Evaluation of Terrestrial Water Storage and Flux in North China by Using GRACE Combined Gravity Field Solutions and Hydrometeorological Models

Abstract

To enrich the understanding of the dynamic evolution of the water resources in North China, terrestrial water storage anomalies (TWSA) from January 2003 to June 2017 are derived using the new GRACE time-variable gravity field model Tongji-GraceCom. Additionally, the spatiotemporal characteristics of terrestrial water fluxes (TWF) at multiple time scales are analyzed based on the water budget theory in conjunction with hydrometeorological and statistical data. The results show that the quality of the Tongji-GraceCom model is superior to the state-of-art spherical harmonic models (CSR RL06 and JPL RL06), with the signal-to-noise ratio improving by 10–16%. After correcting the leakage errors with a reliable correction method, the inferred TWSA in North China presents a significant downward trend, amounting to −1.61 ± 0.05 cm/yr, with the most serious TWSA depletion mainly clustering in the south-central area. The TWFs derived from GRACE and from hydrometeorological elements are in good agreement and both exhibit significant seasonal fluctuations induced by tracking the periodic movements of meteorological factors. However, unlike precipitation which manifests in an increasing trend, both TWFs reflect the obvious decreasing trends, indicating that North China is suffering from severe water deficits, which are mainly attributed to the enhanced evaporation and extensive groundwater pumping for agricultural irrigation.

1. Introduction

North China (Figure 1), covering an area of 3.74 × 10⁵ km² and with a permanent population of 149 million, is one of the seven geographical regions in China, as well as part of the Haihe River Basin. The main provinces and municipalities include Hebei, Shanxi, Beijing and Tianjin, which are known as the famous grain production base, coal mining base, political and cultural center and advanced manufacturing base, respectively [1,2,3]. Thanks to the booming development of agriculture, industry and commerce, the dependence on water resources here has reached a staggering extent [4,5]. As a result, predatory exploitation has caused severe water crises, as well as a series of ecological and environmental disasters, such as land subsidence and soil salinization, which, in turn, have posed a serious threat to socio-economic stability [3,6,7]. To guarantee sustainable development, water-resource-management issues should be reconsidered by adopting effective means to investigate the elusive changes in terrestrial water flux (TWF), so as to provide data support for understanding the water movement mechanism and formulating conservation measures.

TWF describes the changes in terrestrial water storage (TWS) within a given hydrological system over time, which, in other words, is represented as the difference between input and output in total water quantity. Under natural conditions, the input for a catchment area mainly refers to precipitation, while the output includes evaporation and both surface and subsurface runoff [8,9]. Normally there are three ways to obtain the TWF components. The first one is to monitor their changes through ground-based observation stations. However, installing and maintaining observation stations is generally costly and labor-intensive, thereby it is impractical to construct dense networks for large-scale monitoring [10,11]. Especially for evaporation, only a few sparse stations are available in North China to our knowledge [1,12]. Satellite-based remote sensing provides an alternative way to measure TWF components at a large spatial and temporal scale. However, generating final products from raw satellite observations requires complicated location-specific calibration [9,13]. The third way is the use of modeling methods based on numerical simulation, which depend on the climatic conditions (air temperature, latent heat flux, etc.) and the surface conditions (vegetation index, soil type, etc.) used as model inputs. However, these conditions are generally cumbersome for both precipitation and evaporation, making it difficult to collect the complete required background information. Furthermore, excessive parameterization also brings in significant uncertainties associated with these models [12,14]. Despite these limitations, the TWF components acquired from both remote sensing and modeling methods are roughly satisfied for the study of TWF at large scales.

The satellite mission Gravity Recovery and Climate Experiment (GRACE) offers a precious opportunity to measure large-scale TWS with unprecedented accuracy [15,16]. TWS represents the total quantity of all forms of water stored on and below the surface of the Earth, including surface water, snow, ice, soil moisture and groundwater. In this manner, a simpler and more efficient method has been developed to determine the TWF, that is, directly solving the derivative of TWS with respect to time [8,9]. During the last two decades, GRACE-based time-variable gravity field models with various temporal and spatial resolutions have been widely applied to estimate the changes in TWS and TWF, and the accuracy has been verified to be sufficiently reliable in global [13,16,17,18,19] and representative regions [9,10,11,20,21]. The multifaceted applications of GRACE in North China have also scored tremendous achievements. Numerous studies have focused on estimating the change rates of TWS-related elements using GRACE-based models over different periods [1,2,22,23,24,25,26], and the driving factors and mechanisms of water resource change have been further investigated [27,28]. Furthermore, the environmental disasters induced by the depletion of water resources have been studied in-depth [3,6,7,29]. These efforts, not only facilitate the improvement of inversion methods for various hydrological elements but also provide sufficient references for realizing the serious challenges of water resources and formulating disaster prevention measures for North China. For their recent related studies, Moiwo et al. [1] and Pan et al. [24] analyzed the TWF before 2012 and revealed a water flux depletion in North China. However, their post-processing for GRACE data needs to be improved, especially the consideration of leakage errors. Meanwhile, the more in-depth drivers of flux depletion remain to be quantitatively elucidated.

