Statistical challenges in paleoclimatology: independent component analysis of lake hazar and Lake Van data, and a bayesian test for 4.2 ka bp event

There are numerous statistical and numerical methodological problems of paleoclimate studies. In this study, I offer solutions for two problems of paleoclimatology in three different studies. It is a well known fact that, each geochemical measurement and especially each micro-X-ray fluorescence (μ-XRF) measurement through a sediment core is a reflection of different independent processes, i.e. an indirect indicator of paleoenvironments. That's why most studies present μ-XRF measurements as elemental ratios, in order to eliminate a possible dependence upon a single profile. Some studies use second order statistical methods, such as principal component analysis, to eliminate dependence, however there are systematic problems of second order statistical methods as is used in these studies. In order to overcome this issue, we offer an almost well-defined signal processing technique, independent component analysis of geochemistry data gathered from paleoclimate archives. Accordingly, we propose data based models of paleo-precipitation and paleo-temperature for the studied regions. In the first study (Chapter 2), a 3.5 m long piston core (Hz11-P03) has been recovered from Lake Hazar and it is used for multiproxy measurements. μ-XRF, magnetic susceptibility (MS) and stable isotope (δ 18 O and δ 13 C) measurements have been carried out for 3 mm, 1 cm and 3 cm resolutions, respectively. A Bayesian age-depth model according to six radiocarbon dates shows that Hz11-P03 represents the last 17.3 ka BP. We apply independent component analysis on Lake Hazar μ-XRF data (namely, Ca, Fe, K, Mn, Sr and Ti counts). By the measure of distance correlation of resulting independent components with the analyzed data and other regional well-defined paleorecords, we select two independent components as proxies of temperature (Hz-ic5) and precipitation (Hz-ic4) of the region. According to the results, the region was wet/cold during 17.3 ka BP and 14.8 ka BP and wet/warm during the Bølling-Allerød period. According to the age model, there is a hiatus at the Younger Dryas period. At the start of the Holocene, temperatures rose gradually and reached the Holocene "normals" around 8 ka BP. During that period, it was wet. Between 8 ka BP and 5 ka BP, it was warm but exceptionally dry. Between 5 ka BP and 3.5 ka BP, it was warm/wet. After 3.5 ka BP within the oscillations there are abrupt cold/dry phases around 3.5 ka BP, 2.8 ka BP and 1.8 ka BP. In the second study (Chapter 3), ICA method is applied to previously published data from Lake Van, which span the last 250 ka BP. The data used through ICA were element concentrations of Ca, Fe, K, Mn, Si from XRF measurement, TOC and CaCO 3 content and B* (color reflectance) of the Ahlat Ridge sediment record. The analysis is based on applying the algorithm several times by changing the initial random unit vector and clustering the possible independent components through average–link agglomeration, which make it different and innovative than Lake Hazar study. Appropriate components are selected by mutual information method. Accordingly, we claim that Van-IC8 is a proxy for temperature variability for the region, by its similarity with Greenland δ 18 O data and (Van-IC7) is a proxy for precipitation variability for the region, by its similarity with B* (Van-IC7) data. The results reveal that, temperature of the region follows the Northern Hemisphere records, i.e. warm during interglacials, cold during stadials with abrupt warming episodes. On the other hand, precipitation record shows that, it was not dry, or at least as much wet as today, during the LGM and at the end of penultimate glacial as previous studies claim. It was previously proposed that an abrupt climatic change around 4.2 ka BP was the cause of the collapse of the Akkadian Empire. Afterwards, many geological studies arose, which claim to support the climatic deterioration hypothesis. In the third study (Chapter 4), we apply a Bayesian test on the records from Eastern Mediterranean and Arabian Peninsula which claim to show an abrupt climatic change around 4.2 ka BP. To do this, time series are reconstructed using "unaffected" ones in a fully Bayesian framework by the Bayesian structural time series method and then a Bayesian hypothesis test is applied on the results. Our results show that some studies which have previously been cited to support the abrupt 4.2 ka BP event hypothesis hold true, we also show that in a number of other studies, there is no statistically significant abrupt climatic change effect.