Spatial Variation and Uncertainty Analysis of Black Sea Level Change from Virtual Altimetry Stations Over 1993.0-2021.0

Sea level rise constitutes a globally pervasive phenomenon, regional manifestations often exhibit substantial heterogeneity due to local environmental and climatic factors. In semi-enclosed basins like the Black Sea, sea level changes are marked by distinctive spatial and temporal patterns. Understanding the spatiotemporal evolution of sea level in such regions is essential for elucidating localized responses to broader climatic drivers. This study utilizes sea surface height (SSH) data derived from satellite altimetry (SA) to investigate sea level variability in the Black Sea over eight distinct time periods: 1993–2000, 1993–2003, 1993–2005, 1993–2008, 1993–2011, 1993–2013, 1993–2017, and 1993–2021 corresponding to time series durations of 7, 10, 12, 15, 18, 20, 24, and 28 years. Four noise models were applied to estimate sea level trends, uncertainties, and annual amplitudes, the optimal model was identified to characterize sea level change, revealing long-term trend, spatial variation, and seasonal variability across the basin. The results indicate that: (1) Sea level change in the Black Sea is not linear over time and exhibits spatial heterogeneity. The estimated sea level trends over eight distinct periods are 21.68 ± 4.05 mm/a, 10.61 ± 1.61 mm/a, 8.84 ± 1.62 mm/a, 3.68 ± 0.89 mm/a, 6.74 ± 0.83 mm/a, 4.14 ± 0.69 mm/a, 3.07 ± 0.61 mm/a, and 2.34 ± 0.59 mm/a, respectively; (2) These results demonstrate that sea level trends estimates are strongly dependent on the length of the observational record. Shorter time series are associated with greater variability and higher uncertainty in trend estimates, whereas longer records provide more stable and statistically robust results. Accordingly, a minimum observation period of 24 years is recommended to ensure reliable and accurate estimation of sea level trend in the region. (3) An analysis of the SSH and phase over the period 1993–2021 at virtual altimetry stations reveals that the Black Sea experiences peak annual amplitudes during the winter and early spring months, particularly in November, December, January, and February. In contrast, an examination of data from six selected tide gauge (TG) stations indicates that the maximum annual amplitude generally occurs in April-June (June, May, June, May, April, May). The discrepancy in seasonal peak timing between SA and TG derived estimates can be attributed to differences in the spatial and temporal characteristics of sea level signals. Tide gauges, situated along coastlines, are more influenced by local factors such as tidal patterns and vertical land motion, whereas satellite altimetry primarily captures basin-wide sea level variability. (4) To mitigate the uncertainty in sea level estimates induced by noise in the SSH time series, principal component analysis (PCA) was applied to denoise the SSH records for the period 1993–2021. The resulting mean sea level trend was estimated at 1.76 ± 0.56 mm/a, which is in agreement with the Copernicus Marine Service estimate of 1.4 ± 0.83 mm/a for the period 1993–2022. After PCA-based noise reduction, 96.8% of the altimetry stations exhibited a reduction in trend uncertainty, with an average decrease of 1.92 mm/a, the root means square error of SSH time series decreased by 5.06 mm, and the annual amplitude diminished by 23.35%. These results demonstrate the efficacy of PCA in suppressing noise while retaining the long-term trend and spatial characteristics of sea level change.