2 1 Introduction
from a climate model that we use as a workbench to illustrate the various methods,
their limitations and their potential. The algorithms have been implemented using
M
ATLAB and we include some sample source codes for a few of the key methods
employed. All pictures and examples used in the book may be reproduced by using
the data sets and the routines available in the book WebSite.
Though the main thrust of the book is for climatological and meteorological ex-
amples, we feel that the treatment is sufficiently general that the discussion is useful
also for student and practitioners in other fields, as long as they deal with variables
that depend on two parameters like for instance space and time. This book can then
be used as a reference for practical applications or it can be used in graduate courses
as a companion to a more extensive book like (von Storch and Zwiers 1999; Wilks
2005; Preisendorfer 1988).
For most of this book we will use two data sets to illustrate our discussion. The
first is a time series of monthly mean geopotential data at 500 mb (Z500), obtained
from a simulation with a general circulation model forced by observed values of
monthly mean Sea Surface Temperatures (SST). The data sets cover 34 years, cor-
responding to the calendar years 1961–1994. Z500 is a very good indicator of upper
air flow, since the horizontal wind is predominantly aligned along the geopotential
isolines. Figure 4.1 shows a few examples taken from the data set. It is possible to
note the large variability from 1 month to the other (top panels), but also the large
variability at the same geographical point, as the time series for the entire series
(lower panels) show. It is clear that the geopotential at 500 mb is characterized by
intense variability in space and time and a typical month may be as different from
the next month as another one chosen at random. The large variability in space and
time makes it a very good test case to practice at will. In the final chapter we will
use two more time series, also 34 years long, obtained imposing the same SST dis-
tribution but with a small perturbation in the initial condition of the atmospheric
numerical model. These small errors grow very quickly in a typical expression of
the chaotic nature of the atmosphere and soon the two simulations are as different
from each other as any other two started independently.
The second data set is the set of Sea Surface Temperatures (SST) used to force
the simulations. The data have been compiled in monthly means on the same grid
as the atmospheric data. The SST force a special signal on the geopotential field,
leaving an identifiable signature in the atmosphere. The variability of the Z field
is therefore composed of variability that is intrinsic to the atmosphere and maybe
other components of the Earth system and variability that is induced by the SST
variability, that varies more slowly. This mixture creates a very rich and challenging
situation for the methods presented here. In the last chapter we will use two data
sets obtained from simulations from a climate models. They represent the tropical
SST and the east-west wind and they also are monthly means for about 200 years of
simulations. This is a case of tightly coupled fields that show how the generalized
regression methods can really identify covarying fields.
The Empirical Orthogonal Functions are introduced in Chap. 4,aftertwoin-
troductory chapters on basic algebra and basic statistics that are needed to refresh
elementary notions and fix the vocabulary. Extensions to the EOF concept are