Bathymetry, geographical regionalization and diversification of Brepollen (Hornsund, Spitsbergen) based on bathymetric profiles interpolation and Cluster Analyses chosen mathematical parameters

Mateusz Moskalik1, Piotr Grabowiecki 1 , Monika Żulichowska2, Jarosław Tęgowski 3 1Department of Polar Research, Institute of Geophysics Polish Academy of Sciences, Warsaw, Poland 2Faculty of Biology, Jagiellonian University, Kraków, Poland 3Institute of Oceanography, University of Gdańsk, Gdynia, Poland

INTRODUCTION RESULTS The poor level of information around Brepollen (Fig.1) and its continued expansion connected with revealing new, hitherto inaccessible terrains from melting ice-cover, are the main imperatives driving the presented research, and render the obtained results of great significance. Detailed recognition of bottom morphology in connection with knowledge about the glacial genesis of the region will help better understanding of glacial processes and their reflection in various morphological forms. Certainly, it will also initiate and enable commencement of new research projects in the area of Brepollen. Due to health and safety regulations, data recording is usually performed in the areas covered in marine publications and navigational maps. Existing publications very often do not include areas where glaciers have retreated. It is then necessary to use small boats with a shallow draught. They can provide a safer working environment during navigation of unexplored areas. Such difficult measuring conditions only enable to use of single-beam echosounders. Direct interpolation of such profiles allows for geographic regionalisation by identification of individual bays which were under the influence of glaciers. These characteristics explain whole post-glacier valleys, but do not describe their fine elements. In the analysis it was assumed that areal diversity was defined by the diversity of profiles in the region. Taking such assumption under consideration further analysis, where depth records are characterised by a much denser distribution than distance between profiles, it was possible to calculate characteristics of the additional seabed formation. The measurements (Fig.1) were performed from a small boat equipped with a Lowrance LMS- 527cDF type echosounder, coupled with a GPS receiver. The system is not recommended for navigation but it can provide the data to create the bathymetry model for environmental analyses. Figure 2. Bathymetry of Brepollen calculated with Ordinary Kriging interpolation on 25 m grid, slope, aspect and geographical regionalisation in Brepollen. Coastline in black; glaciers’ reach in 2010 in grey; determined Brepollen bay regions – thin dashed black line. Determined geographical units: 1 – Storbreen valley, 2 – Hornbreen valley, 3 – Svalis glacier valley, 4 – Mendelejev glacier valley, 5 – Chomjakov glacier valley, 6 – Treskelbukta, 7 – Hyrne glacier valley, 8 – Central Brepollen.

C Figure 3. Example profile with sections (B) and its Figure 1. Map of Hornsund, Svalbard (Alos Avnir © JAXA [2011]) and bathymetric profiles locations during localization (black line) on Brepollen bathymetry 2007 (grey dashed line) and 2008 (black dashed line) at Brepollen, Svalbard. map (A) and division of exemplary bathymetric profile into 2, 3, 4, 5 and 6 clusters based on all profiles for all type of deviations (C).

