A poincaré model for the earth's fluid core

Abstract

The superconducting-gravimeter data of Melchior and Ducarme (1986) has been interpreted as internal motion in the Earth's core by Aldridge and Lumb (1987) using a Poincaré model. Several low-order modes with periods of 13–16 hours have been tentatively identified in the core which is taken to be an incompressible, homogeneous fluid within a rigid, rotating container. The identification is based on asymptotic values of the frequencies which change slowly with time while the modes decay with an e-folding time of about 280 days. The slow change in frequency with time implies a small temporal variation in the rotation rate of the core. This mean flow is a nonlinear effect often observed in laboratory experiments designed to excite Poincaré modes. Interaction among modes during free ringdown is also observed in those experiments and apparently in the data of Melchior et al. (1988) as well. Laboratory work thus provides the link to extend the Poincaré model to include viscous and nonlinear effects in order to interpret the gravimetric observations as core modes.     

Using low-density discrete Airborne Laser Scanning data to assess the potential carbon dioxide emission in case of a fire event in a Mediterranean pine forest

The aim of study is to map the carbon dioxide (CO₂) emission of the aboveground tree biomass (AGB) in case of a fire event. The suitability of low point density, discrete, multiple-return, Airborne Laser Scanning (ALS) data and the influence of several characteristics of these data and the study area on the results obtained have been evaluated. A sample of 45 circular plots representative of Pinus halepensis Miller stands were used to fit and validate the model of AGB. The ALS point clouds were processed to obtain the independent variables and a multivariate linear regression analysis between field data and ALS-derived variables allowed estimation of AGB. Then, the influence of several characteristics on the residuals of the model was analyzed. Finally, conversion factors were applied to obtain the CO₂ values. The AGB model presented a R² value of 0.84 with a relative root-mean-square error of 27.35%. This model included ALS variables related to vegetation height variability and to canopy density. Terrain slope, aspect, canopy cover, scan angle and the number of laser returns did not influence AGB estimations at plot level.     

Improvement of the geoid in local areas by satellite gradiometry

Summary Satellite gradiometry is studied as a means to improve the geoid in local areas from a limited data coverage. Least-squares collocation is used for this purpose because it allows to combine heterogeneous data in a consistent way and to estimate the integrated effect of the attenuated spectrum. In this way accuracy studies can be performed in a general and reliable manner. It is shown that only three second-order gradients contribute significantly to the estimation of the geoidal undulations and that it is sufficient to have gradiometer data in a 5°×5° area around the estimation point. The accuracy of the geoid determination is strongly dependent on the degree and order of the reference field used. An accuracy of about ±1 m can be achieved with a reference field of (12, 12). There is an optimal satellite altitude for each reference field and this altitude may be higher than 300 km for a field of low degree and order. The influence of measuring errors is discussed and it is shown that only gradiometer data with accuracies better than ±0.05 E will give a significant improvement of the geoid. Finally, some results on the combination of satellite gradiometry and terrestrial gravity measurements are given. The proposed method seems to be well suited for local geoid determinations down to the meter range. It is especially interesting for unsurveyed and difficult areas because no terrestrial measurements are necessary. Furthermore, it has the practical advantage that only a local data coverage is needed.     

Effect of spatial resolution on regionalization of hydrological model parameters

Lack of availability of historical data series is one of the major hindrances in hydrological modelling. Regionalization of hydrological model parameters is one of the solutions to obtain the parameters for ungauged basins. Recently, lots of methodologies have been developed. They can be categorized as model calibration then fitting regression between model parameters and catchments characteristics, using some kind of transfer function. The aim of this study was to compare different regionalization methods as well as to look how the spatial resolution affects regionalization. In this study, a modified Lipschitz and monotony condition was used for regionalization. To identify the effect of the model resolution, the parameters of a distributed and semi‐distributed version of the Hydrologiska Byråns Vattenbalansavdelning (HBV) model were regionalized. The study was conducted at the upper Neckar catchment of southwest Germany. It has been found that the combination of Lipschitz and monotony condition has performed reasonably. It has been seen that the distributed model structure has outperformed the semi‐distributed model structure. It shows under present data conditions that higher model resolution can describe processes of ungauged basins reasonably. Copyright © 2011 John Wiley & Sons, Ltd.     

Analysis of Photoelectric Occultations and Development of a Digital Model of the Lunar Libration Zone

Astronomy Reports - One of the priority tasks of modern astronomy is the observation and study of transient celestial processes, which also concerns photoelectric observations of lunar occultations...     

Planetons: An example of large amplitude solitary waves

Abstract

The term ‘‘solitary wave'’ is usually used to denote a steadily propagating permanent form solution of a nonlinear wave equation, with the permanency arising from a balance between steepening and dispersive tendencies. It is known that large-scale thermal anomalies in the ocean are subject to a steepening mechanism driven by the beta effect, while at the smaller deformation scale, such phenomena are highly dispersive. It is shown here that the evolution of a physical system subject to both effects is governed by the ‘‘frontal semi-geostrophic equation'’ (FSGE), which is valid for large amplitude thermocline disturbances. Solitary wave solutions of the FSGE (here named planetons) are calculated and their properties are described with a view towards examining the behavior of finite amplitude solitary waves. In contrast, most known solitary wave solutions belong to weakly nonlinear wave equations (e.g., the Korteweg—deVries (KdV) equation).

The FSGE is shown to reduce to the KdV equation at small amplitudes. Classical sech² solitons thus represent a limiting class of solutions to the FSGE. The primary new effect on planetons at finite amplitudes is nonlinear dispersion. It is argued that due to this effect the propagation rates of finite amplitude planetons differ significantly from the ‘‘weak planeton'', or KdV, dispersion relation. Planeton structure is found to be simple and reminiscent of KdV solitons. Numerical evidence is presented which suggests that collisions between finite amplitude solitary waves are weakly inelastic, indicating the loss of true soliton behavior of the FSGE at moderate amplitudes. Lastly, the sensitivity of solitary waves to the existence of a nontrivial far field is demonstrated and the role of this analysis in the interpretation of lab experiments and the evolution of the thermocline is discussed.