An effective filtering for GRACE time‐variable gravity: Fan filter

Spatial low‐pass filtering is necessary for processing the GRACE time‐variable gravity (TVG) data which are otherwise plagued with short‐wavelength noises. Here we devise a new non‐isotropic filter, called the fan filter: In terms of the spherical harmonic spectrum, the fan filter is simply a 2‐D double filter consisting of a low‐pass along the degree n (the same as the conventional isotropic filter) simultaneously with a low‐pass along the order m , whose contour projection onto the ( n , m ) plane is fan‐shaped. It is deterministic and independent of a priori or external information, its implementation is straightforward, and the result is objective. Most importantly, we show that this simple filter performs well among its counterparts under similar conditions, in particular against the N‐S striping noises prevalent in the GRACE TVG solutions. We demonstrate this with Gaussian weights at filter length and hence spatial resolution as fine as 300 km. We also deduce the fan filter's nominal amplitude‐reduction factor as a function of the filter length for TVG signals that follow the Kaula rule.