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A motivational talk during the Mathematics Awareness Month in 2009, introducing students into the applications of elementary ideas of Mathematics to understand the weather and climate.

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  • - Percentage of N2 & O2 constant. There’s a balance between destruction & production of these gases at the surface. Give examples. - Note variable gases, especially H2O.
  • math-wx-climate2009

    1. 2. What is Mathematics and Why it is important to be mathematically literate?
    2. 3. Some common misconceptions about Mathematics 1. Learning mathematics requires special and rare abilities. 2. Math in modern issues is too complex. 3. Math makes you less sensitive, and is irrelevant to my life 4. Math makes no allowance for creativity. 5. Math provides exact answers. What is Mathematics after all? The word mathematics is derived from the Greek word Mathematikos , which means “ inclined to learn ”. Thus, literally speaking, to be mathematical is to be curious, open-minded, and interested in always learning more !! Do you consider yourself to be either “ math phobic” ( fear of mathematics ) of “ math loathing” ( dislike math )? Many adults harbor fear or loathing of mathematics and, unfortunately, these attitudes are often reinforced by classes that present mathematics as an obscure and sterile subject . Mathematics also may be viewed as a tool for creating models , or representations that allow us to study real phenomena Mathematical Modeling Medicine and Physiology Psychology and Sociology Bioinformatics Engineering Biology and Ecology Computer science and Artificial Intelligence Physics and Chemistry Economics Business Management Atmospheric Physics or Meteorology
    3. 4. Branches of Mathematics Logic Descriptive Statistics Probabilities Geometry Calculus and Differential Equations
    4. 5. What is Quantitative Literacy? Literacy is the ability to read and write, and it comes in varying degrees. Some people can recognize only a few words and write only their names; others read and write in many languages. Today, the abilities to interpret and reason with quantitative information - information that involves mathematical ideas or numbers – are crucial aspects of this literacy. This so called quantitative literacy is essential to understanding modern issues that appear in the news everyday. The process of interpreting and reasoning with quantitative information is called quantitative reasoning . Adapted from Education: The knowledge gap , supplement to The Wall Street Journal , February 9,1990 Work with advanced calculus, modern algebra, and statistics. Same types of skills as level 5, but more advanced. 6 Knows calculus and statistics, able to deal with econometrics. Reads literature, book and play reviews, scientific and technical journals, financial reports, and legal documents. Can write editorials, speeches, and critiques. 5 Deals with complex algebra and geometry, including linear and quadratic equations, logarithmic functions, and axiomatic geometry. Reads novels, poems,newspapers, and manual. Prepares business letters, summaries, and reports. Participates in panel discussions and debates. Speaks extemporaneously on a variety of subjects. 4 Understand basic geometry and algebra. Calculates discount, interest, profit and loss, markup, and commissions. Read novels and magazines, as well as safety rules and equipment instructions. Writes reports with proper format and punctuation. Speak well before an audience. 3 Adds, subtracts, multiplies, and divides all units of measure. Compute ratio, rate, and percentage. Draws and interpret bar graphs. Recognizes 5000-6000 words. Reads 190-125 words per minute. Read adventure stories and comic books, as well as instructions for assembling model cars. Writes compound and complex sentences. 2 Adds and subtracts two digit numbers. Does simple calculations with money, volume, length, and weight. Recognizes 2500 two or three syllable words. Reads at a rate of 95-120 words per minute. Writes and speaks simple sentences. 1 Math Skill Language Skill Level
    5. 6. Adapted from Education: The knowledge gap , supplement to The Wall Street Journal , February 9,1990 1 1 Laundry worker 5 4 Financial analyst 2 2 Toll collector 3 5 Disc jockey 2 2 Assembly-line worker 4 5 Elementary teacher 2 3 Short-order cook 5 5 Secondary teacher 2 3 Janitor 5 5 Weather forecaster 2 3 Telephone operator 5 5 Corporate president 3 3 Travel agent 5 5 Personnel manager 3 3 Tile setter 5 5 Accountant 3 3 Poultry farmer 4 6 Newspaper editor 3 3 Dairy farm manager 4 6 Tax Attorney 3 3 Cement mason 4 6 Lawyer 4 3 Retail store manager 5 6 Social psychologist 4 3 Insurance sales agent 5 6 Cardiologist 4 4 Management trainee 6 6 Mathematician 4 4 Computer sales agent 6 6 Computer Engineer 5 4 Corporate executive 6 6 Biochemist Math Level Language Level Occupation Math Level Language Level Occupation
