A Case Study on the Effects of Heterogeneous Soil Moisture on Mesoscale Boundary-Layer Structure in the Southern Great Plains, U.S.A. Part I: Simple Prognostic Model

The atmospheric boundary-layer (ABL) depth was observed by airborne lidar and balloon soundings during the Southern Great Plains 1997 field study (SGP97). This paper is Part I of a two-part case study examining the relationship of surface heterogeneity to observed ABL structure. Part I focuses on observations. During two days (12–13 July 1997) following rain, midday convective ABL depth varied by as much as 1.5 km across 400 km, even with moderate winds. Variability in ABL depth was driven primarily by the spatial variation in surface buoyancy flux as measured from short towers and aircraft within the SGP97 domain. Strong correlation was found between time-integrated buoyancy flux and airborne remotely sensed surface soil moisture for the two case-study days, but only a weak correlation was found between surface energy fluxes and vegetation greenness as measured by satellite. A simple prognostic one-dimensional ABL model was applied to test to what extent the soil moisture spatial heterogeneity explained the variation in north–south ABL depth across the SGP97 domain. The model was able to better predict mean ABL depth and variations on horizontal scales of approximately 100 km using observed soil moisture instead of constant soil moisture. Subsidence, advection, convergence/divergence and spatial variability of temperature inversion strength also contributed to ABL depth variations. In Part II, assimilation of high-resolution soil moisture into a three-dimensional mesoscale model (MM5) is discussed and shown to improve predictions of ABL structure. These results have implications for ABL models and the influence of soil moisture on mesoscale meteorology     

A simple model to predict the effect of volume fraction,diameter, and length of fibres on strength of fibre reinforced brittle matrix composites

A simplified model is presented to predict the strength variations of brittle matrix composites, reinforced by steel fibres, with the variations of fibre parameters—length, diameter and volume fraction. This model predicts that its tensile and flexural strength increase non‐linearly with the fibre volume fraction. It also predicts that similar non‐linear behaviour should be observed with the reduction of the fibre diameter when other parameters are kept constant. The experimental results support both these theoretical predictions. It is also explained why an increase in the fibre length does not always significantly increase the fracture toughness. The objective of this paper is not to explain and understand in great detail the science of all phenomena responsible for the strength increase of fibre reinforced brittle matrix composites, but to provide a simple engineering explanation as to why its strength increases with the fibre addition, and how this increase can be quantitatively related to the variations in fibre parameters—fibre volume fraction, fibre length and diameter. These simplifying steps are needed to provide a tool that the practicing engineers can use to predict the brittle matrix strength variation with the fibre parameters. In the area of geomechanics, the results presented here can be used to assess and predict the behaviour of fibre‐reinforced earth. Copyright © 2000 John Wiley & Sons, Ltd.     

A concept of correction functions to account for non-associative characteristics of geologic media

A new and simple concept based on the idea of correcting for non-associative characteristics of (geologic) media is presented. A special form of the concept is adopted and introduced in a critical state plasticity model. An example problem of behaviour of a soil tested under triaxial conditions is included. The concept can permit a simplified treatment of non-associativeness and under certain assumptions can allow use of existing formulations of plasticity by maintaining symmetry of the associated matrices.     

A general basis for yield,failure and potential functions in plasticity

A new concept based on the use of a function expressed as a (complete) polynomial expansion in terms of the three invariants of the stress tensor is proposed for deriving yield, failure and plastic potential functions for use in plasticity based constitutive laws. A mathematical interpretation and physical meaning of the proposed concept are provided by using the idea of the singular nature of constiutive matrices in incremental hypoelastic laws. It is suggested that the proposed function and (polynomial) forms of material moduli can be synonymous. A number of specialized forms of the general function are adopted and their values at failure from advanced three-dimensional tests for a number of (geological) media are evaluated. The results indicate the possibility that there exist invariant numbers associated with the functions(s) that may apply to a wide range of materials. Some ideas on implementation of the proposed concept are also presented.     

