arXiv subjects

Jonathan L. Mitchell

Publications and source records attributed to Jonathan L. Mitchell.

14 recordsLinked to original sources

arXiv2023

A simple model for the emergence of relaxation-oscillator convection

Earth's tropics are characterized by quasi-steady precipitation with small oscillations about a mean value, which has led to the hypothesis that moist convection is in a state of quasi-equilibrium (QE). In contrast, very warm simulations of Earth's tropical convection are characterized by relaxation-oscillator-like (RO) precipitation, with short-lived convective storms and torrential rainfall forming and dissipating at regular intervals with little to no precipitation in between. We develop a model of moist convection by combining a zero-buoyancy model of bulk-plume convection with a QE heat engine model, and we use it to show that QE is violated at high surface temperatures. We hypothesize that the RO state emerges when the equilibrium condition of the convective heat engine is violated, i.e., when the heating rate times a thermodynamic efficiency exceeds the rate at which work can be performed. We test our hypothesis against one- and three-dimensional numerical simulations and find that it accurately predicts the onset of RO convection. The proposed mechanism for RO emergence from QE breakdown is agnostic of the condensable, and can be applied to any planetary atmosphere undergoing moist convection. To date, RO states have only been demonstrated in three-dimensional convection-resolving simulations, which has made it seem that the physics of the RO state requires simulations that can explicitly resolve the three-dimensional interaction of cloudy plumes and their environment. We demonstrate that RO states also exist in single-column simulations of radiative-convective equilibrium with parameterized convection, albeit in a different surface temperature range and with much longer storm-free intervals.

astro-ph.EP↗

arXiv2021

Toward a unified theory for the Hadley cell descending and ascending edges

We present theories for the latitudinal extents of both Hadley cells throughout the annual cycle by combining our recent scaling for the ascending edge latitude (Hill et al. 2021) with the uniform Rossby number (Ro), baroclinic instability-based theory for the poleward, descending edge latitudes of Kang and Lu 2012. The resulting analytic expressions for all three Hadley cell edges are predictive except for diagnosed values of Ro and two proportionality constants. The theory captures the climatological annual cycle of the ascending and descending edges in an Earth-like simulation in an idealized aquaplanet general circulation model (GCM), provided the descending edge prediction is lagged by one month. In simulations in this and two other idealized GCMs with varied planetary rotation rate ($\Omega$), the winter, descending edge of the solsticial, cross-equatorial Hadley cell scales approximately as $\Omega^{-1/2}$ and the summer, ascending edge as $\Omega^{-2/3}$, both in accordance with our theory.

physics.ao-ph↗

arXiv2020

Constraints from invariant subtropical vertical velocities on the scalings of Hadley cell strength and downdraft width with rotation rate

Weak-temperature-gradient influences from the tropics and quasigeostrophic influences from the extratropics plausibly constrain the subtropical-mean static stability in terrestrial atmospheres. Because mean descent acting on this static stability is a leading-order term in the thermodynamic balance, a state-invariant static stability would impose constraints on the Hadley cells, which this paper explores in simulations of varying planetary rotation rate. If downdraft-averaged effective heating (the sum of diabatic heating and eddy heat flux convergence) too is invariant, so must be vertical velocity -- an "omega governor." In that case, the Hadley circulation overturning strength and downdraft width must scale identically -- the cell can strengthen only by widening or weaken only by narrowing. Simulations in two idealized, dry GCMs with a wide range of planetary rotation rates exhibit nearly unchanging downdraft-averaged static stability, effective heating, and vertical velocity, as well as nearly identical scalings of the Hadley cell downdraft width and strength. In one, eddy stresses set this scaling directly (the Rossby number remains small); in the other, eddy stress and bulk Rossby number changes compensate to yield the same, ({\sim}Ω^{-1/3}) scaling. The consistency of this power law for cell width and strength variations may indicate a common driver, and we speculate that Ekman pumping could be the mechanism responsible for this behavior. Extending to moist atmospheres, in an idealized aquaplanet GCM the subtropical static stability is also insensitive to rotation rate but the effective heating and vertical velocity are not.

