MASTER's THESIS Wind Driven Plate Tectonics
2007:082 MASTER'S THESIS
Wind Driven Plate Tectonics
Asim Mohamed Widatalla
Luleå University of Technology Master Thesis, Continuation Courses Environmental Engineering Department of Civil and Environmental Engineering Division of Renewable Energy
2007:082 - ISSN: 1653-0187 - ISRN: LTU-PB-EX--07/082--SE
Dept. of Environmental Engineering Wind Driven Plate Tectonics Master thesis Asim Mohamed Widatalla 2
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 3
Abstract The objective of this project was to investigate if plate tectonics could be partly influenced by the dominating winds i.e. to investigate how predominate winds over the continents are correlated to tectonic plate movements. This report presents the principle explanations and calculation methods to the hypothesis. The required data of the monthly mean wind velocity and the wind direction at 117 locations on the continents of the world were collected. By calculating the monthly mean wind force the resulting monthly force was calculated. The result indicates a relatively strong correlation between the plate movement and predominant wind in four out of five cases. These results are mainly of scientific interest but could also be of interest for the climate change, since changing wind pattern would eventually affect the tectonic plate movements. Key words: plate tectonics, wind velocity and direction, climate change effects
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 4
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 5
Preface While looking for a topic for the master thesis, I was planning to select a topic in renewable energy, I meet Professor Bo Nordell, where we discussed different things and topics, and he mentioned that he kept an idea for several years, in which he assumed that the plate tectonics may be influenced by the wind forces. Because my background is far from the earth sciences, it was the first time for me to know about this tectonics theory, so I was a little bit aware of that. But since still I should work in a senior design project in Renewable Energy, and this topic was suggested to be one of the options for that project, I planned to start and to give the final decision later. After a while, I found that, I had the chance to see the whole world in a different view. Plates move in slow motion, this could be measured typically about 2 cm per year. I was supposed to investigate if the dominant wind could be among the factors that will affect this motion. So at the end of the day, I found myself, spent not only a single course period, but most of the winter and spring in front of a computer, selecting different cites and locations all around the five continents, drawing maps, analyzing the data, correlating the results with the actual movement of the plates, and trying to come up with amazing conclusion, this is quite a challenging thing to do. Even though I am glad this period is now over, it has been a very interesting learning process to go through, which has been facilitated by quite a few people whom I would like to thank: ◙ Professor Bo Nordell for his friendly and fruitful way of supervision, and for giving the constructive feedback and comments; ◙ My beloved parents – who they ever believe in science and knowledge for their continuous supporting, caring, prayers, and still they are encouraging me to go further. ◙ Hisham my brother for being a part of every nice step in my life; ◙ Reem my wife for taking the right decision at the difficult time, studying the nanophysics, and caring of our kids, giving me the strength and a reason to overcome challenges and achieve things. ◙ To Mohamed and Omer my sons, for giving the real meaning and lovely taste to the life, and making me look at the future as a world of possibilities. ◙ Finally, I would like to thanks my sisters, relatives and friends, especially those who spent the nights praying for me, and those who keep thinking of me and believing that, I will do it. My thanks will ever be at the beginning and the end to Allah who said: ……….. ‘‘And when your Lord made it known: If you are grateful, I would certainly give to you more, and if you are ungrateful, My chastisement is truly severe’’ ……………………………….. (14:7) Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 6
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 7
Table of Content Abstract ...... 3 Preface...... 5 Preface...... 5 Table of Content...... 7 List of Figures ...... 8 List of Tables...... 9 1 BACKGROUND...... 10 1.1 Plate Tectonics ...... 10 1.2 Major plates...... 11 1.3 Climate Change...... 11 2 OBJECTIVES ...... 12 3 METHOD...... 13 3.1 The force Equation:...... 13 3.2 The Torque Equations ...... 13 4 PROCEDURE AND RESULTS ...... 14 4.1 General ...... 14 4.2 Australia ...... 14 4.2.1 Overall Site method...... 15 4.2.2 Overall Time method ...... 17 5 DISCUSSION AND SUMMARY...... 19 5.1 General: ...... 19 5.2 Australia ...... 19 6 CONCLUSION ...... 22 7 REFERENCES...... 24 APPENDIX ...... 25 A: South America:...... 25 B: North America...... 32 C: Africa...... 40 D: Eurasia...... 48 REFERENCES:...... 54
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 8
List of Figures Figure 1: Major and minor tectonics plates of Earth [UPRM, 4]...... 11 Figure 2: Simplified picture illustrating the wind over land...... 13 Figure 3: Location of selected 20 sites and area center of Australia...... 14 Figure 4: The Australian plate, center of continent (Alice Springs) and centre of plate [ESUM, 10] ...... 19 Figure 5: Monthly wind force over Australia...... 20 Figure 6: Monthly wind force direction over Australia...... 20 Figure 7: The arrows indicate the actual and calculated direction of the Australian plate movement, [ESUM, 10] ...... 21 Figure 8: Major plates, plate boundaries, and plate movements. [Christopherson, 11]...... 21 Figure 9: Digital Tectonics Activity Map plate boundaries plate movements. [NASA , 12]...... 22 Figure 10: Location of selected 21 sites and mass center of gravitation, South America...... 25 Figure 11: South American plate and the location of Sao Carlos city, the area center of the continent, and the suggested location of the center of the plate, [USGS, 13]...... 29 Figure 12: Calculated monthly wind force of South America...... 30 Figure 13: Calculated monthly wind force direction of South America...... 30 Figure 14: Actual and calculated direction of the South American plate movement. [USGS, 13]...... 31 Figure 15: Location of the selected 30 sites in North American. [Theodora, 14]...... 32 Figure 16: The North America plate and the location of International Falls city, the area center of the continent, and the suggested location of the center of the [15]...... 37 Figure 17: Total monthly wind force in North America...... 37 Figure 18: Monthly wind force direction over North America...... 38 Figure 19: Actual and calculated direction of the North American plate movement. [15]...... 38 Figure 20: Modified map of San Andreas Fault, [16]...... 39 Figure 21: Location of the selected 29 sites in Africa, [ABC, 17]...... 40 Figure 22: The African plate, Africa and the location of Yangambi city the area center of the continent, and the suggested location of the center of the plate [18]...... 45 Figure 23: Calculated monthly wind force in Africa...... 46 Figure 24: Calculating wind force direction in Africa over the year...... 46 Figure 25: Actual and calculated direction of the African plate movement [18]...... 47 Figure 26: Location of the selected 18 sites on the Eurasian continent [19] ...... 48 Figure 27: The Eurasian plate and its center at Ekibastuz city, the area center of the continent, and the suggested location of the center of the plate [19]...... 52 Figure 28: Calculated monthly wind force over the year...... 52 Figure 29: Calculated wind force direction over Eurasia during the year...... 53 Figure 30: Actual and calculated direction of the Eurasian plate movement [19]...... 53
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 9
List of Tables Table 1: Calculated wind force and wind direction at specific sites...... 15 Table 2: Calculated overall wind force for different sites...... 16 Table 3: Calculated wind force in Australia (January)...... 17 Table 4: The overall wind force based on monthly resultant force calculation...... 18 Table 5: Results of the Overall Site and Overall Time methods for Australia ...... 20 Table 6: Summary of calculated wind force, torque, actual plate movement of major plates...... 23 Table 7: Calculated monthly wind force and wind direction at Vladivia-Pichoy ... Erreur ! Signet non défini. Table 8: Calculated wind force and direction at difference locations in South America...... 27 Table 9: Calculated wind force for a specific month (South America)...... 28 Table 10: Resulting overall wind force based on monthly data, South America...... 28 Table 11: Results of the Overall Site and Overall Time methods for South America...... 29 Table 12: Calculated wind force and direction at a specific site (Astoria)...... 33 Table 13: Overall wind force and direction based on site calculations...... 34 Table 14: Calculated wind force in North America for January...... 35 Table 15: Calculated overall wind force based on monthly force calculations...... 36 Table 16: Overall Site and Time methods (North America)...... 36 Table 17: Calculated monthly wind force and wind direction at ‘Port Sudan’...... 41 Table 18: Overall wind force in Africa based on the sites calculation...... 42 Table 19: The wind force calculation in a specific month (Africa) ...... 43 Table 20: The overall wind force based on monthly resultant force calculation...... 44 Table 21: The results of the Overall Site and Time methods (Africa) ...... 45 Table 22: Calculated wind force at Bolsoj Santar...... 49 Table 23: The overall wind force based on monthly resultant force calculation...... 49 Table 24: Show the calculation of the wind force in a specific month (January) ...... 50 Table 25: The result of the overall Site and Time methods (Eurasia)...... 51 Table 26: The results of the Overall Site and Time methods (Eurasia) ...... 51
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 10
1 BACKGROUND 1.1 Plate Tectonics
Plate Tectonics is the theory that provides an explanation for the behaviour of the Earth's crust, particularly the global distribution of mountain building, earthquake activity, and volcanism in a series of linear belts. Numerous other geological phenomena such as lateral variations in surface heat flow, the geology of ocean basins, and various associations of igneous, metamorphic, and sedimentary rocks can also be logically related by plate tectonics theory.
