immediate result was the decision of the TV weather forecasters to extend their
forecasts from 3 days until the early 1990’s to 5 and even 7 days in the mid 1990’s.
In addition to introducing perturbations in the initial conditions, it was found by
the NWP community that introducing model perturbations, or even using multiple models
from different centers also resulted in a major improvement in the forecast skill and the
usefulness of the forecasts. It has been a consistent result that a multimodel ensemble
has a performance that is better than that derived using a single model, even the model
that has the best performance.
- Encourage a hierarchy of models from simple to complex and across scales.
In the quest for realism, some models tend to incorporate a high level of detail in an
attempt to reflect the complicated interacting properties of the system under study.
However, there remains a need for simple models that may be more efficient in providing
insight at a higher level or that may explain the data equally well. One recommendation
of our working group is recognition of the tremendous benefits that “model biodiversity”
can bring to a particular issue or problem. This diversity refers not only to employing
ensembles of models, but also to the application of a variety of approaches and
paradigms to solving common problems, including both simple and complicated models.
As has long been known in biological sciences, biodiversity produces systems that are
both robust and adaptable to different conditions and contexts, as well as developing
innovative solutions to a multiplicity of potential problems. The diversity of paradigms
and approaches would also function like portfolio theory, to spread society’s research
investments out across various “asset” types whose performance is not tied to one
specific approach. Building models from the approach of other disciplines will also lead
to the development of solutions that would have been entirely non-intuitive from a
different discipline. We have found that the coupling of Human and Environmental
Systems (HES) in order to address the issues of sustainability presents additional
reasons to emphasize the need for the application of diverse paradigms. Coupled HES
involve unique challenges not found in solely physical, biological, or social models, as
each involves different classes and kinds of scales, properties, behaviors, and data.
Coupling human to environmental systems therefore entails developing theories and
models composed of submodels requiring very different sets of knowledge. While this
calls for interdisciplinary collaboration, it also calls for the application of approaches from
different fields. We are therefore recommending that mathematical sciences encourage
and participate in the marshaling of a variety of approaches and paradigms to the
theorizing about and modeling of sustainability problems. - Introduce ensemble methods for model comparison
The mathematical framework to statistically assess the validity of simulations has
been developed significantly by theoretical computer scientists in the last decades.
Unfortunately, modelers outside the community have passively ignored this theory. In
view of the considerable challenges presented above, the time has come to integrate
these considerations in model comparisons and validations. In particular, the statistical
foundation for a systematic determination of ranges of predictions needs to be put on
firm, convincing basis to infer public policy recommendations. Lessons can be learned
from the machine-learning community, which has matured in an analogous way over the
last decades, to develop a sound basis for understanding convergence properties in
both algorithmic and heuristic senses.