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Ocean tide loading refers to the periodic redistribution of water masses due to tidal forcing, which causes deformations of the solid Earth and perturbations of the gravity field. The resulting elastic and gravitational responses of the solid Earth are termed "load tides" (e.g., Farrell, 1972). Load tides at the Earth's surface can be described as vertical displacement, horizontal displacement and the gravitational potential increment. In ocean areas, the geoid undulation relative to the vertical displacement is specified by the "self-attraction and loading" (SAL: e.g., Ray, 1998) elevation. Load tides are as important as body tides (e.g., Takeuchi, 1950) in making up the total tide of the solid Earth induced by the astronomical forces. On the other hand, the SAL potential (SAL elevation times surface gravity) induces secondary barotropic accelerations that influence ocean tide dynamics, and, as a result, their consideration is a necessity for generating an accurate ocean

We revisit the results of the ISMIP-HEINO benchmark by first analyzing the differences in various model outputs using a wavelet-based spectral technique. Second, the ISMIP-HEINO benchmark experiments are recomputed with a novel numerical ice-sheet model based on the SIA-I algorithm that enables both the shallow-ice and a higher-order approximation of the ice-flow equations to be performed. To assess the significance of the higher-order approximation in the ISMIP-HEINO experiment, a numerical sensitivity study for the shallow-ice approximation (SIA) simulations is also carried out. A high sensitivity of the SIA model response to surface temperature perturbations is found. We conclude that the variations in ISMIP-HEINO results are due to the differences in (1) simulated basal temperatures and (2) numerical treatment of the basal sliding condition.

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We present a new algorithm for a fast iterative improvement of the shallow-ice approximation (SIA) for the modeling of glacier flow. Based on the traditional SIA scaling assumptions, the solution of the Stokes problem is found by an operator-splitting iterative technique. The SIA solution obtained in the first step is successively improved to obtain a higher-order approximation. Each iterative step has computational demands comparable to solving the SIA, which makes the algorithm substantially faster than other higher-order or full-Stokes solvers. The performance of the algorithm is tested on a model example taken from the ISMIP-HOM intercomparison project.

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