The theory of plate tectonics arose out of two separate geological observations: continental drift, noticed in the early 20 th century, and seafloor spreading, noticed in the 1960s. The theory itself was developed during the late 1960s and has since been universally accepted by virtually all scientists. It has revolutionized the earth sciences and, because of its unifying and explanatory power for diverse geological phenomena, and because it was very successful at predicting many features of Earth's crust. Essential features of the plate tectonics hypothesis are widely accepted [Keith 2001, 1] ; but even so, some geologists were not satisfied until the slow motion of the plates could be measured typically about 2 cm per year. This was accomplished in the 1980s using satellites, lasers, and the positions of very distant galaxies. The main features of plate tectonics are: • The surface of Earth consists of several lithospheric plates; the plates encompass the crust and the upper mantle. • Plate boundaries are of four types: midocean ridges where new material is added to the plates, subduction zones where denser and more ductile parts of plates are destroyed, transform faults where plates slide past another, and basal viscous shear zones along which motion between the base of lithospheric plates and underlying mantle (asthenosphere) occurs. • Convection currents beneath the plates move the lithospheric plates in different directions. • The energy source driving the convection currents is radioactivity of Earth’s mantle. Convection is also driven by density contrasts of the Earth.
The Plate Tectonics theory asserts that Earth is divided into core, mantle, and crust. The crust is subdivided into oceanic and continental crust. This theory is based on a simple model of the Earth in which a rigid outer shell of 50–150 km thick, the lithosphere, consisting of both oceanic and continental crust as well as the upper mantle, is considered to lie above a hotter, weaker semi plastic asthenosphere. The asthenosphere extends from the base of the litho sphere to a depth of about 700 km.
The important geologic theory of plate tectonics asserts that the Earth's surface is composed of about seven major blocks, or plates, and many more minor plates that move across the Earth's surface at a very slow rate. Although the plates creep along at a rate of just cm per year, this movement still causes stress and strain in the Earth's crustal structure. These shifting plates cause faults, mountains, trenches, mid oceanic ridges and rifts, and even ocean basins, some movements may result in violent earthquakes and volcanic eruptions. The theory is explaining geologic changes that result from the movement of litho spheric plates over the
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 11
asthenosphere. The visible continents, a part of the lithospheric plates upon which they ride, shift slowly over time as a result of the forces driving plate tectonics.
Plate tectonics is the surface expression of mantle convection driven by radiogenic heat [Dickinson 1981, 2] and the plates are able to move because of the relative weakness of the asthenosphere. Dissipation of heat from the mantle is acknowledged to be the source of energy driving plate tectonics. Three dimensional imaging of the Earth's interior indicates that, convection of some sort is occurring throughout the mantle [Tanimoto 2000, 3]. Somehow, this energy must be translated to the lithosphere in order for tectonic plates to move. There are essentially two forces that could be accomplishing this: friction and gravity. 1.2 Major plates The main plates as shown in the map in Figure 1 below are:
1. African Plate, covering the African Continent. 2. Antarctic Plate, covering the Antarctican Continent. 3. Australian Plate, covering the Australian Continent. 4. Eurasian Plate covering the Eurasia Continent. 5. North American Plate covering the North American Continent and north east Siberia. 6. South American Plate covering the South American Continent. 7. Pacific Plate, covering the Pacific Ocean.
Notable minor plates include the Indian Plate, the Arabian Plate, the Caribbean Plate, and the Scotia Plate.
Figure 1: Major and minor tectonics plates of Earth [UPRM,4]. 1.3 Climate Change
Climate change refers to the variation in the Earth's global climate or regional climates over time. It describes changes in the variability or average state of the atmosphere over time
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 12
scales ranging from decades to millions of years. These changes may come from internal processes, be driven by external forces or, most recently, be caused by human activities.
In recent usage, especially in the context of environmental policy, the term "climate change" is often used to refer only to the ongoing changes in modern climate, including the rise in average surface temperature known as global warming.
The global climate change has large implications for both humans and wildlife. Many threatened and endangered species, which already lead a precarious existence, are likely to suffer further declines. It’s checked clearly that the climatic changes have significantly affected natural ecosystems in many regions of the world. These changes include alterations in plant community structure, composition, biological productivity, biodiversity and spatial patterns [Wang et al. 2007, 5]. Global warming also threatens populations of species that were once relatively secure, and is likely to result in the endangerment of more species in the future. A study of habitats comprising 20 percent of the earth's surface suggested that 15 to 37 percent of the world's species may be extinct by 2050 if recent warming trends continue [Pounds et al, 2004, 6] and the alterations in these ecosystems lead to dramatic changes in soil physical properties, soil and surface water dynamics and in the soil carbon cycle, which in turn exert a profound influence on the entire biosphere [Christensen et al., 2004, 7] and [Wang et al. 2007, 5].
Earth's climate is a delicate balance of energy input, chemical and biological processes, and physical phenomena. The Earth's atmosphere plays a critical role in planetary surface temperature. Some gases, such as carbon dioxide (CO 2) and methane (CH 4), absorb and maintain heat in the same way that glass traps heat in a greenhouse. These greenhouse gases in Earth's atmosphere allow temperatures to build up, keeping the planet warm and habitable to the life forms that have evolved here. This phenomenon is called the greenhouse effect.
This study is based on the idea that plate tectonics could be party influenced by dominating winds, i.e. the resulting wind force on the different plates. As a consequence the ongoing climate change and possible changes in wind direction and wind velocities might change the movements of the plates.
2 OBJECTIVES
The aim of this initial study is to investigate if there is any correlation between plate movements and predominant wind directions. More specifically the aim is to investigate:
1 To analyse the global wind directions and the wind velocities. 2 To calculate resulting wind force in order to check the influence of that force on the Plate Tectonics movements. 3 To correlate the resulting wind force with the plate movement.
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 13
3 METHOD 3.1 The force Equation: The wind causes a skin friction on the ground surface. According to [Taylor 1916, 8], if it were possible to measure the tangential force exerted by the wind as it blows over a large tract of land, it should be equal to the skin friction on a similar small surface when subjected to the action of the very high wind. So, to reduce the tract of land to a similar small flat plate, the trees and houses would be reduced to a mere roughness on the plate. It is to be expected, if the skin friction on unit area of the earth's surface, the wind force, F (N/m 2), can be expressed Figure 2: Simplified picture illustrating the wind over land. . F = kρQ² (1) Where Q is the wind velocity near the surface (m/s), ρ is the density of the air assumed to be 1.29 Kg/m³, and according to: G. I. Taylor (1916), the value of the skin friction coefficient k will be the same as the constant which would be found in the laboratory by experimenting with a small, slightly roughened plate. So since the actual values of the skin friction coefficient k are of the same order of magnitude, but probably somewhat smaller than those found in the laboratory, being 0.002 to 0.003 as against the value 0.004 found for skin friction in a pipe, so we assumed the value of the constant to be 0.003.
3.2 The Torque Equations Torque is known as the application of force where there is rotational motion, and it can be expressed according to the following relation:
T=F tot *r (2) Where F tot is the total force on the specific continent (resulting force per m² x area of the continent) attached in centre, and r is the perpendicular (or smallest) distance to the mass center of the plate. Here we are assuming that the mass center is equivalent to the area center.
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 14
4 PROCEDURE AND RESULTS 4.1 General The wind data were investigated at many locations, selected all around each continent, as shown by the maps illustrating chosen locations (see blow), Monthly wind data of the selected points were determined by using the METEONORM Version 5.1 software [Meteonorm, 2007, 9]. The different locations in each continent or plate were selected randomly, but the basic idea behind the selection is that: 1 Evenly distributed on all sides of the continent. 2 The selection of the specific locations is to give an idea of the actual effects of the wind forces on the specific continent and the specific plate. Two calculations methods have been used to determine the wind force in this study; In the Overall Site Method the overall annual wind force of the sites was used as the basic data for the final overall result. In the Overall Time Method the overall monthly wind force was used as the basic data for calculating the final overall result. 4.2 Australia For the analytical study of the Australian plate, the wind data were investigated at twenty locations all around Australia, as shown in Figure 3. Alice Springs city which located at the center of the Australian continent, assumed as the area center of the continent.
