Calculating slope gradient variations in the submarine landforms by R and Python statistical libraries

Year 2019, Volume: 7 Issue: 2, 99 - 113, 25.12.2019

Polina Lemenkova

Abstract

Multiple factors affect submarine geomorphology causing variations in the gradient slope: geological settings (rock composition, structure, permeability, erodibility of the materials), submarine erosion, gravity flows of water streams, tectonics, sediments from the volcanic arcs, transported by transverse submarine canyons. Understanding the slope geomorphology is important for the precise bathymetric mapping. However, analysis of such a complex geomorphic structure as ocean trench requires numerical computation and advanced statistical analysis of the data set. Such methods are proposed by R and Python programming languages that include libraries of machine learning algorithms for the data processing used in this research: {tidyverse}, {ggsignif}, {ggplot} and {magrittr} by R, StatsModels, Matplotlib, NumPy, Pandas and Seaborn by Python. The research workflow can be summarized in five steps: 1) Partial least squares regression analysis; 2) Violin plots, modified box plot approach; 3) Modelling variations of depth and slope gradient, facetted in multi-panel plots by 4 tectonic plates; 4) Calculating normalized steepness angle; 5) Sorting, ranking and grouping of the cross-sectioning profiles by gradient slope degree, to estimate differences in the geomorphic shapes. As a result of the ranking performed in step 5, slopes were classified into five classes based on the calculated tangent angles: strong, very strong, extreme, steep, very steep. The results show differences in the gradient slope between various segments of the Mariana Trench located in four tectonic plates: Mariana, Caroline, Pacific and Philippine Sea, performed by statistical data modelling. Programming codes and snippets are presented for repeatability of the methods in similar research tasks.

Keywords

Geomorphology, Slope Calculation, Gradient, R, Python, Programming

Supporting Institution

China Scholarship Council (CSC)

Project Number

2016SOA002

Thanks

This research was funded by the China Scholarship Council (CSC), State Oceanic Administration (SOA), Marine Scholarship of China, Grant Nr. 2016SOA002, People’s Republic of China.

