Exploring the Concept of Scale and its Explanation in Geomorphology

Document Type : Full length article

Author

Assistant Professor, Geomorphology, Department of Geography, University of Guilan, Rasht, Iran

Abstract

Introduction
There are several fundamental issues in geomorphology, one example of which is scale. There is a special correlation between landscapes, on the one hand, and their forms’ components, on the other. This indicates a kind of scale continuity. Such rules and scale relations prevail not only at perspective level but also at the level of land forms, and thanks to the complexities of this concept in geomorphic studies, they have received less attention. However, accuracy of many geomorphic concepts is related to such concepts. Usually in scale geographic literature, a simple ratio is defined that is often used to represent the extent to which a phenomenon is reduced to its actual ratio in the maps, yet truth be told scale in geomorphology involves a broader concept: any subject that expresses a ratio lies within the conceptual realm of scale, though few geomorphologists have pointed this important issue out. Scale plays a vital role in geomorphology, both in the realm of performance and in the field of epistemology. For example, in the field of soil geology, particles’ chemical processes alter as the dimension reduces to two microns. Also, the properties of their elements generally change. Hence, in the geography of clays, which can only express the size of each substance (not their sex), chemical performance is extra important, since many vital and mineral reactions in the soil depend only on the size of the elements, not the elements themselves.  Therefore, in statistical analysis, relation measurement, i.e., correlation techniques, is a concept of scale, because when you write a linear formula or other form of correlation, the ratio between the two variables is actually defined. Therefore, scale is one of the fundamental issues that, from a theoretical point of view, leads to the formation of other concepts, such as universality, fractal, river networks, geo-allometry, specific scale, etc.
Materials and Methods
In order to achieve an advanced concept of scale in geomorphology, following a relatively extensive search for books and articles in this field, several geomorphological pioneers, who used this concept in the field of scale in their works with a special theoretical innovation got selected. They included:
-       John Charles Doornkamp, geographer from the University of Nottingham, England
-       John Tilton Hack, American geologist and geomorphologist
-       Evans, geomermologist from Durham University in UK and a graduate of York University, Canada
-       Donald Lawson Turcotte, geologist from Cornell University, USA
-       Benot Mendelobert, French-American mathematician from Yale University
-       Dave Rosgon, hydrologist and geomorphologist from the Universities of Nevada, Montana and Colorado
-       Leila Goli Mokhtari, geomorphologist from Sabzevar University, Iran
Afterwards, by selecting the books and writings of these researchers in this field, we began to study, separate, and classify their opinions, removing their repetitive content, at times shared by all of them in the process. In the final stage, we began to extract newly-found writings, specific to each of them, summarizing and analyzing their content as an opinion.
Results and Discussion
In the first step of this research, the most important result, achieved in terms of time, was the way of developments and the volume of work that has been done in this field. Review of the researchers' scientific papers showed that studies on the subject of scale of the trend have increased in the last 30 years with theoretical innovations in applying this concept becoming increasingly complex.
The second step, wherein thematic classification of the seven researchers’ opinions was of high account, dealt with semantic difference of the subject of scale. Although all these writings could be regarded as concerning the scale, the novelty of the works by these seven researchers was that they presented completely different and original interpretations and concepts, e.g. the specific scale of Evans' innovation, invariance scale of Turcotte, or geoallometry of Golemokhtari's theoretical innovations. With these initial achievements, the views of these seven researchers were then described and analyzed.
Conclusion
Scale in general is called the actual size of a phenomenon in geography, usually shown as a deduction or line. Fraction in numerical scales can be expressed with a fixed face and multiple denominators, e.g. in maps (1:50000 or 1:250000) and so on. Another pattern of scale display is expressed by showing a fraction with a different face and a fixed denominator, is called gradient, such as two in a thousand or five in a thousand, etc. Finally, ratio in geometry is expressed as an angle and is called a tangent.
During the last three decades, geomorphologists and related sciences have been able to apply some of the most complex concepts of scale in their works, with specific titles. These concepts include Universality Scaling, which is due to hacking, or the concept of "specific" that can be found in Evans' work. Turcotte defines the concept of invariance scale (meta-scale), whereas Mendelobert’s work on fractional scale and Rosgon’s on the thematic scale along with Goli Mokhtari, can be considered the creators and determinants of scale in geoallometry.
Finally, it can be said that each researcher has presented different concepts in the discussion of scale but the common ground among these researchers is their deeper understanding of the importance of earth and the phenomena of geomorphology. It must be confessed that the depth of their understanding of geomorphology has played a leading role in their theoretical innovation.