Computational procedures for non-linear three-dimensional analysis with some advanced constitutive laws

Computational procedures for implementing some constitutive models are described and introduced in three-, and two-dimensional finite element procedures; here variable moduli, Drucker–Prager, critical state and cap models are considered. Consistent numerical schemes are presented with applications to a number of example problems. These procedures can provide successful results with advanced constitutive laws for three-dimensional analysis of a wide range of non-linear problems.     

Viscoplastic model for geologic materials with generalized flow rule

The general yield function in the hierarchical approach for constitutive modelling of materials is used with Perzyna's theory to characterize viscoplastic behaviour of geologic materials: a sand and rock salt. Particular attention is given to determination of the constants from laboratory quasistatic or short term, and creep tests. The proposed model is verified with respect to observed laboratory response of the sand and salt. It is implemented in a non-linear finite element procedure and applied to analyse time-dependent behaviour of a cavity in the rock salt.     

Spectral analysis of monsoonal global energy and enstrophy and their nonlinear exchanges in the zonal wavenumber domain

Vertical distributions of various components of the tropospheric global rotational kinetic energy, enstrophy and available potential energy during July 1979, and the contributions to these from different zonal wave categories were studied. Representative levels in the lower and upper troposphere for the stationary and transient energetics were identified on the basis of different components of energy and enstrophy. The eddy energy and enstrophy contained in different zonal scale components in the lower and upper troposphere were studied to find out the preferred scales for stationary and transient monsoonal motion in the two atmospheric layers. The role of different zonal wave categories in the nonlinear exchanges of energy and enstrophy arising due to stationary-stationary, transient-transient, stationary-transient and observed flow interactions was examined. Stationary and transient global spectra of the aforesaid dynamical variables in terms of the zonal wavenumber(m) with triangular truncation atm = 42 were utilized for this purpose. It was found from the global average kinetic energy in lower and upper troposphere that the global stationary and transient motions were comparable in the lower troposphere while in the upper troposphere stationary motion dominated over the transient motion. The computed zonal and eddy energy confirmed that the stationary motion was predominantly zonal while the transient motion was dominated by eddies. From the time mean nonlinear interaction of kinetic energy (enstrophy) of observed flow it was seen that the long and short waves as well as the zonal flow gained kinetic energy (enstrophy) from medium waves due to nonlinear interactions. The transfer of available potential energy due to nonlinear interaction was down the scale except for short waves in the upper troposphere. The stationary-transient interaction was found to be an important element of the spatial-temporal varying atmospheric flow.     

One-Centimeter Orbit Determination for Jason-1: New GPS-Based Strategies

The U.S./French Jason-1 satellite is carrying a state-of-the-art GPS receiver to support precise orbit determination (POD) requirements. The performance of the Jason-1 “BlackJack” GPS receiver was strongly reflected in early POD results from the mission, enabling radial accuracies of 1-2 cm soon after the satellite's 2001 launch. We have made further advances in the GPS-based POD for Jason-1, most notably in describing the phase center variations of the on-board GPS antenna. We have also adopted new geopotential models from the Gravity Recovery and Climate Experiment (GRACE). The new strategies have enabled us to better exploit the unique contributions of the BlackJack GPS tracking data in the POD process. Results of both internal and external (e.g., laser ranging) comparisons indicate that orbit accuracies of 1 cm (radial RMS) are being achieved for Jason-1 using GPS data alone.     

Jason-1 Geophysical Performance Evaluation

The Jason-1 satellite was launched on 7 December 2001 with the primary objective of continuing the high accuracy time series of altimeter measurements that began with the TOPEX/Poseidon mission in 1992. To achieve this goal, it is necessary to validate the performance of the Jason-1 measurement system, and to verify that its error budget is at least at the same level as that of the TOPEX/Poseidon mission. The article reviews the main components of the Jason-1 altimetric error budget from instrument characterization to the geophysical use of the data. Using the Interim Geophysical Data Records (16DR) that were distributed to the Jason-1 Science Working Team during the verification phase of the mission, it is shown that the Jason-1 mission is performing well enough to continue studies of the large-scale features of the ocean, and especially to continue time series of mean sea-level variations with an accuracy comparable to TOPEX/Poseidon.