arXiv subjects

Raymond T. Pierrehumbert

Publications and source records attributed to Raymond T. Pierrehumbert.

33 records · Page 2Linked to original sources

arXiv2021

Simulating gas giant exoplanet atmospheres with Exo-FMS: Comparing semi-grey, picket fence and correlated-k radiative-transfer schemes

Radiative-transfer (RT) is a fundamental part of modelling exoplanet atmospheres with general circulation models (GCMs). An accurate RT scheme is required for estimates of the atmospheric energy transport and for gaining physical insight from model spectra. We implement three RT schemes for Exo-FMS: semi-grey, non-grey `picket fence', and real gas with correlated-k. We benchmark the Exo-FMS GCM using these RT schemes to hot Jupiter simulation results from the literature. We perform a HD 209458b-like simulation with the three schemes and compare their results. These simulations are then post-processed to compare their observable differences. The semi-grey scheme results show qualitative agreement with previous studies in line with variations seen between GCM models. The real gas model reproduces well the temperature and dynamical structures from other studies. After post-processing our non-grey picket fence scheme compares very favourably with the real gas model, producing similar transmission spectra, emission spectra and phase curve behaviours. Exo-FMS is able to reliably reproduce the essential features of contemporary GCM models in the hot gas giant regime. Our results suggest the picket fence approach offers a simple way to improve upon RT realism beyond semi-grey schemes.

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arXiv2021

Vertically resolved magma ocean-protoatmosphere evolution: H$_2$, H$_2$O, CO$_2$, CH$_4$, CO, O$_2$, and N$_2$ as primary absorbers

The earliest atmospheres of rocky planets originate from extensive volatile release during magma ocean epochs that occur during assembly of the planet. These establish the initial distribution of the major volatile elements between different chemical reservoirs that subsequently evolve via geological cycles. Current theoretical techniques are limited in exploring the anticipated range of compositional and thermal scenarios of early planetary evolution, even though these are of prime importance to aid astronomical inferences on the environmental context and geological history of extrasolar planets. Here, we present a coupled numerical framework that links an evolutionary, vertically-resolved model of the planetary silicate mantle with a radiative-convective model of the atmosphere. Using this method we investigate the early evolution of idealized Earth-sized rocky planets with end-member, clear-sky atmospheres dominated by either H$_2$, H$_2$O, CO$_2$, CH$_4$, CO, O$_2$, or N$_2$. We find central metrics of early planetary evolution, such as energy gradient, sequence of mantle solidification, surface pressure, or vertical stratification of the atmosphere, to be intimately controlled by the dominant volatile and outgassing history of the planet. Thermal sequences fall into three general classes with increasing cooling timescale: CO, N$_2$, and O$_2$ with minimal effect, H$_2$O, CO$_2$, and CH$_4$ with intermediate influence, and H$_2$ with several orders of magnitude increase in solidification time and atmosphere vertical stratification. Our numerical experiments exemplify the capabilities of the presented modeling framework and link the interior and atmospheric evolution of rocky exoplanets with multi-wavelength astronomical observations.

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arXiv2020

The Phase-curve Signature of Condensible Water-rich Atmospheres on Slowly Rotating Tidally Locked Exoplanets

We use an idealized three-dimensional general circulation model to study condensible-rich atmospheres with an ineffective cold trap on slowly rotating tidally locked terrestrial planets. In particular, we show the climate dynamics in a thin and temperate atmosphere with condensible water vapor. The similarities between our thin and temperate atmosphere and the warm and thick atmosphere approaching the water vapor runaway greenhouse in previous works are discussed, including the reversal of the thermal emission between the day and night hemispheres. Different from the transit spectroscopy of water vapor that depends on the absolute amount of atmospheric water vapor, the contrast between the dayside and nightside thermal emission provides information regarding the relative ratio of water vapor to the background atmosphere as well as the atmospheric pressure near the substellar tropopause and the emission level on the nightside on potentially habitable worlds.

