Section 3.3: Stochastic Climate Model
35
Wavenumber spectra of tropospheric variables have been primarily estimated from hemispheric or global data derived from operational products.
Some spectra have been calculated for surface variables and fiuxes, but they
are difficult to interpret in view of the spatial heterogeneity of the fields and
their limited spatial resolution, so that idealized representations have been
constructed for air-sea inter action studies (Frankignoul and Müller, 1979).
Note that Freilich and Chelton (1986) have analyzed surface winds measured
by satellite, showing that an approximately k- 2 behavior holds for their spectrum in the Pacific ocean over wavelengths from 200 to 2200 km. As discussed
in Chave et al. (1991), there is also spatial and interannual variability in the
atmospheric frequency-wavenumber spectra.
When atmospheric spectra are estimated from long time series, some redness is found at very low frequencies, in particular for the dominant large
scale atmospheric patterns. This is illustrated in Figure 3.5 for the areaweighted sea level pressure over the north Pacific region 30° to 65° N, 160° E
to 140 o W, which depicts changes in the Aleutian low in winter and is wellcorrelated with the Pacific North American (PNA) teleconnection pattern, a
preferred mode of variability in the Northern Hemisphere winter. Although
no spectral peak is significant, there is enhanced variance between 2 and
6 years, and a marked redness at periods > 20 years (interdecadal climate
variability). This variability is found throughout the troposphere and is associated with large scale changes in sea surface temperature. It appears to be
associated to a small extent with the EI Niiio-Southern Oscillation (ENSO)
phenomenon, with changes in the tropical Pacific slightly leading the extratropicalones (Trenberth and Hurrell, 1994; Zhang et al., 1994).
3.3 Stochastic Climate Model
At a time when most climate researchers were trying to link climatic changes
to (sometimes far-fetched) variable extern al factors and hypothetical positive
feedback within the climate system, Hasselmann (1976) pointed out that
climate variability might be explained more simply as the integral response
of the slowly varying parts of the climate system to internal random forcing
by the always present short time scale weather fiuctuations. The resulting
climate fiuctuations would have a random walk character, in agreement with
the observed redness of the climate spectra, and the challenge was to find
the positive and negative feedback mechanisms which enhance or damp this
continual generation of climate fiuctuations.
Because there is aseparation of time scale between the fast (atmosphere)
and the slow (ocean, cryosphere, soil, etc.) components of the climate system, its evolution can be described by two subsystems: a system for the
fast "weather" variables i of short time scale t:1: (geopotential height, wind
stress, ... ) where the slow "climate" variables Y can be regarded as constant,
as in most weather prediction models, and a system for the slow climate vari-
35
Wavenumber spectra of tropospheric variables have been primarily estimated from hemispheric or global data derived from operational products.
Some spectra have been calculated for surface variables and fiuxes, but they
are difficult to interpret in view of the spatial heterogeneity of the fields and
their limited spatial resolution, so that idealized representations have been
constructed for air-sea inter action studies (Frankignoul and Müller, 1979).
Note that Freilich and Chelton (1986) have analyzed surface winds measured
by satellite, showing that an approximately k- 2 behavior holds for their spectrum in the Pacific ocean over wavelengths from 200 to 2200 km. As discussed
in Chave et al. (1991), there is also spatial and interannual variability in the
atmospheric frequency-wavenumber spectra.
When atmospheric spectra are estimated from long time series, some redness is found at very low frequencies, in particular for the dominant large
scale atmospheric patterns. This is illustrated in Figure 3.5 for the areaweighted sea level pressure over the north Pacific region 30° to 65° N, 160° E
to 140 o W, which depicts changes in the Aleutian low in winter and is wellcorrelated with the Pacific North American (PNA) teleconnection pattern, a
preferred mode of variability in the Northern Hemisphere winter. Although
no spectral peak is significant, there is enhanced variance between 2 and
6 years, and a marked redness at periods > 20 years (interdecadal climate
variability). This variability is found throughout the troposphere and is associated with large scale changes in sea surface temperature. It appears to be
associated to a small extent with the EI Niiio-Southern Oscillation (ENSO)
phenomenon, with changes in the tropical Pacific slightly leading the extratropicalones (Trenberth and Hurrell, 1994; Zhang et al., 1994).
3.3 Stochastic Climate Model
At a time when most climate researchers were trying to link climatic changes
to (sometimes far-fetched) variable extern al factors and hypothetical positive
feedback within the climate system, Hasselmann (1976) pointed out that
climate variability might be explained more simply as the integral response
of the slowly varying parts of the climate system to internal random forcing
by the always present short time scale weather fiuctuations. The resulting
climate fiuctuations would have a random walk character, in agreement with
the observed redness of the climate spectra, and the challenge was to find
the positive and negative feedback mechanisms which enhance or damp this
continual generation of climate fiuctuations.
Because there is aseparation of time scale between the fast (atmosphere)
and the slow (ocean, cryosphere, soil, etc.) components of the climate system, its evolution can be described by two subsystems: a system for the
fast "weather" variables i of short time scale t:1: (geopotential height, wind
stress, ... ) where the slow "climate" variables Y can be regarded as constant,
as in most weather prediction models, and a system for the slow climate vari-