Uncertainties in future climate predictions due to convection parameterisations

In the last decades several convection parameterisations have been developed to consider the impact of small-scale unresolved processes in Earth System Models associated with convective clouds. Global model simulations, which have been performed under current climate conditions with different convection schemes, significantly differ among each other in the simulated transport of trace gases and precipitation patterns due to the parameterisation assumptions and formulations, e.g. the computation of convective rainfall rates, calculation of entrainment and detrainment rates etc. Here we address sensitivity studies comparing four different convection schemes under alternative climate conditions (with doubling of the CO₂ concentrations) to identify uncertainties related to convective processes. The increase in surface temperature reveals regional differences up to 4 K dependent on the chosen convection parameterisation. These differences are statistically significant almost everywhere in the troposphere of the intertropical convergence zone. The increase in upper tropospheric temperature affects the amount of water vapour transported to the lower stratosphere, leading to enhanced water vapour contents between 40% and 60% at the cold point temperature in the Tropics. Furthermore, the change in transporting short-lived pollutants within the atmosphere is highly ambiguous for the lower and upper troposphere. These results reflect that different approaches to compute mass fluxes, detrainment levels or trigger functions determine the transport of short-lived trace gases from the planetary boundary layer to lower, middle or upper tropospheric levels. Finally, cloud radiative effects have been analysed, uncovering a shift in different cloud types in the Tropics, especially for cirrus and deep convective clouds. These cloud types induce a change in net cloud radiative forcing varying from 0.5 W m⁻² to 2.0 W m⁻²

A caricature of a singular curvature flow in the plane

We study a singular parabolic equation of the total variation type in one dimension. The problem is a simplification of the singular curvature flow. We show existence and uniqueness of weak solutions. We also prove existence of weak solutions to the semi-discretization of the problem as well as convergence of the approximating sequences. The semi-discretization shows that facets must form. For a class of initial data we are able to study in details the facet formation and interactions and their asymptotic behavior. We notice that our qualitative results may be interpreted with the help of a special composition of multivalued operators

Astrometric Control of the Inertiality of the Hipparcos Catalog

Based on the most complete list of the results of an individual comparison of the proper motions for stars of various programs common to the Hipparcos catalog, each of which is an independent realization of the inertial reference frame with regard to stellar proper motions, we redetermined the vector $\omega$ of residual rotation of the ICRS system relative to the extragalactic reference frame. The equatorial components of this vector were found to be the following: $\omega_x = +0.04\pm 0.15$ mas yr$^{-1}$, $\omega_y = +0.18\pm 0.12$ mas yr$^{-1}$, and $\omega_z = -0.35\pm 0.09$ mas yr$^{-1}$.Comment: 8 pages, 1 figur

Proceedings of minisemester on evolution of interfaces, Sapporo 2010

conf: Special Project A, Proceedings of minisemester on evolution of interfaces, Sapporo (Department of Mathematics, Hokkaido University, July 12- August 13, 2010