Non-isotropic Gaussian smoothing and leakage reduction for determining mass changes over land and ocean using GRACE data

We present a new non-isotropic Gaussian filter for smoothing mass changes computed from Gravity Recovery and Climate Experiment (GRACE) L2 products and a new method to reduce land-ocean signal leakage caused by Gaussian smoothing. The kernel of our non-isotropic filter is the product of two Gaussian functions with distinct latitudinal and longitudinal smoothing radii. When expressed as number of kilometres at the Earth's surface, the longitudinal smoothing radius, defined as a fixed longitude interval, is longer at the equator, and shorter at higher latitude. This is principally in accordance with the resolution of the GRACE data, and permits us to produce homogeneously smoothed results without excessive smoothing in latitudinal direction. This filter is not applicable in polar regions, where we choose to use the classical isotropic Gaussian filter. A smoothing radius choice scheme is proposed for the two filters to mesh seamlessly. In our leakage reduction method, the inputs are the mass change data after smoothing using a Gaussian filter. Along coasts where mass change signal on land is far larger than that over ocean ( or signal over ocean is reduced to a very small magnitude by removing a model beforehand, and adding the model back afterwards), our method approximately recovers a smoothed mass change signal over both land and ocean sides as if a regional Gaussian filter with the same smoothing radius were applied over land and ocean separately, in which no signal leakages appear. The side lobe problem does not appear in our approach. Our leakage reduction method could also be used to study mass changes within a region where signal is far larger than that in surrounding regions, or where signal in surrounding regions could be reduced to very low magnitude by removing a model.