4.1. GWSA Inversion Results Using CORS Data
The time series of non-linear geodetic height changes were first processed using gross error detection and linear item removal, as shown by the red points in
Figure 5. The black curve in
Figure 5 shows the time series of geodetic heights after the periodic fast Fourier transformation (FFT) reconstruction. According to the magnitude of the power spectral density, this paper uses the first eight periodic signals to reconstruct [
42,
43]. Indeed, the periodic FFT reconstruction is a low-pass filtering method used to decrease or inhibit the high-frequency noise of the time series, thus improving the stability of the inversion results. The geodetic heights of CORS stations corresponded to the temporal resolution of surface mass loads. In order to improve the accuracy of the CORS inversion, the influences of high-resolution surface mass loads, including atmospheric, soil water, and non-tidal oceanic loads, were removed from the reconstructed time series of non-linear geodetic heights, as shown by the purple, blue and green curves in
Figure 5. The residual time series obtained after the removal process, according to Equations (2) and (5), can therefore be used to invert GWSA within the coverage of the CORS network, which is reflected by EWH.
Figure 6 shows the annual differences between the maximum and minimum values of the reconstructed geodetic height time series at the 66 CORS stations, ranging from 15 to 35 mm. According to
Figure 5, the atmospheric and soil water loads revealed the highest effects among the three types of loads. The results revealed that the vertical deformation, caused by the soil water loads, ranged from −8 to 8 mm, while non-tidal oceanic load showed the lowest effect, with a vertical deformation range of −2–2 mm.
Surface mass loads, namely atmospheric, non-tidal oceanic, and soil water loads, showed different correlations with the geodetic height time series of CORS stations, demonstrating the influences of these surface mass loads. Therefore, in order to compare the obtained results, the influences of loads were first removed, then the WRMS ratio of the GNSS time series was calculated according to the following formula [
44]:
where
is the WRMS of the reconstructed GNSS geodetic height time series. Positive and negative values of
indicate a decrease and increase in the WRMS of the GNSS time series, respectively. It should be noted that the absolute value of
can reflect the load influences on the GNSS’s non-linear geodetic height time series.
On the other hand, the Pearson correlation coefficient (
) was computed in this study according to the following equation. It is widely used to measure the degree of correlation between two variables [
45,
46]:
where
denotes the reconstructed time series of the observed GNSS geodetic heights;
denotes the time series of the vertical deformation caused by surface mass loads. The R values range from −1 to 1, indicating strong negative and positive correlations, respectively, between the periodic phases of the two series.
In total, 12 stations were selected to assess the influences of the three surface mass loads on the reconstructed time series of CORS geodetic heights using
R and
WRMS values (
Table 4). Unlike the non-tidal oceanic load, the
and
WRMS values of atmospheric and soil water loads were all positive. According to the obtained results, the
and
WRMS values of the atmospheric load ranged from 0.50 and 0.66 and 7.61 to 12.80%, respectively, whereas the
and
WRMS values of the soil water load ranged from 0.64 to 0.81 and 20.54 to 34.80%, respectively. On the other hand, the non-tidal oceanic load was negatively correlated with the reconstructed time series of the CORS geodetic heights, which is consistent with the reported by Munekane and Nordman [
47,
48]. However, the absolute
WRMS value of the non-tidal oceanic load ranged from 3.24 to 6.39%, suggesting a low influence on the CORS geodetic heights. This result was due to the offsetting effects of the atmospheric and soil water loads, making the influence of the non-tidal oceanic load difficult to reflect in the time series of the CORS geodetic heights. In other words, atmospheric and soil water loads exhibited stronger influences than that of the non-tidal oceanic load. The
R and
WRMS values of total loads ranged from 0.81 to 0.89 and 33.84 and 43.93%, respectively (
Table 4). On the other hand, by removing the surface mass loads, decreases in the
values were observed. This finding demonstrates not only the reliability of the reconstructed CORS geodetic height time series and surface mass load deformations but also the effectiveness of the integrated solving process used in the present study.
In order to ensure the reliability of the inversion and reduce the influence of the low-quality CORS data, the quality of each CORS dataset was first evaluated before inversion, and then different weights were assigned to CORS stations. The initial weight of every station was set at 1, while the weight of the low-quality stations was decreased based on the entire time series data and their RMS values.
It was demonstrated earlier that the integration solution of the CORS data revealed a weekly GWSA grid over the 3 January 2018–30 December 2020 period was established, with the GWSA expressed in EWH. As is shown in
Figure 7, the GWSA showed significant spatial and seasonal variations. The results revealed decreases in GWS from February to June each year, which might be due to the significant seasonal and spatial decreases in groundwater recharge (e.g., rainfall infiltration). From August to the next January, however, increases in GWS were observed in the study area from August to January due to the increase in rainfall amounts. In addition, the inverted GWS using the CORS network showed a relatively high spatial resolution (
Figure 7).
The errors generated from the GNSS data processing, the surface mass model, and the uncertainty in the CORS inversion model may affect the accuracy of the GWSA inversion. The inverse distance weight interpolation method was used in this study to map the time series of the GWSA of CORS stations.
Table 5 shows the statistical results of the interpolated GWSA time series of 12 CORS stations. The maximum and minimum values of the inverted GWSA were −200 and 200 mm, respectively. In addition, there were some differences in the amplitude variation of GWSA at different CORS stations, indicating that the CORS inverse results had a high resolution. The mean and standard deviation (SD) values of GWSA at all CORS stations ranged from 3.16 to 15.03 mm and 55.87 to 110.39 mm, respectively. The reliability of the CORS inverse results was assessed in the subsequent part using the GRACE inverse results and groundwater monitoring station data.
