40
Chapter 3: Climate Spectra and Stochastic Climate Models
Figure 3.6: SST anomalyspectrum at Ocean Weather Station 1(59 0 N, 19°W)
for the period 1949-1964, with 95% confidence interval. The smooth curve is
the stochastic model prediction. (From Frankignoul and Hasselmann, 1976).
10'~----------------------------------~
(OC)'/Hz
('/, .. r)
IST .nom.ly, N. Atl.ntlc
('INDIA')
(Vmonth)
10. 1
fluxes. In a simple one-dimensional mixed-Iayer model, the he at content
equation is
h dd T + we(T - Td) = ~hvr~T + Q - Qd
t
pCp
(3.18)
where T denotes temperature, h the mixed-Iayer depth, W e the entrainment
velo city, ~ the horizontal mixing coefficient, Q the surface heat flux into the
ocean, p the water density, Cp the specific heat at constant pressure and vr~
the horizontal Laplacian, and the index d indicates values just below the
mixed layer base. Denoting anomalies by a prime and means by an overbar,
and neglecting the advection by the mean current, the SST anomalyequation
can be approximately written (Frankignoul, 1985)
Vt T ' =
Q' _ _ (Mi)' . vrh T + ~' v/i"
pCph
h
h
(3.19)
(T' - T~)( we + w~) T - Td,
n2T'
-
h
- --;;-we + ~ v h
It can be shown that this equation has the form (3.13), where v' includes
the terms involving both the short time scale atmospheric forcing and the
mixed layer depth response, and A represents the (Iinearized) dissipation and
feedback processes. The model explains most mid-Iatitude SST anomaly