GRACE and GRACE-FO data can provide global TWSA at monthly scales. In this study, the average of three types of GRACE and GRACE-FO solutions is estimated in order to characterize the variations of TWSA in the YRB and its individual subbasins during the period of 2003–2020, all of which are the latest versions of Release Number 06 (RL06). These products are provided by the Center for Space Research (CSR; at the University of Texas at Austin) (Save et al., 2016), the Goddard Space Flight Center (GSFC; at NASA) (Loomis et al., 2019) and the Jet Propulsion Laboratory (JPL; at NASA and California Institute of Technology, California) (Landerer et al., 2020) respectively. All these GRACE and GRACE-FO solutions represented by equivalent water thickness units (mm) are anomalies relative to the time-mean baseline during January 2004–December 2009. It should also be noteworthy that GRACE data are not available in a few months because of the problem of “battery management”. In addition, there was a gap period for 11 consecutive months from July 2017 to May 2018 between the GRACE and GRACE-FO satellites. Here we have not filled the data gaps between the two GRACE satellites with linear interpolation since it may not fully describe the seasonal variation of TWSA during these missing months. All these GRACE and GRACE-FO satellite data are available at https://podaac.jpl.nasa.gov (last access: 17 November 2022). As documented in previous studies (Long et al., 2014; Xie et al., 2022), there are slight differences between these three GRACE and GRACE-FO solutions when estimating the variation of regional TWSA. The differences between these three GRACE and GRACE-FO solutions mainly arise from the processing algorithms or constrained solutions.

In this study, daily time series of precipitation and temperature from 2003–2020 are provided by the China Meteorological Administration (CMA) (http://data.cma.cn/, last access: 17 November 2022) with a total of 150 National Meteorological Observatory stations distributed in the YRB (shown in Fig. 1). Areal precipitation in the YRB and its individual subbasins at daily scales can be calculated according to the Thiessen polygon method. Monthly precipitation for regions is calculated by summing all daily values of precipitation. Meanwhile, areal temperature in the YRB and its basins at daily timescales is calculated by directly averaging the respective daily temperature from all meteorological stations over regions. Similarly, monthly temperature estimates are calculated by summing all daily values of temperature.

From the Yangtze River Conservancy Commission of Ministry of Water Resources, daily streamflow observations during the period of 2003–2020 can be obtained at the Shigu hydrological station, the Yichang hydrological station, the Hankou hydrological station and the Datong hydrological station (shown in Fig. 1). More specifically, the Shigu station represents the outlet of the source regions of the Yangtze River basin (SYRB), the Yichang station represents the outlet of the upper regions of the Yangtze River basin (UYRB), the Hankou station represents the outlet of the upper and the middle regions of the Yangtze River basin (UMYRB), and the Datong station represents the outlet of the entire Yangtze River basin (YRB). Meanwhile, extreme flood events in the YRB and its individual subbasins during the study period can be extracted from daily time series of streamflow observed from the above hydrological stations (Tarasova et al., 2018). More details about how the extreme flood events are extracted will be described in the Sect. 4.4.

As documented in Xie et al. (2019a), soil moisture storage (SMS), as one of critical components of terrestrial water storage, usually shows a significantly positive correlation with variations of regional TWSA. Therefore, in this study we adopt the SMS (kg m-2) with a spatial resolution of 0.25∘ × 0.25∘ from the Global Land Data Assimilation System version 2.1 (GLDAS 2.1) Noah land surface model to estimate their correlations with regional TWSA derived from the GRACE and GRACE-FO satellite data. This product can provide the simulations of SMS at four different depths of soil layers from 0 to 200 cm, that is, 0–10, 10–40, 40–100 and 100–200 cm depths per 3 h. To keep consistent with the TWSA, the original value of SMS should be transferred into soil moisture storage anomaly (SMSA) values after subtracting the time-mean baseline during the period of 2004–2009. Furthermore, the temporal resolution of original SMS derived from GLDAS 2.1 Noah land surface model can be decreased from 3 h to 1 d and 1-month composite respectively, which is consistent with the methods applied in previous studies (Mulder et al., 2015; Mohanasundaram et al., 2021; Syed et al., 2008). An overview of all datasets used in this study can be found in Table 2.

