2.1 Study Regions 2.1 研究区域

WE and CC are densely populated, industrialized, and frequently flooded. However, Zhengzhou and its environs have more dams and reservoirs and a larger proportion of arable land than WE, including the Xiaolangdi Dam (XD) with a total capacity of 12.8 km³ (Kong et al., 2022). In mid-July 2021, WE experienced intense rainstorm events and flooding caused by a persistent low-pressure system, which led to the accumulated precipitation reaching 200%–400% of the long-term average (1982–2010) in Western European countries. The record-breaking rainfall on 14 July 2021, caused widespread flooding of the Meuse and Rhine Rivers, resulting in severe casualties and property damage (Koks et al., 2021). Meanwhile, from 17 to 23 July 2021, Zhengzhou and its adjacent areas suffered from extraordinary rainfall and flooding due to the western Pacific subtropical pressure and the continental high pressure (Su et al., 2021; Xiao et al., 2022).
WE 和 CC 人口稠密、工业化且经常被洪水淹没。然而，郑州及其周边地区的水坝和水库数量比WE多，耕地比例更大，包括总容量为12.8公里 ³ 的小浪地大坝（XD）（Kong et al.， 2022）。2021 年 7 月中旬，西欧国家经历了持续低压系统引发的雨和洪水，导致西欧国家的累积降水量达到长期平均水平（1982-2010 年）的 200%-400%。2021 年 7 月 14 日创纪录的降雨导致默兹河和莱茵河大面积洪水泛滥，造成严重人员伤亡和财产损失（Koks et al.，2021）。同时，2021年7月17日至23日，受西太平洋副热带气压和大陆高压影响，郑州及其邻近地区遭受特异大降雨和洪涝灾害（Su et al.， 2021;Xiao 等人，2022 年）。

2.2 Inter-Satellite Measurements of GFO
2.2 GFO的星间测量

We use the inter-satellite measurements of GFO, KBR1B, and LRI1B, to derive TWS change (TWSC). Both KBR1B and LRI1B data sets encompass the inter-satellite quantities (range, its first derivative called range-rate, and its second derivative called range-acceleration) and the light-time correction, necessitated by the finite velocity of light (Yan et al., 2021). Moreover, an additional correction, the so-called antenna offset correction, needs to be added to KBR data. This correction projects the inter-satellite distance between individual satellites' KBR antenna phase centers into that along the line-of-sight direction. After these corrections, KBR1B and LRI1B reflect the static gravity signal, the non-gravitational accelerations and the perturbations caused by surface mass change, like floods.
我们利用GFO、KBR1B和LRI1B的星间测量来推导TWS变化（TWSC）。KBR1B 和 LRI1B 数据集都包含卫星间量（距离，其一阶导数称为距离速率，二阶导数称为距离加速度）和光时校正，这是有限光速所必需的（Yan et al.， 2021）。此外，还需要在KBR数据中添加额外的校正，即所谓的天线偏移校正。该校正将单个卫星的KBR天线相位中心之间的星间距离投影到沿视线方向的距离中。经过这些修正后，KBR1B和LRI1B反映了静态重力信号，非重力加速度以及由表面质量变化引起的扰动，如洪水。

This paper uses the KBR1B and LRI1B of release (RL) 04 with a latency of ∼2 weeks. During the period from June to August 2021, the LRI intermittently entered diagnostic mode for a total of 29 days and the GFO satellites were transitioned to nadir pointing. Hence, no LRI data was available during the diagnostic mode periods. Consequently, for the analysis of floods in WE, we examine 87 arcs of KBR1B data and 50 arcs of LRI1B data from June to August. Similarly, for studying floods in CC, we analyze 43 arcs of KBR1B data and 30 arcs of LRI1B data.
本文使用版本 （RL） 04 的 KBR1B 和 LRI1B，延迟为 ∼2 周。在2021年6月至8月期间，LRI间歇性进入诊断模式共29天，GFO卫星过渡到最低点指向。因此，在诊断模式期间没有可用的LRI数据。因此，为了分析WE的洪水，我们检查了6月至8月的87个KBR1B数据弧和50个LRI1B数据弧。同样，为了研究 CC 中的洪水，我们分析了 43 个 KBR1B 数据弧和 30 个 LRI1B 数据弧。

2.3 Soil Moisture Changes From Models
2.3 模型土壤水分变化

We use a land surface model (LSM) of Global Land Data Assimilation System (GLDAS) to derive soil moisture changes (SMC). GLDAS ingests satellite- and ground-based data to produce land surface results. GLDAS currently operates four LSMs: Mosaic, NOAH CLM and VIC (Rodell et al., 2004) and NOAH is use in this study. The temporal and spatial resolution of GLDAS/NOAH is 0.25° × 0.25° and 3 hours. In this study, we use four-layer soil moisture, rain precipitation rate and runoff from GLDAS/NOAH v2.1.
本文采用全球土地数据同化系统（GLDAS）的地表模型（LSM）推导土壤水分变化（SMC）。GLDAS摄取卫星和地面数据以生成地表结果。GLDAS目前运行着四种LSM：Mosaic，NOAH CLM和VIC（Rodell等人，2004年），NOAH用于本研究。GLDAS/NOAH的时空分辨率为0.25°×0.25°和3小时。在这项研究中，我们使用了来自GLDAS/NOAH v2.1的四层土壤水分、降雨量和径流。

