Mathematical Geology

, Volume 37, Issue 2, pp 127–140

Estimating Climatic Timeseries From Multi-Site Data Afflicted With Dating Error


DOI: 10.1007/s11004-005-1305-6

Cite this article as:
Loehle, C. Math Geol (2005) 37: 127. doi:10.1007/s11004-005-1305-6


Timeseries of estimated temperature have been combined to create global or hemispheric climate series over periods exceeding 1000 yr. The data used in these studies, however, may be subject to dating errors. It is shown that when timeseries with dating error are combined, the noise in the data smoothes periodic signals but leaves linear trends intact. This means that the effect of dating error of sample data in a timeseries reconstruction is to smooth out any signals (waves, cycles) that may be present. The purpose of this study was to develop signal extraction methods that will work for this type of historical data. The method used was nonlinear estimation of sample series where dating error has been added by Monte Carlo sampling. Several algorithms were tested for handling the dating error problem. Results were that using nonlinear model fitting, the periods of signals can be identified even from the averaged data. In a second stage of the estimation procedure, the cycle magnitudes can be estimated. Very good fits were achieved for two example cases. Temperature estimation error (white noise due to the use of proxies) was also considered and the method was extended to cover this case with quite good results. Using the new estimation methods, the information inherent in multiple series can be used to overcome the problem of dating error.


Kalman filter nonlinear estimation proxy data climate reconstruction 

Copyright information

© International Association for Mathematical Geology 2005

Authors and Affiliations

  1. 1.National Council for Air and Stream Improvement, Inc. NCASINaperville

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