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DYNAMICS OF SEASONAL PATTERNS IN GEOCHEMICAL,

ISOTOPIC, AND METEOROLOGICAL RECORDS OF THE

ELBRUS REGION DERIVED FROM FUNCTIONAL DATA

CLUSTERING

RESEARCH PAPER

Gleb A. Chernyakov1*, Valeria Vitelli2, Mikhail Y. Alexandrin1, Alexei M. Grachev1, Vladimir N. Mikhalenko1,

Anna V. Kozachek3, Olga N. Solomina1, Vladimir V. Matskovsky1

1Institute of Geography, Russian Academy of Sciences, 29 Staromonetniy lane, 119017, Moscow, Russia

2Department of Biostatistics, University of Oslo, Sognsvannsveien 9, 0372, Oslo, Norway

3Arctic and Antarctic Research Institute, 38 Bering st., 199397, St. Petersburg, Russia

*Corresponding author: glchern@igras.ru

Received: December 31th, 2019 / Accepted: August 9th, 2020 / Published: October 1st, 2020

https://

DOI-10.24057/2071-9388-2019-180

ABSTRACT.

A nonparametric clustering method, the Bagging Voronoi K-Medoid Alignment algorithm, which simultaneously

clusters and aligns spatially/temporally dependent curves, is applied to study various data series from the Elbrus region

(Central Caucasus). We used the algorithm to cluster annual curves obtained by smoothing of the following synchronous

data series: titanium concentrations in varved (annually laminated) bottom sediments of proglacial Lake Donguz-Orun; an

oxygen-18 isotope record in an ice core from Mt. Elbrus; temperature and precipitation observations with a monthly resolution

from Teberda and Terskol meteorological stations. The data of different types were clustered independently. Due to restrictions

concerned with the availability of meteorological data, we have fulfilled the clustering procedure separately for two periods:

1926–2010 and 1951–2010. The study is aimed to determine whether the instrumental period could be reasonably divided

(clustered) into several sub-periods using different climate and proxy time series; to examine the interpretability of the

resulting borders of the clusters (resulting time periods); to study typical patterns of intra-annual variations of the data series.

The results of clustering suggest that the precipitation and to a lesser degree titanium decadal-scale data may be reasonably

grouped, while the temperature and oxygen-18 series are too short to form meaningful clusters; the intercluster boundaries

show a notable degree of coherence between temperature and oxygen-18 data, and less between titanium and oxygen-18 as

well as for precipitation series; the annual curves for titanium and partially precipitation data reveal much more pronounced

intercluster variability than the annual patterns of temperature and oxygen-18 data.

KEY WORDS: Central Caucasus; paleoclimate archives; lake sediments; ice cores; clustering; functional data

CITATION: Gleb A. Chernyakov, Valeria Vitelli, Mikhail Y. Alexandrin, Alexei M. Grachev, Vladimir N. Mikhalenko, Anna V. Kozachek,

Olga N. Solomina, Vladimir V. Matskovsky (2020). Dynamics Of Seasonal Patterns In Geochemical, Isotopic, And Meteorological

Records Of The Elbrus Region Derived From Functional Data Clustering.

Geography, Environment, Sustainability.

https://

DOI-10.24057/2071-9388-2019-180

ACKNOWLEDGEMENTS: The data analysis of the lake sediment core was supported by the RFBR project No. 17-05-01170 A;

the ice core data analysis was fulfilled with the support of RSF project No. 17-17-01270-П; the analysis of meteorological data

was performed in the framework of the State Assignment of Institute of Geography RAS No. 0148-2019-0004.

Conflict of interests: The authors reported no potential conflict of interest.

INTRODUCTION

In the last decade, new paleoclimate archives were

obtained in the course of expeditionary work involving

the Institute of Geography of the Russian Academy of

Sciences. Among them are ice cores of the Western plateau

of Elbrus (Mikhalenko et al. 2015; Kozachek et al. 2017),

bottom sediments of the lakes Karakel, Donguz-Orun,

Khuko (Solomina et al. 2013; Alexandrin et al. 2018), etc.

The obtained cores were studied and dated by laboratory

methods; their elemental and isotopic compositions

were determined (Darin et al. 2015a; Darin et al. 2015b;

Kozachek et al. 2015). Until now, among the existing

statistical approaches, mostly the correlation-regression

and component analysis have been applied to study the

new data (Alexandrin et al. 2018). Among the applications

of cluster analysis to these data, only works on studying the

backward air mass trajectories and dust transfer are known

(Kutuzov et al. 2017; Khairedinova et al. 2017).

