range of the data and facilitates greater insight into the underlying mechanisms
producing the observed patterns.
Another issue that we face in applying a more process-based modeling approach
is the need to balance complexity (detail) with simplicity (transparency). In the
construction of models for sustainability science, we have the potential to build complex
systems of equations that define the process model(s). If such models are to be
informed by datasets such as those described above, then we must be able to link the
datasets to different model components. That is, if the models are overly complex, then
we are potentially faced with an over-parameterization problem such that available data
may not contain enough information to identify or estimate all parameters in the process
model. Such issues are important to consider if such models are to be used for
forecasting or making inferences related to sustainability. In general, models, especially
if informed by data, can be used for many things including making projections and
forecasts, scenario evaluation, capturing nonlinearities, for space/time scaling, to
quantify and propagate uncertainty, and to inform the construction of monitoring
networks. However, care will need to be taken so to avoid poorly-parameterized
models.
Finally good data visualization techniques allow modelers to convey complex
ideas in simple terms and allow non-experts to understand the results (e.g.,
http://www.gapminder.org)..)
- Role of the mathematical sciences
We identified several research themes that the mathematical sciences can
contribute to in the context of advancing both basic and applied sustainability research.
These themes focus on issues associated with measuring, monitoring, and forecasting
elements of sustainability, and are broadly applicable across a range of disciplines in this
general area. An important motivation underlying these themes is the collection and use
of diverse datasets in the context of relatively complex, process-based models related to
sustainability. The idea is that these models will be informed by and improved upon by
existing and new datasets, and the models in turn should be applied to update sampling
and monitoring designs. The data-informed models can subsequently be applied to
forecast quantities relevant to evaluating sustainability. The major themes that we
identified include: - Focus on uncertainty quantification via probabilistic modeling approaches
- Develop sampling designs for monitoring and measuring quantities relevant to
sustainability - Develop data fusion methods for integrating diverse datasets
- Use computer experiment methods as related to sustainability data and models
- Develop model diagnostics for complex, hierarchical models
- Develop model assessment tools for integration or comparison of multiple models
- Develop the aforementioned methods in the context of dynamic spatio-temporal
models - Develop and apply complex networks and network theory in sustainability research
Below we provide more detail on the issues underlying these eight research themes, and
the important role that the mathematical sciences can play in addressing these themes.