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

Abstract

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 transport from the boundary current. These three time scales and the precipitation amplitude determine the strength of the ocean response to changes in precipitation and the phase relation between precipitation, changes in salinity and temperature, and changes in heat fluxes. It is demonstrated that the theoretical predictions agree qualitatively well with results from the eddy-resolving numerical model. This demonstrates the fundamental role of mesoscale eddies in the ocean response to time-dependent forcing and provides a framework with which to assess the extent to which observed variability in marginal sea convection and water mass transformation are consistent with an external forcing by variations in precipitation.

Thermally Forced Transients in the Thermohaline Circulation

“…Following Spall (2012) and Yasuda and Spall (2015), a simple model is now developed to represent the gross characteristics of the water mass properties and transports associated with deep convection. The model consists of two regions: an interior where deep convection takes place and a buoyant cyclonic boundary current that flows around the deep convection site (see the appendix).…”

“…A similar set of equations was also analyzed by Yasuda and Spall (2015) subject to time-dependent precipitation. A brief summary of the derivation is given in the appendix, and a more detailed derivation can be found in Yasuda and Spall (2015).…”

“…A similar set of equations was also analyzed by Yasuda and Spall (2015) subject to time-dependent precipitation. A brief summary of the derivation is given in the appendix, and a more detailed derivation can be found in Yasuda and Spall (2015). The nondimensional difference between the temperature in the boundary current and the temperature in the basin interior is DT, and the nondimensional salinity difference is DS.…”

“…Yasuda and Spall (2015) consider such solutions for changes in the mean precipitation. They are characterized by an exponential adjustment with an e-folding time scale of the eddy flushing time scale (see also Straneo 2006).…”

“…The ocean response to variations in atmospheric temperature differs from that due to variations in precipitation primarily by the introduction of the atmospheric restoring term, represented by 2m/ in the definition of C 1 . The equivalent constant for the precipitation-forced system is DT 0 2 DS 0 (Yasuda and Spall 2015). In the weakly eddying regime, 2m/ 1, and it dominates the terms due to eddy fluxes 2DT 0 2 DS 0 .…”