Cluster analysis is used to split a certain set of objects

into relatively homogeneous groups (clusters). In this work,

the clustering procedure was applied independently to

investigate several synchronous time series characterizing

the dynamics of the natural environment in the Central

Caucasus in the 20th century. As the result of this procedure,

each time series is divided into intervals corresponding to

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dierent clusters. Thus, a time sequence of clusters or parts

of them appears in each data series.

In our work a nonparametric method of clustering

functional data, the Bagging Voronoi K-Medoid Alignment

(BVKMA) algorithm, was applied to analyze the data.

This clustering method and its application for studying

bottom sediments are described in detail in (Abramowicz

et al. 2017) and summarized in the Method section of our

paper. A specic feature of this approach is that splitting

annual data into clusters is based on the shape of intra-

annual variations of the parameter under investigation. In

that way, the analysis is aimed at answering the question

«which time periods are similar and which are dierent

in terms of their intra-annual variability». This clustering

method may be only applied to the data that have several

measurements for each period.

Moreover, the advantage of BVKMA compared to

previously developed methods of clustering functional

data is the ability of the method to deal jointly with two

eects, revealing by data, that can lead the clustering

procedure to a tendency of considering substantially

similar or interconnected data as completely dierent or

independent, what may be regarded as misclassication.

The rst issue is the eect of misalignment functional

data that is typically manifested in time lags. For instance,

if the functional data are represented as time-dependent

curves, one can notice time lags of peaks of some curves

compared to the others, despite a common shape and

reasons of the observed variability (see, e.g., Sangalli et al.

2010). The Alignment procedure, implemented in BVKMA,

is intended to prevent possible misclassication of the

curves during clustering due to their misalignment. In

climatic research, the misalignment may naturally occur in

annually repeated seasonal patterns.

The second eect that is important to account for, is a

possible time/spatial dependence of functional data. For

example, the neighboring annual curves, derived from

high resolution paleoclimatic records, may be regarded

as «dependent» because they are supposed to reect

common processes and eects characterizing the natural

environment of a given period. In BVKMA algorithm the

account for data dependency, expressed by a tendency to

attribute consecutive curves to the same cluster, is provided

by the usage of the Voronoi tessellation (Abramowicz et al.

2017). Also, the type of dependency (spatial or temporal)

does not impose restrictions on the applicability of the

method. Moreover, the spatial dependence observed for

the parameter of interest in annual layers of proxy data can

be transformed into temporal dependence on the base of

known dating of the proxy. In our study, this is the case for

lake sediment and ice core data.

The main purpose of our investigation is to assess

the degree of consistency of the resulting clusters for

geochemical, isotopic and meteorological data series and

to nd out essential or close time boundaries in dierent

series. This approach of combining various types of data in

order to reveal their implicit interrelations may be a useful

tool for creating paleoclimate reconstructions.

In many palaeoclimatic studies, researchers aim to nd

modern analogues for past climates, and thus reconstruct

specic parameters or palaeoenvironments for specic

time periods. The clustering method used in this study

previously was applied to cluster millennia-long time-

series, resulting in only one cluster covering the whole

instrumental period. The results of such an approach

could be hardly interpreted in terms of nding modern

analogues for past climates. Here for the rst time we apply

this method for time-series which are several decades

long and fully intersect with the instrumental period. The

purpose of this approach is (i) to determine whether an

instrumental period of usual length could be reasonably

divided (clustered) into several sub-periods using this

method and dierent climate and proxy time-series; (ii) to

study the shape of medoids (which represent intra-annual

variations of parameters) for dierent climate and proxy

time-series and their associations; and (iii) to examine the

resulting borders of the clusters, or resulting time periods,

in terms of their interpretability.

MATERIALS AND METHODS

Study area

The Greater Caucasus borders the Russian Plain from the

south. It is located in the temperate and subtropical zones

between the Black and Caspian Seas. Elbrus volcano (5642

m) – the highest peak of the Caucasus, supports extensive

modern glaciation. The climate in the region is dominated

by the westerlies. The continentality is increasing from the

west to east: the mean June temperature at the foothills

of Greater Caucasus is approximately +23–24 °C, while in

the east it is higher (25–29 °C): the annual precipitation,

on the contrary, decreases in the west-east direction from

4000 mm (Kodory valley) to 1000–1500 mm in the eastern

Caucasus (Gvozdetsky and Golubchikov 1987). Precipitation

maxima occur in July–September; the warmest month is

July, the coldest one is January.