METHODOLOGY General linear interpolation formula can be written as: =⋅∀ = = x∑ w x ; > w 0 ; ∑ w 1 int iii, xi , xint RoI i i i i where: xint - the interpolated value, xi - the value of a known parameter, wi –interpolation weights, RoI – range of interpolation. Semivariogram was used for the description of correlation Figure 4. Brepollen region divisions into 2, 3, 4 and 5 between neighbouring depth values and calculated RoI. The change in increase of semivariation, morphological differentiation class based on cluster was clear on the derivative of semivariation d( γ(h))/dh in the range of 400 to 500 m. Based on this, analyses of all parameters where corresponding colours all all the RoI was established as 500 m. are defined as: blue – C (2,3,4,5)_1 , light blue – C (2,3,4,5)_2 , light green – Call , yellow – Call , orange – Call . Groups of fitting polynomial functions (first end second stage), inverse distance weights (exponent (3,4,5)_3 (4,5)_4 5_5 indexes: 0, 0.25, 0.5, 1, 2, 4 and infinity) and kriging methods (Ordinary Kriging, Universal Kriging Appointed areas: with first and second stages polynomial trends) were used for interpolation bathymetry in the all -2 clusters: flat or mildly inclined areas (C 2_2 ), slopes Brepollen area. In order to indicate one method of interpolation the following criteria was used: all (C 2_1 ); all - calculate sensitivity of the methods on the grid size; -3 clusters: sharp slopes (C 3_1 ), flat seabed, mild all - compliance of the distribution of the results of interpolation with distribution of input value; hillsides with small morphological forms (C 3_3 ), all - visual assessment and rejection of the methods which give unrealistic values. undulated sections (C 3_2 ); -5 clusters: flat seabed (C all ), sections with mildly As a conclusion of the above analyses the Ordinary Kriging method was chosen for bathymetry 5_5 inclined slopes and small forms (C all ), areas with interpolation to characterise Brepollen (Fig.2A). Based on such information it was possible to 5_2 diverse morphology and numerous bottom forms define 8 geographical regions in the Brepollen. All geographical units were determined by two (C all ), steep slopes (C all ) major features: 5_3 5_1 - the boundary of the geographical units are the beginning of valleys’ slope (Fig.2B); - the boundaries between the two units, which are in contact with each other are drawn due to uneven directions of the maximum slope decline (Fig.2C). These characteristics explain whole post-glacier valleys, but do not describe their fine elements. In CONCLUSIONS the analysis it was assumed that areal diversity was defined by the diversity of profiles in the Ordinary Kriging interpolation techniques were determined for the most probable morphological region. Taking such assumption under consideration further analysis, where depth records are formations in-between bathymetric profiles. In total, eight geographical units were separated in characterised by a much denser distribution than distance between profiles, it was possible to Brepollen, based on the bathymetry, slope and aspect maps. The seafloor morphological calculate characteristics of the additional seabed formation. In order to characterise morphological differentiation was determined by calculating statistical, spectral and wavelet transformation, seabed differences, the following data analysis scheme was introduced: fractal and median filtration parameters of segments of bathymetric profiles. The set of - evaluation of mathematical parameters allowing for characterisation of bathymetric sections parameters constituted to the input of Principal Component Analysis and next in the form of diversification; Principal Components to the Clustering Analysis. As the result of such procedure a classification of - the first step in the reduction of parameters, based on the analysis of entire bathymetric Brepollen to three morphological regions was proposed: (i) steep slopes (southern Brepollen), (ii) profiles; here chaotic parameters were rejected; in the case of correlated parameters – only one flat bottoms (central Brepollen) and mild slopes (Storbreen valley and southern part of Hornbreen remained; valley), (iii) the most morphologically diverse region (central Storebreen valley, northern part of - standardization of parameters; Hornbreen valley and NE part of central Brepollen). - the second step of reduction was based on Principal Component Analysis (PCA); - determination of the number of clusters; - assignment of individual profile sections to clusters, based on cluster analysis; - assignment of morphological feature classes to defined clusters. REFERENCES The statistical (7 parameters), spectral (17 parameters) and wavelet (8 parameters for 2 wave Moskalik M., Grabowiecki P., Tęgowski J., Żulichowska M. (2013): Bathymetry and geographical mother functions) transformations, fractal (4 parameters) and median filtration (6 parameters) regionalization of Brepollen (Hornsund, Spitsbergen) based on bathymetric profiles interpolations were used. These parameters were determined not for the depth profiles, but for the deviations Polish Polar Research 34(1):1-22 from the Mean Value, a Linear Trend and Square Trend of all segments of profiles with a length of Moskalik M., Tęgowski J., Grabowiecki P., Żulichowska M. (under review): Diversification of 256m. After reduction of above parameters based on the chaotic variability, correlation between Brepollen (Hornsund, Spitsbergen) based on Cluster Analyses chosen mathematical parameters on parameters and PCA remain 9 parameters for every deviation from trends and 16 when including bathymetric profiles. Polish Polar Research all parameters. Cluster analysis was conducted for 2 to 6 clusters. The most complex differentiation distribution of the exemplary profile was seen while considering all parameters (Fig.3). In order to draw a map with suggested morphological forms classification on the exemplary profile, a new interpolation procedure was used. Due to quantification of results, a percentage ACNOWLEDGEMENTS number of all clusters had been identified in the distance of 500 m for every location. Maximum We would like to acknowledge the Polish Polar Station in Hornsund staff, for practical help during value cluster was used as corresponding to the sea bottom morphological differentiation class. research studies. The research was partly supported by The Polish Ministry of Sciences and Higher Maps of seabed diversity from 2nd to 5th class from cluster analysis of all parameters were Education (Grant No. N N525 350038). prepared (Fig.4).