The higher the accuracy of TWSA estimation, the more reliable the assessment of TWF. With the advances in modeling methods and post-processing technologies, the updated GRACE-based models are expected to overcome some shortcomings in previous models and reduce corresponding uncertainties. Therefore, the specific objective of this study is to re-estimate the TWS change in North China by using the latest GRACE time-variable gravity field solution, the Tongji-GraceCom model. The good performance of Tongji-GraceCom in reducing high-frequency noise is promising for achieving more accurate TWS estimates in our study area. To address the signal leakage problem generated by GRACE post-processing, an effective leakage-correction method is adopted to restore the leaked signals. Combining the inferred TWS and hydrometeorological elements (precipitation, evaporation and runoff), we quantitatively evaluate the spatiotemporal variability characteristics of TWF based on the water budget theory and further determine the driving factors, which is beneficial to establish targeted regulation strategies for decision-makers. In the following, Section 2 introduces the data and methodology. Section 3 reports the evaluation results of TWS and TWF in North China, as well as an applicability test for the signal-leakage-correction method. Discussions regarding the methods used and the results derived are presented in Section 4. Conclusions are drawn in Section 5.

2. Data and Methodology

2.1. Data Analysis

2.1.1. GRACE Data

The new Tongji-GraceCom model, whose spherical harmonic (SH) coefficients are up to d/o 96, was used in this study to estimate the monthly TWS anomalies (TWSA) from January 2003 to June 2017. Similar to the GRACE-FO solution by Chen et al. [30], the Tongji-GraceCom model is a combined gravity field solution, in which the SH coefficients up to d/o 6 are formulated with a daily period function, while the rest are modeled as the monthly mean SH coefficients. By using the combined SH coefficients with two kinds of temporal resolutions, the monthly average SH coefficients up to d/o 6 are calculated to form the final monthly Tongji-GraceCom model together with the rest of the SH coefficients. Benefitting from the high temporal formulation of the lower coefficients, the most prominent improvement for the Tongji-GraceCom model is the obvious reduction in high-frequency noise, coupled with the detectable mass variations within a month [30]. In original SH solutions, the degree-one coefficients associated with geocenter motion were not provided, and the C₂₀ coefficient tended to be less accurate [15]. Therefore, we added the degree-one coefficients from Technical Note 13 into SH solutions [31] and substituted the C₂₀ coefficients with satellite laser ranging solutions [32]. Moreover, the ICE6G-D model was used to correct the glacial isostatic adjustment (GIA) effects [33], and the 19 months of missing data over the study period in the TWSA time series were filled with the cubic spline interpolation method [23,24,28].

Three representative GRACE SH models (http://icgem.gfz-potsdam.de/home, accessed on 1 May 2023), including CSR RL06, JPL RL06 and Tongji-Grace2018, issued by the Center for Space Research (CSR), Jet Propulsion Laboratory (JPL) and Tongji University, respectively, were utilized to validate the quality of the Tongji-GraceCom model. To keep comparability, the post-processing strategies of the three contrast models were the same as that of Tongji-GraceCom. The comparisons were conducted in terms of the signal-to-noise ratio (SNR) of calculated TWSA under two conditions: (i) without filtering and (ii) filtered with de-correlation P4M6 and 300 km Gaussian smoothing [34]. SNR is defined as the ratio of the signal power to the noise power, and both the signal and noise were separated from the TWSA time series using the least-squares adjustment [35], with the detailed process being described in Section 2.2.3. It can be seen from Figure 2 that, when there is no filtering (condition i), SNRs of all four models show obvious stripe-shaped distributions, suggesting that geophysical signals are severely contaminated by striping noises. After conducting the filtering (condition ii), SNRs of the three models were significantly improved, especially in Shanxi, where the signal strength was much higher than the noise. On the whole, the Tongji-GraceCom model prevailed over the three contrast models, with mean SNRs of 0.50 and 2.37 in unfiltered and filtered conditions (

Table 1. Mean SNRs of TWSA from four GRACE models over the entire region.

Models	Mean SNR
	Without Filtering	Filtered with P4M6 and 300 km Gaussian Smoothing
CSR RL06	0.44	2.14
JPL RL06	0.42	2.11
Tongji-Grace2018	0.43	2.14
Tongji-GraceCom	0.50	2.37

), which means that the Tongji-GraceCom model is more effective to analyze the mass change characteristics in North China.

According to the above validations, the two-step filter (P4M6 and 300 km Gaussian smoothing) is sufficient to remove the noise in the GRACE models and thus was adopted as the eventual filtering method for post-processing of the Tongji-GraceCom model. However, the filtering process is inevitably accompanied by a certain degree of leakage errors, generally including “leakage-in” errors and “leakage-out” errors [2,36]. The leakage-in errors are reported to be weak in North China and can be ignored [22], therefore this paper only considers the signals within the study area leaking into the surrounding area, i.e., leakage-out errors. Here we employed an inversion method with leakage correction (see Section 2.2.1) to restore the lost signals as much as possible. To evaluate the correction effect, CSR mascon (version 02) [37] and JPL mascon solutions (version 02) [38] were adopted as references due to their significant advantages over standard SH solutions in capturing spatial localization and amplitude of the mass signal [17]. The spatial resolutions of CSR and JPL mascon solutions are 0.25° × 0.25° and 0.5° × 0.5°, respectively.

