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Research Article

Analysis of mass flux variations in the southern Tibetan Plateau based on an improved spatial domain filtering approach for GRACE/GRACE-FO solutions

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Pages 3563-3591 | Received 13 Jan 2022, Accepted 04 Jul 2022, Published online: 19 Jul 2022

References

  • Agutu, N. O., J. L. Awange, C. Ndehedehe, F. Kirimi, and M. Kuhn. 2019. “GRACE-Derived Groundwater Changes Over Greater Horn of Africa: Temporal Variability and the Potential for Irrigated Agriculture.” The Science of the Total Environment 693: 133467. doi:10.1016/j.scitotenv.2019.07.273.
  • Basu, M. 2002. “Gaussian-Based Edge-Detection Methods-A Survey.” IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews) 32 (3): 252–260. doi:10.1109/TSMCC.2002.804448.
  • Beveridge, A. K., C. Harig, and F. J. Simons. 2018. “The Changing Mass of Glaciers on the Tibetan Plateau, 2002–2016, Using Time-Variable Gravity from the GRACE Satellite Mission.” Journal of Geodetic Science 8 (1): 83–97. doi:10.1515/jogs-2018-0010.
  • Bonin, J. A., S. Bettadpur, and B. D. Tapley. 2012. “High-Frequency Signal and Noise Estimates of CSR GRACE RL04.” Journal of Geodesy 86 (12): 1165–1177. doi:10.1007/s00190-012-0572-5.
  • Boyle, D. P., H. V. Gupta, and S. Sorooshian. 2000. “Toward Improved Calibration of Hydrologic Models: Combining the Strengths of Manual and Automatic Methods.” Water Resources Research 36 (12): 3663–3674. doi:10.1029/2000WR900207.
  • Brun, F., E. Berthier, P. Wagnon, A. Kaab, and D. Treichler. 2017. “A Spatially Resolved Estimate of High Mountain Asia Glacier Mass Balances, 2000-2016.” Nature Geoscience 10 (9): 668–673. doi:10.1038/NGEO2999.
  • Chao, B. F., W. P. O’-Connor, A. T. C. Chang, D. K. Hall, and J. L. Foster. 1987. “Snow Load Effect on the Earth’s Rotation and Gravitational Field, 1979–1985.” Journal of Geophysical Research: Solid Earth 92 (B9): 9415–9422. doi:10.1029/JB092iB09p09415.
  • Chen, J. L., C. R. Wilson, and B. D. Tapley. 2006. “Satellite Gravity Measurements Confirm Accelerated Melting of Greenland Ice Sheet.” Science 313 (5795): 1958–1960. doi:10.1126/science.1129007.
  • Chen, J. L., C. R. Wilson, D. Blankenship, and B. D. Tapley. 2009. “Accelerated Antarctic Ice Loss from Satellite Gravity Measurements.” Nature Geoscience 2 (12): 859–862. doi:10.1038/ngeo694.
  • Chen, J., J. Li, Z. Zhang, and S. Ni. 2014. “Long-Term Groundwater Variations in Northwest India from Satellite Gravity Measurements.” Global and Planetary Change 116: 130–138. doi:10.1016/j.gloplacha.2014.02.007.
  • Chen, T., Y. Shen, and Q. Chen. 2016. “Mass Flux Solution in the Tibetan Plateau Using Mascon Modeling.” Remote Sensing 8 (5): 439. doi:10.3390/rs8050439.
  • Chen, J. L., C. R. Wilson, B. D. Tapley, H. Save, and J.-F. Cretaux. 2017. “Long-Term and Seasonal Caspian Sea Level Change from Satellite Gravity and Altimeter Measurements.” Journal of Geophysical Research: Solid Earth 122 (3): 2274–2290. doi:10.1002/2016JB013595.
  • Chen, J., B. Tapley, H. Save, M. E. Tamisiea, S. Bettadpur, and J. Ries. 2018. “Quantification of Ocean Mass Change Using Gravity Recovery and Climate Experiment, Satellite Altimeter, and Argo Floats Observations.” Journal of Geophysical Research: Solid Earth 123 (11): 10.212–10.225. doi:10.1029/2018jb016095.
