Variability of the Gravity-to-Height Ratio Due to Surface Loads

Abstract

We study the ratio between the gravity variation and vertical displacement on the surface of a self-gravitating earth model when a surface load is applied. We adopt a theoretical and numerical point of view, excluding any observations. First, we investigate the spectral behavior of the ratio of the harmonic components of the gravity variation and vertical displacement. Then, we model the gravity-to-height ratio for different surface loads (continental hydrology, atmospheric pressure, ocean tides) using outputs of global numerical models in order to relate the predicted spatial values to theoretical mean values deduced from the spectral domain. For locations inside loaded areas, the ratio is highly variable because of the Newtonian attraction of the local masses and depends on the size of the load. For the hydrological loading (soil moisture and snow), the mean ratio over the continents is  −0.87 μGal mm⁻¹, but increases with decreasing size of the river basins. For the atmospheric loading, assuming an inverted-barometer response of the ocean, the ratio is positive, with larger values for high latitudes (0.49 μGal mm⁻¹)—particularly on the coasts—than for lower latitudes (0.30 μGal mm⁻¹). The ratio, however, is much less variable outside the loaded areas: in desert areas such as the Sahara and Arabia, its mean value is  −0.28 μGal mm⁻¹. For the ocean tidal loading, we find a mean ratio of  −0.26 μGal mm⁻¹ over the continents for the diurnal tidal waves. Both results are close to the theoretical mean value of  −0.26 μGal mm⁻¹ combining elastic and remote attraction contributions.