Meteorological data at the high elevation of the

Caucasus are quite scarce. In this paper, we used the

data from Terskol station located in the area where

our other proxies (ice core and lake sediments) are

situated and Teberda station with longer meteorological

records. Shahgedanova et al. (2014) noticed positive

trends in summer temperature and precipitation of the

accumulation period (October–April) recorded at the high-

elevation Terskol and Klukhorsky Pereval stations in the

period between 1987 and 2010.The glaciers are however

retreating since the early 20th century and the retreat rate

is increasing.

The study area and the locations of the proxy records

and meteorological stations used as the sources of data are

marked on the map below (Fig. 1).

Data

The following data were used in the work.

a) Data on the elemental composition of the core of

the annually laminated bottom sediments of Lake Donguz-

Orun. The top core used (160 mm) contains annual layers

formed during the period 1922–2010 (Alexandrin et al.

2018). Among the chemical elements present in the

sample, the terrigenous element titanium (Ti) was selected

for cluster analysis, because variations in its content

correlate most strongly with the series of meteorological

observations in the region (Alexandrin et al. 2018).

b) The vertical prole of the oxygen isotope content

(δ18O) in the ice cores of the Western plateau of Elbrus

(depth – up to 182 m; dated part – from 1774 to 2013; see

(Preunkert et al. 2019; Kutuzov et al. 2019)).

c) Monthly data on average air temperature from

observations at the Teberda (since 1926) and Terskol (since

1951) weather stations.

d) Monthly data on precipitation totals from

observations at the above mentioned meteorological

stations for the same periods.

For data (a) and (b), the vertical proles were converted

to a time distribution based on the known depth–age

correspondence.

Gleb A. Chernyakov, Valeria Vitelli et al. DYNAMICS OF SEASONAL PATTERNS IN GEOCHEMICAL ...

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GEOGRAPHY, ENVIRONMENT, SUSTAINABILITY 2020/03

Clustering of annual curves was carried out separately

for the following two periods.

1) 1926–2010 – the maximum period of time provided

simultaneously by geochemical, isotopic and

meteorological data. The Teberda weather station was

selected as providing the longest series of observations in

the region.

2) 1951–2010 – the period of observations at the Terskol

weather station and the simultaneous availability of lake

sediment and ice core data. The weather station Terskol

was selected as the closest to Lake Donguz-Orun and Mt.

Elbrus.

In accordance with the designations introduced, below

we will indicate the data type with a letter (a – d), and the

study period with a number (1 or 2). For example, (a1) will

denote the titanium data for 1926–2010.

Method

To study the data, we have applied a recently developed

nonparametric method of clustering functional data,

the Bagging Voronoi K-Medoid Alignment, which

simultaneously clusters and aligns by phase the data

elements (annual curves), using the information about the

dependence (sequence) of these curves (Abramowicz et

al. 2017). The method is a generalization of the previous

Bagging Voronoi Clustering (Secchi et al. 2013), which does

not handle misalignment of the data. All computations and

analysis of the data are performed in the R programming

language (R Core Team 2020).

Preprocessing. From the time series representing our

raw data, the associated functional form was reconstructed

via a smoothing procedure. In order to do that, a series of

each parameter (Ti, δ18O, temperature, precipitation) was

divided into sub-series of observations for individual years.

The annual data were centered with respect to their mean

value. Without loss of information the yearly time scale was

converted to a reference one by uniformly distributing the

time instances on the interval [0, 1] (such that for each year

the rst time instance is associated to 0 and the last one to 1).

Next, the centered annual data were normalized with respect

to the maximum absolute value of the whole time series.

Finally, after all previously described normalizations and

transformations, a continuous function was reconstructed

from each annual series by smoothing via a sum of the rst

few Fourier harmonics. Typically, we used from 5 to 9 Fourier

basis functions depending on the stability or oscillations of

the initial data. Thus, a series of annual curves was obtained

for each parameter. This allowed us to apply the BVKMA

algorithm designed for clustering functional data.

