Dynamical system analysis of Quintom Dark Energy Model

The present work deals with dynamical system analysis of a Quintom Model of Dark Energy. By suitable transformation of variables the Einstein field equations are converted to an autonomous system. The critical points are determined and stability of hyperbolic critical points are determined by Hartman-Grobman theorem. To analyze non-hyperbolic critical points different tools (notably Center Manifold theory) are used. Possible bifurcation scenarios have also been explained.Comment: 8 pages, 6 figure

Interaction between aerosols and the mesoscale convective systems over the tropical continents

Presence of aerosols in the upper troposphere can have significant impacts on the Earth’s radiative energy budget. However, the aerosol–cloud relationship represents the largest uncertainty in the radiative energy budget. Relationships between aerosols and the mesoscale convective systems (MCSs) are complicated and difficult to ascertain, due in large part to inadequate availability of satellite datasets until recent years. Variation of aerosol impacts with meteorological parameters and the relative influence of these parameters on the convective strength of the MSCs can also be attributed to limited detectability of aerosol invigoration effects. To address the interaction between aerosol and the MCSs, I first address the influence of MCS on the distribution of the aerosols, which is poorly known on a global scale. Then, I investigate the influence of aerosol on MCSs. This dissertation addresses these problems by collocating a suite of geostationary and polar orbital satellites at three different phases of their convective lifecycle. First, I estimate the extent of upper tropospheric aerosol layers (UT ALs) surrounding the MCSs and explore the relationships between UT AL extent and the morphology, location, and developmental stages of collocated MCSs in the tropics over equatorial Africa, South Asia, and the Amazon basin between June 2006 and June 2008. I identify that the most extensive UT ALs over equatorial Africa are associated with the mature MCSs, while the most extensive UT ALs over South Asia and the Amazon basin are associated with the growing MCSs. Convective aerosol transport over Amazonia is weaker than that observed over the other two regions despite similar transport frequencies, likely due to smaller sizes and shorter mean lifetimes of Amazonian MCSs. Variations in UT ALs in the vicinity of tropical MCSs are primarily explained by variations in the horizontal sizes of the associated MCSs and are not related to aerosol loading in the lower troposphere. Relationships between convective properties and aerosol transport are relatively weak during the decaying stage of convective development. Then I estimate the relative influence of aerosols and other meteorological parameters on MCS strength and longevity using collocated samples of MCSs from January 2003 to June 2008. The results show that relative humidity (RH) and convective available potential energy (CAPE) have the strongest impacts on MCS lifetime and enhance the lifetime of the MCSs by 6-36 hours when other parameters such as vertical wind shear (VWS) and aerosols are kept constant. Aerosols also enhance the convective lifetime of MCSs, however at a much weaker rate (6-24h) and only when RH and VWS are high. Moreover, aerosol influence on convective lifetime is detected during the mature and decaying phases only. At the continental scale, aerosols explain 20-27% of the total variance of MCSs’ lifetime over equatorial South America, but explain only 8% of the same over equatorial Africa. South Asian MCSs are more strongly influenced by meteorological parameters and MCS-associated aerosols when they are over the ocean than when over the land since most MCSs form and develop over the oceans. After that, I estimate the influence of aerosols and other meteorological parameters on MCSs’ rain rate (RR). Results show that an increase in aerosol concentration enhance IWC and suppress RR and LH during all three phases of convective lifetime. Increasing aerosol concentrations suppress RR at the rate of -0.38 mm/h and -0.47 mm/h during the growing, decaying phases when VWS is high and at a rate of -0.30 mm/h during the mature phase when RH is low. Meteorological parameters such as VWS and RH have significant effects on these aerosol influences. The suppression of RR is also associated with a decrease in latent heat released by large hydrometeors. Aerosols explain 16%, 23%, and 29% of RR’s variance during the growing, mature and decaying phases, respectively, as estimated by a multiple linear regression method. Consequently, aerosols enhance IWC of the MCSs inside the anvil up to 0.72, 1.41, 0.82 mg/m3 and enhance the total integrated reflectivity of the larger-sized ice particles up to 8, 11, and 18 dBZ in the convective core regions during the growing, mature and decaying phases, respectively. In contrast, changes (one standard deviation) in CAPE and RH enhance the RR up to 0.35 mm/h. This dissertation study provides the first satellite based global tropical assessment of the relative influences of aerosols and meteorological conditions on MCSs’ lifetime, rain rate, and IWC and the mutual dependence of these influences. It also shows how aerosols influence the rain rate, cloud ice and lifetime of the MCSs, varying within their lifecycle and between different tropical continents ranging from humid equatorial South America during wet season and big monsoonal systems over South Asia to relatively dry equatorial Africa with high aerosol loading. In doing so, this work has also advanced our capability to evaluate whether or not aerosols could increase convective lifetime by suppressing rain rate and invigorating the MCSs on climate scale and what are the favorable meteorological conditions for aerosol to affect the lifetime of the MCSs. Our results also provide an interpretive framework for devising and evaluating numerical model experiments that can examine relationships between convective properties and ALs transported in the upper troposphere. In the future, we would like to investigate the influence of different meteorological parameters and aerosols on extra tropical MCSs and on self-aggregation of convection.Geological Science