GRACE zaman serilerinin gürültü karakteri analizi

Year 2024, Volume: 9 Issue: 1, 45 - 53, 15.04.2024

Özge Güneş Cüneyt Aydın

https://doi.org/10.29128/geomatik.1307208

Abstract

GRACE uydu sistemi 2002’den beri toplam su bütçesi değişimlerinin küresel ölçekte izlenmesine olanak sağlamaktadır. Eşdeğer su kütlesi değişimi cinsinden ifade edilen toplam su bütçesi zaman serilerinin analizinde trend ve mevsimsel sinyalleri içeren fonksiyonel model olan harmonik regresyon yaklaşımı kullanılır. Bu modelde gözlemlerin eşit ağırlıklı ve korelasyonsuz olduğu varsayılmaktadır. Yani, stokastik modelin sadece beyaz gürültüden oluştuğu kabul edilir. Ancak, zaman serisi spektral anlamda analiz edildiğinde zamansal korelasyonların var olduğu ve renkli gürültüyü meydana getirdiği görülmektedir. Bu çalışmada, söz konusu bu gürültüye ilişkin spektral güç yoğunluk değerleri 2002-2022 periyodunu kapsayan, aylık örneklemeli Goddard Space Flight Center mascon veri seti kullanılarak analiz edilmiştir. Toplam su bütçesi değişimi zaman serilerinde negatif spektral indekse sahip renkli gürültü yapısı görülmüştür. Küresel ölçekte gerçekleştirilen analizlerde karasal alanları temsil eden mascon (mass concentration) zaman serilerinde kırpışma gürültüsüne benzer özellikte kesirli Brownian güç spektrumunda tanımlı renkli gürültü olduğu ortaya çıkarılmıştır. Aynı zamanda küresel aylık harmonik katsayılardan filtrelenerek üretilen DDK (Decorrelation Filter) veri seti ile de çalışılmış ve benzer sonuçlar elde edilmiştir.