Let us set out at a qualitative level the main stages of the

BVKMA algorithm, following (Abramowicz et al. 2017), and

the procedure for tuning its input parameters.

For the sake of clarity, let us describe an input dataset

as a rectangular array of numbers (matrix), organized as

follows1. Each row of the array contains the sequential

values of the parameter of interest, belonging to a particular

year (annual curve). We will call any row of the array and

the data contained in it as a site. For instance, in the case

of the temperature data, the ith row contains the values

of temperature during the ith year of the studied period,

obtained by smoothing of 12 monthly observations at a

meteorological station. Thanks to the Fourier smoothing, for

each type of data we have increased the number of annual

values up to 50. Therefore, each of our datasets contains 50

columns. The number of rows N in our datasets is either 85

or 60, depending on the number of years in the analyzed

time period, starting either from 1926 or from 1951.

The execution of the BVKMA proceeds in two phases –

bootstrap phase and aggregation phase.

Bootstrap phase. This three-step procedure is being

applied to the same input data array a specied number

of times B. The individual replications of this procedure are

independent and their results are being saved.

Step 1. Generation of a random Voronoi tessellation. At this

step the data array is randomly divided into a given number n of

Fig. 1. The study area. The map of the Elbrus region (Central Caucasus) with the marked locations of data sources: Lake

Donguz-Orun, Mt. Elbrus, the weather stations Terskol and Teberda. Space image from Google Earth

1Note that for each parameter (Ti, δ18O, temperature, precipitation), each meteorological station (Teberda, Terskol), and each study

period (1926–2010, 1951–2010) a separate dataset is formed and analyzed independently.

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sub-arrays (Voronoi cells). Each cell is a set of several consecutive

sites. The cells can vary in size, since being formed randomly.

This step demands an input parameter L=N/n – the expected

number of sites within a Voronoi cell. Varying L, we change the

measure of supposed dependence of annual data as preliminary

information given to the algorithm.

Step 2. Identication of local representatives (medoids) for each

cell of the tessellation. First, the Alignment procedure is applied

to annual curves (sites) of each cell. Then medoids are chosen as

the curves in each cell which are the most similar to all the other

aligned curves in the same cell. The similarity of the curves is

determined by a metric (see below). As a result of this procedure,

for each Voronoi cell a new 1-dimensional array (an additional

annual curve, also called local representative) is created, which

summarizes the information carried by all sites of the cell. So,

having completed the second step, we have a set of Voronoi

cells and a set of their local representatives – one for each cell.

Step 3. Clustering of the local representatives, formed at the

previous step. The number K of clusters is assigned a priori, before

executing the algorithm, and the clustering algorithm used on

the local representatives is the K-medoid algorithm. All clusters

are being labeled, and the label of each cluster refers also to all

local representatives forming it. Next, all sites of each Voronoi

cell get the same cluster label as the one that was assigned to

the local representative of this cell. Thus, after completion of

this step, the entire initial data array will be divided into clusters.

In other words, for each site it will be indicated which one of K

clusters it belongs to.

Aggregation phase. Since the Bootstrap phase is repeated

B times, and every time a Voronoi tessellation is created

randomly, the resulting cluster distributions are expected to be

dierent. Thus, for each site (year) a frequency distribution of

cluster assignments along the B replicates is provided. At the

Aggregation phase these frequencies are calculated for each

site, and the cluster label, which was encountered more often

than others, is nally assigned to a site. As the result of this

majority vote procedure the nal partitioning of the data array

into clusters is formed.

Parameter selection. The above mentioned variables B, L,

and K are the input parameters of the BVKMA algorithm.

In all runs of the algorithm we kept the number of bootstrap

replications B equal to 1000. This value turned out to be sucient

to provide the robustness of the results.

The expected length of a Voronoi cell L was varied signicantly

in order to encompass all possible numbers of Voronoi cells n. The

inevitable restriction imposed by the algorithm on n is K+1≤n≤N,

expressing the fact that the number of Voronoi cells should be

greater than the number of clusters, but cannot exceed the

number of sites in the dataset. Hence, using the equality L=N/n,

one can easily derive the restrictions on it: 1≤L≤N/(K+1). Thus,

for each number of clusters K we executed the algorithm with

various possible values of the expected length of a Voronoi cell L.

To determine the most adequate value of L we used the average

entropy estimator implemented in BVKMA. The mean entropy

Ē is the measure of the misclassication of the data during

clustering. Therefore, the optimal value of L is the one, providing

the minimum of Ē.