2.1.2. Hydrometeorological Data

The monthly gridded precipitation data, generated by interpolating 2472 rain gauge records [24,39], were downloaded from the China Meteorological Data Service Centre (http://data.cma.cn, accessed on 1 May 2023). These data were subjected to quality control and validated to have good applicability in China [24,29]. The bilinear interpolation method, a two-dimensional spatial interpolation algorithm, is easy to implement with full consideration of the information of the neighboring points, therefore it was used here to downscale the original spatial resolution of 0.5° × 0.5° to 0.25° × 0.25°, in order to match the TWSA spatial map [40]. Evaporation is generally difficult to quantify accurately due to the limited measurements. To reduce uncertainties, the monthly gridded evaporation data were computed by averaging two evaporation products from the Global Land Evaporation Amsterdam Model (GLEAM, https://www.gleam.eu/, accessed on 1 May 2023) [41] and the Noah model of Global Land Data Assimilation System (GLDAS, https://disc.gsfc.nasa.gov/datasets?keywords=GLDAS&page=1, accessed on 1 May 2023) [42]. Meanwhile, the Noah model was also used to output monthly gridded runoff data despite the runoff having been reported to be extremely limited in North China [1,43]. The above-mentioned hydrometeorological data all span the period from January 2003 to June 2017, with a spatial resolution of 0.25° × 0.25°. In addition, the WaterGAP Global Hydrology Model (WGHM [44]) (https://doi.pangaea.de/10.1594/PANGAEA.918447?, accessed on 1 May 2023) was employed to derive the monthly reservoir water storage (RWS) in North China from January 2003 to December 2016 with a spatial resolution of 0.5° × 0.5°.

2.1.3. Statistical Data

Annual statistical data on water resources supply and consumption of four provinces and municipalities were collected from the Water Resources Bulletins of Beijing (http://swj.beijing.gov.cn/, accessed on 1 May 2023), Tianjin (http://swj.tj.gov.cn/, accessed on 1 May 2023), Hebei (http://slt.hebei.gov.cn/, accessed on 1 May 2023) and Shanxi (http://slt.shanxi.gov.cn/, accessed on 1 May 2023), and from the China Statistical Yearbook (https://data.stats.gov.cn/, accessed on 1 May 2023). Annual water diversion data were also collected from the above Water Resources Bulletins and supplemented by the Haihe River Water Resources Bulletin (http://www.hwcc.gov.cn/, accessed on 1 May 2023).

The map of the area equipped for irrigation (AEI), with a spatial resolution of 5 arc minutes, was downloaded from the Food and Agriculture Organization of the United Nations (https://www.fao.org/aquastat/en/databases/, accessed on 1 May 2023), which represents the amount of area equipped for irrigation in percentage of the total area [45]. Additionally, maps of areas irrigated with groundwater and surface water were also downloaded.

2.2. Methodology

2.2.1. TWSA Inversion with Signal-Leakage Correction

The main challenge for TWSA inversion from the GRACE SH model is to optimize the trade-offs between noise reduction and signal attenuation since the filtering process for reducing noise inevitably involves signal attenuation and leakage problems [17]. To reduce the leakage errors, Tang et al. [46] established a linear relationship between the true mass change within the study area and the filtered mass change with appropriate grid division, and then iteratively adjusted it to infer the optimal estimate of true mass change, which has been further applied to estimate the mass changes in glacier and terrestrial water [22,36,47]. We used this method for the TWSA inversion and correction in North China and briefly introduce it as follows.

With the SH coefficients of the GRACE model, the filtered TWSA at any gridpoint is computed as [15]

$$\mathsf{\Delta }\overline{\sigma }\left({\theta }_j,\hspace{0.17em}{\lambda }_j\right)=\frac{a{\rho }_e}{3{\rho }_w}{\displaystyle \sum _{l=1}^{l_{\max }}\frac{2l+1}{1+k_l}{\displaystyle \sum _{m=0}^l{W}_{lm}{\overline{P}}_{lm}\left(\cos {\theta }_j\right)\left(\mathsf{\Delta }{C}_{lm}\cos m{\lambda }_j+\mathsf{\Delta }{S}_{lm}\sin m{\lambda }_j\right)}},$$

