The fast Fourier transform (FFT) technique is a very powerful tool for the efficient evaluation of gravity field convolution integrals. It can handle heterogeneous and noisy data, and thus presents a very attractive alternative to the classical, time consuming approaches, provided gridded data are available. This paper reviews the mathematics of the FFT methods as well as their practical problems, and presents examples from physical geodesy where the application of these methods is especially advantageous. The spectral evaluation of Stokes', Vening Meinesz' and Molodensky's integrals, least-squares collocation in the frequency domain, integrals for terrain reductions and for airborne gravity gradiometry , and the computation of covariance and power spectral density functions are treated in detail. Numerical examples illustrate the efficiency and accuracy of the FFT methods.

[1] Four years of data provided by the NASA/German Aerospace Center Gravity Recovery and Climate Experiment (GRACE) satellite mission are analyzed over North America using principal component analysis (PCA). Three hydrology models [Global Land Data Assimilation System (GLDAS), Climate Prediction Center (CPC), and Land Dynamics (LaD)] are used to analyze the water mass changes over the same area and time period. The GRACE-observed and the hydrology models mass changes are compared spatially and temporally, and good agreement is observed. Two signal modes are found to represent more than 65% of the GRACE-observed mass variability. The first mode represents mainly mass changes related to the snow accumulation and melting and has maximum amplitude in the western Cordillera and Québec-Labrador regions. The second mode comprises long-term positive mass changes in central and eastern Canada and negative mass changes in Alaska. In addition, two more spatiotemporal patterns that explain 14% of the GRACE-observed mass variability are extracted and studied, but no definite relation to hydrology is established. While the GLDAS model agrees very well with the GRACE observations, it is found that the CPC model also provides useful information for validating the GRACE-observed mass changes in North America. On the basis of the results of this study, we can state that principal component analysis is a useful technique for extracting and validating regional hydrology signals from GRACE gravity field data. The main advantage of PCA is the capability to extract interannual and nonperiodic mass changes in addition to long-term and periodic variations.

No abstract

No abstract

No abstract

No abstract

No abstract

No abstract