indicators of sustainable development relate to ‘green’ output and productivity measures
in which the depreciation of natural capital is being considered.
The above brief snippets indicate the wide variety of problems of sustainability that
arise from the interplay between natural and human processes and the opportunities for
mathematical sciences to address these problems. The power of mathematical sciences
methods is that tools developed for one application are often generalizable and
applicable to other applications. Still, specific critical applications have historically been
the driver of new mathematics and problems of sustainability are certainly likely to be
such a driver. Thus, though we would be tempted to organize a discussion around
mathematical sciences topics that cross over into a wide variety of applied areas, we
have chosen to organize the rest of this report around illustrative examples of applied
topics that are clearly connected to the need for new mathematical sciences
approaches.
- Seven Specific Examples
We focus here on seven examples in more detail where mathematical sciences
methods are already utilized or seen to be relevant. We highlight inadequacies in current
methods and propose new mathematical sciences frameworks for their investigation. We
also discuss research areas related to major challenges in sustainability that cannot be
addressed without these analytical, numerical, computational and statistical tools.
Example 1: Impacts of Climate Change
As policy makers and politicians formulate the policies and make the decisions
for a sustainable Earth, the effects of climate change exacerbate the problems and
issues they face. With the engagement of mathematicians and statisticians and
scientists, new paradigms for decision making in the face of the Earth’s changing climate
will be needed to face these challenges which will require novel mathematical and
statistical tools. Below, we outline some of the issues and the some of the areas where
mathematics and statistics can contribute.
Climate projection/prediction is fraught with uncertainty. The natural variability of
the climate system contributes to such uncertainty, as well as a lack of knowledge about
the trajectories of future emissions of greenhouse gases and aerosols and how the Earth
system will respond to these forcings. When climate models are a part of the mix, there
are additional uncertainties that arise from the parametric uncertainty resulting from
approximations to processes that exist below the spatial scale of the climate model as
well as the structural uncertainty resulting from the processes that are unknown and not
implemented in climate models or processes that are poorly implemented in the climate
models. Current approaches to studying these uncertainties involve creating climate
model ensembles that are essentially collections of model runs that result from
perturbing initial conditions or physical parameterizations, using completely different
models, or some combination of all of these.
There is an emerging field of uncertainty quantification that combines many of
the elements of computational mathematics and statistical science, and there is a great
opportunity for research in this area to contribute in climate science by working with
climate models to improve calibration and assessment (although these are serious
challenges made all the more difficult since the Earth system is not itself in equilibrium),