The terrestrial water storage anomaly (TWSA) from the observations of the preceding Gravity Recovery and Climate Experiment (GRACE) and the contemporary follow-one (GRACE-FO) missions is the sum of the water stored as snow/ice, surface waters, soil moisture, groundwater, and biomass. It is assumed to be concentrated on a virtual layer of water thickness at the Earth’s surface (Ferreira et al., 2020b). TWSA is a critical component of the hydrologic cycle, and thus, an instrumental dataset that underpins our understanding of water availability on different spatial scales and how its variability is affected by climate change and anthropogenic activities. Consequently, the monthly fields of TWSA have been used globally in hydrological studies to provide essential outcomes such as identifying key drivers of land water storage across the globe (Rodell et al., 2018). For example, a GRACE hydrological assessment over North India, as was undertaken by Rodell et al. (2009), highlighted the unsustainable consumption of groundwater for irrigation and other anthropogenic uses. While this assessment was revisited by Long et al. (2016), the combined impacts of climate variability and human water management on freshwater stocks across several continents have been detailed (see, e.g., Ahmed et al., 2014; Ndehedehe and Ferreira, 2020). Also notable is the work of Reager et al. (2014), who investigated the suitability of GRACE observations to infer the flood potential of various river basins at a lead time of several months. Indeed, GRACE applications are varied and transdisciplinary. This includes the possibility of estimating the evapotranspiration (Rodell et al., 2004a), river discharge (Syed et al., 2005) over data-poor regions, estimating water mass changes over permafrost regions (Velicogna et al., 2012), and data assimilations to improve the outputs of hydrological models (Zaitchik et al., 2008). Despite the importance of the TWSA datasets retrieved from the GRACE mission in hydrological studies, the relatively short period of approximately 20 years which contain a 11-month gap between the GRACE and GRACE-FO missions pose a challenge to an accurate assessment of key hydrological metrics. In particular, several gaps due to the lack of reliable measurements constrain the full potential of TWSA in, for example, drought studies and understanding the pace of climate change (e.g., Vishwakarma, 2020).

Several studies have attempted to reconstruct the TWSA series to cover long-term periods relying on different methods. For instance, Li et al. (2021) incorporated machine learning, analysis of time series, with techniques of statistical decomposition to globally reconstruct TWSA fields from 1979 to 2020. Wang et al. (2021) combined the GRACE data with soil moisture, precipitation, evapotranspiration, and temperature to reconstruct a long-term TWSA based on an extended short-term memory model. A simple linear version combining TWSA above the Amazon together with sea surface temperature (SST) indices has additionally been proposed (de Linage et al., 2014). Utilizing GRACE-derived TWSA and in situ river discharge data, Becker et al. (2011) applied a principal component analysis, which makes a linear and steady time-series supposition, to reconstruct GRACE–TWSA from 1980 to 2008 over the Amazon Basin. Other approaches include the use of an autoregressive model with the independent component analysis to predict TWSA in West Africa incorporating precipitation records and SST indices (Forootan et al., 2014b). However, this autoregressive version assumes a constant status of TWSA over the area and the prediction accuracy decreases after a 2-year forecast length. The water balance approach has also been applied to increase the TWSA series back to 1980 (cf. Yin et al., 2019). This approach uses multi-source datasets as inputs in the terrestrial water budget equation. All examples mentioned here require the use of mathematical models. It must be mentioned that the formulation of these techniques, which is primarily based on experimental datasets, and the rise in performance, has frequently been undertaken by way of increased model complexity, and the manner that they come to decisions, makes them a pattern/machine learning recognition problem (Wilby et al., 2003).

