Environmental Engineering Reference
In-Depth Information
2.16 Emulating Complex Calculations for Regulatory
Decisions
Bernard Fisher
1
, Charles Chemel
2
, Rong-Ming Hu
2
, and Ranjeet Sokhi
2
1
Environment Agency, UK
2
University of Hertfordshire, UK
Abstract
The application of Gaussian process emulators to air pollution models of
low and intermediate complexity is demonstrated using the health impact of a
power station footprint as an illustrative example. In the future it is planned to
apply the emulator approach to more complex models such as CMAQ.
Keywords
Emulator, Gaussian process, complex models, TAPM model, CMAQ
model, life years, simulator, decisions
1. Introduction to Model Emulators
Complex models are built to simulate the behaviour of real-world systems. These
models may be empirical or represent detailed scientific understanding of the real-
world process. They are usually implemented in computer programs, which can
run to many thousands of lines of code and can take from a fraction of a second to
several weeks to run. Such a simulator can be regarded as a mathematical function
f(x)
, that takes a vector
x
of inputs and produces an output vector
y =
f(x)
. The
outputs
y
of a simulator are a prediction of the real-world phenomena that are
simulated by the model, though there will be uncertainty about how close the true
real-world quantities will be to the outputs
y
. This uncertainty arises from many
sources, particularly uncertainty in the correct values to give the inputs x and
uncertainty about the correctness of the model
f(x)
in representing the real-world
system.
An emulator is a statistical representation of a simulator. A Gaussian process
emulator makes use of Gaussian stochastic processes which have convenient
mathematical properties to approximate the simulator and to describe the
uncertainty associated with the simulator (Kennedy and O'Hagan, 2001). These
authors have also provided a freely available code for calibrating Gaussian process
emulators and for producing a free standing representation. These tools are
available from: http://www.tonyohagan.co.uk/academic/GEM/GEM-SA1_1.zip.
For additional explanation, see Rasmussen and Williams (1996). The purpose of