physics.ao-ph↗

arXiv2020

Solsticial Hadley Cell ascending edge theory from supercriticality

How far the Hadley circulation's ascending branch extends into the summer hemisphere is a fundamental but incompletely understood characteristic of Earth's climate. Here, we present a predictive, analytical theory for this ascending edge latitude based on the extent of supercritical forcing. Supercriticality sets the minimum extent of a large-scale circulation based on the angular momentum and absolute vorticity distributions of the hypothetical state were the circulation absent. We explicitly simulate this latitude-by-latitude radiative-convective equilibrium (RCE) state. Its depth-averaged temperature profile is suitably captured by a simple analytical approximation that increases linearly with $\sin\varphi$, where $\varphi$ is latitude, from the winter to the summer pole. This, in turn, yields a one-third power-law scaling of the supercritical forcing extent with the thermal Rossby number. In moist and dry idealized GCM simulations under solsticial forcing performed with a wide range of planetary rotation rates, the ascending edge latitudes largely behave according to this scaling.

physics.ao-ph↗

arXiv2019

Axisymmetric constraints on cross-equatorial Hadley cell extent

We consider the relevance of known constraints from each of Hide's theorem, the angular momentum conserving (AMC) model, and the equal-area model on the extent of cross-equatorial Hadley cells. These theories respectively posit that a Hadley circulation must span: all latitudes where the radiative convective equilibrium (RCE) absolute angular momentum ($M_\mathrm{rce}$) satisfies $M_\mathrm{rce}>Ωa^2$ or $M_\mathrm{rce}<0$ or where the RCE absolute vorticity ($η_\mathrm{rce}$) satisfies $fη_\mathrm{rce}<0$; all latitudes where the RCE zonal wind exceeds the AMC zonal wind; and over a range such that depth-averaged potential temperature is continuous and that energy is conserved. The AMC model requires knowledge of the ascent latitude $φ_\mathrm{a}$, which need not equal the RCE forcing maximum latitude $φ_\mathrm{m}$. Whatever the value of $φ_\mathrm{a}$, we demonstrate that an AMC cell must extend at least as far into the winter hemisphere as the summer hemisphere. The equal-area model predicts $φ_\mathrm{a}$, always placing it poleward of $φ_\mathrm{m}$. As $φ_\mathrm{m}$ is moved poleward (at a given thermal Rossby number), the equal-area predicted Hadley circulation becomes implausibly large, while both $φ_\mathrm{m}$ and $φ_\mathrm{a}$ become increasingly displaced poleward of the minimal cell extent based on Hide's theorem (i.e. of supercritical forcing). In an idealized dry general circulation model, cross-equatorial Hadley cells are generated, some spanning nearly pole-to-pole. All homogenize angular momentum imperfectly, are roughly symmetric in extent about the equator, and appear in extent controlled by the span of supercritical forcing.

physics.ao-ph↗

arXiv2019

Simulating Venus' Cloud Level Dynamics Using a Middle Atmosphere General Circulation Model

The atmosphere of Venus is characterized by strong superrotation, in which the wind velocities at cloud heights are around 60 times faster than the surface rotation rate. The reasons for this strong superrotation are still not well understood. Motions in the atmosphere below the thick cloud deck are hard to determine remotely and in-situ measurements of the circulation below 40 km altitude are scarce. No model to date has been able to simulate superrotating winds with magnitudes comparable with those measured by entry probes, in the dense atmosphere between the surface and the clouds. However, important information on the dynamics and circulation of Venus' atmosphere can be determined by studying the atmosphere at cloud levels, where there are significantly more measurements than in the sub-cloud region, including the many recent observations made during the Venus Express and Akatsuki missions. In this work we describe a new Venus Middle atmosphere general circulation Model (VMM) to study the dynamics of the atmosphere at cloud altitudes. The model simulates the atmosphere from just below cloud deck to around 95 km altitude. We present simulations using the VMM with a simplified Newtonian cooling radiation scheme. Sensitivity studies have been performed to determine the most appropriate values for model parameters and the model has been validated by comparison with observations, including those from Venus Express and Akatsuki. The validated model provides some constraints on parameters which are poorly measured close to the boundary such as the mean winds and temperatures, and provides a basis for further investigations of the dynamics of Venus' cloud-level atmosphere. In future studies we will also investigate the influence of atmospheric waves, such as Kelvin and Rossby waves, to determine the role they play in generating the poorly-understood cloud-level structure at all latitudes.