There is no mathematical model that can efficiently describe hydrological phenomena (cf. Mukhopadhyay, 2003). However, algorithms that make supposition(s) of the time-series with adaptive abilities provide an excellent alternative to predict the TWSA fields over a region. Consequently, many studies have explored the feasibility of artificial neural networks (ANNs) to reconstruct the TWSA series due to their ability to model linear and non-linear systems based on learning and prediction algorithms (Ahmed et al., 2019). ANN extracts complex relationships between model inputs and targets and builds complex and non-linear relationships that are robust as a forecasting tool for hydrological variables. For instance, extended TWSA time- series using an ANN approach to examine the long-term hydrological properties of TWSA have been investigated by several authors (see, e.g., Long et al., 2014; Zhang et al., 2016; Mukherjee and Ramachandran, 2018; Ferreira et al., 2019; Ahmed et al., 2019; Chen et al., 2019, and references therein). Overall, these studies agreed that the ANN’s performance improved when climatic observations were integrated with the GRACE–TWSA datasets. Nevertheless, this might be a disadvantage since the accuracy of the reconstruction depends a lot on data availability, especially for architectures with many layers. For many regions and river basins, this might impose limitations in using ANN. As a result, economical methods that can still faithfully reconstruct actual observations would be preferable, especially over data-poor regions. The present study proposes the use of a new approach, the boosted regression tree (BRT) technique to reconstruct the TWSA series.

The BRT technique depends on the insights and methodologies of both statistical and machine-learning approaches. This method varies mainly from conventional regression strategies, which produce a single excellent model, rather than utilizing the boosting approach to adaptively combine a large number of several simple tree models to improve the predictive process (Elith et al., 2006; Leathwick et al., 2006; Leathwick et al., 2008). The boosting process utilized in BRT locates its origins within machine learning (Schapire, 2003). However, posterior evolutions within the society of statistics re-explain it as a developed type of regression (Friedman et al., 2000). BRT has many vital benefits of tree-based strategies: 1) it could be used with an assortment type of response (binomial, Gaussian, and Poisson) through specifying the distribution of the error and the link function; 2) it contains a probabilistic or random component, which improves predictive performance, decreasing the definitive model variance through the use of just a random data subset to adequate every new tree (Friedman, 2002); 3) the algorithm automatically detects the best fit; 4) the model shows the impact of each predictor on the reconstruction after accounting for their overall contributions; and 5) the algorithm is robust and unaffected by missing values and outliers (Abeare, 2009). Fitting numerous trees in BRT overcomes the most significant obstacle of single tree models (i.e., their comparatively weak prediction achievement). BRT models are complicated; however, they can be concise in forms which provide a robust hydrological perception. Thereby, BRT is suitable for many environmental applications as well.

The main aim of this study is to evaluate the use of BRT to reconstruct the TWSA series of the Yangtze River basin (YRB), China. So far, BRT has been used only in groundwater level prognosis (Rahman et al., 2020; Sharafati et al., 2020) and, as far as we know, this study presents the first application of BRT to fill the missing gaps in the GRACE-derived TWSA. Furthermore, a comparison of the performance of BRT and ANN techniques has not been attempted in recent few studies that focused on TWSA reconstruction. Therefore, the focus of this study is to generate a continuous and uninterrupted TWSA series and develop a robust predictive technique that can backcast TWSA to address the hydrological and environmental problems over a given river basin. Furthermore, this study compares BRT outputs with those from a non-linear–autoregressive neural network with exogenous inputs (NARX) to define the most accurate method. Due to the nature of GRACE–TWSA, it has a statistical and physical relationship with the hydro-climatic variables (e.g., precipitation and soil moisture). For instance, Mo et al. (2016) found a strong correlation between precipitation and TWSA in southern China. Also, the availability of TWSA affects evapotranspiration and runoff (ibid). Ma et al. (2017) indicated that GRACE observations and Climate Change Initiative Soil Moisture could be used as significant indices of the spatial allocation of the drought procedure and its effect on the environment and local communities. This could improve water resource management and the early detection and monitoring of droughts. Consequently, the present study also uses a comprehensive and different data spectrum, replicating the dynamics in the energy and water cycles that affect TWSA for training the network over the YRB. Hence, the performance of the BRT model is the focus of the analyses, whilst also assessing the relative importance of the predictors used to reconstruct the TWSA.

