Physical Mechanism Of Non-linear Signal Driven By Temperature Variation In GPS Position Time Series

Coordinate time series of continuous GNSS reference stations(short for time series)are fundamental datasets for research fields both in geodesy and geodynamic.Apparent non-linear variations in time series,which exhibit periodical oscillations of site positions,are mainly induced by different geophysical processes.The precise position and velocity of GNSS station,along with their uncertainties,can be estimated once the non-linear variations of time series are extracted and quantified precisely from the perspective of the origin of the deformation signal.This will contribute to the improvement of GNSS station motion model,and can provide some scientific reference for the establishment and maintainence of the mm-level terrestrial reference frame,which have great significance in geoscience.The origins of non-linear signal in time series induced by geophysical process include tides(such as earth body tides,ocean tides and atmospheric tides,which are mostly corrected in GNSS precise processing),surface loadings(such as atmospheric loading,non-tidal ocean loading,and continential water-storage loading)and thermal expansion of the monument and the bedrock.The best result indicates that surface loading can only explain less than 60% of the vertical annual amplitude in time series,and the origin,the mechanism and the quantitative analysis of other contributor of seasonal signal need to be solved in urgent.The thermal expansion of the monument(TEM)and the bedrock(TEB)driven by periodical temperature variations are believed to be one of the potential contributors to the non-linear signal in time series.Raising or modifying the TEM and TEB models,quantifying and analyzing the displacement induced by thermal expansion,and explaining the physical mechanism of the non-linear signal in GNSS time series driven by temperature variations have become the most advanced domain in the field of GNSS coordinate time series analysis nowadays.Focus on the origin of non-linear signal driven by temperature variation in time series,the characteristics and disciplines of thermal expansion effects in various temporal and spatial scales are discussed in this research.Firstly,the basic theory and methodology of GPS coordinate time series analysis and the modeling of thermal expansion effects were introduced.Next,a modified TEM model considering the annex structure beneath the monument itself was raised and then compared with the observed seasonal signals in GPS short-baseline time series.And then,the diurnal and subdiurnal signal induced by TEM was extracted from other contributors of the non-linear signal and noise.The characteristics of spurious low-frequency induced by the aliasing of high-frequency TEM signal were discussed and quantified for the first time.Meanwhile,the global 3-D TEB displacement time series grids were estimated and the spatial distribution both for global and regional scales were discussed in detail.Eventually,the contribution of thermal expansion to the non-linear signal is quantified by applying the deformation as geophysical corrections along with surface loading displacements,and the optimal geophysical process model was determined to best correct the time series.The main contents and contributions include:(1)An improved TEM model was raised to estimate the TEM displacement more precisely,which can take different type,structure and annex height of the monument into account.GPS short-baselines with apparent monument differences were adopted to verify the improved model.The result showed that annual signal with maximum amplitude of 1.86 ± 0.17 mm was found in GPS short-baseline time series,and there was ~84% of the vertical annual amplitude could be explained by the improved TEM model,with an improvement of 80% when comparing with the previous model.In addition,60% of the stochastic processes in short-baseline time series could be best described by band-pass or by first-order Gauss-Markov noise instead of flicker and random-walk noise.(2)The diurnal and sub-diurnal TEM displacements were extracted and isolated from other non-linear signal sources and noise by differencing GPS short-baseline 4-hour and 24-hour session solutions as well as adopting the singular spectral analysis method,and then were analyzed in detail.The spurious low-frequency signals induced by the aliasing of high-frequency TEM signals were quantified for the first time.The results showed that diurnal temperature periodical variations were the main contributors to the diurnal and sub-diurnal signals existed in GPS short-baseline time series with the maximum amplitude of 5 mm in the vertical direction,and the horizontal displacements were coherent with daily temperature variations.In addition,the high-frequency TEM signal will aliasing into spurious low-frequency signal in GPS position time series,with amplitude ratio of 7%,25% and 25%,36% for the North,East annual and North,East semi-annual signal,respectively.(3)The TEB model based on a uniform elastic sphere assumption and a more precise land surface temperature numerical model from ECMWF was adopted to estimated the 3-D displacement induced by TEB,which was of obvious advantage over the previous TEB model based on a simple half-space assumption without taking the horizontal temperature gradient into account.The 3-D displacement time series were estimated with a data span over 19 years and a spatial resolution of 0.5°×0.5° for the global grid.The results of global and regional characteristics of the TEB displacements showed that the maximum TEB annual amplitude was 1.77 mm,1.55 mm and 3.72 mm for the North,East,and Up component,respectively,appeared in the southeast Iran,Yakutsk and the east Siberia in Russian Federation.For Chinese mainland,the TEB vertical amplitude was higher than the horizontal directions The annual amplitude can exceed 1 mm on the North component generally with an decreasing trend from the Southwest to the Northeast of China,and the large amplitudes were mainly distributed in high altitude areas such as the Tibetan Plateau,the Yunnan-Kweichow Plateau and the Southeast Xinjiang Province.(4)Based on the previous results,the contribution of thermal expansion to the nonlinear signal in GPS time series was quantified.Meanwhile,the optimal geophysical model was chosen to best correct the GPS time series,including the surface loading model and thermal expansion model data.When comparing with the modeled 3-D displacement time series induced by thermal expansion and the observed GPS time series for 262 global distributed IGS stations during 2000 and 2018,it was found that there were 84%(220/262),49%(129/262)and 90%(236/262)of the stations with their annual amplitude decreased for the N,E,and U component,respectively,after applying the thermal expansion corrections,with average decreasing ratio of 25.3%,-0.6% and 17.8% for the three components.That meant,in other words,thermal expansion was responsible for ~25% and ~18% of the annual amplitude in GPS coordinate time series for the horizontal and vertical direction,respectively.The average correlation coefficient could be 0.6 between the modeled surface loading and thermal expansion displacements and the observed GPS displacements,especially on the vertical component.After applying the geophysical corrections to GPS observations,the GPS vertical RMS value could reduce 1.56 mm on average,and the geophysical models(including surface loading and thermal expansion models)could explain up to 80% of the vertical annual amplitude in the global scale.