Computing and Plotting Correlograms by Python and R Libraries for Correlation Analysis of the Environmental Data in Marine Geomorphology Polina Lemenkova

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Polina Lemenkova. Computing and Plotting Correlograms by Python and R Libraries for Correlation Analysis of the Environmental Data in Marine Geomorphology. Jeomorfolojik Araştırmalar Dergisi / Journal of Geomorphological Researches, 2019, 3, pp.1 - 16. 10.6084/m9.figshare.10012808. hal- 02327797

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Araştırma Makalesi / Research Article

COMPUTING AND PLOTTING CORRELOGRAMS BY PYTHON AND R LIBRARIES FOR CORRELATION ANALYSIS OF THE ENVIRONMENTAL DATA IN MARINE GEOMORPHOLOGY

Polina LEMENKOVA

Ocean University of China, Department of Marine Geo-sciences, Qingdao, Shandong Province, People’s Republic of China [email protected] https://orcid.org/0000-0002-5759-1089

Makale Tarihçesi ABSTRACT Geliş 19 Nisan 2019 Düzenleme 13 Mayıs 2019 The geomorphology of the Mariana Trench, the deepest ocean trench on the Earth, has a Kabul 15 Mayıs 2019 complex character: its transverse profile is asymmetric, the slopes are higher on the side of the Mariana island arc. The shape of the Mariana Trench is a strongly elongated, arched in Article History plan and lesser rectilinear depression. The slopes of the trench are dissected by deep Received April 19, 2019 Received in revised form May 13, underwater canyons with various narrow steps on the slopes of various shapes and sizes, 2019 caused by active tectonic and sedimentation processes. Understanding of factors that may Accepted May 15, 2019 affect the shape of the geomorphology of such complex structure requires advanced methods of numerical computing. Current research is focused on the analysis of the geomorphology of Anahtar Kelimeler the Mariana Trench by application of statistical libraries embedded in Python and R Denizaltı Jeomorfolojisi, Mariana programming languages for the data analysis. Workflow algorithms include processing a data Çukuru, Pasifik Okyanusu, Denizel Jeoloji, Python, R Programlama Dili, set by analysis, computing and visual plotting of the graphs. The research aims is to Mekânsal Analiz understand the environmental interactions affecting submarine geomorphology of the Mariana Trench by statistical data analysis. Technically, used algorithms included libraries of Keywords Python (Seaborn, Matplotlib, Pandas, SciPy and NumPy) and libraries of R ({hexbin}, {ggally}, Submarine Geomorphology, Mariana {ggplot2}). Technically, following types of the statistical analysis were tested for computing Trench, Pacific Ocean, Marine and plotting: correlograms, histograms, strip plots, ridgeline plots and hexagonal diagrams Geology, Python, R Programming Language, Geospatial Analysis for the bathymetric and geomorphic analysis. Python, being a high-level language, shown more straightforward approach for the statistical data analysis, while R implies more power Atıf Bilgisi / Citation Info in the data visualization. The results of the geospatial data modelling show detected Lemenkova, P. (2019) Computing and correlation between various factors (geology, bathymetry, tectonics) affecting submarine Plotting Correlograms by Python and geomorphology that reveal unevenness in its structure. Both programming languages R Libraries for Correlation Analysis of the Environmental Data in Marine demonstrated significant functionality for the spatial data analysis. The effective and Geomorphology, Jeomorfolojik accurate geospatial data visualization demonstrated by Python and R proves high potential Araştırmalar Dergisi / Journal of of their application in the geomorphological studies. Geomorphological Researches, 2019 (3): 1-16 © 2019 Jeomorfoloji Derneği. Tüm hakları saklıdır. All rights reserved.

INTRODUCTION

The study area is focused on the Mariana strongly elongated, arched in plan and Trench, the deepest ocean hadal trench on lesser rectilinear depression approximating the Earth is located in the west Pacific a form of the arc with a modeled center Ocean. Its geometric shape presents a located at 140°E 18°N (Figure 1).

