The North China Plain (NCP) has been experiencing the most severe groundwater depletion in China, leading to a broad region of vertical motions of the Earth’s surface. This paper explores the seasonal and linear trend variations of surface vertical displacements caused by the groundwater changes in NCP from 2009 to 2013 using Global Positioning System (GPS) and Gravity Recovery and Climate Experiment (GRACE) techniques. Results show that the peak-to-peak amplitude of GPS-derived annual variation is about 3.7~6.0 mm and is highly correlated (R > 0.6 for most selected GPS stations) with results from GRACE, which would confirm that the vertical displacements of continuous GPS (CGPS) stations are mainly caused by groundwater storage (GWS) changes in NCP, since GWS is the dominant component of total water storage (TWS) anomalies in this area. The linear trends of selected bedrock-located IGS CGPS stations reveal the distinct GWS changes in period of 2009–2010 (decrease) and 2011–2013 (rebound), which are consistent with results from GRACE-derived GWS anomalies and in situ GWS observations. This result implies that the rate of groundwater depletion in NCP has slowed in recent years. The impacts of geological condition (bedrock or sediment) of CGPS stations to their results are also investigated in this study. Contrasted with the slight linear rates (−0.69~1.5 mm/a) of bedrock-located CGPS stations, the linear rates of sediment-located CGPS stations are between −44 mm/a and −17 mm/a. It is due to the opposite vertical displacements induced by the Earth surface’s porous and elastic response to groundwater depletion. Besides, the distinct renewal characteristics of shallow and deep groundwater in NCP are discussed. The GPS-based vertical displacement time series, to some extent, can reflect the quicker recovery of shallow unconfined groundwater than the deep confined groundwater in NCP; through one month earlier to attain the maximum height for CGPS stations nearby shallow groundwater depression cones than those nearby deep groundwater depression cones.

Mass redistribution of the Earth causes variable loading that deforms the solid Earth. While most recent studies using geodetic techniques focus on regions (such as the Amazon basin and the Nepal Himalayas) with large seasonal deformation amplitudes on the order of 1–4 cm due to hydrologic loading, few such studies have been conducted on the regions where the seasonal deformation amplitude is half as large. Here, we use joint GPS and GRACE data to investigate the vertical deformation due to hydrologic loading in the North China Plain, where significant groundwater depletion has been reported. We found that the GPS- and GRACE-derived secular trends and seasonal signals are in good agreement, with an uplift magnitude of 1–2 mm/year and a correlation of 85.0%–98.5%, respectively. This uplift rate is consistent with groundwater depletion rate estimated from GRACE data and in-situ groundwater measurements from earlier report studies; whereas the seasonal hydrologic variation reflects human behavior of groundwater pumping for agriculture irrigation in spring, leading to less water storage in summer than that in the winter season. However, less than 20% of weighted root-mean-squared (WRMS) reductions were detected for all the selected GPS stations when GRACE-derived seasonal deformations were removed from detrended GPS height time series. This discrepancy is probably because the GRACE-derived seasonal signals are large-scale, while the GPS-derived signals are local point measurements.

In this paper, we construct a new 1′ $\times$ 1′ global seafloor topography model, BAT_VGG2021, using the satellite altimetric vertical gravity gradient anomaly model (VGG), SIO curv_30.1.nc, and ship soundings. Approximately 74.66 million single-beam depths and more than 180 GB of multibeam grids were downloaded and adopted from the National Centers for Environmental Information (NCEI), Japan Agency for Marine-Earth Science and Technology (JAMSTEC), and Geosciences Australia (GA). The SIO curv_30.1.nc model was used to predict seafloor topography at 15~160 km wavelengths, and ship soundings were used to calibrate topography to VGG ratios. The accuracy of the new BAT_VGG2021 model was assessed by comparing it with ship soundings and existing models. The results indicate that the standard deviation of differences between the predicted model and ship soundings is about 40~80 m, and ~93% of the differences are within 100 m, similar to that of the SIO topo_20.1.nc model. The new BAT_VGG2021 model shows better accuracy than the DTU18BAT, ETOPO1, and GEBCO_08 models, and has been improved significantly from our last model, BAT_VGG2014.

