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Mass anomalies over Russia from GRACE
Leonid Zotov
1Sternberg

1,2

(wolftempus@gmail.com), Natalya Frolova3 and C.K. Shum

4,5

Astronomical Institute, MSU, Russia; 2Moscow Institute of Electronics and Mathematics (MIEM) HSE; 3Department of Hydrology, Faculty of Geography, MSU; 4Division of geodetic sciences, School of Earth Sciences, Ohio State University, USA; 5Institute of Geodesy & Geophysics, CAS, Wuhan, China
Abstract: Gravity Recovery and Climate Experiment (GRACE) satellites, launched 17.03.2002 from Plesetsk, provide a set of monthly Earth's gravity field observations. They present a big interest for hydrological studies. Gravity data reflect changes, related to the groundwater redistribution, ice melting, and precipitation accumulation. However, de-stripping/filtering is required to use the GRACE data products. We apply Multichannel Singular Spectrum Analysis (MSSA, or extended EOF) technique to filter GRACE data and separate the principal components (PCs) of different periods. We performed data averaging over the large river basins of Russia. Winter 2012-2013 was the most snowy winter in Russia since 1960s. Melting of this snow induced large floods and river levels increase. The exceptional maxima are seen in the curves obtained from GRACE. Next spring and summer 2014 were much less snowy. Long-periodic climate-related changes were separated into PC 1. Gravity field increase in Siberia, Black sea, and decrease around Caspian sea are seen. Data: We used JPL Level-2 RL05 monthly GRACE spherical harmonic data since 01.2003 till 09.2015 with coefficients complete to degree 60. 13 files (06.03, 01.11, 06.11, 05.12, 10.12, 03.13, 08.13, 09.13, 02.14, 12.14, 02.12, 05.15, 06.15) were cubically-interpolated (overall N=153 files). C20 coefficients were replaced by SLRderived. Average field over 10 years was subtracted. GIA effect according to Paulson 2007 model was removed. Results are represented in form of equivalent water height (EWH) level (cm) maps. Fig 1. Vertical "stripes" manifest as high-frequency correlated errors dominates each of the monthly temporal gravity field solutions. Initial data contains mostly stripes, and illustrates constant (geographically-correlated) spatial behavior. MSSA can be used for de-striping. Fig 2. Sum of MSSA PCs 1-10 (L=48) represent main signal variability (energy). Stripes are mostly removed (they go to larger PCs). Simulated Topological Networks (STN-30p) database is used to constrain the region of study to the basins of 15 large Russian rivers (left). The map for 06.2014 is presented (below). MSSA Method: Multichannel Singular Spectrum Analysis (MSSA), also called Extended EOF, is a generalization of Singular Spectrum Analysis (SSA) for the multidimensional (multichannel) time series. SSA, in its turn, is a Principal Component Analysis, generalized for the time series in such way, that instead of the simple correlation matrix, the trajectory matrix is analyzed. It is obtained through the time series embedding into the L-dimensional space. Parameter L is called lag or "caterpillar" length. When L=1, SSA becomes PCA. In every point ij on the map we have time series Aij(tk) of length N. The trajectory matrix for every XAij should be build and incorporated into large block matrix X as follows:
X Aij Aij (t0 ) Aij (t1 ) ..... Aij (t K 1 ) X [ X A1,1 , X A2,1 , X A1, 2 Aij (t1 ) Aij (t2 ) ..... Aij (t K ) K N L 1 SVD: ..................................................... X = U SV Aij (t L 1 ) Aij (t L ) ..... Aij (t N 1 )

..., X Aij ,..., X

AP

1,Q

,X

AP

,Q

]

T

PC-i matrix:
T

X

i

T = si ui vi

Then Singular Value Decomposition (SVD) should be applied to X. As a result, a sequence of singular numbers (SN) si standing along the diagonal of matrix S in order of decreasing values and the corresponding eigenvectors ui, vi are obtained. The Principal Components (PCs) can be reconstructed from them, knowing the structure of the matrix Xi. Some of SNs may be related to one and the same PC and represent similar behavior. Than SN-components should be grouped together and reconstructed as one PC. As a result, the set of PCs with decreasing amplitudes representing different modes of time series variability are obtained. MSSA is more flexible for recognition of trend, modulated oscillations of different periods, denoising of multidimensional time series, then simple EOF. Different channels "help" each other to capture spatio-temporal correlation patterns. We applied MSSA in frequency domain to the matrix of Stokes coefficients. Lag parameter was selected to be L=48 (4 years). Fig 4. Singular numbers for MSSA
Snow maxima

with parameter L=48

Trend PC 1 (SN 1+4) Annual mode PC 2 (SN 2+3) Heat wave Transients and noises (SN>10)

Fig 5. Difference between 2014 and 2003 for the trend component (PC 1).
Black Sea Aral Sea Caspian Sea Baikal

Amur flood

Fig 3. C20 coefficients are badly estimated from GRACE and should be replaced by those, obtained from Stellate Laser Ranging (SLR) Fig 4. Results of averaging over the basins of large Russian rivers. Black curve is sum of SNs 1-10. Purple curve - initial data (sum of all SNs). Trend (PC 2) is shown in blue. It increases until 2009, then reaches a plateau.

Fig 6. Sum of PCs 1-10 for particular rivers basins. Different trends' behavior for European and Siberian rivers is seen. Fig 7. MSSA sum SN 1-10 and initial GRACE data for big seas and lakes of Russia. Regions were selected as rectangles with coordinates shown in the label.

Draft

Conclusion: GRACE data is very useful for hydrological and climatological studies, 1. L.V. Zotov, C.K. Shum, N.L. Frolova Gravity changes over Russian rivers basins from GRACE, especially over large territory, not completely covered by the meteorological and chapter in "Planetary Exploration and Science: Recent Results and Advances", Springer, 2014. hydrological networks, like Russia. MSSA is a promising method for GRACE data 2. .., .., .., processing, de-striping, filtering, and Principal Components (PCs) separation. GRACE, N3 2015, After averaging over 15 large Russian rivers basins mass trend component was found to 142-158 , be increasing. It is mostly dominated by Siberian rivers. European river basins mass 3. Frappart, F., et al.: Interannual variations of the terrestrial water storage in the Lower Ob' Basin decreases. Map for the trend (Fig. 6) show mass anomaly increase in Siberia, at Back sea from a multisatellite approach, Hydrol. Earth Syst. Sci., 14, 2443-2453, 2010. 4. Golyandina N. et al., Analysis of time series structure: SSA and related techniques, Chapman & and decrease over Caspian sea since 2003. It is also seen on the plots for the selected seas and lakes (Fig. 7) . The spatial resolution of data is around 300 km. Thus, averaging Hall, 2001 over small regions is still noisy. This work is supported by HSE and RFBI grant. References: