Auxiliary material for paper 2008GL035515 Strong jet and a new thermal wave in Saturn’s equatorial stratosphere Li Liming and Peter J. Gierasch Department of Astronomy, Cornell University, Ithaca, New York, USA Richard K. Achterberg Department of Astronomy, University of Maryland, College Park, Maryland, USA Barney J. Conrath Department of Astronomy, Cornell University, Ithaca, New York, USA F. Michael Flasar NASA Goddard Space Flight Center, Greenbelt, Maryland, USA Ashwin R. Vasavada Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA Andrew P. Ingersoll Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California, USA Don Banfield Department of Astronomy, Cornell University, Ithaca, New York, USA Amy A. Simon-Miller NASA Goddard Space Flight Center, Greenbelt, Maryland, USA Leigh N. Fletcher Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA Liming, L., P. J. Gierasch, R. K. Achterberg, B. J. Conrath, F. M. Flasar, A. R. Vasavada, A. P. Ingersoll, D. Banfield, A. A. Simon-Miller, and L. N. Fletcher (2008), Strong jet and a new thermal wave in Saturn’s equatorial stratosphere, Geophys. Res. Lett., 35, L23208, doi:10.1029/2008GL035515. Introduction A modified thermal wind equation The standard thermal wind equation, which relates the vertical wind shear to the horizontal temperature gradient along isobaric surfaces, can be used to derive the vertical structure of wind if the temperature field is known, or vice verse. However, the simple-format standard thermal wind equation stops working in the equatorial region because the geostrophic balance, which is one assumption behind the standard thermal wind equation, ceases to be valid when approaching the equator. More importantly, the large variation of large-scale jets, rotation periods, and radii of different planets means that some forces discarded in the geostrophic balance and the hydrostatic balance are not negligible. We have examined a modified thermal wind equation, which is applicable to the low latitudes of planets. The modified thermal wind equation has already been validated by Earth's observed wind and temperature fields (Li et al., 2008). Please refer to the following link for the detailed discussion for the modified thermal wind equation. http://www.astro.cornell.edu/~liming/papers/Thermal_wind_newA_Aug_25.pdf Validation of the equatorial wave in the stratosphere of Saturn Figure S1 is a periodogram analysis of one map shown in Figure 2. The periodogram (D), which is based on the temperature at the equator (0 dgree) after removing linear trend and mean (B and C), shows a peak at 40 degree for the wave-length in the longitudinal direction. The confidence-level of spectrum suggests that the peak at 40 degree is pretty robust with confidence-level larger than 99%, which is red dashed line in panel D. Vertical extension of the equatorial wave in the stratosphere The inversion kernel of temperature retrieval (Flasar et al., 2004) shows that there are two peaks around 1-mbar and 3-mbar for the radiance from the focal plane FP4. It means that the temperature maps at 1-mbar and 3-mbar retrieved from the CIRS FP4 radiance have the maximal confidence. Figure S2 shows the simultaneous temperature maps at the two pressure levels (1-mbar and 3-mbar). From both visual inspection and cross-correlation of the two maps (panel C), the equatorial wave at the two pressure levels does not show any noticeable shift in longitudinal direction, which suggests that the vertical wavelength of the stratospheric wave has vertical wavelength longer than the distance between 1- mbar and 3-mbar (~ 1 scale height). We also examine the raw ISS multi-filter images on the planetary data system (PDS), which are processed to global maps to help our study based on the CIRS observations. The image-process of ISS Saturn images is described elsewhere (Porco et al., 2004; Vasavada et al., 2006). The limitations of the ISS public data and the obscuring of Saturn's rings make it a little difficult to get simultaneous observations covering the equator of Saturn between the CIRS and ISS. Here, we show processed multi-filter ISS images in September of 2004 (Figure S3), which is ~ 0.5 Earth-year earlier than the date of the first CIRS thermal map shown in Figure 2 (March, 2005). Considering that the life-time