Browsing by Author "Beattie, Christopher"
Now showing 1 - 3 of 3
Results Per Page
Sort Options
- Block-Circulant Approximation of the Precision Matrix for Assimilating SWOT Altimetry DataYaremchuk, Max; Beattie, Christopher; Panteleev, Gleb; D’Addezio, Joseph (MDPI, 2024-05-29)The recently deployed Surface Water and Ocean Topography (SWOT) mission for the first time has observed the ocean surface at a spatial resolution of 1 km, thus giving an opportunity to directly monitor submesoscale sea surface height (SSH) variations that have a typical magnitude of a few centimeters. This progress comes at the expense of the necessity to take into account numerous uncertainties in calibration of the quality-controlled altimeter data. Of particular importance is the proper filtering of spatially correlated errors caused by the uncertainties in geometry and orientation of the on-board interferometer. These “systematic” errors dominate the SWOT error budget and are likely to have a notable signature in the SSH products available to the oceanographic community. In this study, we explore the utility of the block-circulant (BC) approximation of the SWOT precision matrix developed by the Jet Propulsion Laboratory for assessment of a mission’s accuracy, including the possible impact of the systematic errors on the assimilation of the wide-swath altimeter data into numerical models. It is found that BC approximation of the precision matrix has sufficient (90–99%) accuracy for a wide range of significant wave heights of the ocean surface, and, therefore, could potentially serve as an efficient preconditioner for data assimilation problems involving altimetry observations by space-borne interferometers. An extensive set of variational data assimilation (DA) experiments demonstrates that BC approximation provides more accurate SSH retrievals compared to approximations, assuming a spatially uncorrelated observation error field as is currently adopted in operational DA systems.
- The Effect of Spatially Correlated Errors on Sea Surface Height Retrieval from SWOT AltimetryYaremchuk, Max; Beattie, Christopher; Panteleev, Gleb; D’Addezio, Joseph M.; Smith, Scott (MDPI, 2023-08-31)The upcoming technology of wide-swath altimetry from space will enable monitoring the ocean surface at 4–5 times better spatial resolution and 2–3 times better accuracy than traditional nadir altimeters. This development will provide a chance to directly observe submesoscale sea surface height (SSH) variations that have a typical magnitude of a few centimeters. Taking full advantage of this opportunity requires correct treatment of the correlated SSH errors caused by uncertainties in environmental conditions beneath the satellite and in the geometry and orientation of the on-board interferometer. These observation errors are highly correlated both along and across the surface swath scanned by the satellite, and this presents a significant challenge for accurate processing. In particular, the SWOT precision matrix has off-diagonal elements that are too numerous to allow standard approaches to remain tractable. In this study, we explore the utility of a block-diagonal approximation to the SWOT precision matrix in order to reconstruct SSH variability in the region east of Greenland. An extensive set of 2dVar assimilation experiments demonstrates that the sparse approximation proposed for the precision matrix provides accurate SSH retrievals when the background-to-observation error ratio ν does not exceed 3 and significant wave height is below 2.5 m. We also quantify the range of ν and significant wave heights over which the retrieval accuracy of the exact spatially correlated SWOT error model will outperform the uncorrelated model. In particular, the estimated range is found to be substantially wider (ν<10 with significant wave heights below 8–10 m), indicating the potential benefits of further improving the accuracy of approximations for the SWOT precision matrix.
- A Linear Immersed Finite Element Space Defined by Actual Interface Curve on Triangular MeshesGuo, Ruchi (Virginia Tech, 2017-03-21)In this thesis, we develop the a new immersed finite element(IFE) space formed by piecewise linear polynomials defined on sub-elements cut by the actual interface curve for solving elliptic interface problems on interface independent meshes. A group of geometric identities and estimates on interface elements are derived. Based on these geometric identities and estimates, we establish a multi-point Taylor expansion of the true solutions and show the estimates for the second order terms in the expansion. Then, we construct the local IFE spaces by imposing the weak jump conditions and nodal value conditions on the piecewise polynomials. The unisolvence of the IFE shape functions is proven by the invertibility of the well-known Sherman-Morrison system. Furthermore we derive a group of fundamental identities about the IFE shape functions, which show that the two polynomial components in an IFE shape function are highly related. Finally we employ these fundamental identities and the multi-point Taylor expansion to derive the estimates for IFE interpolation errors in L2 and semi-H1 norms.