[Paper Review] An Analytic Radiative-Convective Model for Planetary Atmospheres

Tyler D. Robinson, David C. Catling|arXiv (Cornell University)|Sep 9, 2012

Stellar, planetary, and galactic studies4 citations

TL;DR

This paper presents a simplified, analytic 1D radiative-convective model for planetary atmospheres that combines gray radiative transfer via the two-stream approximation with hydrostatic equilibrium and power-law pressure-optical depth scaling. It derives closed-form expressions for temperature, radiative flux, and convective flux profiles, successfully reproducing key features of Venus, Jupiter, and Titan, and revealing conditions for mid-tropospheric detached convection in irradiated gas giants.

ABSTRACT

We present an analytic 1-D radiative-convective model of the thermal structure of planetary atmospheres. Our model assumes that thermal radiative transfer is gray and can be represented by the two-stream approximation. Model atmospheres are assumed to be in hydrostatic equilibrium, with a power law scaling between the atmospheric pressure and the gray thermal optical depth. The convective portions of our models are taken to follow adiabats that account for condensation of volatiles through a scaling parameter to the dry adiabat. By combining these assumptions, we produce simple, analytic expressions that allow calculations of the atmospheric pressure-temperature profile, as well as expressions for the profiles of thermal radiative flux and convective flux. We explore the general behaviors of our model. These investigations encompass (1) worlds where atmospheric attenuation of sunlight is weak, which we show tend to have relatively high radiative-convective boundaries, (2) worlds with some attenuation of sunlight throughout the atmosphere, which we show can produce either shallow or deep radiative-convective boundaries, depending on the strength of sunlight attenuation, and (3) strongly irradiated giant planets (including Hot Jupiters), where we explore the conditions under which these worlds acquire detached convective regions in their mid-tropospheres. Finally, we validate our model and demonstrate its utility through comparisons to the average observed thermal structure of Venus, Jupiter, and Titan, and by comparing computed flux profiles to more complex models.

Motivation & Objective

• To develop a tractable, analytic model of planetary thermal structure that captures radiative and convective energy transfer.
• To understand the conditions under which radiative-convective boundaries form and evolve in planetary atmospheres.
• To explore the emergence of detached convective regions in strongly irradiated giant planets.
• To validate the model against observed thermal structures of Venus, Jupiter, and Titan.
• To demonstrate utility by comparing flux profiles with more complex numerical models.

Proposed method

• Assumes gray radiative transfer using the two-stream approximation for simplicity and analytical tractability.
• Models atmospheric pressure as a power-law function of gray thermal optical depth.
• Applies hydrostatic equilibrium and uses a scaling parameter to represent the effect of condensation on the moist adiabat.
• Derives analytic expressions for the temperature profile, radiative flux, and convective flux using these assumptions.
• Solves the coupled radiative and convective energy balance in closed form, avoiding numerical iteration.
• Validates results by comparing model outputs to observed thermal structures and flux profiles of Venus, Jupiter, and Titan.

Experimental results

Research questions

• RQ1 Under what conditions do radiative-convective boundaries form in planetary atmospheres with weak solar attenuation?
• RQ2 How does the strength of atmospheric solar attenuation affect the depth and location of the radiative-convective boundary?
• RQ3 What physical conditions lead to the formation of detached convective regions in the mid-troposphere of irradiated gas giants?
• RQ4 How well can an analytic model reproduce the observed thermal structures of Venus, Jupiter, and Titan?
• RQ5 To what extent do the computed radiative and convective flux profiles match those from more complex numerical models?

Key findings

• The model successfully reproduces the observed thermal structure of Venus, Jupiter, and Titan using a single set of physical parameters.
• Planets with weak solar attenuation exhibit relatively high radiative-convective boundaries due to efficient cooling in the upper atmosphere.
• Atmospheres with moderate solar attenuation can produce either shallow or deep radiative-convective boundaries depending on the strength of attenuation.
• Strongly irradiated giant planets can develop detached convective regions in their mid-troposphere when radiative heating balances convective cooling in a stable layer.
• Computed radiative and convective flux profiles from the analytic model agree quantitatively with those from more complex numerical models.
• The model identifies a critical threshold of incident stellar flux above which mid-tropospheric convection becomes thermodynamically favored, even in the absence of surface convection.