(1)

where $\Delta \overline{\sigma }\left(\theta ,\lambda \right)$ is the filtered TWSA at colatitude θ and longitude λ. a is the equatorial radius; ρ_e and ρ_w are the Earth’s average density and water density, respectively. ${\overline{P}}_{lm}\left(\cos \theta \right)$ denotes the fully normalized associated Legendre function of degree l and order m, and k_l is the Love number. W_lm is the degree- and order-dependent smoothing function. ΔC_lm and ΔS_lm are the fully normalized SH coefficients after the mean gravity fields from 2004 to 2009 are removed. In reverse, ΔC_lm and ΔS_lm can be represented as the summation of the true TWSA over the entire region,

$$\left[\begin{array}{l}\Delta C_{lm}\\ \Delta S_{lm}\end{array}\right]=\frac{3{\rho }_w}{4\pi a{\rho }_e}\frac{1+k_l}{2l+1}{\displaystyle \sum _{i=1}^I\sin {\theta }_i\Delta {\theta }_i\Delta {\lambda }_i\Delta \sigma \left({\theta }_i,{\lambda }_i\right){\overline{P}}_{lm}\left(\cos {\theta }_i\right)}\left[\begin{array}{l}\cos m{\lambda }_i\\ \sin m{\lambda }_i\end{array}\right],$$

(2)

where $\Delta \sigma$ is the true TWSA, and I denotes the number of gridpoints within the region. By substituting Equation (2) into (1), we can establish the linear relationship between the filtered TWSA at gridpoint j (j = 1, 2, …, J) and the true TWSA at gridpoint i (i = 1, 2, …, I) as follows:

$$\Delta \overline{\sigma }\left({\theta }_j,\hspace{0.17em}{\lambda }_j\right)=\frac{1}{4\pi }{\displaystyle \sum _{l=1}^{l_{\max }}{\displaystyle \sum _{m=0}^l{\displaystyle \sum _{i=1}^I\sin {\theta }_i\Delta {\theta }_i\Delta {\lambda }_i{\overline{P}}_{lm}\left(\cos {\theta }_i\right){\overline{P}}_{lm}\left(\cos {\theta }_j\right)W_{lm}\cos m\left({\lambda }_i-{\lambda }_j\right)\Delta \sigma \left({\theta }_i,\hspace{0.17em}{\lambda }_i\right)}}}.$$

(3)

Equation (3) can be reformulated in vector and matrix form as

$$\Delta \overline{\sigma }=\mathit{A}\cdot \Delta \sigma ,$$

(4)

where the bold letters $\Delta \overline{\sigma }$ and $\Delta \sigma$ are the J-dimensional and I-dimensional vectors of filtered and true TWSA, respectively. A is the J × I-dimensional coefficient matrix, whose element at the jth row and ith column is represented as

$$\mathit{A}\left(j,i\right)=\frac{1}{4\pi }{\displaystyle \sum _{l=1}^{l_{\max }}{\displaystyle \sum _{m=0}^l\sin {\theta }_i\Delta {\theta }_i\Delta {\lambda }_i{\overline{P}}_{lm}\left(\cos {\theta }_i\right){\overline{P}}_{lm}\left(\cos {\theta }_j\right)W_{lm}\cos m\left({\lambda }_i-{\lambda }_j\right)}}.$$

(5)

Since matrix A is ill-conditioned [22,36], the classic least-squares adjustment cannot derive a reasonable solution from Equation (4). Similar to Mu et al. [36], we adopt the Tikhonov regularization method [48] to yield a stable solution by minimizing the following cost function,

$$\min \hspace{0.33em}\left(\hspace{0.33em}{‖\mathit{A}\Delta \sigma -\Delta \overline{\sigma }‖}_2^2+\kappa {‖\Delta \sigma ‖}_2^2\hspace{0.33em}\right),$$

(6)

where κ is the regularization parameter and is determined based on the criterion by minimizing the mean square error criteria (MSE) [49,50]. Then, the optimal solution of TWSA is derived from the cost function (6) as

$$\Delta {\widehat{\sigma }}^R={\left({\mathit{A}}^{\mathrm{T}}\mathit{A}+\kappa \mathit{I}\right)}^{-1}{\mathit{A}}^{\mathrm{T}}\Delta \overline{\sigma },$$

(7)

where I is the identity matrix. In this study, North China is divided into a regular grid of 0.25° × 0.25° (note that the setting of 0.25° is only intended to cover the study area with a tight grid, not the real spatial resolution of GRACE). The TWSA signal to be corrected is denoted by the green gridpoints in Figure 1, while the filtered TWSA is denoted by red plus green gridpoints. The leakage range, approximately 100 km outside the study area, was determined using the manual cut-and-try method with different GRACE models in the given filtering conditions.

2.2.2. Water Budget Estimates

The water budget equation is used to characterize the water flow in and out of a region/basin hydrological system during a given period [8,51,52], and its specific expression in North China can be established as [1,24]

$$\frac{\mathrm{d}TWSA}{\mathrm{d}t}=P-E-R+WD,$$

(8)

where P is precipitation, E is evaporation and R is net outflow runoff. dTWSA/dt represents the TWF, which can be directly computed as the differential of the TWSAs of two consecutive months [13]. Water diversion (WD) is included as it is an important water supply way in North China during the dry season [24]. Irrigation water is partially lost via evaporation, and the remaining return flow is regarded as internalized water redistribution [1], which is therefore not considered in the water budget equation. For convenience, the left-hand side is noted as TWF_GRACE hereinafter, and the right-hand side is noted as TWF_PER or TWF_PERW (WD is only considered in the yearly scale).

