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.

中文翻译：

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使用 k 扩展拉丁超立方体的环境模型的探索性集成设计

在本文中，我们提出了一种新颖、灵活且多用途的设计，用于初步探索计算机模型的参数空间，例如用于研究环境许多特征的模型。这个想法应用了旨在扩展拉丁超立方体 (LHC) 的现有技术，以生成由许多较小的 LHC 组成的初始 LHC 设计。最终的设计及其组成部分被设计成每个部分都近似正交，并最大化参数空间的覆盖范围。当我们想要同时量化参数不确定性和任何由初始条件、边界条件或运行模型所需的强制函数引起的不确定性时，本文所提倡的设计类型特别有用。这使得该类设计特别适合环境模型，例如包含所有这些特征的气候模型。所提出的设计特别适合初始探索性​​集成，其目标是指导旨在校准模型的进一步集成的设计。我们引入了一种新的仿真器诊断，它利用了所提倡的集成设计的结构，并允许评估统计建模中的结构弱点。我们通过一个简单的示例提供了该方法的说明，并描述了使用该方法设计的欧洲海洋建模核 (NEMO) 海洋模型的 400 成员集合。我们使用创建的设计为 NEMO 构建了一个模拟器，以说明我们的模拟器诊断测试的使用。© 2015 作者。John Wiley & Sons Ltd. 出版的Environmetrics