Decision Making and Uncertainty: Bayesian Analysis of Potential Flood Heights
Manson, Steven M., Ratick, Samuel J., Solow, Andrew R., Geographical Analysis
This paper provides a case study of a method to estimate the value of additional information, before its acquisition, to aid decision making in the face of uncertainty. The approach employs conditional simulation in a Monte Carlo framework to conduct a Bayesian assessment of the value of information in an explicitly spatial setting. This paper demonstrates the procedure as applied by a hypothetical decision maker concerned with coastal flood control where flood damage is dependent on the spatial distribution of elevation. A set of known survey points provides the decision maker with limited knowledge of elevation. The method explored in the paper allows the decision maker to ascertain the potential value of additional survey information in terms of its ability to reduce uncertainty about flood damage.
Floods are one of the most common hazards faced by humans. The risk posed by flooding has become more significant in light of global environmental change. In particular, there is general agreement in the global change research community on the potential for an increase in the mean global temperature resulting in subsequent sea-level rise (Wigley and Raper 1992). In addition to higher flood heights, a raised base water level accelerates beach erosion, increases flood frequency, and affords greater energy to waves and storm surges (Leatherman 1992).
Decision makers, ranging from individuals to national governments, must decide among a variety of mitigative and adaptive responses to flooding. This decision process is fraught with uncertainty stemming from scientific disagreement over the magnitude of sea-level rise, the changing nature of coastal landform processes, and insufficient knowledge of the topography of susceptible areas. Uncertainty affects how decision makers plan for flooding given that flood alleviation measures have different social and economic costs. Decision makers must, therefore, often acquire additional information in order to reduce uncertainty and better understand potential flood processes.
This study is an outgrowth of a project sponsored by the National Oceanic and Atmospheric Administration (NOAA) to examine the role of uncertainty about topography in understanding the potential effects of sea-level rise (Ratick et al. 1994). The present research examines decision making about flooding by joining geographic information system (GIS) methods and spatial analysis to implement Bayesian decision theory. The paper offers a case study in which a hypothetical decision maker employs Bayesian analysis in a real world setting.
Section 1 describes the Bayesian procedure and its underlying theoretical framework. This section first describes the relationship between Bayesian decision theory and geostatistics. It then describes a Monte Carlo process that employs conditional simulation to model topographic uncertainty in a GIS setting.
Section 2 demonstrates the Bayesian procedure described in section 1. This section presents a situation in which a hypothetical decision maker with limited information models uncertainty in flood processes and ascertains the potential value of further information. A hypothetical but representative case study is then developed based on an actual data set. This allows for a realistic demonstration of the procedure and enables verification of its performance.
Section 3 evaluates how well the procedure works as an aid to decision making. It first compares model results to actual elevation and flood data and then demonstrates how a decision maker may successfully use the procedure in both a generic Bayesian sense and in a more spatially explicit manner.
Section 4 concludes with key findings and future research directions.
1. UNCERTAINTY ASSESSMENT
Uncertainty is a "fundamental dimension" of decision making analogous to time or space (Chrisman 1991, p. …