What is Mathematics What is Mathematics and and

Why it is important to be Why it is important to be mathematically literate?mathematically literate?

Some common misconceptions about Some common misconceptions about MathematicsMathematics

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 life4. Math makes no allowance for creativity.5. Math provides exact answers.

What is Mathematics after all?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 forcreating models, or representations that allowus to study real phenomena

Mathematical Modeling

Medicine and Physiology

Psychology and Sociology

Bioinformatics

Engineering

Biology and Ecology

Computer science andArtificial Intelligence

Physics and Chemistry

Economics Business Management

Atmospheric Physics or Meteorology

Branches of Mathematics Branches of Mathematics

Logic

Descriptive StatisticsProbabilities

Geometry

Calculus andDifferential Equations

What is Quantitative Literacy?LiteracyLiteracy 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.

LevelLevel Language SkillLanguage Skill Math SkillMath Skill

11Recognizes 2500 two or three syllable words. Reads at a rate of 95-120 words per minute. Writes and speaks simple sentences.

Adds and subtracts two digit numbers. Does simple calculations with money, volume, length, and weight.

22Recognizes 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.

Adds, subtracts, multiplies, and divides all units of measure. Compute ratio, rate, and percentage. Draws and interpret bar graphs.

33Read novels and magazines, as well as safety rules and equipment instructions. Writes reports with proper format and punctuation. Speak well before an audience.

Understand basic geometry and algebra. Calculates discount, interest, profit and loss, markup, and commissions.

44Reads novels, poems,newspapers, and manual. Prepares business letters, summaries, and reports. Participates in panel discussions and debates. Speaks extemporaneously on a variety of subjects.

Deals with complex algebra and geometry, including linear and quadratic equations, logarithmic functions, and axiomatic geometry.

55Reads literature, book and play reviews, scientific and technical journals, financial reports, and legal documents. Can write editorials, speeches, and critiques.

Knows calculus and statistics, able to deal with econometrics.

66 Same types of skills as level 5, but more advanced.Work with advanced calculus, modern algebra, and statistics.

Adapted from Education: The knowledge gap, supplement to The Wall Street Journal, February 9,1990

OccupationOccupation Language Language LevelLevel

Math LevelMath Level OccupationOccupation Language Language LevelLevel

Math Math LevelLevel

Biochemist 6 6 Corporate executive 4 5

Computer Engineer 6 6 Computer sales agent 4 4

Mathematician 6 6 Management trainee 4 4

Cardiologist 6 5 Insurance sales agent 3 4

Social psychologist 6 5 Retail store manager 3 4

Lawyer 6 4 Cement mason 3 3

Tax Attorney 6 4 Dairy farm manager 3 3

Newspaper editor 6 4 Poultry farmer 3 3

Accountant 5 5 Tile setter 3 3

Personnel manager 5 5 Travel agent 3 3

Corporate president 5 5 Telephone operator 3 2

Weather forecaster 5 5 Janitor 3 2

Secondary teacher 5 5 Short-order cook 3 2

Elementary teacher 5 4 Assembly-line worker 2 2

Disc jockey 5 3 Toll collector 2 2

Financial analyst 4 5 Laundry worker 1 1

Adapted from Education: The knowledge gap, supplement to The Wall Street Journal, February 9,1990

What is Meteorology What is Meteorology and and

Why scientists study it ? Why scientists study it ?

• 525 BCE Greek philosopher Anaximenes of Miletus proposedthat winds, clouds, rain, and hailare formed by thickening of air, the primary substance.• 500 BCE Parmenides classified World Climates by latitude as torrid, temperate, or frigid 350 – 340 BCE Aristotle produced his

Meteorologica, the first work on theatmospheric sciences.Meteor – a Greek word meaning falling from sky.Logica – StudyMeteorologica – The study of bodiesfalling from the sky

Natural & Human Induced

Disasters

Human Health &

Well-Being

Energy Resources

Climate Variability &

Change

Water Resources

Weather Information,

Forecasting & Warning

Ecosystems

Sustainable Agriculture & Desertificatio

n

Oceans

Benefits of Earth ObservationsBenefits of Earth Observations

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.

