Global climate modeling of Saturn's atmosphere. Part II: Multi-annual high-resolution dynamical simulations

Highlights

• A new Global Climate Model for Saturn with radiative transfer

• High-resolution numerical simulations on a duration of 15 Saturn years

• Results on zonal jets, waves, eddies in Saturn's troposphere

Abstract

The Cassini mission unveiled the intense and diverse activity in Saturn's atmosphere: banded jets, waves, vortices, equatorial oscillations. To set the path towards a better understanding of those phenomena, we performed high-resolution multi-annual numerical simulations of Saturn's atmospheric dynamics. We built a new Global Climate Model [GCM] for Saturn, named the Saturn DYNAMICO GCM, by combining a radiative-seasonal model tailored for Saturn to a hydrodynamical solver based on an icosahedral grid suitable for massively-parallel architectures. The impact of numerical dissipation, and the conservation of angular momentum, are examined in the model before a reference simulation employing the Saturn DYNAMICO GCM with a 1/2° latitude-longitude resolution is considered for analysis. Mid-latitude banded jets showing similarity with observations are reproduced by our model. Those jets are accelerated and maintained by eddy momentum transfers to the mean flow, with the magnitude of momentum fluxes compliant with the observed values. The eddy activity is not regularly distributed with time, but appears as bursts; both barotropic and baroclinic instabilities could play a role in the eddy activity. The steady-state latitude of occurrence of jets is controlled by poleward migration during the spin-up of our model. At the equator, a weakly-superrotating tropospheric jet and vertically-stacked alternating stratospheric jets are obtained in our GCM simulations. The model produces Yanai (Rossby-gravity), Rossby and Kelvin waves at the equator, as well as extratropical Rossby waves, and large-scale vortices in polar regions. Challenges remain to reproduce Saturn's powerful superrotating jet and hexagon-shaped circumpolar jet in the troposphere, and downward-propagating equatorial oscillation in the stratosphere.

Introduction

It has been decades since Saturn's meteorological phenomena observed by Earth-based and space telescopes, and the pioneering Voyager missions, are challenging the fundamental knowledge of geophysical fluid mechanics (e.g., Ingersoll, 1990, Dowling, 1995). Yet, a mission as richly instrumented as Cassini (Porco et al., 2005), offering from 2004 to 2017 an unprecedented spatial and seasonal coverage of Saturn's weather layer, brought a new impulse to the studies of giant planets' atmospheric dynamics (e.g., review papers by Del Genio et al., 2009, Showman et al., 2018a).

In Saturn's troposphere, the Cassini measurements confirmed the banded structure of alternating westward (retrograde) and eastward (prograde) jets, which features a 450 m s⁻¹ super-rotating equatorial jet (Porco et al., 2005, García-Melendo et al., 2010, Studwell et al., 2018). Furthermore, the Cassini instruments assessed the remarkable stability of the enigmatic hexagonal jet in the northern polar region (Baines et al., 2009, Sánchez-Lavega et al., 2014, Antuñano et al., 2015, Fletcher et al., 2018), with exquisite details on the structure of the turbulent polar vortex (Sayanagi et al., 2017, Baines et al., 2018). They also offered a detailed record of mid-latitude convective storms (Dyudina et al., 2007, del Río-Gaztelurrutia et al., 2012) and vortices (Vasavada et al., 2006, Dyudina et al., 2008, Trammell et al., 2016, del Río-Gaztelurrutia et al., 2018), including a chain of infrared bright spots named the “String of Pearls” (Sayanagi et al., 2014) and an exceptional coverage of Saturn's latest Great White Spot (Fischer et al., 2011, Sánchez-Lavega et al., 2011, Sayanagi et al., 2013). Cassini observations of Saturn's cloud layer was also employed to demonstrate the high rate of conversion of energy from eddies to jets (Del Genio et al., 2007, Del Genio and Barbara, 2012), to detail the structure of vorticity (Read et al., 2009a), and to explore Jupiter's and Saturn's atmospheric energetic spectra across spatial scales (Galperin et al., 2014, Young and Read, 2017), confirming pre-Cassini theoretical studies about geostrophic turbulence and the inverse energy cascade (Sukoriansky et al., 2002). All those observations strongly suggest that large-scale tropospheric banded jets emerge from forcing by smaller-scale eddies and waves arising from hydrodynamical instabilities.

