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ISSN : 1225-6692(Print)
ISSN : 2287-4518(Online)
Journal of the Korean earth science society Vol.42 No.4 pp.445-458
DOI : https://doi.org/10.5467/JKESS.2021.42.4.445

# Reconstruction of Terrestrial Water Storage of GRACE/GFO Using Convolutional Neural Network and Climate Data

Woohyu Jeon1, Jae-Seung Kim1*, Ki-Weon Seo1,2
1Department of Earth Science Education, Seoul National University, Seoul 08826, Korea
2Center for Educational Research, Seoul National University, Seoul 08826, Korea
*Corresponding author: rlawotmd2246@snu.ac.kr Tel: +08-2-880-4070
August 10, 2021 August 24, 2021 August 24, 2021

## Abstract

Gravity Recovery and Climate Experiment (GRACE) gravimeter satellites observed the Earth gravity field with unprecedented accuracy since 2002. After the termination of GRACE mission, GRACE Follow-on (GFO) satellites successively observe global gravity field, but there is missing period between GRACE and GFO about one year. Many previous studies estimated terrestrial water storage (TWS) changes using hydrological models, vertical displacements from global navigation satellite system observations, altimetry, and satellite laser ranging for a continuity of GRACE and GFO data. Recently, in order to predict TWS changes, various machine learning methods are developed such as artificial neural network and multi-linear regression. Previous studies used hydrological and climate data simultaneously as input data of the learning process. Further, they excluded linear trends in input data and GRACE/GFO data because the trend components obtained from GRACE/GFO data were assumed to be the same for other periods. However, hydrological models include high uncertainties, and observational period of GRACE/GFO is not long enough to estimate reliable TWS trends. In this study, we used convolutional neural networks (CNN) method incorporating only climate data set (temperature, evaporation, and precipitation) to predict TWS variations in the missing period of GRACE/GFO. We also make CNN model learn the linear trend of GRACE/GFO data. In most river basins considered in this study, our CNN model successfully predicts seasonal and long-term variations of TWS change.

GRACE , GRACE FO , CNN , TWS

## Introduction

It is important to understand terrestrial water storage (TWS) changes because water cycle is a critical component of global climate change. TWS has been estimated by numerical models (Kumar et al., 2017; Doll et al., 2003). The models reasonably estimate TWS and other hydrological components, but still include some limitations due probably to missing realization of groundwater recharge/discharge or anthropogenic effects (Sun et al., 2019).

TWS changes are also observed by Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GFO) satellites. GRACE and GFO have measured time-varying gravity solutions with unprecedented accuracy and provided insight of water cycle and climate changes (Chen et al., 2013;Scanlon et al., 2018;Shepherd et al., 2018;Tapley et al., 2019;Wada et al., 2016). During 2002-2014, TWS of Amazon river basin increased about 40 Gt/yr, and Ganges river basin experienced decrease of TWS about −12 Gt/yr (Scanlon et al., 2018). Although GRACE and GFO have measured gravity fields of the Earth continuously, several months were missed due to instrumental issues, data calibration, and transition period between GRACE and GFO missions. Especially, GRACE mission ended at June 2017, and GFO started to be operated at June 2018, which makes 11 months gap. It is very important to fill the data during missing period because there is no global observation associated with the Earth gravity. For continuous time series, various methods were proposed such as multichannel singular spectrum analysis (Wang et al., 2021), GPS-derived surface mass load (Rietbroek et al., 2014), and machine learning combing GRACE, hydrological model, and other satellites such as altimetry, satellite laser ranging (SLR), and Swarm (Humphrey et al., 2017;Irrgang et al., 2020;Mo et al., 2021;Richter et al., 2021; Sun et al., 2021). Recently, there were studies associated with TWS predictions using a convolutional neural network (CNN) frequently used in image processing (Mo et al., 2021;Sun et al., 2019). Sun et al. (2019) showed CNN method was effective for learning and prediction TWS changes in local-scale during GRACE era. In addition, Mo et al. (2021) predicted the TWS during the gap of GRACE and GFO missions using Bayesian CNN globally, but they removed linear trends in GRACE/GFO and input climate data because the linear trends would be controlled by anthropogenic effect and climate changes which are poorly reflected in climate data. Alternatively, the linear trend of GRACE and GFO was added back to the predicted results after finishing learning. However, it is cautious to apply the linear trends from GRACE/GFO observation to other periods when GRACE/GFO missed. This is because causes of such trends were not understood, and certainly the same TWS trends are not expected over other periods under very complicated hydrological processes. Further, most previous studies adopted hydrological data (e.g. soil moisture, accumulated snow, and canopy water contents) as the predictor. However, TWS estimation from hydrological models would be uncertain particularly for TWS linear trends (Scanlon et al., 2018).