  • Chen, J., B. Tapley, K. Seo, C. Wilson, and J. Ries. 2019. “Improved Quantification of Global Mean Ocean Mass Change Using GRACE Satellite Gravimetry Measurements.” Geophysical Research Letters 46 (23): 13984–13991. doi:10.1029/2019gl085519.
  • Chen, T., J. Kusche, Y. Shen, and Q. Chen. 2020. “A Combined Use of TSVD and Tikhonov Regularization for Mass Flux Solution in Tibetan Plateau.” Remote Sensing 12 (12). doi:10.3390/rs12122045.
  • Croteau, M. J., R. S. Nerem, B. D. Loomis, and T. J. Sabaka. 2020. “Development of a Daily GRACE Mascon Solution for Terrestrial Water Storage.” Journal of Geophysical Research: Solid Earth 125 (3): e2019JB018468. doi:10.1029/2019JB018468.
  • Dimri, A.P., S. Allen, C. Huggel, S. Mal, J.A. Ballesteros-Canovas, M. Rohrer, and A. Shukla, et al. 2021. ”Climate Change, Cryosphere and Impacts in the Indian Himalayan Region.” Current Science 120 (5): 774–790. doi:10.18520/cs/v120/i5/774-790.
  • Ditmar, P. 2018. “Conversion of Time-Varying Stokes Coefficients into Mass Anomalies at the Earth’s Surface Considering the Earth’s Oblateness.” Journal of Geodesy 92 (12): 1401–1412. doi:10.1007/s00190-018-1128-0.
  • Dobslaw, H., R. Dill, M. Bagge, V. Klemann, E. Boergens, M. Thomas, C. Dahle, and F. Flechtner. 2020. “Gravitationally Consistent Mean Barystatic Sea Level Rise from Leakage‐corrected Monthly GRACE Data.” Journal of Geophysical Research: Solid Earth 125 (11). doi:10.1029/2020jb020923.
  • Döll, P., H. Müller Schmied, C. Schuh, F. T. Portmann, and A. Eicker. 2014. “Global-Scale Assessment of Groundwater Depletion and Related Groundwater Abstractions: Combining Hydrological Modeling with Information from Well Observations and GRACE Satellites.” Water Resources Research 50 (7): 5698–5720. doi:10.1002/2014wr015595.
  • Ferreira, V. G., Z. Liu, H. C. Montecino, P. Yuan, C. I. Kelly, A. S. Mohammed, and L. Y. Han. 2020. “Reciprocal Comparison of Geodetically Sensed and Modeled Vertical Hydrological Loading Products.” Acta Geodaetica Et Geophysica 55 (1): 23–49. doi:10.1007/s40328-019-00279-z.
  • Groh, A. and M. Horwath. 2021. “Antarctic Ice Mass Change Products from GRACE/GRACE-FO Using Tailored Sensitivity Kernels.” Remote Sensing 13 (9): 1736. doi:10.3390/rs13091736.
  • Gupta, D. and C. T. Dhanya. 2020. “The Potential of GRACE in Assessing the Flood Potential of Peninsular Indian River Basins.” International Journal of Remote Sensing 41 (23): 9009–9038. doi:10.1080/01431161.2020.1797218.
  • Jekeli, C. 1981. Alternative Methods to Smooth the Earth’s Gravity Field. Report No. 327. Ohio: Department of Geodetic Science, Ohio State University.
  • Jia, Y., H. Lei, H. Yang, and Q. Hu. 2020. “Terrestrial Water Storage Change Retrieved by GRACE and Its Implication in the Tibetan Plateau: Estimating Areal Precipitation in Ungauged Region.” Remote Sensing 12 (19): 3129. doi:10.3390/rs12193129.
  • Jing, W., P. Zhang, and X. Zhao. 2019. “A Comparison of Different GRACE Solutions in Terrestrial Water Storage Trend Estimation Over Tibetan Plateau.” Scientific Reports 9 (1): 1765. doi:10.1038/s41598-018-38337-1.
  • Jing, W., X. Zhao, L. Yao, H. Jiang, J. Xu, J. Yang, and Y. Li. 2020. “Variations in Terrestrial Water Storage in the Lancang-Mekong River Basin from GRACE Solutions and Land Surface Model.” Journal of Hydrology 580: 124258. doi:10.1016/j.jhydrol.2019.124258.
