Correction to: “Geophysical implications of the long-wavelength topography of the Saturnian satellites”


  • F. Nimmo,

  • B. G. Bills,

  • P. C. Thomas


This article corrects:

  1. Geophysical implications of the long-wavelength topography of the Saturnian satellites Volume 116, Issue E11, Article first published online: 9 November 2011

[1] In the paper “Geophysical implications of the long-wavelength topography of the Saturnian satellites” by F. Nimmo, B. G. Bills, and P. C. Thomas (Journal of Geophysical Research, 116, E11001, doi:10.1029/2011JE003835, 2011), we published spherical harmonic coefficients Clm, Slm for the long-wavelength topography of the Saturnian satellites, based on limb profiles [Thomas, 2010]. Unfortunately, a 180° phase shift in longitude was incorrectly introduced, resulting in sign errors in some of these coefficients. All the figures shown in Nimmo et al. [2011] are correct, but Tables 2 and 3 and the supporting information data sets need correcting. The corrected tables are presented below. The corrected coefficients Clm′, Slm′ may be derived from the published coefficients as follows:

display math(1)
display math(2)
Table 2. Corrected Normalized Degree-2 Spherical Harmonic Topography Coefficients (in km)a
Satellitemath formulamath formulamath formulamath formulamath formulaMisfitSDC20/C22aR0bR0cR0
  1. a

    Overbars signify normalized coefficients. Numbers in parentheses are the uncertainties (1 sigma) in the last digit; thus, −3.46(7) should be read as −3.46±0.07. In column 9, the coefficients are unnormalized and the uncertainties (2 sigma) are calculated using the upper bound on C20 and the lower bound on C22. The expected hydrostatic ratio is 3.33. Also tabulated (in km) are the RMS misfit between the best fit model topography and the raw topography, the standard deviation of the raw topography relative to a sphere, and the implied axes a, b, and c, where R0 is the mean radius. Uncertainties in the latter are derived from the 2 sigma uncertainties in C20 and C22, assuming that errors add quadratically. To allow comparison with Thomas [2010], we calculate a from the radial values at 0°W, 0°N and 180°W, 0°N, and similarly with b and c.

Mimas−3.46(7)0.10(6)0.00(6)2.83(4)0.07(5)0.684.384.24 ± 0.319.34 ± 0.23−1.61 ± 0.23−7.74 ± 0.31
Enceladus−1.72(8)0.00(4)−0.05(4)1.42(3)−0.06(3)0.442.364.20 ± 0.634.67 ± 0.23−0.83 ± 0.23−3.85 ± 0.36
Tethys−2.13(7)0.01(3)−0.13(5)2.59(5)−0.17(4)1.183.712.85 ± 0.337.39 ± 0.27−2.63 ± 0.27−4.76 ± 0.31
Dione−0.86(7)−0.01(5)−0.01(4)0.57(5)−0.01(4)0.591.235.26 ± 2.172.06 ± 0.25−0.13 ± 0.25−1.92 ± 0.31
Rhea−0.5(1)−0.10(5)−0.13(5)0.8(1)0.01(4)1.011.372.30 ± 1.622.11 ± 0.35−0.94 ± 0.35−1.16 ± 0.45
Table 3. Corrected Normalized Degree-3 Spherical Harmonic Topography Coefficientsa
Satellitermath formulamath formulamath formulamath formulamath formulamath formulamath formulaV3V4V5V6V7V8
  1. a

    Numbers in parentheses are the formal uncertainties in the last digit; thus, 0.019(2) should be read as 0.019±0.002. The higher degree variances math formula are also given. Units are km for the coefficients and km2 for the variances.

  2. b

    All solutions use topography referenced to the best fit shapes of Thomas [2010], except for the final row, in which Rhea's degree-2 shape from Table 2 is used.


[2] Thus, the previously published values of C20, C22, and C30 are correct, but C21 and S22 have the incorrect sign.

[3] Thanks to Doug Hemingway for checking our calculations.