    6. 7. What is Meteorology and Why scientists study it ? <ul><li>525 BCE Greek philosopher </li></ul><ul><li>Anaximenes of Miletus proposed </li></ul><ul><li>that winds, clouds, rain, and hail </li></ul><ul><li>are formed by thickening of air, </li></ul><ul><li>the primary substance. </li></ul><ul><li>500 BCE Parmenides classified </li></ul><ul><li>World Climates by latitude as </li></ul><ul><li>torrid, temperate, or frigid </li></ul>350 – 340 BCE Aristotle produced his Meteorologica , the first work on the atmospheric sciences. Meteor – a Greek word meaning falling from sky. Logica – Study Meteorologica – The study of bodies falling from the sky
    7. 8. Benefits of Earth Observations Natural & Human Induced Disasters Human Health & Well-Being Energy Resources Climate Variability & Change Water Resources Weather Information, Forecasting & Warning Ecosystems Sustainable Agriculture & Desertification Oceans
    8. 9. Environmentally Sustainable Development and the Climate Change Debate An environmentally sustainable society satisfies the basic needs of its people for food, clean water, clean Air, and shelter into the indefinite future without: 1. Depleting or degrading the earth’s natural resources and 2. thereby preventing current and future generations of humans and other species from meeting their basic needs. <ul><li>Good News about Economic Development </li></ul><ul><li>Between 1900 and 2002, global life expectancy at birth more </li></ul><ul><li>than doubled from 33 to 67 years (76 in developed countries </li></ul><ul><li>and 65 in developing countries). </li></ul><ul><li>Between 1955 and 2002, the world’s average infant mortality </li></ul><ul><li>during the first year of life dropped by 60% in developed </li></ul><ul><li>countries and 40% in developing countries. </li></ul><ul><li>Global food production has outpaced population growth since </li></ul><ul><li>1978. </li></ul><ul><li>Since 1950 the percentage of rural families in developing </li></ul><ul><li>countries with access to safe drinking water has increased </li></ul><ul><li>from 10% to almost 75%. </li></ul><ul><li>We have learned how to produce more goods with less raw </li></ul><ul><li>materials. </li></ul><ul><li>Since 1970 levels of most major air and water pollutants have </li></ul><ul><li>been reduced in most of the world’s developed countries. </li></ul><ul><li>Bad News about Economic Development </li></ul><ul><li>Average life expectancy in developing countries is 11 years </li></ul><ul><li>less than in developed countries. </li></ul><ul><li>Infant mortality in developing countries is more than eight </li></ul><ul><li>times higher than in developed countries. </li></ul><ul><li>The harmful environmental effect of industrialized food </li></ul><ul><li>production may eventually limit future food production unless </li></ul><ul><li>there is a shift to more sustainable ways to produce food. </li></ul><ul><li>Air and water pollution levels in most developing countries </li></ul><ul><li>are much too high according to the World Health Organization </li></ul><ul><li>Because of increased population growth and per capita </li></ul><ul><li>resource use, some of the natural resources that support all life </li></ul><ul><li>are being used unsustainably:1. premature extinction of a </li></ul><ul><li>growing number of the world’s plant and animal species, 2. </li></ul><ul><li>destruction or degradation of wetlands, coral reefs, and forests </li></ul><ul><li>in some parts of the world, and 3. gradual degradation of </li></ul><ul><li>underground water supplies in some areas. </li></ul><ul><li>Gases emitted into the atmosphere from burning fossil fuels and </li></ul><ul><li>clearing forests could cause the world’s climate to become </li></ul><ul><li>warmer during this century , causing: 1. shifting areas where </li></ul><ul><li>crops can be grown, 2. altering water supplies by shifting </li></ul><ul><li>patterns of precipitation, 3. shifting where various animals and </li></ul><ul><li>plants can survive, 4. raising average sea levels. </li></ul>
    9. 10. Global Warming Ideas, Myths, and Media Coverage: Fears versus Education <ul><li>Prior to Industrial Revolution CO 2 concentrations were stable at 280 ppm </li></ul><ul><li>As CO 2 increases, so should average global surface temperatures </li></ul><ul><li>Warming from 2.5 to 10° F </li></ul><ul><li>It is worth to notice the variability in carbon dioxide concentrations </li></ul><ul><li>superimposed over this general trend. Namely; this trend is the one </li></ul><ul><li>scientists associate with the excessive greenhouse warming. </li></ul><ul><li>How far the greenhouse effect may still being considered an allies? </li></ul><ul><li>It will depend on the ability to keep these concentrations under </li></ul><ul><li>control and avoid the Runaway Greenhouse Effect already seen in </li></ul><ul><li>the planet Venus </li></ul>
    10. 11. 2008 2007
    11. 12. What about the Mathematics involved in the study of the Weather and the Climate?
