- The oceans contain large amounts of methane, currently in a frozen state, but
subject to release if the ocean temperature increases by a few degrees. Since
methane is itself a potent greenhouse gas, this could lead to a dangerous
feedback cycle. - Glacial melting (increases in fresh water flow into the oceans has the potential to
induce massive changes on ocean currents, which could have extreme effects on
future climate conditions.
These factors all impact marine ecosystems, including fisheries and coral reefs,
so their effects need to be incorporated into models and management decisions on the
long time scale. The mathematical techniques that we suggest be developed further
would help in addressing these ecosystem models on longer time scales.
2.2. Forest management
Forests are ecosystems which are important for sustainability at many levels,
ranging from the provision of renewable resources to carbon storage to provision of
habitat for other species. Forests are under continual threat from many directions
including development, changing climate, diseases, and many other issues. A
comprehensive approach to sustainability is obviously required, but the problem is so
large that important questions that are less comprehensive must be solved first.
Two interrelated threats to forest health are forest insect pests and forest fires,
both of which can have impact beyond the forest. These threats are both subjects of
extensive work in the mathematical sciences, and build upon a wide array of both
classical and cutting edge mathematical, statistical, and computational tools.
One critical issue in the management of forests is the policies maintained for fire
suppression. For many years, the US government had maintained a policy of total
suppression, but this has been reversed from the gradual understanding that it is not in
the long-term interest of sustainability of the forests. A number of unintended
consequences contributed to this change of perspective: for example, suppressing forest
fires leads to the exaggerated build-up of undergrowth and younger stands of trees,
which make catastrophic fires more likely; the seeds of the sequoia are released only
with the heat of fires from the forest floor; the extended aging of the pine forests of
British Columbia was a contributing factor in their devastation by the pine beetle, which
destroyed 50% of those forests.
Once one determines that some fires should be suppressed and others not, then
one must introduce a process to decide which fires to suppress. This has been the
domain of a great deal of mathematical modeling already. For example, Parija, Kumar,
Xi, and Keller (2007) apply a mixed-integer programming approach to the question of
budget allocation for fire program analysis (based on an earlier model of Rideout and
Kirsch, 2002), where the objective is to minimize the total utility of the acres burned. This
approach is one of static deterministic planning, in contrast to, for example, the work of
Hof and Bevers (2000, 2002) that provides mathematical programming tools for longer-
term decision-making in a stochastic setting.
However, what is absent from the current state of the art is the ability to provide
real-time support for making fire suppression decisions in the context of a stochastic
model of the state of the forest as it evolves over an intermediate time frame. This is not
surprising - the computational intractability of such a stochastic optimization model (even