3.1 Uncertainty quantification
The topic of uncertainty quantification arises whenever complex, process-based
models⎯which often must be implemented via computational approaches⎯are used for
simulating real-world process. Typical issues include:
- Characterizing the bias or discrepancy between models and reality (data);
- Recognizing that cost constraints often mean that models can only be run for
certain combinations of input parameters, requiring extrapolation of model output
to other input parameters; - Accounting for uncertainties in the initial conditions;
- Estimating unknown parameters in the process model, and those arising by
embedding the model in a stochastic framework (i.e., when coupling the model to
data); - Accommodating stochastic features of the process models, independent of the
framework for linking the models to data; - Producing predictions that arise by combining models and observational data, as
might occur via data assimilation methods.
Addressing these issues requires the combination of expertise from
mathematics, statistics, and computer science, as well as the specific subject expertise
required to build the process models and understand the intricacies of the datasets.
Existing tools are available for addressing many of the above issues for simpler models
and datasets, but the challenge that we face is expanding upon these tools, and perhaps
developing new tools that can accommodate the types of complex systems, data
sources, and models that are necessary for advancing sustainability research.
It is possible to capture some aspects of the uncertainty in process-based
models by using randomness. For example, consider the problem of understanding the
basic biogeochemical cycles (BGC) of large water bodies like oceans and their
estuaries. This is a very important problem, since marine life relies on the relationship
between nutrients, phytoplankton, and zooplankton and how they react to temperature,
light, and resource availability. The relationship can be described by a series of non-
linear ordinary differential equations in time, yielding the process model. It is recognized
that the equations are approximations, but standard BGC analyses ignore this. A
physical-statistical approach embraces the uncertainties in the model; i.e., the equations'
coefficients (model parameters) could be modeled as random to account for the size
distribution of phytoplankton and zooplankton (i.e., incorporate parameter uncertainty),
and the equations themselves could still capture the "mass balance" but have a random
closure term (i.e., include process “error” or uncertainty). The coupling of the process-
based BGC model to data may be facilitated by a hierarchical, probabilistic framework
that acknowledges that the data are often measured with error.
Thus, the uncertainty in the data can also be described by measurement or
observational error terms. An issue related to uncertainty quantification in sustainability
science is that complex, process-based models such as the aforementioned BGC model
will often be necessary for synthesizing diverse data and for producing forecasts. As part
of this, we need to develop methods for, and emphasize the importance of quantifying
the various components of uncertainty related to parameters, the process model(s), and
the observational data sets. This uncertainty should be propagated via, for example,
probability theory such that accurate and realistic forecasts are obtained. For example,