The results from weak gravitational lensing analyses are subject to a cosmic variance error term that has previously been estimated assuming Gaussian statistics. In this letter we address the issue of estimating cosmic variance errors for weak lensing surveys in the non-Gaussian regime. Using standard cold dark matter model ray-tracing simulations characterized by Omega_m=0.3, Omega_Lambda=0.7, h=0.7, sigma_8=1.0 for different survey redshifts z_s, we determine the variance of the two-point shear correlation function measured across 64 independent lines of sight. We compare the measured variance to the variance expected from a random Gaussian field and derive a redshift-dependent non-Gaussian calibration relation. We find that the ratio can be as high as ~30 for a survey with source redshift z_s ~ 0.5 and ~10 for z_s ~ 1. The transition scale theta_c above which the ratio is consistent with unity, is found to be theta_c ~ 20 arcmin for z_s ~ 0.5 and theta_c ~ 10 arcmin for z_s ~ 1. We provide fitting formula to our results permitting the estimation of non-Gaussian cosmic variance errors for any weak lensing analysis, and discuss the impact on current and future surveys. A more extensive set of simulations will however be required to investigate the dependence of our results on cosmology, specifically on the amplitude of clustering.
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