number of examples of HES which illustrate the essential features of CAS noted above,
and that may serve as motivation to the mathematical sciences community. Not all
examples have the same level of mathematical maturity, as reflected in the differentiated
level of mathematical precision that can be provided in their formulation.
- Examples
We outline five examples that illustrate these research themes. For each
example, emerging challenges and questions in the mathematical sciences are also
described. We will present three examples in sufficient detail to give the reader a clear
sense of the scientific and mathematical issues, followed by two shorter examples to
illustrate the enormous range of coupled human-environment systems
3.1. Fully coupled earth-human systems (Kalnay)
The interaction between human and natural systems has been typically studied
in a unidirectionally coupled fashion, i.e., one component provides input, the other
responds. Examples of this one-way coupling approach include demographic projections
used to predict demand for natural resources (water, energy), and natural disasters
triggering human migration patterns. In a more realistic representation of the Earth
system, its human and natural components are fully coupled, meaning that their coupling
is bi-directional.
It is essential to fully couple systems to allow for important feedbacks. For
example, the atmosphere and the ocean are coupled in both directions, so that the
important chaotic phenomenon of El Niño-Southern Oscillation (ENSO) takes place as
the result of an instability in the coupled ocean-atmosphere system. By contrast, until the
late 1990’s atmospheric and ocean models used to be coupled in a “one-way” mode: the
atmospheric models would affect the sea surface temperature (SST) but could not
change it, and the ocean models would be driven by the atmospheric wind stress and
surface fluxes, but could not change them. As a result these models were not able to
predict the ENSO chaotic oscillations. Since the late 1990’s climate models switched to
fully coupled atmosphere-ocean-land-ice submodels. More recently, biosphere systems
are also being fully coupled, allowing for changes in vegetation able to affect climate
through changes in albedo and soil moisture, but also the local climate determining the
type of vegetation that can grow in a region.
It should be noted that realistic coupled models are considerably harder to develop than
one-way coupled models because there is much more freedom for the coupled model to
drift away from reality. For example, with a one-way coupling, the atmosphere can feel
the ocean sea surface temperature (SST) but cannot change it, so that the SST
“anchors” the atmosphere within realistic limits of temperature. In a two-way coupling, by
contrast, the temperatures of the coupled atmosphere-ocean system have much more
freedom to drift away. This requires a more careful model to develop realistic solutions.
At present, fully coupled climate models (known as Earth System models) have been
developed to the extent that they are now fairly realistic, and there is general agreement
among climate modelers that full coupling is essential in order to have a realistic climate
system.
The human system in many ways now dominates the natural system, with, for
example, domesticated animals making up the vast majority of large mammals , and
most of the land that can be cultivated already devoted to agriculture. Humans are