On non-Gaussian sea surface height variability

Sea surface height anomalies measured by the TOPEX/Poseidon satellite altimeter indicate high values of skewness and kurtosis. Except in a few regions, including the Gulf Stream, the Kuroshio Extension, and the Agulhas Retroflection, which display bimodal patterns of sea surface height variability, kurtosis is uniformly greater than 1.5 times the squared skewness minus an adjustment constant. This relationship differs substantially from what standard Gaussian or double-exponential noise would produce. However, it can be explained by a simple theory in which the noise is assumed to be state-dependent (or multiplicative), meaning that a larger background state implies larger random noise elements. The existence of multiplicative noise can be anticipated from the equations of motion, if ocean dynamics are split into a slowly decorrelating deterministic component and a rapidly decorrelating contribution that is approximated as noise. Such a model raises the possibility of predicting the probabilities of extreme sea surface height anomalies from first physical principles and may provide a useful null-hypotheses for non-Gaussian sea surface height variability.