Resolving the Azimuthal Ambiguity in Vector Magnetogram Data with the Divergence-Free Condition: Implementations for Disambiguating Each Height Independently

We continue the investigation of how to use the divergence-free condition to resolve the azimuthal ambiguity present in vector magnetogram data. In previous articles, by Crouch, Barnes, and Leka (Solar Physics, 260, 271, 2009) and Crouch (Solar Physics, 282, 107, 2013), all methods used an expression for the divergence of the magnetic field that involves differentiation of quantities that depend on the choice of azimuthal angle. As a result, all heights used to approximate line-of-sight derivatives should generally be disambiguated simultaneously. In this article, we investigate a set of methods that use an expression for the divergence that involves differentiation of quantities that do not depend on the choice of azimuthal angle. This results in an expression for the divergence that can be used to disambiguate each height independently. We test two methods using synthetic and find that the two-step, hybrid method, adapted to disambiguate each height independently, generally produces reasonable results. Moreover, the time required to compute solutions is substantially decreased in comparison to the corresponding method that disambiguates all relevant heights simultaneously.