Model assessment and verification - Air Pollution Modeling and Its Application - page 305

4.5 Est modus in Rebus: Thoughts on Ensemble
Modeling from Darwin to Horace
S. Galmarini and S. Potempski
European Commission - DG Joint Research Centre, Institute for Environment and
Sustainability, Via E. Fermi 2749, 21027, Ispra, VA, Italy
Abstract The use of multi-model ensembles in atmospheric dispersion applications
is becoming more and more popular. Methodologies for the combination of model
results explored in the past are being adopted even in the operational or pre-
operational contexts. However several questions remain unanswered like these
relating to the way in which the ensemble should be set up. In other words, which
criteria should be adopted to guarantee that the ensemble results will always be
superior to those of any individual member? By means of mathematical formalism
the paper tries to address this problem.
1. Introduction
The properties of ensembles have been demonstrated in various situations and
case studies and often in the scientific literature we read the mantra : “ … the
performance of ensemble of models is shown to be (systematically) superior to
that of individual models ”. However, although the results from those case studies
are undisputable evidence of the fact that the technique works, the above mentioned
conclusions relate to heuristic considerations that are confined to the cases analyzed.
In this context, the ensemble practice relies on what we could define phenotypical
model distinction . Models differ for a limited number of modules or simply for the
data used; the differentiation of a common model genotype occurs whenever
the model is adopted or used in a specific modeling environment (modeling group,
modeling application). In most of the cases the ensemble practice brings together
models that show no substantial difference and that are available since they
survived the natural selection of individual model evaluation. Therefore one may
ask: is it automatically guaranteed that the ensemble performance is superior to the
one of the individual members? Is it always the case?
To deal with such generally posed issues we will try to make use of mathematical
formalism for describing multi-model ensemble systems. This will allow us to
find some basic properties of such systems, which can be deduced from general
characteristics of statistical distributions of the ensemble members.