Good News about Economic Development Between 1900 and 2002, global life expectancy at birth more than doubled from 33 to 67 years (76 in developed countries and 65 in developing countries).• Between 1955 and 2002, the world’s average infant mortality during the first year of life dropped by 60% in developed countries and 40% in developing countries.• Global food production has outpaced population growth since 1978.• Since 1950 the percentage of rural families in developing countries with access to safe drinking water has increased from 10% to almost 75%.• We have learned how to produce more goods with less raw materials.• Since 1970 levels of most major air and water pollutants have been reduced in most of the world’s developed countries.

Bad News about Economic Development• Average life expectancy in developing countries is 11 years less than in developed countries.• Infant mortality in developing countries is more than eight times higher than in developed countries.• The harmful environmental effect of industrialized food production may eventually limit future food production unless there is a shift to more sustainable ways to produce food.• Air and water pollution levels in most developing countries are much too high according to the World Health Organization• Because of increased population growth and per capita resource use, some of the natural resources that support all life are being used unsustainably:1. premature extinction of a growing number of the world’s plant and animal species, 2. destruction or degradation of wetlands, coral reefs, and forests in some parts of the world, and 3. gradual degradation of underground water supplies in some areas.• Gases emitted into the atmosphere from burning fossil fuels and clearing forests could cause the world’s climate to become warmer during this century, causing: 1. shifting areas where crops can be grown, 2. altering water supplies by shifting patterns of precipitation, 3. shifting where various animals and plants can survive, 4. raising average sea levels.

• Prior to Industrial Revolution CO2 concentrations were stable at 280 ppm• As CO2 increases, so should average global surface temperatures• Warming from 2.5 to 10° F

• It is worth to notice the variability in carbon dioxide concentrationssuperimposed over this general trend. Namely; this trend is the onescientists associate with the excessive greenhouse warming.• How far the greenhouse effect may still being considered an allies? It will depend on the ability to keep these concentrations undercontrol and avoid the Runaway Greenhouse Effect already seen inthe planet Venus

2008

200

7

What about the Mathematics What about the Mathematics involved in the studyinvolved in the study

of the Weather and the Climate? of the Weather and the Climate?

PHYSICAL QUANTITIES AND UNITSPHYSICAL QUANTITIES AND UNITSObservations produce qualitative

information about a system

Measurements produce quantitative information which is needed in any

science that strives for exactness

English UnitsInch (in)

Second (s)Pound (lb)

Metric System Meter (m)Second (s)

Kilogram (kg)

Fundamental Physical QuantitiesDistance - Time - Mass

Scientific Notation Prefix | Abbreviation | Regular Notation | Scientific NotationTera T 1,000,000,000,000 = 1012 Giga G 1,000,000,000 = 109

Mega M 1,000,000 = 106

Kilo k 1,000 = 103

Hecto h 1,00 = 102

Deca da 10 = 101

-------- ---------- 1 = 100

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

Earth Globe and the Geometry of the Sphere 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 360o. In orderto convert degrees into units of distance asimple proportion is used:

a

BAdRnceCircumfereo

),(

360

2

3600

Latitudes – small circumferences on the sphere,they changes from 0o (Equator) to 90o (Pole) in both directions, South and North.Longitudes – large circumferences on the sphere, they all merge in both poles. The prime longitudeor prime meridian is the Greenwich meridian.

The Atmosphere: Basic concepts and definitionsThe Atmosphere: Basic concepts and definitions

Earth’s Atmosphere is a relatively thinenvelope of gases and tiny, suspendedparticles that encircles the globe.

