Evaluation of Seasonality in Sea Surface Salinity Balance Equation via Function Registration

Sea surface salinity (SSS) is known to change over time due to the transport of freshwater and the dynamics of the ocean. The relationship between SSS and its main determinant, freshwater forcing minus horizontal advection and vertical entrainment (FMAV), is described by a salinity balance equation (SBE). We investigate the dynamics of these two component terms of SBE using the tools of functional data analysis. Specifically, we explore how quickly changes in FMAV are associated with changes in SSS by estimating the time lag between two components through function registration. While existing studies have assumed a constant time lag between the two components, we allow for a time-varying lag, referred to as phase, which more realistically reflects the temporal dynamics of variables. Adopting the functional data analysis framework, we treat SSS and FMAV as functional objects. We estimate the phase between SSS and FMAV by a function that matches seasonal features between the two variables that explains the continuous time lag between SSS and FMAV. We compare the estimation results to a more traditional approach involving harmonic analysis and show that the presented method is more effective in aligning their seasonal features, as measured by the distance between the aligned variables at multiple spatial locations.