2.2.3. Evaluation Metrics

SNR is a common index to evaluate the performance of the time-variable gravity field model, and its processing strategies are as follows [35,37,38]: firstly, the dominant signals in the TWSA time series, including bias, trend, acceleration and annual and semiannual terms (for some regions where inter-annual variations are significant, the octennial, quadrennial and S2 alias terms should also be considered) are estimated using a least squares adjustment [23]. Then, noises are computed by subtracting the dominant signals from the TWSA time series. Lastly, the SNR is computed as the ratio of the powers of signal and noise.

Pearson’s correlation coefficient [40] (PR) and root mean squared error [28] (RMSE) are used to quantitatively assess the correlation and difference between the time series u_i and v_i, which are defined as follows:

$$PR=\frac{{\displaystyle \sum _{i=1}^N\left(u_i-\overline{u}\right)\left(v_i-\overline{v}\right)}}{\sqrt{{\displaystyle \sum _{i=1}^N{\left(u_i-\overline{u}\right)}^2}{\displaystyle \sum _{i=1}^N{\left(v_i-\overline{v}\right)}^2}}},$$

(9)

$$\mathrm{RMSE}=\sqrt{\frac{1}{N}{\displaystyle \sum _{i=1}^N{\left(u_i-v_i\right)}^2}}$$

(10)

where $\overline{u}$ and $\overline{v}$ are the means of u_i and v_i, respectively. N is the number of epochs.

3. Results

3.1. TWSA Estimation in North China

3.1.1. Applicability Test of Signal-Leakage-Correction Method in North China

The TWSA estimate from the filtered Tongji-GraceCom model needs to be corrected due to unavoidable leakage errors, otherwise, it will introduce a large bias to the TWF_GRACE estimate. Therefore, we designed a simulation experiment to test the reliability of the leakage-correction method. First, The TWSA from CSR mascon and JPL mascon in December 2009 were treated as simulated signals (i.e., true signals). Then the simulated TWSAs were expanded into the SH models up to d/o 96 (Equation (2)). After implementing P4M6 and 300 km Gaussian filters on the SH models, they were converted back to TWSA (Equation (1)), which are noted as filtered TWSAs. As shown in Figure 3, the spatial distributions of filtered TWSAs were distorted, especially for CSR mascon-based simulations, where the largest mass loss of simulated TWSA occurred in the south-central region. This location, however, shifted to central North China after filtering. Meanwhile, the mass amplitude attenuated considerably. The total masses of simulated and filtered TWSAs were −22.04 and −13.14 km³, respectively, with an attenuation rate reaching 40.38% (

Table 2. Statistical results of simulation experiment (all masses are in volume units (km³) considering the different spatial resolutions of CSR and JPL mascon).

Model	Simulated Mass	Filtered Mass	Corrected Mass
CSR mascon	−22.04	−13.14	−21.18
JPL mascon	−25.72	−19.14	−25.82

). In the simulation with JPL mascon, the spatial distribution after filtering did not change a lot due to the relatively uniform distribution pattern of simulated TWSA, but the total mass also reduced significantly, with an attenuation rate of 25.58% (Table 2). Subsequently, we corrected the filtered TWSA using the leakage-correction method and compared it with the simulated TWSA. The masses of corrected TWSA were −21.18 and −25.82 km³ for CSR and JPL mascons, respectively, meaning that at least 96% of the simulated signals were recovered. More importantly, the misplaced signals were pulled back to the right locations. Therefore, the correction method can restore the leaked signals for both amplitude and spatial localization. It is worth noting that the total mass of corrected TWSA was slightly larger than simulated TWSA with JPL mascon, which can possibly be attributed to the less refined demarcations of the leakage ranges for different models.

3.1.2. Spatiotemporal Pattern of TWSA in North China

Given the good applicability of the leakage-correction method in North China, we therefore applied it to correct the TWSA derived from Tongji-GraceCom solutions. By using the least-squares harmonic analysis [23,29], the long-term spatial trends of TWSA changes were estimated. Meanwhile, those from CSR and JPL mascon solutions are also presented as further comparisons. As shown in Figure 4, the spatial patterns of TWSA trends from the three solutions were basically consistent, all reflecting the water depletion throughout North China. The depletion degree gradually aggravated from north to south, with a depleted center located in the south-central zone where agricultural activities are extensive, which highlights the uneven spatial distribution of water resources in North China.