  • Johnson, D. H. 2006. “Signal-To-Noise Ratio.” Scholarpedia 1 (12): 2088. doi:10.4249/scholarpedia.2088.
  • Kiamehr, R. and L. E. Sjöberg. 2005. “Effect of the SRTM Global DEM on the Determination of a High-Resolution Geoid Model: A Case Study in Iran.” Journal of Geodesy 79 (9): 540–551. doi:10.1007/s00190-005-0006-8.
  • Kiamehr, R. 2006. “Precise Gravimetric Geoid Model for Iran Based on GRACE and SRTM Data and the Least-Squares Modification of Stokes’ Formula : with Some Geodynamic Interpretations.” Doctoral thesis, comprehensive summary, KTH.
  • Klosko, S., D. Rowlands, S. Luthcke, F. François Lemoine, and D. Chinn, M. Rodell. 2009. “Evaluation and Validation of Mascon Recovery Using GRACE KBRR Data with Independent Mass Flux Estimates in the Mississippi Basin.” Journal of Geodesy 83 (9): 817–827. doi:10.1007/s00190-009-0301-x.
  • Kusche, J. 2007. “Approximate Decorrelation and Non-Isotropic Smoothing of Time-Variable GRACE-Type Gravity Field Models.” Journal of Geodesy 81 (11): 733–749. doi:10.1007/s00190-007-0143-3.
  • Kusche, J., R. Schmidt, S. Petrovic, and R. Rietbroek. 2009. “Decorrelated GRACE Time-Variable Gravity Solutions by GFZ, and Their Validation Using a Hydrological Model.” Journal of Geodesy 83 (10): 903–913. doi:10.1007/s00190-009-0308-3.
  • Landerer, F. W. and S. C. Swenson. 2012. “Accuracy of Scaled GRACE Terrestrial Water Storage Estimates.” Water Resources Research 48 (4). doi:10.1029/2011wr011453.
  • Landerer, F. W., F. M. Flechtner, H. Save, F. H. Webb, T. Bandikova, W. I. Bertiger, S. V. Bettadpur, et al. 2020. ”Extending the Global Mass Change Data Record: GRACE Follow‐on Instrument and Science Data Performance.” Geophysical Research Letters 47 (12). doi:10.1029/2020gl088306.
  • Li, F., Z. Wang, N. Chao, and Q. Song. 2018. “Assessing the Influence of the Three Gorges Dam on Hydrological Drought Using GRACE Data.” Water 10 (5). doi:10.3390/w10050669.
  • Long, D., L. Longuevergne, and B. R. Scanlon. 2015. “Global Analysis of Approaches for Deriving Total Water Storage Changes from GRACE Satellites.” Water Resources Research 51 (4): 2574–2594. doi:10.1002/2014wr016853.
  • Loomis, B. D., K. E. Rachlin, and S. B. Luthcke. 2019. “Improved Earth Oblateness Rate Reveals Increased Ice Sheet Losses and Mass-Driven Sea Level Rise.” Geophysical Research Letters 46 (12): 6910–6917. doi:10.1029/2019GL082929.
  • Loomis, B. D., S. B. Luthcke, and T. J. Sabaka. 2019. “Regularization and Error Characterization of GRACE Mascons.” Journal of Geodesy 93 (9): 1381–1398. doi:10.1007/s00190-019-01252-y.
  • Loomis, B. D., K. E. Rachlin, D. N. Wiese, F. W. Landerer, and S. B. Luthcke. 2020. “Replacing GRACE/GRACE-FO with Satellite Laser Ranging: Impacts on Antarctic Ice Sheet Mass Change.” Geophysical Research Letters 47 (3): e2019GL085488. doi:10.1029/2019GL085488.
  • Loomis, B. D., D. Felikson, T. J. Sabaka, and B. Medley. 2021. “High‐spatial‐resolution Mass Rates from GRACE and GRACE‐FO: Global and Ice Sheet Analyses.” Journal of Geophysical Research: Solid Earth 126 (12). doi:10.1029/2021jb023024.
  • Makandar, A. and B. Halalli. 2015. “Image Enhancement Techniques Using Highpass and Lowpass Filters.” International Journal of Computer Applications 109 (14): 21–27. doi:10.5120/19256-0999.