When flooding occurs, the SMC is expected to be weaker than that in TWS due to the additional contribution of SWS that occurs in terms of inundation and deep infiltration. Therefore, the difference between GFO and LSM can be used to derive SWS changes (SWSC). Even so, since these models do not simulate human activities, such as groundwater extraction and dam construction, the difference may also be attributable to the anthropogenic influences (Yi et al., 2016).
当洪水发生时，由于SWS在淹没和深层渗透方面的额外贡献，预计SMC将弱于TWS。因此，GFO 和 LSM 之间的差异可用于推导 SWS 变化 （SWSC）。即便如此，由于这些模型没有模拟人类活动，例如地下水开采和大坝建设，因此差异也可能归因于人为影响（Yi et al.， 2016）。

2.4 Streamflow, Sedimentation, Reservoir Storage Within the Yellow River Basin
2.4 黄河流域内的径流、沉积、水库蓄水

The Yellow River Basin (YRB), renowned as one of the most disaster-vulnerable river basins in human history, has witnessed the implementation of a series of pivotal water conservancy management projects, including XD. The streamflow, sedimentation and reservoir storage data used in this study is measured by ground-based stations and obtained from the Information Center, Ministry of Water Resources, China.
黄河流域被誉为人类历史上最易受灾害影响的河流流域之一，见证了包括黄河流域在内的一系列关键水利管理项目的实施。本研究使用的流量、沉积和水库蓄水数据由地面站测量，并从中国水利部信息中心获得。

2.5 Daily and Monthly Snapshot of the Global Gravity Field
2.5 全球重力场的每日和每月快照

To compare with the GFO LGD measurements, we employ the daily gravity solution processed by ITSG (Kvas et al., 2019) and the monthly gravity solution processed by ITSG and JPL (NASA Jet Propulsion Laboratory, 2022) to generate synthetic LGDs. Both solutions are presented in the form of spherical harmonics coefficients (SHCs), with the ITSG daily solution having a maximum degree of 40, the JPL monthly solution having a maximum degree of 96 and the ITSG monthly solution having a maximum degree of 120.
为了与 GFO LGD 测量值进行比较，我们采用 ITSG 处理的每日重力解（Kvas 等人，2019 年）和 ITSG 和 JPL（NASA 喷气推进实验室，2022 年）处理的月重力解来生成合成 LGD。两种解都以球谐波系数 （SHC） 的形式表示，ITSG 每日解的最大度数为 40，JPL 月度解的最大度数为 96，ITSG 月度解的最大度数为 120。

3.1 Processing LGD From GFO L1B Data
3.1 从GFO L1B数据处理LGD

In accordance with the algorithm developed by Han, Ghobadi-Far, et al. (2021), LGD is computed as follows: First, we use Gravity Recovery Object Oriented Programming System to integrate dynamic reference orbits of GFO twin satellites (Mayer-Gürr et al., 2021), and Table 1 provides a full compilation of perturbation models and GFO measurements, including Earth's gravity force, solid Earth tide, ocean tide, N-body perturbation, non-gravitational force, atmosphere and ocean de-aliasing, etc. Notably, the Earth's gravity force is calculated by combining the JPL monthly L2 solution (degrees 0–96) with the high-degree (97–200) portion of GOCO06s for a full consideration of global gravity field before the flooding occurrence. This hybrid gravity field is an equivalence of rectifying low-degree temporal gravity signals that are not captured by GOCO06s through the integration of JPL data (Ghobadi-Far et al., 2020, 2022). Then, we synthesize range-rate using the integrated orbits and derive range-rate residual by subtracting the range-rate in LRI1B and KRB1B from the synthetic reference range-rate. Next, the LGD is computed by filtering range-acceleration residual—the numerical difference of the range-rate residual—by the frequency domain transfer function (Z(f) = 1.0 + 3.5⁻⁴f ^−1.04) described in Ghobadi-Far et al. (2018). As shown in Figures 4c and 4f, the LGD reflects the instantaneous gravity perturbation caused by TWSC referenced to the mean TWS in June 2021.
根据Han， Ghobadi-Far， et al. （ 2021）开发的算法，LGD的计算方法如下： 首先，我们使用重力恢复面向对象的规划系统来整合GFO双卫星的动态参考轨道（Mayer-Gürr et al.， 2021），表1提供了扰动模型和GFO测量的完整汇编，包括地球的重力， 固体地球潮汐、海洋潮汐、N体扰动、非引力、大气和海洋去混叠等。值得注意的是，地球的重力是通过将JPL每月L2解（0-96度）与GOCO06s的高度（97-200度）部分相结合来计算的，以充分考虑洪水发生前的全球重力场。这种混合重力场是通过整合 JPL 数据来纠正 GOCO06 未捕获的低度时间重力信号的等价物（Ghobadi-Far 等人，2020 年，2022 年）。然后，我们使用积分轨道合成距离率，并通过从合成参考距离率中减去LRI1B和KRB1B中的距离率来推导出距离率残差。接下来，通过Ghobadi-Far等人（2018）中描述的频域传递函数（Z（f）= 1.0 + 3.5 ⁻⁴ f ^−1.04 ）滤波距离-加速度残差（距离-速率残差的数值差）来计算LGD。如图4c和图4f所示，LGD反映了2021年6月TWSC与平均TWS相关的瞬时重力扰动。