Keywords

GRACE, Renkli Gürültü, Zamansal Korelasyon, Stokastik Model, Welch Yöntemi

References

• Agnew, D. C. (1992). The time‐domain behavior of power‐law noises. Geophysical Research Letters, 19(4), 333-336. https://doi.org/10.1029/91GL02832
• Amiri‐Simkooei, A. R., Tiberius, C. C. J. M., & Teunissen, P. J. G. (2007). Assessment of noise in GPS coordinate time series: methodology and results. Journal of Geophysical Research: Solid Earth, 112(B7). https://doi.org/10.1029/2006JB004913
• Aydin, C., Duman, H., Günes, Ö., & Ugur Sanli, D. (2021). Effect of stochastic model errors on significance test for velocities in analysis of GPS position time series. Journal of Surveying Engineering, 147(1), 04020025. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000341
• Başçiftçi, F. (2021). TUSAGA-AKTİF Noktalarında Gürültü Analizi, Türkiye’nin Güneydoğusu Örneği. Geomatik, 6(2), 135-147. https://doi.org/10.29128/geomatik.731486
• Bogusz, J., & Klos, A. (2016). On the significance of periodic signals in noise analysis of GPS station coordinates time series. GPS Solutions, 20, 655-664. https://doi.org/10.1007/s10291-015-0478-9
• Bos, M. S., Williams, S. D. P., Araújo, I. B., & Bastos, L. (2014). The effect of temporal correlated noise on the sea level rate and acceleration uncertainty. Geophysical Journal International, 196(3), 1423-1430. https://doi.org/10.1093/gji/ggt481
• Brockwell, P. J., & Davis, R. A. (2016). Introduction to time-series and forecasting (3rd ed.). New York: Springer.
• Chatfield, C. (2003). The analysis of time series: An introduction (6th ed.). London: Chapman and Hall CRC.
• Dobslaw, H., Bergmann-Wolf, I., Dill, R., Poropat, L., & Flechtner, F. (2017). Product Description Document for AOD1B Release 06, GRACE 327-750, GFZ German Research Centre for Geosciences, Department 1: Geodesy and Remote Sensing.
• Flechtner, F., Sneeuw, N., & Schuh, W. D. (2014). Observation of the system earth from space: CHAMP, GRACE, GOCE and future missions. Berlin, Germany: Springer.
• Gardner, M. (1978). Mathematical games: White and brown music, fractal curves and one-over-f fluctuations. Scientific American, 238(4), 16-32.
• Gauer, L. M., Chanard, K., & Fleitout, L. (2023). Data‐driven gap filling and spatio‐temporal filtering of the GRACE and GRACE‐FO records. Journal of Geophysical Research: Solid Earth, e2022JB025561. https://doi.org/10.1029/2022JB025561
• Gunes, O., & Aydin, C. (2022). Applying autoregressive models in analysis of GRACE-Mascon time-series. Advances in Geodesy and Geoinformation, 71(2), e25. https://doi.org/10.24425/agg.2022.141299
• Guo, X., Zhao, Q., Ditmar, P., Sun, Y., & Liu, J. (2018). Improvements in the monthly gravity field solutions through modeling the colored noise in the GRACE data. Journal of Geophysical Research: Solid Earth, 123(8), 7040-7054. https://doi.org/10.1029/2018JB015601
• Humphrey, V., Gudmundsson, L., & Seneviratne, S. I. (2016). Assessing global water storage variability from GRACE: Trends, seasonal cycle, subseasonal anomalies and extremes. Surveys in Geophysics, 37, 357-395. https://doi.org/10.1007/s10712-016-9367-1
• King, M. A., & Watson, C. S. (2020). Antarctic surface mass balance: Natural variability, noise, and detecting new trends. Geophysical Research Letters, 47(12), e2020GL087493. https://doi.org/10.1029/2020GL087493
• Kusche, J., Schmidt, R., Petrovic, S., & Rietbroek, R. (2009). Decorrelated GRACE time-variable gravity solutions by GFZ, and their validation using a hydrological model. Journal of Geodesy, 83, 903-913. https://doi.org/10.1007/s00190-009-0308-3
• Langbein, J. (2012). Estimating rate uncertainty with maximum likelihood: differences between power-law and flicker–random-walk models. Journal of Geodesy, 86(9), 775-783. https://doi.org/10.1007/s00190-012-0556-5
• Langbein, J. (2017). Improved efficiency of maximum likelihood analysis of time series with temporally correlated errors. Journal of Geodesy, 91, 985-994. https://doi.org/10.1007/s00190-017-1002-5
• Loomis, B. D., Luthcke, S. B., & Sabaka, T. J. (2019). Regularization and error characterization of GRACE mascons. Journal of Geodesy, 93, 1381-1398. https://doi.org/10.1007/s00190-019-01252-y
• Loomis, B. D., Rachlin, K. E., Wiese, D. N., Landerer, F. W., & Luthcke, S. B. (2020). Replacing GRACE/GRACE‐FO with satellite laser ranging: Impacts on Antarctic Ice Sheet mass change. Geophysical Research Letters, 47(3), e2019GL085488. https://doi.org/10.1029/2019GL085488
• Luthcke, S. B., Sabaka, T. J., Loomis, B. D., Arendt, A. A., McCarthy, J. J., & Camp, J. (2013). Antarctica, Greenland and Gulf of Alaska land-ice evolution from an iterated GRACE global mascon solution. Journal of Glaciology, 59(216), 613-631. https://doi.org/10.3189/2013JoG12J147
• Mandelbrot, B. (1983). The Fractal Geometry of Nature. New York: W.H. Freeman and Company
• Mandelbrot, B. B., & Van Ness, J. W. (1968). Fractional Brownian motions, fractional noises and applications. SIAM Review, 10(4), 422-437. https://doi.org/10.1137/1010093
• Mao, A., Harrison, C. G., & Dixon, T. H. (1999). Noise in GPS coordinate time series. Journal of Geophysical Research: Solid Earth, 104(B2), 2797-2816. https://doi.org/10.1029/1998JB900033
• Peltier, W. R., Argus, D. F., & Drummond, R. (2015). Space geodesy constrains ice age terminal deglaciation: The global ICE‐6G_C (VM5a) model. Journal of Geophysical Research: Solid Earth, 120(1), 450-487. https://doi.org/10.1002/2014JB011176
• Ries, J., Bettadpur, S., Eanes, R., Kang, Z., Ko, U., McCullough, C., Nagel, P., Pie, N., Poole, S., Richter, T., Save, H., & Tapley, B. (2016). The Combined Gravity Model GGM05C. GFZ Data Services. https://doi.org/10.5880/icgem.2016.002
• Rodell, M., Famiglietti, J. S., Wiese, D. N., Reager, J. T., Beaudoing, H. K., Landerer, F. W., & Lo, M. H. (2018). Emerging trends in global freshwater availability. Nature, 557(7707), 651-659. https://doi.org/10.1038/s41586-018-0123-1
• Santamaría‐Gómez, A., Bouin, M. N., Collilieux, X., & Wöppelmann, G. (2011). Correlated errors in GPS position time series: Implications for velocity estimates. Journal of Geophysical Research: Solid Earth, 116(B1). https://doi.org/10.1029/2010JB007701
• Schmidt, R., Petrovic, S., Güntner, A., Barthelmes, F., Wünsch, J., & Kusche, J. (2008). Periodic components of water storage changes from GRACE and global hydrology models. Journal of Geophysical Research: Solid Earth, 113(B8). https://doi.org/10.1029/2007JB005363
• Steffen, H., Petrovic, S., Müller, J., Schmidt, R., Wünsch, J., Barthelmes, F., & Kusche, J. (2009). Significance of secular trends of mass variations determined from GRACE solutions. Journal of Geodynamics, 48(3-5), 157-165. https://doi.org/10.1016/j.jog.2009.09.029
• Sun, Y., Riva, R., & Ditmar, P. (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. https://doi.org/10.1002/2016JB013073
• Tapley, B. D., Watkins, M. M., Flechtner, F., Reigber, C., Bettadpur, S., Rodell, M., ... & Velicogna, I. (2019). Contributions of GRACE to understanding climate change. Nature Climate Change, 9(5), 358-369. https://doi.org/10.1038/s41558-019-0456-2
• Welch, P. (1967). The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Transactions on Audio and Electroacoustics, 15(2), 70-73. https://doi.org/10.1109/TAU.1967.1161901
• Williams, S. D. P. (2003). The effect of coloured noise on the uncertainties of rates estimated from geodetic time series. Journal of Geodesy, 76, 483-494. https://doi.org/10.1007/s00190-002-0283-4
• Williams, S. D., Moore, P., King, M. A., & Whitehouse, P. L. (2014). Revisiting GRACE Antarctic ice mass trends and accelerations considering autocorrelation. Earth and Planetary Science Letters, 385, 12-21. https://doi.org/10.1016/j.epsl.2013.10.016