The ANN is a black-box model which has the ability to imitate the thought processes of the human brain and thus can be applied to deal with complex and nonlinear problems (Bomers et al., 2019; Boucher et al., 2020; Lecun et al., 2015; Q. Wang et al., 2020). Among different types of ANNs, the multi-layer perceptron neural network (MLP) with the Levenberg–Marquardt back-propagation training algorithm is the most widely used method as it requires relatively less time in the process of convergence (Rumelhart et al., 1986; Xie et al., 2019a). Therefore, a three-layer MLP model and the logarithmic sigmoid as a transfer function are jointly used for temporal downscaling in this study, which has been proved to be effective and reliable in statistical downscaling (Nourani et al., 2018; Sharifi et al., 2019). This MLP model consists of three parts, namely, an input layer, a hidden layer and an output layer, all of which finally form a network through many neurons. Meanwhile, the weights, which are connections between different neurons, can adjust as learning proceeds until the most optimum network is derived in this process (Fig. 3a).

In this study, the variables included in the input layer are precipitation, temperature and SMS, whereas the variable included in the output layer is the detrended TWSA. Based on trial and error, the most optimal number of hidden neurons is set to five. After minimizing the discrepancy between the simulated TWSA with the observed results at the output layer, the most optimal network architecture can finally be obtained.

The recurrent neural network (RNN) (Rumelhart et al., 1986) is a unique type of deep learning algorithm that was developed to process sequential data and predict future trends. One of the most dominant features of the RNN layer is a unique feedback connection which can allow past information to continuously affect the current output. The characteristics of all related time series data can be eventually learned through this structure. The long short-term memory network (LSTM) is one of the most representative RNNs as it has a fabulous memory ability and can effectively avoid the vanishing gradient problem existing in other RNNs (Hochreiter and Schmidhuber, 1997; Guo et al., 2021). Considering the time series characteristics of meteorological data and TWSA data, the LSTM model is very suitable as a statistical downscaling model for its excellent capacity to process sequence-to-sequence learning problems.

One typical LSTM model usually consists of three layers, that is, an input layer, a hidden layer and an output layer (Fig. 3b). Different from other traditional ANNs, the LSTM model replaces the hidden block in RNNs with a memory cell state coupled with three logic gates, that is, the forget gate, the input gate and the output gate. In the training process, the memory cell state mainly stores the accumulation of past information. The input gate determines how much information of a new input flows into the memory cell state at the current time. Then, the useless information in long-term memory would be forgotten by the forget gate, which determines how much of the former moment is retained to the current time. Finally, the output gate determines how much information of the memory cell state is used to compute output (Bai et al., 2021; Wu et al., 2020; Vu et al., 2021).

Multiple linear regression (MLR) is a typical statistical approach that can be applied to establish the relationships between inputs and outputs (Sousa et al., 2007). This approach has a wide range of hydrological applications since it can explain the linkage between various variables well (Lyu et al., 2021; Ramesh et al., 2020; Sun et al., 2020). Here we assume that the GRACE-/GRACE-FO-derived TWSA is linearly regressed onto the meteorological variables (i.e., precipitation and temperature) and the SMS obtained from GLDAS 2.1 simultaneously, that is 1y=∑i=13ai×xi+b, where y represents TWSA at monthly (or daily) scales; xi (i=3) represents three independent inputs including precipitation, temperature and SMS at monthly (or daily) scales; ai represents the corresponding regression coefficients of each input, which can be calculated by the least-squares regression method; and b represents a constant offset.

A nonparametric algorithm suggested by Tarasova et al. (2018) is adopted to identify runoff events in this study, which has been widely applied in many different basins over the world because of its advantages in identifying flood events (Fischer et al., 2021; Giani et al., 2022; Lu et al., 2020; Winter et al., 2022). The brief procedure of this algorithm is described as follows: (1) picking out local minima within nonoverlapping 5 d windows with respect to the entire streamflow time series; (2) examining the extracted series of minima with the goal of finding turning points, all of which are usually defined as the points that are at least 1.11 times smaller than their neighboring minima; (3) reconstructing the base flow hydrograph according to the linear interpolation between the turning points, which are previously obtained in Step (2); and (4) screening the streamflow time series to identify runoff events after the separation of base flow. Traditionally, a typical runoff event can be characterized by three main components, namely peak, beginning and end points. A peak refers to the maximum of streamflow for a specific period. The beginning point refers to the closest point in time when total runoff is equal to base flow before the peak. Similarly, the end point denotes the closest point in time when total runoff is equal to base flow after the peak.

The flood potential index provides a surrogate measure of the potential flood risks for a specific region, which can be obtained from monthly average precipitation anomalies and GRACE-derived TWSA (Reager and Famiglietti, 2009). In this study, we further propose a new normalized daily flood potential index (NDFPI) with reference to Reager and Famiglietti (2009) and Abhishek et al. (2021). Compared to the original flood potential index, the NDFPI can not only provide useful information on the early signs of the region's transition from a normal state to a flood-prone situation, but also effectively detect the flood events at sub-monthly timescales, which is calculated via the following steps: 2TWSAdeft=TWSAmax⁡-TWSA(t-1), where TWSAdef(t) (mm) represents the terrestrial water storage deficit for a specific day (t) that is defined as the difference between the historic storage anomaly time series maximum during the entire period (TWSAmax⁡) and the storage amount from the previous day (TWSA (t-1)).