We restricted the number of clusters K to be equal to 2, 3

or 4. We have not enlarged this number because the amount

of sites (years) is relatively small (maximum 85). To tune K, we

applied another built-in estimator of the BVKMA algorithm – the

so-called λ-criterion (for more details, see (Abramowicz et al.

2017; Sangalli et al. 2010)). Again, the optimal value of K is the

one, providing the minimum of λ.

Thus, the way to nd the optimal values of the parameters

for each dataset was the following. First, for each K the optimal

value of L was determined with the help of the entropy criterion.

After that, we found the optimal number of clusters K, using the

λ-criterion, among the cases of optimal values of L.

The optimal values of the parameters and corresponding

values of the statistical indicators, resulting from our analysis, are

presented in Table 1.

In addition to the numeric input parameters discussed

above, for running BVKMA one has to set a metric to quantify

the similarity between annual curves, and a family of warping

functions necessary for the Alignment procedure. Our choice of

these two functional parameters is the same as in (Abramowicz

et al. 2017). Namely, we used the normalized L2-based distance as

a metric, and the group of positive slope ane transformations

as a family of warping functions. More details and denitions can

be found in (Abramowicz et al. 2017; Vantini 2012).

RESULTS AND DISCUSSION

As a result of applying the BVKMA algorithm to dierent

types of data in the dierent studied cases, we have obtained

either 2 or 3 clusters. Typically, the resulting cluster assignment

led to one cluster less than the prescribed number K. This means

that in the nal year-by-year cluster assignment by majority vote

one of the clusters never comes out as the modal one.

The results of applying the algorithm are depicted in

Fig. 2: the cluster distributions over time (left side), and the

corresponding medoids of each cluster (right side). The medoids

represent intra-annual variability of the data, thus the left end

of each medoid corresponds to the beginning of the year, and

the right end – to the end of the year. They may be shifted in

the direction of the abscissa due to the Alignment procedure.

The Alignment is essential in the process of clustering, thought

it has no physical signicance for representation of the

resulting medoids. In fact, the medoid of the cluster is the most

representative curve in the cluster transformed in abscissa as

a result of the Alignment (shifted and stretched/compressed).

Nevertheless, the overall shape of the curve, subjected to such

transformation, is preserved.

Gleb A. Chernyakov, Valeria Vitelli et al. DYNAMICS OF SEASONAL PATTERNS IN GEOCHEMICAL ...

Case K L Ē λ

(a1) 3 20 0.71 0.48

(a2) 4 12 0.68 0.37

(b1) 3 10 0.61 0.93

(b2) 3 15 0.55 0.86

(c1) 4 12 0.61 0.81

(c2) 4 10 0.59 0.81

(d1) 2 15 0.60 0.45

(d2) 3 8 0.58 0.67

Table 1. The cases of optimal parameter selection and their numerical characteristics

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Fig. 2. The results of clustering of smoothed annual curves (left), and the corresponding medoids (right) for two study

periods: 1926–2010 (1) and 1951–2010 (2). The clustered data are: titanium content in the bottom sediment core from

Lake Donguz-Orun (a); oxygen-18 isotope content in the ice core from Elbrus (b); monthly average temperature at

Teberda and Terskol weather stations (c); monthly sum of precipitation at the same weather stations (d). The colors of

the medoids match the colors used in the diagrams of cluster distribution over time for each type of data

115

The data on titanium concentrations in the Donguz-

Orun sediment core show the most prominent inter-

cluster diversity (Fig. 2 (a1, a2, right)). In the original

study by Alexandrin et al. (2018) titanium was related to

precipitation, having signicant correlation (r = 0.44) with

annual precipitation measured at Teberda weather station.

However, clustering fullled for the two parameters

showed dierent results (Fig. 2 (a1, a2, d1, d2, left)). It

might be related to mild correlation strength, but also to

dierent factors driving intra-annual patterns of variability

of two parameters. Titanium is sometimes claimed to

mimic terrigenous runo, and thus reecting precipitation.

However, precipitation during the cold season may

generate runo only in spring during snow melt, hence

the intra-winter distribution of precipitation would not be

related to the spring peak of runo, but the total amount of

precipitation in the winter will matter. Hence, we underline

that the results of the BVKMA clustering algorithm

should be always interpreted keeping in mind possible

disagreement in intra-annual variability of interconnected

parameters.