In this study, we model TWS changes including linear trends with CNN only using climate data, temperature, evaporation, and precipitation. TWS estimation during the missing period between GRACE and GFO missions is also predicted by the constructed CNN.

## Data

### TWS of GRACE and GFO

Time-varying gravity solutions and surface mass redistributions from GRACE and GFO are provided as spherical harmonics (SH) coefficients and mass concentration (mascon), respectively, by Center for Space Research (CSR), Jet Propulsion Laboratory (JPL), and Goddard Space Flight Center (GSFC). Although the SH coefficients are widely used in GRACE applications, they are contaminated by aliasing and signal leakage errors. In addition, many reduction procedures of SH coefficients such as low degree SHs replacement, Gaussian smoothing, and GIA model correction to note only a few are required. Alternatively, GRACE data processing centers provide mascon solutions after correcting those errors and completing necessary data reduction. Three mascon data show similar TWS change (Loomis et al., 2019;Scanlon et al., 2016), but there are minor discrepancies among the three. Because it is hard to directly assess uncertainties of GRACE/GFO data, we can analyze a root mean square (RMS) of linear trend and annual amplitude, dominant components in TWS change, as GRACE/ GFO TWS uncertainties. Figure S1 represents linear trend of three mascon solutions and RMS from differences between the linear trends such as CSR mascon - JPL mascon, JPL mascon - GSFC mascon, and GSFC mascon - CSR mason. Figure S2 is associated with annual amplitude of each mascon data and their RMS. As shown in Figure S1 and S2, the RMSs of linear trend and annual amplitudes are much smaller than TWS changes. In previous studies associated with machine learning, CSR and JPL mascon data have been widely used (Humphrey et al., 2017;Li et al., 2020;Mo et al., 2021;A. Y. Sun et al., 2019;Z. Sun et al., 2020). In this study, we used CSR mascon data (Save, 2019) from April 2002 to December 2020 as the reference because CSR mascon has higher native resolution (1° ×1°) than JPL (3° ×3°). Although CSR mascon data is provided in 0.25° ×0.25° spatial resolution, we interpolated the data to 1° ×1° grid for computational efficiency.

### Climate data set of ERA5

In order to learn and predict the TWS of GRACE/ GFO, European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 data (Hersbach et al., 2019) from April 2002 to December 2020 are used. There are various versions of variables associated with atmosphere, ocean, and hydrology. Among them, we used only three climate variables of 2 m temperature (T), evaporation (E), and total precipitation (P) from the ERA5 monthly data. Although many other previous studies (e.g. Humphrey et al. (2017);Li et al. (2020);Mo et al. (2021);Sun et al. (2021)) used hydrological variables like soil moisture, runoff, accumulated snow, and canopy water storage, there were significant model-to-model differences in those hydrological variables (Scanlon et al., 2018). Therefore, TWS prediction using the hydrological variables would be contaminated by much noise, and thus we only use climate reanalysis data set. Like the CSR mascon data, ERA5 data are also spatially interpolated to 1° ×1° grid.

## Method

### Learning Model

We construct CNN model to learn TWS anomalies satisfying a function (f) using T, E, and P in major river basins (Eq. (1)),

$T W S G R A C E / G F O = f ( T , E , P ) .$
(1)

Figure 1 shows an architecture of CNN model employed in this study. We use typical CNN model that are widely used in image processing (Albawi et al., 2017). Our CNN consists of three convolution layers and two fully connected (FC) layers. Before convolution, we reconstruct input variables (T, E, and P) to 3×m×n matrix. The first dimension of the reconstructed data represents the number of input variable kinds, and the other dimensions (m×n) mean the size of image which includes a boundary of selected river basin. For both convolution and FC layers, ReLU (Rectified Linear Unit) function is used as activation function (Nair & Hinton, 2010). Also, He initialization and batch normalization are used for prevention of gradient vanishing and overfitting (He et al., 2015;Ioffe & Szegedy, 2015). Filter size for convolution layer is 3×3 and stride is 1. In order to preserve image size, we do not apply pooling and add one layer of zero-padding. After the output of convolution layers is flattened to one column vector, it goes through two FC layers with dropout rate 0.6.

Objective for our learning process is to minimize mean square error between the estimated and observed data. We use Adam optimization algorithm (Kingma & Ba, 2014), which was implemented by Pytorch (Paszke et al., 2019), to minimize objective function. Hyper parameters for our CNN model are as follows; learning rate is 0.0016, momentum is 0.9, and the mini batch size is 32.

We used 192 months (April 2002~December 2020) data set from GRACE/GFO and ERA5 to learn CNN model. About 80% of the monthly data (154 month) is used for model training, and 20% is for testing (38 month). We selected 10 study areas showing large variations of TWS, such as Amazon and Congo, and having noticeable linear trends (Kim et al., 2019), like river basins at the northern Asia (Fig. S3).