Then, the daily flood potential amount (DFPA) is further calculated as follows: 3DFPAt=Pt-TWSAdeft=Pt-(TWSAmax⁡-TWSA(t-1)), where DFPA (t) (mm) represents the daily flood potential amount for a specific day (t), P(t) (mm) represents the daily precipitation, and TWSA (t-1) (mm) represents the TWSA from the previous day (t-1).

Finally, we can calculate the normalized daily flood potential index (NDFPI) from the DFPA with the goal of removing the effects of hydrological heterogeneity varying from region to region and the typical difference between the storage change and precipitation that may not always result in floods (Reager and Famiglietti, 2009), which can be described as follows: 4NDFPI(t)=DFPA(t)-DFPAmin⁡DFPAmax⁡-DFPAmin⁡, where DFPAmax⁡ and DFPAmin⁡ represent the maximum DFPA and minimum DFPA during the study period respectively. The NDFPI indicates the corresponding probability of flood occurrence with a range from 0 to 1. More flooding is likely to occur when the NDFPI is closer to 1 for a specific region.

Monthly TWSA estimates during the extreme flood events occurred in the YRB can be reconstructed at regional scales based on the above three different learning-based models, namely the MLP model, the LSTM model and the MLR model. Meanwhile, these three models are further validated in four different basins covering the upstream to downstream parts of the Yangtze River in order to better evaluate their applications. For more detailed information about all these four different basins, the reader can also refer to Table S1 in the Supplement. According to previous findings in Liu et al. (2021), different periods of data used for training (i.e., identification of model parameter sets) and validation can eventually influence the corresponding performances of a specific model when simulating TWSA. Therefore, we design a total of three scenarios according to the way of dividing training periods and validation periods for a specific model. As shown in Fig. 2, periods of GRACE data used for training and validation in each experiment are listed, which include (1) Scenario 1, training period (January 2003–July 2014, a total of 129 months) and validation period (August 2014–December 2020, a total of 56 months); (2) Scenario 2, training period (June 2005–June 2018, a total of 129 months) and validation period (January 2003–May 2005 and July 2018–December 2020, a total of 56 months); and (3) Scenario 3: training period (October 2007–December 2020, a total of 129 months) and validation period (January 2003–September 2007, a total of 56 months).

Furthermore, three kinds of statistical measures including the root mean square error (RMSE), correlation coefficient (r), and Nash–Sutcliffe efficiency coefficient (NSE) are used in this study as they can jointly measure the matching quality in terms of both magnitude and phase between the simulated and the observed time series. These statistical measures are defined as 5RMSE=∑i=1N(xs,i-xo,i)2N,6r=∑i=1N(xs,i-x‾s,i)(xo,i-x‾o,i)∑i=1N(xs,i-x‾s,i)2×∑i=1N(xo,i-x‾o,i)2,7NSE=1-∑i=1N(xs,i-xo,i)2∑i=1N(xo,i-x‾o,i)2, where xs,i and xo,i represent the simulated and observed TWSA in month i, respectively; x‾s,i and x‾o,i represent the average of simulated and observed TWSA series; and N is the total months of observed (or simulated) TWSA available.

Figure 4 shows the monthly time series of SMSA, TWSA, streamflow and the main climatic variables including precipitation and temperature across the YRB during 2003–2020. The results show that monthly TWSA over the YRB has a wide range from -58.0 to 130.9 mm during the study period. Monthly TWSA estimated by three GRACE and GRACE-FO solutions changes synchronously with precipitation across the entire YRB, showing a significantly positive correlation between TWSA and precipitation (r=0.54; p<0.01) during the study period. According to the statistics collected by Yangtze River Conservancy Commission of Ministry of Water Resources, the accumulative rainfall across the entire YRB exceeds 680 mm in summer 2020 from April to October, which is far more than the mean rainfall (approximately 540 mm) during the same period from 2003 to 2019. Accordingly, TWSA reaches its maximum in July 2020 with an estimate of 130.9 mm during 2003–2020, reflecting the evolution of TWSA in response to heavy rainfall during this period. In addition to precipitation, TWSA is also highly consistent with temperature over the YRB during 2003–2020, showing a positive correlation coefficient of r=0.57 (p<0.01) with monthly temperature.

