N 25n 30n 35n 40n 45n 50n

Fig. 4.113 The -3° C anomaly isotherms for 1977-81 (dashed line), 1982-6 (dotted line), and 1987-91 (solid line), superimposed upon the mean late-winter isopycnals (thin solid lines labeled with numbers, in kg/m3) (Deser et al, 1996).

From Figure 4.ii2, during the period from i977 to i989 the temperature anomaly moved down about 260 m, so the vertical velocity is slightly more than 20 m/year, which is on the same order as the vertical velocity in this area of ocean, as inferred from the Ekman pumping rate on the order of 30 m/year. Since Deser's work, there have been many papers published using this line of reasoning, and they all show a similar structure.

Reappearance of the temperature anomaly in the upper ocean An interesting phenomenon identifiable from Figure 4.ii2 is the reappearance of the temperature anomaly in the upper ocean several years after the initial impact of a strong cooling event. Based on the ideas of ventilated thermocline theory, we can define an annual subduction depth Ds = SannT, where Sann is the annual mean subduction rate, and T = i year is the time duration in defining the annual mean subduction rate. The subduction depth ratio is defined as Rs = Ds/hmax.

The distribution of this depth ratio for the North Pacific, inferred from an ideal-fluid thermocline model with continuous stratification, is shown in Figure 4.ii4. The inverse of this ratio is closely related to the time (in years) that a surface temperature anomaly can survive in the upper ocean, which can be seen by comparing this figure with the corresponding figures presented by Frankignoul and Reynolds (i983).

Using a simple one-dimensional model to analyze the thermal balance of the upper ocean heat content, it can readily be seen that it takes about i /Rs years to renew the water property in the mixed layer. In addition, it is clear that the optimal season to form the anomaly is late winter (March i) when the mixed layer is coldest and densest. In addition, only a cold

Fig. 4.114 Subduction depth ratio for the North Pacific, inferred from an ideal-fluid thermocline model (Huang and Russell, 1994).

anomaly is able to survive, because a warm anomaly does not penetrate deep enough and will be wiped out during the following late winter of a normal year, when the late-winter mixed layer is denser and deeper.

4.10 Inter-gyre communication due to regional climate variability 4.10.1 Introduction

Wind-driven circulation has been discussed in previous sections. However, in most cases, our discussions have focused on the steady circulation in individual gyres. For climate study, it is interesting to explore the climate variability of the circulation under different forcing.

A key element of decadal climate changes in the ocean is the possibility of inter-gyre communication. For example, Gu and Philander (1997) proposed an exchange between the subtropical and equatorial gyres through the subduction driven by Ekman pumping in the subtropical basin. This link has been actively pursued by many investigators.

In this section, we discuss a simple mechanism which can drive an inter-gyre communication over decadal time scales. It is well known that changes in wind-stress curl can lead to changes in the thermocline in a given gyre. However, a possible inter-gyre communication due to such a change can be studied as follows.

For a simple reduced-gravity model, the upper layer covers the whole surface, so the lower layer is isolated from air-sea interaction. The total volume of the lower layer is controlled by some rather slow processes such as deepwater formation and diapycnal mixing. We will make the further assumption that over a few decades these processes will not be affected by changes in the wind stress distribution. Therefore, the total amount of the lower layer water will remain unchanged over a relatively short decadal time scale. Because the total volume of the ocean is unchanged, the total volume of the upper layer water should remain unchanged. In order to conserve the volume of water masses, therefore, the global thermocline structure will change correspondingly. In this section, we use a simple steady-state reduced-gravity model to demonstrate the inter-gyre communication due to changes of forcing, such as wind stress and heating/cooling, in an individual basin.

4.10.2 Model formulation

The basic equations of a reduced-gravity model in spherical coordinates were discussed in Section 4.3, and the upper layer thickness obeys the following equation:

2a fx g Jx

Prd X


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