Figure 1 compares the KBR and LRI LGD with and without reference orbits on 17 July 2021. Below 10 mHz, the reference-free LGDs from KBR/LRI are four orders of magnitude smaller than the reference-reserved counterparts, indicating that the subtraction of the reference orbits is effective in removing background signals at mid and low frequencies. Furthermore, the frequency components for reference-free KBR LGD and LRI LGD show similarity, demonstrating mutual validation of data quality. The SNRs of the reference-free KBR and LRI LGD reach one at 25 and 40 mHz, respectively. Beyond the frequencies where the SNR equals one, the LGD components are predominantly influenced by high-frequency noise that can hardly be reduced by the reference orbits. Additionally, the LGD component at 10 mHz corresponds to gravity signals at degree ∼54, or a surface gravity anomaly with a scale of ∼360 km. Therefore, the LGDs of KBR and LRI are capable of capturing the flooding in WE and CC during July 2021. To suppress the high-frequency stochastic noise, we apply a band-pass filter with cutoff frequencies of 1 and 12 mHz for the KBR LGDs and 1 and 30 mHz for the LRI LGDs. It is to mention that the LGDs used in the subsequent text refer to the reference-free LGDs. Furthermore, it is important to note that the discontinuity in the reference-free LRI LGD (black box in Figure 1) is likely due to the different error levels between the JPL temporal gravity model and the GOCO06s.
图 1 比较了 2021 年 7 月 17 日有和没有参考轨道的 KBR 和 LRI LGD。在10 mHz以下，KBR/LRI的无参考LGD比保留参考的LGD小4个数量级，表明减去参考轨道可以有效地去除中低频的背景信号。此外，无参考KBR LGD和LRI LGD的频率分量具有相似性，表明数据质量相互验证。无参考 KBR 和 LRI LGD 的 SNR 分别在 25 和 40 mHz 时达到 1。除了 SNR 等于 1 的频率之外，LGD 分量主要受高频噪声的影响，而参考轨道几乎无法降低这些噪声。此外，10 mHz 的 LGD 分量对应于 ∼54 度的重力信号，或尺度为 ∼360 km 的地表重力异常。因此，KBR 和 LRI 的 LGD 能够捕获 2021 年 7 月期间 WE 和 CC 的洪水。为了抑制高频随机噪声，我们应用了一个带通滤波器，KBR LGD的截止频率为1和12 mHz，LRI LGD的截止频率为1和30 mHz。值得一提的是，后续文本中使用的 LGD 是指无引用的 LGD。此外，需要注意的是，无参考LRI LGD（图1中的黑匣子）的不连续性可能是由于JPL时间重力模型和GOCO06之间的误差水平不同。

3.2 Synthesize LGD From Models
3.2 从模型合成LGD

3.3 Estimation of TWSC
3.3 TWSC的估计

4.1 Temporal Evolution of Floods
4.1 洪水的时间演变

Following the algorithm in Figure 2a, we obtain the GFO LGD from KBR1B and LRI1B relative to the monthly mean gravity field of June 2021 (the month right before the flooding occurs). Our data processing covers the period from June to August 2021, including 87 arcs (3°–13°E and 20° to 70°N) crossing over the study area in WE (∼396,215 km²) and 43 arcs (112°–119°E and 10° to 60°N) over the study area in CC (∼285,218 km²). Figures 4a and 4d show the ground tracks ranging from 20° to 70°N in WE and 10 to 60°N in CC, respectively. Figures 4b and 4e show the daily average precipitation from GLDAS within each study area. Figures 4c and 4f compare the GFO LGD measurements, the synthetic LGDs from GLDAS SMC and those from ITSG daily solution. To facilitate visual comparison across different times, we incrementally accumulated 3 nm/s² to the LGD data of each arc in Figure 4c and 5 nm/s² to the data in Figure 4f. This separation aids in intuitively analyzing the variation trends of LGD anomalies.
按照图 2a 中的算法，我们从 KBR1B 和 LRI1B 获得了相对于 2021 年 6 月（洪水发生前一个月）的月平均重力场的 GFO LGD。我们的数据处理涵盖 2021 年 6 月至 8 月期间，包括 87 条弧线（3°-13°E 和 20°-70°N）越过 WE 的研究区域（∼396,215 公里 ² ）和 43 条弧线（112°–119°E 和 10° 至 60°N）越过 CC 的研究区域（∼285,218 公里 ² ）。图 4a 和 4d 分别显示了 WE 的 20° 至 70°N 和 CC 的 10 至 60°N 的地面轨迹。图4b和图4e显示了每个研究区域内GLDAS的日平均降水量。图 4c 和 4f 比较了 GFO LGD 测量值、GLDAS SMC 的合成 LGD 和 ITSG 日常溶液的测量值。为了便于在不同时间进行视觉比较，我们对图4c中每个弧的LGD数据进行了3 nm/s ² 的增量累积，对图4f中的数据进行了5 nm/s ² 的累积。这种分离有助于直观地分析LGD异常的变化趋势。