  • Mu, D., H. Yan, W. Feng, and P. Peng. 2017. “GRACE Leakage Error Correction with Regularization Technique: Case Studies in Greenland and Antarctica.” Geophysical Journal International. doi:10.1093/gji/ggw494.
  • Müller Schmied, H., D. Cáceres, S. Eisner, M. Flörke, C. Herbert, C. Niemann, and T. A. Peiris, et al. 2021. ”The Global Water Resources and Use Model WaterGap V2.2d: Model Description and Evaluation.” Geoscientific Model Development 14 (2): 1037–1079. doi:10.5194/gmd-14-1037-2021.
  • Nash, J. E. and J. V. Sutcliffe. 1970. “River Flow Forecasting Through Conceptual Models Part I — a Discussion of Principles.” Journal of Hydrology 10 (3): 282–290. doi:10.1016/0022-1694(70)90255-6.
  • Ni, S., J. Chen, C. Wilson, and X. Hu. 2017. “Long-Term Water Storage Changes of Lake Volta from GRACE and Satellite Altimetry and Connections with Regional Climate.” Remote Sensing 9 (8). doi:10.3390/rs9080842.
  • Pan, Y., C. K. Shum, Shen, W., and R. Chen. 2018. “Spatially Varying Surface Seasonal Oscillations and 3-D Crustal Deformation of the Tibetan Plateau Derived from GPS and GRACE Data.” Earth and Planetary Science Letters 502: 12–22. doi:10.1016/j.epsl.2018.08.037.
  • Pei-Yung, H., C. Chia-Hsiung, C. Shin-Shian, L. Le-Tien, and C. Sao-Jie. 2006. A Parameterizable Digital-Approximated 2D Gaussian Smoothing Filter for Edge Detection in Noisy Image. Paper presented at the 2006 IEEE International Symposium on Circuits and Systems. Kos, Greece, 21-24 May 2006.
  • Prevost, P., K. Chanard, L. Fleitout, E. Calais, D. Walwer, T. van Dam, and M. Ghil. 2019. “Data-Adaptive Spatio-Temporal Filtering of GRACE Data.” Geophysical Journal International 219 (3): 2034–2055. doi:10.1093/gji/ggz409.
  • Pu, L., D. Fan, W. You, X. Yang, Z. M. Nigatu, and Z. Jiang. 2022. “Extracting Terrestrial Water Storage Signals from GRACE Solutions in the Amazon Basin Using an Iterative Filtering Approach.” Remote Sensing Letters 13 (1): 14–23. doi:10.1080/2150704x.2021.1981557.
  • Purcell, A., P. Tregoning, and A. Dehecq. 2018. ““Reply to Comment by W. R. Peltier, D. F. Argus, and R. Drummond on “An Assessment of the ICE6G_C (Vm5a) Glacial Isostatic Adjustment Model”.” Journal of Geophysical Research: Solid Earth 123 (2): 2029–2032. doi:10.1002/2017JB014930.
  • Qiu, J. 2008. “China: The Third Pole.” Nature 454 (7203): 393–396. doi:10.1038/454393a.
  • Ran, J., P. Ditmar, R. Klees, and H. H. Farahani. 2018. “Statistically Optimal Estimation of Greenland Ice Sheet Mass Variations from GRACE Monthly Solutions Using an Improved Mascon Approach.” Journal of Geodesy 92 (3): 299–319. doi:10.1007/s00190-017-1063-5.
  • Ran, J., N. Tangdamrongsub, and X. Wan. 2020. “The Impact of Error Covariance Matrix Structure of Grace’s Gravity Solution on the Mass Flux Estimates of Greenland Ice Sheet.” Advances in Space Research. doi:10.1016/j.asr.2020.07.012.
  • Rodell, M., P. R. Houser, U. Jambor, J. Gottschalck, K. Mitchell, C. Meng, and K. Arsenault, et al. 2004. ”The Global Land Data Assimilation System.” Bulletin of the American Meteorological Society 85 (3): 381–394. doi:10.1175/BAMS-85-3-381.
  • Rodell, M., I. Velicogna, and J. S. Famiglietti. 2009. “Satellite-Based Estimates of Groundwater Depletion in India.” Nature 460 (7258): 999–1002. doi:10.1038/nature08238.
