SOFT feature-tracking software handbook

This handbook (SOFT_WP31_handbook.pdf) describes the suite of MATLAB programs developed within Work Package 3, task 3.1 of the SOFT Project, for the tracking of large-scale, westward propagating features (planetary waves or westward-travelling eddies) in altimeter data and the removal of the identified features from the datasets. The suite has been applied to TOPEX/POSEIDON data over the Azores region (one of the SOFT study regions) but its modularity makes it adaptable in a straightforward way to other datasets and other regions. The companion to this handbook is the progress report on task 3.1 released in January 2003 (SOFT_WP31_report.pdf), which presents the rationale to the study and gives ample details on the scheme adopted for the fitting of elementary waves (according to a Gaussian wave shape model) to altimeter data. A synopsis of the fitting scheme is briefly recalled in the following sections of this document, for the benefit of the reader. All the code listings are in the appendix. The forecasting of the westward-propagating fields (which is the object of task 3.2 in Work Package 3 id described in version 1 of another report, SOFT_WP32_rep1.pdf

SOFT Wave forecasting report - v.1.0

This report (SOFT_WP32_rep1.pdf) describes the first version of the wave forecasting code developed within Work Package 3, task 3.2 (implementation of a hybrid SOFT tracking system) of the SOFT Project. The forecasting of westward propagating signals (planetary waves or westward-travelling eddies), using the fields of tracked wave from Work Package 3, task 3.1, is one of the two components of the hybrid system which is the overall deliverable of task 3.2. The results presented here are provisional and are likely to be replaced as research proceeds. Related to this report are two other documents:- the progress report on task 3.1 released in January 2003(SOFT_WP31_report.pdf), which presents the rationale to the study and gives ample details on the scheme adopted for the fitting of elementary waves (according to a Gaussian wave shape model) to altimeter data (see also the paper by Cipollini, 2003);- the handbook SOFT_WP31_handbook.pdf describing the suite of MATLAB programs developed within Work Package 3, task 3.1 of the SOFTProject, for the tracking of large-scale, westward propagating features (planetary waves or westward-travelling eddies) in altimeter data and the removal of the identified features from the datasets. The suite has been applied to TOPEX/POSEIDON data over the Azores region (one of the SOFTstudy regions) and the output results have been used for the forecast

SOFT Development of feature tracking methods

The present report describes the work carried out within task 3.1 of Work Package 3 of the SOFT Project. The above task is ‘Development of feature tracking methods’ and consists of the development of a software to track large-scale, westward propagating features (planetary waves or westward-travelling eddies) in the altimetric datasets, and in the removal of the identified features from the datasets. The residual field (that is the original dataset minus the tracked features) is then made available to the other work packages in the Project

Emulating dynamic non-linear simulators using Gaussian processes

The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models of the climate or the functioning of the human brain. The models we are interested in are highly non-linear and exhibit tipping points, bifurcations and chaotic behaviour. However, each simulation run could be too time-consuming to perform analyses that require many runs, including quantifying the variation in model output with respect to changes in the inputs. Therefore, Gaussian process emulators are used to approximate the output of the code. To do this, the flow map of the system under study is emulated over a short time period. Then, it is used in an iterative way to predict the whole time series. A number of ways are proposed to take into account the uncertainty of inputs to the emulators, after fixed initial conditions, and the correlation between them through the time series. The methodology is illustrated with two examples: the highly non-linear dynamical systems described by the Lorenz and Van der Pol equations. In both cases, the predictive performance is relatively high and the measure of uncertainty provided by the method reflects the extent of predictability in each system

Predicting the Output From a Stochastic Computer Model When a Deterministic Approximation is Available

The analysis of computer models can be aided by the construction of surrogate models, or emulators, that statistically model the numerical computer model. Increasingly, computer models are becoming stochastic, yielding different outputs each time they are run, even if the same input values are used. Stochastic computer models are more difficult to analyse and more difficult to emulate - often requiring substantially more computer model runs to fit. We present a method of using deterministic approximations of the computer model to better construct an emulator. The method is applied to numerous toy examples, as well as an idealistic epidemiology model, and a model from the building performance field

