Combination of the Levenberg–Marquardt and differential evolution algorithms for the fitting of postseismic GPS time series

Li, Jingwei; Wei, Zehong; Guo, Biao; Li, Shuiping; Binghui, Guo

doi:10.1007/s11600-021-00556-y

Cited by 5 publications

(2 citation statements)

References 26 publications

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“…Nontidal atmospheric loading (NTAL) and nontidal oceanic loading (NTOL) effects were removed from the GPS time series (Figures S1 and S2 in Supporting Information ). The daily three‐dimensional site positions were decomposed into the following components using Equation (Li et al., 2021; Yan et al., 2019; Zhang et al., 2021):

x(t)={x}_{0}+v\left(t-{t}_{0}\right)+\sum\limits _{i}\left[{S}_{i}\,\mathit{sin}\left({2pi\omega }_{i}t\right)+{C}_{i}\,\mathit{cos}\left({2pi\omega }_{i}t\right)\right]+\sum\limits _{k}\left[H\left({t}_{k}-{t}_{e}\right)\right]{F}_{k}+r

where x 0 is offset bias, v denotes velocity, S i and C i represent sine and cosine terms of the annual ( i = 1) and semiannual ( i = 2) components, respectively. H ( t k − t e ) is the step function, F k is the offset resulting from instrumental changes or metadata changes, and r is the residual error.…”

Section: Data and Processingmentioning

confidence: 99%

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High Spatial Resolution in Total Water Storage Variations Inferred From GPS: Case Study in the Great Lakes Watershed, US

Zheng,

Zhang,

Scanlon

et al. 2024

Water Resources Research

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Assessing spatiotemporal water storage variability in the Great Lakes Watershed (GLW) is critical given its transboundary status impacting both Canada and the United States. Here, we apply a novel inversion strategy to global positioning system (GPS) vertical movements to achieve high spatial resolution total water storage (TWS) variations in GLW through improved processing. The steps are composed of removing load changes driven by the lake water fluctuation by forward modeling, isolating the Great Lakes grids to solve the ill‐conditioned problem in inversion, and inverting the GPS residual series to estimate TWS variations on land (TWSGPS). The results show that the regional dense continuous GPS observation network can successfully resolve TWS on land at monthly timescales with 30–45 km spatial resolution. We also could effectively capture fine‐scale TWS features than GRACE/GFO mascon products. GRACE/GFO satellites largely underestimate seasonal and long‐term TWS spatial fluctuations, but their temporal patterns coincide with those from GPS. The average annual amplitude of TWSGPS on land reaches 82.0 mm, greatly exceeding estimates from GRACE/GFO (∼48.0 mm) and composite hydrological model outputs (∼62.0 mm). The seasonal groundwater fluctuations inferred from GPS have peak‐to‐peak amplitudes of ∼40 km3 with the maximum around September. This coincides with that from GRACE/GFO. However, the magnitudes and phases of groundwater storage from GPS vary markedly among the subbasins in GLW, and the different snow and soil moisture amounts measured in each subbasin cause discrepancies among these GPS estimates. This study shows the value of GPS data in spatially downscaling GRACE/GFO data and providing high‐resolution output at spatiotemporal scales with low latency.

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x(t)={x}_{0}+v\left(t-{t}_{0}\right)+\sum\limits _{i}\left[{S}_{i}\,\mathit{sin}\left({2pi\omega }_{i}t\right)+{C}_{i}\,\mathit{cos}\left({2pi\omega }_{i}t\right)\right]+\sum\limits _{k}\left[H\left({t}_{k}-{t}_{e}\right)\right]{F}_{k}+r

Section: Data and Processingmentioning

confidence: 99%

“…Nontidal atmospheric loading (NTAL) and nontidal oceanic loading (NTOL) effects were removed from the GPS time series (Figures S1 and S2 in Supporting Information S1). The daily three-dimensional site positions were decomposed into the following components using Equation 1 (Li et al, 2021;Yan et al, 2019;Zhang et al, 2021):…”

Section: Introductionmentioning

confidence: 99%