Determining the depth of Jupiter's Great Red Spot with Juno: a Slepian approach
One of Jupiter's most prominent atmospheric features, the Great Red Spot (GRS), has been observed for more than two centuries, yet little is known about its structure and dynamics below its observed cloud-level. While its anticyclonic vortex appearance suggests it might be a shallow weather-layer feature, the very long time span for which it was observed implies it is likely deeply rooted, otherwise it would have been sheared apart by Jupiter's turbulent atmosphere. Determining the GRS depth will shed light not only on the processes governing the GRS, but on the dynamics of Jupiter's atmosphere as a whole. The Juno mission single flyby over the GRS (PJ7) discovered using microwave radiometer measurements that the GRS is at least a couple hundred kilometers deep (Li et al. 2017). The next flybys over the GRS (PJ18 and PJ21), will allow high-precision gravity measurements that can be used to estimate how deep the GRS winds penetrate below the cloud-level. Here we propose a novel method to determine the depth of the GRS based on the new gravity measurements and a Slepian function approach that enables an effective representation of the wind-induced spatially-confined gravity signal, and an efficient determination of the GRS depth given the limited measurements. We show that with this method the gravity signal of the GRS should be detectable for wind depths deeper than 300 kilometers, with reasonable uncertainties that depend on depth (e.g., $\pm$100km for a GRS depth of 1000km).