    12. 13. PHYSICAL QUANTITIES AND UNITS Observations produce qualitative information about a system Measurements produce quantitative information which is needed in any science that strives for exactness English Units Inch (in) Second (s) Pound (lb) Metric System Meter (m) Second (s) Kilogram (kg) Fundamental Physical Quantities Distance - Time - Mass Scientific Notation Prefix | Abbreviation | Regular Notation | Scientific Notation Tera T 1,000,000,000,000 = 10 12 Giga G 1,000,000,000 = 10 9 Mega M 1,000,000 = 10 6 Kilo k 1,000 = 10 3 Hecto h 1,00 = 10 2 Deca da 10 = 10 1 -------- ---------- 1 = 10 0 Deci d 0.1 = 10 -1 Centi c 0.01 = 10 -2 Milli m 0.001 = 10 -3 Micro μ 0.000,001 = 10 -6 Nano n 0.000,000,001 = 10 -9 Pico p 0.000,000,000,001 = 10 -12 Length : 1 kilometer (km) = 1000 meters (m) = 3281 feet (ft) = 0.62 miles (mi) 1 mile (mi) = 5280 feet (ft) = 1.61 kilometers (km) = 0.87 nautical mile (nm) 1 centimeter (cm) = 0.39 inch (in) 1 inch (in) = 2.54 centimeters (cm) 1 yard (yd) = 3 feet (ft) = 36 inches (in) Time : 1 hour (hr) = 60 minutes (min) = 3600 seconds (s) Mass : 1 kilogram (kg) = 1000 grams (g) = 2.2 pounds (lb) Speed (rate of change of a coordinate in time): 1 knot (kt) = 1 nautical mile per hour (nmph) = 1.15 miles per hour (mph) 1 mile per hour (mph) = 1.61 kilometers per hour (km/hr) = 0.45 m/s
    13. 14. Earth Globe and the Geometry of the Sphere Equator Tropic of Cancer Tropic of Capricorn South Pole Parallels or Latitudes Meridians or Longitudes The full circumference equals 360 o . In order to convert degrees into units of distance a simple proportion is used: Latitudes – small circumferences on the sphere, they changes from 0 o (Equator) to 90 o (Pole) in both directions, South and North. Longitudes – large circumferences on the sphere, they all merge in both poles. The prime longitude or prime meridian is the Greenwich meridian.
    14. 15. The Atmosphere: Basic concepts and definitions Earth’s Atmosphere is a relatively thin envelope of gases and tiny, suspended particles that encircles the globe. Earth Atmosphere Compared to the planet’s diameter (12,740 km or 7918 mi), the atmosphere is like the thin skin of an apple. About half of the atmosphere’s mass is concentrated within 5500 m (18,000 ft) of Earth’s surface 99% of atmosphere’s mass is below an altitude of 32 km = 32,000 m = 20 mi. These numbers are about 4 Mounts Everest piled up one over another D E R E D E = 12,740 km = 2 R E R E = 6,370 km = 3959 mi R A = 32 km = 32,000 m = 20 mi If we would consider Earth as a ball 2 meters in diameter, then its radius will be 1 meter. Since 1 m = 1,000 millimeters, in this Earth’s model the atmosphere will comprise only about 5 mm above the ball’s surface. Air is a mixture of gases and particles, both of which are made of atoms. Within the Air you may find elements, molecules, compounds, gases, and suspended particles.
