44
Chapter 3: Climate Spectra and Stochastic Climate Models
of the atmospheric forcing is measured, namely the surface heat ßux which
itself includes the atmospheric feedback. The SST anomaly equation is then
written
8t T' = H' + m' - >'aT',
where
H' = q' - >'aT'
(3.20)
(3.21)
is the heat ßux term in (3.19), which contributes a feedback >'a, q' and m ' are
white noise processes, and >' 0 is the oceanic contribution to the total feedback
>. (>' = >'a + >'0). The shape of the cross-correlation function between T' and
H' then depends primarilyon the atmospheric feedback (Figure 3.9). When
>'a = 0, the curve is as in Figure 3.7 (dashed line). When >'a < 0 (negative
feedback, as expected ifthe heat ßux contributes to SST damping), the crosscorrelation function takes an antisymmetric appearance, with zero crossing
near zero lag. When >'a > 0 (positive feedback), it peaks when SST lags
but has the same positive sign for alliags (the same signature would occur if
the atmospheric forcing had a slow component, however). As in Figure 3.7,
smoothing would increase the correlation and shift the maxima toward lags
of plus or minus one.
These signatures can be used to interpret the correlations in Figure 3.10 between monthly anomalies in zonally-averaged SST and turbulent heat ßux in
the Atlantic during the period 1949-1979. The anomalies were derived from
the COADS data set, and a second order trend removed from the anomaly
time series to remove some of the artificial trends introduced by the changes
in the wind measurement methods. In the extratropical regions, the atmospheric anomalies lead the oceanic ones, but the slightly anti-symmetric shape
of the cross-correlation functions and the sm aller peak when the ocean leads
by one month suggests that the turbulent heat ßux not only contributes to
generating the SST anomalies, but also acts as a negative feedback. Below
10° N, however, the progressive change in the shape of the cross-correlations
suggests an enhancement of the negative feedback, and at the equator, the
curve simply peaks at zero lag, indicating that heat ßux and SST anomalies
vary in phase: the turbulent heat exchanges play no role in generating the
SST anomalies, but contribute to their damping. This occurs because SST
ßuctuations are in part remotely forced by the wind, because of equatorial
wave propagation, and because cumulus convection creates an intense air-sea
coupling.
In the equatorial Pacific, the SST anomalies are predominantly associated with ENSO and generated through large scale ocean-atmosphere feedbacks involving remote atmospheric forcing, oceanic adjustment and unstable
ocean-atmosphere oscillating modes. These SST anomalies have a longer time
scale than in midlatitudes, and a stronger inßuence on the global climate. It
is not known whether "random" short time scale atmospheric perturbations
Chapter 3: Climate Spectra and Stochastic Climate Models
of the atmospheric forcing is measured, namely the surface heat ßux which
itself includes the atmospheric feedback. The SST anomaly equation is then
written
8t T' = H' + m' - >'aT',
where
H' = q' - >'aT'
(3.20)
(3.21)
is the heat ßux term in (3.19), which contributes a feedback >'a, q' and m ' are
white noise processes, and >' 0 is the oceanic contribution to the total feedback
>. (>' = >'a + >'0). The shape of the cross-correlation function between T' and
H' then depends primarilyon the atmospheric feedback (Figure 3.9). When
>'a = 0, the curve is as in Figure 3.7 (dashed line). When >'a < 0 (negative
feedback, as expected ifthe heat ßux contributes to SST damping), the crosscorrelation function takes an antisymmetric appearance, with zero crossing
near zero lag. When >'a > 0 (positive feedback), it peaks when SST lags
but has the same positive sign for alliags (the same signature would occur if
the atmospheric forcing had a slow component, however). As in Figure 3.7,
smoothing would increase the correlation and shift the maxima toward lags
of plus or minus one.
These signatures can be used to interpret the correlations in Figure 3.10 between monthly anomalies in zonally-averaged SST and turbulent heat ßux in
the Atlantic during the period 1949-1979. The anomalies were derived from
the COADS data set, and a second order trend removed from the anomaly
time series to remove some of the artificial trends introduced by the changes
in the wind measurement methods. In the extratropical regions, the atmospheric anomalies lead the oceanic ones, but the slightly anti-symmetric shape
of the cross-correlation functions and the sm aller peak when the ocean leads
by one month suggests that the turbulent heat ßux not only contributes to
generating the SST anomalies, but also acts as a negative feedback. Below
10° N, however, the progressive change in the shape of the cross-correlations
suggests an enhancement of the negative feedback, and at the equator, the
curve simply peaks at zero lag, indicating that heat ßux and SST anomalies
vary in phase: the turbulent heat exchanges play no role in generating the
SST anomalies, but contribute to their damping. This occurs because SST
ßuctuations are in part remotely forced by the wind, because of equatorial
wave propagation, and because cumulus convection creates an intense air-sea
coupling.
In the equatorial Pacific, the SST anomalies are predominantly associated with ENSO and generated through large scale ocean-atmosphere feedbacks involving remote atmospheric forcing, oceanic adjustment and unstable
ocean-atmosphere oscillating modes. These SST anomalies have a longer time
scale than in midlatitudes, and a stronger inßuence on the global climate. It
is not known whether "random" short time scale atmospheric perturbations