### Estimation of Model Efficiency

We calculate Nash-Sutcliffe model efficiency coefficient (NSE: Eq. (2)) (Nash & Sutcliffe, 1970) and correlation coefficient (CC: Eq. (3)) (Ross, 2004) to estimate a performance of the constructed model. Let y = (y1, y2, …, yn ) be real data observed, p = (p1, p2, …, pn ) be a predicted data. $y ¯$ and $p ¯$ denote the mean of y and p, respectively. Then, NSE and CC can be calculated as follows,

$N S E = 1 − ∑ i = 1 n ( p i − y i ) 2 ∑ i = 1 n ( y i − y ¯ ) 2$
(2)

$C C = ∑ i = 1 n ( p i − p ¯ ) ( y i − y ¯ ) ∑ i = 1 n ( p i − p ¯ ) 2 ∑ i = 1 n ( y i − y ¯ ) 2$
(3)

NSE has value between −∞ and 1, while CC does between −1 and 1. Both coefficients are close to 1 when predictions are close to observation.

## Results

### TWS Anomaly

TWS trends estimated by the CNN model are compared to those observed by GRACE/GFO over Amazon, Congo, Lena, and Yenisei river basins during April 2002 December 2020 including both training and testing periods (Fig. 2). Comparison between observation and estimation during the testing period will be examined later. Although a linear trend can be affected by various factors, for example, groundwater pumping, glacier melting, and irrigation, the CNN model sufficiently learns and estimates the linear trend of TWS changes of GRACE/GFO using the three climate data. The trend differences (right column) are much smaller than observation and estimation. In addition to above 4 basins, results of 6 basins (Ob, Mackenzie, Volga, Indus, Ganges, and Sao Francisco basins) are represented in supplementary information (Figure S4). The river basins of Figure S4 also show good agreement between GRACE/GFO and estimation except Ob river basin.

Figure 3 shows annual amplitudes of TWS changes estimated by GRACE/GFO (left column), estimated by CNN model (center column), and difference of them (right column) over the same basins shown in Fig. 2. Figure S5 represents annual amplitudes of the other river basins. Similar to previous studies (Humphrey et al., 2017;Li et al., 2020), annual amplitudes of GRACE/GFO are also well estimated by using only climate data.

We also examine variations of basin-average TWS. Figure 4 shows time series of TWS estimated by GRACE/GFO (grey lines) and CNN (red lines). The pink box in each panel represents the missing period between GRACE and GFO mission, and green lines are TWS prediction during the same period. In basinscale TWS changes also show good agreement between GRACE/GFO and estimations. Further, after removing the annual cycle, we estimate the linear trend (grey and red numbers) of basin-scale TWS from April 2002 to December 2020 when missing periods are not included. Linear trends in grey lines agree with those in red lines within confidence interval. Time series of the other basins are shown in supplementary information (Fig. S6). During the missing period, predicted TWS changes show similar variations to those in other periods but it needs cross validation using other estimations such as GPS-derived surface mass change in future study.

### Validation of CNN performance

In order to conduct performance test of the constructed CNN model, NSE and CC values are calculated. These model efficiency coefficients are calculated over both the train period and test period. According to Moriasi et al. (2007), performance of model could be categorized into 4 groups; ‘Very good’, ‘Good’, ‘Satisfactory’ and ‘Unsatisfactory’ when NSE values range from 0.75 to 1, 0.65 to 0.75, 0.50 to 0.65, under 0.50, respectively.

Table S1 shows NSE and CC values during the training period. Naturally, NSEs of all river basins are higher than 0.5, and most CCs are close to 1, which means the CNN model sufficiently learned the relation between input and output data. Table 1 shows NSE and CC values when using constructed CNN model during testing period. Amazon river basin shows the highest NSE values which is classified to ‘Very good’. NSE values of most river basins are higher than 0.5, which means that our CNN model performs well. Indus river basin, however, the NSE value is only 0.14. According to aridity index (AI), Indus river basin is ‘dry’ basin (Trabucco & Zomer, 2018). Prediction results in dry regions are usually poorer than in humid regions (Sun et al. 2020). Further, Indus river have affected by over-pumping of groundwater. Such anthropogenic effect makes a prediction more difficult. In terms of CC, almost all basins show high correlation of TWS changes, and CC values very close to 1 except Indus. It is likely that the TWS change is influenced by the seasonal components which are well predicted by CNN.

Lastly, we compared the performance of CNN with previous researches. Becker et al. (2011) constructed a model for estimation of water storage anomaly over Amazon basin using in situ river gauging data, and the CC value was 0.90. Humphrey et al. (2017) also modelled TWS anomaly of Amazon basin employing temperature and precipitation, resulting in the CC value of 0.96. Our model shows the CC value of 0.97 at the Amazon which seems fairly good compared to previous research. Meanwhile, Ahmed et al. (2019) modelled TWS over Africa basins using nonlinear autoregressive with exogenous input (NARX) model. The model of Ahmed et al. (2019) showed NSE of 0.54 and CC of 0.79 on Congo basin, which are lower than NSE and CC from this study.

