4.1. High-level Recommendations
Four major high-level recommendations emerged from our working group
discussions:
A. Develop a mathematical formulation of sustainability;
B. Foster innovation through a diversity of modeling paradigms;
C. Provide opportunities for involving a broader set of mathematicians;
D. Require that both data and models should be kept open source and made fully
public, and encourage citizen science.
We expand on these recommendations below.
A. Develop a mathematical formulation of sustainability
We recommend development of a common mathematical language to facilitate
integration of different disciplinary approaches to modeling. This may require going
beyond the conveniences of existing mathematical theory. We recommend that
researchers
- Develop theories of dynamics that goes beyond current dynamical systems
theory to address the “messy” real-world problems that exist in complex, adaptive
human-environment systems (put succinctly, “sustainability does not equal
stability”). Whereas dynamical systems address questions of asymptotic
stability, transient behavior naturally occurs in real systems and may be more
important, as in stuttering chains of transmission in the spread of zoonoses for
example (Lloyd-Smith et al., 2009). - Develop theoretical frameworks to aid understanding and interpreting large-scale
computational models
B. Foster innovation through a diversity of modeling paradigms
This recommendation entails several specific steps, including:
- Use ensembles of models for better system forecasting and understanding.
Often, combining the results from different models produced by independent groups
can provide better predictive power than any single model. An example comes from the
history of climate modeling. In December 1991, two major operational Numerical
Weather Prediction (NWP) centers started a major new approach to weather prediction
with the introduction of ensemble forecasting. Until then NWP forecasts were
deterministic, with twice a day forecasts started from the best estimate of the state of the
atmosphere (known as analysis) and run for 10 days at the European Center for Medium
Range Weather Forecasts (ECMWF) and 15 days at the US National Centers for
Environmental Prediction (NCEP). Both centers introduced the idea of running an
ensemble of forecasts started from initial conditions that were given by the analysis to
which different initial perturbations had been added. The difference between the two
approaches was the type of initial perturbations, with NCEP using Breeding of Lyapunov
Vectors, and ECMWF using Singular Vectors.
The introduction of ensemble forecasting had a major positive impact on the
usefulness of the forecasts since the ensembles indicated not only the most probable
forecast but also the uncertainty associated with it. As a result, human forecasters
learned how and where to have confidence in longer forecasts, since weather
predictability depends on the growth of errors in the initial conditions due to atmospheric
instabilities, and is therefore quite dependent on the evolution of the weather itself. An