Subsequently, the area-weighted TWSA time series are plotted in Figure 5, which were calculated with the weight proportional to the area of the gridpoint within the region [53]. As we can see, the TWSA time series from three solutions all present significantly negative trends over the whole study period, amounting to −1.40 ± 0.07, −1.61 ± 0.05, −1.61 ± 0.05 cm/yr (the uncertainties are fitting errors). However, there were obvious discrepancies in TWSA changes regarding different sub-periods. It started with a period of rapid decline (2004–2009), then tended to be stable, accompanied by a subtle recovery sign due to intensive precipitation (2010–2013), after which a sharp decline was present again (2014–2017). This implies that North China experienced an alternation of dry and wet in climate during the study period. Overall, the time series of TWSA from the Tongji-GraceCom model agreed well with those from both CSR and JPL mascon, with PRs of 0.91 and 0.92, and RMSEs of 3.38 and 3.59 cm, respectively. Therefore, without using any geophysical models as constraints, the TWSA derived from the Tongji-GraceCom model, after correcting the leakage errors purely based on GRACE information, can also achieve basically equivalent results to the mascon solutions. However, some differences can also be observed between Tongji-GraceCom and both mascon solutions, especially the local peak values, which can possibly be attributed to the different solution strategies of SH-type and mascon-type solutions, since constraints imposed on the mascon solutions may cause an underestimation of TWS amplitude in North China [37,38]. Finally, the TWSA estimate from Tongji-GraceCom with leakage correction was used to calculate the subsequent TWF_GRACE in North China.

3.2. Evaluation of TWF Based on the Water Budget Equation

3.2.1. Budget Components

The long-term trends of precipitation, evaporation and runoff were estimated and are shown in Figure 6. As we can see, the spatial patterns of the three budget components were similar or interlaced owing to their interdependent or mutually restrained relationships [54]. Therein, precipitation presented upward trends in most areas, with the wettest zones distributed in west-central Shanxi and surrounding Beijing, which mainly benefit from the abundant water vapor transported to North China by the East Asian monsoon [55]. Furthermore, the marginal zone in south Shanxi presented a weakly decreasing trend. As for evaporation, the entire study area was covered by an upward trend in the context of global warming, and the trend gradually increased in magnitude from the east-central plain to the western Shanxi and northern Hebei, due to elevation-dependent warming. Namely, the warming generally intensifies with altitude, which in turn induces more intense evaporation [56]. The variations in runoff occurred mainly in the boundary zones, among which southern North China presented a clear downward trend, while some sporadically increasing trends were reflected in northern Shanxi. Therefore, runoff was extremely limited in our study region and had little impact on the estimate of TWF.

We plot the TWSA time series and three budget components at multiple time scales in Figure 7. From Figure 7a,b, the monthly precipitation ranged from 0.03 to 21.88 cm, with a mean of 4.25 cm, and evaporation ranged from 0.32 to 11.41 cm and was 3.87 cm in mean. The significant difference between the maximum and minimum suggests an extremely uneven temporal distribution of water resources in North China. Similar to previous findings [1,43], runoff was highly limited, with a range of 0.44 to 1.96 cm and 0.33 cm in mean, due to repeated dam constructions in the waterways. The most notable feature in Figure 7 is that all components were dominated by significant seasonal variations. Especially precipitation and evaporation were in favorable agreement, with PRs of 0.90 and 0.96 on monthly and seasonal scales, respectively, indicating that both components play an important role in the land-atmosphere cycle. Except for the seasonal fluctuations, TWSA was also characterized by a long-term trend. Furthermore, TWSA changed in the wake of precipitation but with a time-lag of about 2 months (e.g., the TWSA recovery relative to the heavy rainfall from 2012 to 2013), which we attribute to the fact that TWSA includes precipitation that remained in the region before that month, and a complex and slow infiltration process is required for its exchange.

From Figure 7c,d, precipitation and evaporation were generally high in summer (June–August) and low in winter (December–February), with the peak and trough in July and January, respectively. The average TWSA time series of each month roughly follows a V-shaped curve by taking June as a demarcation point, implying that annual water depletion usually occurs before the onset of summer rain. TWSA drops continuously from January until reaching the intra-annual trough in June (−7.67 cm), with a total depletion of −5.23 cm, because of groundwater withdrawal for human activities such as agricultural irrigation [24,28]. Then the arriving rainy season prompts a sharp rise in TWSA from June to October. After that, the TWSA drops again driven by the secondary irrigation requirement for winter wheat, while the irrigation pressure with groundwater is effectively alleviated due to the accumulated rainfall [28]. Figure 7e shows that the inter-annual variations in precipitation, evaporation and runoff are relatively stable except for TWSA which performs a prolonged decreasing trend. Here we also present the change in yearly water diversion, which shows a significant increase after implementing the South-to-North water diversion project. Nonetheless, the effectiveness of this measure in alleviating the water crisis in North China is still open to question [25,26].

3.2.2. Spatiotemporal Pattern of TWF

Based on the water budget equation, TWF_GRACE and TWF_PER in North China were estimated, and their spatial patterns in terms of annual amplitude and long-term trend are depicted in Figure 8. Clearly, the annual amplitudes of TWF_GRACE and TWF_PER were basically consistent with means of 1.49 and 1.44 cm, respectively. The magnitude gradually increased from north to south, implying that water flux in southern North China is subjected to more significant seasonal fluctuations under the effect of land-atmosphere interaction. However, the long-term trends of TWF_GRACE and TWF_PER were somewhat different. The spatial pattern of TWF_GRACE confirmed the severe depletion of water resources in the south-central region. The spatial pattern of TWF_PER, however, was relatively capricious. The increasing TWF_PER was reflected in west-central Shanxi and surrounding Beijing where the precipitation increased (Figure 6), while a decreasing trend dominated the zones along the Taihang-Yanshan Mountains, which we attribute to intense forest evaporation inhibiting the effect of precipitation.

