Vortex Statistics in the Saturn DYNAMICO GCM: Manual and Automated Detection
Authors: Donnelly Padraig , Spiga Aymeric , Guerlet Sandrine , James Matt , Bardet Deborah 
Published: September 2022

&lt;p&gt;&lt;strong data-stringify-type=&quot;bold&quot;&gt;Abstract&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;The Saturn DYNAMICO Global Climate Model (GCM) is a high-resolution, multi-annual numerical simulation of Saturn's atmospheric dynamics [1], combining a radiative-convective equilibrium model [2] and a hydrodynamical solver on an icosahedral grid. The model reproduces well the observed behaviour of jets and eddy-momentum transfer to the mean flow. Vortices arise naturally in the model over time but until now they have not been given direct consideration. Here we investigate the long-term statistical distribution and organization of vortices using (1) a manual visual inspection method and (2) automated techniques that utilise machine learning and analytical calculations as a means of validating the first approach.&lt;/p&gt;
&lt;p&gt;&lt;strong data-stringify-type=&quot;bold&quot;&gt;Manual Detection&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;This vortex detection method is similar to previous observational studies of Jupiter and Saturn [3, 4, 5, 6] and shows how the spatial and temporal distributions of the modelled vortices compares to those observed on Saturn [4, 5, 6], as well as studying the formation conditions and long-term temporal evolution of vortex distributions. With seven simulated model years at &amp;#189;-degree spatial resolution, we&amp;#160;constrain well the size and location of vortices, the horizontal wind field components and the magnitude and sign of horizontal vorticity, enabling direct comparison of the manual and automated methodologies.&lt;/p&gt;
&lt;p&gt;&lt;strong data-stringify-type=&quot;bold&quot;&gt;Automated Detection&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;A convolutional neural network is used to reproduce the manual visual detection method across the entire timeseries using the same assumptions and using the results of the manual study as a training set. We also study the Angular Momentum Eddy Detection Algorithm (AMEDA, [7]) designed for the analysis of terrestrial oceanic eddies. The machine learning study is ongoing and the results of the AMEDA algorithm are largely consistent with the manual approach, meaning that this algorithm can be used in future studies of Jupiter and Saturn DYNAMICO GCM outputs.&lt;/p&gt;
&lt;p&gt;&lt;img src=&quot;&quot; /&gt;&lt;/p&gt;
&lt;p&gt;Figure 1: Vortex count over the entire mature model timeline for the manual (black) and AMEDA (red) approaches. Manual technique measures at each seasonal peak, AMEDA measures at each timestep to create a seasonal average for comparison. AMEDA analysis to be extended to earlier years.&lt;/p&gt;
&lt;p&gt;&lt;img src=&quot;&quot; /&gt;&lt;/p&gt;
&lt;p&gt;Figure 2: Vortex east-west size (left), north-south size (centre) and shape (right), in units of 10&lt;sup&gt;3&lt;/sup&gt;km, for the manual (top) and AMEDA (bottom) approaches.&lt;/p&gt;
&lt;p&gt;&lt;img src=&quot;&quot; /&gt;&lt;/p&gt;
&lt;p&gt;Figure 3: Overall distribution of vortices for entire timeseries with the manual (left subplot) and AMEDA (right subplot) approaches. In each subplot: (Left) histogram of total vortex count. (Centre) instantaneous zonal wind speed at the vortex centre with the mean zonal wind profile. (Right) vortex average size and vorticity sign.&lt;/p&gt;
&lt;p&gt;&amp;#160;&lt;/p&gt;
&lt;p&gt;&lt;img src=&quot;&quot; /&gt;&lt;/p&gt;
&lt;p&gt;Figure 4: (Top) Maximum tangential velocity at vortex edge as a function of distance from the vortex centre (scatter), derived from the AMEDA approach, alongside the geostrophic balance condition (black straight line), all vortices are subgeostrophic. (Bottom) the ratio of vortex V&lt;sub&gt;max&lt;/sub&gt; and the geostrophic condition as a measure of &quot;vortex geostrophy&quot;, with respect to latitude, smaller and higher-latitude vortices tend to be clsoer to the geostrophic condition.&lt;/p&gt;
&lt;p&gt;&lt;strong data-stringify-type=&quot;bold&quot;&gt;Acknowledgements&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;Donnelly and the France authors were supported by Agence Nationale de la Recherche (ANR) and the UK authors acknowledge the Science and Technology Facilities Council (STFC, James) and the European Research Council (ERC, Bardet).&lt;/p&gt;
&lt;p&gt;References&lt;/p&gt;
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&lt;p&gt;[2] Guerlet et al. (2014), Icarus, 238, https://doi.org/10.1016/j.icarus.2014.05.010.&lt;/p&gt;
&lt;p&gt;[3] Li et al. (2004), Icarus, 172, https://doi.org/10.1016/j.icarus.2003.10.015.&lt;/p&gt;
&lt;p&gt;[4] Vasavada et al. (2006), J. Geophys. Res. Planets, 111, https://doi.org/10.1029/2005JE002563.&lt;/p&gt;
&lt;p&gt;[5] Trammell et al. (2014), Icarus, 242, https://doi.org/10.1016/j.icarus.2014.07.019.&lt;/p&gt;
&lt;p&gt;[6] Trammell et al. (2016), J. Geophys. Res. Planets, 121, https://doi.org/10.1002/2016JE005122.&lt;/p&gt;
&lt;p&gt;[7] Le Vu et al. (2018), J. Atmos. Ocean. Tech., 35, https://doi.org/10.1175/JTECH-D-17-0010.1&lt;/p&gt;