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arXiv2020

The Equatorial Jet Speed on Tidally Locked Planets: I -- Terrestrial Planets

The atmospheric circulation of tidally locked planets is dominated by a superrotating eastward equatorial jet. We develop a predictive theory for the formation of this jet, proposing a mechanism in which the three-dimensional stationary waves induced by the day-night forcing gradient produce an equatorial acceleration. This is balanced in equilibrium by an interaction between the resulting jet and the vertical motion of the atmosphere. The three-dimensional structure of the zonal acceleration is vital to this mechanism. We demonstrate this mechanism in a hierarchy of models. We calculate the three-dimensional stationary waves induced by the forcing on these planets, and show the vertical structure of the zonal acceleration produced by these waves, which we use to suggest a mechanism for how the jet forms. GCM simulations are used to confirm the equilibrium state predicted by this mechanism, where the acceleration from these waves is balanced by an interaction between the zonal-mean vertical velocity and the jet. We derive a simple model of this using the "Weak Temperature Gradient" approximation, which gives an estimate of the jet speed on a terrestrial tidally locked planet. We conclude that the proposed mechanism is a good description of the formation of an equatorial jet on a terrestrial tidally locked planet, and should be useful for interpreting observations and simulations of these planets. The mechanism requires assumptions such as a large equatorial Rossby radius and weak acceleration due to transient waves, and a different mechanism may produce the equatorial jets on gaseous tidally locked planets.

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arXiv2020

Simplified 3D GCM modelling of the irradiated brown dwarf WD0137-349B

Context: White dwarf - Brown dwarf short period binaries (P$_{\rm orb}$ $\lesssim$ 2 hours) are some of the most extreme irradiated atmospheric environments known. These systems offer an opportunity to explore theoretical and modelling efforts of irradiated atmospheres different to typical hot Jupiter systems. Aims: We aim to investigate the three dimensional atmospheric structural and dynamical properties of the Brown dwarf WD0137-349B. Methods: We use the three dimensional GCM model Exo-FMS, with a dual-band grey radiative-transfer scheme to model the atmosphere of WD0137-349B. The results of the GCM model are post-processed using the three dimensional Monte Carlo radiative-transfer model \textsc{cmcrt}. Results: Our results suggest inefficient day-night energy transport and a large day-night temperature contrast for WD0137-349B. Multiple flow patterns are present, shifting energy asymmetrically eastward or westward depending on their zonal direction and latitude. Regions of overturning are produced on the western terminator. We are able to reproduce the start of the system near-IR emission excess at $\gtrsim$ 1.95 $μ$m as observed by the GNIRS instrument. Our model over predicts the IR phase curve fluxes by factors of $\approx$1-3, but generally fits the shape of the phase curves well. Chemical kinetic modelling using \textsc{vulcan} suggests a highly ionised region at high altitudes can form on the dayside of the Brown dwarf. Conclusions: We present a first attempt at simulating the atmosphere of a short period White dwarf - Brown dwarf binary in a 3D setting. Further studies into the radiative and photochemical heating from the UV irradiation is required to more accurately capture the energy balance inside the Brown dwarf atmosphere. Cloud formation may also play an important role in shaping the emission spectra of the Brown dwarf.

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arXiv2018

Wave-Mean Flow Interactions in the Atmospheric Circulation of Tidally Locked Planets

We use a linear shallow-water model to investigate the global circulation of the atmospheres of tidally locked planets. Simulations, observations, and simple models show that if these planets are sufficiently rapidly rotating, their atmospheres have an eastward equatorial jet and a hot-spot east of the substellar point. We linearize the shallow-water model about this eastward flow and its associated height perturbation. The forced solutions of this system show that the shear flow explains the form of the global circulation, particularly the hot-spot shift and the positions of the cold standing waves on the night-side. We suggest that the eastward hot-spot shift seen in observations and 3D simulations of these atmospheres is caused by the zonal flow Doppler-shifting the stationary wave response eastwards, summed with the height perturbation from the flow itself. This differs from other studies which explained the hot-spot shift as pure advection of heat from air flowing eastward from the substellar point, or as equatorial waves travelling eastwards. We compare our solutions to simulations in our climate model Exo-FMS, and show that the height fields and wind patterns match. We discuss how planetary properties affect the global circulation, and how they change observables such as the hot-spot shift or day-night contrast. We conclude that the wave-mean flow interaction between the stationary planetary waves and the equatorial jet is a vital part of the equilibrium circulation on tidally locked planets.