The Sahara Desert is characterized by minimal hydrological processes, leading to subtle gravity changes that are presumed to be negligible. Consequently, both the measured LGDs and the synthetic LGDs (Figure 4c) display magnitudes on the order of 0.1 nm/s², underscoring the inherent uncertainty in LGD computations, typically at the level of a few 0.1 nm/s². Moreover, the independent KBR and LRI LGD measurements (Figure 4c) show similar temporal patterns, demonstrating the mutual validation of LGD computation, and also suggesting that the discontinuity in Figure 1 has minimal impact on short-term and regional studies such as monitoring of flooding events. However, it is crucial to recognize the potential limitations of the ad-hoc hybrid gravity field for long-term and large-scale applications of satellite gravimetry.
撒哈拉沙漠的特点是水文过程极少，导致细微的重力变化，据推测可以忽略不计。因此，测量的LGD和合成的LGD（图4c）都显示出0.1 nm/s ² 的量级，强调了LGD计算中固有的不确定性，通常在0.1 nm/s ² 的水平上。此外，独立的KBR和LRI LGD测量（图4c）显示出相似的时间模式，证明了LGD计算的相互验证，也表明图1中的不连续性对短期和区域研究（如洪水事件监测）的影响最小。然而，至关重要的是要认识到临时混合重力场对卫星重力测量的长期和大规模应用的潜在局限性。

The GFO LGD around 50°N indicate the TWSC in the WE study region. Priori to day of year (DOY) 186 (July 5), the GFO LGD and the GLDAS LGDs show a near convergence around 50°N, owing to the absence of surface flooding. In essence, the TWSC, as detected by GFO, can be attributed to the alteration in SMC. However, discernible divergence between the observed and synthetic LGDs commenced as early as July 5, coinciding with a series of daily rainfall events. This suggests a growing contribution from SWSC, and that the soil had likely become saturated since July 5. Consequently, the notable surge of precipitation on July 13 and 14 (DOY 194 and 195) (Figure 4b) accentuated the SWSC, leading to a more noticeable divergence. Meanwhile, negative anomalies appeared in the GFO LGD around 50°N, changing from >−1 nm/s² to around −2 nm/s² (Figure 4c), indicating the TWSC surplus due to the extensive floods. The results of the two LGDs converged as the flooding receded on July 21 and 23 (DOY 202 and 204).
50°N附近的GFO LGD表示WE研究区域的TWSC。先验到186年（7月5日）的某一天（DOY），由于没有地表洪水，GFO LGD和GLDAS LGD在北纬50°附近显示出接近收敛。从本质上讲，GFO检测到的TWSC可以归因于SMC的改变。然而，观测到的LGD和合成的LGD之间早在7月5日就开始出现明显的差异，这与一系列日降雨事件相吻合。这表明SWSC的贡献越来越大，并且自7月5日以来土壤可能已经饱和。因此，7月13日和14日（DOY 194和195）的降水量明显激增（图4b）加剧了SWSC，导致了更明显的差异。同时，在北纬50°左右的GFO LGD中出现了负异常，从>-1 nm/s ² 变化到-2 nm/s ² 左右（图4c），表明由于大范围的洪水，TWSC过剩。随着7月21日和23日洪水的消退，两个LGD的结果趋于一致（DOY 202和204）。

In Figure 4c, the GFO LGD reflect signals sources outside the study region as well. For example, the GFO LGD and the synthetics both contain positive anomalies between 52° and 70°N and around 45°N, likely attributed to TWS loss in Northern Europe and Southern Europe, including the Apennines, the Balkans and the Iberian Peninsula, respectively (Figure 4a). These signal sources underscore the necessity of peripheral regions divided in Figure 4. However, positive anomalies between 52° and 70°N in the synthetic LGDs continued from early July to early August, while the GFO LGD only shows such anomalies starting from July 29 (DOY 210) with a smaller latitude span, indicating the temporal evolution and spatial distribution of the LSM in some regions are different from the observation.
在图4c中，GFO LGD也反映了研究区域之外的信号源。例如，GFO LGD和合成物都包含52°至70°N和45°N左右的正异常，可能归因于北欧和南欧的TWS损失，包括亚平宁山脉、巴尔干半岛和伊比利亚半岛（图4a）。这些信号源强调了图4中划分外围区域的必要性。然而，从7月初到8月上旬，合成LGD在52°和70°N之间的正异常持续存在，而GFO LGD仅从7月29日（DOY 210）开始出现此类异常，纬度跨度较小，表明LSM在一些区域的时间演化和空间分布与观测结果不同。