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Figure 1. Geographic location and geometric approximated arc form of the Mariana Trench The transverse profile of the Mariana precipitation moving along the bottom Trench is asymmetric: the slope is higher from the part of the trough which is closer on the side of the Mariana island arc. The to the continent (Taira et al., 2004). At the slopes of the trench are dissected by deep bottom of the trough there is a transverse underwater canyons. Various narrow steps threshold, which can present kind of a are also often found on the slopes of the dam, in front of which there is trench. On the longitudinal profiles of the accumulation of a thick layer of sediment bottom of the Mariana there are many precipitation. deep-water detected transverse steps and Bathymetry of the Mariana Trench has a thresholds connected by the movements of complex character and includes a system the earth's crust along transverse faults of cracks. This includes a complicated set (Zhou et al., 2015). These thresholds can of steps of various shapes and sizes, play important role in the evolution of the caused by active tectonic and sedimental deep-water trough, for example, to control processes. The steepness of its geomorphic the intensity of its filling by sedimental depth averages in 4-5 degrees, but its precipitation. In this process very individual parts can be limited to steeper important are the streams of the

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slopes as subjects to the gravitational flow prominent group of wide seamounts, system of the submarine canyons and intersects the trench at distance of 1600- valleys (Kawabe, 1993). Complex 2000km (Zhang et al 2014). The effects of distribution of the various geomorphic the volcanism on the biological materials on the adjacent abyssal plains of communities were recently demonstrated the ocean contributes to the formation of by Kitahashi et al (2014), who proved the the geomorphic features of the particular relationship earthquake events and the region of the Mariana Trench. assemblage structures. Because rapid A special focus in this study was laid on sedimentation was induced by the turbidity the analysis of the geomorphology of the currents, the organic matter content Mariana Trench including the steepness increased in the topmost layers which angle of the slopes of the bathymetric indicate that disturbances to deep-sea cross section profiles. The seafloor sediments affects vertical distribution bathymetry of the Mariana Trench varies structure of meiofauna in the trenches. The significantly seaward of the trench axis. complex character of the geomorphology The Caroline Ridge is located near and off of the Mariana Trench deserves constant the trench axis at distance of about 0- attention of the scientific world (Chadwick 250km. A prominent trench-parallel belt of et al, 2018; Curtis & Moyer, 2005; seamounts with trench-perpendicular Faccenna et al., 2018; Fujioka et al, 2002; width of about 250 km, is located not far Theberge, 2008; Tian et al 2018. than 1350km (Figure 2, A). Another

Figure 2. Geologic settings of the Mariana Trench: seamounts, faults, ophiolites (A); tectonic plates (B) The structure of the submarine the adjusting slope areas, plays an geomorphology of the hadal trenches is a important role in sculpting the complex interplay of various processes. geomorphology of the deep hadal Multiple factors affect the geometry of the trenches. Due to their physical hadal trench: plate tectonic movements, inaccessibility, the ocean hadal trenches sediment thickness, ocean streams are very distinct from other objects on the determine the local geomorphological Earth. Two methods available to study conditions that strongly depend on the such unreachable areas include first, sediment deposition processes. Besides, remote sensing echo-sounding approach, the submarine geologic erosion occurring and second, a computer-based modeling. within the main channel of the trench and Since the first method is significantly more

3 Jeomorfolojik Araştırmalar Dergisi / Journal of Geomorphological Researches, 2019 (3): 1-16 resource- and cost-intensive, this paper The methodology of the research in both presents the second one, that is, computer hadal and riverine geomorphology is assisted data analysis and modeling. traditionally being supported by the GIS Strong topographical isolation and software, mainly in the geological complex mix of different water masses modeling and investigations. Thus, the distinct hadal trenches from other ocean geomorphic studies of the hydrological regions. The difficulties to understand the effects on the sites location often use GIS deep-sea hadal life and habitats hadal modeling and digital terrain analysis for zone (6,000–11,000m) that represents the geospatial analysis (Berger, 2011). Various last great frontier in marine science are examples of the geomorphological caused by the remote location of such analysis of the landforms by spatial data study object as ocean trenches. Given the analysis using GIS include application of above-mentioned difficulties in studies of satellite imagery, topographic and land marine geomorphology, the advanced cover maps using ESRI ArcGIS, Google methods of the statistical analysis were EarthView plugin for QGIS and algorithms applied for computing correlation matrices of the remote sensing data processing of factors affecting the geomorphic (Bertoldi et al, 2015; Arrospide et al, 2018; structure of the Mariana Trench using Bechter et al, 2018; Marchese et al, 2017; methods discussed below. Hudson et al, 2008). The novelty of this research consists in the The visual schematically mind map multi-disciplinary approach of this work summarizing the approaches, tools and that combines methods of the statistical methods of the work is given on Figure 3. analysis and computing with mapping and The initial map of study area (Figure 1) was spatial analysis of the geomorphology and done using Generic Mapping Tools using marine geology of the study area. The available documentation (Wessel et al., main aim of the work is to statistically 2017; Wessel & Smith 1995). Digitizing visualize and compute various factors that profiles and retrieving information about influence submarine geomorphic shapes the geomorphic structure of the Mariana causing variability, environmental triggers Trench was done using QuantumGIS. and interplay between them: geology, Further geostatistical approaches and bathymetry, tectonics, oceanography. methods were performed by R and Python programming languages. The initial MATERIAL AND METHOD geodata were extracted from the QGIS project as cross-section bathymetric The work methodology aims at profiles drawn across the trench with a understanding the geological factors length of 1000 km (Figure 4). The profiles affecting the geomorphology of the cross four tectonic plates: Mariana, Mariana Trench by means of the numerical Caroline, Pacific and Philippine Sea (Figure computing and plotting correlograms. The 2, B). statistical analysis was based on Python The initial statistical data analysis in data and R libraries using existing algorithms distribution was visualized by ridge line and methods of the machine-based data plots (Figure 5) showing distribution of analysis (Cielen & Meysman, 2016; depths by profiles and observation points Halterman, 2011; Harrington, 2015; R by tectonic plates. The attribute data set Development Core Team, 2014). was derived from the QGIS vector layers:

