Analysing the effects of apodizing windows on local correlation tracking using Nirvana simulations of convection

TL;DR

This study evaluates how different apodizing window shapes affect the accuracy of local correlation tracking in retrieving horizontal velocities from convection simulations, highlighting the importance of window width and shape.

Contribution

It systematically compares Gaussian, Lorentzian, trapezoidal, and triangular windows in LCT, revealing optimal shapes and widths for improved velocity correlation with simulations.

Findings

Triangular and trapezoidal windows perform best and worst, respectively.

Higher correlation for intermediate and high velocities across all windows.

Residual errors are larger near granule boundaries.

Abstract

We employ different shapes of apodizing windows in the local correlation tracking (LCT) routine to retrieve horizontal velocities using numerical simulations of convection. LCT was applied on a time sequence of temperature maps generated by the Nirvana code with four different apodizing windows, namely--Gaussian, Lorentzian, trapezoidal and triangular, with varying widths. In terms of correlations (between the LCT-retrieved and simulated flow field), the triangular and the trapezoidal perform the best and worst, respectively. On segregating the intrinsic velocities in the simulations on the basis of their magnitudes, we find that for all windows, a significantly higher correlation is obtained for the intermediate and high-velocity bins and only modest or weak values in the low-velocity bins. The differences between the LCT-retrieved and simulated flow fields were determined spatially which show large residuals at or close to the boundary of granules. The extent to which the horizontal flow vectors retrieved by LCT compare with the simulated values, depends entirely on the width of the central peak of the apodizing window for a given $\sigma$. Even though LCT suffers from a lack of spatial content as seen in simulations, its simplicity and speed could serve as a viable first-order tool to probe horizontal flows--one that is ideal for large data sets.