Figure 3: Location of selected 20 sites and area center of Australia.
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 15
4.2.1 Overall Site method Based on the above equation and assumptions, for each of the twenty sites, the wind force and direction was calculated, to show the calculation process here below is Carnarvon Airp site mentioned as example. Table 1: Calculated wind force and wind direction at specific sites. Site: Carnarvon Airp.
Month Wind Speed Wind Direction F (N/m2) Fy (N/m2) Fx (N/m2) Jan 7.5 194 0.22 0.2 0.1 Feb 6.9 197 0.18 0.2 0.1 Mar 6.5 212 0.16 0.1 0.1 Apr 5.2 230 0.10 0.1 0.1 May 4.5 207 0.08 0.1 0.0 Jun 4.3 229 0.07 0.0 0.1 Jul 4.4 224 0.07 0.1 0.1 Aug 4.9 231 0.09 0.1 0.1 Sep 6.1 214 0.14 0.1 0.1 Oct 7 211 0.19 0.2 0.1 Nov 7.3 198 0.21 0.2 0.1 Dec 7.8 185 0.24 0.2 0.0 Yearly mean 6.0 211 0.147 0.128 0.063 Wind Direction 206.3 Wind Force 0.143 By calculating the wind force and wind direction of each location, we can get the overall wind force and wind direction.
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 16
Table 2: Calculated overall wind force for different sites.
Location Wind Force Wind Direction Fy= F*COS(Θ 180) Fx= F*SIN(Θ 180) Carnarvon Airp 0.143 206.3 0.13 0.06 Sheoaks Aws 0.003 180.2 0.00 0.00 Elcho island 0.001 90.7 0.00 0.00 Double IsI pT 0.194 195.9 0.19 0.05 Mallacoota Aws 0.036 136.2 0.03 0.02 Adele isi awa 0.019 125.9 0.01 0.02 thursday/hall 0.013 128.6 0.01 0.01 Gooseberry Hill 0.118 255.5 0.03 0.11 Williamtown Airp 0.024 245.5 0.01 0.02 Thangool 0.011 127.3 0.01 0.01 Learmonth airp 0.042 120.9 0.02 0.04 Mt Gambier 0.017 180.3 0.02 0.00 Lancelin 0.074 246.4 0.03 0.07 Esperance 0.004 223.7 0.00 0.00 Cooktown Mission 0.071 167.6 0.07 0.02 Greater Wollongo 0.042 208.9 0.04 0.02 Swanburne Aws 0.112 252.8 0.03 0.11 Albany Airp 0.002 152.1 0.00 0.00 Naracoorte 0.018 213.9 0.01 0.01 Green Island 0.23 167.7 0.22 0.05 0.043 0.015 Wind Direction 199.2 Wind Force 0.046
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 17
4.2.2 Overall Time method Since the wind varies in velocity and direction over the year the effect of the wind force on the different sites was studied during each month, as the calculations procedure and the results shown for the first month of the year in the table below Table 3: Calculated wind force in Australia (January).
Location Wind ForceWind Force Wind Direction Fy= F*COS(Θ 180) Fx= F*SIN(Θ 180) Carnarvon Airp 0.22 194 0.21 0.05 Sheoaks Aws 0.09 180 0.09 0.00 Elcho island 0.01 270 0.00 0.01 Double IsI pT 0.25 188 0.25 0.03 Mallacoota Aws 0.09 90 0.00 0.09 Adele isi awa 0.08 293 0.03 0.07 thursday/hall 0.02 315 0.01 0.01 Gooseberry Hill 0.19 213 0.16 0.10 Williamtown Airp 0.07 180 0.07 0.00 Thangool 0.02 120 0.01 0.02 Learmonth airp 0.14 293 0.05 0.13 Mt Gambier 0.1 180 0.10 0.00 Lancelin 0.12 213 0.10 0.07 Esperance 0.13 90 0.00 0.13 Cooktown Mission 0.04 168 0.04 0.01 Greater Wollon. 0.07 180 0.07 0.00 Swanburne Aws 0.14 213 0.12 0.08 Albany Airp 0.07 90 0.00 0.07 Naracoorte 0.06 225 0.04 0.04 Green Island 0.16 168 0.16 0.03 0.054 0.005 Wind Force Wind Force 0.054 Wind direction ΘWind direction Θ 364.7 Based on the above results of January and the results of the rest months of the year, one can observe the overall effect of the wind force from the different locations around Australia, through the year. This can be calculated easily by the following procedure, where the wind force and the angle of direction of each month were used as basic data, and then both the overall resultant force and the angle of direction can be calculated as an average value:
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 18
Table 4: The overall wind force based on monthly resultant force calculation. Wind Wind Fy=F*COS(Θ Fx=F*SIN(Θ Month Force Direction PI/180 180) 180) Jan 0.054 364.7 0.017456 0.05 0.00 Feb 0.042 314.3 0.017456 0.03 0.03 Mar 0.044 222.3 0.017456 0.03 0.03 Apr 0.045 315 0.017456 0.03 0.03 May 0.038 297.3 0.017456 0.02 0.03 Jun 0.023 292 0.017456 0.01 0.02 Jul 0.021 252.7 0.017456 0.01 0.02 Aug 0.011 174.9 0.017456 0.01 0.00 Sep 0.013 227.7 0.017456 0.01 0.01 Oct 0.022 187.6 0.017456 0.02 0.00 Nov 0.039 179.6 0.017456 0.04 0.00 Dec 0.035 172.1 0.017456 0.03 0.00 0.001 0.014 Wind Force 0.014 Wind direction Θ 265.7
The total land area of Australia is 7,617,930 km 2 (7.6.1012 m 2) is affected by a total wind force of 0.04 N/m²* 7.6 10 12 m 2 =3.04 .10 11 N. This resulting wind force is attacking the continent in its area centre. Since the centre of the Australian plate is not the same as the centre of the continent this force results in an anti clockwise torque. The perpendicular distance between the force and the area centre of the plate was estimated 293 km. The total torque in anti clockwise direction is according to eq. (2) given by; 5 11 16 Torque T = F ∗ r = .2 93∗10 ∗ .3 04 ∗10 = .8 91∗10 Nm
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 19
5 DISCUSSION AND SUMMARY 5.1 General: By using the calculation procedures, and the results mentioned above, it will be possible to analyse the global wind directions and the wind velocities, and this will lead to the calculation of the resulting wind force needed for investigating its influence on the different plate tectonics movement. As shown in the calculation procedure, there two different ways of calculations were used. The Overall Site method is based in the overall annual wind force of the site. In the second method, the Overall Time Method, the overall monthly wind force is the basic data of the final overall result. By using the second method we will be able to recognize the seasonal variation of the wind force. As mentioned above, the main objectives behind the study are to correlate the resulting wind force with the plate movement. The actual direction of plate movement is seen in Figure 7.
5.2 Australia The force of the Overall Site Method was used to calculate the torque of the wind force. Here Over which depend on the assumption of a specific location as a centre of gravitation and by measuring the distance of each location from this centre and according to the first relation that mentioned previously, we can calculate the overall torque, the location of the centre of gravitation shown in Figure 4 below.
Figure 4: The Australian plate, center of continent (Alice Springs) and centre of plate [ESUM, 10 ]
Based on the result of the second method of calculation – the Overall Time Method – Figure 5 illustrates the different wind force value of each Month. From the graph it can be seen that the greatest wind force over the Australian plate occurs during January – 0.048 N/m² while the lowest wind force value occurs in September where the value used to reach 0.012 N/m².
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 20
The results of the wind force and the wind angle of direction based on the two methods of calculations, beside the wind torque results were shown here in the table below:
Table 5: Results of the Overall Site and Overall Time methods for Australia Method Overall Site Method Overall Time Method Wind Force 0.046 N/m² 0.014 N/m² Wind Direction 199.2 º 265.7 º Wind Torque 8.91 .10 16 Nm
Wind Force
0.06 0.05 0.04 Wind force 0.03 N/m2 0.02 0.01 0 Jan Mar May Jul Sep Nov Months Figure 5: Monthly wind force over Australia. The corresponding wind force directions through the year are shown in Figure 6.