In Saturn's stratosphere, not only the Cassini instruments led to key discoveries, but the longevity of the mission permitted a seasonal monitoring of the unveiled phenomena. Cassini's highlights in atmospheric science for the stratosphere include a spectacular stratospheric warming associated with the 2010 Great White Spot (Fletcher et al., 2011b, Fletcher et al., 2012, Fouchet et al., 2016), an equatorial oscillation of temperature in Saturn's stratosphere (Fouchet et al., 2008, Guerlet et al., 2011, Li et al., 2011) with semi-annual periodicity (Orton et al., 2008, Guerlet et al., 2018), and a seasonal monitoring of the meridional distribution of Saturn's stratospheric hydrocarbons (Guerlet et al., 2009, Guerlet et al., 2010, Sinclair et al., 2013, Fletcher et al., 2015, Sylvestre et al., 2015, Guerlet et al., 2015b), hinting at a possible interhemispheric transport of chemical species. Cassini measurements even enabled to link a disruption in the downward propagation of the equatorial oscillation to the 2010 Great White Spot occurrence (Fletcher et al., 2017). Analogies can be drawn between Saturn's and the Earth's stratospheres (Dowling, 2008). Saturn's equatorial oscillation is reminiscent of Earth's Quasi-Biennal Oscillation and Semi-Annual Oscillation (Andrews et al., 1987, Baldwin et al., 2001, Lott and Guez, 2013, Guerlet et al., 2018), driven by the propagation and breaking of Rossby, Kelvin and inertio-gravity waves. The interhemispheric transport of chemical species, which may affect the hydrocarbons distribution, might be analogous to the Earth's Brewer-Dobson circulation (Butchart, 2014).

In this stimulating observational context, new modeling efforts are needed to broaden the knowledge of Saturn's atmospheric dynamics by demonstrating the mechanisms underlying the above-mentioned observed phenomena. A great deal of past modeling work focused on the processes responsible for the banded tropospheric jets. A major difficulty with a giant planet is that the depth at which the atmosphere merges with the internal dynamo region and the strength at which the atmospheric circulations couple with magnetic disturbances have remained poorly constrained by observations (Ingersoll, 1990, Liu et al., 2008) until gravity measurements were recently performed on board Juno and Cassini (Kaspi, 2013, Galanti and Kaspi, 2017, Kaspi et al., 2018, Galanti et al., 2019). Two distinct modeling approaches have been adopted to account for Saturn's tropospheric jets: “shallow-forcing” climate models [see next paragraph for references] account for processes in the weather layer (baroclinic instability, moist convective storms), while “deep-forcing” dynamo-like models (Heimpel et al., 2005, Yano et al., 2005, Kaspi et al., 2009, Heimpel and Gómez Pérez, 2011, Gastine et al., 2014, Heimpel et al., 2016, Cabanes et al., 2017) resolve convection throughout gas giants' molecular envelopes. Contrary to deep models, shallow climate models have had difficulties reproducing gas giants' equatorial super-rotating jets. This has been overcome by including either bottom drag and intrinsic heat fluxes to simulate deep interior phenomena (Lian and Showman, 2008, Schneider and Liu, 2009, Liu and Schneider, 2010), or latent heating by moist convective storms (Lian and Showman, 2010), although the simulated equatorial jets are still about twice as less strong in simulations than in observations (e.g., García-Melendo et al., 2010). The situation for off-equatorial jets is reversed, with better agreement with observations obtained by shallow models compared to deep models, although the latter can be modified to obtain more realistic results (Heimpel et al., 2005). The recent results from the Juno mission for Jupiter (Kaspi et al., 2018, Guillot et al., 2018) and the Cassini mission for Saturn (Galanti et al., 2019) show that banded jets extend several thousand kilometers below the cloud layer, i.e. deeper than what shallow models consider and shallower than what deep models consider, which probably indicates that shallow and deep models have both their virtues to represent part of the reality.

Here, we adopt the approach of “shallow-forcing” climate modeling to study Saturn. In the last decade, the traditional approach using idealized modeling (Cho and Polvani, 1996, Williams, 2003, Vasavada and Showman, 2005) – which still has great value to study how baroclinic and barotropic instabilities shape Saturn's jets (Li et al., 2006, Kaspi and Flierl, 2007, Showman, 2007), including its polar hexagonal jet (Rostami et al., 2017) and central vortex (O’Neill et al., 2015) – has been complemented by the development of complete three-dimensional Global Climate Models (GCMs) for Saturn and giant planets (Dowling et al., 2006, Dowling et al., 1998, Lian and Showman, 2010, Liu and Schneider, 2010, Young et al., 2019a, Young et al., 2019b). A GCM is obtained by coupling a hydrodynamical solver of the Navier-Stokes equations for the atmospheric fluid on the sphere (the GCM's “dynamical core”) with realistic models for physical processes operating at unresolved scales: radiation, turbulent mixing, phase changes, chemistry (the GCM's “physical packages”). Most of those existing GCM studies for Saturn address the formation of tropospheric jets by angular momentum transfer through eddies and waves, often with either a theoretical approach aiming to address giant planets' atmospheric dynamics (Schneider and Liu, 2009, Lian and Showman, 2010, Liu and Schneider, 2010, Liu and Schneider, 2015) rather than a focused approach aiming to address Saturn specifically, or with a limited-domain approach using a latitudinal channel enclosing one specific jet to explain structures such as the Ribbon wave or the String of Pearls (Sayanagi et al., 2014, Sayanagi et al., 2010), to investigate the impact of convective outbursts (Sayanagi and Showman, 2007, García-Melendo et al., 2013), or to discuss the polar hexagonal jet (Morales-Juberías et al., 2011, Morales-Juberías et al., 2015). The idealized GCM approach can also be employed to study equatorial oscillations in gas giants (Showman et al., 2018b). All those existing studies use simple radiative forcing rather than computing a realistic “physical package” that includes seasonally-varying radiative transfer. The latter approach has been explored to study Saturn's stratosphere, either to constrain large-scale advection / eddy mixing in photochemical models (Friedson and Moses, 2012), or to build a modeling framework applicable to extrasolar hot gas giants (Medvedev et al., 2013). Those studies of Saturn's stratosphere make use, however, of prescribed, ad hoc, tropospheric jets.

