wavelength topography

In this repository there is a series of data files for outputs of Mimas modeled
under different assumptions. The biggest indicators of well-fitting models are
the r_sq, which is the coefficient of determination that shows how well the
inferred heating pattern beneath the ice shell can be fit by spatial
patterns of tidal heating, and the RMS, which is the root mean square
difference between the observed topography of Mimas and the topography forward
modeled from the best fit tidal heating pattern weights. In the associated
paper, we conclude there was a past epoch of strong obliquity tides in a solid
Mimas.

Additionally, there is one last file that is input for the TIRADE solid-body
tidal heating code of Roberts & Nimmo 2008. That code is not ours to provide,
but we can at least provide the input. Further, the Roberts & Nimmo code needs
to be updated to calculate the tidal dissipation and potential due to obliquity
tides. The tidal dissipation is equation 42 of Beuthe 2013, while the tidal
potential is equation 88 of Beuthe 2013. These updates must be made to to the
file "tidal_module.c" at about lines 139 (the variable "Ediss") and 979 (the
variable "potential"). The derivatives of Equation 88 must also be calculated
to update variable "dpot". The input file is "Mimas_AGU2022_conv" and requires
the creation of a directory "mimas_agu2022_conv_dir" in the same directory as
the input file. Then the command "./tidal_cond.x Mimas_AGU2022_conv" will place
all outputs within "mimas_agu2022_conv_dir", assuming all the TIRADE code is
within the same directory as the input file.

Description of the data and file structure

The header of each file should describe what each column refers to. MoI is the
moment of inertia. From these data, one can compute density profiles for each
model of Tethys (or Enceladus) and judge whether it is consistent with the
inferred heating pattern weight. Values were not printed to file if the
calculated average heat flux was NaN, if any of chi_A,B,C were not between 0
and 1, or if any of the spherical harmonic weights of forward-modeled
topography were NaN. Further descriptions of parameters and their uses are
described in the paper for which this dataset was produced. Further, we include
files for Enceladus. While the Tethys data include "no_odysseus" in the
filename, the spherical harmonic coefficients utilized were derived from limb
profiles that do include those that pass over Odysseus crater (Nimmo et al.,
2011)

The headers contained appear like so:
Assuming [isostasy-type] isostasy and [tide-type] tides upon Tethys,
[True/False] weighted regression [states whether the multilinear regression was
weighted] and [True/False] pressure isostasy [did we use equal-pressure or
equal-mass isostasy],
each given porosity, MoI [Moment of Inertia], basal temperature T_B, and total
shell thickness d we
calculate necessary basal heat flux (F_B).
We then calculate the following values:
chi_a, chi_b, chi_c: heating pattern weights
r_sq: coefficient of determination
rms: Square root of the weighted average of the square of modeled
topography minus observed. Weighted by area of degree bin.
CF20/CF22: Spherical harmonic coefficients of flux ratioed.
normClm for l=2,4;m=0,2,4<=l: normalized spherical harmonic
weights of topography from our best-fit interior.
z_Clm: z-score of the normClm we calculate vs. those observed.
This is (normClm-normClm_observed)/SD_normClm_observed
where SD is the standard deviation