Super-parameterisation of ocean deep convection

Technical report on the use of emulators in the parameterisation of ocean convectionSub-grid scale processes play an important role in ocean and climate modelling. Typical examples include clouds in atmospheric models, flows over restricted topographies or the resolution of con- vective plumes in ocean models. Detailed numerical models of these sub-grid scale processes exist, but embedding them in a Global Circulation Model (GCM) for example, would be computationally prohibitive. In the present work we investigate the applicability of emulators for representing the sub-grid scale processes within a GCM simulation. Emulators can be thought as encapsulating our beliefs about the sub-grid dynamical model, derived from a designed computer experiment using a Bayesian framework. In particular, we propose to employ an emulator for parameterising the sub-grid scale process, and embed this within a GCM as a surrogate for the actual sub-grid scale model. The result of combining the GCM with the emulator will be a Super-parameterised model, which will also be computationally efficient, since the emulator incurs a very small computational overhead. The example we chose to illustrate the proposed methodology is deep ocean convection. The sub-grid scale dynamical model simulates deep convective plumes, while the large scale dy- namics simulate the geostrophic eddy scale. We present details on building the emulator of the convective plumes and its coupling with the large scale process model. We also discuss whether the emulator should be run as a deterministic or stochastic parameterisation

Modelling Numerical Systems with Two Distinct Labelled Output Classes

We present a new method of modelling numerical systems where there are two distinct output solution classes, for example tipping points or bifurcations. Gaussian process emulation is a useful tool in understanding these complex systems and provides estimates of uncertainty, but we aim to include systems where there are discontinuities between the two output solutions. Due to continuity assumptions, we consider current methods of classification to split our input space into two output regions. Classification and logistic regression methods currently rely on drawing from an independent Bernoulli distribution, which neglects any information known in the neighbouring area. We build on this by including correlation between our input points. Gaussian processes are still a vital element, but used in latent space to model the two regions. Using the input values and an associated output class label, the latent variable is estimated using MCMC sampling and a unique likelihood. A threshold (usually at zero) defines the boundary. We apply our method to a motivating example provided by the hormones associated with the reproductive system in mammals, where the two solutions are associated with high and low rates of reproduction

Emulating complex dynamical simulators with random Fourier features

A Gaussian process (GP)-based methodology is proposed to emulate complex dynamical computer models (or simulators). The method relies on emulating the short-time numerical flow map of the system, where the flow map is a function that returns the solution of a dynamical system at a certain time point, given initial conditions. Here, the flow map is emulated via a GP whose kernel is approximated with random Fourier features. This yields a random predictor whose realisations are approximations to the flow map. In order to predict a given time series (i.e., the model output), a single realisation of the approximate flow map is taken and used to iterate from the initial condition ahead in time. Repeating this procedure with multiple realisations from the distribution of approximate flow maps creates a distribution over the time series whose mean and variance serve as the model output prediction and the associated uncertainty, respectively. The proposed method is applied to emulate several dynamic nonlinear simulators including the well-known Lorenz and van der Pol models. The results suggest that our approach has a high predictive performance and the associated uncertainty can capture the dynamics of the system accurately. Additionally, our approach has potential for "embarrassingly" parallel implementations where one can conduct the iterative predictions performed by a realisation on a single computing node

The implications of transporting architecture on human health

This is the author accepted manuscript.Where modern buildings are unable to maintain the internal environment to within comfort levels they often rely on mechanical systems to become habitable. This could be due to bad design or putting the building in an environment for which it is not suited. Due to climate change it is likely that all buildings will in effect and time be moved to an environment for which it is not suited. In this work the effects of changes in climate on the internal environment will be explored and an index to define how moveable a construction might be, will be developed.The authors would like to thank the EPSRC for their support [grant ref: EP/J002380/1