approached a value of 3%.
    Tellus. 03/2010; 29(6):484 - 501.
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    ABSTRACT: ABSTRACTA two-level, s̀-coordinate, β-plane, general circulation model (10,000 km meridional and 30,000 km zonal dimensions) is used to study the effect of planetary scale mountain barriers on vacillation of energy and heat transfer. The results of numerical experiments using models with flat topography (and land-sea heating contrasts) are compared with those using model representations of the Rockies and Himalayas. The mountain barriers were seen to have a crucial effect on the time variation of total eddy kinetic energy, K', meridional temperature gradients, ∇T, and in creating the stationary components of poleward transport of heat and westerly momentum. Preferred regions of high meridional temperature gradients and cyclonic systems formed north-east of the Rockies but north-west of the Himalayas. When K' was partitioned into the values appropriate to the western and eastern halves of the β-plane channel, the time variations of K' associated with each half were frequently out of phase; increasing K'(t) in one half and decreasing K'(t) in the other half was related to eastward moving peaks of baroclinic activity (created downstream of a barrier). A similar process was found in an analysis of atmospheric data for 1961–63, the orientation of the polar vortex being closely related to the west-east oscillation of K'; the model results suggest that the mountain barrier system has a large influence. Time variations in regional weather characteristics are likely to be closely related to this process; it is clearly an important factor to be represented in climatic change modelling.
    Tellus. 03/2010; 31(3):199 - 216.
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    ABSTRACT: Previously, radio Doppler data, generated with NASA's Galileo spacecraft during its second encounter with Jupiter's moon Ganymede, were used to infer the locations and magnitudes of mass anomalies on Ganymede using point-mass models. However, the point-mass solutions do not provide the vertical and horizontal extent of the anomalous mass concentrations. Here, we provide the results of a new study using spherical cap disks to model Ganymede's mass anomalies. The spherical cap disk models not only provide the locations and magnitudes of the mass anomalies, but also their vertical and horizontal dimensions. The new models show that three disks, a positive mass located at (53.0° N, 127.0° W) and two negative masses located at (22.0° N, 87.0° W) and (49.0° N, 219.0° W), can explain the data. The magnitudes of the mass anomalies are on the order of 1018 kg. The diameters of the anomalies are a few thousand kilometers. The positive anomaly is about 100 meters thick and both negative anomalies have a thickness of less than a kilometer. We use the additional information provided by the disk models to investigate the viability of mass anomalies at Ganymede's surface by comparing the diameters of the anomalies to the sizes of regiones and sulci and the anomalies' thicknesses to accumulated layers of rock and clean ice on the surface. We find that the dimensions of the mass anomalies could be explained by concentrations of rock in the regio and rock-free ice in the sulci. These results confirm that mass anomalies may reside on or near Ganymede's surface and that positive mass anomalies are contained within areas of dark terrain and negative mass anomalies within bright terrain.
    Icarus 01/2009;
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    ABSTRACT: In this paper, adaptive discrete-time low-gain integral control strategies are presented for tracking constant reference signals for infinite-dimensional discrete-time power-stable linear systems. The discrete-time results are applied in the development of adaptive sampled-data low-gain integral control of well-posed infinite-dimensional exponentially stable linear systems. Our results considerably extend, improve and simplify previous work by two of the authors [H. Logemann, S. Townley, Discrete-time low-gain control of uncertain infinite-dimensional systems, IEEE Trans. Automat. Control 42 (1997) 22–37].
    Systems & Control Letters 01/2009;
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    ABSTRACT: Hydrothermal convection of pore water with a temperature-dependent viscosity within a permeable, internally heated, moderately thin spherical shell is investigated by both a perturbation analysis and a direct numerical simulation. The analysis and simulation are mainly focused on a thin spherical shell in that convective instabilities are characterized by the spherical harmonic degree l=6 with a 13-fold mathematical degeneracy. Four different three-dimensional analytical solutions of convection are derived by removing the degeneracy through the nonlinear effect. A direct numerical simulation of the nonlinear problem is also carried out, showing satisfactory agreement between the analytical solutions and the numerical simulations.
    Physical Review Letters 08/2008; 101(2):028501.
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    ABSTRACT: The interference of superposed families of curves is considered, for various types of superposition available through computer graphics. It is shown that the use of interference of this type for illustration and experimentation in hydrodynamics, optics, and in certain other situations, is rather limited. To use the technique of superposition most effectively in these areas it is found to be necessary to eliminate the interference, and to use cine techniques.
    Computer Graphics Forum 10/2007; 4(3):209 - 216.
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    ABSTRACT: The inverse problem of electromagnetic induction for an assumed spherically symmetric conductivity distribution within the Earth is considered. In particular an adaptation (applicable in the case of external source fields) is made of the method proposed by Johnson & Smylie. This is based on the Gel'fand-Levitan integral equation and is relevant to the determination of electrical conductivity in the lower mantle and internally generated source-fields. A characteristic of this approach is that the predicted conductivity is a twice differentiable function with respect to the Earth's radius. It is shown here that the inversion procedure satisfactorily recovers the conductivity profile with data generated from a variety of synthetic conductivity structures. Typical response measurements covering a range of frequencies from 0.1 cycles per year to 11 cycles per day for the Earth allowed estimates of the conductivity profile for depths to about 2000 km.
    Geophysical Journal International 04/2007; 92(1):111 - 123.
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    ABSTRACT: An approach to the inverse problem of electromagnetic induction in spherically symmetric layered Earth models is described. In the first case single periodic variations alone are considered and it is assumed that the conductivity is uniform in a single thick shell which surrounds a perfectly conducting sphere. The conductivity and thickness of the shell are determined for each variation separately by using the observed value of the ratio of internal to external parts of the magnetic potential at the surface of the Earth. Results have been obtained by using a variational technique, for Sq variations, the 27-day variation and its harmonics, and the annual variation. In the second case several variations are used simultaneously to obtain a multilayered model. Finally the method is used to give an estimate of the maximum screening effect of the oceans.
    Geophysical Journal International 04/2007; 36(2):399 - 410.
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    ABSTRACT: The theory of electromagnetic induction in a uniformly conducting sphere by aperiodic variations was first studied by Price, and extended to the case when the conductivity varies as any power of the radial distance by Lahiri & Price. In this paper the governing electromagnetic diffusion equation is solved numerically using a Crank-Nicolson type formula. Various profiles that have been proposed for the mantle are tested using the analyses of Dst by Chapman & Price, Rikitake & Sato, Anderssen & Seneta, and the provisional results for the latest analysis by Anderssen, Doyle, Petersons & Seneta.It is found that the Dst analyses are not accurate enough to allow a conductivity structure to be determined with precision. They are, however, useful in providing additional checks on models that have been determined by other long-period variations. In this paper it is found that they are compatible with a conductivity profile determined by the harmonics of Sq and the 27-day variation. The main features of this profile are a rise in conductivity, between 500 and 600 km, to about 1 mho m--1, and a levelling off at this value to at least 1200 km, or so, from the surface.
    Geophysical Journal International 04/2007; 40(1):67 - 83.
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