The GLDAS Noah-derived SMSA and GRACE-/GRACE-FO-derived TWSA both show a seasonal variation through the entire study period in the YRB, but there is a significant difference in the intensity of anomalies between them, especially in the summer season, as depicted in Fig. 4. This phenomenon can be explained by the discrepancies resulting from the components of SMSA and TWSA. Although the SMSA is an important component of the TWSA for many regions, the latter usually contains some other components, such as the anomalies of surface water and groundwater, besides the SMSA (Xie et al., 2021). There is a significant correlation between the TWSA and SMSA, with a positive correlation coefficient of r=0.84 (p<0.01), both of which reach maximum and minimum values almost simultaneously. In general, the TWSA shows a significant correlation with precipitation, temperature and the SMSA during the study period, all of which have been therefore selected as the inputs applied to simulate the monthly TWSA over different regions.

To achieve the temporal downscaling of monthly TWSA data and fill the missing months for TWSA, we should firstly build the relationships between GRACE-/GRACE-FO-derived TWSA and various hydroclimatic factors including precipitation, temperature and the SMSA at monthly timescales. The results of the TWSA are estimated by the mean value in different regions upstream of the corresponding hydrological stations shown in Fig. 1. In this study, three different models including MLP, LSTM and MLR are adopted to reconstruct TWSA for regions. Table 3 shows the summary of model performances in reconstructing monthly TWSA across the YRB during the study period. GRACE and GRACE-FO satellite data used for training (i.e., identification of model parameter sets) and validation shown in each scenario mainly depend on the periods of series of data, as suggested by Liu et al. (2021). According to Table 3, we find that all models including the MLP, the LSTM and the MLR with Scenario 3 show the best performances in simulating monthly TWSA under all three designed scenarios. This result indicates that the models with Scenario 3 are relatively superior to the models with the other two scenarios when simulating TWSA because the data in Scenario 3 contain more extremely high (or low) values during the study period in the process of training models. Therefore, in the following sections, we decide to directly divide the training periods and validation periods of all these models according to Scenario 3 (shown in Table 3) when simulating the monthly TWSA for other regions besides the YRB.

Figure 5 shows the comparison between the monthly TWSA derived from GRACE and GRACE-FO satellite data and that simulated by different models for all regions during 2003–2020. The corresponding evaluation values are also presented in this figure. We find that the maximum NSEs between the GRACE-/GRACE-FO-derived TWSA estimates and those simulated by models are 0.68, (Fig. 5a), 0.82 (Fig. 5f), 0.86 (Fig. 5g) and 0.89 (Fig. 5j) during the validation periods for the SYRB, the UYRB, the UMYRB and the YRB, respectively. The corresponding RMSEs are 13.2, 13.7, 12.4 and 10.9 mm per month (validation periods, hereafter) for the SYRB, the UYRB, the UMYRB and the YRB, respectively. In general, the detrended TWSA estimates present consistent values between the observations and the modeled results from 2003–2020 for most regions except for the SYRB, as shown in Fig. 5. Compared to the other regions, all models show a relatively poor performance in simulating monthly TWSA for the SYRB with NSEs less than 0.70 during the validation periods, which can be mainly attributed to the increased uncertainties in precipitation and temperature induced by the sparse distribution of meteorological stations over this region (shown in Fig. 1).

We further separately compare the performances of all models in simulating monthly TWSA for a specific region. Taking the entire YRB as an example (Fig. 5j–l), GRACE-/GRACE-FO-derived TWSA estimates show a RMSE of 10.9 mm per month for the MLP-derived TWSA estimates, which is lower than that of 15.1 mm per month for the LSTM-derived TWSA estimates (∼ 39 % difference) and that of 13.3 mm per month for the MLR-derived TWSA estimates (∼ 22 % difference). Meanwhile, the NSE shows similar improvements when applying the MLP model to simulate the TWSA for the YRB (Fig. 5j–l), which can also be found in the SYRB (Fig. 5a–c) and the UMYRB (Fig. 5g–i). In general, the MLP and MLR models achieve high metrics (0.81/12.8 and 0.75/14.2 mm per month of NSE/RMSE on average for all regions) during the validation periods, both of which are significantly higher than the metrics between the GRACE-/GRACE-FO-derived TWSA estimates and that simulated by the LSTM model (0.75/14.7 mm of NSE/RMSE on average for all regions). For the UYRB (Fig. 5d–f), the MLP model shows a slightly poorer performance in simulating TWSA in terms of a higher RMSE (14.7 mm per month) than the LSTM model (14.5 mm per month; ∼ 1.2 % increase) and the MLR model (13.7 mm per month; ∼ 7.2 % increase). In addition, it seems that the larger the study region, the higher the correspondence between the GRACE-/GRACE-FO-derived TWSA estimates and that simulated by models for the MLP model. This result can be explained in that the large area for a specific region may smooth more uncertainties in GRACE signals and meteorological observations (Long et al., 2015).