The Yangtze River is the longest in Asia, with a length of approx. 6,397 km. It flows from the Tibetan Plateau and runs through Qinghai, then turns south to Sichuan and Tibet; after that, it reaches Yunnan, Chongqing, and continues to Hubei, Hunan, running through Jiangxi, Anhui, and Jiangsu, and then emptying into the East China Sea near Shanghai. Its basin (hereafter YRB), extends for about 3,200 km from west to east and more than 1,000 km from north to south and drains an area of 1.8 × 10⁶ km², nearly one-fifth of the total land area of China (Figure 1). The YRB has succumbed to considerable modifications in climate and land cover/use, including the largest hydroelectric power station in the world (Three Gorges Dam—TGD). The TGD’s reservoir is the most vital anthropogenic feature in the YRB. It extends for 2.3 km with 185 m in height.

The Yangtze River is very famous and has a significant role in China’s development of its economy, agriculture, tourism, transportation, culture, etc. Albeit for climate and water resource fields, the Qingling Mountain and Huaihe River are the more commonly recognized borders between northern and southern China. The Yangtze River is also perceived as the north–south boundary, at least from a cultural perspective. The climate in the north of the Yangtze River is dry with low temperatures and light rain, whereas, in the south, the climate is humid and warm with sufficient rainfall. Climate variation, floods and drought events, and irrigation have profoundly affected the water resources, bringing significant impacts on humans and nature. Three severe catastrophic floods happened in the YRB in 1931, 1956, and 1998. Although catastrophic floods like these have not happened in the YRB since the beginning of the 21st century, the YRB has faced a lot of medium and small floods. For instance, eight drought events have been identified in the YRB during the GRACE era, with three major droughts occurring in 2004, 2006, and 2011 (Sun et al., 2018).

Predictions gained from modeling and simulations are now considered an important goal of environmental studies, as they underpin important decisions by hydrologists and engineers, which can help inform on policy. With this in mind, the principal focus of this study was to reconstruct the actual time series of GRACE–TWSA backward from 2014 to 1982 (32 years). The reconstruction of the GRACE-derived TWSA over the YRB used BRT and ANN (represented by NARX) algorithms. Consequently, the contributions of the present work are 1) validating the BRT algorithm, given that errors are within a tolerable range such as the GRACE uncertainty range, and 2) providing an extended time-series that support studies such as droughts. Although several studies have considered the potential of TWSA reconstruction over the YRB (e.g., Zhang et al., 2016), none has considered the use of BRT to reconstruct TWSA.

First, BRT was used to reconstruct GRACE–TWSA over the YRB, where 80% of the data were utilized for training, whereas the remaining 20% of the data were utilized for testing the network. Notably, this partitioning of data was selected after several trials to get the best accuracy. The model was constructed based on its physical relationships with ten hydro-climatic variables (the predictors). These variables are: precipitation (P), surface temperature (SMTL1), soil temperature (level 2/3/4) (SMTL2, SMTL3, SMTL4), surface air pressure (SP), soil moisture (SM), 2-meter temperature (T2m), instantaneous moisture flux (IE), and climate indices (CI). This network’s results showed an RMSE value of 18.94 mm, NSE value of 0.89, and PCC value of 0.95. This shows the consistency of the reconstructed (predicted) and the observed (actual) TWSA series (Figures 5A,C). Second, ANN was trained precisely in the same way as BRT, in which the performance of the series indicated a slight underperformance of about 7.4%, 2.2%, and 2.1%, respectively, in terms of RMSE, NSE, and PCC (cf. Table 1). Both methods present RMSE values within GRACE’s overall accuracy of about 20–30 mm over most river basins (Scanlon et al., 2016). Although the data used in this study were of coarse spatial resolution (1°-by-1°), they were valuable to prove the effectiveness of both algorithms for prediction with an acceptable accuracy.

