NASA’s Planetary Geology, Geophysics and Geochemistry Laboratory

LOLA MOON_PA gridded dataset

Lunar shape models are determined by LOLA in the Principal Axes (MOON_PA) body-fixed reference system, using the high-accuracy lunar orientation data provided by the JPL Solar System Dynamics Group. The axes of this system are defined by the principal axes of the solid Moon. Due to the nature of the Moon's orbit and rotation, the Z axis of this system differs somewhat from Moon's mean spin axis, and the X axis is offset from the mean direction to the center of the Earth. The LRO Project adopted a Lunar Mean Earth/Polar Axis (MOON_ME) body-fixed reference system for cartographic registration of datasets in 2008, because of the Earth-centric nature of astronomical work. In practice, the latter is realized by a constant coordinate transformation from MOON_PA to MOON_ME, which results in an offset of approximately 875 m when expressed as a displacement along a great circle on the Moon's surface.

Following the GRAIL Mission, lunar gravity is known sufficiently precisely that the offset arising from this transformation is apparent when gravity is combined with topographic datasets. Thus, it is been necessary to transform the LOLA shape models back to the MOON_PA reference system for geophysical studies. A previous dataset consisted of a cylindrical equidistant model "LDEM_PA" at a resolution of 64 pixels per degree (ppd), or approximately 0.5 km at the equator. The non-uniform density of observations necessitated some interpolation to produce this model, and it did not incorporate the later improvements in resolution afforded by the SELENE Terrain Camera merged with LOLA (Barker et al., 2016), nor the increased precision of polar tracks registered to remove slight orbital errors (Barker et al., 2023). Thus the topographic power (e.g., Ermakov, et al., 2018) was biased downwards at spherical harmonic degrees approaching 720, comparable to the resolution of GRAIL models.

To improve the shape model, we transformed the SLDEM2015 256 ppd and the LDEM 60°, 75°, 80°, and 83° N/S polar stereographic gridded data to MOON_PA pointwise, and averaged them within global cylindrical arrays at 64 and 128 ppd, with geographic boundary conditions applied at 0° and 360°. The resulting arrays are suitable for expansion in spherical harmonics via Gauss-Legendre quadrature to spherical harmonic degrees up to 11,519 (e.g., with SHTOOLS; Wieczorek and Meschede, 2018). But to resample at this density, interpolation with minimal distortion is required at the highest latitudes. We implemented this piecewise in latitude using the Generic Mapping Tools 6.5 (gmt; Wessel et al., 2019) sphinterpolate routine, a Delauney triangulation on a sphere, for the latitudes in excess of 85°. Computationally this was too time-consuming for lower latitudes. The gmt nearneighbor routine for latitudes from 75 to 85° and the simpler gmt blockmean averaging routine sufficed for latitude to 75° N/S. The resulting pieces were assembled using the gmt grdpaste routine into geographic arrays, in both grid-line registered (boundary pixels at 0°/360° longitude) and pixel-registered versions (boundary pixels centered on 0° plus half the grid spacing). The reference radius used for this elevation dataset is 1737.4 km, the same as used for the typical LOLA PDS gridded products.

The spherical harmonic power, or degree variance, of the resulting MOON_PA model is a few percent greater than previous models, with the 128 ppd model having the greatest amplitudes. Interestingly, a steeper power-law exponent (-5/2) than proposed by Vening Meinesz (-2) appears to fit the data better from degree 180 to 1800.

Notes

  
call furnsh('moon_080317.tf')
call furnsh('moon_assoc_me.tf')
call PXFORM('MOON_ME','MOON_PA', et, tsip_moon)
call mxv(tsip_moon, vec_me, vec_pa)
  

  
TKFRAME_31007_SPEC            = 'ANGLES'
TKFRAME_31007_RELATIVE        = 'MOON_PA_DE421'
TKFRAME_31007_ANGLES          = (   67.92     78.56     0.30    )
TKFRAME_31007_AXES            = (   3,        2,        1       )
TKFRAME_31007_UNITS           = 'ARCSECONDS'
  

Data

Pixel-registered

Gridline-registered

Spherical harmonics

Data Usage Policy

References

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