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Functional clustering of varved lake sediment to reconstruct past seasonal climate
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences. (Arcum)
Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (Arcum)
2016 (English)In: Environmental and Ecological Statistics, ISSN 1352-8505, E-ISSN 1573-3009, Vol. 23, no 4, 513-529 p.Article in journal (Refereed) Published
Abstract [en]

Annually laminated (varved) lake sediments constitutes excellent environmental archives, and have the potential to play an important role for understanding past seasonal climate with their inherent annual time resolution and within-year seasonal patterns. We propose to use functional data analysis methods to extract the relevant information with respect to climate reconstruction from the rich but complex information in the varves, including the shapes of the seasonal patterns, the varying varve thickness, and the non-linear sediment accumulation rates. In particular we analyze varved sediment from lake Kassjon in northern Sweden, covering the past 6400 years. The properties of each varve reflect to a large extent weather conditions and internal biological processes in the lake the year that the varve was deposited. Functional clustering is used to group the seasonal patterns into different types, that can be associated with different weather conditions. The seasonal patterns were described by penalized splines and clustered by the k-means algorithm, after alignment. The observed (within-year) variability in the data was used to determine the degree of smoothing for the penalized spline approximations. The resulting clusters and their time dynamics show great potential for seasonal climate interpretation, in particular for winter climate changes.

Place, publisher, year, edition, pages
Springer, 2016. Vol. 23, no 4, 513-529 p.
Keyword [en]
Climate, Clustering, Curve registration, Functional data analysis, Penalized least squares, Varved lake diment
National Category
Probability Theory and Statistics Environmental Sciences
Identifiers
URN: urn:nbn:se:umu:diva-130095DOI: 10.1007/s10651-016-0351-1ISI: 000387424200002OAI: oai:DiVA.org:umu-130095DiVA: diva2:1064925
Available from: 2017-01-13 Created: 2017-01-11 Last updated: 2017-01-30Bibliographically approved
In thesis
1. Functional clustering methods and marital fertility modelling
Open this publication in new window or tab >>Functional clustering methods and marital fertility modelling
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of two parts.The first part considers further development of a model used for marital fertility, the Coale-Trussell's fertility model, which is based on age-specific fertility rates. A new model is suggested using individual fertility data and a waiting time after pregnancies. The model is named the waiting model and can be understood as an alternating renewal process with age-specific intensities. Due to the complicated form of the waiting model and the way data is presented, as given in the United Nation Demographic Year Book 1965, a normal approximation is suggested together with a normal approximation of the mean and variance of the number of births per summarized interval. A further refinement of the model was then introduced to allow for left truncated and censored individual data, summarized as table data. The waiting model suggested gives better understanding of marital fertility and by a simulation study it is shown that the waiting model outperforms the Coale-Trussell model when it comes to estimating the fertility intensity and to predict the mean and variance of the number of births for a population.

The second part of the thesis focus on developing functional clustering methods.The methods are motivated by and applied to varved (annually laminated) sediment data from lake Kassj\"on in northern Sweden. The rich but complex information (with respect to climate) in the varves, including the shapes of the seasonal patterns, the varying varve thickness, and the non-linear sediment accumulation rates makes it non-trivial to cluster the varves. Functional representations, smoothing and alignment are functional data tools used to make the seasonal patterns comparable.Functional clustering is used to group the seasonal patterns into different types, which can be associated with different weather conditions.

A new non-parametric functional clustering method is suggested, the Bagging Voronoi K-mediod Alignment algorithm, (BVKMA), which simultaneously clusters and aligns spatially dependent curves. BVKMA is used on the varved lake sediment, to infer on climate, defined as frequencies of different weather types, over longer time periods.

Furthermore, a functional model-based clustering method is proposed that clusters subjects for which both functional data and covariates are observed, allowing different covariance structures in the different clusters. The model extends a model-based functional clustering method proposed by James and Suger (2003). An EM algorithm is derived to estimate the parameters of the model.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2017. 24 p.
Keyword
censoring, Coale-Trussell model, EM-algorithm, functional data analysis, functional clustering, marital fertility, normal approximation, Poisson process, varved lake sediments, warping
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-130734 (URN)978-91-7601-669-5 (ISBN)
Public defence
2017-02-24, Hörsal 1, Lindellhallen, Umeå Universitet, Umeå, 10:15 (English)
Opponent
Supervisors
Available from: 2017-02-03 Created: 2017-02-01 Last updated: 2017-02-09Bibliographically approved

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Arnqvist, PerBigler, ChristianRenberg, IngemarSjöstedt de Luna, Sara
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