Keywords


Alimia Zadeh, Hiva and Mah Peykar, Omid (2017). A Study of Fractal Theory in Zarrineh River Using the Box Counting Method, Journal of Geographical Space, 17(59): 255-270.
Chorley, R. J., Schumm , S, A, Sugden, D.E. (1977). Geomorphology , translated by Ahmad Motamed, 2010, Vol. 1, Tehran, Samat Publications.
Dodds, P .S , Rotman, D.H. (2003). Scaling, Universality and geomorphology, Publication: Annual Review of Earth and Planetary Sciences, 28: 571-610.
Doornkamp, J.C. and King, C.A.M. (1971). Numerical analysis in geomorphology, Londen, Edward Arnold.
Dunlap, R.A. (1997). The Golden Ratio and Fibonacci Numbers, World Scientific Publications, 162 pages.
Evans, I. S.; Dikau, R.; Tokunaga, E.; Ohmori, H. and Hirano, M. (2003). Scale-Specific Landforms and Aspects of the Land Surface, Concepts and Modelling in Geomorphology: International Perspectives TERRAPUB, Tokyo, P. 61-84.
Gates, Alexander E. (2003). "Turcotte, Donald L. 1932". A to Z of earth scientists. New York: Facts on File. pp. 265–266. ISBN 9781438109190
Ghorbani, Abolghasem (1971). Kashaniyehnameh, Tehran, University of Tehran Press.
Ghorbani, Abolghasem (1986). Biography of Mathematicians of the Islamic Period, Tehran, University Press.
Goli Mokhtari, Leila (2014). A Study of Growth Rules in Floating Basins, Iranian Conference on Geographical Sciences, University of Tehran.
Hammel, Garland Trudi (1987). Fascinating Fibonaccis: Mystery and Magic in Numbers, D. Seymour Publications, 103 pages.
Keramati, Younes (2002). In the field of mathematics (rewriting of the book Muftah al-Hesab by Ghiasuddin Jamshid Kashani), Tehran, Ahl Ghalam Cultural Institute.
Lague, D.; Alain, Crave and Philippe, Davy (2003). A stochastic ‘‘precipiton’’ model for simulating erosion/sedimentation dynamics , Journal of Geophysical Research, 108(B1).
Loller, Robert (1989). Sacred Geometry, translated by Hayedeh Moayeri, Tehran, Institute for Cultural Studies and Research Publications.
McClean, C. J. and Evans, I. S. (2000). Apparent fractal dimensions from continental scale digital elevation models using variogram methods: Transactions in GIS, 4(4): 361-378.
Mandelbrot BB. (1983). The Fractal Geometry of Nature. San Francisco: Freeman Manna SS, Dhar D, Majumdar SN. (1992). Spanning trees in two dimensions. Phys. Rev. A 46:4471–74
Olsen, Scott (2006). Golden Section, Wooden Books Publisher, 64 pages
Osterkamp, W.R. , Hupp, C.R. (1993). "Memorial to John T. Hack", Memorials, Publications of the Geological Survey, P. 59-61.
Rigon, Riccardo et al. (1996). On Hack's law, Water Resources Research, 32(11): 3367-3374.
Rosgon, Dave (1996). Applied River Morphology, Published by Wildland Hydrology in Pagosa Springs, Colo.
Runion, Garth E. (1990). The golden section, Dale Seymour Publications, pages 173.
Tate, Nicholas J. and Atkinson, Peter M. (2001). Modeling Scale in Geographical Information Science, John Wiley and sons Ltd, England.
Temple Bell, Eric (1984). Famous Mathematicians, translated by Hassan Saffari, Tehran, Sepehr Publishing, second edition.
Thorn, C.E. (1982). Space and time in geomorphology. London: George Allen and Unwin.
Thornes, J.B. and Brunsden, D. (1977). Geomorphology and Time, Methuen, London.
Turcotte, L. (1997). Fractals and Chaos in Geology and Geophysics, Cambridge University Press.
Walser, Hans (2001). The Golden Section, Translated by Peter Hilton, Publisher MAA (The Mathematical Association of America), 158 pages.
Volume 52, Issue 4
January 2021
Pages 659-672
  • Receive Date: 27 April 2020
  • Revise Date: 19 October 2020
  • Accept Date: 19 October 2020
  • First Publish Date: 21 December 2020