Overall, Fig. 5 clearly suggests the MLP model's superior performances in simulating the TWSA, with an average value of NSE of 0.81 and an average value of RMSE of 12.8 mm per month during the validation periods for all regions, showing the outstanding capability of the MLP model in learning the complicated relationships between the TWSA and hydroclimatic factors. As documented in Shu and Ouarda (2007), the MLP model can show its unique superiority and great advantages compared with other statistical models, particularly when explaining the underlying processes that have complex nonlinear interrelationships. The results shown in Fig. 5 also indicate that the MLP model can show a relatively better performance in simulating monthly TWSA than the LSTM model in this study. As described in Zhang et al. (2018), one of main drawbacks of the LSTM model is its complexity compared with the MLP model, which indicates that the LSTM model may not show better performances in simulating time series data than other traditional ANN models in some cases, especially when limited trained data are available. In addition, the moderate performance of LSTM model in reconstructing TWSA compared to the MLP model can be partly attributed to the possibly limited role of the memory function in the LSTM model (Wei et al., 2021; Yin et al., 2022), since relations between inputs and the output of this model (shown in Fig. 4) are pretty direct without many memory effects. Therefore, in the following discussion, only the MLP model is applied to further achieve the temporal downscaling of monthly TWSA data for regions.

Relationships between monthly TWSA and hydroclimatic inputs with respect to the entire YRB have been fully established, as presented in Sect. 5.2. As documented in Herath et al. (2016) and Requena et al. (2021), the same scaling properties have been commonly assumed for baseline and future periods in temporal downscaling. Therefore, it is reasonable and acceptable to assume that scaling properties at monthly timescales are valid at daily timescales in this study (Kumar et al., 2012). That is, the relationship between temporally downscaled TWSA and daily hydroclimatic inputs is consistent with that previously established by the downscaling model (e.g., the MLP model) at monthly timescales for a specific region. By merging the daily hydroclimatic inputs into the previously established relationships between TWSA estimates and hydroclimatic factors based on the MLP model, we can downscale the TWSA estimates from monthly time series to daily time series for all regions.

Figure 6 shows daily time series of the TWSA temporally downscaled by the MLP model for different regions during 2003–2020. It can be seen that the daily TWSA shows sub-monthly signals in response to changes in hydroclimatic factors as expected. Both GRACE-/GRACE-FO-derived TWSA estimates and daily TWSA estimates temporally downscaled by the MLP model show obvious seasonal cycles and reach their respective extreme values almost simultaneously. More specifically, amplitudes of daily TWSA estimates are slightly higher (or lower) than monthly TWSA estimates in summer (or winter) seasons from 2003 to 2020. This can be deemed reasonable because monthly TWSA estimates are defined as the mean average of daily TWSA estimates for a specific month. It should also be noted that there are still some discrepancies between temporally downscaled TWSA at sub-monthly timescales and monthly TWSA estimates derived from GRACE and GRACE-FO satellite data for the SYRB, particularly in some extreme low values, which can be attributed to the relatively poor relationship between TWSA estimates and hydroclimatic factors for this region, as described in Fig. 5a. As documented in previous studies (Liu et al., 2020; Shi et al., 2020), it has long been challenging to accurately perform hydrological simulations across the SYRB because of the complex hydrological processes in this alpine basin. For example, parameter settings calibrated by GLDAS Noah land surface model might not be highly accurate for SMS simulation across the SYRB because field measurements of SMS in this region are extremely limited. Harsh climatic conditions and limited weather stations can additionally influence the accuracy of meteorological observations such as precipitation and temperature across the SYRB, especially for some extreme values. Given the above reasons, there is a relatively poor relationship between TWSA estimates and hydroclimatic factors across the SYRB based on the MLP (shown in Fig. 5a). Furthermore, the uncertainties in the observed precipitation and temperature and SMS derived from the GLDAS Noah land surface model can eventually result in some discrepancies between the temporally downscaled TWSA at sub-monthly timescales and monthly TWSA estimates derived from GRACE and GRACE-FO satellite data, as described in Fig. 6a.

