Dynamics of ENSO
289
12.4. Exercises on chapter 12
(12.1) Ocean-atmosphere interaction
Assume that the temperature in the eastern Pacific (in the NINO3 region) increases by 1 ◦ C.
a. Use Fig. 12.4 and information in section 2.1 such as (2.1) to determine the
amplitude response of the zonal wind stress τ x
∗ caused by a SST (NINO3)
anomaly.
Assume that the wind-stress anomaly is purely zonal, i.e., τ y =0.
b. Calculate the amplitude of the equatorial upwelling anomaly w E∗ caused
by the zonal wind-stress anomaly.
c. Calculate the amplitude of the thermocline anomaly h e∗ in the west Pacific
caused by the zonal wind-stress anomaly.
(12.2) Equatorial upwelling
In section 12.2.2 the Ekman layer equations (12.7) were given in case of linear
friction with damping coefficient a s . Assume that τ y =0.
a. Determine the horizontal Ekman velocities u E∗ and v E∗ in terms of the
wind stress τ x
∗ .
b. Explain why v E∗ =0at the equator.
c. Determine the upwelling velocity w E∗ at the equator for a constant zonal
wind stress τ x = −τ 0 .
d. With a wind stress amplitude τ 0 =0 .1 Pa and a damping coefficient a s =
5.0 × 10 −6 s −1 , determine w E in m/day.
(12.3) The zonal advection feedback
Apart form the thermocline and the upwelling feedback, there is a third feedback: the zonal advection feedback. Assume that there is a region with a strong
zonal background temperature gradient with ∂ ¯
T ∗ /∂x ∗ < 0. Such a region, for
289
12.4. Exercises on chapter 12
(12.1) Ocean-atmosphere interaction
Assume that the temperature in the eastern Pacific (in the NINO3 region) increases by 1 ◦ C.
a. Use Fig. 12.4 and information in section 2.1 such as (2.1) to determine the
amplitude response of the zonal wind stress τ x
∗ caused by a SST (NINO3)
anomaly.
Assume that the wind-stress anomaly is purely zonal, i.e., τ y =0.
b. Calculate the amplitude of the equatorial upwelling anomaly w E∗ caused
by the zonal wind-stress anomaly.
c. Calculate the amplitude of the thermocline anomaly h e∗ in the west Pacific
caused by the zonal wind-stress anomaly.
(12.2) Equatorial upwelling
In section 12.2.2 the Ekman layer equations (12.7) were given in case of linear
friction with damping coefficient a s . Assume that τ y =0.
a. Determine the horizontal Ekman velocities u E∗ and v E∗ in terms of the
wind stress τ x
∗ .
b. Explain why v E∗ =0at the equator.
c. Determine the upwelling velocity w E∗ at the equator for a constant zonal
wind stress τ x = −τ 0 .
d. With a wind stress amplitude τ 0 =0 .1 Pa and a damping coefficient a s =
5.0 × 10 −6 s −1 , determine w E in m/day.
(12.3) The zonal advection feedback
Apart form the thermocline and the upwelling feedback, there is a third feedback: the zonal advection feedback. Assume that there is a region with a strong
zonal background temperature gradient with ∂ ¯
T ∗ /∂x ∗ < 0. Such a region, for