Mathematics of Planet Earth


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Through the project the students will learn that the temperature of Earth is increasing which is threat to human civilization.We should minimise the fuel consumption to reduce green house gases.The students will learn real life Mathematics .They will learn to predict the amount of ice amount of Arctic sea by using linear equation.
The amount of sea ice in ( sq km) is a linear function of year.
Some pictures are taken from
The project was selected for seminar " Development of quality teaching in Mathematics" at RIE, Ajmer under Poster presentation category .

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  • Monthly August ice extent for 1979 to 2013 shows a decline of 10.6% per decade.
  • Mathematics of Planet Earth

    1. 1. Mathematics of Planet Earth Global Warming
    2. 2. Essential Question: Global Warming
    3. 3. Can Mathematics help? Global Warming
    4. 4. World is getting warmer… Global Warming
    5. 5. Content questions: Contents
    6. 6. Except for a levelling off between the 1940s and 1970s, the surface temperature of our planet has increased since 1880. The last decade has seen global temperatures rise to the highest levels ever recorded. This graph illustrates the change in global surface temperature relative to 1951-1980 average temperatures. As shown by the orange line, long-term trends are more apparent when temperatures are averaged over a 5-year
    7. 7. World is getting warmer… Global Warming
    8. 8. A layer of greenhouse gases – primarily water vapour, and including much smaller amounts of carbon dioxide, methane and nitrous oxide – act as a thermal blanket for the Earth, absorbing heat and warming the surface to a life-supporting average of 59 degrees Fahrenheit (15 degrees Celsius). Not enough greenhouse effect on the planet Mars Too much greenhouse effect on the planet Venus
    9. 9. The greenhouse effect is a process caused by greenhouse gases, which occur naturally in the atmosphere. This process plays a crucial role in warming the Earth's surface, making it habitable. First, the Sun emits energy that is transmitted to Earth. Because the Sun is very hot, the energy is emitted in high-energy short wavelengths that penetrate the Earth's atmosphere.
    10. 10. Absorption About 30% of the Sun's energy is reflected directly back into space by the atmosphere, clouds, and surface of the Earth. The rest of the Sun's energy is absorbed into the Earth's system. Emission The Earth emits energy into the atmosphere. Because the Earth is cooler than the Sun, the energy is emitted in the form of infrared radiation, at wavelengths longer than the incoming solar energy.
    11. 11. Role of Greenhouse Gases Greenhouse gases in the atmosphere absorb much of the long-wave energ emitted from the Earth's surface, preventing it from immediat escaping from the Earth's system. Th greenhouse gases then re-emit this energy in all directions, warming the Earth's surface and lower atmospher Human Role The atmospheric concentration of greenhouse gases has increased over past two centuries, largely due to hum generated carbon dioxide emissions f burning fossil fuels. This increase has amplified the natura greenhouse effect by trapping more o energy emitted by the Earth. This cha causes Earth's surface temperature to increase.
    12. 12. Global Greenhouse Gas Emissions by Gas Global Greenhouse Gas Emissions by Source Carbon dioxide (CO2) - Fossil fuel use is the primary source of CO2. Methane (CH4) - Agricultural activities, waste management. Nitrous oxide (N2O) - Agricultural activities, such as fertilizer use Fluorinated gases (F-gases) - Industrial processes, refrigeration which include hydro fluorocarbons (HFCs), per fluorocarbons (PFCs), and sulphur hexafluoride (SF6). Source: Intergovernmental Panel on Climate Change Report -2007
    13. 13. Carbon dioxide is the primary greenhouse gas that is contributing to recent climate change. CO2 is absorbed and emitted naturally as part of the carbon cycle, through animal and plant respiration, volcanic eruptions, and ocean-atmosphere exchange. Human activities, such as the burning of fossil fuels and changes in land use, release large amounts of carbon to the atmosphere, causing CO2 concentrations in the atmosphere to rise.
    14. 14. Mathematical Models that account only for the effects of natural processes are not able to explain the warming over the past century. Models that also account for the greenhouse gases emitted by humans are able to explain this warming.
    15. 15. Atmospheric Concentrations of Greenhouse Gases Concentrations of carbon dioxide and other greenhouse gases in the atmosphere have increased since the beginning of the industrial era. Almost all of this increase is attributable to human activities. Global Greenhouse Gas Emissions Worldwide, emissions of greenhouse gases from human activities increased by 26 percent from 1990 to 2005. Emissions of carbon dioxide, which account for nearly three-fourths of the total, increased by 31 percent over this period.
    16. 16. This has been the warmest decade since 1880. In 2010, global surface temperatures tied 2005 as the warmest on record, according to the National Oceanic and Atmospheric Administration. Scientists say that the earth could warm by an additional 7.2 degrees Fahrenheit during the 21st century if we fail to reduce emissions from burning fossil fuels, such as coal and oil. This rise in average temperature will have far-reaching effects on the earth's climate patterns and on all living things. Many of these changes have already begun.