Figures 7 and 8 show the daily TWSA temporally downscaled by the MLP model and observed streamflow within the YRB in 2010 and 2020 when extreme flood events occurred according to the information published by the Yangtze River Conservancy Commission of Ministry of Water Resources. As described in Figs. 7 and 8, the nonparametric simple smoothing method introduced in Sect. 4.4 can effectively identify the corresponding flood events that occurred in each region based solely on the analysis of streamflow time series. It shows an apparent increase in streamflow from the beginning to the peak of all flood events. Accordingly, the daily TWSA shows a distinct increase similar to streamflow during the same periods as expected. It is also interesting to note that the beginning of the increase shown in the daily TWSA is earlier than that of streamflow. This is partly because high antecedent soil moisture, which is an important component of TWSA, has been identified as an important driver of flood events for regions (Fatolazadeh and Goïta, 2022; Jing et al., 2020; Reager et al., 2014; Wasko and Natthan, 2019). Meanwhile, this result indicates that the daily TWSA can be potentially useful in building early flood warning systems since it may identify the extreme flood events much more earlier than streamflow.

To better monitor severe flood events over the YRB, we propose a new index, i.e., NDFPI, by jointly using the temporally downscaled TWSA data and daily precipitation data, as introduced in Sect. 4.5. According to the Yangtze River Conservancy Commission of Ministry of Water Resources, the YRB suffered from catastrophic flooding in the year 2020. Therefore, in this study, the severe flood events that occurred in 2020 for the YRB will serve as an example to present the capability of NDFPI in detecting extreme flood events. The threshold values of daily streamflow and NDFPI for the 90th percentile floods during 2003–2020 are presented in Fig. 9. According to the results shown in Fig. 9, the larger threshold values of NDFPI usually indicate severity of flood occurrence increases for a specific region. In addition, the shape of percentile duration curve of daily streamflow across the UYRB (Fig. 9b) is different to that shown in other regions. It is noted that the outlet of the UYRB, the Yichang hydrological station, is located approximately 45 km downstream of the Three Gorges Reservoir (shown in Fig. 1), which is one of the largest hydroelectric reservoirs in the world. Given that the operations of the Three Gorges Reservoir can directly affect the streamflow at Yichang station (Yang et al., 2022), the result shown in Fig. 9b is reasonable.

Figure 10 shows the comparison between basin-averaged NDFPI and daily streamflow observations for the 90th percentile floods in 2020. The results indicate that the ups and downs of the streamflow observed at different hydrological stations are highly consistent with the NDFPI results through the whole season. For example, the observations of streamflow from the Shigu hydrological station (Fig. 10a) reached the corresponding 90th percentile in 12 July. In comparison, the NDFPI estimated by the temporally downscaled TWSA and daily precipitation reached its 90th percentile in 4 July (Fig. 10a), which is 9 d earlier than that of daily streamflow. As expected, these high-streamflow observations during the wet season are usually accompanied by high NDFPI values, which could be attributed to the effects of high precipitation on streamflow during this period. For the YRB (Fig. 10d), daily streamflow detected at the Datong hydrological station reached its 90th percentile in 29 June and eventually peaked in 13 July, with a maximum value of 7.2×109 m3 d-1, which is in line with the findings in Jia et al. (2021). Accordingly, the series of NDFPI reached its 90th percentile in 18 June with a value of 0.58. In general, Fig. 10 clearly suggests that the proposed NDFPI calculated by temporally downscaled TWSA data and daily precipitation changes synchronously with the reality of flood disasters in 2020 for the YRB. Meanwhile, it also indicates that such flood events can be monitored by the proposed NDFPI earlier than traditional streamflow observations.

Previous studies usually focus on monitoring the long-term flood events, while the flood events at sub-monthly timescales using GRACE and GRACE-FO satellite data have been limitedly investigated due to the limitation of their temporal resolution (i.e., month) (Gouweleeuw et al., 2018; Long et al., 2014). In this study, however, Fig. 10 clearly shows the incremental process of TWSA during the wet season using the newly proposed NDFPI estimated by temporally downscaled GRACE and GRACE-FO satellite data and daily precipitation for different regions. This means that the proposed NDFPI has the great potential to detect the evolution of extreme flood events within the short period. It is also interesting to note that the NDFPI reached the threshold of different classes of flood events earlier than that defined by streamflow observations during the wet season in 2020, which can be repeatedly found in the SYRB, the UYRB, the UMYRB and the YRB (Fig. 10) respectively. The comparison results indicate that the lag time between the threshold values of flood events monitored by the NDFPI and that monitored by daily streamflow during the wet season ranges from 8 to 15 d for the 90th percentile floods among all regions in 2020, all of which are far less than the temporal resolution of original GRACE and GRACE-FO satellite data (i.e., month). In addition to the 90th percentile floods, we also compare the basin-averaged NDFPI and daily streamflow observations for the 95th and 99th percentile floods in 2020 (shown in Figs. S1–S4). The results also show that the series of NDFPI reached the threshold values earlier than that of daily streamflow observations for the 95th and 99th percentile floods. For example, there is a 11 d lag time between the threshold value of NDFPI and that of the streamflow observed by Datong hydrological station for the 99th percentile floods in 2020 (Fig. S4d), which provides useful information for accurate and timely flood forecasts and can be very beneficial for protecting people and infrastructure over regions in a changing climate.

