Ramisch, A., Tjallingii, R., Hartmann, K., Diekmann, B. & Brauer, A. (2018). Echo of the Younger Dryas in Holocene lake sediments on the Tibetan Plateau. Geophysical Research Letters, 45. doi: 10.1029/2018GL080225

Ramisch et al. (2018) analyzed the erosional landscape response to climatic forcing based on Holocene lake sediments from three lakes on the Tibetan Plateau. By consequently applying log-ratio transformations to the compositional input data (element intensities) and phase space reconstruction a sedimentary response model was developed. This allows interpretation of the variations in sediment composition in response to climatic changes.

For more background on compositional data analysis please look into the according sections of SOGA. Further details on the dynamical system approach are given in the paper and the Supporting Information. Here, only a brief summary of the analysis is presented.

Method

Holocene lake sediment proxy records of three lake systems on the Tibetan Plateau, Lake Nam Co (NC), Lake Tangra Yumco (TY), and Lake Heihai (HH) were analyzed. X-ray fluorescence (XRF) core scanning was used to provide geochemical intensity records (in counts per second) of eight elements (Al, Si, K, Ca, Ti, Ca, Sr, and Rb). Sediment samples for the three lakes were obtained and dated using ¹⁴C chronology (Doberschütz et al. (2014), Ahlborn et al. (2017), Haberzettl et al. (2015), among others).

In order to overcome the inherent data constraints, element intensities were center-log-ratio transformed prior to statistical analyses. Then a principle component analysis (PCA) was applied to identify correlations between elements and the elements most responsible for the XRF record variance. Element correlations of the log-ratio transformed XRF element intensity records are visualized by the biplots:

Biplots of first two principal components with element correlation for the three lakes individually (a-c) and combined for all lakes (d). (Figure S1, Supporting Information for Ramisch et al. (2018)).

For element combinations indicative for variations in PC1 additive log-ratio (alr) time series were calculated, e.g. \(ln(Ti/Sr)\).

Further, a dynamical system approach was adapted to develop a sedimentary response model from the geochemical time series. The reconstructed phase space corresponds to a linear dynamical system of two coupled differential equations. In order to incorporate the role of an external forcing a second-order linear time invariant (LTI) system model was used.

Results

The model obtained by the inverse modeling approach matches the dynamics recorded by the element intensity records (alr time series) well. This can be seen in the phase space by comparing the reconstructed and modeled trajectories:

Reconstructed (a) and response model (b) phase space trajectories for a time series of Lake Nam Co (Figure 2, Ramisch et al. (2018). Used under a Creative Commons Attribution-NonCommercial-NoDerivs License).

On a millennial time scale the dynamics of sediment supply based on proxy records (grey areas) correspond well to the model simulations (blue line):

Response in sediment supply (a) to interglacial forcing (b) of three different lakes on the Tibetan Plateau (Figure 3, Ramisch et al. (2018). Used under a Creative Commons Attribution-NonCommercial-NoDerivs License).

The initiation times t_i for the best-fit forcing functions are within the \(2\sigma\) range for the three lakes. Thus, a simultaneous change in external forcing between 11.6 and 11.9 cal ka BP can be assumed. As this coincides with the termination of the Younger Dryas cold period the authors interpret the forcing as the rapid shift from glacial to interglacial climate conditions on the Northern Hemisphere.

All three alr time series start at a low level when they increase abruptly, followed by an oscillation slowly dissipating towards a new higher steady state. Mainly only the period of these oscillations is different for the three lakes. The damped oscillations in sediment supply are inferred as a transient response to the increase in temperatures and seasonal precipitation. However, responses to the common climatic forcing are asynchronous with differences in the duration of the transitional phase for the three sites. The site-specific oscillation frequency is interpreted as differences in the efficiency of the erosional systems of the respective catchment areas.

While some oscillations in the sediment records have been attributed to direct regional forcing such as monsoons in the past (e.g. Doberschütz et al. (2014)), the results presented here rather suggest a dynamical response of the sedimentary systems on millennial time scales. Overall, this stresses the importance of consistently considering data constraints and applying log-ratio transformations when analyzing data to avoid spurious interpretations. In addition, the dynamical system approach with phase space reconstruction provides a suitable method to identify response models for higher-order dynamical systems.

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Citation

The E-Learning project SOGA-R was developed at the Department of Earth Sciences by Kai Hartmann, Joachim Krois and Annette Rudolph. You can reach us via mail by soga[at]zedat.fu-berlin.de.

You may use this project freely under the Creative Commons Attribution-ShareAlike 4.0 International License.

Please cite as follow: Hartmann, K., Krois, J., Rudolph, A. (2023): Statistics and Geodata Analysis using R (SOGA-R). Department of Earth Sciences, Freie Universitaet Berlin.