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tectonics, bathymetry, geomorphology and The information was derived in the QGIS geology. These include cross-section project from the attribute tables of the profiles having data from various vector points where profiles crossed the layers. GIS layers: bathymetry, coordinates, Then the table was stored in .csv format bathymetry, geology, tectonics, ophiolites, for further statistical processing by R and seamounts, igneous volcanic zones: Figure Python libraries. 2 and Figure 6.

Figure 3. Mind map of the project: methods, concepts, approaches and tools. Plotting: LaTeX.

Figure 4. Location of the cross-sectioning track profiles.

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Figure 5. Visualization of the data distribution by bathymetric profiles (left); data distribution by geology and tectonic plates (right) by {ggridges} library.

Figure 6. Map of location of the large igneous provinces and volcanos in the study area.

2.1. Hexagonal plots for modelling are being repeated by profiles. Hexagonal, bathymetric data range or 'hexbin', plots (Figure 7) serve as a useful alternative to scatter plots, because Plotting hexagonal plot was performed the bathymetric data in the current data using R language using specially designed set are too dense (518 observation points library {hexbin}. This plot aims to show by 25 profiles make 12,950 points all how the bathymetric data are distributed together). Therefore, plotting each point by the profiles in terms of frequency. individually in this case is not effective: the Specifically, it shows how often the values

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data would be indistinguishable on the (that is, moderately often recorded depths) graph. The R {hexbin} library demonstrates correspond to the major depth range generated hexagonal binning plot of the (-3,000 to -5,000 meters). Finally, range of depth’s values in Mariana Trench “Hundreds” (colored magenta) are the most by 25 profiles. frequent depth values that are the most The explanation of the Figure 7 is as often repeated depths. The thickness of the follows. The X axe shows profiles from 1 to line of each hexagonal bin (1, 3, 5, 7 and 9) 25. The Y axe shows recorded depth values by each of the 3 categories shows the (in meters) in observation points by frequency within the group (Figure 7). profiles. The colors show the frequency of 2.2. Histograms of the bathymetric data the depth distribution by observation distribution by tectonic plates points in profiles. Thus, there are 3 Since Mariana Trench crosses 4 tectonic gradations of the data distribution by plates – Mariana, Pacific, Philippine and repeatability: “hundreds” (very often Caroline (Figure 2, B), the data set recorded values, i.e. there are hundreds of contained environmental variables points with such depths), “tens” (moderate separately for these plates that should be frequency), and “ones” (very rare values). analyzed. This required merging the The frequency is colored in magenta, cyan columns into one category: ‘tectonic and blue, respectively. The frequency of plates’. Therefore, the columns with the the data repetition across the trench, can plate names were melted into one class be read as such: for example, “Ones” using the Python code. Now the analysis of (colored blue) are the rarest, i.e. the least the bathymetric data divided and classified frequent recorded depth values. One can by four tectonic plates (Pacific, Philippine see that the profiles 21, 22 and 23 have Sea, Caroline and Mariana) became the deepest values are the rarest in the possible. The data was then read in again trench. The cyan-colored “Tens” values to the Python and processed as such.

Figure 7. Hexagonal plots showing distribution of depths by bathymetric cross-secting profiles. The values density is colored (turquoise, blue, magenta).