On the contrary, the temperature and especially

oxygen-18 records reveal similar and stable seasonal

patterns (Fig. 2 (b1, b2, c1, c2, right)), and therefore the

dierences among clusters are less signicant for these

types of data. Temperature is known to have larger

correlation distance than precipitation. In this regard, we

cannot nd a realistic explanation for dierent clustering

results for temperature measured on two weather stations

having similar results for precipitation. Hence we interpret

these results as follows. The instrumental period may be not

long enough to obtain reasonable clusters for a parameter

with stable intra-annual variability, such as temperature.

Moreover, some inter-cluster time boundaries occur closely

in timing for some series of data (Fig. 2): in the 1940s (b1,

c1, left) and in the late 1960s (b2, c2, left).

We also nd very close inter-cluster boundaries in the

titanium and oxygen-18 data (Fig. 2 (a1, b2, left)).

The precipitation data series of meteorological stations

Teberda and Terskol have a similar structure of cluster

distributions over time: a large cluster encompassing

most part of the studied period followed by a small cluster

attributed to the latter period (Fig. 2 (d1, d2, left)).

Intra-annual patterns revealed by the respective

medoids (Fig. 2 (d1, d2, right)) also have a similarity: for

both weather stations we can observe maximum values

of precipitation in the middle of the season (summer)

for the rst period (green) and two local maxima (spring

and autumn) with reduction in summer for the second

period (magenta). These results show that, in contrast to

very stable intra-annual variations of temperature, those

of precipitation are variable enough to be reasonably

clustered into several periods. The consistency of these

periods for two remote weather stations may indicate that

the results of the clustering catch common underlying

forcing of changed precipitation seasonality in 2000s.

Originally, the BVKMA algorithm was applied for a 6000-

year long varved sedimentary sequence (Abramowicz

et al. 2017). It had proven to be suitable for registering

centennial to millennial scale variations in the distribution

of the seasonal values of the selected parameters, thus

providing important paleoclimatic implications. In this

study, we apply the BVKMA algorithm for signicantly

shorter sequences (60 and 85 years long). The climatic

variations (temperature and precipitation) as well are their

proxies (sedimentary Ti-values and ice core δ18O) at such a

short time scale were obviously incomparably smaller than

those for the half Holocene time span.

The two-three clusters provided by the algorithm tend

to represent minor uctuations – especially clear with the

curves of temperature and δ18O. A certain incoherence

of the Ti-values can be attributed to the uncertainty of

distinguishing the annual layers in varved sediments (done

with the use of geochemical markers rather than direct

visual observation in the case of Lake Donguz-Orun).

On the time scale of centuries to millennia the physical

basis for cluster analysis of the paleoclimatic data is

much more robust. Application of the BVKMA algorithm

for shorter sequences provides a necessary basis for its

application for the longer ones that are expected for lake

sediments, ice core data and possibly other sources of

paleoclimatic information in the Caucasus.

CONCLUSIONS

The seasonal patterns of four types of proxy and

meteorological data series from the Elbrus region (Ti

concentrations, δ18O, temperature, and precipitation) are

derived by applying the clustering algorithm Bagging

Voronoi K-Medoid Alignment, separately for two periods:

1926–2010 and 1951–2010.

The time dynamics of clusters and the corresponding

cluster medoids are obtained.

The seasonal patterns of oxygen-18 and temperature

data occurred to be relatively similar and unchangeable.

A notable degree of consistency of the resulting

clusters and their time boundaries for oxygen-18 and

temperature data is gured out. This result is encouraging

for future attempts to dene modern analogues of past

climates using this clustering technique.

A less pronounced, but still the observable consistency

of the cluster distributions is found for Ti and O-18 data,

as well as for precipitation data of meteorological stations

Teberda and Terskol.

Our results demonstrate that for parameters with

relatively stable intra-annual patterns of variability (like

temperature) the usual length of instrumental period may

be not enough for its reasonable division into sub-periods.

Highly variable parameters (like precipitation), on the

contrary, may be reasonably clustered even inside several

decades of data.

Also, we underline that the results of the BVKMA

clustering algorithm should be always interpreted keeping

in mind possible disagreement in intra-annual variability

of interconnected parameters, as we demonstrated in

titanium data from Donguz-Orun sediment core and

precipitation from Teberda weather station.

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