Detecting rainfall through prediction of precipitation forcing in the salinity balance equation

This work explores the possibility of using sea surface salinity (SSS) as a rain gauge. Specifically, we investigate the predictive ability of a parametric model, given by the salinity balance equation to detect rainfall events in the ocean, based on data from the SPURS-1 mooring in the subtropical North Atlantic. Precipitation data is a zero-inflated time series with "spikes" corresponding to rainfall events, which can be modeled parametrically by defining the location, intensity, and duration of such events. Therefore, rainfall detection can by formulated as the statistical problem of predicting these lower-dimensional parameters. Qualitatively, rainfall events are associated with a sudden dip and recovery of SSS, which agrees with the dynamics of the salinity balance equation. We show that the salinity balance equation can reproduce the qualitative response of SSS to precipitation, allowing the specification of a statistical model for their relationship. By fitting this statistical model to the SPURS-1 SSS and evaporation data, we are able to predict a sudden impulse change in the rainfall time series within a limited time horizon. Seasonal variables and covariates may be added to this model to further improve prediction.