Wind force direction
400 350 300 250 200 150 100 Angle of direction 50 0 0 2 4 6 8 10 12 14 Months Figure 6: Monthly wind force direction over Australia.
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 21
So from the calculated wind force direction that mentioned above in table 26, where the angle of direction is between 199.2 and 265.7 that can be illustrated in the map as in the figure 10 below if we compare that with the actual movement of the Australian plate as shown in the map from After Christopherson (1997), figure 11, we will find the same direction of movement of the plate.
Figure 7: The arrows indicate the actual and calculated direction of the Australian plate movement, [ESUM, 10]
Figure 8: Major plates, plate boundaries, and plate movements. [Christopherson, 11]
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 22
5.3 SUMMARY The described calculation methods of the wind, wind force and torque used for the Australian plate were applied on the rest of the major plates (South America, North America, Africa and Eurasia). The resulting wind forces were correlated with the size of the actual movement of these plates based on the data of Digital Tectonics Activity Map of the Earth in Figure 9. A summary of these results are given in Table 6. All the details of the calculations processes are available in the Appendices A, B, C and D.
Figure 9: Digital Tectonics Activity Map plate boundaries plate movements. [NASA, 12]. 6 CONCLUSION As seen in the Table 6, the correlation of the calculated force of the wind direction of North America is almost the same as the actual plate movement, where the difference in the angle of direction is 7.3 o. The difference in the angles of direction for South America reach 16.4 o, even the plates of Eurasia and Africa based on the above correlation were found in directions near to the actual movement directions of these plates, but the difference in the angles of direction was found 37.8 o and 93.8 o respectively.
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 23
Table 6: Summary of calculated wind force, torque, actual plate movement of major plates. Calculated wind force data Difference Plate mm 2 Torque Wind force Force (N/m ) movement per Θ1 Θ2 (Nm) direction Θ1 Θ2 year . 16 Australia 0.014 0.046 8.91 10 199.2 265.7 230 72 30.8 35.7 South 1.17 .10 15 0.022 0.047 55.0 73.6 90 35 35.0 16.4 America North 4.3 .10 15 0.0075 0.021 210.0 187.3 180 35 7.3 30.0 America . 16 Africa 0.007 0.025 1.66 10 176.2 152.8 270 33 93.8 . 16 Eurasia 0.019 0.023 7.34 10 376.2 352.8 315 19 37.8 61.2 The wind velocity values are not random, but the random selection of the locations from all around a specific plate, will not give enough data, which will reflect a very clear view of the actual situation of the effect of the wind force. The angle of direction for the wind force that obtained from the study for the all five plates is closer to the actual movement direction of these plates, where the difference varies from plate to other. Both methods show that, even the result value of the wind force at the study is small, but the influence of the wind force on the plate tectonics movements, expected to be higher, if the wind velocities increased due to any reasons such as the global climate change.
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 24
7 REFERENCES 1. MacKenzie, Keith, Evidence for a plate tectonics debate, Earth Science Reviews 55 2001 235–336. 2. W. R. Dickinson, Plate tectonics through geological time, Phil. Trans. R. SOG.LOIUI. A 301, 207 215 (1981). 3. Tanimoto, Toshiro and Thorne Lay (2000) Mantle dynamics and seismic tomography, Proc. Natl. Acad. Sci. USA, Vol. 97, No. 23 (Jan. 1, 1916), pp. 12409 12410. 4. The website of Universidad de Puerto Rico Mayagüez, http://geology.uprm.edu/Morelock/1_image/plate.jpg 5. Genxu Wang a,c, Yibo Wang b, Yuanshou Li c, Huiyan Cheng, Influences of alpine ecosystem responses to climatic change on soil properties on the Qinghai–Tibet Plateau, China. Catena 70 (2007) 506–514. 6. J. Alan Pounds and Robert Puschendorf, Clouded futures, NATURE, 2004. http://www.nature.com/nature/journal/v427/n6970/pdf/427107a.pdf et al, 2004 7. Christensen, T.R., Johansson, Torbjom, Akerman, Jonas H., Masterpanov, Mihail, 2004. Thawing sub arctic permafrost: effects on vegetation and methane emissions. Geophysical Research Letters 31, L04501. 8. G. I. Taylor (1916) Skin Friction of the Wind on the Earth's Surface, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, Vol. 92, No. 637 (Jan. 1, 1916), pp. 196 199. 9. Meteonorm, 2007. The Meteonorm Model. http://software.cstb.fr/soft/present.asp?page_id=us!meteonorm 10. ESUM The website of the School of Earth Sciences University of Melbourne Australia http://web.earthsci.unimelb.edu.au/antarctica/plateTectonics.html 11. Christopherson. R.W., 1997. Geosystems, 3 rd Ed. Prentice Hall corp. Upper Saddle River, NJ. 656 pp. 12. NASA, Planetary Geodynamics Laboratory at the National Aeronautics and Space Administration. http://denali.gsfc.nasa.gov/dtam/data/ftp/dtam.jpg 13. USGS, The website of the U.S. Geological Survey, http://pubs.usgs.gov/publications/text/slabs.html 14. The popular educational web site of Information Technology Associates (ITA). http://www.theodora.com/maps/ 15. The Zetatalk website, http://www.zetatalk.com/info/tinfo05t.htm 16. Geology, http://geology.com/articles/images/san andreas fault map.jpg 17. ABC, The ABC teach website, http://www.abcteach.com/Savannah/map.htm 18. The Zetatalk website, http://www.zetatalk.com/info/tinfo05r.htm 19. The Zetatalk website, http://www.zetatalk.com/info/tinfo05s.htm
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 25
APPENDIX A: South America: For the analytical study of the South American plate, the wind data were investigated at twenty one locations, all around South America, as shown in figure 6. Ji Parana BR city which located at the center of the South American continent, assumed as the area center of the continent.
Figure 10: Location of selected 21 sites and mass center of gravitation, South America.
Overall Site method Based on the above equations and assumptions, for each of the twenty one sites, the wind force and direction was calculated, to show the calculation process here below is Vladivia Pichoy site mentioned as example.
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 26
Table 7: Calculated monthly wind force and wind direction at Vladivia Pichoy . Month Wind Speed Θ F (N/m2) Fy (N/m2) Fx (N/m2) Jan 3.4 180 0.04 0.0 0.0 Feb 3.1 180 0.04 0.0 0.0 Mar 2.6 180 0.03 0.0 0.0 Apr 2.1 0 0.02 0.0 0.0 May 2 0 0.02 0.0 0.0 Jun 2.6 0 0.03 0.0 0.0 Jul 2.6 0 0.03 0.0 0.0 Aug 2.8 0 0.03 0.0 0.0 Sep 2.9 0 0.03 0.0 0.0 Oct 3 0 0.03 0.0 0.0 Nov 3.1 180 0.04 0.0 0.0 Dec 3.2 180 0.04 0.0 0.0 Yearly mean 2.783 75.000 0.031 0.000 0.000 Wind Direction 172.9 Wind Force 0.000 By calculating the resulting wind force and direction at different locations (e.g. Table 8), we can easily get the overall wind force, direction and torque, as shown in Table 9.
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 27
Table 8: Calculated wind force and direction at difference locations in South America.
