Abstract. Tree-rings tell of past climates. To do so, tree-ring chronologies comprising numerous climate-sensitive livingtree and subfossil time-series need to be "transferred" into palaeoclimate estimates using transfer functions. The purpose of this study is to compare different types of transfer functions, especially linear and nonlinear algorithms. Accordingly, multiple linear regression (MLR), linear scaling (LSC) and artificial neural networks (ANN, nonlinear algorithm) were compared. Transfer functions were built using a regional tree-ring chronology and instrumental temperature observations from Lapland (northern Finland and Sweden). In addition, conventional MLR was compared with a hybrid model whereby climate was reconstructed separately for short-and long-period timescales prior to combining the bands of timescales into a single hybrid model. The fidelity of the different reconstructions was validated against instrumental climate data. The reconstructions by MLR and ANN showed reliable reconstruction capabilities over the instrumental period (AD 1802(AD -1998. LCS failed to reach reasonable verification statistics and did not qualify as a reliable reconstruction: this was due mainly to exaggeration of the low-frequency climatic variance. Over this instrumental period, the reconstructed low-frequency amplitudes of climate variability were rather similar by MLR and ANN. Notably greater differences between the models were found over the actual reconstruction period (AD 802-1801). A marked temperature decline, as reconstructed by MLR, from the MeCorrespondence to: S. Helama (samuli.helama@helsinki.fi) dieval Warm Period (AD 931-1180) to the Little Ice Age (AD 1601-1850), was evident in all the models. This decline was approx. 0.5 • C as reconstructed by MLR. Different ANN based palaeotemperatures showed simultaneous cooling of 0.2 to 0.5 • C, depending on algorithm. The hybrid MLR did not seem to provide further benefit above conventional MLR in our sample. The robustness of the conventional MLR over the calibration, verification and reconstruction periods qualified it as a reasonable transfer function for our forest-limit (i.e., timberline) dataset. ANN appears a potential tool for other environments and/or proxies having more complex and noisier climatic relationships.

Nowadays, there is a large number of time series of natural data to study geophysical and astrophysical phenomena and their characteristics. However, short length and data gaps pose a substantial problem for obtaining results on properties of the underlying physical phenomena with existing algorithms. Using only an equidistant subset of the data with coarse steps leads to loss of information. We present a method to recover missing data in time series. The approach is based on modeling the time series with manifolds of small dimension, and it is implemented with the help of neural networks. We applied this approach to real data on cosmogenic isotopes, demonstrating that it could successfully repair gaps where data was purposely left out. Multi-fractal analysis was applied to a true radiocarbon time series after recovering missing data.

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The physics of terrestrial radioactive contamination is complex, primarily due to the mixtures of radionuclides, their migration, the effects of soil chemistry, and the prevalent climate. Consequently, application of classical techniques is inappropriate in modeling such an environment. The classification of territories contaminated with radioactive isotopes is vital in establishing a detoxification plan. Application of the fractal geometry provides a good insight and helps in such classification. Several techniques are implemented to determine geometric aspects of contaminated fields, and these show a way to differentiate between natural and man-made isotopes.

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