2 1 Introduction
The interactions between subsystems condition, change, and manage many pro-
cesses inside subsystems. It is the need to study the evolution of ES and understand
these inter-component interactions, relationships, and the changes they cause in
subsystem processes that defines ESS as a discipline in its own right. We still do not
understand all of these feedbacks and cannot, as yet, build a model that reproduces
all of the changes in ES, but these problems now hold center stage in ESS.
A large variety of highly nonlinear processes with tremendously wide spectrum
of spatial and temporal scales contributes to ES, which adds to its extreme complex-
ity. The temporal scales range from hundreds of millions of years (paleoclimatic
phenomena) to several minutes (microscale weather events), and the spatial scales
range from thousands of kilometers (global phenomena) to several millimeters (size
of water droplets in the clouds).
Considering subsystems of ES formally, we can say that each subsystem in ES
receives information (input) from other subsystems. This information comes as a
set or a vector of input signals or parameters, which inform the subsystem about
the status of the system as a whole and about the states of the related subsystems.
Air and ocean water temperature and pressure, concentration of CO
2
, radiation, and
heat fluxes are just several examples of such parameters. The subsystem, in turn,
communicates with the system and other subsystems, transmitting information to
them concerning its state as a part of ES. This output information is transmitted
as a set or vector of output parameters or signals. Thus, formally speaking, any
subsystem of ES can be considered as a relationship, usually complex and nonlinear,
between two vectors: a vector of input and a vector of output parameters. Such a
relationship is called mapping.
Various mathematical methods are applied to describe, model, and emulate
mappings that represent the subsystems of ES. Deterministic and statistical ap-
proaches are both employed. The deterministic approach is based on a more or less
complete understanding of first principles or basic processes in the subsystem. This
understanding is usually codified into a set of partial differential equations (PDE).
Statistical approaches are based on working with data and extracting information
directly from the data. They are also called statistical learning (a.k.a. machine
learning, learning from data, predictive learning, data-driven) techniques because,
in a sense, they learn relationships or mappings directly from the data. Such
approaches are used when the understanding of processes in the subsystems is poor
or incomplete or when deterministic approaches become too resource intensive (e.g.,
numerical solutions of PDE).
This book introduces a particular nonlinear CI or statistical learning technique
(SLT), namely, the NN approach, and demonstrates how to apply it for modeling
or emulation of important subsystems of ES. In this chapter in Sect. 1.1, a notion
of ES as a complex dynamical system of interacting components (subsystems) is
presented; the role of organization and structure of a system is discussed. Weather
and climate systems are introduced as subsystems of the ES. It is shown that any
subsystem of ES can be considered as a multidimensional relationship or mapping,
which is usually complex and nonlinear. In Sect. 1.2, evolution of approaches to ES
and its subsystems is discussed, and in Sect. 1.3 the neural network (NN) technique
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