Assessment of sea level variability derived by EOF reconstruction

The empirical orthogonal function (EOF) reconstruction (EOFR) combines the dense observations, for example, satellite altimetry data or model output covering a short period, and sparse tide gauge records (TGRs) spanning a long period to infer the past sea level variability (SLV). Given that the number of the TGRs reduces significantly backward over time, it is necessary to assess how the sparse TGRs affect the reconstructed SLV. Meanwhile, EOFR involves two techniques, that is, using error matrix or not, which has not yet been fully assessed. We find that error matrix plays an important role in the EOFR. Using error matrix produces better reconstructed SLV than those without error matrix, especially when the TGRs are sparse (e.g. <100). If the error matrix is not included, the SLV reconstructed with sparse TGRs tends to be seriously overestimated. It is also found that global mean sea level variability reconstructed with sparse TGRs is not reliable even the error matrix is used. However, the recovery of first EOF pattern is shown to be robust through the entire 20th century (correlation > 0.7). Since the first EOF is highly related to El Nino-Southern Oscillation (ENSO), this suggests that EOFR is useful for revealing the evolution of ENSO variability.