Use of Bayesian techniques in hydroclimatic prognosis

Tyralis, Hristos

dc.contributor.author	Tyralis, Hristos	en
dc.date.accessioned	2015-11-25T07:57:51Z
dc.date.available	2016-11-25T03:00:30Z
dc.date.issued	2015-11-25
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/41622
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.1971
dc.rights	Default License
dc.subject	Bayesian statistics	en
dc.subject	general circulation models	en
dc.subject	Hurst-Kolmogorov	en
dc.subject	hydroclimatic prognosis	en
dc.subject	posterior predictive distribution	en
dc.subject	Μπεϋζιανή στατιστική	el
dc.subject	μοντέλα γενικής κυκλοφορίας	el
dc.subject	Hurst-Kolmogorov	el
dc.subject	υδροκλιματική πρόγνωση	el
dc.subject	εκ των υστέρων κατανομή πρόβλεψης	el
dc.title	Use of Bayesian techniques in hydroclimatic prognosis	en
dc.contributor.department	Department of Water Resources and Environmental Engineering	el
heal.type	doctoralThesis
heal.secondaryTitle	Χρήση Μπεϋζιανών τεχνικών στην υδροκλιματική πρόγνωση	el
heal.classification	Civil Engineering	en
heal.classification	Statistics	en
heal.language	en
heal.access	free	el
heal.recordProvider	ntua	el
heal.publicationDate	2015-11-06
heal.abstract	Climatic prognosis is performed, using the deterministic General Circulation Models. These models whose use started half a century ago, are based on the Navier – Stokes equations and are numerical representations of the climate system based on the physical, chemical and biological properties of its components, their interactions and feedback processes. Recently it was proved that their older versions failed to provide adequate predictions, while newer versions are still not able to reproduce the climate of the past. Thus a shift of paradigm has been proposed. Toy models have shown that stochastic models are more capable of predicting for long horizons, and additionally they can quantify the uncertainty on their predictions. We prefer to follow the path less travelled and model geophysical processes stochastically. Whereas a usual approach to stochastic modelling is the ad hoc choice of the appropriate stochastic model for the time series at hand, we again prefer to use results obtained from the implementation of general notions of physics, such as the maximization of entropy, albeit a satisfactory answer to the question, which is an appropriate stochastic model for climate has not yet been given. Maximization of entropy under certain constraints results in models exhibiting Hurst-Kolmogorov behaviour. In this thesis the Hurst-Kolmogorov stochastic process will be used to model this behaviour. The overall aim of this thesis is the development of tools for climate prediction. Attempts to achieve this aim in a typical statistical context have been proved successful so far, but they do not offer much space for further improvements. A Bayesian approach offers more flexibility at the cost an additional assumption, i.e. the introduction of the prior distribution for the parameters of the models. The main questions that are addressed in this thesis are: - How can the uncertainty in the estimation of the parameters of the model be integrated in the uncertainty of the prediction? - How can the data be used for the prediction? - Which is an appropriate framework to gain information from the available deterministic models? The main components of the framework that will be developed in this thesis are the stochastic model and the data. The development of tools should contribute in quantifying the uncertainty in the prediction of climate. Uncertainty quantification contrary to point estimation may explain climate variability. To answer these questions, a previous typical statistical approach of the problem is investigated and is justified analytically. The general algorithm for the estimation of confidence intervals of parameters of interest that was used in this study is compared to other general algorithms and it is found that it performs satisfactorily. Properties of the algorithm are discovered within an analytical framework strengthening the arguments in favour of its use in this earlier study. However this approach is not adequate to solve the problem, owing to its indirect but encouraging results. Thus to continue the research, another path is chosen, namely the Bayesian approach. To strengthen the Bayesian choice some results on the estimation of the parameters of the Hurst - Kolmogorov process using a maximum likelihood estimator are presented. A novel estimator is proposed as well and its properties are examined analytically. It is shown that handling all parameters of the process simultaneously is critical to obtain valid results. The posterior predictive distributions of the climate variables for the Hurst - Kolmogorov process are calculated conditional on past observations within a Bayesian stochastic framework. The examined variables are assumed to be normal or truncated normal. The results are compared with cases where some of the parameters are considered known and the effect of the uncertainty in their estimation is shown. Uncertainties not previously given attention are revealed. We conclude trying to use information from deterministic model outputs to improve stochastic prediction. To this end properties of the maximum likelihood estimator of the bivariate Hurst - Kolmogorov process are analysed. A stochastic framework including both data and model outputs is developed. On a more practical level the stochastic framework is applied to temperature, rainfall and runoff data from Greece and Europe and it is shown that it is able to explain climatic variability within a stationary context. The latter framework is applied to historical global temperature and over land precipitation data. General Circulation Models are used as deterministic models. It is shown that the information added by the General Circulation Models to that contained in the historical datasets is not substantial. This means that the output of the General Circulation Models has almost null effect on the stochastic predictions.	en
heal.advisorName	Koutsoyiannis, Demetris	en
heal.committeeMemberName	Onof, Christian	en
heal.committeeMemberName	Lagaros, Nikos	en
heal.committeeMemberName	Burnetas, Apostolos	en
heal.committeeMemberName	Montanari, Alberto	en
heal.committeeMemberName	Pavlopoulos, Harrry	en
heal.committeeMemberName	Langousis, Andreas	en
heal.academicPublisher	Σχολή Πολιτικών Μηχανικών	el
heal.academicPublisherID	ntua
heal.numberOfPages	166
heal.fullTextAvailability	true