  • Rodell, M., J. S. Famiglietti, D. N. Wiese, J. T. Reager, H. K. Beaudoing, F. W. Landerer, and M. H. Lo. 2018. “Emerging Trends in Global Freshwater Availability.” Nature 557 (7707): 651–659. doi:10.1038/s41586-018-0123-1.
  • Rudolf, B., C. Beck, J. Grieser, and U. Schneider. 2005. “Global Precipitation Analysis Products of the GPCC.” Global Precipitation Climatology Centre Report 8.
  • Sakumura, C., S. Bettadpur, H. Save, and C. McCullough. 2016. “High-Frequency Terrestrial Water Storage Signal Capture via a Regularized Sliding Window Mascon Product from GRACE.” Journal of Geophysical Research: Solid Earth 121 (5): 4014–4030. doi:10.1002/2016JB012843.
  • Save, H., S. Bettadpur, and B. D. Tapley. 2016. “High-Resolution CSR GRACE RL05 Mascons.” Journal of Geophysical Research: Solid Earth 121 (10): 7547–7569. doi:10.1002/2016jb013007.
  • Schneider, U., A. Becker, P. Finger, R. Elke, and M. Ziese. 2020. GPCC Monitoring Product: Near Real-Time Monthly Land-Surface Precipitation from Rain-Gauges Based on SYNOP and CLIMAT Data. doi:10.5676/DWD_GPCC/MP_M_V2020_100.
  • Seo, K., S. Oh, J. Eom, J. Chen, and C. R. Wilson. 2020. “Constrained Linear Deconvolution of GRACE Anomalies to Correct Spatial Leakage.” Remote Sensing 12 (11). doi:10.3390/rs12111798.
  • Sun, Y., R. Riva, and P. Ditmar. 2016. “Optimizing Estimates of Annual Variations and Trends in Geocenter Motion and J2 from a Combination of GRACE Data and Geophysical Models.” Journal of Geophysical Research: Solid Earth 121 (11): 8352–8370. doi:10.1002/2016JB013073.
  • Swenson, S. and J. Wahr. 2006. “Post-Processing Removal of Correlated Errors in GRACE Data.” Geophysical Research Letters 33 (8). doi:10.1029/2005gl025285.
  • Swenson, S., D. Chambers, and J. Wahr. 2008. “Estimating Geocenter Variations from a Combination of GRACE and Ocean Model Output.” Journal of Geophysical Research: Solid Earth 113 (B8). doi:10.1029/2007jb005338.
  • Tang, J., H. Cheng, and L. Liu. 2012. “Using Nonlinear Programming to Correct Leakage and Estimate Mass Change from GRACE Observation and Its Application to Antarctica.” Journal of Geophysical Research: Solid Earth 117 (B11): n/a–n/a. doi:10.1029/2012jb009480.
  • Tapley, B. D., S. Bettadpur, M. Watkins, and C. Reigber. 2004. “The Gravity Recovery and Climate Experiment: Mission Overview and Early Results.” Geophysical Research Letters 31 (9): n/a–n/a. doi:10.1029/2004gl019920.
  • Tapley, B. D., M. M. Watkins, F. Flechtner, C. Reigber, S. Bettadpur, M. Rodell, and I. Sasgen, et al. 2019. ”Contributions of GRACE to Understanding Climate Change.” Nature Climate Change 5 (5): 358–369. doi:10.1038/s41558-019-0456-2.
  • Velicogna, I. and J. Wahr. 2006. “Acceleration of Greenland Ice Mass Loss in Spring 2004.” Nature 443 (7109): 329–331. doi:10.1038/nature05168.
  • Wahr, J., M. Molenaar, and F. Bryan. 1998. “Time Variability of the Earth’s Gravity Field: Hydrological and Oceanic Effects and Their Possible Detection Using GRACE.” Journal of Geophysical Research: Solid Earth 103 (B12): 30205–30229. doi:10.1029/98jb02844.
  • Wang, J., C. Song, J. T. Reager, F. Yao, J. S. Famiglietti, Y. Sheng, G. M. MacDonald, et al. 2018. ”Recent Global Decline in Endorheic Basin Water Storages”. Nature Geoscience 11: 926–932. 10.1038/s41561-018-0265-7.
