Time series regression of sea level on weather

Analysis of sea‐level and weather records by frequency is done by the usual methods of spectrum analysis, whereupon a regression analysis is performed in each frequency band. The very complete array of existing statistical procedures, for testing hypotheses and allocating confidence intervals, is then available, suitably modified to take account of the fact that the regression coefficients are complex numbers. Associated statistics, such as partial and multiple coherences and residual spectral matrices, may be treated similarly. The combination of estimates from neighboring frequency bands is also discussed. These methods are used to study records of sea level, surface atmospheric pressure, and wind components at Kwajalein and Eniwetok in the Marshall Islands. An 8 × 8 spectral matrix of these variables covering the frequency range of 0 to 0.85 cycles per day is the starting point for the study. The spectra are characteristic of other sea‐level and weather spectra at islands in low latitudes. There is good coherence between the two islands, especially in sea level and atmospheric pressure. At each island there is the usual strong coherence between sea level and pressure, with moderate coherence between sea level and wind at each island. Several regression models of sea level on the weather records are considered in order to study oceanic influences on the sea‐level records free from local weather noise. However, the spatial coherence of the residual sea level is less than that of the original sea‐level records, apparently because most of the original spatial coherence results from coherent weather patterns and not from coherent water motions. If the computed statistical relations are taken as the true relations, the results are not compatible with a simplified theory of free planetary barotropic waves on the surface of an ocean of constant depth. Because of statistical uncertainty, however, little can be deduced regarding the presence or absence of planetary waves.