The comparison results indicate that the proposed NDFPI reached the threshold values of different classes of flood events earlier than that defined by streamflow observations in 2020 with respect to the YRB and its individual subbasins (shown in Figs. 8 and S1–S4). This is consistent with the results found at the Missouri River basin by Reager et al. (2014). Reager et al. (2014) indicated that the regional TWSA may lead river discharge slightly before the flood season, which can provide useful information on the signal of high streamflow in the coming flood season. However, the study of Reager et al. (2014) only demonstrated the application of GRACE data to characterize regional flood potential at monthly timescales. More accurate information about the complete hydrologic state of a specific region at sub-monthly timescales during the wet season has been limitedly investigated, which is very vital for flood warnings. Given this, we proposed a new index, i.e., NDFPI, by jointly using the temporally downscaled TWSA data and daily precipitation data to better analyze the hydrologic state of the study region during the wet season at finer timescales.

The comparison analysis of the NDFPI and daily streamflow with respect to the YRB may explain the possible reasons why the NDFPI can detect extreme flood events for a specific river basin. Intense rainfall of long duration can cause continuous increases in the surface water (e.g., water stored in lakes and wetlands), soil moisture storage and groundwater storage that are totally represented by the TWSA in this study through the process of infiltration. Many studies also revealed that changes in surface water, soil moisture and groundwater under intense rainfall can exert obvious effects on the status of regional TWSA (Döll et al., 2012; Felfelani et al., 2017; Sinha et al., 2019; Velicogna et al., 2012). All these changes may ultimately result in the saturation of aquifer over regions. However, the saturated state of aquifers is not persistent because there is a great need for the basin to relieve its saturated state by discharging excessive water stored on and below the land surface into the river channels, which may eventually lead to the dramatic increase in streamflow and greatly increase the risk of widespread and damaging regional flooding.

The traditional flood monitoring approaches can provide useful information about the evolution of flood events over the study region through the measurements of rainfall and streamflow. All these measurements largely depend on the in situ hydrological stations and rainfall gauging stations distributed over the regions, which are difficult to achieve in some regions with harsh environment and climatic conditions. In comparison, satellite remote sensing has no such limitation of traditional point-based observations, making it a promising approach to monitor extreme flood events particularly in some poorly gauged basins. Given the large spatial extent, complicated climatic conditions and inaccessible hydrological observations for some high-altitude regions (e.g., SYRB), the GRACE TWSA has shown great advantages and superiority in flood monitoring and water resources management for the YRB than traditional flood monitoring approaches.

Furthermore, all these traditional flood monitoring approaches mainly focus on the meteorological conditions or the status of surface water reflected by various hydroclimatic factors and pay little attention to the importance of antecedent terrestrial water storage conditions before flood events, which can play a critical role in capturing the flood formation processes (Xiong et al., 2021b). For example, Reager and Famiglietti (2009) applied the TWSA from GRACE data and monthly precipitation to assess the likelihood for flooding at the regional scale and emphasized the importance of terrestrial water storage signal in the accurate prediction of floods and general runoff. Long et al. (2014) employed the index of flood potential amount using GRACE data and monthly precipitation to investigate hydrological floods and droughts for a large karst plateau in Southwest China and found that higher TWSA estimates are more prone to result in large potential for flooding during rainy season because of the excessive water that cannot be stored further. Therefore, the new proposed index incorporating the TWSA can more holistically quantify the potential of the development of severe floods for regions than common flood potential indices using hydroclimatic observations.

While previous studies have proposed several standardized indices for large-scale flood monitoring based on the GRACE-derived TWSA (Chen et al., 2010; Tangdamrongsub et al., 2016), flood monitoring and assessment at sub-monthly timescales remains a challenge using GRACE data due to its coarse temporal resolution (month). Flood monitoring at finer timescales is pivotal in understanding the regional water cycle under climate change, which ultimately helps to manage the basin-scale water resources effectively and improve the efficiency of early flood warning systems. The application of daily series of TWSA temporally downscaled from GRACE and GRACE-FO satellite data can provide a useful method to comprehensively assess the integrated flood conditions, considering the changes of both surface and subsurface water storage at sub-monthly timescales. The highest difference in the temporally downscaled TWSA and the daily precipitation during the wet season, as revealed by the NDFPI, can indicate the early signs of the region's transition from normal state to a flood-prone situation. Overall, the new proposed NDFPI is proven to be a useful tool for flood monitoring with the finer timescale over large-scale basins, which also makes it possible to monitor extreme flood events in a timely manner, especially for some regions with limited in situ streamflow observations.

