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.

2. What is Mathematics and Why it is important to be mathematically literate?

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

4. Branches of Mathematics Logic Descriptive Statistics Probabilities Geometry Calculus and Differential Equations

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

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

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

11. 2008 2007

12. What about the Mathematics involved in the study of the Weather and the Climate?

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

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.

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.

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.

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.

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

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 =

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

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.

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.

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.

27. Composition of the Atmosphere

29. Globally Warming Climates ? or Cyclically Changing Climates?

30. St. Thomas University, Miami Gardens, FL Boyd Buchanan, Chattanooga, TN Eagle Valley HS, Eagle Bend, MN

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)

34. Pacific Decadal Oscillations What about these extensive global cooling events? Atlantic Multidecadal Oscillation

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

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

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

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

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.

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

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.

46. Strong Dynamical Instabilities known as Chaos, restrict the predictability of models… Statistical Analysis

48. Theory of Graphs & Networks

49. Feedback networks of interconnected interacting subsystems within the climatic Graph – a very useful mathematical technique for complex systems.

51. Sea level rise due to Greenland ice loss. Source: Rignot and Kanagaratnam , 2006 .

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

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

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.

55. Mathematics and Atmospheric Sciences Ongoing research project # 1: The effect of Climate and Weather Variability on Hurricane Dynamics

56. Hurricane’s Science

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

60. The question is… Can we cross the bridge?