Regional gravity field modeling with high-precision and high-resolution is one of the most important scientific objectives in geodesy, and can provide fundamental information for geophysics, geodynamics, seismology, and mineral exploration. Rectangular harmonic analysis （RHA） is proposed for regional gravity field modeling in this paper. By solving the Laplace＇s equation of gravitational potential in local Cartesian coordinate system, the rectangular harmonic expansions of disturbing potential, gravity anomaly, gravity disturbance, geoid undulation and deflection of the vertical are derived, and so are the formula for signal degree variance and error degree variance of the rectangular harmonic coefficients （RHC）. We also present the mathematical model and detailed algorithm for the solution of RHC using RHA from gravity observations. In order to reduce the edge effects caused by periodic continuation in RHA, we propose the strategy of extending the size of computation domain. The RHA-based modeling method is validated by conducting numerical experiments based on simulated ground and airborne gravity data that are generated from geopotential model EGM2008 and contaminated by Gauss white noise with standard deviation of 2 mGal. The accuracy of the 2.5＇×2.5＇ geoid undulations computed from ground and airborne gravity data is 1 and 1.4 cm, respectively. The standard error of the gravity disturbances that downward continued from the flight height of 4 km to the geoid is only 3.1 reGal. Numerical results confirm that RHA is able to provide a reliable and accurate regional gravity field model, which may be a new option for the representation of the fine structure of regional gravity field.
Monitoring glacier mass balance is crucial to managing water resources and also to understanding climate change for the arid and semi-arid regions of Central Asia. This study extracted the inter-annual oscillations of glacier mass over Central Asia from the first ten principal components（S-PCs） of filtered variability via multichannel singular spectral analysis（MSSA）, based on gridded data of glacier mass inferred from Gravity Recovery and Climate Experiment（GRACE） data obtained from July 2002 to March 2015. Two significant cycles of glacier mass balance oscillations were identified. The first cycle with a period of 6.1-year accounted for 54.5% of the total variance and the second with a period of 2.3-year accounted for 4.3%. The 6.1-year oscillation exhibited a stronger variability compared with the 2.3-year oscillation. For the 6.1-year oscillation, the results from lagged cross-correlation function suggested that there were significant correlations between glacier mass balances and precipitation variations with the precipitation variations leading the response of glacier mass balances by 9–16 months.
An investigation has been made on the models and characteristics of triple-frequency carrier-phase linear combinations for the Bei Dou Navigation Satellite System(BDS). Based on the three frequencies of the BDS, three categories of combinations are developed: ionosphere-free combinations(i.e., those that eliminate the ionospheric effect), minimum-noise combinations(those that mitigate the effects of thermal noise and multiple paths), and troposphere-free combinations(those that mitigate tropospheric effects). Both the ionosphere-free and troposphere-free combinations can be expressed as planes, whereas the minimum-noise combinations can be expressed as a line. The relationships between these three categories of linear combinations are investigated from the perspective of geometry. The angle between the troposphere-free plane and ionosphere-free plane is small, while the angles between the troposphere-free plane and the minimum-noise line, and between the ionosphere-free plane and the minimum-noise line, are large. Specifically, the troposphere-free plane is orthogonal to the minimum-noise line. By introducing the concepts of lane number and integer ionosphere number, the characteristics of the long-wavelength integer combinations and ionosphere-free integer combinations are investigated. The analysis indicates that the longest wavelength that can be formed for integer combinations is 146.53 m, and the ionosphere-free integer combinations all have large noise amplification factors. The ionosphere-free integer combination with minimum noise amplification factor is(0, 62, 59). According to the lane number, integer ionosphere number, and noise amplification factor, optimal integer combinations with different characteristics are presented. For general short baselines and long baselines, three independent integer combinations are suggested.
At seasonal and intraseasonal time scales, polar motions are mainly excited by angular momentum fluctuations due to mass redistributions and relative motions in the atmosphere, oceans, and continental water, snow, and ice, which are usually provided by various global atmospheric, oceanic, and hydrological models（some with meteorological observations assimilated; e.g., NCEP, ECCO, ECMWF, OMCT and LSDM etc.）. Unfortunately, these model outputs are far from perfect and have notable discrepancies with respect to polar motion observations, due to non-uniform distributions of meteorological observatories,as well as theoretical approximations and non-global mass conservation in these models. In this study,the LDC（Least Difference Combination） method is adopted to obtain some improved atmospheric,oceanic, and hydrological/crospheric angular momentum（AAM, OAM and HAM/CAM, respectively）functions and excitation functions（termed as the LDCgsm solutions）. Various GRACE（Gravity Recovery and Climate Experiment） and SLR（Satellite Laser Ranging） geopotential data are adopted to correct the non-global mass conservation problem, while polar motion data are used as general constraints. The LDCgsm solutions can reveal not only periodic fluctuations but also secular trends in AAM, OAM and HAM/CAM, and are in better agreement with polar motion observations, reducing the unexplained excitation to the level of about 5.5 mas（standard derivation value; about 1/5-1/4 of those corresponding to the original model outputs）.
