X. Zhang1, R.L. Shia1, M. Allen1,2, M.C. Liang3, & Y. L. Yung1 1Caltech, 2JPL, 3Academia Sinica, Taiwan

Chemical-Transport Modeling of the Hydrocarbon Distributions in Jovian

Stratosphere

AbstractThe chemical and dynamical processes in the stratosphere of Jupiter are poorly known. We constrain the meridinal transport processes using the latitudinal distributions of ethane and ethylene obtained by Cassini and Voyager (Nixon et al. 2010; Zhang et al., 2012). Previous studies (Kunde et al., 2004; Liang et al., 2005) have suggested that the horizontal transport timescale between 1 and 10 mbar should fall within 1 to 300 years, i.e., the chemical lifetimes of ethylene and ethane, respectively. But the relative roles of diffusion (eddy mixing) and advection in the horizontal transport are highly uncertain, as also revealed by other tracers such as HCN and CO2 (Lellouch et al., 2006). We introduce a two-dimensional (2-D, latitude and pressure) photochemical-diffusive-advective model to simulate the stratospheric maps of hydrocarbons. Analytical solutions, both in one-dimensional (1-D, in pressure) and 2-D coordinates, are derived to gain the physical insight of the coupled chemical-transport processes, and also used for validating the numerical methods. Simple tracer transport cases demonstrate that the short-lived species is dominated by the local chemical sources and sinks, while the long-lived species is significantly influenced by the circulation pattern. Our realistic 2-D chemical-transport simulations suggest that an equator-to-pole circulation could qualitatively explain the the opposite latitudinal distributions between C2H2 and C2H6, but a pure diffusive transport process could not.

1-D SystemIn the 1-D system, we show that CH4 and C2H6 are mainly in diffusive equilibrium, and C2H2 profile can be approximated by the modified Bessel functions. Numerical simulations are from the state-of-art Jupiter photochemical-diffusive model (Moses et al., 2005).

Contact: xiz@gps.caltech.edu (Xi Zhang)

P13B-194303-Dec-2012

2-D System

In the 2-D system, simple analytical tracer transport cases demonstrate that a short-lived species (with chemical loss rate faster than transport, such as C2H2) is dominated by the local chemical sources and sinks, while a long-lived species (with chemical loss rate slower than transport, such as C2H6) is significantly influenced by the circulation pattern.

Figure 1. Numerical simulations (black) compared with analytical solutions (red) in the 1-D system, for CH4 (left), C2H6 (middle) and C2H2 (right). The dashed lines are asymptotic profiles.

Figure 2. 2-D system results for two stream functions, PSI_A (left) and PSI_B (right), respectively. Analytic mass stream functions in units of g cm-1 s-1 (upper panel). For PSI_A case, the prescribed production is higher at equator, and loss is higher at the poles. For PSA_B case, we prescribe higher production rate in the southern hemisphere and a linear loss rate independent with latitude. Numerical simulations (lines) are compared with analytical solutions (dots), for a short-lived tracer (middle panel) and a long-lived tracer (lower panel), respectively. The four curves in bottom two panels correspond to 5, 10, 50, and 100 mbar, from the lightest color (lowest pressure) to the darkest color (highest pressure), respectively.

Voyager and Cassini ObservationsThe flybys of Jupiter by Voyager in1979, and by Cassini in 2000, has provided us detailed spatial information of the stratosphere of Jupiter. Two complete sets of global maps of temperature, C2H2 and C2H6, have been retrieved from the Cassini/CIRS and Voyager/IRIS observations in the latitude and vertical plane (Nixon, et al., 2010; Zhang et al., 2012). The latitudinal profiles of C2H2 and C2H6 show opposite trends, implying that the transport timescale is probably located within the two lifetimes. Previous studies (Kunde et al., 2004; Liang et al., 2005) have suggested that the horizontal transport timescale between 1 and 10 mbar should fall within 1 to 300 years.

Figure 3. Retrieval results from Voyager/IRIS (left panel) and Cassini/CIRS (right panel) observations (Nixon, et al., 2010; Zhang et al., 2012). For each panel, left: zonally averaged stratospheric C2H2 map; right: zonally averaged stratospheric C2H6 map.

Voyager Cassini

The Nature of the ProblemZonal-averaged Eulerian mean transport equation for 2-D chemical system (Andrews et al., 1987; Shia et al. 1990):

Note: The vertical coordinate is z=H ln(ps/p), where p is pressure and ps is the reference pressure. H is the pressure scale height. A dimensionless vertical coordinate is ξ=z/H. The meridonal coordinate is y=aθ, where a is planetary radius, and θ is the latitude. w and v are the vertical and meridional velocities, respectively. The eddy transport is parameterized in a diagonal “diffusion” tensor (Kyy and Kzz). The volume mixing ratio of gas (or tracer) i is χ=Ni/N, where Ni and N are the concentrations of gas and background atmosphere, respectively. P and L are the chemical source and loss terms, respectively.

C2 Hydrocarbon Model Simulations

C2 hydrocarbon chemistry (including about 80 photochemical reactions) is enough to simulate acetylene (C2H2) and ethane (C2H6) on Jupiter. We adopted the same vertical eddy diffusivity (Kzz) from Moses et al. (2005) and tested different cases. Specifically, we tested the horizontal eddy mixing case (Kzz+Kyy) and the equator-to-pole circulation case (Kzz+PSI_A). The results (Figure 4) show that the horizontal mixing case fails to reproduce the latitudinal distribution of C2H6, while a analytic streamfunction (PSI_A) could qualitatively explain the trend.

PSI_A PSI_B

Acetylene Ethane

Kzz only

Kzz + Kyy

(Kyy~1010 cm2 s-1)

Kzz + PSI_A

Figure 4. Distributions of C2H2 (left) and C2H6 (right) from C2 hydrocarbon chemical models.

Conclusion• We systematically investigated the possible analytical benchmark cases in the

photochemical-advective-diffusive system. Although our solutions are highly idealized, we can still gain physical insights on what control the vertical and latitudinal profiles of the short-lived and long-lived species in the stratosphere of Jupiter.

• In the 1-D system, we show that CH4 and C2H6 are mainly in diffusive equilibrium, and C2H2 profile can be approximated by the modified Bessel functions.

• In the 2-D system in the meridional plane, analytical solutions for two typical circulation patterns are derived. Simple tracer transport cases demonstrate that the short-lived species is dominated by the local chemical sources and sinks, while the long-lived species is significantly influenced by the circulation pattern.

• Realistic 2-D chemical-transport simulations suggest that, in order to explain both of the latitudinal distributions of C2H2 and C2H6 on Jupiter, an equator-to-pole circulation is more favorable. On the other hand, a pure diffusive transport process is not able to reverse the mixing ratio profile set by the pure chemical production and loss.ReferencesAndrews, D.G., Holton, J.R., & Leovy, C.B., 1987, Middle atmosphere dynamics. (Academic Pr).Kunde et al., 2004, Science 305: 1582.Lellouch, E., Bézard, B., Strobel, D., et al., 2006, Icarus 184(2): 478.Liang, M.C., Shia, R.L., Lee, A.Y.T., et al., 2005, ApJ 635(2): L177.Nixon, C.A., Achterberg, R.K., Romani, P.N., et al., 2010, Planet. Space Sci. 58(13): 1667.Shia, R., Ha, Y.L., Wen, J.S., & Yung, Y.L., 1990, J. Geophys. Res. 95(D6): 7467.Zhang, X., Nixon, C.A., Shia, R.L., et al., 2012, Planet. Space Sci., submitted.