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Influences of time-dependent precipitation on water mass transformation and heat budgets in an idealized marginal sea are examined using theoretical and numerical models. The equations proposed by Spall in 2012 are extended to cases with time-dependent precipitation whose form is either a step function or a sinusoidal function. The theory predicts the differences in temperature and salinity between the convective water and the boundary current as well as the magnitudes of heat fluxes into the marginal sea and across the sea surface. Moreover, the theory reveals that there are three inherent time scales: relaxation time scales for temperature and salinity and a precipitation time scale. The relaxation time scales are determined by a steady solution of the theoretical model with steady precipitation. The relaxation time scale for temperature is always smaller than that for salinity as a result of not only the difference in the form of fluxes at the surface but also the variation in the eddy transpor...

Influences of Time-Dependent Precipitation on Water Mass Transformation, Heat Fluxes, and Deep Convection in Marginal Seas