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Figure 8. The histograms of the data frequency distribution: bathymetry by 4 tectonic plates. The histograms show the underlying geomorphology (slope angles) as frequency distribution of a submarine compared by four tectonic plates crossing topography of the Mariana Trench (Figure Mariana Trench. The strip plots visualize 8). It allows the inspection of the data for categorical data analysis across four the type of distribution that in this case is tectonics plates. Mariana, Caroline, Pacific normal distribution, as well as outliers, and Philippine Sea. The particularity of the skewness. The data are distributed and scatter strip plots (stripplot()) (Figure 9) lies colored by tectonic plates: Mariana, in its nature: this is a categorical types of Caroline, Pacific and Philippine Plates. The plot showing variable dependance histograms of the data distribution across (maximal depths values by each profile) tectonic plates (Figure 8) states that upon another variable, i.e. tectonic plates. among tested tectonic plates the Caroline It represents the depth values by Plate shows the least data distribution, bathymetric profiles sorted along each of which could explain the lower values of the tectonic plates crossing the trench. On the correlation between the data in this the above plot, one can see the difference particular plate comparing to the on data distribution: the Caroline Plates Philippine Sea, Mariana and Pacific plates. has just only several points, since it crosses 2.3. Strip plots showing geological data the trench in the south-western small part distribution by four tectonic plates of the trench. Pacific and Mariana plates The next step included visualizing strip are relatively comparable, while Philippine plot showing the relationship between the Plate covers the majority of the data. geologic factors (sediment thickness) and

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Figure 9. Processing data table by Python Pandas library (left); categorical strip plot showing variations of the bathymetry by four tectonic plates (right). 2.4. Correlograms done using NumPy and Pandas objects The associated names of the read in as tables and imported by the environmental variables (e.g. slope angles, Seaborn library. The correlograms show sediment thickness, maximal, minimal and the correlation between the factors mean depths) shown on the correlograms affecting the Mariana Trench based on the (Figure 10 and Figure 11) were annotated relationships of the values. on the axes, because the matrices were

Figure 10. Correlogram matrix of the environmental data affecting Mariana Trench geomorphology, computed by Kendall method.

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The external factors potentially affect # Step 5: Drawing the correlogram specific geomorphic features include the heatmap following: tectonics, geology and sb.heatmap(corr, cmap=cmap, vmax=0.3, bathymetry of the study area. The center=0, annot=True, effectiveness of the correlograms lies in its annot_kws={"size":8}, properties: the diagonal shows the square=True, linewidths=.05, distribution of each of the environmental linecolor='grey', variables by a representative square plot cbar=True, mask=False, cbar_kws={"shrink": which helps to analyze the relationship .5}, ) between the pairs of numerical variables within a matrix. The data were processed # Step 6: Adding titles, adjusting subplots using NumPy, Pandas, Matplotlib and and labelling x/y ticks Seaborn libraries by Python code plt.title('Mariana Trench: Spearman presented in the following listing in 6 correlation for the environmental factors', steps: fontsize=13, fontfamily='serif') plt.subplots_adjust(bottom=0.20,top=0.90, # Step 1: loading Python libraries right=0.90, left=0.10) plt.xticks(rotation=30, size=9) from string import ascii_letters plt.yticks(rotation=0, size=9) import numpy as np plt.show() import pandas as pd import seaborn as sb The correlation between each pair of from matplotlib import pyplot as plt variable is visualize through a numerical symbols and highlighted by colors. The use # Step 2: Importing data of both Spearman and Kendall correlation import os techniques is widely used for exploratory os.chdir('/Users/pauline/Documents/Python analysis to observe a matrix. In this sense, ') it may be observed (Figure 10 and Figure sb.set(style="white") 11) that to some degree the interplay df = pd.read_csv("Tab-Morph.csv") between various tested environmental factors has a state of intercorrelation # Step 3: Computing correlograms which is characteristic of the corr = df.corr(method='kendall') # for interdependencies between the factors: Kendall correlogram geology, oceanography, tectonics and corr = df.corr(method='spearman') # for bathymetry that affects the environmental Spearman correlogram dynamics and geomorphic structure of the f, ax = plt.subplots(figsize=(11, 9)) trench as a whole. Thereby can be cmap="RdYlBu" # for Kendall correlogram concluded that the environmental linkages exist between these particular factors # Step 4: Selecting palettes presented on the correlograms (Figure 10 pal = sb.color_palette("RdGy_r") # for and Figure 11) highlight a significant level Spearman correlogram reversed color of dependence between the individuals palette variables, such as bathymetry (maximal cmap=pal # for Spearman correlogram and minimal depths), geography (location of the observation points), tectonics and geology (crossing four tectonic plates:

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Mariana, Caroline, Pacific and Philippine affecting the morphology of the trench. Sea). The correlogram ellipses and The methodological approach includes numerical correlograms (Figure 12 and calling and executing algorithm of ellipse Figure 13, respectively) were plotted to correlogram {ellipse} library by R visualize correlation between the factors programming language.