Tropospheric delay caused by spatiotemporal variations in pressure, temperature, and humidity in the lower troposphere remains one of the major challenges in Interferometric Synthetic Aperture Radar (InSAR) deformation monitoring applications. Acquiring an acceptable level of accuracy (millimeter-level) for small amplitude surface displacement is difficult without proper delay estimation. Tropospheric delay can be estimated from the InSAR phase itself using the spatiotemporal relationship between the phase and topography, but separating the deformation signal from the tropospheric delay is difficult when the deformation is topographically related. Approaches using external data such as ground GPS networks, space-borne spectrometers, and meteorological observations have been exploited with mixed success in the past. These methods are plagued, however, by low spatiotemporal resolution, unfavorable weather conditions or limited coverage. A phase-based power law method recently proposed by Bekaert et al. estimates the tropospheric delay by assuming the phase and topography following a power law relationship. This method can account for the spatial variation of the atmospheric properties and can be applied to interferograms containing topographically correlated deformation. However, the parameter estimates of this method are characterized by two limitations: one is that the power law coefficients are estimated using the sounding data, which are not always available in a study region; the other is that the scaled factor between band-filtered topography and phase is inverted by least squares regression, which is not outlier-resistant. To address these problems, we develop and test a power law model based on ERA-Interim (PLE). Our version estimates the power law coefficients by using ERA-Interim (ERA-I) reanalysis. A robust estimation technique was introduced in the PLE method to estimate the scaled factor, which is insensitive to outliers. We applied the PLE method to ENVISAT ASAR images collected over Southern California, US, and Tianshan, China. We compared tropospheric corrections estimated from using our PLE method with the corrections estimated using the linear method and ERA-I method. Accuracy was evaluated by using delay measurements from the Medium Resolution Imaging Spectrometer (MERIS) onboard the ENVISAT satellite. The PLE method consistently delivered greater standard deviation (STD) reduction after tropospheric corrections than both the linear method and ERA-I method and agreed well with the MERIS measurements.

In addition to studies of sea level change and mantle rheology, reliable Glacial Isostatic Adjustment (GIA) models are necessary as a background model to correct the widely used Gravity Recovery and Climate Experiment (GRACE) monthly gravity solutions to determine subsecular, nonviscous variations. Based on spherical harmonic analyses, we developed a method using degree-dependent weighting to assimilate the Global Positioning System (GPS) derived crustal uplift rates into GIA model predictions, in which the good global pattern of GIA model predictions and better local resolution of GPS solutions are both retained. Some systematic errors in global GPS uplift rates were also corrected during the spherical harmonic analyses. Further, we used the refined GIA uplift rates to infer the GIA-induced rates of Stokes coefficients (complete to degree/order 120) relying on the accurate relationship between GIA vertical surface deformation and gravitational potential changes. The results show notable improvements relative to GIA model outputs, and may serve as a GIA-correction model for GRACE time-variable gravity data.

Spatial and temporal variations in the vertical stratification of the troposphere introduce significant propagation delays in interferometric synthetic aperture radar (InSAR) observations. Observations of small amplitude surface deformations and regional subsidence rates are plagued by tropospheric delays, and strongly correlated with topographic height variations. Phase-based tropospheric correction techniques assuming a linear relationship between interferometric phase and topography have been exploited and developed, with mixed success. Producing robust estimates of tropospheric phase delay however plays a critical role in increasing the accuracy of InSAR measurements. Meanwhile, few phase-based correction methods account for the spatially variable tropospheric delay over lager study regions. Here, we present a robust and multi-weighted approach to estimate the correlation between phase and topography that is relatively insensitive to confounding processes such as regional subsidence over larger regions as well as under varying tropospheric conditions. An expanded form of robust least squares is introduced to estimate the spatially variable correlation between phase and topography by splitting the interferograms into multiple blocks. Within each block, correlation is robustly estimated from the band-filtered phase and topography. Phase-elevation ratios are multiply- weighted and extrapolated to each persistent scatter (PS) pixel. We applied the proposed method to Envisat ASAR images over the Southern California area, USA, and found that our method mitigated the atmospheric noise better than the conventional phase-based method. The corrected ground surface deformation agreed better with those measured from GPS.