Using the method of linear detrending, long-term trends in series of TWSA estimates have been removed during the reconstruction of the TWSA because they are generally driven by various human activities such as irrigation, reservoir operation and water withdrawals, all of which cannot be well reconstructed by hydroclimatic factors (Humphrey and Gudmundsson, 2019). Although the detrending method can reduce the impacts of human activities on reconstructing the TWSA to some degree, it could still result in some discrepancies between the results of the detrended TWSA and the natural TWSA under climatic variability, particularly in some regions where intense human activities existed. In future, more attention should be paid to reconstruct the series of the regional TWSA under climatic variability when more detailed statistics related to human use such as water consumption, reservoir operation and inter-basin water diversion projects are available. Meanwhile, TWSA estimates in some months are not available for the GRACE and GRACE-FO satellite due to the problem of battery management. Although all these missing months can be effectively filled by different machine-learning-based models, this method may overestimate or underestimate the actual TWSA, especially for some extreme values in the peak of the wet or dry season (Abhishek et al., 2022).

Furthermore, this study presents an effective way to temporally downscale the TWSA estimates from monthly time series into daily values. This temporal downscaling method is assessed through four case studies across the entire YRB, which could present the temporal evolution of TWSA at sub-monthly timescales during the wet season well. As this study mainly focuses on characterizing regional flood potential based on the new proposed NDFPI incorporating temporally downscaled TWSA estimates, we applied this temporal downscaling method on the basin scale. In theory, this method is also suitable for the temporal downscaling of GRACE and GRACE-FO satellite data at the grid cell scale. However, as pointed out by previous studies (Landerer and Swenson, 2012; Save et al., 2016; Scanlon et al., 2016), gridded TWSA estimates derived from GRACE and GRACE-FO satellite data involved relatively large uncertainty induced by associated measurement errors and signal leakage errors. As a result, the accuracy of TWSA estimates can ultimately exert a direct influence on the optimized parameter sets that are obtained for trained models in each grid cell, which is a contributing factor of the uncertainty. In addition, the forcing data of these models used for temporal downscaling, including air temperature, precipitation and the GLDAS Noah-derived SMSA, may also contain some errors and uncertainties due to the uneven spatial distribution of meteorological stations and natural measurement errors (Lv et al., 2017). These errors and uncertainties from the input data could be propagated into the machine-learning-based models (e.g., MLP model), resulting in a broad range of differences between the observations and the simulated results. The latest study has made some initial attempts to learn the spatiotemporal patterns of difference between the TWSA derived from GRACE data and that simulated by land surface models based on the convolutional neural network (CNN) models, with the goal of providing more accurate TWSA estimates (Mo et al., 2022; Sun et al., 2019). Therefore, thorough consideration of the spatiotemporal patterns of difference between the TWSA derived from GRACE and GRACE-FO satellite data and that simulated by other hydrological models will be further taken in our future work when downscaling the TWSA estimates in order to better understand the complex underlying mechanism for TWSA variations during the wet season. Additionally, more efforts should be made to further validate the reliability of temporally downscaled relations proposed in this study when more independent data sources (e.g., groundwater level measurements) are available in YRB.

Overall, the present study shows the great potential of temporally downscaled GRACE and GRACE-FO satellite data in monitoring the extreme flood events. The study provides an effective means for the temporal downscaling of original TWSA estimates from GRACE and GRACE-FO satellite data and will help facilitate the sustainable management of water resources and develop monitoring and early-warning systems for severe flood events over large-scale basins. The methods and results shown in this study can provide important implications of flood hazard prevention and water resource management for other similar basins that are prone to suffer from severe extreme floods. Furthermore, this study can also provide broader implications for flood monitoring in ungauged or poorly gauged basins. For example, advances in satellite remote sensing have made remote sensing a promising approach to capture various hydrological variables (e.g., precipitation, temperature and soil moisture) (Table S2), since they can substantially reduce the limitations of traditional ground-based observations. This is extremely useful and important in hydrological research and applications, particularly in ungauged or poorly gauged basins. Therefore, we can calculate the flood potential index proposed in this study (i.e., NDFPI) by jointly using remote-sensing-based precipitation, temperature and soil moisture estimates combined with GRACE and GRACE-FO satellite data, which can further provide the potential of remote sensing data for flooding in ungauged or poorly gauged basins.