    17. 17. GLOBAL WARMING EFFECTS  Geographical effects  Climate change  Wildlife  humans
    18. 18. Part of the Arctic Ocean stays frozen year-round. The area covered by ice is typically smallest in September, after the summer melting season. Arctic sea ice fell to its lowest extent in the satellite record in September 2012, having declined to 49 percent below the 1979 to 2000 historical average. In addition, since 1982, the proportion of older, longterm sea ice has
    19. 19. The Arctic Ocean could be ice-free in summer by 2040 2000 2040 (U.S National Center for Atmospheric Research, 2006)
    20. 20. Glaciers in the United States and around the world have generally shrunk since the 1960s, and the rate at which glaciers are melting appears to have accelerated over the last decade. The loss of ice from glaciers has contributed to the observed rise in sea level.
    21. 21. EFFECTS OF HIGHER TEMPERATURES ON CLIMATE Duration and intensity of tropical storms. more frequent wildfires greater number of Category 4 and 5 hurricanes. longer periods of drought in some regions.
    22. 22. ON GLACIERS According to NASA, the polar ice cap is now melting at the alarming rate of nine percent per decade. Arctic ice thickness has decreased 40 percent since the 1960s. Greenland lost 150 to 250 cubic kilometers (36 to 60 cubic miles) of ice per year between 2002 and 2006.( Nasa) Arctic summers could be ice-free by 2040, and sea levels could rise as much as 23 inches by 2100 if current warming patterns continue. Multiple climate models indicate that sea ice will increasingly retreat as the earth warms. Scientists at the U.S. Centre for Atmospheric Research predict that if the current rate of global warming continues, the Arctic could be ice-free in the summer by 2040.
    23. 23. On Sea Levels Sea-level rise projections : a few inches to a few feet •2 ft: U.S. would lose 10,000 square miles •3 ft: Would inundate Miami •Affects erosion, loss of wetlands, freshwater supplies •Half of the world’s population lives along coasts •Big question: Ice sheets
    24. 24. Wildlife effects
    25. 25. Threat to life Polar Bear Polar bear who depend on sea ice announced as an endangered species The numbers in the western Hudson bay down by 22% in 17 years. The cubs perished from 61 to Caribou 22 per 100 females Increase in Since 1989,cannibalism the Porcupine Caribou Herd has declined at 3.5% per year to a low of 123,000 animals in 2001 Brown Bear Hibernation disturbances for reproducing females (Jan-May) *2 months to implant*Flooding of dens *Reduction in productivity and survival rates
    26. 26. Migration Singing common whitethroat's migration is likely to lengthen from 3,417 miles to between 3,541-3,759 miles. -RSPB.
    27. 27. Save Earth from further heating Reduce your carbon foot print. Your carbon footprint is the amount of carbon dioxide released into the air because of your own energy needs. You need transportation, electricity, food, clothing, and other goods. Your choices can
    28. 28. Plant more During photosynthesis, trees trees and other plants absorb carbon dioxide and give off oxygen. They are an integral part of the natural atmospheric exchange cycle here on Earth, Choose a "green career.“ You can create awareness among others how even increase of one degree of temperature create grave problems for our Earth. You can help to solve climate change
    29. 29. Save Energy save electricity Swap old incandescent light bulbs for the new compact fluorescent lights (CFLs). They use only 25% as much electricity to give the same light. They last ten times longer. Use alternative energy sources Disconnect power vampires! Many appliances and electronics suck energy even when they are not on. Power strips like these make it easier to unplug.
    30. 30. Reduce Reuse Recycle Recycle everything you can.
    31. 31. Walk or ride your bicycle instead of taking a car. Even a 2-mile car trip puts 2 pounds of CO2 into the atmosphere! Riding a bicycle adds no greenhouse gases to the atmosphere. We need to keep a close watch on this number. Carbon dioxide levels have gone sky-high in the past 100 years. Many scientists think that 350 ppm is a much healthier number and that we should try to reduce our use of fossil fuels to get that number back.
    32. 32. Global Warming
    33. 33. Carbon dioxide passes symbolic mark! Concentrations of greenhouse gases in the atmosphere have reached 400 Part Per Million, this level for the first time in millions of years. May 9, 2013 |
    34. 34. Carbon dioxide is a greenhouse gas. Too much carbon dioxide in the air makes Earth get warmer and warmer. When humans burn fossil fuels, like gasoline and coal, carbon dioxide is produced. This number tells how many parts of carbon dioxide there are in one million parts of air. So, if carbon dioxide is at 390 parts per million (or ppm), that means in one million pounds of air there are 390 pounds of carbon dioxide. We need to keep a close watch on this number. Carbon dioxide levels have gone sky-high in the past 100 years. Many scientists think that 350 ppm is a much healthier number and that we should try to reduce our use of fossil fuels to get that number back.
    35. 35. GLOBAL SURFACE TEMPERATURE This graph illustrates the change in global surface temperature relative to 1951-1980 average temperatures. Global surface temperatures in 2012 were the ninth warmest on record. (Source: NASA/GISS)
    36. 36. GLOBAL TEMPERATURE RISE All three major global surface temperature reconstructions show that Earth has warmed since 1880. Most of this warming has occurred since the 1970s, with the 20 warmest years having occurred since 1981 and with all 10 of the warmest years occurring in the past 12 years. Even though the 2000s witnessed a solar output decline resulting in an unusually deep solar minimum in 2007-2009, surface temperatures continue to increase.