The results for CC are shown in Figures 4d–4f. The TWSC in the CC study region is represented by the GFO LGDs around 35°N. With the advent of the rainstorm (Figure 4e) and the subsequent floods on DOY 201 (July 20), the negative anomalies around 35°N are reduced from about –1 nm/s² to <−2 nm/s², indicating an abrupt increase of TWSC in CC. Meanwhile, the positive anomalies around 28°N and the negative anomalies around 50°N indicate TWS deficits in Southern China and TWS increases in Mongolia. Contrary to the situations in WE, GFO LGD in the CC study region shows weaker negative anomalies than the synthetic GLDAS LGD.
CC 的结果如图 4d–4f 所示。CC研究区域的TWSC由35°N附近的GFO LGDs表示。 随着暴雨的到来（图4e）和随后的DOY 201（7月20日）洪水，35°N附近的负异常从约-1 nm/s ² 减少到<-2 nm/s ² ，表明CC中的TWSC突然增加。同时，28°N附近的正异常和50°N附近的负异常表明华南地区TWS不足，蒙古国TWS增加。与WE的情况相反，CC研究区域的GFO LGD显示出比合成GLDAS LGD更弱的负异常。

For better visualization, the relative magnitude differences between GFO and GLDAS are sampled at two key latitudes: 50°N (Figure 5b) and 35°N (Figure 5f), which are located in the center of the study regions. As stated previously, it is anticipated that the GFO series, reflecting the total changes in surface water, soil moisture, and groundwater, will have a greater (more negative) amplitude than the GLDAS series, which represents only changes in soil moisture. The results for WE conform to this expectation, but those for CC show an unexpected pattern—the TWSC is even less variable than its soil moisture component. It indicates that additional differences between GFO and GLDAS must influence, and we speculate that the most likely cause is the absence of the CC's considerable human activities in GLDAS.
为了更好地可视化，GFO和GLDAS之间的相对星等差异在两个关键纬度进行采样：50°N（图5b）和35°N（图5f），它们位于研究区域的中心。如前所述，预计反映地表水、土壤湿度和地下水总变化的GFO系列将比仅代表土壤湿度变化的GLDAS系列具有更大（更负）的振幅。WE的结果符合这一预期，但CC的结果显示出一个意想不到的模式——TWSC的可变性甚至小于其土壤水分。这表明GFO和GLDAS之间的其他差异必须产生影响，我们推测最可能的原因是CC在GLDAS中没有大量的人类活动。

The TWSCs relative to the June mean in the study regions are estimated based on the overpassing LGD arcs from June to August. Figures 5c and 5g show the high-resolution time series of TWSC estimated from the GFO LGDs and the SMC from GLDAS model of the study regions in WE and CC, respectively. Ten examples of LGD fitting (Figures 5d and 5h) illustrate the details of the inversion process. In Figure 5c, the TWSC from GFO LGDs consistently exceeded the SMC values. Their differences (gray lines) clearly present the temporal evolution of the SWSC, which was developing in a bimodal pattern peaking on July 4 and July 26 (DOY 185 and 207) due to the prolonged precipitation in June and July. From Figure 5a, an abrupt increase of ∼15 Gt in the SWSC began on July 13 (DOY 194) and lasted until July 19 (DOY 200), coinciding with the arrival of the mid-July rainstorm in WE. Afterward, as no further precipitation until July 24 (DOY 205), SWSC remained at ∼20 Gt, while GFO TWSC and SMC decreased. By late July, the TWSC and SWSC reached their maximum of approximately 40 Gt and 25 Gt, respectively. Within 12 days after August 3 (DOY 215), the accumulated water (∼25 Gt) for over a month vanished. The green bar in Figure 5c shows the TWSC between July and June based on the monthly L2 product, which only roughly provides the average quantity. This comparison illustrates how the inversion of the GFO LGD contributes to comprehending the temporal and magnitude characteristics of transient climate events compared to the traditional monthly resolution.
根据 6 月至 8 月的超 LGD 弧估计了研究区域相对于 6 月平均值的 TWSC。图5c和图5g分别显示了从WE和CC研究区域的GFO LGDs和GLDAS模型估计的TWSC的高分辨率时间序列。LGD拟合的10个示例（图5d和5h）说明了反转过程的细节。在图5c中，GFO LGD的TWSC始终超过SMC值。它们的差异（灰线）清楚地表明了SWSC的时间演变，由于6月和7月的长时间降水，SWSC以双峰模式发展，在7月4日和7月26日（DOY 185和207）达到峰值。从图5a可以看出，SWSC从7月13日（DOY 194）开始突然增加约15 Gt，一直持续到7月19日（DOY 200），恰逢7月中旬暴雨的到来。此后，由于直到7月24日（DOY 205）才有进一步的降水，SWSC保持在∼20 Gt，而GFO TWSC和SMC下降。到7月下旬，TWSC和SWSC分别达到约40 Gt和25 Gt的最大值。在8月3日（DOY 215）之后的12天内，一个多月的积水（∼25 Gt）消失了。图 5c 中的绿色条形显示了 7 月至 6 月期间基于月度 L2 产品的 TWSC，该产品仅粗略地提供了平均数量。这种比较说明了与传统的月度分辨率相比，GFO LGD的反转如何有助于理解瞬态气候事件的时间和震级特征。

