Journal of Conference Abstracts

Utilising GLUE in the Estimation of the Predictive Uncertainty of a Dynamic Biogeochemical Model

S. K. Zak¹ (skz@ctr.columbia.edu), K. J. Beven¹ (Keith.Beven@lancaster.ac.uk) &
K. T. Goulding² (Keith.Goulding@bbsrc.ac.uk)

¹ Institute of Environmental and Biological Sciences, Lancaster University, U.K.

² Soil Science Department, IACR-Rothamsted, U.K.

Acid deposition constitutes a major environmental problem over large regions of Europe, the British Isles, and North America. Currently, soil, surface and ground water ecosystems in these regions are undergoing accelerated acidification due to anthropogenic atmospheric pollution. The critical loads approach has been adopted as the basis for decision making in the context of developing and implementing future control strategies for transboundary pollutant gas emissions. A critical load is intended to be a threshold deposition which ecosystems can tolerate without damage and is considered an inherent property of an ecosystem.

Different models, from empirical steady-state calculations through steady-state mass balance geochemical to dynamic models may be expected to produce different predictions of the critical load at a site or within a region. All critical load estimates are based to some extent on models of the nonlinear hydrological, ecological and atmospheric processes controlling the impact of atmospheric pollution. These models contain parameters that may be difficult to estimate precisely and use data associated with varying degrees of measurement and interpretation errors. The result will be uncertainty in the prediction of acid deposition to a particular ecosystem. Error and uncertainty arise from numerous sources: (1) from errors in field measurements of the state of the system; (2) errors in input boundary conditions; (3) errors in the estimation of effective parameter values; and (4) model structural errors. Model structural errors will tend to reflect current limitations in scientific understanding and knowledge.

In this work it is shown how the limitations of the modeling process can be reflected in the estimation of predictive uncertainty. The methodology used is the Generalised Likelihood Uncertainty Estimation (GLUE) of Beven and Binley (1992). This is a Bayesian Monte Carlo simulation-based technique. The background of the GLUE methodology has been an attempt to recognize more explicitly the fundamental limitations of ecological models as simulators of ecosystem processes. One implication of such a recognition is that it should not be assumed that there is one "optimal" model structure or parameter set that can be found to represent a natural system (whether a lumped or distributed representation). The result of this approach is a range of likelihood weighted predictions that may be compared with observed site behaviour. Each likelihood weight may be based on a number of different quantitative as well as qualitative measures. The term likelihood is applied in the GLUE approach in a very broad sense, as some specified measure of how well the model and its associated parameter set conforms to the observed behaviour of the system. For full details of this approach see Zak et al. (1997)

The GLUE methodology is demonstrated here in an application to the simulation of the Park Grass research site at the Rothamsted Experimentation Station, UK, using the SAFE model. SAFE is a dynamic, process oriented soil model created to calculate soil acidification resulting from atmospheric deposition and site specific parameters (e.g, Warfvinge et al., 1993).The model is designed to reconstruct past and future ecosystem characteristics and has been used as a tool in the development of critical load values. The Classical Experiments at the Rothamsted Experimental Station, UK have provided some of the best historical ecosystem data sets. Model simulations for the years 1790 - 2010 have be carried out. Reconstruction/predictions by SAFE of the Park Grass site have been placed within the GLUE framework utilising various likelihood functions, likelihood weights, scaling values and behavioural/non-behavioural delineations. The resulting uncertainty bounds are presented.

References

Beven, K. & Binley, A., Hydrological Processes, 6, 279, (1992).

Warfvinge, P., Falkengren-Grerup, U. & Sverdrup, H., Environ. Poll. 80, 1, (1993).

Zak, S.K., Beven, K. & B. Reynolds, Water, Air and Soil Poll. (in press).