  • Watkins, M. M., D. N. Wiese, D.-N. Yuan, C. Boening, and F. W. Landerer. 2015. “Improved Methods for Observing Earth’s Time Variable Mass Distribution with GRACE Using Spherical Cap Mascons.” Journal of Geophysical Research: Solid Earth 120 (4): 2648–2671. doi:10.1002/2014JB011547.
  • Wei, Y., G. Tang, M. Wang, and X. Yang. 2015. Remote Sensing Digital Image Processing Tutorial. Second ed: Science Press.
  • Wiese, D. N., F. W. Landerer, and M. M. Watkins. 2016. “Quantifying and Reducing Leakage Errors in the JPL RL05M GRACE Mascon Solution.” Water Resources Research 52 (9): 7490–7502. doi:10.1002/2016WR019344.
  • Xiang, L., H. Wang, H. Steffen, P. Wu, L. Jia, L. Jiang, and Q. Shen. 2016. “Groundwater Storage Changes in the Tibetan Plateau and Adjacent Areas Revealed from GRACE Satellite Gravity Data.” Earth and Planetary Science Letters 449: 228–239. doi:10.1016/j.epsl.2016.06.002.
  • Yang, X., S. Tian, W. Feng, J. Ran, W. You, Z. Jiang, and X. Gong. 2020. “Spatio-Temporal Evaluation of Water Storage Trends from Hydrological Models Over Australia Using GRACE Mascon Solutions.” Remote Sensing 12 (21): 3578. doi:10.3390/rs12213578.
  • Yao, F., J. Wang, K. Yang, C. Wang, B. A. Walter, and J.-F. Crétaux. 2018. “Lake Storage Variation on the Endorheic Tibetan Plateau and Its Attribution to Climate Change Since the New Millennium.” Environmental Research Letters 13 (6). doi:10.1088/1748-9326/aab5d3.
  • Yi, S. and W. Sun. 2014. “Evaluation of Glacier Changes in High-Mountain Asia Based on 10 year GRACE RL05 Models.” Journal of Geophysical Research: Solid Earth 119 (3): 2504–2517. doi:10.1002/2013JB010860.
  • Yi, S., W. Sun, K. Heki, and A. Qian. 2015. “An Increase in the Rate of Global Mean Sea Level Rise Since 2010.” Geophysical Research Letters 42 (10): 3998–4006. doi:10.1002/2015gl063902.
  • Yi, S., Q. Wang, and W. Sun. 2016. “Basin Mass Dynamic Changes in China from GRACE Based on a Multibasin Inversion Method.” Journal of Geophysical Research: Solid Earth 121 (5): 3782–3803. doi:10.1002/2015jb012608.
  • Yi, S. and N. Sneeuw. 2021. “Filling the Data Gaps Within GRACE Missions Using Singular Spectrum Analysis.” Journal of Geophysical Research: Solid Earth 126 (5): e2020JB021227. doi:10.1029/2020JB021227.
  • Yi, S. and N. Sneeuw. 2022. “A Novel Spatial Filter to Reduce North–south Striping Noise in GRACE Spherical Harmonic Coefficients.” Journal of Geodesy 96 (4): 23. doi:10.1007/s00190-022-01614-z.
  • Zheng, Y., L. Wang, C. Chen, Z. Fu, and Z. Peng. 2020. “Using Satellite Gravity and Hydrological Data to Estimate Changes in Evapotranspiration Induced by Water Storage Fluctuations in the Three Gorges Reservoir of China.” Remote Sensing 12 (13): 2143. doi:10.3390/rs12132143.
  • Zhou, H., M. Dai, P. Wang, M. Wei, L. Tang, S. Xu, and Z. Luo. 2022. “Assessment of GRACE/GRACE Follow-On Terrestrial Water Storage Estimates Using an Improved Forward Modeling Method: A Case Study in Africa.” Frontiers in Earth Science 9. doi:10.3389/feart.2021.796723.
  • Zou, F., R. Tenzer, and S. Jin. 2019. “Water Storage Variations in Tibet from GRACE, Icesat, and Hydrological Data.” Remote Sensing 11 (9): 1103. doi:10.3390/rs11091103.

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