The situation in CC presents a more intricate scenario. Following several days of rainfall from July 2 (DOY 183), TWSC steadily increased from −10 Gt to 10 Gt, mirroring a rise in SMC from 0 Gt to 30 Gt. Notably, heavy rainfall on July 20 (DOY 201) caused a significant ∼20 Gt jump in TWSC by July 21 (DOY 202) compared to the levels observed on July 18 (DOY 199). TWSC continued to rise by 7 Gt with subsequent rainfall and remains at ∼33 Gt until July 29 (DOY 210). Afterward, TWSC gradually decreased until August 8 (DOY 220). While the TWSC curve (red) suggests a seemingly typical flood evolution based on GFO LGD inversion, Figure 5g highlights a notable finding: throughout July, the TWSC estimated by GFO consistently falls below the SMC from GLDAS. The maximum deviation of the TWSC by GFO from the SMC reaches around −25 Gt from July 11 to July 17 (DOY 192 to 198). Interestingly, the heaviest precipitation occurred on July 20 (DOY 201). However, the residual (GFO–GLDAS, supposedly representing SWSC) on July 20 had already continuously dropped to nearly −17 Gt relative to the June average. This pre-flooding process mostly cancel out the following increase in SWSC caused by flooding. Logically, the SWSC cannot be negative because we indeed experienced widespread inundation (Feng, 2021). Therefore, a more plausible explanation is that the LSM overestimates the soil moisture. CC comprises several large populated cities and is undergoing intense manipulation of water resources, including dam construction, groundwater extraction and various ecological restoration (ER) programs (Cao et al., 2022), possibly transforming the environments in CC from nature-dominated to human-dominated.
CC 中的情况呈现出更复杂的情况。从7月2日（DOY 183）开始连续几天的降雨之后，TWSC从-10 Gt稳步增加到10 Gt，反映了SMC从0 Gt上升到30 Gt。 值得注意的是，7月20日（DOY 201）的强降雨导致7月21日（DOY 202）的TWSC大幅上升了∼20 Gt，而7月18日（DOY 199）观察到的水平。在随后的降雨中，TWSC继续上升了7 Gt，并一直保持在∼33 Gt，直到7月29日（DOY 210）。之后，TWSC逐渐下降，直到8月8日（DOY 220）。虽然TWSC曲线（红色）表明基于GFO LGD反转的看似典型的洪水演变，但图5g突出了一个值得注意的发现：整个7月，GFO估计的TWSC一直低于GLDAS的SMC。从7月11日到7月17日（DOY 192至198），GFO对TWSC与SMC的最大偏差达到-25 Gt左右。有趣的是，最强的降水发生在 7 月 20 日（DOY 201）。然而，7月20日的残差（GFO-GLDAS，据称代表SWSC）相对于6月的平均值已经持续下降到近-17 Gt。这种洪水前的过程主要抵消了洪水引起的SWSC的以下增加。从逻辑上讲，SWSC 不可能是负面的，因为我们确实经历了广泛的洪水泛滥（Feng，2021 年）。因此，一个更合理的解释是LSM高估了土壤湿度。CC 由几个人口稠密的大城市组成，并且正在经历对水资源的密集操纵，包括大坝建设、地下水开采和各种生态恢复 （ER） 计划（Cao et al.， 2022），可能会将 CC 的环境从自然主导转变为人类主导。

