Exploratory ensemble designs for environmental models using k-extended Latin Hypercubes

In this paper we present a novel, flexible, and multi-purpose class of designs for initial exploration of the parameter spaces of computer models, such as those used to study many features of the environment. The idea applies existing technology aimed at expanding a Latin Hypercube (LHC) in order to generate initial LHC designs that are composed of many smaller LHCs. The resulting design and its component parts are designed so that each is approximately orthogonal and maximises a measure of coverage of the parameter space. Designs of the type advocated for in this paper are particularly useful when we want to simultaneously quantify parametric uncertainty and any uncertainty due to the initial conditions, boundary conditions, or forcing functions required to run the model. This makes the class of designs particularly suited to environmental models, such as climate models that contain all of these features. The proposed designs are particularly suited to initial exploratory ensembles whose goal is to guide the design of further ensembles aimed at, for example, calibrating the model. We introduce a new emulator diagnostic that exploits the structure of the advocated ensemble designs and allows for the assessment of structural weaknesses in the statistical modelling. We provide illustrations of the method through a simple example and describe a 400 member ensemble of the Nucleus for European Modelling of the Ocean (NEMO) ocean model designed using the method. We build an emulator for NEMO using the created design to illustrate the use of our emulator diagnostic test. © 2015 The Authors. Environmetrics published by John Wiley & Sons Ltd.