Simulating possible regions of delayed sprite inception above thunderstorms using piecewise-varying lightning discharge time dependence

The appearance of transient luminous events (TLEs) in the mesosphere is known to be associated with strong (almost exclusively) positive cloud-to-ground (+CG) strokes with large charge moment change (CMC) values in tropospheric thunderstorms. Nevertheless, despite numerous observational campaigns from ground and space-based platforms, robust theoretical models, and laboratory experiments, there are some open questions concerning the exact circumstances for the appearance of sprites, their morphological attributes and extent, the time delay and lateral offset from their parent flash, and the actual properties of that flash that enable the inception of TLEs. Among these are the causes for the observed delay in sprite appearance relative to the onset of the current in the parent stroke, and how physical metrics of the parent + CG, such as the peak current, multiplicity, impulse charge moment change (iCMC), and continuing current, match with sprite shape, luminosity, and number of elements. Curiously, seemingly identical + CG discharges with the same CMC that should lead to a mesospheric discharge do not initiate sprites, while sometimes even weaker + CG discharges are able to do so. In an effort to seek an explanation for such phenomena, previous studies have investigated effects such as mesospheric inhomogeneities, the presence of meteoritic ablation products, discharges in neighboring cloud cells, associative detachment of electrons from atomic oxygen ions, and long continuing current. Here, we investigate another effect, one that can be associated with continuing current but to the best of our knowledge has hitherto not been simulated explicitly, namely, piecewise-varying discharge time dependence. We present the results of simulations using a 3D quasi-electrostatic model with various patterns of the parent flash discharge current. We show how short, moderate, and long delayed sprites can be incepted due to piecewise-varying discharge time dependence, and how discharges possessing low iCMC values can still produce electric fields in the mesosphere with magnitudes above the conventional electrical breakdown field. The model is validated by simulating a sprite event observed from the International Space Station during the ILAN-ES campaign in 2022, showing how a delayed sprite is incepted by a prolonged piecewise pattern of the current in the parent + CG flash.