4.2 Human Activities Not Covered in GLDAS
4.2 GLDAS未涵盖的人类活动

Water resources in the CC region is strongly manipulated by human activities, particularly in terms of dam building and groundwater extraction. These human activities are not accounted for in the GLDAS model but included in GFO observations. Therefore, the examination of the ∼25 Gt deficit in GFO–GLDAS allows for an exploration of human effects. The XD located in the study region ranks as the largest dam in the middle and downstream of YRB (inset in Figure 6) and it is the main factor we examined here. The XD has at least three impacts on local mass transport that may result in changes in GFO–GLDAS values. First, the GLDAS model lacks representation of the water storage in reservoirs. The reservoir storage of the XD changes yearly and keeps a relatively high-water level most of the year (Figure 6a). As a countermeasure against potential advent of floods in July every year, the XD releases its storage in advance from June and maintains the lowest water level in July until resuming water retention in August. In 2021, the monthly mean reservoir storage reduced from 4 Gt in June to 0.3 Gt in July.
CC地区的水资源受到人类活动的严重操纵，特别是在大坝建设和地下水开采方面。这些人类活动没有被纳入GLDAS模型，但被纳入GFO观测。因此，对GFO-GLDAS中∼25 Gt赤字的检查允许探索人类影响。位于研究区域的XD是YRB中下游最大的大坝（图6插图），也是我们在这里研究的主要因素。XD对局部质量输送至少有三个影响，可能导致GFO-GLDAS值的变化。首先，GLDAS模型缺乏对水库储水量的表示。XD的水库蓄水量每年都在变化，一年中的大部分时间都保持着相对较高的水位（图6a）。为了应对每年7月可能发生的洪水，XD从6月开始提前释放蓄水，并在7月保持最低水位，直到8月恢复蓄水。2021年，月平均水库蓄水量从6月的4 Gt减少到7月的0.3 Gt。

Second, together with upstream dams, water supply from the Yellow River runoff to the local water system may be partially intercepted. By comparing the in-situ runoffs observations in the Yellow River with the simulated one in GLDAS simulations, we find that the GLDAS model overestimates the accumulated runoff at the XD by about 8 Gt during the study period, which is likely stems from a dozen of dams in the upper stream (Xie et al., 2019). The deficit indicates that the study region is less replenished by upper stream than GLDAS suggests, potentially resulting in an equivalent loss in TWS. Third, as the Yellow River is abundant in sediment (its particular water color also gives its name), the timely water storage and release of the XD creates artificial flood peaks to scour and transport sediment, thereby reducing the siltation of downstream of the YRB. We estimate the mass change in sediment content in the river, although it is crucial to note that in-situ measurements of sediment content are notably incomplete (Figure 6c). As a result, the estimation is based on the maximum observed value in early July, approximating it to be around 2 Gt.
其次，与上游大坝一起，黄河径流到当地水系统的供水可能会被部分截留。通过比较黄河原位径流观测结果与GLDAS模拟结果，我们发现GLDAS模型在研究期间高估了XD的累积径流约8 Gt，这可能源于上游的十几座水坝（Xie et al.， 2019）。赤字表明，研究区域上游的补充比GLDAS所暗示的要少，这可能导致TWS的等效损失。第三，由于黄河泥沙丰富（黄河特殊的水色也得名），黄河的及时蓄水和放水形成了人工洪峰，冲刷和输送泥沙，从而减少了黄河下游的淤积。我们估计了河流中沉积物含量的质量变化，但必须注意的是，沉积物含量的原位测量明显不完整（图6c）。因此，估计是基于7月初的最大观测值，大约为2 Gt。

Our investigation into these three contributors that directly reflect the human interference with water resources in the YRB accounts for 14 Gt of the total 25 Gt mass deficit. In fact, the enormous civil and agricultural water use can greatly exaggerate the observed reduction of water in reservoirs and runoff. Accurate model and quantification of these human activities is beyond the scope of this study. Annual water withdrawals in the YRB have steadily increased from 33.6 Gt in 2003 to 40.5 Gt in 2021 (http://www.yrcc.gov.cn/other/hhgb). Additionally, the ER programs in the YRB drives dominantly an increase in natural land cover types (such as forest and grassland) at the expense of human-intensive land uses (such as farms), resulting in a severe 3.6 Gt/year loss in TWS from 2002 to 2021.
我们对这三个贡献者的调查直接反映了人类对 YRB 水资源的干扰，占总 25 Gt 质量赤字的 14 Gt。事实上，大量的民用和农业用水会大大夸大观察到的水库和径流中的水量减少。这些人类活动的准确建模和量化超出了本研究的范围。YRB 的年取水量从 2003 年的 33.6 Gt 稳步增加到 2021 年的 40.5 Gt （http://www.yrcc.gov.cn/other/hhgb）。此外，YRB 中的 ER 计划主要推动了自然土地覆盖类型（如森林和草原）的增加，而牺牲了人类密集型土地利用（如农场），导致 2002 年至 2021 年的 TWS 严重损失 3.6 Gt/年。

Our results reveal a significant shift in water resource allocation and condition due to extensive and long-term use and manipulation. This has led to differences between LSM simulations (e.g., 50 Gt simulated mass increase) and observed reality (39 Gt). This divergence highlights the substantial impact of human activities on hydrological processes, especially in regions with extensive water management infrastructure.
我们的研究结果显示，由于广泛和长期的使用和操纵，水资源分配和条件发生了重大变化。这导致了LSM模拟（例如，50 Gt模拟质量增加）和观察到的现实（39 Gt）之间的差异。这种差异凸显了人类活动对水文过程的重大影响，特别是在拥有广泛水管理基础设施的地区。

