are caused by large-scale internal atmospheric with the 1950“80 segment of a data set that

processes so that the EOFs have a simple large- extends back to 1901. Since the 1901“49 segment

scale structure. In case of the ocean (SST), is independent of that used to ˜train™ the model

however, the coherent variations (EOFs) are the (14.27), it can be used to validate the model.

oceanic response to the large-scale atmospheric Figure 14.5 shows both the speci¬ed and observed

variations. This response really does not have winter mean rainfall averaged over all Iberian

simple structure (recall our description in [14.3.3] stations for this period. The overall upward trend

of the ocean™s response to NAO variations). and the low-frequency variations in observed

precipitation are well reproduced by the indirect

14.3.3 North Atlantic SLP and Iberian method indicating the usefulness of the technique

Rainfall: Analysis and Historic Reconstruction. (14.27) as well as the reality of both the trend and

In this example, winter (DJF) mean precipitation the variations in the Iberian winter precipitation.

14: Canonical Correlation Analysis

326

Figure 14.5: Five-year running mean of winter

mean rainfall averaged across Iberian rain

gauges. The solid curve is obtained from station

data, and the dotted curve is imputed from North

Atlantic SLP variations [403].

14.3.4 North Atlantic SLP and Iberian

Rainfall: Downscaling of GCM output. The

regression approach described above has an

interesting application in climate change studies.

GCMs are widely used to assess the impact

that increasing concentrations of greenhouse gases Figure 14.6: Downscaled and grid point response

might have on the climate system. But, because of of Iberian precipitation in a ˜2—CO2 experiment™

their resolution, GCMs do not represent the details [403].

of regional climate change well. The minimum

scale that a GCM is able to resolve is the distance

statistical relationship between R and L of the

between two neighbouring grid points whereas the

form

skilful scale is generally accepted to be four or

more grid lengths. The minimum scale in most

R = G(L, ±) + (14.28)

climate models in the mid 1990s is of the order

of 250“500 km so that the skilful scale is at least

in which G(L, ±) represents a substantial

1000“2000 km.

fraction of the total variance of R. Vector ±

Thus the scales at which GCMs produce

contains parameters that can be used to adjust

useful information does not match the scale at

the ¬t of (14.28).

which many users, such as hydrologists, require

• is reliably simulated in a climate model.

information. Statistical downscaling [403] is a

possible solution to this dilemma. The idea

3 Use historical realizations (rt , lt ) of (R, L) to

is to build a statistical model from historical

estimate ±.

observations that relates large-scale information

that can be well simulated by GCMs to the 4 Validate the ¬tted model on independent

desired regional scale information that can not be historical data or by cross-validation (see

simulated. These models are then applied to the [18.5.2]).

large-scale model output.

5 Apply the validated model to GCM simulated

The following steps must be taken.

realizations of L.

1 Identify a regional climate variable R of This is exactly the process that was followed

interest. in the previous subsection. A model (14.27) was

constructed that related Iberian rainfall R to

North Atlantic SLP L through a simple linear

2 Find a climate variable L that

functional. The adjustable parameters ± consisted

• controls R in the sense that there is a of the canonical correlation patterns Fpr e and

1

14.4: Redundancy Analysis 327

onto the ¬rst eight EOFs of daily winter SLP.

Analyses were performed for lags „ = 1, . . . , 5

days, but we discuss only the „ = 3 days results

below.

The ¬rst pair of PPPs is shown in Figure 14.7.

The patterns are normalized such that the variance

1

of the coef¬cient of F0 is 1, and that of

√

the coef¬cient of F3 is 1/ ρ1 . With this

1

normalization, the coef¬cient for the regression

1 1

of the F0 -coef¬cient on the F3 -coef¬cient is the

identity. Also, the patterns are scaled so that if

-4

1

the initial state is a multiple of F0 , then the best

-2 1

predictor is the same multiple of F3 . Patterns

0

F01 and F31 are rather similar indicating that

2

the analysis has selected the regional SLP mode

4

that is most persistent on synoptic time scales.

6

The reduction of the magnitude by about 1/3

indicates that this persistence goes with some

damping. Thus, the forecast incorporated in this

pair of patterns implies constancy in the pattern,

but a reduction of the intensity, i.e., ˜damped

Figure 14.7: Principal Prediction Patterns F01 persistence™.

= 3 days (bottom) for the

(top) and F 1 with This statement also holds for the other patterns

North Atlantic / European Sector daily winter SLP. and is further supported by comparing the

From Dorn and von Storch [103]. forecast skill, as given by the anomaly correlation

coef¬cient11 between the true SLP ¬eld and

FS1L P and the canonical correlation ρ1 . These the ¬eld predicted by either PPP or persistence

(Figure 14.8). The skill of the two forecast

parameters were estimated from 1950 to 1980

schemes is practically identical and exhibits the

data. Observations before 1950 have been used to

characteristic decay with increasing lag. Thus, the

validate the model.

PPP forecast is no more skilful than the simpler

Downscaling model (14.27) was applied to the

˜competitor™ persistence.

output of a ˜2—CO2 ™ experiment performed with

However, the PPP forecast scheme should not

a GCM. Figure 14.6 compares the ˜downscaled™

be dismissed out of hand. By conditioning on the

response to doubled CO2 with the model™s grid

proportion of spatial variance represented by F01 ,

point response. The latter suggests that there will

the PPP forecast was found to be more skilful

be a marked decrease in precipitation over most

when the proportion is large (Figure 14.8, bottom).

of the Peninsula whereas the downscaled response

Thus the PPP scheme also gives a forecast of

is weakly positive. The downscaled response

forecast skill.

is physically more reasonable than the direct

The utility of the PPP technique needs further

response of the model.

exploration and the user is advised to examine

all results obtained with this technique critically.

14.3.5 Principal Prediction Pattern of North In particular, surprisingly good results may be

Atlantic / European SLP. Dorn and von generated by using short time series or by failing

Storch [103] used the Principal Prediction Pattern to adequately reduce the degrees of freedom of the

(PPP) analysis technique to study the synoptic problem.

predictability of sea-level pressure (SLP) over the

eastern North Atlantic and Western Europe. This