Long-term temporal prediction of terrestrial water storage changes over global basins using GRACE and limited GRACE-FO data

Abstract

Gravity Recovery and Climate Experiment (GRACE) and the GRACE-Follow-On (GRACE-FO) gravimetric missions provide essential data for remotely measure large-scale Terrestrial Water Storage (TWS) changes on a regional and global scale. However, during the operating time of the gravimetric missions, monthly or almost yearly data gaps may induce and fail to provide continuous information. Quantifying and predicting the TWS variations is very important for uninterrupted environmental monitoring, to be prepared for the consequences of the climatic change and water resources studies. This paper proposes to predict the TWS variability of 19 global basins from 2019 to 2022 using the traditional Seasonal Autoregressive Integrated Moving Average, Error Trend Seasonal, and Singular Spectrum Analysis as newer time series analysis modeling and prediction approach. For this purpose, the integrated GRACE/GRACE-FO Level-3 Release 06 data from the German Research Centre (GFZ) have been privileged. The accuracy of the resulted TWS predictions has been evaluated based on the use of the mentioned approaches, the cross-validation method, and the root-mean-square-error. Using integrated GRACE/GRACE-FO data, the research strategy in this paper is to become a reference to study the TWS prediction of the new GRACE-FO mission and to bridge the gap between GRACE/GRACE-FO missions. For some global basins, the obtained TWS prediction results reveal a continuous negative or positive TWS during the study period 2019–2022. In conclusion, September 2020 and 2021 are expected to be important dates in terms of TWS decrease affecting all basins in different order of magnitude.

Appendices

Appendix 1: The use of the cross-validation method

The Cross-validation method is crucial because it will provide after a multiple trial of training-test data sets, the best-fitting time series prediction method which will be used for the prediction of unknown GRACE-FO data. Figure 

Fig. 7

Time-series Cross-validation training-test sets modeling approach adopted for the multiple selections of training-test sets and thus best-fitting time series analysis method (one of SSA, ETS, and SARIMA methods) over GRACE time series. Blue dots: observations, red dots: test data, white dots: discarded observations for the corresponding iteration. Each row and column expresses an iteration level and a time unit (e.g. month, year) respectively. https://robjhyndman.com/hyndsight/tscv/

7 represents the application of the time series Cross-validation method.

Starting with 5-years training (2002/04–2007/04) and 1-year test data (2007/05–2008/05), in the first iteration, 12 monthly data have been predicted (2007/05–2008/05). The second iteration consists of selecting (2002/04–2007/05) as training data with a 1-month increment and a 1-year test data (2007/06–2008/06) by obtaining at the end again 12 monthly predicted data. The prediction accuracy is computed by the averaging errors between the observed and predicted values over the test sets for each iteration. The equation of Root Mean Squared Error (RMSE) represents the formula of estimation accuracy as follows:

$$RMSE = \left( {\frac{1}{N}\sum\limits_{i = 1}^{N} {\left( {y_{T + i} - \hat{y}_{T + i} } \right)^{2} } } \right)^{1/2} ,$$

(4)

where $N$ is the number of train data,$y_{T + i}$ is the real values in the test data, and $\hat{y}_{T + i}$ is the predicted values. The mean of the RMSE values is calculated with the RMSE value obtained from each iteration of the training-test sets.

Appendix 2: Magnitudes of GRACE-FO TWS prediction and the statistical RMSE results

See Tables 3 and 4.