    15. 16. WEATHER AND CLIMATE <ul><li>Weather is defined as the state of the </li></ul><ul><li>atmosphere at a given time at a given </li></ul><ul><li>place. Weather is described by: </li></ul><ul><li>Temperature </li></ul><ul><li>Air pressure </li></ul><ul><li>Humidity </li></ul><ul><li>Cloudiness </li></ul><ul><li>Wind speed and direction </li></ul><ul><li>Visibility </li></ul><ul><li>Weather is going to be defined as the </li></ul><ul><li>intersection of above Six sets of </li></ul><ul><li>physical parameters. </li></ul>Weather is a short term event, whereas Climate is a long-term one. Weather can change over a short time span. Climate , on the other hand, must be measured over periods of years, because climate is the average weather condition of a place . Weather and Climate are sensitive indicators of changes in the Earth System.
    16. 17. Energy: Units and Related Quantities Experiments show conclusively that there is a lowest temperature below which it is impossible to cool an object. This is referred to as absolute zero . Though absolute zero can be approached from above arbitrarily closely, it can never be attained. The Kelvin temperature scale , named for the Scottish physicist William Thomson, Lord Kelvin (1824 – 1907), is based on the existence of the absolute zero . In fact, the zero of the Kelvin scale, abbreviated 0 K, is set exactly at absolute zero . Thus, in this scale there are no negative equilibrium temperatures. The Kelvin scale is also chosen to have the same degree size as the Celsius scale.
    17. 18. X intercept of a line Y intercept of a line X Y Y = m X + b Equation of a line in the slope-intercept form m – slope or rate of change, m > 0 line goes up, m < 0 goes down b – y intercept of a line Larger the value of “m” closer to the y-axis a line is located Y = m X is called a linear variation or proportion Y = m / X is called an inverse variation or inversely proportional Graphical Representation in a plane Average lapse rate of 6.5°C per km or 3.6°F per 1,000 feet T = m H + To  Y = m X + Yo Temperature plays the role of Y, and Height the role of X. The parameter “m” that we call slope is the lapse rate, or how fast temperature drops with height. To is the value of T at the ground level.
    18. 19. The variation of temperature with altitude in the atmosphere Temperature, and Layers of the Atmosphere <ul><li>Average lapse rate of 6.5 °C per km or 3.6°F per 1,000 feet </li></ul><ul><li>The lapse rate fluctuates and temperature may even increase with height creating a temperature inversion </li></ul><ul><li>Gravity holds air molecules near the Earth, compressing them together </li></ul><ul><li>Air density is greatest at the surface and decreases as we climb (first rapidly then slowly) </li></ul><ul><li>Air molecules have weight and exert a force called Air Pressure </li></ul><ul><li>As we climb the weight of the air above us decreases and pressure decreases </li></ul>
    19. 20. Air pressure decreases with altitude because air is compressible and behaves like a pile of springs. P = F/ S Pressure is the Force (F) exerted on a unit of Area (S) Unit of Pressure = Pascal Standard Atmosphere = 760 mm of Hg 1 st. At = 1013.25 hPa = 1013.25 mbar = 29.92 in of Hg
    20. 21. Graphical Representation in the space X Y Z = F(X,Y) Surface Plot – The coordinate Z represents the value of a function F(x,y) after plugging in values for coordinates X and Y and defining the surface. Contour Plot – It represents a projection of a given surface plot onto a particular plane. Lines observed in this kind of plot represents points on the surface with the same numerical values. Contour Plots are called also Isopleths (“ iso ”meaning “equal,” “ pleth ” meaning “value”) . T (Longitude,Latitude) Temperature as a function of values of longitude and latitude on Earth. Longitude plays the