4.3 Cross-Validation With ITSG Daily Solution
4.3 与ITSG日常解决方案的交叉验证

To further access the effectiveness and accuracy of our LGD inversion method, we conducted a comparative analysis with the ITSG daily solution, known for its success in flood monitoring (Gouweleeuw et al., 2018). As depicted in Figure 7, we compare the TWSC estimated from GFO LGD and the ITSG daily solution for both the WE and CC cases spanning from June to October 2021. In the WE case, the TWSCs from both GFO LGD and ITSG daily solution aligned during the flood development and peaking stages, demonstrating the detectability of GFO LGD observations in this flooding event. However, we noted that the ITSG daily solutions experienced a suspiciously giant post-flooding decline in September and October (purple shaded area in Figure 7a), reaching the lowest point on September 6. This amount of mass loss is equivalent to 1 year's melting of the Greenland Ice Sheet and is therefore physically impossible. As a result, the overall RMSE between the two estimates reaches 39.47 Gt over the entire period.
为了进一步了解我们的 LGD 反演方法的有效性和准确性，我们与 ITSG 日常解决方案进行了比较分析，该解决方案以其在洪水监测方面的成功而闻名（Gouweleeuw 等人，2018 年）。如图 7 所示，我们比较了 2021 年 6 月至 10 月期间 WE 和 CC 案例的 GFO LGD 和 ITSG 每日解决方案估计的 TWSC。在WE案例中，来自GFO LGD和ITSG日溶液的TWSC在洪水发展和峰值阶段对齐，证明了GFO LGD观测值在这次洪水事件中的可探测性。然而，我们注意到，ITSG每日解决方案在9月和10月经历了可疑的巨大洪水后下降（图7a中的紫色阴影区域），在9月6日达到最低点。这种质量损失相当于格陵兰冰盖1年的融化，因此在物理上是不可能的。因此，在整个期间内，两个估计值之间的总体RMSE达到39.47 Gt。

For the CC case, the RMSE was 13.32 Gt, indicating a better agreement compared to the WE case. In this case, against the background of a seasonal uptrend (orange line in Figure 7b), the LGD TWSC time series shows a notable jump caused by rainfall (red shaded area). This sharp jump reflects the complete flooding process of rapid onset, retreat and return to the seasonal pattern. In contrast, the ITSG TWSC time series depicts the cumulative flooding session initiating much earlier on June 29th (DOY 180), 17 days before the LGD estimation, and barely captures the receding stages, resulting in a prolonged and flat flooding process (green shaded area). This indicates that stronger temporal filtering and smoothing are applied in the ITSG daily solutions. Moreover, we also show two suspicious mass change (>50 Gt) in the ITSG daily solution for the CC case. Besides, the standard deviations of ITSG TWSC values within the purple shaded area show higher variability compared to those outside the region. Specifically, the standard deviations outside the purple shaded area are 19.20 Gt and 9.53 Gt for the CC and WE cases, respectively, which are considerably lower than the values inside (26.99 Gt and 32.23 Gt).
对于CC案例，RMSE为13.32 Gt，表明与WE案例相比具有更好的一致性。在这种情况下，在季节性上升趋势的背景下（图7b中的橙色线），LGD TWSC时间序列显示出降雨引起的显着跳跃（红色阴影区域）。这种急剧的跳跃反映了快速开始、退去和回归季节性模式的完整洪水过程。相比之下，ITSG TWSC 时间序列描绘了 6 月 29 日（DOY 180）更早开始的累积洪水时段，比 LGD 估计早 17 天，并且几乎没有捕捉到消退阶段，导致洪水过程延长且平坦（绿色阴影区域）。这表明在 ITSG 日常解决方案中应用了更强的时间过滤和平滑。此外，我们还在 CC 案例的 ITSG 每日解决方案中显示了两个可疑的质量变化 （>50 Gt）。此外，与区域外相比，紫色阴影区域内的ITSG TWSC值的标准差表现出更高的变异性。具体而言，CC 和 WE情况的紫色阴影区域外的标准差分别为 19.20 Gt 和 9.53 Gt，远低于内部值（26.99 Gt 和 32.23 Gt）。

As the GFO LGD estimates are tuned to the regional characteristics and manual quality control is applied, they are expected to demonstrate greater quality stability and heightened sensitivity to storm-induced TWSC signals. Therefore, theoretically, our approach has an improved performance in accurately capturing the intricate dynamics of flood evolution.
由于GFO LGD的估计值根据区域特征进行了调整，并应用了手动质量控制，因此预计它们将表现出更高的质量稳定性和对风暴引起的TWSC信号的高度敏感性。因此，从理论上讲，我们的方法在准确捕捉洪水演变的复杂动态方面具有更高的性能。