astro-ph.EP↗

arXiv2016

Search for methane isotope fractionation due to Rayleigh distillation on Titan

We search for meridional variation in the abundance of CH$_3$D relative to CH$_4$ on Titan using near-IR spectra obtained with NIRSPAO at Keck, which have a photon-limited signal-to-noise ratio of $\sim$50. Our observations can rule out a larger than 10% variation in the column of CH$_3$D below 50 km. The preferential condensation of the heavy isotopologues will fractionate methane by reducing CH$_3$D in the remaining vapor, and therefore these observations place limits on the amount of condensation that occurs in the troposphere. While previous estimates of CH$_3$D fractionation on Titan have estimated an upper limit of -6 per mil, assuming a solid condensate, we consider more recent laboratory data for the equilibrium fractionation over liquid methane, and use a Rayleigh distillation model to calculate fractionation in an ascending parcel of air that is following a moist adiabat. We find that deep, precipitating convection can enhance the fractionation of the remaining methane vapor by -10 to -40 per mil, depending on the final temperature of the rising parcel. By relating fractionation of our reference parcel model to the pressure level where the moist adiabat achieves the required temperature, we argue that the measured methane fractionation constrains the outflow level for a deep convective event. Observations with a factor of at least 4 to 6 times larger signal-to-noise are required to detect this amount of fractionation, depending on the altitude range over which the outflow from deep convection occurs.

astro-ph.EP↗

arXiv2015

Meridional variation in tropospheric methane on Titan observed with AO spectroscopy at Keck and VLT

The spatial distribution of the tropospheric methane on Titan was measured using near-infrared spectroscopy. Ground-based observations at 1.5$μ{\rm m}$ (H-band) were performed during the same night using instruments with adaptive optics at both the W. M. Keck Observatory and at the Paranal Observatory on 17 July 2014 UT. The integral field observations with SINFONI on the VLT covered the entire H-band at moderate resolving power, $R=λ/Δλ\approx1,500$, while the Keck observations were performed with NIRSPAO near 1.55254$μ{\rm m}$ at higher resolution, $R\approx25,000$. The moderate resolution observations are used for flux calibration and for the determination of model parameters that can be degenerate in the interpretation of high resolution spectra. Line-by-line calculations of CH$_4$ and CH$_3$D correlated $k$ distributions from the HITRAN 2012 database were used, which incorporate revised line assignments near 1.5$μ{\rm m}$. We fit the surface albedo and aerosol distributions in the VLT SINFONI observations that cover the entire H-band window and used these quantities to constrain the models of the high-resolution Keck NIRSPAO spectra when retrieving the methane abundances. Cassini VIMS images of the polar regions, acquired on 20 July 2014 UT, are used to validate the assumption that the opacity of tropospheric aerosol is relatively uniform below 10 km. We retrieved methane abundances at latitudes between 42$^{\circ}$ S and 80$^{\circ}$ N. The tropospheric methane in the Southern mid-latitudes was enhanced by a factor of $\sim$10--40% over the nominal profile that was measured using the GCMS on Huygens. The Northern hemisphere had $\sim$90% of the nominal methane abundance up to polar latitudes (80$^{\circ}$N). These measurements suggest that a source of saturated polar air is equilibrating with dryer conditions at lower latitudes.