Because the BRT technique is insensitive to multi-collinearity and outliers, it can fit complicated non-linear relationships, and it can automatically deal with the interactive impacts among predictors (Elith et al., 2006; Elith et al., 2008; Dedman et al., 2017). Hitherto, BRT seems a highly feasible technique to reconstruct TWSA using only one predictor like soil moisture (Figure 5E), and that is reasonable because SM is very similar and highly correlated with TWSA in the YRB (see Figure 2, and also cf. Ferreira et al., 2020a). This result also aligns with the finds of Naghibi and Pourghasemi (2015). They found that BRT used only eight variables selected from the original data (14 variables). Some authors also declared that a close model would be more steady and easier to generalize (Catry et al., 2009; Vilar et al., 2010). Conversely, ANN-based reconstruction seems to necessitate more predictors. It used all predictors to achieve the prediction process and showed that SM got the lowest contribution in the TWSA prediction (Figure 5F). This seems to be an obvious advantage of BRT compared to ANN. One could rely upon only one of the most accurate datasets (e.g., precipitation) based on remotely sensed or in-situ measurements to reconstruct TWSA instead of using all potential predictors (compare Figures 5E,F).

Finally, based on BRT and ANN, the GRACE–TWSA was backcasted from December 2014 to January 1982 (Figure 6). However, an important question regarding the suitability of the extended GRACE–TWSA series is how reliable are GRACE–TWSA reconstructed series (Figure 6)? In the absence of the observed TWSA between January 1982 and March 2002, a closed-loop simulation using TWSA from GLDAS–VIC to evaluate the reliability of BRT and ANN was considered. A period equivalent to the GRACE data (April 2002–November 2014) was used to generate BRT and ANN and then reconstruct the GLDAS–VIC TWSA till 1982 (Figure 7). Both networks were trained to simulate GLDAS–VIC TWSA based on their non-linear physical relationships with the ten hydro-climatic variables. The BRT results showed a slightly better accuracy than those based on ANN (Table 2). Overall, BRT and ANN showed excellent performances with RMSE values of 6.93 and 7.30 mm, respectively. This finding aligns with those from previous studies (e.g., Pourghasemi and Rahmati, 2018), which proved that BRT has a better performance than ANN. Additionally, some studies evaluated several different machine-learning techniques and found that BRT performed better than other popular algorithms (see, e.g., Cunningham et al., 2011; Naghibi and Pourghasemi, 2015; Nolan et al., 2015; Naghibi et al., 2016, for an exhaustive comparison of BRT with other algorithms applied to different subjects). Considering the ratio between the RMSE of the reconstructed GRACE–TWSA with those from GLDAS–VIC–TWSA during the training phases (Tables 1, 2) for the respective algorithms (BRT and ANN), it is possible to derive scale factors to infer the respective RMSEs of GRACE–TWSA of 23.10 and 25.96 mm, respectively. Again, such accuracies are akin to that of the GRACE era TWSA. Hence, this indicates that the temporal series shown in Figure 6 can be used in hydrological studies such as hydrological drought characterizations and the assessment of long-term changes of TWSA. This could be the subject of a separate study.

In the case of long-term studies (e.g., drought and flood assessments), TWSA from GRACE and GRACE-FO missions cover a relatively short period of approximately 20 years. This means that it cannot be effectively applied for impact assessments from droughts and floods, and deduce long-term water availability over the YRB. To address this limitation, this study compared two machine-learning approaches over the YRB to predict and reconstruct the TWSA back to 1982. To this end, boosted regression tree (BRT), a popular machine learning algorithm that increases the model’s accuracy, was used to reconstruct GRACE–TWSA. BRT is a robust algorithm that works very well with large datasets or when there are many hydro-climatic variables compared to the number of observations. They are also very robust in circumventing problems associated with missing values and outliers. This study found that BRT and artificial neural network (ANN, represented by a non-linear-autoregressive neural network with exogenous inputs—NARX) methods appeared robust enough to sufficiently reconstruct GRACE–TWSA over the YRB with accuracy akin to the GRACE dataset. The validation results of both techniques indicated that the BRT technique is a more reliable and “economic” model to reconstruct TWSA over the YRB. That is, the most correlated predictors, in our case, soil moisture and precipitation, could be enough to reconstruct the TWSA time-series. Hence, the method is highly recommended for study areas where only a few datasets are available as predictive variables (e.g., soil moisture and/or precipitation).