role of X and latitude the role of Y. The space between contour lines indicates how fast the coordinate Z = F(x,y) changes around this local area. When contour lines are grouped very close each other it represents a sharp descend or increase around these points. On the other hand, more spaced contour lines is an indication of smooth changes. Isopleths of Temperature are known as Isotherms Isopleths of Pressure are known as Isobars The change in a variable over a given distance is known as the gradient of that quantity, often used to describe the steepness of a slope of a mountain or hill Difference in elevation between the points Distance between the points Gradient =
    21. 22. Surface Analysis Map 250 mb Map 500 mb Map Weather Charts for different altitudes above the ground. Isopleths of barometric pressure, known as Isobars are represented. L – low barometric pressure H – high barometric pressure
    22. 23. <ul><li>Is out there any unifying concept or principle </li></ul><ul><li>describing processes in the atmosphere, oceans </li></ul><ul><li>and the land? </li></ul><ul><li>Is out there a more serious and/or challenging </li></ul><ul><li>formulation for processes in the atmosphere, </li></ul><ul><li>oceans and the land? </li></ul>
    23. 24. Energy: Units and Related Quantities Energy Units – Metric System Energy Units – English System Joule = 1 J = 1 N ∙ m = 6.24 10 18 eV = 0.239 cal Foot per Pound = 1 ft ∙ lb British Thermal Unit (Btu) Temperature : The average kinetic energy of an assemble of particles forming part of a given system. Heat : The Energy transferred between objects because of a Temperature difference. T 1 T 2 T 1 > T 2 When we say that there is a transfer of heat or a heat flow from object A to object B, it means that the total energy of object A decreases and the total energy of object B increases. Objects are said to be in thermal contact if heat can flow between them. After some time in thermal contact, the transfer of heat ceases. At this point, we say that the objects are in thermal equilibrium . Celsius Scale ( o C) Swedish astronomer Andres Celsius (1701 – 1744). The original idea was modified by the biologist Carolus Linnaeus (1707 – 1778), assigning 0 o C to freezing temperature of water and 100 o C the boiling water. Fahrenheit Scale ( o F) was developed by Gabriel Fahrenheit (1686 – 1736). He assigned 98.6 o F to body temperature, 32 o F freezing water, and 212 o F the boiling water.
    24. 25. Forms of Energy Transfer Conduction : Particle by particle transfer of thermal and electric energy. Radiation : Transfer of Electro- magnetic Energy through empty Space in form of waves, traveling at a constant speed - c. Convection : Transfer of thermal energy by mass movement of a fluid. Advection : The horizontally moving part of the circulation (called winds ) carries properties of the air in that particular area with it. Conduction : Heat transferred in this fashion always flows from warmer to colder regions. Generally, the greater the temperature difference, the more rapid the heat transfer. Convection : In a convective circulation the warm, rising air cools. In our atmosphere, any air that rises will expand and cool, and any air that sinks is compressed and warm.
    25. 26. The total amount of energy radiated outward each second by the Sun or any other star is called Luminosity 3.8 x 10 26 W Power Radiated by the Sun Power Received by Earth per square Meter = Solar Constant 1370 W / m 2 The Science of the Radiant Energy or Radiative Physics Stefan – Boltzmann Law – Represents the energy emitted by a body per square meter per second. The constant σ is the Stefan – Boltzmann Constant, and it is equal to 5.67x10 -8 Wm -2 K -4 . For the Sun T=6,000 K.
    26. 27. Composition of the Atmosphere
    27. 29. Globally Warming Climates ? or Cyclically Changing Climates?