    37. 37. Land Ice Data from NASA's Grace Satellites show that the land ice sheets in both Antarctica and Greenland are losing mass. The continent of Antarctica (left chart) has been losing more than 100 cubic kilometres (24 cubic miles) of ice per year since 2002.
    38. 38. SEA LEVEL
    40. 40. 23% smaller than previous minimum; 39% smaller than average.  Ice 53% thinner in region of North Pole between 2001 and 2007 (NOAA Report Card 2008) Ice only 3 feet thick in most locations (NOAA FAQ, 2007 In September 2007 an area the size of Florida (69,000 square miles) melted in six days (NSIDC 2007)  Humpback whales spotted in Arctic Ocean for first time in 2007 Snow and Ice Data center.
    41. 41. Arctic sea ice extent averaged for September 2013 was 5.35 million square kilometers (2.07 million square miles). This was 1.17 million square kilometers (452,000 square miles) below the 1981 to 2010 average extent. September 2013 ice extent was 1.72 million square kilometers (664,000 square miles) higher than the previous record low for the month that occurred in 2012 Snow and Ice Data center.
    42. 42. The graph above shows Arctic sea ice extent as of September 30, 2013, along with daily ice extent data for the previous five years. 2013 is shown in light blue, 2012 in green, 2011 in orange, 2010 in light purple, 2009 in dark blue, and 2008 in dark purple.
    43. 43. The seasonal decline of extent through the month of August 2013. This year’s August extent was the sixth lowest in the 1979 to 2013 satellite record. August 2013 ice extent was 1.38 million square kilometers (533,000 square miles) above the record low August extent in 2012. The monthly trend is –10.6% per decade relative to the 1981 to 2010 average. Overall, 10.03 million square kilometers (3.87 million square miles) of ice were lost between the 2013 maximum and minimum extents Snow and Ice Data center.
    44. 44. SO HOW LONG WILL IT TAKE UNTIL THE SUMMER ICE IS GONE? Many different computer models have been developed to predict when summer sea ice will disappear from the Arctic.  Fifty per cent of these models say it will have gone by 2060.  Snow and Ice Data center.
    45. 45. Mathematics of Planet Earth Global Warming
    46. 46. September/March(mi nimum/maximum) September Average Extent(millions of square kilometers) March Average Extent(millions of square kilometers) 1979–2000 mean 1999/2000 2000/2001 2001/2002 2002/2003 2003/2004 2004/2005 2005/2006 2006/2007 2007/2008 2008/2009 2009/2010 2010/2011 2011/2012 2012/2013 7.0 6.2 6.3 6.8 6.0 6.2 6.1 5.6 5.9 4.3 4.7 5.4 4.9 4.6 3.6 15.7 15.3 15.6 15.4 15.5 15.1 14.7 14.4 14.7 15.2 15.2 15.1 14.6 15.2 15.0
    47. 47. Ice count in 2013 September average sea ice extent for 2013 was the sixth lowest in the satellite record. The 2012 September extent was 32% lower than this year’s extent, while the 1981 to 2010 average was 22% higher than this year’s extent. Through 2013, the September linear rate of decline is 13.7% per decade relative to the 1981 to 2010 average.
    48. 48. Average September extent
    49. 49. Graph using Excel 7 6 Amount of Million per square Kilometers year 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Extent of Ice (Million per sqaure 5.96 6.15 6.04 5.57 5.89 4.28 4.67 5.36 4.9 4.61 3.61 5.35 5 4 3 2 1 0 2000 2002 2004 2006 2008 Year 2010 2012 2014
    50. 50. Our findings In Excel, we used the Chart – Add Trend line feature and found that the line gives a linear equation. Y= 0.08 x + 166.4 Which is a linear equation
    51. 51. To determine when the Arctic will be ice free:Applying linear equation, Y = m x + c They took the year 2003 to 2013. 6.15 = 2003 X m + c 5.35 = 2013 X m + c Solving two equations, m = – 0.08 and c = 166.4 So the final linear equation Y = 0.08 x + 166.4 The Arctic sea will be Ice free in 2070 summer. So , increased ice of summer 2013 leaves a little
    52. 52. CONCLUSIONS: While a 1-degree temperature rise may sound puny, global warming has set in motion lots of changes: glaciers are melting, many birds are beginning their migrations earlier, some islands are becoming submerged by rising seas, melting ice is causing polar bears to starve and so on. If nothing is done, an international consortium of 2,000 scientists (called the Intergovernmental Panel on Climate Change) predicts temperatures could rise 11 degrees by century's end. To avoid the most dangerous effects of warming, scientists say an 80 percent reduction in greenhouse-gas emissions is needed by 2050.
    53. 53. ACKNOWLEDGEMENT    tml Global Warming, Climate Change and the Environment The Daily Green
    54. 54. A project by students of Kendriya Vidyalaya, Fort William,Kolkata Under the guidance of Mrs.Pratima Nayak,Mathematics Teacher