40

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•

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SO Index (0.1 mb)

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•

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••• ••• •• • the radiative transfer calculation can be performed

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20

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once estimates of „ and ln „ are available. The

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•• •

latter can be obtained from „ and Ac by means of

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0

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•• •

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a simple regression model.

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-20

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We use satellite data described by Barker,

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Wielicki, and Parker [18] in Section 8.4 to

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examine the observed relationship between ln „

•

and corresponding („ , Ac ) pairs. The data consists

-200 -100 0 100 200

SST Index (0.01 C)

of 45 estimates of (ln „ , „ , Ac ) that were derived

from 45 ocean images taken by the Landsat

Figure 8.1: Scatter plot of monthly values of the SO

satellite. Each image covers an area of about

index versus the SST index for 1933“84 inclusive.

3400 km2 . Figure 8.2 shows three of these images,

Units: 0.1 mb (SOI), 0.01 —¦ C (SST Index).

and Figure 8.3 shows the derived data. Note that

the relationship between „ and ln „ is curvilinear

¯

(Figure 8.3, left). Also, note that, even though there

shown in Figure 8.1, and their corresponding time

are a substantial number of scenes that are fully

evolutions are shown in Figure 1.4. Both diagrams

covered (i.e., Ac = 1), this does not preclude

show the strong tendency for the two indices to

variability of ln „ .

co-vary; when the SOI is large and positive, the

tropical Paci¬c SSTs east of the date line also tend

to be large and positive. We return to this example 8.2 Correlation

in Sections 8.2 and 8.3.

8.2.1 Covariance. The covariance between two

random variables X and Y is de¬ned as

8.1.4 Example: Radiative Transfer Parame-

Cov(X, Y) = E((X ’ µ X )(Y ’ µY )),

terization in a GCM. AGCMs use parame- (8.2)

terizations to describe the effect of unresolved

where µ X and µY are the mean values of X and Y

sub-grid scale processes in terms of larger resolved

respectively. (See also Section 2.8.)

scale quantities [6.6.6]. One such process is the

Climatologists often interpret covariances in-

transmission of short wave radiation (i.e., light)

volving winds as transports [311]. For example,

through the atmosphere to the land surface, where

Figure 8.4 displays the meridional transient eddy

this energy is either re¬‚ected or converted into

transport of zonally averaged zonal momentum, as

other forms (such as latent and sensible heat). The

simulated by a GCM in the December, January,

propagation of light through the atmosphere at a

February (DJF) season. The ˜eddy component™

speci¬c location is strongly affected by factors

of any variable, here the wind, is the deviation

such as the three-dimensional structure of the

from the spatial mean, here the zonal mean. A

cloud ¬eld and the distribution of other materials,

signi¬cant part of the variability in this component

such as aerosols that may re¬‚ect, refract, or absorb

stems from cyclones or ˜eddies.™ The ˜transient™

light.

part of the wind statistic is the variability around

AGCMs need to know the grid box average of

the time mean (the ˜stationary™ component). The

light energy incident upon the ground (or passing

transient eddy transport is the zonally averaged

though an atmospheric layer). Radiation transfer

covariance between the space“time variable part

codes used in AGCMs estimate these averages

of, for instance, the zonal and meridional wind.

from other grid scale parameters that are simulated