    28. 30. St. Thomas University, Miami Gardens, FL Boyd Buchanan, Chattanooga, TN Eagle Valley HS, Eagle Bend, MN
    29. 31. World Physical Geography UTC or Z – time = Universal Standard Time = It is the time Measured at Royal Observatory in Greenwich. EDT = Eastern Day Time = UTC - 5 hr (4 hr during time adjustment)
    30. 32. Cyclical Factors - Solar <ul><li>9 of 12 solar cycle predicting models/schemes suggest upcoming 11-year solar cycle(s) could be much weaker (Lund). Last cycle was 25% weaker than prior two cycles. </li></ul><ul><li>Hathaway (NASA) says “Solar Cycle 25, which peaks in the year 2022, should be one of the weakest ever observed” </li></ul><ul><li>Very weak solar cycles have been historically associated with cold periods, even mini-ice-ages </li></ul>Active cycle periods 1700 1800 1900 2000 Quieter cycle periods 11 year solar cycles themselves vary in their strength on a longer term with cycles of 80 and 200 years Gleissberg Cycle
    31. 33. Cyclical Factors - Oceans <ul><li>Multi-decadal cycles in the ocean temperature patterns in both Pacific and Atlantic </li></ul><ul><ul><li>Pacific Decadal Oscillation </li></ul></ul><ul><ul><li>Atlantic Multidecadal Oscillation </li></ul></ul><ul><li>They have a major influence on temperatures over adjacent land areas and the frequency and strength of storms </li></ul>Cold 1947-1977 Warm 1978 - Warm 1930-1963 Warm 1995- Cold 1964-1994 Positive PDO favors warm Alaska and more El Ninos
    32. 34. Pacific Decadal Oscillations What about these extensive global cooling events? Atlantic Multidecadal Oscillation
    33. 35. St. Helens El Chichon Pinatubo Cerro Hudson Agung, others Volcanic aerosols in the high atmosphere block solar radiation and increase cloud cover leading to widespread cooling, especially significant in summer Krakatoa, others Santa Maria Global cooling after major eruptions quite clear Lowest levels of high atmosphere volcanic aerosols since records began allowed more solar heating since 2000
    34. 36. Long term climate changes <ul><li>Rotation of the </li></ul><ul><li>Earth every 24 h leads </li></ul><ul><li>to days and nights; </li></ul><ul><li>T 1 =24 h </li></ul><ul><li>Revolution of the </li></ul><ul><li>Earth every 365 days </li></ul><ul><li>leads to seasons; </li></ul><ul><li>T 2 =365 days=1 year </li></ul><ul><li>Solar Cycle </li></ul><ul><li>T 3 =11 – 12 years </li></ul><ul><li>Precession of the </li></ul><ul><li>Equinoxes </li></ul><ul><li>T 4 =23,000 years </li></ul><ul><li>Tilt of the Earth’s axis </li></ul><ul><li>T 5 =41,000 years </li></ul>
    35. 37. Periodic Patterns in Nature and its Graphical Representation Daily variations – Days and Nights Period = T = 24 hr Daily, monthly, and yearly variations - three periods T 1 = 24 hr, T 2 = 90 days, T 3 = 365 days Time Series Analysis Maximum Minimum Mean or Average Range More complicated behaviors are indicators of hidden dynamical processes to be studied
    36. 38. Slopes, Trigonometric Functions, Average Values, and Global Warming It is worth to notice the periodicity (24 hrs) of these peaks; however it is clear the irregular shape of all these peaks too – Why? Range of variation Cloudiness and Random Fluctuations in the weather are responsible for these irregularities
    37. 39. Slopes, Trigonometric Functions, Average Values, and Global Warming Trigonometric Interpolation Case 1: The free term T o is a constant Case 2: The free term T o is a linear function of time Case 3: The free term To is a quadratic function of time Climate is all about the value of this Integral, known as the average value Weather is all about the values of these Functions at some moments of time, known as the time series
    38. 40. Slopes, Trigonometric Functions, Average Values, and Global Warming It is worth to notice how the trigonometric function oscillates around the main value function T o (t). A minimum of 30 years it is needed to make a conclusion about a warming Climate. It is worth to notice also, how short Cold intervals may coexist with a warming trend.