astro-ph.EP↗

arXiv2012

Titan's transport-driven methane cycle

The strength of Titan's methane cycle, as measured by precipitation and evaporation, is key to interpreting fluvial erosion and other indicators of the surface-atmosphere exchange of liquids. But the mechanisms behind the occurrence of large cloud outbursts and precipitation on Titan have been disputed. A gobal- and annual-mean estimate of surface fluxes indicated only 1% of the insolation, or $\sim$0.04 W/m$^2$, is exchanged as sensible and/or latent fluxes. Since these fluxes are responsible for driving atmospheric convection, it has been argued that moist convection should be quite rare and precipitation even rarer, even if evaporation globally dominates the surface-atmosphere energy exchange. In contrast, climate simulations that allow atmospheric motion indicate a robust methane cycle with substantial cloud formation and/or precipitation. We argue the top-of-atmosphere radiative imbalance -- a readily observable quantity -- is diagnostic of horizontal heat transport by Titan's atmosphere, and thus constrains the strength of the methane cycle. Simple calculations show the top-of-atmosphere radiative imbalance is $\sim$0.5-1 W/m$^2$ in Titan's equatorial region, which implies 2-3 MW of latitudinal heat transport by the atmosphere. Our simulation of Titan's climate suggests this transport may occur primarily as latent heat, with net evaporation at the equator and net accumulation at higher latitudes. Thus the methane cycle could be 10-20 times previous estimates. Opposing seasonal transport at solstices, compensation by sensible heat transport, and focusing of precipitation by large-scale dynamics could further enhance the local, instantaneous strength of Titan's methane cycle by a factor of several.

astro-ph.EP↗

arXiv2010

The Transition to Superrotation in Terrestrial Atmospheres

We show that by changing a single non-dimensional number, the thermal Rossby number, global atmospheric simulations with only axisymmetric forcing pass from an Earth-like atmosphere to a superrotating atmosphere that more resembles the atmospheres of Venus or Titan. The transition to superrotation occurs under conditions in which equatorward-propagating Rossby waves generated by baroclinic instability at intermediate and high latitudes are suppressed, which will occur when the deformation radius exceeds the planetary radius. At large thermal Rossby numbers following an initial, nearly axisymmetric phase, a global baroclinic wave of zonal wavenumber one generated by mixed barotropic-baroclinic instability dominates the eddy flux of zonal momentum. The global wave converges eastward zonal momentum to the equator and deposits westward momentum at intermediate latitudes during spinup and before superrotation emerges, and the baroclinic instability ceases once superrotation is established. A global barotropic mode of zonal wavenumber one generated by a mix of high- and low-latitude barotropic instability is responsible for maintaining superrotation in the statistically steady state. At intermediate thermal Rossby numbers, momentum flux by the global baroclinic mode is subdominant relative to smaller baroclinic modes, and thus strong superrotation does not develop.

astro-ph.EP↗

arXiv2010

The Mechanical Greenhouse: Burial of Heat by Turbulence in Hot Jupiter Atmospheres

The intense irradiation received by hot Jupiters suppresses convection in the outer layers of their atmospheres and lowers their cooling rates. "Inflated" hot Jupiters, i.e., those with anomalously large transit radii, require additional sources of heat or suppressed cooling. We consider the effect of forced turbulent mixing in the radiative layer, which could be driven by atmospheric circulation or by another mechanism. Due to stable stratification in the atmosphere, forced turbulence drives a downward flux of heat. Weak turbulent mixing slows the cooling rate by this process, as if the planet was irradiated more intensely. Stronger turbulent mixing buries heat into the convective interior, provided the turbulence extends to the radiative-convective boundary. This inflates the planet until a balance is reached between the heat buried into and radiated from the interior. We also include the direct injection of heat due to the dissipation of turbulence or other effects. Such heating is already known to slow planetary cooling. We find that dissipation also enhances heat burial from mixing by lowering the threshold for turbulent mixing to drive heat into the interior. Strong turbulent mixing of heavy molecular species such as TiO may be necessary to explain stratospheric thermal inversions. We show that the amount of mixing required to loft TiO may overinflate the planet by our mechanism. This possible refutation of the TiO hypothesis deserves further study. Our inflation mechanism requires a deep stratified layer that only exists when the absorbed stellar flux greatly exceeds the intrinsic emitted flux. Thus it would be less effective for more luminous brown dwarfs and for longer period gas giants, including Jupiter and Saturn.