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arXiv2018

Global or Local Pure-Condensible Atmospheres: Importance of Horizontal Latent Heat Transport

The distribution of a pure condensible planetary atmosphere in equilibrium with a surface reservoir is revisited employing the energy budget of the climate system, emphasizing the atmospheric horizontal latent heat transport. This configuration is applicable to icy Solar System bodies such as Triton as well as a range of possible exoplanet atmospheres, including water or $\mathrm{CO_2}$ iceballs or ocean worlds, and lava planets with mineral vapor atmospheres. Climate regimes for slowly rotating planets with the hot-spot near the substellar point, and for rapidly rotating planets with a warm equatorial belt, are both treated. A non-dimensional parameter controlling the fractional variation of the surface pressure is derived; it measures whether the pure condensible atmosphere is global or localized. The global pure condensible atmosphere with the non-dimensional parameter much less than order of unity is maintained by the strong horizontal latent heat transport associated with an "evaporation/sublimation-driven flow" from warm to cold places that compensates for the incoming differential radiative forcing. We show that the variation of surface temperature can be estimated in terms of this non-dimensional parameter if it is not too large. In the case of a pure water-vapor atmosphere with an ice or liquid surface, we show that the atmosphere is thick enough to maintain nearly isothermal surface conditions even when the substellar surface temperature is around the freezing point. Finally, it is proposed that the evaporation/sublimation-driven flow regime for global atmospheres could be detected via its effect on the inhomogeneous distribution of minor non-condensible components in the atmosphere.

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arXiv2018

Exploring the Atmosphere of Neoproterozoic Earth: The Effect of O$_{2}$ on Haze Formation and Composition

Previous studies of haze formation in the atmosphere of the Early Earth have focused on N$_{2}$/CO$_{2}$/CH$_{4}$ atmospheres. Here, we experimentally investigate the effect of O$_{2}$ on the formation and composition of aerosols to improve our understanding of haze formation on the Neoproterozoic Earth. We obtained in situ size, particle density, and composition measurements of aerosol particles produced from N$_{2}$/CO$_{2}$/CH$_{4}$/O$_{2}$ gas mixtures subjected to FUV radiation (115-400 nm) for a range of initial CO$_{2}$/CH$_{4}$/O$_{2}$ mixing ratios (O$_{2}$ ranging from 2 ppm to 0.2\%). At the lowest O$_{2}$ concentration (2 ppm), the addition increased particle production for all but one gas mixture. At higher oxygen concentrations (20 ppm and greater) particles are still produced, but the addition of O$_{2}$ decreases the production rate. Both the particle size and number density decrease with increasing O$_{2}$, indicating that O$_{2}$ affects particle nucleation and growth. The particle density increases with increasing O$_{2}$. The addition of CO$_{2}$ and O$_{2}$ not only increases the amount of oxygen in the aerosol, but it also increases the degree of nitrogen incorporation. In particular, the addition of O$_{2}$ results in the formation of nitrate bearing molecules. The fact that the presence of oxygen bearing molecules increases the efficiency of nitrogen fixation has implications for the role of haze as a source of molecules required for the origin and evolution of life. The composition changes also likely affect the absorption and scattering behavior of these particles but optical properties measurements are required to fully understand the implications for the effect on the planetary radiative energy balance and climate.

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arXiv2016

Dynamics of atmospheres with a non-dilute condensible component

The diversity of characteristics for the host of recently discovered exoplanets opens up a great deal of fertile new territory for geophysical fluid dynamics, particularly when the fluid flow is coupled to novel thermodynamics, radiative transfer or chemistry. In this paper, we survey one of these new areas-the climate dynamics of atmospheres with a non-dilute condensible component, defined as the situation in which a condensible component of the atmosphere makes up a substantial fraction of the atmospheric mass within some layer. Non-dilute dynamics can occur for a wide range of condensibles, generically applying near both the inner and the outer edges of the conventional habitable zone and in connection with runaway greenhouse phenomena. It also applies in a wide variety of other planetary circumstances. We first present a number of analytical results developing some key features of non-dilute atmospheres, and then show how some of these features are manifest in simulations with a general circulation model adapted to handle non-dilute atmospheres. We find that non-dilute atmospheres have weak horizontal temperature gradients even for rapidly rotating planets, and that their circulations are largely barotropic. The relative humidity of the condensible component tends towards 100% as the atmosphere becomes more non-dilute, which has important implications for runaway greenhouse thresholds. Non-dilute atmospheres exhibit a number of interesting organized convection features, for which there is not yet any adequate theoretical understanding.