Location Wind ForceWind Force Wind Direction Fy= F*COS(Θ 180) Fx= F*SIN(Θ 180) Vladivia Pichoy 0 172.9 0.00 0.00 Concepcion 0.03 239.8 0.02 0.03 Arica Shacalluta 0.027 253.2 0.01 0.03 San Juan de Marcona 0.041 180 0.04 0.00 Lima 0.064 180 0.06 0.00 Islotes Evangelista 0.49 258 0.10 0.48 Esmeraldas EC 0.04 180.1 0.04 0.00 Cali/Alfonso Bonill 0.005 180.1 0.00 0.00 Simon Bolivar Airp. 0.086 206.6 0.08 0.04 Caracas/La Carlota 0.018 258.1 0.00 0.02 Mabaruma 0.018 248.1 0.01 0.02 Cayenne Rochea 0.063 263.6 0.01 0.06 Sao Luiz 0.061 90 0.00 0.06 Macau 0.071 92.1 0.00 0.07 Loao Pessoa 0.038 92.2 0.00 0.04 Salvador 0.093 94.9 0.01 0.09 Punta Del Este 0.131 253 0.04 0.13 Viedma Castello 0.139 256.2 0.03 0.13 Comodoro Rivadavi 0.144 112.9 0.06 0.13 Rio Gallegos Airp 0.172 258 0.04 0.17 Ushuaia Airp 0.112 258 0.02 0.11 0.027 0.039 Wind Force 0.047 Wind direction Θ 55.0
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 28
Overall Time Method Table 9: Calculated wind force for a specific month (January). Fx= F*SIN( Θ Location Wind Force Wind Direction Fy= F*COS( Θ 180) 180) Vladivia Pichoy 0.04 180 0.04 0.00 Concepcion 0.08 225 0.06 0.06 Arica Shacalluta 0.04 248 0.01 0.04 San Juan de Marcona 0.06 180 0.06 0.00 Lima 0.08 180 0.08 0.00 Islotes Evangelista 0.6 258 0.13 0.59 Esmeraldas EC 0.06 0 0.06 0.00 Cali/Alfonso Bonill 0.01 0 0.01 0.00 Simon Bolivar Airp. 0.13 23 0.12 0.05 Caracas/La Carlota 0.02 78 0.00 0.02 Mabaruma 0.02 68 0.01 0.02 Cayenne Rochea 0.07 68 0.03 0.06 Sao Luiz 0.06 90 0.00 0.06 Macau 0.06 90 0.00 0.06 Loao Pessoa 0.03 90 0.00 0.03 Salvador 0.1 90 0.00 0.10 Punta Del Este 0.12 78 0.02 0.12 Viedma Castello 0.2 248 0.07 0.19 Comodoro Rivadavia 0.21 293 0.08 0.19 Rio Gallegos Airp 0.24 258 0.05 0.23 Ushuaia Airp 0.15 258 0.03 0.15 0.009 0.044 Wind Force 0.045 Wind direction Θ 257.9 Based on the above results of January and the results of the rest months of the year, one can observe the overall effect of the wind force from the different locations around South America, through the year as shown below: Table 10: Resulting overall wind force based on monthly data, South America. Month Wind ForceWind Force Wind Direction Fy= F*COS( Θ 180) Fx= F*SIN( Θ 180) Jan 0.045 257.9 0.01 0.04 Feb 0.027 257.7 0.01 0.03 Mar 0.022 256.2 0.01 0.02 Apr 0.022 263.6 0.00 0.02 May 0.018 100.6 0.00 0.02 Jun 0.013 110.9 0.00 0.01 Jul 0.027 265.7 0.00 0.03 Aug 0.021 248.3 0.01 0.02 Sep 0.021 256.4 0.00 0.02 Oct 0.026 255.7 0.01 0.03 Nov 0.04 253.2 0.01 0.04 Dec 0.038 254 0.01 0.04 0.006 0.021 Wind Force 0.022 Wind direction Θ 73.6
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 29
The total land area of South America is 17,858,520 km 2 i.e. 17.9 .10 12 m 2, with a mean wind force of 0.04 N. Consequently, the total force affecting the continent is affected by a total wind force of: = .0 04N / m2 ∗17 9. ∗1012 m2 = .7 16 ∗1011 N This resulting wind force is attacking the continent in its area centre. Since the centre of the South American plate is not the same as the centre of the continent this force results in an anti clockwise torque. The perpendicular distance between the force and the area centre of the plate was estimated 1639 km. This wind force acting on its continental area and the total torque in anti clockwise direction is 7.16*10 11 * r The total torque in anti clockwise direction is according to eq. (2) given by; Torque T = F ∗ r = .7 16 ∗1011 ∗ .1 64 ∗103 = .1 17 ∗1015 Nm Table 11: Results of the Overall Site and Overall Time methods for South America. Method Overall Site Method Overall Time Method Wind Force 0.047 N/m² 0.022 N/m² Wind Direction 55.03 º 73.6 º Wind Torque 1.17 .10 15 Nm The first method was used to calculate the torque of the wind force which depend on the assumption of a specific location as a centre of gravitation and by measuring the distance of each location from this centre and according to the first relation that mentioned previously, we can calculate the overall torque, the location of the centre of gravitation shown in Figure (11) below.
Figure 11: South American plate and the location of Sao Carlos city, the area center of the continent, and the suggested location of the center of the plate, [USGS, 13]
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 30
Based on the result of the second method of calculation – the Overall Time Method – Figure (12) illustrates the different wind force value of each month. From the graph it can be seen that the greatest wind force over the South American plate occurs during the winter season from November to January 0.035 – 0.04 N/m² while the lowest wind force value occurs in June where the value used to reach 0.014 N/m².
Wind Force
0.05 0.045 0.04 0.035 0.03 0.025 0.02 0.015 Wind Force (N/m2) 0.01 0.005 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Months Figure 12: Calculated monthly wind force of South America. The corresponding wind force directions through the year are shown in Figure below.
Wind Force direction
300
250
200
150
Degrees 100
50
0 0 2 4 6 8 10 12 14 Months Figure 13: Calculated monthly wind force direction of South America. So from the calculated wind force direction that mentioned above in table 11, where the angle of direction is between 55.03 and 73.6 that can be illustrated in the map as in the figure (14) below , if we compare that with the actual movement of the Australian plate as shown in the
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 31
map from After Christopherson (1997), figure (8) above, we will find the same direction of movement of the plate.
Figure 14: Actual and calculated direction of the South American plate movement. [USGS, 13]
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 32
B: North America For the analytical study of the North American plate, the wind data were investigated at twenty nine locations, all around North America, as shown here below in figure 4. International Falls station, which located at the center of the North American continent, was assumed as the area centre of the continent.
Figure 15: Location of the selected 30 sites in North American. [Theodora, 14 ]
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 33
Overall Site Method: Based on the above equations and assumptions, for each of the 30 sites, the wind force and direction was calculated, to show the calculation process here below is Astoria site mentioned as example. Table 12: Calculated wind force and direction at a specific site (Astoria).
Month Wind Speed Wind Direction F (N/m2) Fy (N/m2) Fx (N/m2) Jan 4.4 90 0.07 0.00 0.07 Feb 4.4 90 0.07 0.00 0.07 Mar 4.3 113 0.07 0.03 0.07 Apr 4.2 248 0.07 0.03 0.06 May 4.1 293 0.07 0.03 0.06 Jun 4.2 315 0.07 0.05 0.05 Jul 4.1 315 0.07 0.05 0.05 Aug 3.9 315 0.06 0.04 0.04 Sep 3.7 225 0.05 0.04 0.04 Oct 3.7 113 0.05 0.02 0.05 Nov 4.3 113 0.07 0.03 0.07 Dec 4.4 90 0.07 0.00 0.07 Yearly mean 4.1 193 0.07 0.00 0.01 Wind Direction 259.0 Wind Force 0.009 By calculating the wind force and direction at the different locations, we can easily get the overall wind force, direction and torque, as shown in the following table.
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 34
Table 13: Overall wind force and direction based on site calculations.
Location Wind Force Wind Direction Fy= F*COS(Θ 180) Fx= F*SIN(Θ 180) Astoria 0.009 259 0.00 0.01 Colima 0.024 254.7 0.01 0.02 Campbell River Airp. 0.002 109.5 0.00 0.00 Mclnnes Islands BC 0.063 237.2 0.03 0.05 Middleton Isl. Amos 0.15 259.5 0.03 0.15 Point Hope 0.059 265.3 0.00 0.06 San Felipe 0.073 142 0.06 0.04 San Francisco CA 0.079 250.9 0.03 0.07 Stika Japonski 0.045 106.8 0.01 0.04 Togiac Village 0.03 207.4 0.03 0.01 Barrow AK 0.128 253.1 0.04 0.12 Henrik Koreyerholme 0.131 177.9 0.13 0.00 Isachsen 0.008 254.2 0.00 0.01 Sachs Harbour 0.059 90 0.00 0.06 Kap tobin 0.046 260.2 0.01 0.05 Prins Christian Sund 0.135 97.8 0.02 0.13 Cartwright 0.081 103.9 0.02 0.08 Port Aux Basques 0.071 269.9 0.00 0.07 Longue Pt De Mongue 0.014 258.5 0.00 0.01 Chatham Airp. NB 0.042 248.3 0.02 0.04 Western Head 0.047 126.5 0.03 0.04 Portland ME 0.023 238.6 0.01 0.02 Storrs CT 0.045 250 0.02 0.04 Atlantic City 0.037 96.3 0.00 0.04 Kinston 5se 0.026 223.1 0.02 0.02 Jacksonville Airp. 0.006 264.4 0.00 0.01 West Palm Beach 0.029 94.4 0.00 0.03 Tampa FL 0.026 247.4 0.01 0.02 Houston Airp. 0.016 100.1 0.00 0.02 0.018 0.010 Wind Force 0.021 Wind direction Θ 210.0
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 35
Overall Time Method:
Table 14: Calculated wind force in North America for January.