    39. 41. Climate The average weather patterns for an area over a long period of time (at least 30 years, and above – 1,000,000 years) Average Precipitation Average Temperature Latitude Ocean currents Altitude Where people live? How people live? What they grow and eat? Average It is determined by and Which are influenced by And affects
    40. 42. Systems and Complex Systems Key Components of most systems <ul><li>Inputs of things such as matter, energy, or information into the system. </li></ul><ul><li>Flows , or throughputs , of matter, energy, or information within the system at certain rates. </li></ul><ul><li>Stores , or storage areas , within a system where energy, matter, or information can accumulate for various lengths of time before being released. </li></ul><ul><li>Outputs of certain forms of matter, energy, or information that flow out of the system into sinks in the environment . </li></ul>Inputs Outputs Stores Flows Environment Feedback mechanism A feedback loop occurs when an output of matter, energy, or information is fed back into the system as an input that changes The system. Positive feedback loops Negative feedback loops
    41. 43. Hurricanes Tropical Storms Mesoscale Convective Systems “ Long” Waves Small – Scale Motions (Turbulence) Land / Sea Breezes Thunderstorms High / Low Pressure “ Short” Waves Tornadoes seconds to minutes minutes to hours hours to days days to weeks weeks to months 0.000001 km 1 km 10 km 100 km 1000 km 10000 km Microscale Mesoscale Synoptic Scale Temporal Scales The spatial and temporal scales of various weather phenomena Characteristic length L – defines the spatial range for a particular event Characteristic time T – defines the time interval for a particular event to occur Ratios = L / Lc or T / Tc When numerical values of ratios are becoming large enough, then processes occurring at scales of the order of Lc (Tc) are averaged and appear as fixed for scales larger than those previously analyzed.
    42. 46. Strong Dynamical Instabilities known as Chaos, restrict the predictability of models… Statistical Analysis
    43. 47. Statistical Analysis of Time Series Data Descriptive Statistics <ul><li>Finding of average values of weather </li></ul><ul><li>parameters whose time series is </li></ul><ul><li>available. We will get: </li></ul><ul><li>Normals == averages over 30 years </li></ul><ul><li>Standard deviations == anomalies </li></ul><ul><li>Medians and Modes </li></ul><ul><li>Distribution of outcomes </li></ul>Fourier Analysis <ul><li>Search for periodicities in the </li></ul><ul><li>Time series…a very important </li></ul><ul><li>information, since it will provide </li></ul><ul><li>clues about the internal dynamics </li></ul><ul><li>Trigonometric functions </li></ul><ul><li>Wavelet functions </li></ul><ul><li>Power spectra </li></ul><ul><li>Filtering and smoothing </li></ul><ul><li>Singular spectrum analysis </li></ul><ul><li>Noise </li></ul><ul><li>Detrending and prewithening </li></ul>Correlation Analysis <ul><li>Establish functional </li></ul><ul><li>relationships between </li></ul><ul><li>different weather sets: </li></ul><ul><li>Canonical correlation </li></ul><ul><li>Analysis (CCA) </li></ul><ul><li>Multiple Discriminant </li></ul><ul><li>Analysis (MDA) </li></ul><ul><li>Cluster Analysis </li></ul>
    44. 48. Theory of Graphs & Networks
    45. 49. Feedback networks of interconnected interacting subsystems within the climatic Graph – a very useful mathematical technique for complex systems.
    46. 51. Sea level rise due to Greenland ice loss. Source: Rignot and Kanagaratnam , 2006 .