Earth

Atmosphere Compared to the planet’s diameter (12,740 km or7918 mi), the atmosphereis 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

DE

RE

DE = 12,740 km = 2 RE

RE = 6,370 km = 3959 mi RA = 32 km = 32,000 m = 20 mi

00502.06370

32

km

km

R

A

E

If we would consider Earth as a ball 2 meters indiameter, then its radius will be 1 meter. Since 1 m = 1,000 millimeters, in this Earth’s modelthe atmosphere will comprise only about 5 mmabove the ball’s surface.

Air is a mixture of gases and particles, bothof which are made of atoms. Within the Airyou may find elements, molecules, compounds, gases, and suspended particles.

WEATHER AND CLIMATE

Weather is defined as the state of the atmosphere at a given time at a given place. Weather is described by:1. Temperature2. Air pressure3. Humidity4. Cloudiness5. Wind speed and direction6. VisibilityWeather is going to be defined as the intersection of above Six sets of physical parameters.

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 isthe average weather condition of a place.

Weather and Climate are sensitive Weather and Climate are sensitive indicators of changes in the Earth indicators of changes in the Earth System.System.

Energy: Units and Related QuantitiesEnergy: Units and Related Quantities

Experiments show conclusively that there is a lowesttemperature below which it is impossible to cool anobject. This is referred to as absolute zero. Thoughabsolute zero can be approached from above arbitrarily closely, it can never be attained.The Kelvin temperature scale, named for the Scottishphysicist 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 setexactly at absolute zero. Thus, in this scale there are nonegative equilibrium temperatures. The Kelvin scale is also chosen to have the same degree size as the Celsiusscale.

15.273

325

9

)32(9

5

CK

CF

FC

X intercept of a line Y intercept of a line

X

Y

Y = m X + b Equation of a line in the slope-intercept formm – slope or rate of change, m > 0 line goes up, m < 0 goes downb – y intercept of a lineLarger the value of “m” closer to the y-axis a line is locatedY = m X is called a linear variation or proportionY = m / X is called an inverse variation or inversely proportional

Graphical Representation in a plane

run

rise

xx

yym

12

12

Average lapse rate of 6.5°C per km or 3.6°F per 1,000 feet

T = m H + To Y = m X + YoTemperature plays the role of Y, and Height the role of X. The parameter “m” that we call slopeis the lapse rate, or how fast temperature dropswith height. To is the value of T at the ground level.

The variation of temperature withaltitude in the atmosphere

Temperature, and Layers of the AtmosphereTemperature, and Layers of the Atmosphere• Average lapse rate of 6.5°C per km or

3.6°F per 1,000 feet

• The lapse rate fluctuates and temperature may even increase with height creating a temperature inversion

gasidealanforstateofEquationTV

NkP

CinmeasuredetemperaturTz

T

metersperC

ground

1000

10005.6

• Gravity holds air molecules near the Earth, compressing them together

• Air density is greatest at the surface and decreases as we climb (first rapidly then slowly)

• Air molecules have weight and exert a force called Air Pressure

• As we climb the weight of the air above us decreases and pressure decreases

Air pressure decreases with altitude because air is compressible and behaves like a pile of springs.

zepzp 0)(

P = F/ SPressure is the Force (F) exerted on a unit ofArea (S)

Unit of Pressure = PascalStandard Atmosphere = 760 mm of Hg1 st. At = 1013.25 hPa = 1013.25 mbar = 29.92 in of Hg

Graphical Representation in the space

-2

0

2

-2

0

2

-2

-1

0

1

2

-2

0

2

-2

0

2

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”).

-2

0

2

-2

02

-2

-1

0

1

2

-2

0

2

-2

02

T(Longitude,Latitude)

Temperature as a function of values of longitude and latitudeon Earth. Longitude plays therole of X and latitude the roleof Y.