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arXiv2016

Convection in Condensible-rich Atmospheres

Condensible substances are nearly ubiquitous in planetary atmospheres. For the most familiar case-water vapor in Earth's present climate-the condensible gas is dilute, in the sense that its concentration is everywhere small relative to the noncondensible background gases. A wide variety of important planetary climate problems involve nondilute condensible substances. These include planets near or undergoing a water vapor runaway and planets near the outer edge of the conventional habitable zone, for which CO2 is the condensible. Standard representations of convection in climate models rely on several approximations appropriate only to the dilute limit, while nondilute convection differs in fundamental ways from dilute convection. In this paper, a simple parameterization of convection valid in the nondilute as well as dilute limits is derived and used to discuss the basic character of nondilute convection. The energy conservation properties of the scheme are discussed in detail and are verified in radiative-convective simulations. As a further illustration of the behavior of the scheme, results for a runaway greenhouse atmosphere for both steady instellation and seasonally varying instellation corresponding to a highly eccentric orbit are presented. The latter case illustrates that the high thermal inertia associated with latent heat in nondilute atmospheres can damp out the effects of even extreme seasonal forcing.

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arXiv2015

Comparison of "warm and wet" and "cold and icy" scenarios for early Mars in a 3D climate model

We use a 3D general circulation model to compare the primitive Martian hydrological cycle in "warm and wet" and "cold and icy" scenarios. In the warm and wet scenario, an anomalously high solar flux or intense greenhouse warming artificially added to the climate model are required to maintain warm conditions and an ice-free northern ocean. Precipitation shows strong surface variations, with high rates around Hellas basin and west of Tharsis but low rates around Margaritifer Sinus (where the observed valley network drainage density is nonetheless high). In the cold and icy scenario, snow migration is a function of both obliquity and surface pressure, and limited episodic melting is possible through combinations of seasonal, volcanic and impact forcing. At surface pressures above those required to avoid atmospheric collapse (~0.5 bar) and moderate to high obliquity, snow is transported to the equatorial highland regions where the concentration of valley networks is highest. Snow accumulation in the Aeolis quadrangle is high, indicating an ice-free northern ocean is not required to supply water to Gale crater. At lower surface pressures and obliquities, both H2O and CO2 are trapped as ice at the poles and the equatorial regions become extremely dry. The valley network distribution is positively correlated with snow accumulation produced by the cold and icy simulation at 41.8 degrees obliquity but uncorrelated with precipitation produced by the warm and wet simulation. Because our simulations make specific predictions for precipitation patterns under different climate scenarios, they motivate future targeted geological studies.

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arXiv2013

The Effect of Host Star Spectral Energy Distribution and Ice-Albedo Feedback on the Climate of Extrasolar Planets

Planetary climate can be affected by the interaction of the host star spectral energy distribution with the wavelength-dependent reflectivity of ice and snow. Here we explore this effect using a one dimensional (1-D), line-by-line, radiative-transfer model to calculate broadband planetary albedos as input to a seasonally varying, 1-D energy-balance climate model. A three-dimensional general circulation model is also used to explore the atmosphere's response to changes in incoming stellar radiation, or instellation, and surface albedo. Using this hierarchy of models we simulate planets covered by ocean, land, and water ice of varying grain size, with incident radiation from stars of different spectral types. Terrestrial planets orbiting stars with higher near-UV radiation exhibit a stronger ice-albedo feedback. We find that ice-covered conditions occur on an F-dwarf planet with only a 2% reduction in instellation relative to the present instellation on Earth, assuming fixed CO2 (present atmospheric level on Earth). A similar planet orbiting the Sun at an equivalent flux distance requires an 8% reduction in instellation, while a planet orbiting an M-dwarf star requires an additional 19% reduction in instellation to become ice-covered, equivalent to 73% of the modern solar constant. The surface ice-albedo feedback effect becomes less important at the outer edge of the habitable zone, where atmospheric CO2 can be expected to be high in order to maintain clement conditions for surface liquid water. We show that 3-10 bars of CO2 will entirely mask the climatic effect of ice and snow, leaving the outer limits of the habitable zone unaffected by the spectral dependence of water ice and snow albedo. However, less CO2 is needed to maintain open water for a planet orbiting an M-dwarf star, than would be the case for hotter main-sequence stars.