References

• Jamieson, A.J., Fujii, T., Mayor, D.J., Solan, M. and Priede, I. G. Hadal trenches: the ecology of the deepest places on Earth. Trends in Ecology and Evolution, 25 (3), (2009), 190-197. doi: 10.1016/j.tree.2009.09.009
• Duineveld, G. “Activity and composition of the benthic fauna in the Whittard Canyon and the adjacent continental slope (NE Atlantic)”. Oceanologica Acta, 24, (2001), 69–83.
• McCullagh, P. Slopes, in: FitzGerald, B.P. (ed.), Modern Concepts in Geomorphology, 1988.
• Ritter, D.F., Kochel, C.R., and Miller, J.R. Process Geomorphology (3rd Edition): Wm. C. Brown Publishers, Dubuque, IA, 2002, pp. 544.
• Chorley, R.J., Schumm, S.A. and Sugden, D.E. Geomorphology. London: Methuen and Co. Ltd.,1984.
• Summerfield, M.A. Global Geomorphology. New York: John Wiley and Sons, 1991.
• Easterbrook, D. J. Surface Processes and Landforms: Macmillan Pub. Co., 1993.
• Bloom, A. Geomorphology, A systematic analysis of Late Cenozoic landforms, 3rd ed., Prentice Hall, Upper Saddle River, N.J., 1998.
• Harris, P. T., Macmillan-Lawler, M., Rupp, J. and Baker E.K. “Geomorphology of the oceans”. Marine Geology, 352, (2014), 4–24.
• Wilson, M.F.J., O'Connell, B., Brown, C., Guinan, J.C. and Grehan, A.J. “Multiscale terrain analysis of multibeam bathymetry data for habitat mapping on the continental slope”. Marine Geodesy 30, (2007), 3–35.
• Pickering, K.T. and Hiscott, R.N. Deep marine systems: processes, deposits, environ- ments, tectonics and sedimentation. Wiley, Chichester, 2015.
• Wu, S., Takahashi, N., Tokuyama, H. and Wong, H.K. “Geomorphology, sedimentary processes and development of the Zenisu deep-sea channel, northern Philippine Sea”. Geo-Marine Letters, 25(4), (2005), 230–240. doi: 10.1007/s00367-005-0210-9
• Okada, H. “Anatomy of trench-slope basins: examples from the Nankai trough”. Palaeo- geography, Palaeoclimatology, Palaeoecology, 71 (1-2), (1989), 3–13. doi: 10.1016/0031- 0182(89)90026-6
• Yu, H.S. “Geological characteristics and distribution of submarine physiographic features in the Taiwan region”. Marine Georesources and Geotechnology, 21 (3-4), (2003), 139–153. doi: 10.1080/ 713773391
• VanderPlas, J. Python Data Science Handbook. Essential Tools for Working with Data. O’Reilly, 2016.
• McKinney, W. and PyData Development Team. Pandas: powerful Python data analysis toolkit Release 0.24.0. [Online] http://www.python.org [Accessed: 10 April 2019].
• Duchesnay, E. and Löfstedt, T. Statistics and Machine Learning in Python Release 0.2, 2019. [Online] http://www.python.org [Accessed: 10 April 2019].
• R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna, Austria, 2014. http://www.R-project.org [Accessed: 13 March. 2019].
• Rossum, G. van. Python Programming Language, 2011. https://www.python.org/ [Accessed: 10 April 2019].
• Rossetier, D.G. Tutorial: An example of statistical data analysis using the R environment for statistical computing, 2017.
• NumPy community. NumPy Reference. Release 1.16.1, 2019, https://www.python.org/ [Accessed: 10 April 2019].
• Crozier, M. Slope Evolution, in Goudie, A.S., ed., Encyclopedia of Geomorphology, Volume 2, Routledge, New York, NY, 2004.
• Savage, L.J. The Foundations of Statistics, 2nd revised ed., Dover, New Yor, 1972.
• Bretz, F., Hothorn, T. and Westfall, P. Multiple Comparisons Using R. Taylor andFrancis Group, LLC. 2011.
• Gardner, J.V., Armstrong, A.A., Calder, B.R. and Beaudoin, J. “So, How Deep Is the Mariana Trench?” Marine Geodesy, 37, (2014), 1-13, doi: 10.1080/01490419.2013.837849
• Covault, J.A., Fildani A., Romans B.W. and McHargue T. “The natural range of submarine canyon-and-channel longitudinal profiles”. Geosphere, 7, (2011), 313–332. doi:10.1130/GES00610.1
• Clark, M.J. and Small, R.J. Slopes and weathering: Cambridge University Press, Cambridge, England, 1982.
• Harrison, S.E., Locker, S.D., Hine, A.C., Edwards, J.H., Naar, D.F., Twichell, D.C. and Mallinson, D.J. “Sediment-starved sand ridges on a mixed carbonate/siliciclastic inner shelf off west-central Florida”. Marine Geology, 200, 2003, 171–194. doi: 10.1016/ S0025-3227(03)00182-8.
• Dominguez, S., Lallemand, S., Malavieille, J. and Schnürle, P. “Oblique subduction of the Gagua ridge beneath the Ryukyu accretionary wedge system: insights from marine observations and sandbox experiments”. Marine Geophysical Research, 20 (5), (1998), 383–402. doi:10.1023/A: 1004614506345
• Jones, O.P., Simons, R.R., Jones, E.J.W. and Harris, J.M. “Influence of seabed slope and Coriolis effects on the development of sandbanks near headlands”. Journal of Geophysical Research, 111, (2006), 1–23. doi: 10.1029/2005JC002944
• Dadson, S., Hovius, N., Pegg, S., Dade, W.B., Horng, M.J. and Chen H. “Hyperpycnal river flows from an active mountain belt”. Journal of Geophysical Research Earth Surface, 110 (F4), (2005). doi: 10.1029/2004JF000244
• Karig, D.E. and Sharman. G.F. “Subduction and accretion in trenches”. Geological Society of America Bulletin, 86 (3), (1975), 377–389.
• Mayer, L. Introduction to Quantitative Geomorphology: Prentice Hall, Englewood Cliffs, NJ, 1990.
• Kazhdan, A.B. and Gus’kov, O.I. Matematicheskie metody v geologii (Mathematical methods in geology), Moscow, Nedra, (1990).
• Davis, J. Statistics and Data Analysis in Geology. Kansas Geological Survey. John Wiley and Sons, 1990.
• Myers, J.L. and Well, A.D. Research Design and Statistical Analysis. Ed. 2, Lawrence Erlbaum, U.S., 2003.
• Cowan, G. Statistical Data Analysis. Oxford Science Publications. Clarendon Press, Oxford, UK, 1998.
• Brownlee, K.A. Statistical theory and methodology in science and engineering. 2nd ed., New York: John Wiley & Sons, 1965.
• Bulmer, M.G. Principles of statistics. New York: Dover Publications, 1979.
• Everitt, B.S. The Cambridge Dictionary of Statistics. Cambridge, UK. 2002. Doi: 10.1016/j.geoderma.2003.11.001