A relook at NEH‐4 curve number data and antecedent moisture condition criteria

This paper investigates the variation of the popular curve number (CN) values given in the National Engineering Hand Book–Section 4 (NEH‐4) of the Soil Conservation Service (SCS) with antecedent moisture condition (AMC) and soil type. Using the volumetric concept, involving soil, water, and air, a significant condensation of the NEH‐4 tables is achieved. This leads to a procedure for determination of CN for gauged as well as ungauged watersheds. The rainfall‐runoff events derived from daily data of four Indian watersheds exhibited a power relation between the potential maximum retention or CN and the 5‐day antecedent rainfall amount. Including this power relation, the SCS‐CN method was modified. This modification also eliminates the problem of sudden jumps from one AMC level to the other. The runoff values predicted using the modified method and the existing method utilizing the NEH‐4 AMC criteria yielded similar results. Copyright © 2006 John Wiley & Sons, Ltd.     

On Relativistic Equations of Motion of an Earth Satellite

For numerical integration of the geocentric equations of motion of Earth satellites in the general relativity framework one may choose now between rather simple equations involving in their relativistic dynamical part only the Earth-induced terms and very complicated equations taking into account the relativistic third-body action. However, it is possible quite easily to take into account the relativistic indirect third-body perturbations and to neglect much lesser direct third-body perturbations. Such approach is based on the use of the Newtonian third-body perturbations in geocentric variables with expressing them in the relativistic manner in terms of the barycentric arguments. Together with it, to extend the known results for the spheroid model of the Earth, the Earth-induced terms are treated in great detail by including the non-spin part of the Earth vector-potential and the Earth triaxial non-sphericity.This revised version was published online in October 2005 with corrections to the Cover Date.     

The free precession and libration of Mercury

An analysis based on the direct torque equations including tidal dissipation and a viscous core-mantle coupling is used to determine the damping time scales of O(¹⁰⁵) years for free precession of the spin about the Cassini state and free libration in longitude for Mercury. The core-mantle coupling dominates the damping over the tides by one to two orders of magnitude for the plausible parameters chosen. The short damping times compared with the age of the Solar System means we must find recent or on-going excitation mechanisms if such free motions are found by the current radar experiments or the future measurement by the MESSENGER and BepiColombo spacecraft that will orbit Mercury. We also show that the average precession rate is increased by about 30% over that obtained from the traditional precession constant because of a spin-orbit resonance induced contribution by the C₂₂ term in the expansion of the gravitational field. The C₂₂ contribution also causes the path of the spin during the precession to be slightly elliptical with a variation in the precession rate that is a maximum when the obliquity is a minimum. An observable free precession will compromise the determination of obliquity of the Cassini state and hence of C/MMR² for Mercury, but a detected free libration will not compromise the determination of the forced libration amplitude and thus the verification of a liquid core.     

Probing the Formation and Evolution of early-type galaxies: the SAURON project

We are conducting a systematic study of a carefully selected sampleof nearby E/S0 galaxies and Sa bulges using the unique panoramic integral-fieldspectrograph SAURON, mounted at the WHT. The goal of the SAURON projectis to fully map the gaseous/stellar kinematics and the stellar populations of a representative sample of 80 early-type galaxies up to 1 Re,probing different environments (clusters, field). These data, used in combination with existing ground-based and HST observations, and fed to the theoretical machinery we have developed, will allow to determine theintrinsic dynamical structure of the galaxies. We will also measure the masses of central black holes, relate the internal dynamics to the ageand metallicity of the stellar populations, and establish the historyof metal enrichment as a function of Hubble type and environment. Some brief results on two targets observed during the SAURON campaign will serve as an illustration of the unique and high quality data we are currently gathering. This revised version was published online in September 2006 with corrections to the Cover Date.     

Radial orbital anisotropy and the Fundamental Plane of elliptical galaxies

The existence of the Fundamental Plane imposes strong constraints on the structure and dynamics of elliptical galaxies, and thus contains important information on the processes of their formation and evolution. Here we focus on the relations between the Fundamental Plane thinness and tilt and the amount of radial orbital anisotropy: in fact, the problem of the compatibility between the observed thinness of the Fundamental Plane and the wide spread of orbital anisotropy admitted by galaxy models has often been raised. By using N -body simulations of galaxy models characterized by observationally motivated density profiles, and also allowing for the presence of live, massive dark matter haloes, we explore the impact of radial orbital anisotropy and instability on the Fundamental Plane properties. The numerical results confirm a previous semi-analytical finding (based on a different class of one-component galaxy models): the requirement of stability matches almost exactly the thinness of the Fundamental Plane. In other words, galaxy models that are radially anisotropic enough to be found outside the observed Fundamental Plane (with their isotropic parent models lying on the Fundamental Plane) are unstable, and their end-products fall back on the Fundamental Plane itself. We also find that a systematic increase of radial orbit anisotropy with galaxy luminosity cannot explain by itself the whole tilt of the Fundamental Plane, the galaxy models becoming unstable at moderately high luminosities: at variance with the previous case, their end-products are found well outside the Fundamental Plane itself. Some physical implications of these findings are discussed in detail.     

Water balance modelling in lateritic terrain

An analytical approximate model for unsaturated flow in a spatially variable field, coupled with infiltration and evapotranspiration at the upper boundary and a fluctuating water-table at the lower boundary, has been developed. The unsaturated flow equations depend on parameterizations of θ(Φ) and K(Φ). They are based on the notion of a moving, discontinuous front. The field heterogeneity refers to saturated hydraulic conductivity only. Horizontal variability is considered, and the flow medium is approximated as a set of uncorrelated, vertically homogeneous columns. Expectations and variances obtained with this approach have been compared with observations of the field hydrological processes. Three important aspects of the hydrology in this lateritic terrain are rapid water-table response, Hortonian surface runoff generation and soil suction variability. The stochastic conceptualization used explains to a high degree these characteristics, although some limitations are demonstrated.