    47. 52. BS in Mathematics PREREQUISITE REQUIRED COURSES : 19 credits MAT 205 Applied Statistics (3 credits) MAT 232 Calculus I (4 credits) MAT 233 Calculus II (4 credits) CHE 101/L General Chemistry I + Laboratory (4 credits) CHE 102/L General Chemistry II + Laboratory (4 credits) MAJOR REQUIREMENTS : 35 credits total Core Mathematics Courses : (13 credits) MAT 234 Calculus III (4 credits) MAT 306 Differential Equations (3 credits) MAT 311 Linear Algebra (3 credits) MAT 316 Complex Variables (3 credits) Mathematics Electives : (6 credits) Take two mathematics courses at the 300 or 400 level. Computing Requirement : (6 credits) Take two courses. CIS 230 Introduction to Java Programming (3 credits) CIS 235 Introduction to C++ Programming (3 credits) CIS 302 Advanced C++ Programming (3 credits) CIS 310 Advanced Java Programming (3 credits) CIS 360 Data Structures (3 credits) CIS 351 Systems Analysis and Design (3 credits) CIS 430 Database Management Systems (3 credits) Physical Science Requirements : (10 credits) PHY 207/L University Physics I + Laboratory (5 credits) PHY 208/L University Physics II + Laboratory (5 credits) Sub-Total Credits: 54 GENERAL EDUCATION REQUIREMENTS : 42 credits (Program requirements will satisfy 9 credits of the GER.) GENERAL ELECTIVES : 24 credits Total credits: 120
    48. 53. The WeatherBug Network is the largest weather network in the world. More than 8000 schools across the U.S. operate WeatherBug Tracking Stations, including Saint Thomas University , to integrate live, local weather data and technology into classroom learning. This is accomplished through WeatherBug Achieve , an online teaching tool that automatically embeds live weather readings and images from any source on the WeatherBug Network into lessons. +/- 1C -45C – 60C +/- 2F -55F – 150F Auxiliary Temperature N/A 0 – 100% N/A 0 – 100% Light Intensity +/- 2% Unlimited +/- 2% Unlimited Rainfall +/- 5 mbar 900 – 1100 mbar +/- 0.05”Hg 28 – 32” Hg Barometric Pressure +/- 3 deg 0 – 360 deg +/- 3 deg 0 – 360 deg Wind Direction +/- 4 kph 0 – 275 kph +/- 2 mph 0 – 125 mph Wind Speed +/- 2% 0 – 100% +/- 2% 0 – 100% Relative Humidity +/- 0.5C -45C – 60C +/- 1F -55F – 150F Temperature Accuracy (Metric) Range (Metric) Accuracy (English) Range (English) Feature
    49. 54. Data collected by the weather tracking station in campus. It is interesting to notice; how many parameters may be correlated at once by looking at these graphics. Hail storm took place on May 26, 2005 in the area of Miami Gardens and Opa-Locka. Hails of size an inch and a half were collected that day.
    50. 55. Mathematics and Atmospheric Sciences Ongoing research project # 1: The effect of Climate and Weather Variability on Hurricane Dynamics
    51. 56. Hurricane’s Science
    52. 57. Ongoing research project # 2: Asthma – Weather connection <ul><ul><li>Air Quality and Respiratory disorders: Modeling asthma attacks considering the environmental triggers, the mechanics of lung functioning, immune response and genetic factors. </li></ul></ul>Asthma Statistics Worldwide: A brief overview # of people diagnosed: more than 150 M Europe: the # of cases has doubled USA: the # of cases has increased more than 60% India: between 15 and 20 M Africa: between 11 and 18% population # of deaths yearly: around 180,000 Miami Dade County – 7.1% Middle and HS children were reported with asthma The # of hospitalizations due to asthma has doubled. The # 1 cause of school absences and 35 % of parents missed work Urban Heat Island Effect Man is likely playing a role in climate change through urbanization and land use changes competing with greenhouse Gases and cycles of Nature <ul><li>In cities, vertical walls, steel and concrete absorb the sun’s heat and are slow to cool at night </li></ul><ul><li>Nights may be 10 or more degrees warmer in and near cities than in rural areas some nights </li></ul><ul><li>Temperatures measured in cities increase as they grow. </li></ul>
    53. 58. Mesoscopic immune description of an asthma episode A system of differential equations describes the population dynamics of each one of the cells involved in an asthma episode. A very complicated Network of cells (IL4, IL3, IL5, IL13- Cytokines, IgE – Immunoglobuline) Interacting and Competing. In asthmatic individuals, antigen presentation is thought to results in the polarization of T-cells towards a T h2 patterns whereas T cells from non atopic, non-asthmatic individuals show the opposing T h1 (interferon- γ and I L2 ) pattern of cytokine secretion
    54. 59. Science & Mathematics Fellows Program <ul><li>Start Date: August 2008 - 30 freshmen & 30 juniors who transfer with an AA. </li></ul><ul><li>Qualified students may receive financial aid and academic scholarships. </li></ul><ul><li>Research based in state of the art Science & Technology facility. </li></ul>
    55. 60. The question is… Can we cross the bridge?