Predicting surface oscillations in Lake Superior from normal mode dynamics

Satellite observation of sea surface height (SSH) may soon have sufficient accuracy and resolution to map geostrophic currents in Lake Superior. A dynamic atmosphere correction will be needed to remove SSH variance due to basin-wide seiching. Here, the dynamics of rotating barotropic gravity modes are examined using numerical models and lake-level gauges. Gravity modes explain 94% of SSH variance in a general circulation model, and evolve as forced, damped oscillators. These modes have significant SSH, but negligible kinetic energy (2 J m−2) and dissipation rates (0.01 W m−2) relative to other motions in Lake Superior. Removing gravity modes from instantaneous SSH allows geostrophic currents to be accurately computed. Complex empirical orthogonal functions (CEOFs) from 50 years of data at 8 lake-level gauges show patterns consistent with the first two gravity modes. The frequency spectra of these CEOFs are consistent with forced, damped oscillators with natural frequencies of 3.05 and 4.91 cycles per day and decay time scales of 4.5 and 1.0 days. Modal amplitudes from the general circulation model and lake-level gauges are 80% coherent at 1 cpd, but only 50% coherent at 3 cpd, indicating that the atmospheric reanalysis used to force the general circulation model is not accurate at the high natural frequencies of the gravity modes. The results indicate that a dynamic atmosphere correction should combine modeled gravity modes below 1 cpd and observed mode-1 and 2 amplitudes (from lake-level gauges) at higher frequencies. An inverted barometer correction is also recommended to account for low-frequency atmospheric pressure gradients that do not project onto gravity modes.