Covariance of Weak Lensing Observables

Analytical expressions for covariances of weak lensing statistics related to the aperture mass $\Map$ are derived for realistic survey geometries such as SNAP for a range of smoothing angles and redshift bins. We incorporate the contributions to the noise due to the intrinsic ellipticity distribution and the effects of finite size of the catalogue. Extending previous results to the most general case where the overlap of source populations is included in a complete analysis of error estimates, we study how various angular scales in various redshifts are correlated and how the estimation scatter changes with survey parameters. Dependence on cosmological parameters and source redshift distributions are studied in detail. Numerical simulations are used to test the validity of various ingredients to our calculations. Correlation coefficients are defined in a way that makes them practically independent of cosmology. They can provide important tools to cross-correlate one or more different surveys, as well as various redshift bins within the same survey or various angular scales from same or different surveys. Dependence of these coefficients on various models of underlying mass correlation hierarchy is also studied. Generalisations of these coefficients at the level of three-point statistics have the potential to probe the complete shape dependence of the underlying bi-spectrum of the matter distribution. A complete error analysis incorporating all sources of errors suggest encouraging results for studies using future space based weak lensing surveys such as SNAP.