In order to further analyze the temporal features of GWSA based on the sequence data of the GWSA grids, the study area was first divided into four sub-study areas, namely the eastern (BCHU, SYUN, and NJIA), northern (BAIS, YNYL, and JCHU), western (SUDI, YINJ, and TOBG), and southern (CHA3, MENT, and YNSD) sub-study areas, and then four CORS stations were selected randomly as examples. In
Figure 8, the curves show the time series of GWSA at the corresponding stations, while the bar charts indicate the precipitation amounts in certain sub-study areas observed at nearby weather stations (
Figure 1). In comparison with
Figure 7,
Figure 8 more directly reflects the temporal features of GWSA. The GWSA dynamics in different sub-study areas were relatively similar. Indeed, since groundwater recharge is derived mainly from precipitation in the study region, GWSA was strongly correlated with precipitation and exhibited significant seasonal differences. According to the obtained results, GWS exhibited main wave crest shapes. From February and March of each year, GWS showed the lowest values from February/March to June/July, then increased significantly from July to October due to the significant increase in the precipitation amounts, followed by a decrease in GWS in December and January. Therefore, precipitation was the main influencing factor on the GWSA in the study region.
In order to quantitatively analyze the groundwater drought in the study area within 3 years, the groundwater severity index (DSI) [
49] was used in this study. This index was calculated using the following formula:
where
denotes the year from 2018 to 2020;
represents the month from January to December;
represents the groundwater drought index DSI;
and
represent the mean and standard deviation of GWSA, respectively. The classification results of groundwater drought, derived from DSI, are reported in
Table 6. As reported above, the monthly GWSA data were obtained from the monthly average of the weekly GWSA time series.
Figure 9 shows the temporal variation of CORS-DSI in the study area from 2018 to 2020. The results showed a significant seasonal variation in CORS-DSI. In addition, the CORS-DSI values in the eastern and northern sub-regions of the study area were above 0.8 in most months, while only a few months showed CORS-DSI values slightly below 0.8, indicating a mild groundwater drought (
Figure 9a,b). On the other hand, the western and southern sub-regions of the study area showed several months with CORS-DSI values below −0.8, while the southern sub-region exhibited relatively significant groundwater drought, with CORS-DSI close to −1.3 over the November 2018–February 2019 and April 2020–August 2020 periods (
Figure 9c,d). It is worth noting that the groundwater drought analysis requires more than 10 years of observation data, while only 3 years of CORS station data were used in this study to invert the GWSA. Therefore, to obtain more detailed and accurate drought analysis results, it is suggested to consider long-term observation data in future groundwater drought analyses.
4.2. Comparison with GRACE Data
In order to assess the reliability of the CORS inverse results for GWSA, the GRACE inverse results for GWSA and the observed groundwater level data were used in this study. EWH is considered in the GRACE data to reflect the TWS. GWSA can be computed by removing soil water storage provided by the GLDAS data product. In this study, the period between October 2018 and December 2020 was considered due to the loss of data between GRACE and GRACE-FO. The monthly GRACE data were compared in this study with the monthly inverted CORS-based GWSA data during the year 2019. The obtained results are shown in
Figure 10.
Feng [
50] showed a delay in the GRACE-based land water storage changes by 2 months compared to precipitation changes. Therefore, a 2-month phase delay was performed for the GRACE time series. As can be seen from
Figure 10, relatively consistent GRACE- and CORS-based GWSA trends were obtained following the phase delay correction.
In total, 15 CORS were selected randomly as examples. The values in
Table 7 indicate the correlation coefficients of the CORS- and GRACE-based GWSA results. Due to the missing data in 2018, the correlation coefficients were computed in this study based on the 2019 data. Compared with the inversion CORS-based data, the GRACE data had a 2-month phase delay. After phase delay correction, the coefficients were significantly improved. Except for FGON, LJGC, and YNRL, showing correlation coefficients of 0.68, 0.69, and 0.65, respectively, the correlation coefficients of all other stations were above 0.7. The highest correlation coefficient was 0.85 in YNJD, indicating a strong correlation. The computed correlation coefficients showed a spatial variation due to the low spatial resolution of the inversion GRACE-based on data. As is shown in
Figure 10, the interpolation method used in this study resulted in relatively consistent trends of GRACE monitoring results at different sites without showing significant spatial differences. In addition, the CORS-based GWSA results were based on long-term monitoring GNSS data. Indeed, the density of the CORS stations in the study region allowed us to obtain a higher spatial resolution (
Figure 7), showing clear differences in the GWSA time series that are also clearer (
Figure 10).
Figure 11 shows the annual variation in CORS- and GRACE-based GWSA from 2018 to 2020. The spatial distribution characteristics of the two monitoring results were slightly consistent, showing relatively large annual changes in GWSA in the eastern and southern parts of the study area. The main spatial differences between the two monitoring results were observed in the south-central part of the study area. Overall, the amplitude of the annual variation in CORS-based GWSA was greater than that of GRACE-based GWSA. This finding may be due to the different monitoring methods of the two data products. Indeed, GRACE measures the integrated regional effect of mass redistribution. Its low spatial resolution makes it difficult to comprehensively reflect the effective information of the small-scale region, whereas the CORS data product is based on GNSS measurement methods, which provides real-time geometric deformation information at different locations in the study area, thereby fully reflecting the signal changes in the region.
In summary, both inverse results reflected the changes in GWSA. The results indicate that the GNSS-based CORS data are more sensitive to GWSA, showing obvious local spatial characteristics compared to those of the GRACE data.