Location Wind Force Wind Direction Fy= F*COS(Θ 180) Fx= F*SIN(Θ 180) Astoria 0.07 90 0.00 0.07 Colima 0.02 258 0.00 0.02 Campbell River Airp. 0.01 0 0.01 0.00 Mclnnes Islands BC 0.036 180 0.04 0.00 Middleton Isl. Amos 0.23 78 0.05 0.22 Point Hope 0.22 113 0.09 0.20 San Felipe 0.07 111 0.03 0.07 San Francisco CA 0.05 123 0.03 0.04 Stika Japonski 0.06 113 0.02 0.06 Togiac Village 0.1 360 0.10 0.00 Barrow AK 0.14 68 0.05 0.13 Henrik Koreyerholme 0.21 180 0.21 0.00 Isachsen 0.02 90 0.00 0.02 Sachs Harbour 0.11 270 0.00 0.11 Kap tobin 0.05 65 0.02 0.05 Prins Christian Sund 0.26 258 0.05 0.25 Cartwright 0.14 270 0.00 0.14 Port Aux Basques 0.29 270 0.00 0.29 Longue Pt De Mongu 0.03 270 0.00 0.03 Chatham Airp. NB 0.06 270 0.00 0.06 Western Head 0.09 360 0.09 0.00 Portland ME 0.07 270 0.00 0.07 Storrs CT 0.05 258 0.01 0.05 Atlantic City 0.07 293 0.03 0.06 Kinston 5se 0.04 225 0.03 0.03 Jacksonville Airp. 0.04 315 0.03 0.03 West Palm Beach 0.07 315 0.05 0.05 Tampa FL 0.04 45 0.03 0.03 Houston Airp. 0.04 360 0.04 0.00 0.012 0.044 Wind Force 0.046 Wind direction Θ 255.2 Based on the above results of January and the results of the rest months of the year, one can observe the overall effect of the wind force from the different locations around North America, through the year as shown below:
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 36
Table 15: Calculated overall wind force based on monthly force calculations.
Month Wind Force Wind Direction Fy= F*COS(Θ 180) Fx= F*SIN(Θ 180) Jan 0.046 255.2 0.01 0.04 Feb 0.01 243.1 0.00 0.01 Mar 0.011 138 0.01 0.01 Apr 0.013 140.3 0.01 0.01 May 0.016 223.1 0.01 0.01 Jun 0.009 188.2 0.01 0.00 Jul 0.005 102.9 0.00 0.00 Aug 0.014 184 0.01 0.00 Sep 0.009 103.6 0.00 0.01 Oct 0.014 248.8 0.01 0.01 Nov 0.009 160.1 0.01 0.00 Dec 0.036 95.5 0.00 0.04 0.007 0.001 Wind Force 0.0075 Wind direction Θ 187.3
The total land area of North America is 24,490,000 km2 i.e. 24.5.1012 m2, with a mean wind force of 0.0144 N. Consequently, the total force affecting the continent is affected by a total wind force of: = .0 0144N / m2 ∗ 24 5. ∗1012 m2 = .3 53∗1011 N This resulting wind force is attacking the continent in its area centre. Since the centre of the North American plate is not the same as the centre of the continent this force results in a clockwise torque. The perpendicular distance between the force and the area centre of the plate was estimated 1220 km. The total torque in anti clockwise direction is according to eq. (2) given by; Torque T = F ∗ r = .3 53∗1011 ∗ .1 22 ∗103 = 3.4 ∗1015 Nm
Table 16: Overall Site and Time methods (North America). Method Overall Site Method Overall Time Method Wind Force 0.021 N/m² 0.0075 N/m² Wind Direction 210.0 º 187.3 º Wind Torque 4.3 .10 15 Nm
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 37
The first method was used to calculate the torque of the wind force which depend on the assumption of a specific location as a centre of gravitation and by measuring the distance of each location from this centre and according to the first relation that mentioned previously, we can calculate the overall torque, the location of the centre of gravitation shown in Figure (11) below.
Figure 16: The North America plate and the location of International Falls city, the area center of the continent, and the suggested location of the center of the area [15].
Based on the result of the second method of calculation – the Overall Time Method – Figure 17 illustrates the different wind force value of each month. From the graph it can be seen that the greatest wind force over the North American plate occurs during the winter season in December and January 0.036, 0.046 N/m² respectively, while the lowest wind force value occurs in July where the value used to reach 0.005 N/m².
Wind Force
0.050
0.040
Wind Force 0.030 (N/m2) 0.020
0.010
0.000 Jan Mar May Jul Sep Nov Months Figure 17: Total monthly wind force in North America.
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 38
The corresponding wind force directions through the year are shown in Figure below.
Wind force direction
300.0
250.0
200.0
150.0
100.0
Angle of direction 50.0
0.0 0 2 4 6 8 10 12 14 Months Figure 18: Monthly wind force direction over North America. So from the calculated wind force direction that mentioned above in table (16), where the angle of direction is between 187.3 and 210.0 that can be illustrated in the map as in the figure (19) below , if we compare that with the actual movement of the Eurasian plate as shown in the map from After Christopherson (1997), figure (8), we will find the direction of movement of the is same as a function of the effect of the San Andreas Fault, figure (20) below. ‘
Figure 19: Actual and calculated direction of the North American plate movement. [15]
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 39
Figure 20: Modified map of San Andreas Fault, [16]
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 40
C: Africa For the analytical study of the Africa n plate, the wind data were investigated at twenty nine locations, selected all around Africa , as shown here below in figure (14). Yangambi city which located at the center of the African continent , assumed as the area center of continent.
Figure 21: Location of the selected 29 sites in Africa, [ABC, 17]
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 41
Overall Site Method: Based on the above equation and assumptions, for each of the 35 sites, the wind force and direction was calculated, to show the calculation process here below is Port Sudan site mentioned as example. Table 17: Calculated monthly wind force and wind direction at ‘Port Sudan’.
Month Wind Speed Wind Direction F (N/m2) Fy (N/m2) Fx (N/m2) Jan 4.9 360 0.09 0.09 0.00 Feb 4 360 0.06 0.06 0.00 Mar 4 360 0.06 0.06 0.00 Apr 3.6 360 0.05 0.05 0.00 May 3.1 45 0.04 0.03 0.03 Jun 3.1 45 0.04 0.03 0.03 Jul 3.1 360 0.04 0.04 0.00 Aug 3.1 90 0.04 0.00 0.04 Sep 3.1 45 0.04 0.03 0.03 Oct 3.1 360 0.04 0.04 0.00 Nov 4 360 0.06 0.06 0.00 Dec 4.5 360 0.08 0.08 0.00 Yearly mean 3.6 259 0.05 0.05 0.01 Direction 191.6 Force 0.048 By calculating the wind force and direction results of the different locations, we can easily get the overall wind force, direction and torque, as shown in the following table.
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 42
Table 18: Overall wind force in Africa based on the sites calculation.
Location Wind Force Wind Direction Fy= F*COS(Θ 180) Fx= F*SIN(Θ 180) Port Sudan 0.0480 192 0.05 0.01 Alula 0.0150 90.1 0.00 0.01 Djibouti 0.0310 90.1 0.00 0.03 Mogadisho 0.0280 161 0.03 0.01 Dar Es Salaam 0.0310 112 0.01 0.03 Lumbo 0.0180 124 0.01 0.02 Beira 0.0730 120 0.04 0.06 Mabuto/Benfica 0.0420 142 0.03 0.03 Durban 0.0670 0.1 0.07 0.00 Port Elizabeth 0.0920 246.4 0.04 0.08 Cape Town 0.0900 180 0.09 0.00 Alexander Bay 0.0390 117 0.02 0.03 Luanda Observa 0.0160 268 0.00 0.02 Mouila 0.0460 268 0.00 0.05 Cocobeach 0.0470 166 0.05 0.01 Port Harcourt 0.0030 225 0.00 0.00 Lome Airp. 0.0340 225 0.02 0.02 Accra 0.0460 213 0.04 0.03 Sassandra Airp. 0.0080 220 0.01 0.01 Bo 0.0070 187 0.01 0.00 Bolama 0.0200 119 0.01 0.02 Nouadhibou 0.2570 184 0.26 0.02 Al Massira Mc 0.0110 160 0.01 0.00 Casablanca 0.0060 161 0.01 0.00 Mecheria 0.0190 104 0.00 0.02 Jendouba 0.0060 262 0.00 0.01 Jerba 0.0220 264 0.00 0.02 Alexandria 0.0320 168 0.03 0.01 Halaib 0.0400 148 0.03 0.02 0.025 0.002 Wind Force 0.025 Wind direction Θ 176.2 Since the wind varies in velocity and direction over the year the effect of the wind force on the different sites was studied during each month, as the calculations procedure and the results shown for the first month of the year in the table below:
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 43
Overall Time Method: Table 19: The wind force calculation in a specific month (Africa) .