Sun et al. (2020) studied TWS changes over 60 major basins using precipitation, temperature, Noah TWS with three types of model (deep neural network (DNN), multilinear regression (MLR), SARIMAX). Table 2 shows result of NSE from this study and Sun et al. (2020). Compared with the results from DNN and SARIMAX, CNN results are worse or similar except Amazon basin. Meanwhile, most of CNN results are better than MLR except Volga basin. Sun et al. (2020) used not only climate data but also hydrological data from numerical models to predict TWS changes while our study only used climate data. It is cautious to use hydrological data from numerical models because the data includes much uncertainty and show different values from models particularly for trend components. Our results can be improved, on the other hand, by using more reliable climate data. For examples, when considering skin surface temperature and leaf area index, new NSE values increase to 0.77 over Yenisei, 0.61 over Volga and 0.20 over Indus river basins.

Uncertainties in GRACE/GFO data shown in Figs. S1 and S2 would be also important to estimate TWS using climate data. Different NSE values among basins shown in Table 2 can be partly explained by the GRACE/GFO uncertainties. Further study is necessary to consider GRACE/GFO uncertainties to construct CNN model.

## Conclusion

In this study, we derive a relation between three climate variables (temperature, evaporation, and precipitation) and TWS using CNN. Using constructed CNN, we estimate TWS variations during the missing observational periods of GRACE and GFO. Our model shows that estimation performances over most basins are categorized to ‘satisfactory’ or higher. Especially in Amazon basin, it shows ‘very good’ performance. Many previous studies employed both climate data and hydrological data to predict TWS variations. Even though it is expected that hydrological data from numerical model include much uncertainty, previous examination successfully recovered TWS variations. This would be possible because linear trends in TWS, most problematic components in hydrological data, were not included in previous studies. In this study, we include linear trends in TWS and use only climate data not to be contaminated by hydrological data uncertainty. Our prediction results show similar performance to previous studies. We also find some improvement when including more climate data. This result implies that more comprehensive TWS prediction would be possible for the future study.

## Acknowledgments

This study was supported by the Korea Institute of Marine Science and Technology Promotion (KIMST) research grant (KIMST20190361), National Research Foundation of Korea (NRF) grant (NO. 2020R1A2C 2006857).

## Figure

Architecture of CNN model

Trend map of TWS estimated by GRACE/GFO (left), CNN (center), and difference between them (right) over Amazon, Congo, Lena, and Yenisei. Blue numbers in right column represent RMS of difference map. The unit of trend is mmH2O/ yr.

Annual amplitude map of TWS estimated by GRACE/GFO (left), CNN (center), and difference between them (right) over Amazon, Congo, Lena, and Yenisei. Blue numbers in right column represent RMS of difference map. The unit is mmH2O.

Time series of TWS estimated by GRACE/GFO (grey lines) and CNN (red lines). Green lines are TWS changes predicted by CNN for the transition period between GRACE and GFO. The numbers in each panel represent linear trend within 95% confidence interval.

Trend from (a) CSR, (b) JPL, and (c) GSFC mascon and (d) root mean square (RMS) from differences between three linear trend.

Annual amplitude from (a) CSR, (b) JPL, and (c) GSFC mascon and (d) RMS from differences between three annual amplitude.

Studied basins (1: Amazon, 2: Congo, 3: Ob, 4: Yenisei, 5: Lena, 6: Mackenzie, 7: Volga, 8: Indus, 9: Ganges, 10: Sao Francisco)

Trend map of TWS estimated by GRACE/GFO (left), CNN (center), and difference between them (right). From the first row to the last row, names of basins are orderly Ob, Volga, Ganges, Indus, Mackenzie, and Sao Francisco. Blue numbers in right column represent RMS of difference map. The unit of trend is mmH2O/yr.

Annual amplitude map of TWS estimated by GRACE/GFO (left), CNN (center) and difference between them (right). From the first row to the last row, names of basins are orderly Ob, Volga, Ganges, Indus, Mackenzie, and Sao Francisco. Blue numbers in right column represent RMS of difference map. The unit is mmH2O.

Time series of TWS estimated by GRACE/GFO (grey lines) and CNN (red lines). Green lines are TWS changed predicted by CNN for the transition period between GRACE and GFO. The numbers in each panel represent linear trend with 95% confidence interval.

## Table

NSE and CC of selected river basins during the training period

NSE and CC of selected river basins during the test period

Comparison NSE with the result from Sun et al. (2020)

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