Figure 11. Correlogram of the environmental data affecting Mariana Trench geomorphology, computed by Spearman method. The R code used to plot correlation ord <- order(data[1, ]) ellipses is as follows: data_ord = data[ord, ord] data=cor(MDF) #step-3. variant-1, correlation ellipses: plotcorr(data_ord , #step-1Build a Panel of colors by Rcolor col=my_colors[data_ord*50+50], Brewer mar=c(1,1,1,1), outline = TRUE, numbers = FALSE, my_colors <- brewer.pal(5, Spectral) main = 'Mariana Trench: Correlation my_colors=colorRampPalette(my_colors)(1 Ellipses', 00) xlab = 'Geomorphological, bathymetric and geological factors', #step-2. Order the correlation matrix, to ylab = 'Geomorphological, bathymetric and distribute colours by the factors of the geological factors', cex.lab = 0.7) values

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#step-4. variant-3, numerical correlation: Another way of the correlation data plotcorr(data_ord , analysis is presented by scatterplot col=my_colors[data_ord*50+50], combined matrix that enables to visualize mar=c(1,1,1,1), outline = TRUE, numbers = several approaches on one matrix (Figure TRUE, 14): scatter plots, box plots with residuals, main = 'Mariana Trench: Numerical margin plots and surface plots. The Correlation', scatterplot matrix was done using R xlab = 'Geomorphological, bathymetric and language. The scatterplot matrix is plotted geological factors', to visualize correlation and connections ylab = 'Geomorphological, bathymetric and between the environmental variables geological factors', cex.lab = 0.7) constituting Marine Trench system.

Figure 12. Correlation ellipses.

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Figure 13. Numerical correlograms.

RESULTS AND DISCUSSION

Studies revealed that multiple factors and Caroline. There is a notable decrease affect Mariana Trench geomorphology. The of depth (Figure 5, ridge line plots) in statistical analysis performed by Python profiles 20, 21, 22, crossing Caroline and R languages revealed that the major tectonic plate may be caused by the depth observation points of the Mariana changes in the geologic properties of the Trench are located in between the -3000 tectonic plates. Profiles from Nr. 20 to 22 and -5000 meters (Figure 7, hexagonal shows the deepest depth data range with plot, right). Another significant point is Nr 21 the deepest one. that sediment thickness changes notably Since the tectonic attribute values differ both within the trench by profiles and significantly, the comparative analysis of between four tectonic plates that Mariana how the data vary across four distinctive Trench crosses: Philippine, Pacific, Mariana

13 Jeomorfolojik Araştırmalar Dergisi / Journal of Geomorphological Researches, 2019 (3): 1-16 tectonic plates was undertaken. As can be observation points are located in the seen on Figure 7 (hexagonal plot, right) Pacific and Philippine plate, following my and Figure 9 (categorical strip plots Mariana plate, while Caroline plate only showing the distribution of data by covers a few points. tectonic plates), the majority of the

Figure 14. Scatterplot matrix showing geomorphic and geological variables. Geologic factors, such as sedimentation visualize combine information about processes, differ by four tectonic plates statistical data on the 25 bathymetric (Mariana, Pacific, Philippine and Caroline), profiles: arithmetic density distribution, due to the overall complexity of the mean and standard deviation along the sediment oceanological processes and profiles in a facetted way. Two plots show trigger factors and mechanisms. data distribution as depths by profiles (left) Furthermore, the results indicate (Figure and data density across tectonic plates: 14) that sediment sources at the Mariana Mariana, Philippine, Caroline and the Trench are connected with trench Philippine Sea (right). The lines extending tectonics. The ridgeline plots (Figure 5) horizontally from the boxes indicate

14 Jeomorfolojik Araştırmalar Dergisi / Journal of Geomorphological Researches, 2019 (3): 1-16 variability of the trench depths distribution were generated using {ggridges} and across all the profiles. The ridgeline plots {ggplot2} libraries of R.

Figure 15. A graphical word cloud and hierarchical structure of the used algorithms representing the conceptual scheme of the research To schematically demonstrate the use of (12,950 observations taken from the various approaches, tools and ideas used, attribute tables) using Python and R merged, combined and applied in this languages. The application of the study, the attempt to visualize it as a statistical algorithms embedded into graphical word cloud was made (Figure programming languages towards studies in 15). This research uses the statistical marine geomorphology proved to be and approaches to analysis a large dataset effective tool for data analysis.

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