Location Wind Force Wind Direction Fy= F*COS(Θ 180) Fx= F*SIN(Θ 180) Port Sudan 0.0929 360 0.09 0.00 Alula 0.0502 90 0.00 0.05 Djibouti 0.0819 90 0.00 0.08 Mogadisho 0.0372 90 0.00 0.04 Dar Es Salaam 0.0651 23 0.06 0.03 Lumbo 0.0651 0 0.07 0.00 Beira 0.1007 90 0.00 0.10 Mabuto/Benfica 0.1007 90 0.00 0.10 Durban 0.0819 0 0.08 0.00 Port Elizabeth 0.121 225 0.09 0.09 Cape Town 0.1789 180 0.18 0.00 Alexander Bay 0.097 225 0.07 0.07 Luanda Observaor 0.021 270 0.00 0.02 Mouila 0.0262 270 0.00 0.03 Cocobeach 0.03 147 0.02 0.01 Port Harcourt 0.0022 225 0.00 0.00 Lome Airp. 0.0171 225 0.01 0.01 Accra 0.0262 213 0.02 0.01 Sassandra Airp. 0.0074 280 0.00 0.01 Bo 0.0028 40 0.00 0.00 Bolama 0.0367 68 0.01 0.03 Nouadhibou 0.184 45 0.13 0.13 Al Massira Mc 0.0372 180 0.04 0.00 Casablanca 0.0155 180 0.02 0.00 Mecheria 0.0559 248 0.02 0.05 Jendouba 0.0205 270 0.00 0.02 Jerba 0.0589 270 0.00 0.06 Alexandria 0.0784 180 0.08 0.00 Halaib 0.0454 315 0.03 0.03 0.002 0.006 Wind Force 0.0065 Wind direction 109.6 Based on the above results of January and the results of the rest months of the year, one can observe the overall effect of the wind force from the different locations around Africa, through the year as shown below:
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 44
Table 20: The overall wind force based on monthly resultant force calculation. Month Wind Force Wind Direction Fy= F*COS(Θ 180) Fx= F*SIN(Θ 180) Jan 0.0060 109.6 0.00 0.01 Feb 0.0008 197.8 0.00 0.00 Mar 0.0090 150.6 0.01 0.00 Apr 0.0150 105.6 0.00 0.01 May 0.012 166.8 0.01 0.00 Jun 0.0170 187 0.02 0.00 Jul 0.0180 130.4 0.01 0.01 Aug 0.0120 118.5 0.01 0.01 Sep 0.007 212.4 0.01 0.00 Oct 0.001 161 0.00 0.00 Nov 0.006 248 0.00 0.01 Dec 0.004 257 0.00 0.00 0.006 0.003 Wind Force 0.007 Wind direction Θ 152.8
The total land area of Africa is 30,221,532 km2 i.e. 30.221 * 1012 m2, with a mean wind force of 0.0063 N/m². Consequently, the total force affecting the continent is affected by a total wind force of: 12 10 = .0 0063N / m2 ∗30 2. ∗10 m2 = .1 904 ∗10 N This resulting wind force is attacking the continent in its area centre. Since the centre of the African plate is not the same as the centre of the continent this force results in an anti clockwise torque. The perpendicular distance between the force and the area centre of the plate was estimated 873 km. The total torque in anti clockwise direction is according to eq. (2) given by; Torque T = F ∗ r = .1 904 ∗1010 ∗ .8 73∗105 = .1 66 ∗1016 Nm
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 45
Table 21: The results of the Overall Site and Time methods (Africa) Method Overall Site Method Overall Time Method Wind Force 0.025 N/m² 0.007 N/m² Wind Direction 176.2 º 152.8 º Wind Torque 1.66 .10 16 Nm The first method was used to calculate the torque of the wind force which depend on the assumption of a specific location as a centre of gravitation and by measuring the distance of each location from this centre and according to the first relation that mentioned previously, we can calculate the overall torque, the location of the centre of gravitation shown in Figure (19) below.
Figure 22: The African plate, Africa and the location of Yangambi city the area center of the continent, and the suggested location of the center of the plate [18]. Based on the result of the second method of calculation – the Overall Time Method – Figure 23 illustrates the different wind force value of each month. From the graph it can be seen that the greatest wind force over the African plate occurs during July – 0.0180 N/m² while the lowest wind force occurs in October where it reach 0.001 N/m².
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 46
Wind Force
0.0180 0.0160 0.0140 0.0120 Wind Force 0.0100 (N/m2) 0.0080 0.0060 0.0040 0.0020 0.0000 Jan Mar May Jul Sep Nov Months Figure 23: Calculated monthly wind force in Africa.
The corresponding wind force directions through the year are shown in Figure 5.
Wind force direction
300
250
200
150
100
Angle of direction 50
0 0 2 4 6 8 10 12 14 Months
Figure 24: Calculating wind force direction in Africa over the year. So from the calculated wind force direction that mentioned above in table (21), one can observe a big different values of the angle of direction, it’s 152.8 for the Overall time method, while the angle of direction is 176.2 for the Overall site method – the latest will be illustrated by the map in the figure (25) below , and if it compared with the actual movement of the African plate that shown in the map from After Christopherson (1997), figure (8), we will find the direction of actual movement of this plate is not the same to the predominant movement direction.
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 47
Figure 25: Actual and calculated direction of the African plate movement [18].
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 48
D: Eurasia For the analytical study of the Eurasian plate, the wind data were investigated at eighteen locations, all around Eurasia, as shown in figure 18. Ekibastuz city which located at the center of the Eurasian plate, assumed as the area center of continent. 1. Malye Karmakuly 2. Dickson 3. Preodrasheniyai 4. BolsojSantar 5. Poronajs 6. Shanghai 7. Bac Lieu 8. Miri 9. Jambi 10. Sittwe 11. Faizabad 12. Erzincan 13. Roma/Ciampino 14. Porto 15. Belmullet 16. Orland 17. Tromso 18 . Makkaur Figure 26: Location of the selected 18 sites on the Eurasian continent [19] Overall Site Method: Based on the above equations and assumptions, for each of the 25 sites, the wind force and direction was calculated, to show the calculation process here below is the site Bolsoj Santar mentioned as example.
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 49
Table 22: Calculated wind force at Bolsoj Santar.
Month Wind Speed Wind direction F(N/m2) Fy (N/m2) Fx(N/m2) Jan 3.4 217 0.04 0.04 0.03 Feb 3.2 208 0.04 0.03 0.02 Mar 3.4 201 0.04 0.04 0.02 Apr 3.3 171 0.04 0.04 0.01 May 3.1 168 0.04 0.04 0.01 Jun 2.4 183 0.02 0.02 0.00 Jul 2.1 191 0.02 0.02 0.00 Aug 2.2 185 0.02 0.02 0.00 Sep 2.9 195 0.03 0.03 0.01 Oct 4 200 0.06 0.06 0.02 Nov 4.5 207 0.08 0.07 0.04 Dec 3.6 200 0.05 0.05 0.02 Yearly mean 3.2 194 0.04 0.04 0.01 Direction 196.6 Force 0.040 By calculating the wind force and direction results of the different locations, we can easily get the overall wind force, direction and torque, as shown in the following table. Table 23: The overall wind force based on monthly resultant force calculation.
Location Wind Force Wind Direction Fy= F*COS(Θ 180) Fx= F*SIN(Θ 180) Bolsoj Santar 0.0395 196.6 0.04 0.01 Poronajs 0.0380 180.1 0.04 0.00 Shanghai 0.0160 99.6 0.00 0.02 Bac Lieu 0.0100 185 0.01 0.00 Miri 0.0090 114.6 0.00 0.01 Jambi 0.0030 267.3 0.00 0.00 Sittwe 0.0360 146.8 0.03 0.02 Faizabad 0.0058 111.9 0.00 0.01 Erzincan 0.0120 24.9 0.01 0.01 Roma/Ciampino 0.0280 170.6 0.03 0.00 Porto 0.0550 250.6 0.02 0.05 Belmullet 0.1330 260.8 0.02 0.13 Orland 0.1313 0.1 0.13 0.00 Tromso 0.0400 171 0.04 0.01 Makkaur 0.1010 172.8 0.10 0.01 Malye Karmakul 0.1150 182.6 0.11 0.01 Dickson 0.1020 173.2 0.10 0.01 Preodrasheniyai 0.0080 186.2 0.01 0.00 0.023 0.006 Wind Force 0.024 Wind direction Θ 375.5
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 50
Overall Time Method: Since the wind varies in velocity and direction over the year the effect of the wind force on the different sites was studied during each month, as the calculations procedure and the results shown for the first month of the year in the table below: Table 24: Show the calculation of the wind force in a specific month (January) .
