Environmental and Ecological Statistics

, Volume 23, Issue 4, pp 513–529 | Cite as

Functional clustering of varved lake sediment to reconstruct past seasonal climate

  • Per Arnqvist
  • Christian Bigler
  • Ingemar Renberg
  • Sara Sjöstedt de Luna


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 Kassjön 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.


Climate Clustering Curve registration Functional data analysis Penalized least squares Varved lake sediment 



We gratefully acknowledge valuable comments from two anonymous reviewers. This work was supported by the Swedish Research Council, (Project id D0520301 and 90432301).


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mathematics and Mathematical StatisticsUmeå UniversityUmeåSweden
  2. 2.Department of Ecology and Environmental ScienceUmeå UniversityUmeåSweden

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