astro-ph.EP↗

arXiv2010

Generalized Milankovitch Cycles and Longterm Climatic Habitability

Although the Earth's orbit is never far from circular, terrestrial planets around other stars might experience substantial changes in eccentricity that could lead to climate changes, including possible "phase transitions" such as the snowball transition (or its opposite). There is evidence that Earth has gone through at least one globally frozen, "snowball" state in the last billion years, which it is thought to have exited after several million years because global ice-cover shut off the carbonate-silicate cycle, thereby allowing greenhouse gases to build up to sufficient concentration to melt the ice. Due to the positive feedback caused by the high albedo of snow and ice, susceptibility to falling into snowball states might be a generic feature of water-rich planets with the capacity to host life. This paper has two main thrusts. First, we revisit one-dimensional energy balance climate models as tools for probing possible climates of exoplanets, investigate the dimensional scaling of such models, and introduce a simple algorithm to treat the melting of the ice layer on a globally-frozen planet. We show that if a terrestrial planet undergoes Milankovitch-like oscillations of eccentricity that are of great enough magnitude, it could melt out of a snowball state. Second, we examine the kinds of variations of eccentricity that a terrestrial planet might experience due to the gravitational influence of a giant companion. We show that a giant planet on a sufficiently eccentric orbit can excite extreme eccentricity oscillations in the orbit of a habitable terrestrial planet. More generally, these two results demonstrate that the longterm habitability (and astronomical observables) of a terrestrial planet can depend on the detailed architecture of the planetary system in which it resides.

astro-ph.EP↗

arXiv2010

Elastic ice shells of synchronous moons: Implications for cracks on Europa and non-synchronous rotation of Titan

A number of synchronous moons are thought to harbor water oceans beneath their outer ice shells. A subsurface ocean frictionally decouples the shell from the interior. This has led to proposals that a weak tidal or atmospheric torque might cause the shell to rotate differentially with respect to the synchronously rotating interior. As a result of centrifugal and tidal forces, the ocean would assume an ellipsoidal shape with its long axis aligned toward the parent planet. Any displacement of the shell away from its equilibrium position would induce strains thereby increasing its elastic energy and giving rise to an elastic restoring torque. We compare the elastic torque with the tidal torque acting on Europa and the atmospheric torque acting on Titan. For Europa, the tidal torque is far too weak to produce stresses that could fracture the ice shell, thus refuting a widely advocated idea. Instead, we suggest that cracks arise from time-dependent stresses due to non-hydrostatic gravity anomalies from tidally driven, episodic convection in the interior. Two years of Cassini RADAR observations of Titan's surface are interpreted as implying an angular displacement of ~0.24 degrees relative to synchroneity. Compatibility of the amplitude and phase of the observed non-synchronous rotation with estimates of the atmospheric torque requires that Titan's shell be decoupled from its interior. We find that the elastic torque balances the atmospheric torque at an angular displacement <0.05 degrees, thus coupling the shell to the interior. Moreover, if Titan's surface were spinning faster than synchronous, the tidal torque tending to restore synchronous rotation would certainly be larger than the atmospheric torque. There must either be a problem with the interpretation of the radar observations, or with our understanding of Titan's atmosphere and/or interior.

astro-ph.EP↗

arXiv2009

Coupling convectively driven atmospheric circulation to surface rotation: Evidence for active methane weather in the observed spin rate drift of Titan

A large drift in the rotation rate of Titan observed by Cassini provided the first evidence of a subsurface ocean isolating the massive core from the icy crust. Seasonal exchange of angular momentum between the surface and atmosphere accounts for the magnitude of the effect, but observations lag the expected signal by a few years. We argue that this time lag is due to the presence of an active methane weather cycle in the atmosphere. An analytic model of the seasonal cycle of atmospheric angular momentum is developed and compared with time-dependent simulations of Titan's atmosphere with and without methane thermodynamics. The disappearance of clouds at the summer pole suggests the drift rate has already switched direction, signaling the change in season from solstice to equinox.

astro-ph↗