Managing Uncertainty in Complex Geospatial Models

Dan Cornford and Remi Barillec
Non-linearity and Complexity Research Group Aston University Birmingham, UK
{d.cornford, r.barillec}

Abstract: The development of increasingly complex, often processes based, models of geospatial phenomena makes the management of uncertainty in such models ever more pressing. Uncertainties on inputs to the models, including parameters within the models, can have complex and difficult to predict effects on uncertainties on the outputs. One approach to managing uncertainties in complex models is to develop emulators, which are statistical representations of our beliefs about the model we are analysing. The emulator, or surrogate statistical model, can then be applied to a range of typically Monte Carlo based analysis methods including uncertainty analysis, sensitivity analysis, calibration and optimal decision making. Applying such emulation ideas to geospatial models presents several challenges. First it is necessary to be supplied with, or elicit prior beliefs over, the distribution of the various inputs to the model. Where the geospatial model has many inputs joint specification of beliefs remains challenging. Geospatial models often also have high numbers of outputs, for example the value of some variable across a spatial or spatio- temporal field. Handling high dimensional outputs in emulation is challenging since this requires the specification of a multivariate Gaussian process (Bayesian cokriging). The paper describes the emulation framework, including the subjective Bayesian approach within which it forms a component tool. Particular focus is placed on extending emulator approaches to analysing geospatial models in the context of dynamic spatio- temporal simulators. The results illustrate that emulation can be applied jointly to relatively high dimensional outputs particularly where these admit an intrinsically lower dimensional representation. The conclusion addresses the strengths and weaknesses of the emulation approach to managing uncertainties in complex geospatial models.

Keywords: emulation, meta-models, surrogate models, Monte Carlo, Gaussian processes, kriging.

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