Loki Patera is one of the most dramatically time-variable volcanic features on Io, exhibiting episodic brightening events every 1-3 years that may produce over 15% of lo's global heat flow. We observed three such brightening events with adaptive optics imaging at the Keck and Gemini N telescopes over the course of 70 nights of observation in 2013-2016. The high cadence and multi-wavelength nature of the observations provides constraints on models for activity at Loki Patera. The Matson et al. (2006) model for Loki Patera as an overturning basaltic magma sea is adapted to fit the observations of all three events. In particular, we adjust the details of the overturn progression, and modify the lava thermal properties to include dependencies on temperature and porosity, to improve the fit to the data. The preferred models find overturn front propagation velocities of 1.2-1.7 km/day, corresponding to resurfacing rates of 1500-2200 m(2)/s. The time intervals of 440-540 days between successive events are roughly consistent with the 540-day period calculated by Rathbun et al. (2002) for events prior to 2001. The best coverage was obtained for the 2016 brightening; model fits to this event require a lava bulk thermal conductivity of 0.55-0.75 W/m/K, with the best fit obtained for a value of similar to 0.7 W/m/K and an average porosity that decreases during cooling. For all three events, the overturn front appears to propagate around the patera in the clockwise direction, opposite to what has been inferred for past brightening events. There is evidence that the overturn may be more complex than a single propagating wave, perhaps involving multiple simultaneous resurfacing waves as well as portions of the patera that are active even after the nominal bright phase has ended. The measured intensities are anomalously low when Loki Patera is viewed at high emission angles, suggestive of topographic shadowing due to a raised area or the edge of the depression in which the magma sea resides. (C) 2017 Elsevier Inc. All rights reserved.