The Earth's Gravitational Field Model Determined By GOCE And GRACE Data

With the coming of the space era, the theory and methodology of the Earth's gravitational field model have been greatly developed. Moreover, with the successful implementation of three generations of dedicated gravity satellite missions, CHAMP (CHAllenging Minisatellite Payload), GRACE (Gravity Recovery And Climate Experiment) and GOCE (Gravity field and steady-state Ocean Circulation Explorer), the theory of the Earth's gravitational field model determination and its applications is burgeoning. The thesis mainly studied the theory and methodology to determine the Earth's gravitational field model with GOCE and GRACE satellite observations. The Earth's gravitational field models are determinated by combining multi-class observation data of the two generations gravity satellites. At the same time, a new approach is developed to recover global mass change by using gravity satellite data. The main work and innovation of this thesis are summarized in the following aspects:1. The time and coordinate systems in satellite gravity measurement are described in detail. And then the coordinate transform algorithm between International Terrestrial Reference System (ITRS) and Geocentric Celestial Reference System (GCRS) is analyzed and implemented based on the IERS2010 conventions. In addition, various conservative forces perturbation accelerations of the GOCE and GRACE satellites are analyzed too. The expression of the gravitational gradient tensor in each coordinate system is elaborately illustrated.2. The type of coefficients arrangement of the Earth's gravitational field model is systematically analyzed. An index algorithm for each coefficient ordering pattern is given and the structure of normal equation matrix with different coefficients arrangement patterns is analyzed. At the same time, the accuracy and characteristics of various calculation methods of the associated Legendre function and its first-, second-derivative algorithms are analyzed and compared. A fast and stably-recursive algorithm for computing second derivative of associated Legendre's functions is derived. Numerical tests suggest that this new approach is exactly as precise as general ones, but it is much faster than general ones in computation speed (at least twice as fast).3. The spherical harmonic analysis and synthesis algorithms are systematically analyzed, and an improved FFT (Fast Fourier Transform) algorithm for spherical harmonic analysis and synthesis is derived. The improved FFT algorithm does not require grid point starting from zero longitude, which avoids the loss of precision in the grid interpolation. My numerical experiment shows that the improved algorithm keeps the same computation efficiency as the ordinary FFT, and also keeps the same numerical accuracy as summation method. An least squares method for establishing normal equation with Class ? and ? local unknown parameters is introduced, and an algorithm for the variance error of unit weight with eliminating the Class ? and ? local unknown parameters is derived. At last, some regulation methods to deal with ill-posed problems are introduced.4. The GOCE orbit derived gravity field models are calculated by using energy conservation approach, average acceleration approach and short-arc integral approach, respectively. The accuracy and applicability of the three methods are analyzed. At the same time, optimal regularization method for every method is also analyzed. The Fourier series is used to solve the energy conservation law orbit GOCE gravity field model for solving the calculation of dissipative energy and energy constant when GOCE orbit derived gravity field modeis are calculated by energy conservation approach. The result shows that average acceleration approach and short-arc integral approach are more suitable for GOCE satellite orbit data processing and gravity field model can be derived with high accuracy. However, the method drived from energy conservation approach is not good, and it fail to recover gravity field models by GOCE orbit data with the order and degree over 120. The detailed process of the GOCE gradient observations data processing is discussed, and the color noise in the GOCE gradient data is filtered by the zero phase finite impulse band-pass digital filter and remove-restore method, Ultimately, a gradient-only global static gravity field model entitled SWJTU-GO01G up to degree and order 210 is recovered based on 12 months of GOCE gravity gradient data.5. A GOCE-only global static gravity field model entitled SWJTU-GO01S up to degree and order 210 is recovered based on 12 months of GOCE gravity gradient and orbit data. The results show that the geoid error and cumulative error of the SWJTU-GO01S model with degree and order 210 are 2.1cm and 13.7cm compared to EGM2008, respectively, which is better than the ESA's second-generation official model. A satellite-only global static gravity field model entitled SWJTU-GOGR01S up to degree and order 210 is recovered based on 3 years of GOCE gravity gradient data and ITG-Grace2010s model's normal equation calculated from 7 years GPS and K-band rang rate data. The geoid error and cumulative error of the SWJTU-GOGR01S model with degree and order 210 are 1.3cm and 5.7cm, respectively. The overall accuracy of the SWJTU-GOGR01S model is between the ESA's third and fourth generation models.6. The global mean dynamic topography and geostrophic surface circulation are recovered by the combination of the GOCE gravity field model SWJTU-GO01S and the mean sea surface height model CNES-CLS 2011. When compared with the GRACE model result, multi-source data assimilation model CNES-CLS09 and in-situ ocean drogue drifter's observations, its computation accuracy, to some extent, equals that of the ESA's fourth official model and exceeds the accuracy of GRACE model.7. A new three-dimensional acceleration point-mass modeling approach for global mass change monitored by LEO gravity satellite data is derived. This new algorithm do not need harmonic coefficients as the intermediate values which is different from the traditional spherical harmonic coefficient method and the MASCON (Mass Concentration) method. At the same time, the new algorithm adequately uses three-dimensional gravity satellite observation signal, which is also different from gravitational point-mass modeling approach and radial acceleration point-mass modeling approach in which only scalar or one-dimensional vector is used to observe data. Meanwhile, the three-dimensional acceleration point-mass modeling approach can be used flexibly, which means that global surface mass change can be calculated either by using spherical harmonic coefficient or directly by using LEO gravity satellite data.