Location Wind Force Wind Direction Fy= F*COS(Θ 180) Fx= F*SIN(Θ 180) Bolsoj Santar 0.0447 217 0.04 0.03 Poronajs 0.0474 0 0.05 0.00 Shanghai 0.03 293 0.01 0.03 Bac Lieu 0.0089 135 0.01 0.01 Miri 0.0081 106 0.00 0.01 Jambi 0.0155 23 0.01 0.01 Sittwe 0.0171 45 0.01 0.01 Faizabad 0.0039 270 0.00 0.00 Erzincan 0.004 24 0.00 0.00 Roma/Ciampino 0.0373 45 0.03 0.03 Porto 0.1257 90 0.00 0.13 Belmullet 0.2235 270 0.00 0.22 Orland 0.2235 0 0.22 0.00 Tromso 0.1087 180 0.11 0.00 Makkaur 0.2477 180 0.25 0.00 Malye Karmakuly 0.1393 209 0.12 0.07 Dickson 0.1896 180 0.19 0.00 Preodrasheniyai 0.0437 248 0.02 0.04 0.022 0.011 Wind Force 0.024 Wind direction Θ 207.7 Based on the above results of January and the results of the rest months of the year, one can observe the overall effect of the wind force from the different locations around Eurasia, through the year as shown below:
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 51
Table 25: The result of the overall Site and Time methods (Eurasia).
Month Wind Force Wind Direction Fy= F*COS(Θ 180) Fx= F*SIN(Θ 180) Jan 0.0240 207.7 0.02 0.01 Feb 0.0420 159.6 0.04 0.01 Mar 0.0270 183.4 0.03 0.00 Apr 0.0310 159.2 0.03 0.01 May 0.016 259.9 0.00 0.02 Jun 0.0150 127 0.01 0.01 Jul 0.0130 93.4 0.00 0.01 Aug 0.0140 118.6 0.01 0.01 Sep 0.026 207.5 0.02 0.01 Oct 0.024 166.3 0.02 0.01 Nov 0.0250 161 0.02 0.01 Dec 0.026 196.1 0.02 0.01 0.019 0.002 Wind Force 0.019 Wind direction Θ 352.8
Since the total land area of Eurasia continent, Arabian peninsula and the subcontinent of India is 54,000,000, 2,600,000 and 3,287,590 km 2 respectively, So the total land of the Eurasian plate will be around 48,113,410 km 2 i.e. 48.11 * 10 12 m 2, with a mean wind force of 0.019 N/m 2. Consequently, the total force affecting the continent is affected by a total wind force of: 12 10 = .0 019N / m2 ∗ 48.11∗10 m2 = .9 14 ∗10 N This resulting wind force is attacking the continent in its area centre. Since the centre of the Euroasian plate is not the same as the centre of the continent this force results in a clockwise torque. The perpendicular distance between the force and the area centre of the plate was estimated 803 km. The total torque in anti clockwise direction is according to eq. (2) given by; Torque T = F ∗ r = .9 14 ∗1010 ∗ .8 03∗105 = .7 34 ∗1016 Nm The wind force result of both is identical, while there is a small difference in the angle of direction (less than 6 o), and comparing results of both methods will be shown in the table below: Table 26: The results of the Overall Site and Time methods (Eurasia) Method Overall Site Method Overall Time Method Wind Force 0.024 N/m² 0.019 N/m² Wind Direction 375.5 º 352.8 º Wind Torque 7.34 .10 16 Nm The first method was used to calculate the torque of the wind force which depend on the assumption of a specific location as a centre of gravitation and by measuring the distance of Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 52
each location from this centre and according to the first relation that mentioned previously, we can calculate the overall torque, the location of the centre of gravitation shown in Figure (2) below.
Figure 27: The Eurasian plate and its center at Ekibastuz city, the area center of the continent, and the suggested location of the center of the plate [19]
Based on the result of the second method of calculation – the Overall Time Method – Figure (28) illustrates the different wind force value of each month. From the graph it can be seen that the greatest wind force over the Eurasian plate occurs during February – 0.0420 N/m² while the lowest wind force occurs in July where it reach 0.013 N/m².
Wind Force
0.0450 0.0400 0.0350 0.0300 0.0250 0.0200
Wind Force ( N/m2) 0.0150 0.0100 0.0050 0.0000 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Months Figure 28: Calculated monthly wind force over the year. The corresponding wind force directions through the year are shown in Figure 29.
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 53
Wind force direction
300
250
200
150
100
Angle of direction 50
0 0 2 4 6 8 10 12 14 Months Figure 29: Calculated wind force direction over Eurasia during the year. So from the calculated wind force direction that mentioned above in table 26, where the angle of direction is between 352.8 and 375.5 that can be illustrated in the map as in the figure (30) below , if we compare that with the actual movement of the Eurasian plate as shown in the map from After Christopherson (1997), figure (8), we will find the direction of movement of the is closer .
Figure 30: Actual and calculated direction of the Eurasian plate movement [19]. Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics 54
REFERENCES: 1 MacKenzie, Keith, Evidence for a plate tectonics debate , Earth Science Reviews 55 2001 235–336. 2 W. R. Dickinson, Plate tectonics through geological time , Phil. Trans. R. SOG.LOIUI. A 301, 207 215 (1981). 3 Tanimoto, Toshiro and Thorne Lay (2000) Mantle dynamics and seismic tomography, Proc. Natl. Acad. Sci. USA, Vol. 97, No. 23 (Jan. 1, 1916), pp. 12409 12410. 4 The website of Universidad de Puerto Rico Mayagüez, http://geology.uprm.edu/Morelock/1_image/plate.jpg 5 Genxu Wang a,c, Yibo Wang b, Yuanshou Li c, Huiyan Cheng, Influences of alpine ecosystem responses to climatic change on soil properties on the Qinghai–Tibet Plateau, China. Catena 70 (2007) 506–514. 6 J. Alan Pounds and Robert Puschendorf, Clouded futures, NATURE, 2004. http://www.nature.com/nature/journal/v427/n6970/pdf/427107a.pdf et al, 2004 7 Christensen, T.R., Johansson, Torbjom, Akerman, Jonas H., Masterpanov, Mihail, 2004. Thawing sub arctic permafrost: effects on vegetation and methane emissions. Geophysical Research Letters 31, L04501. 8 G. I. Taylor (1916) Skin Friction of the Wind on the Earth's Surface, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, Vol. 92, No. 637 (Jan. 1, 1916), pp. 196 199. 9 Meteonorm, 2007. The Meteonorm Model. http://software.cstb.fr/soft/present.asp?page_id=us!meteonorm 10 ESUM The website of the School of Earth Sciences University of Melbourne Australia http://web.earthsci.unimelb.edu.au/antarctica/plateTectonics.html 11 Christopherson. R.W., 1997. Geosystems , 3 rd Ed. Prentice Hall corp. Upper Saddle River, NJ. 656 pp. 12 NASA, Planetary Geodynamics Laboratory at the National Aeronautics and Space Administration NASA. http://denali.gsfc.nasa.gov/dtam/data/ftp/dtam.jpg 13 USGS, The website of the U.S. Geological Survey, http://pubs.usgs.gov/publications/text/slabs.html 14 The popular educational web site of Information Technology Associates (ITA). http://www.theodora.com/maps/new3/north_america_color.gif 15 The Zetatalk website http://www.zetatalk.com/info/tinfo05t.htm 16 Geology, http://geology.com/articles/images/san-andreas-fault-map.jpg 17 ABC, The ABC teach website. http://www.abcteach.com/Savannah/map.htm 18 The Zetatalk website http://www.zetatalk.com/info/tinfo05r.htm 19 The Zetatalk website http://www.zetatalk.com/info/tinfo05s.htm
Widatalla Asim, LTU, 2007 Wind Driven Plate Tectonics