The existing body of work on “shallow-forcing” modeling has thus paved the path towards a complete three-dimensional Global Climate Model (GCM) for giant planets. However, such a complete troposphere-to-stratosphere GCM for Saturn, capable to address the theoretical challenges opened by observations is yet to emerge. We propose that four challenges shall be overcome to develop a complete state-of-the-art GCM for Saturn and gas giants.

• The radiative transfer computations necessary to predict the evolution of atmospheric temperature, especially in the stratosphere, must be optimized for integration over decade-long giant planets' years, while still keeping robustness against observations.

• Large-scale jets and vortices emerge from smaller-scale hydrodynamical eddies, through an inverse energy cascade driven by geostrophic turbulence. Relevant interaction scales (e.g. Rossby deformation radius) are only 1° latitude-longitude in gas giants vs. 20° on the Earth, making eddy-resolving global simulations over a full year four orders of magnitude more computationally expensive in gas giants.

• Terrestrial experience shows that models need to extend from the troposphere to the stratosphere with sufficient vertical resolution to resolve the vertical propagation of waves responsible for large-scale structures in both parts of the atmosphere. Moreover, a specific requirement of giant planets is to extend the model high enough in the stratosphere to model the photochemistry of key hydrocarbons impacting stratospheric temperatures (Hue et al., 2016).

• Climate models cannot extend neither deep enough to predict how tropospheric jets interact with interior convective fluxes and planetary magnetic field (Kaspi et al., 2009, Heimpel and Gómez Pérez, 2011), nor high enough to capture the coupling of stratospheric circulations with thermospheric and ionospheric processes (Müller-Wodarg et al., 2012, Koskinen et al., 2015). A suitable approach to couple the weather layer with either the slowly-evolving convective interior, or the rapidly-evolving ionized external layers, remains elusive.

Here, we report the development and preliminary dynamical simulations of a new Saturn GCM at Laboratoire de Météorologie Dynamique (LMD), which aims at understanding the seasonal variability, large-scale circulations, and eddy & wave activity in Saturn's troposphere and stratosphere. It is a first step to further design a modeling platform dedicated to atmospheric circulations of Saturn and other solar system's giant planets. Challenge ${\mathcal{C}}_1$ about building fast and accurate radiative transfer for the Saturn GCM is addressed in Guerlet et al. (2014). In Guerlet et al. (2014), which serves as Part I for the present study, a seasonal radiative–convective model of Saturn's upper troposphere and stratosphere is described and the sensitivity to composition, aerosols, internal heat flux and ring shadowing is assessed, with comparisons to the observed thermal structure by Cassini and ground-based telescopes. In this Part II paper, we address Challenge ${\mathcal{C}}_2$ by performing high-resolution dynamical simulations with our Saturn GCM. Our GCM is built by coupling the physical packages (notably, radiative transfer) of Guerlet et al. (2014) with DYNAMICO, a new dynamical core developed at LMD which uses an original icosahedral mapping of the planetary sphere to ensure excellent conservation and scalability properties in massively parallel resources (Dubos et al., 2015). We describe here the insights gained from GCM simulations at high horizontal resolutions (reference at 1/2° latitude/longitude, and tests at 1/4° and 1/8°) with two unprecedented characteristics at those horizontal resolutions: inclusion of realistic radiative transfer and long integration times up to fifteen simulated Saturn years.

The paper is organized as follows. Notations are defined in Table 1. In Section 2, we provide details on the characteristics of our Saturn DYNAMICO GCM, and the assumptions and settings adopted for the simulations discussed in subsequent sections, with Appendix A featuring a necessary analysis of the impact of horizontal dissipation and the conservation of angular momentum in our Saturn GCM. In Section 3, we describe the results obtained with our reference 15-year-long 1/2° Saturn DYNAMICO GCM simulation, with an emphasis on the driving and evolution of jets in Section 4. In Section 5, we summarize our conclusions and draw perspectives for future improvements of our Saturn DYNAMICO GCM needed to fully achieve challenges ${\mathcal{C}}_2$, ${\mathcal{C}}_3$ and ${\mathcal{C}}_4$, as it comes to no surprise that the present study is only a preliminary path towards fulfilling arguably ambitious scientific goals.