Improved tidal estimates from short water level records via the modified harmonic analysis model

To fully resolve eight major tides from short-term records, classical harmonic analysis model usually infers unresolved constituents with the help of inference relationships from nearby long-term tide gauges. Our previous study developed a modified harmonic analysis model using the credo of smoothness (i.e., MHACS) which can achieve this without inference relationships. Via introducing the inherent natural links between major tides, MHACS breaks the restrictions of the Rayleigh criterion and requires only ∼9-day hourly records to resolve eight major tides. However, when data length is shorter than 9 days, the results of MHACS become problematic due to over-fitting. In this study, we introduce ridge regression to replace ordinary least squares (OLS) in the MHACS. Practical experiments on short-term hourly tide gauge records and satellite altimeter observations indicate that ridge regression can effectively eliminate meaningless mathematical artifacts obtained by OLS. The minimum length of records for MHACS to resolve eight major tides dramatically decreases from ∼210 h to ∼75 h as a result of using ridge regression. It is also found that ridge regression can notably reduce the uncertainties of tidal estimates from MHACS. Moreover, other modified harmonic analysis models such as NS_TIDE designed for river tides also suffer from over-fitting which can be solved by ridge regression in a similar way.