Using computer model uncertainty to inform the design of physical experiments: An application in glaciology

Computer models are used as surrogates for physical experiments in many areas of science. They can allow the researchers to gain a better understanding of the processes of interest, in situations where it would be overly costly or time-consuming to obtain sufficient physical data. In this project, we give an approach for using a computer model to obtain designs for a physical experiment. The designs are optimal for modelling the spatial distribution of the response across the region of interest. An additional consideration is the presence of several tuning parameters to the computer model, which represent physical aspects of the process but whose values are not precisely known. In obtaining the optimal designs, we account for this uncertainty in the parameters governing the system. The project is motivated by an application in glaciology, where computer models are often used to model the melt of snow and ice across a glacier surface. The methodology is applied to obtain optimal networks of stakes, which researchers use to obtain measurements of summer mass balance (the difference between the amount of snow/ice before and after the melt season).