[1] EGM2008 is a spherical harmonic model of the Earth's gravitational potential, developed by a least squares combination of the ITG-GRACE03S gravitational model and its associated error covariance matrix, with the gravitational information obtained from a global set of area-mean free-air gravity anomalies defined on a 5 arc-minute equiangular grid. This grid was formed by merging terrestrial, altimetry-derived, and airborne gravity data. Over areas where only lower resolution gravity data were available, their spectral content was supplemented with gravitational information implied by the topography. EGM2008 is complete to degree and order 2159, and contains additional coefficients up to degree 2190 and order 2159. Over areas covered with high quality gravity data, the discrepancies between EGM2008 geoid undulations and independent GPS/ Leveling values are on the order of AE5 to AE10 cm. EGM2008 vertical deflections over USA and Australia are within AE1.1 to AE1.3 arc-seconds of independent astrogeodetic values. These results indicate that EGM2008 performs comparably with contemporary detailed regional geoid models. EGM2008 performs equally well with other GRACE-based gravitational models in orbit computations. Over EGM96, EGM2008 represents improvement by a factor of six in resolution, and by factors of three to six in accuracy, depending on gravitational quantity and geographic area. EGM2008 represents a milestone and a new paradigm in global gravity field modeling, by demonstrating for the first time ever, that given accurate and detailed gravimetric data, a single global model may satisfy the requirements of a very wide range of applications.

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Abstract. Spherical harmonic expansions form partial sums of fully normalised associated Legendre functions (ALFs). However, when evaluated increasingly close to the poles, the ultra-high degree and order (eg. 2700) ALFs range over thousands of orders of magnitude. This causes existing recursion techniques for computing values of individual ALFs and their derivatives to fail. A common solution in geodesy is to evaluate these expansions using Clenshaw's (1955) method, which does not compute individual ALFs or their derivatives. Straightforward numerical principles govern the stability of this technique. This paper employs elementary algebra to illustrate how these principles are implemented in Clenshaw's method. It also demonstrates how existing recursion algorithms for computing ALFs and their first derivatives are easily modified to incorporate these same numerical principles. These modified recursions yield scaled ALFs and first derivatives, which can then be combined using Horner's scheme to compute partial sums, complete to degree and order 2700, for all latitudes (except at the poles for first derivatives). This exceeds any previously published result. Numerical tests suggest that this new approach is at least as precise and efficient as Clenshaw's method. However, the principal strength of the new techniques lies in their simplicity of formulation and implementation, since this quality should simplify the task of extending the approach to other uses, such as spherical harmonic analysis.

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The Gravity Recovery and Interior Laboratory (GRAIL) mission is providing unprecedentedly high-resolution gravity data. The gravity signal in relation to topography decreases from 100 km to 30 km wavelength, equivalent to a uniform crustal density of 2450 kg/m 3 that is 100 kg/m 3 smaller than the density required at 100 km. To explain such frequency-dependent behavior, we introduce rock compaction models under lithostatic pressure that yield radially stratified porosity (and thus density) and examine the depth extent of porosity. Our modeling and analysis support the assertion that the crustal density must vary from surface to deep crust by up to 500 kg/m 3 . We found that the surface density of megaregolith is around 2400 kg/m 3 with an initial porosity of 10-20%, and this porosity is eliminated at 10-20 km depth due to lithostatic overburden pressure. Our stratified density models provide improved fits to both GRAIL primary and extended mission data.