Optimal Surface Excitation of the Thermohaline Circulation

Laure Zanna,Eli Tziperman

doi:10.1175/2008jpo3752.1

Abstract

Abstract The amplification of thermohaline circulation (THC) anomalies resulting from heat and freshwater forcing at the ocean surface is investigated in a zonally averaged coupled ocean–atmosphere model. Optimal initial conditions of surface temperature and salinity leading to the largest THC growth are computed, and so are the structures of stochastic surface temperature and salinity forcing that excite maximum THC variance (stochastic optimals). When the THC amplitude is defined as its sum of squares (equivalent to using the standard L2 norm), the nonnormal linearized dynamics lead to an amplification with a time scale on the order of 100 yr. The optimal initial conditions have a vanishing THC anomaly, and the complex amplification mechanism involves the advection of both temperature and salinity anomalies by the mean flow and of the mean temperature and salinity by the anomaly flow. The L2 characterization of THC anomalies leads to physically interesting results, yet to a mathematically singular problem. A novel alternative characterizing the THC amplitude by its maximum value, as often done in general circulation model studies, is therefore introduced. This complementary method is shown to be equivalent to using the L-infinity norm, and the needed mathematical approach is developed and applied to the THC problem. Under this norm, an amplification occurs within 10 yr explained by the classic salinity advective feedback mechanism. The analysis of the stochastic optimals shows that the character of the THC variability may be very sensitive to the spatial pattern of the surface forcing. In particular, a maximum THC variance and long-time-scale variability are excited by a basin-scale surface forcing pattern, while a significantly higher frequency and to some extent a weaker variability are induced by a smooth and large-scale, yet mostly concentrated in polar areas, surface forcing pattern. Overall, the results suggest that a large THC variability can be efficiently excited by atmospheric surface forcing, and the simple model used here makes several predictions that would be interesting to test using more complex models.

Highlights

The North Atlantic Ocean sea surface temperature (SST) and salinity (SSS) exhibit variability on different time scales from interannual (e.g., Levitus 1989) to interdecadal and decadal (Kushnir 1994) that are often attributed to the variability of the thermohaline circulation (THC)
The nonnormal dynamics and predictability of the Stommel box model were discussed by Lohmann and Schneider (1999), and in addition, transient amplification and stochastic optimals emerging from the nonnormality of the THC dynamics were investigated by Tziperman and Ioannou (2002) and Zanna and Tziperman (2005, hereinafter ZT)
A second objective of this paper is to introduce an alternative in which the amplitude of the THC is measured by its spatial maximum value. We show that this alternative is equivalent to using the Lρ norm and introduce the needed mathematical machinery to find the optimal initial conditions under this norm, and apply it to the THC problem

Summary

Introduction

The North Atlantic Ocean sea surface temperature (SST) and salinity (SSS) exhibit variability on different time scales from interannual (e.g., Levitus 1989) to interdecadal and decadal (Kushnir 1994) that are often attributed to the variability of the thermohaline circulation (THC). Ing to such transient growth are referred to as optimal initial conditions, and the spatial structure of the stochastic forcing leading to maximum variance of the model solution is referred to as stochastic optimal (Farrell and Ioannou 1996; Kleeman and Moore 1997). The calculation of the optimal initial conditions using a standard sum-of-squares measure for the amplitude of the THC perturbations at all spatial locations (i.e., L2 norm) leads to physically meaningful results yet to a singular mathematical problem (Tziperman and Ioannou 2002; Zanna and Tziperman 2005). A second objective of this paper is to introduce an alternative in which the amplitude of the THC is measured by its spatial maximum value We show that this alternative is equivalent to using the Lρ norm and introduce the needed mathematical machinery to find the optimal initial conditions under this norm, and apply it to the THC problem.

Model description

Stochastic optimals of the THC

Findings

Conclusions