The time series of TWF_GRACE and TWF_PER at multiple time scales are plotted in Figure 9. From Figure 9a,b, the monthly TWF_GRACE ranged from −3.25 to 4.12 cm, with a mean of −0.09 cm, while monthly TWF_PER ranged from −2.25 to 5.50 cm and was −0.02 cm in mean. The two TWFs presented good agreement in both amplitudes and phases, with the PRs of 0.68 and 0.86 in monthly and seasonal scales, demonstrating that they were effective in characterizing the hydrological flux in North China, and their differences were further reduced on a larger time scale. From Figure 9c,d, TWF decreased with varying degrees in most months except for the rainy season (June–August). Therefore, although TWF was generally positive in summer and autumn and negative in winter and spring, an overall depletion of water flux from 2003 to 2017 can be observed, with decreasing trends of −0.023 ± 0.017 cm/yr in TWF_GRACE and −0.019 ± 0.011 cm/yr in TWF_PER. It should be noted that the monthly average TWF_GRACE arrived at peak one month later than the monthly average TWF_PER, mainly due to the lagging effect of precipitation on the recharge of terrestrial water.

Comparing Figure 9e with Figure 7e, we can see that TWF completely followed the changes in precipitation during the periods 2003 to 2007 and 2015 to 2016, indicating the key role of precipitation in controlling hydrological flux. However, from 2009 to 2013, the TWF ran counter to the change in precipitation, that is, precipitation increased while TWF decreased, which was induced by the enhanced evaporation and extensive water consumption by human activities [24,28,39,40,57], such as agriculture irrigation, industrial development and a rapidly growing population (analyzed in the subsequent Section 3.3). After adding the water diversion into the flux calculation (Figure 9f), TWF_PERD remained virtually unchanged, implying that the effect of current water diversion was not obvious in alleviating the depletion of the vast water resources system of North China. However, it is undeniable that water diversion (especially the South-to-North water diversion project) contributes an important water supply source other than precipitation for some typical regions (e.g., Beijing [25]) and is expected to benefit the whole region in the future.

3.3. Attributions of Water Resources Depletion

The water supply and consumption in North China are illustrated in Figure 10. From 2003 to 2017, the total volume of water supply increased from 31.23 km³ to 32.35 km³. The water supply constituents mainly included surface water and groundwater, accounting for 29.70% and 66.59%, respectively. Groundwater supply decreased from 23.39 km³ in 2003 to 16.83 km³ in 2017, implying the dependence on groundwater partially shifting to surface water. The main reason is that the reservoir water storage (RWS), one of the most important components of surface water, showed an overall upward trend, amounting to 0.06 ± 0.01 cm/yr, which indicates increased availability of surface water (Figure 11). Nevertheless, groundwater is still undoubtedly the most important water supply source due to its large base [57], and thus, high-intensity utilization is the main cause for the continuous decline in groundwater levels, as reported in previous studies [2,23,28,57]. To date, groundwater over-exploitation has evolved into a global issue [5]. The water consumption constituents mainly include agricultural, industrial, domestic and ecological water, accounting for 63.61%, 15.19%, 17.41% and 3.79%, respectively. According to Feng et al. [40], the agricultural land in North China reduced in the past decades with a rate of 7.16% from 2000 to 2020; hence, the agricultural water consumption decreased accordingly from 20.81 km³ in 2003 to 18.74 km³ in 2017. Additionally, industrial water consumption decreased to some extent. However, the water saved by agriculture and industry was not stored but used for residents’ lives and ecological construction due to the eye-popping expansion in population density [27,40], thus both domestic and ecological water consumption increased visibly. Therefore, it can be tentatively concluded that the decline of water flux is significantly related to human activities.

To link the water supply/consumption to TWF more directly, the spatial distribution of AEI is shown in Figure 12, and corresponding irrigation percentages with groundwater and surface water are shown in Figure 13. Hebei is one of the top-ranking provinces in China in terms of grain production, as well as a naturally densely irrigated area. As can be seen from Figure 12, most of the irrigated area in southern Hebei exceeds 50% and even reaches 75–100%, and its spatial distribution basically overlaps with the area where TWF_GRACE presented a significant decreasing trend (Figure 8). According to Figure 13, the most dominant water source for irrigation areas in southern Hebei is groundwater, which accounts for more than 75%, while surface water accounts for only 26% or less. Therefore, it can be concluded that extensive groundwater pumping for agricultural irrigation is mainly responsible for the water flux depletion in North China.

4. Discussion

4.1. Comparison of TWSA and TWF Estimates with Previous Studies

Our final estimates of the TWSA depletion rate in North China based on the Tongji-GraceCom model from 2003 to 2017 are −1.61 ± 0.05 cm/yr, which is equivalent to a volume rate of −5.98 ± 0.19 km³/yr. We compare it with similar studies in

Table 3. Summary of TWSA depletion rates in this work and previous studies.