of the thermal wave shown in Figure 2 is at least longer than 2.5 Earth years, we think that the equatorial wave in the stratosphere, which is discovered by the CIRS, probably existed at the time of the ISS multi-filter images (September, 2004). The ISS multi-filter images (Figure S3) do not show planetary-scale wave patterns around the equator either. Compared with the CIRS temperature maps, the ISS multi-filter images have relative deeper effective pressure levels (UV3 ~ 200 mbar, MT3 ~ 500 mbar, and CB3 > 10 mbar), which are defined as optical depth equating one in the absence of cloud opacity (West et al., 2004). The different sampling levels of the CIRS and ISS probably results in the absence of equatorial waves in the ISS multi-filter images. The fact that the equatorial wave in the stratosphere does not show in the ISS images and the 100-mbar CIRS thermal maps (not shown) suggests that the vertical wave-length of the 1-mbar equatorial wave is shorter than the distance between 1 mbar and 100 mbar, which is ~ 4.5 scale heights. Phase velocity of the equatorial wave in the stratosphere Figure S4 shows the cross correlation between a pair of thermal maps in Figure 2 (A and B), which are separated by 11 hours. The cross-correlation displays a maximal coefficient ~ 0.6 at the equator when the longitudinal shift is 18 degree, which corresponds to a phase velocity ~ 470 m/s in the longitudinal direction. Therefore, the phase velocity relative to the background current can be estimated as (-130 m/s -30 m/s), considering that the background zonal wind is 500 - 600 m/s based on the CIRS nadir and limb observations. References Flasar, F. M., and 45 colleagues, 2004. Exploring the Saturn system in the thermal infrared: The Composite Infrared Spectrometer, Space Sci. Rev. 115, 169- 297. Li, L., B. J. Conrath, F. M. Flasar, and P. J. Gierasch, 2007. Revisit of the thermal wind equation: application to planetary atmospheres at low latitudes, EOS Transactions American Geophysical Union, Vol., 88(24), P41A-0208. Porco, C. C., and 19 colleagues, 2004. Cassini Imaging Science: Instrument characteristics and anticipated scientific investigations at Saturn, Space Sci. Rev. 115, 363-497. Vasavada, A. R., S. M. Horst, M. R. Kennedy, A. P. Ingersoll, C. C. Porco, A. D. Del Genio, and R. A. West, 2006. Cassini imaging of Saturn: southern hemisphere winds and vortices, J. Geophy. Res. 111, art. no. E05004. West R. A., K. H. Baines, A. J. Friedson, D. Banfield, B. Ragent, and F. W. Taylor, 2004. Jupiter: The Planet, Satellites and Magnetosphere, Combridge Planet. Sci. Ser., edited by F. Bagenal et al., Combridge Univ. Press, New York. Figure Legends of Auxiliary 1. 2008gl035515-fs01.tif A periodogram analysis of the equatorial wave at 1-mbar. (A) Temperature map at 1 mbar in March 23, 2006. (B) Temperature along longitude at the equator (0 degree). (C) Same as (B) except removing the mean and linear trend. (D) FFT analysis of the temperature at the equator. The green, blue, and red dashed lines present confidence levels of 90%, 95%, and 99%, respectively. 2. 2008gl035515-fs02.tif Correlation between temperature maps at different pressure levels. (A) 1-mbar temperature map in March 10, 2005. (B) 3-mbar temperature map in March 10, 2005. (C) Cross correlation coefficients with varying longitudinal shifts in the range of negative 60 degree to positive 60 degree. 3. 2008gl035515-fs03.tif Multi-filter ISS images covering the equatorial region. The upper panel is the ultraviolet filter UV3 (338 nm). The middle panel is the strongest methane filter MT3 (889 nm). The bottom panel is the corresponding continuum band CB3 (938 nm). The multi-filter images were taken in September 19, 2004 with a time separation ~ 3 minutes, which make them virtually simultaneous. The spatial resolution of these processed images in Figure S3 is ~ 150 km per pixel. 4. 2008gl035515-fs04.tif The cross correlations between the two thermal maps in the first pair of Figure 2. The Longitudinal shifts are varied in the range of negative 60 degree to positive 60 degree. The white dashed line is the background zonal winds at 1- mbar. The second pair of thermal maps in Figure 2, which is also separated by 11 hours, shows almost same cross correlation coefficients with the results in Figure S4.