Box replication effects in weak lensing light-cone construction

Weak gravitational lensing simulations serve as indispensable tools for obtaining precise cosmological constraints. In particular, it is crucial to address the systematic uncertainties in theoretical predictions, given the rapid increase in galaxy numbers and the reduction in observational noise. Both on-the-fly and post-processing methods for constructing lensing light-cones encounter limitations due to the finite simulated volume, necessitating the replication of the simulation box to encompass the volume to high redshifts. To address this issue, our primary focus lies on investigating and quantifying the impact of box replication on the convergence power spectrum and higher order moments of lensing fields. Subsequently, a univariate model is utilized to estimate the amplitude parameter A by fitting four statistics measured from partial sky light-cones along specific angles, to the averaged result from random directions. The investigation demonstrates that the systematic bias stemming from the box replication phenomenon falls within the bounds of statistical errors for the majority of cases. However, caution should be exercised when considering high-order statistics on a small sky coverage (${\lesssim} 25~\mathrm{deg^2}$). For this case, we have developed a code that facilitates the identification of optimal viewing angles for the light-cone construction. This code has been made publicly accessible at https://github.com/czymh/losf.