Region	Area (km2)	Period	GRACE Model	Trend (cm/yr)	Reference
North China	3.7 × 105	2003–2017	Tongji-GraceCom	−1.61 ± 0.05	This work
North China	3.7 × 105	2003–2012	CSR RL05 SH	−1.23 ± 0.23	Wang et al. [3]
North China	3.7 × 105	2004–2015	Tongji-Grace2019	−1.00 ± 0.06	Feng et al. [28]
Haihe River Basin	3.2 × 105	2005–2012	RL05 SH of CSR, GFZ, JPL	−1.27 ± 1.4	Pan et al. [24]
Haihe River Basin	3.2 × 105	2003–2013	CSR mascon	−0.86 ± 0.08	Zhong et al. [39]
North China Plain	1.4 × 105	2003–2018	JPL mascon	−2.61	Zhang et al. [26]
North China	2.1 × 106	2002–2009	CSR RL04	−1.68	Moiwo et al. [1]

, from which we can see that the results are basically consistent. The main reasons for the differences are summarized as the inconsistencies in four aspects [24,28]: (i) the actual coverage of study areas, (ii) the study periods, (iii) the different versions of the GRACE solutions, and (iv) post-processing strategies for GRACE solutions. Especially our estimated trend is significantly larger than the results generated without restoring leakage signals, suggesting that leakage errors cause an underestimation of TWSA signals to some extent. The estimated TWF is also comparable to the results from Moiwo et al. [1] and Pan et al. [24]. Therefore, both TWSA and TWF estimated in this paper are reliable. In addition, from Figure 8, limited by the inherent resolution, TWF_PER can provide more details in spatial patterns, while TWF_GRACE is relatively smooth. From another point of view, however, directly monitoring the total water storage using GRACE offers a more convincing accuracy to the TWF_GRACE estimate, while the larger uncertainty of hydrometeorological elements reduces the reliability of TWF_PER. Therefore, combining two means to analyze the water flux variability is undoubtedly more reasonable.

4.2. Challenges for the Leakage-Correction Method

Limited by GRACE spatial resolution and post-processing strategies, the TWSA change derived from the Tongji-GraceCom model was subject to obvious leakage errors, hence a correction method in the spatial domain proposed by Tang et al. [45] and improved by Mu et al. [36] was employed to restore the leaked signals. However, we delineated the leakage range more reasonably with a manual cut-and-try method and better determined the regularization parameter using the minimum MSE method. Our simulation tests and application to real Tongji-GraceCom data all demonstrate that the lost signals can be accurately restored both in the amplitude and spatial pattern via this correction method. However, it still faces some shortcomings, one of which is that only the leakage-out errors were considered, while the leakage-in errors were ignored, thus limiting its applicability. In addition, the regularization matrix in Equation (7) is simply defined as an identity matrix; this is generally acceptable, but not optimal, since it means that the spatial correlation of the signals is ignored. If the spatial correlation is taken into account when constructing the regularization matrix, the leakage-correction effect is expected to be further improved.

5. Conclusions

Restricted by climate change and human activities, water resources in North China are facing serious threats. Therefore, clarifying the dynamic change in water flux is of great significance to the prevention and management of regional water security. In this contribution, the new time-variable gravity field combined model Tongji-GraceCom is used to quantify the TWSA changes in North China over the period January 2003 to June 2017, and the spatiotemporal characteristics of TWF are analyzed based on the water budget equation together with hydrometeorological and statistical data.

By conducting the tests under two cases, the Tongji-GraceCom model is demonstrated to outperform the RL06 SH models of CSR and JPL in terms of SNR due to its more refined processing strategies. To address the signal-leakage problem generated by post-processing, a correction method is employed to restore the lost signal. The simulation experiment suggests that the correction method can recover more than 96% of the simulated signals with identical distributions. In this manner, the TWSA from the Tongji-GraceCom model is corrected and then presents good agreement with that from CSR and JPL mascons, with PRs of 0.94 and 0.97, respectively. A significant downward trend of TWSA amounting to −1.61 ± 0.05 cm/yr was observed over the study period, indicating a severe water deficit in the study area. The degree of depletion gradually aggravated from north to south, eventually forming a depleted center in the south-central region, which therefore highlights the uneven distribution of water resources in North China.

The time series of TWF_GRACE and TWF_PER show good agreement at various time scales, at both the significant seasonal cycles and decreasing trends, with rates of decrease of −0.023 ± 0.017 cm/yr and −0.019 ± 0.011 cm/yr, respectively. The intra- and inter-annual distributions of TWF suggest that water flux is controlled by precipitation and evaporation, but also influenced by human activities. The spatial patterns of long-term trends in two TWFs are slightly different; thus, given the reliability of GRACE and the high resolutions of hydrometeorological elements, skillfully combining the two means to study water flux should be more reasonable. Eventually, by investigating the water supply and consumption records, and with the help of an AEI map and associated irrigation water types, we can conclude that the main cause for water depletion in North China, except for the enhanced evaporation, is the extensive groundwater pumping for agricultural irrigation.