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arXiv2006

Statistical Equilibria of Uniformly Forced Advection Condensation

We examine the state of statistical equilibrium attained by a uniformly forced condensable substance subjected to advection in a periodic domain. In particular, we examine the probability density function (\pdf{}) of the condensable substance in the limit of rapid condensation. The constraints imposed by this limit are pointed out and are shown to result in a \pdf{} -- whenever the advecting velocity field admits a diffusive representation -- that features a peak at small values, decays exponentially and terminates in a rapid "roll-off" near saturation. Possible physical implications of this feature as compared to a \pdf{} which continues to decay slowly are pointed out. A set of simple numerical exercises which employ lattice maps for purposes of advection are performed to test these features. Despite the simplicity of the model, the derived \pdf{} is seen to compare favourably with \pdf{}'s constructed from isentropic specific humidity data. Further, structure functions associated with the condensable field are seen to scale anomalously with near saturation of the scaling exponents for high moments -- a feature which agrees with studies of high resolution aircraft data.

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arXiv2002

The Decay of Passive Scalars Under the Action of Single Scale Smooth Velocity Fields in Bounded 2D Domains : From non self similar pdf's to self similar eigenmodes

We examine the decay of passive scalars with small, but non zero, diffusivity in bounded 2D domains. The velocity fields responsible for advection are smooth (i.e., they have bounded gradients) and of a single large scale. Moreover, the scale of the velocity field is taken to be similar to the size of the entire domain. The importance of the initial scale of variation of the scalar field with respect to that of the velocity field is strongly emphasized. If these scales are comparable and the velocity field is time periodic, we see the formation of a periodic scalar eigenmode. The eigenmode is numerically realized by means of a deterministic 2D map on a lattice. Analytical justification for the eigenmode is available from theorems in the dynamo literature. Weakening the notion of an eigenmode to mean statistical stationarity, we provide numerical evidence that the eigenmode solution also holds for aperiodic flows (represented by random maps). Turning to the evolution of an initially small scale scalar field, we demonstrate the transition from an evolving (i.e., {\it non} self similar) pdf to a stationary (self similar) pdf as the scale of variation of the scalar field progresses from being small to being comparable to that of the velocity field (and of the domain). Furthermore, the {\it non} self similar regime itself consists of two stages. Both the stages are examined and the coupling between diffusion and the distribution of the Finite Time Lyapunov Exponents is shown to be responsible for the pdf evolution.

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arXiv2002

Surface Quasigeostrophic Turbulence : The Study of an Active Scalar

We study the statistical and geometrical properties of the potential temperature (PT) field in the Surface Quasigeostrophic (SQG) system of equations. In addition to extracting information in a global sense via tools such as the power spectrum, the g-beta spectrum and the structure functions we explore the local nature of the PT field by means of the wavelet transform method. The primary indication is that an initially smooth PT field becomes rough (within specified scales), though in a qualitatively sparse fashion. Similarly, initially 1D iso-PT contours (i.e., PT level sets) are seen to acquire a fractal nature. Moreover, the dimensions of the iso-PT contours satisfy existing analytical bounds. The expectation that the roughness will manifest itself in the singular nature of the gradient fields is confirmed via the multifractal nature of the dissipation field. Following earlier work on the subject, the singular and oscillatory nature of the gradient field is investigated by examining the scaling of a probability measure and a sign singular measure respectively. A physically motivated derivation of the relations between the variety of scaling exponents is presented, the aim being to bring out some of the underlying assumptions which seem to have gone unnoticed in previous presentations. Apart from concentrating on specific properties of the SQG system, a broader theme of the paper is a comparison of the diagnostic inertial range properties of the SQG system with both the 2D and 3D Euler equations.

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