Note on nonlinear Rayleigh-Taylor instability

Shivamoggi (1983) has used the method of strained coordinates in investigating the nonlinear Rayleigh-Taylor instability problem. After incorporating the corrections pointed out by Malik and Singh (1983) he obtained a revised expression for the nonlinear cut off wavenumber which separates the region of stability from that of instability.     

Use of Roche coordinates in the problems of small oscillations of tidally-distorted stellar models

Kopal's method of Roche coordinates used by us in an earlier paper (Mohan and Singh, 1978) to study the problems of small oscillations of tidally-distorted stars has been extended further to take into account the effect of second-order terms in tidal distortion. Our results show that the effect of including terms of second order of smallness in tidal distortion in the metric coefficients of the Roche coordinates of tidally distorted stars is quite significant, especially in case of stars with extended envelopes and (or) larger values of the mass ratio of the companion star producing tidal distortion. Some of the models which were earlier found stable against small perturbations now become dynamically unstable with the inclusion of the terms of second order of smallness in tidal effects.At present on leave of absence with the department of Mathematics, College of Science, Baghdad, Iraq.     

Relationships between three dispersion measures used in flood frequency analysis

Three dispersion measures of a random variable, i.e., the standard deviation, the mean deviation (MD) about the mean and the second L-moment, are analyzed in terms of their properties and mutual relationships. Emphasis is placed on the MD, as it is less recognized than two other dispersion measures. The relationships between the dispersion measures are derived for distributions commonly applied in flood frequency analysis (FFA). For distributions that are unbounded, there is a distribution-dependent constant value of the ratio of dispersion measures, or equivalently of respective coefficients of variation. For two-parameter distributions that are lower-bounded, the relationship between the coefficients of variation is also distribution dependent and is not linear. For lower-bounded three-parameter distributions, the dispersion measure ratios, or equivalently the ratios of coefficients of variation, depend on the coefficient of skewness and show a strong distributional dependence. For selected distributions, the three dispersion measures are compared both in terms of the robustness to the largest samples element and the accuracy of upper quantile estimation. The MD statistics may be highly competitive to the two other dispersion measure statistics if applied in FFA for parameters estimation.     

Temporal Assessment of Growing Stock, Biomass and Carbon Stock of Indian Forests

The dynamics of terrestrial ecosystems depends on interactions between carbon, nutrient and hydrological cycles. Terrestrial ecosystems retain carbon in live biomass (aboveground and belowground), decomposing organic matter, and soil. Carbon is exchanged naturally between these systems and the atmosphere through photosynthesis, respiration, decomposition, and combustion. Human activities change carbon stock in these pools and exchanges between them and the atmosphere through land-use, land-use change, and forestry.In the present study we estimated the wood (stem) biomass, growing stock (GS) and carbon stock of Indian forests for 1984 and 1994. The forest area, wood biomass, GS, and carbon stock were 63.86 Mha, 4327.99 Mm³, 2398.19 Mt and 1085.06 Mt respectively in 1984 and with the reduction in forest area, 63.34 Mha, in 1994, wood biomass (2395.12 Mt) and carbon stock (1083.69 Mt) also reduced subsequently. The Conifers, of temperate region, stocked maximum carbon in their woods, 28.88 to 65.21 t C ha⁻¹, followed by Mangrove forests, 28.24 t C ha⁻¹, Dipterocarp forests, 28.00 t C ha⁻¹, and Shorea robusta forests, 24.07 t C ha⁻¹. Boswellia serrata, with 0.22 Mha forest area, stocked only 3.91 t C ha⁻¹. To have an idea of rate of carbon loss the negative changes (loss of forest area) in forest area occurred during 1984–1994 (10yrs) and 1991–1994 (4yrs) were also estimated. In India, land-use changes and fuelwood requirements are the main cause of negative change. Total 24.75 Mt C was lost during 1984–1994 and 21.35 Mt C during 1991–94 at a rate of 2.48 Mt C yr⁻¹ and 5.35 Mt C yr⁻¹ respectively. While in other parts of India negative change is due to multiple reasons like fuelwood, extraction of non-wood forest products (NWFPs), illicit felling etc., but in the northeastern region of the country shifting cultivation is the only reason for deforestation. Decrease in forest area due to shifting cultivation accounts for 23.0% of the total deforestation in India, with an annual loss of 0.93 Mt C yr⁻¹.     

Microwave response of seasonal snow-cover measured by using a ground-based radiometer at 6.93 and 18.7 ghz frequencies and at dual polarization

Snow cover is an important variable for climatic and hydrologic models due to its effects on surface albedo, energy, and moisture budgets. Passive microwave sensors can be used to monitor temporal and spatial variations in large-scale snow cover parameters, avoiding problems of cloud cover and polar nights. In the present study, brightness temperature values were estimated (using calibration curves) for moist snow on natural and blackbody/metal surface. T_B response on snow depth, density, SWE and angular variation from nadir were measured and found that T_B decreases with increase of snow depth and with increase of angle from nadir. Empirical relations were used to estimate emissivity, dielectric constant and dielectric loss factor. It was observed that emissivity decreases with the increase of dielectric constant. The dielectric constant and dielectric loss factor both increases with the increase of density. Experiments were performed during winter of year 2005 at Dhundi and Solang (H.P.), India, using ground based passive microwave radiometer having 6.9 and 18.7 GHz antenna frequencies at dual polarization.