Sea level reconstructions extend spatially dense data sets, such as those from satellite altimetry, by decomposing the data set into basis functions and fitting those functions to in situ tide gauge measurements with a longer temporal record. We compare and evaluate two methods for reconstructing sea level through an idealized study. The compared sea level reconstruction methods differ in the technique for calculating basis functions, i.e., empirical orthogonal functions (EOFs) versus cyclostationary EOFs (CSEOFs). Reconstructions are created using Archiving, Validation, and Interpretation of Satellite Oceanographic (AVISO) satellite altimetry data and synthetic tide gauges. Synthetic tide gauge records are simulated using historical distributions and real high-frequency signal to test reconstruction skill. The CSEOF reconstructions show high skill in reproducing variations in global mean sea level (GMSL) and ocean climate indices, and are affected less by both limited tide gauge distribution and added high-frequency tide gauge signal than EOF reconstructions. Typically, CSEOF reconstructions slightly underestimate sea level amplitudes while EOF reconstructions overestimate sea level amplitudes, in some cases, significantly. Both of these results are accentuated with decreasing quality of the synthetic tide gauge data set. Additionally, we investigate how the reconstructions differ when reconstructing with more of the variance retained in the basis functions. Increasing the variance explained by the basis functions from 70% to 90% reduces the efficacy of an EOF reconstruction to reproduce common ocean indices when noise is included in the tide gauge data sets. These results show that in the idealized comparative cases examined the CSEOF method of sea level reconstruction creates more robust reconstructions, especially when less than ideal tide gauge data are used.