The space between contour lines indicates how fast thecoordinate Z = F(x,y) changes around this local area. When contour lines are grouped very close each other itrepresents a sharp descend or increase around thesepoints. On the other hand, more spaced contour lines isan 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 pointsGradient =

Surface Analysis Map

250 mb Map

500 mb Map

Weather Charts for different altitudes abovethe ground. Isopleths of barometric pressure,known as Isobars are represented.

L – low barometric pressureH – high barometric pressure

• Is out there any unifying concept or principle Is out there any unifying concept or principle describing processes in the atmosphere, oceansdescribing processes in the atmosphere, oceansand the land?and the land?

• Is out there a more serious and/or challenging Is out there a more serious and/or challenging formulation for processes in the atmosphere,formulation for processes in the atmosphere,oceans and the land? oceans and the land?

Energy: Units and Related QuantitiesEnergy: Units and Related Quantities

Energy Units – Metric System Energy Units – Metric System Energy Units – English System Energy Units – English System

Joule = 1 J = 1 N ∙ m = 6.24 1018 eV = 0.239 cal Foot per Pound = 1 ft ∙ lb British Thermal Unit (Btu)

TemperatureTemperature: The average kinetic energy of an assemble of particles forming part of a given system.

HeatHeat: The Energy transferred between objects because of a Temperature difference.

T1 T2

T1 > T2

When we say that there is a transfer of heat ora heat flow from object A to object B, it meansthat the total energy of object A decreases and the total energy of object B increases.

Objects are said to be in thermal contact if heatcan flow between them. After some time inthermal contact, the transfer of heat ceases. At this point, we say that the objects are inthermal equilibrium.

Celsius Scale (oC) Swedish astronomer Andres Celsius (1701 – 1744). The original idea was modified by the biologist Carolus Linnaeus (1707 – 1778), assigning 0oC to freezing temperature of water and 100oC the boiling water.

Fahrenheit Scale (oF) was developed by Gabriel Fahrenheit (1686 – 1736). He assigned 98.6oF to body temperature, 32oF freezing water, and 212oF the boiling water.

325

9

)32(9

5

CF

FC

Forms of Energy TransferForms of Energy Transfer

ConductionConduction: Particle by particle transfer of thermal and electric energy.

RadiationRadiation: Transfer of Electro- magnetic Energy through empty Space in form of waves, traveling at a constant speed - c.

ConvectionConvection: Transfer of thermal energy by mass movement of a fluid.

AdvectionAdvection: The horizontally moving part of thecirculation (called winds) carries properties of the air in that particular area with it.

ConductionConduction: Heat transferred in this fashion always flows from warmer to colder regions. Generally, the greater the temperature difference, the more rapid the heat transfer.

tL

TTAt

L

TAQ AB

ConvectionConvection: 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.

The total amount of energy radiated outward each second by the Sun or any other star is called LuminosityLuminosity

3.8 x 1026 W Power Radiated by the Sun

Power Received by Earth per square Meter = Solar ConstantSolar Constant

1370 W / m2

)4/()( 24 RSTE SunSun

The Science of the Radiant Energy or Radiative PhysicsThe Science of the Radiant Energy or Radiative Physics

4TE

T

c

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-2K-4. For the Sun T=6,000 K.

Composition of the AtmosphereComposition of the Atmosphere

Globally Warming Climates ?or

Cyclically Changing Climates?

St. Thomas University, Miami Gardens, FL

Boyd Buchanan, Chattanooga, TN

Eagle Valley HS, Eagle Bend, MN

World Physical GeographyWorld Physical Geography

UTC or Z – time = Universal UTC or Z – time = Universal Standard Time = It is the time Standard Time = It is the time Measured at Royal Observatory Measured at Royal Observatory in Greenwich.in Greenwich.EDT = Eastern Day Time = EDT = Eastern Day Time = UTC - 5 hr (4 hr during time UTC - 5 hr (4 hr during time adjustment) adjustment)

Cyclical Factors - Solar

Solar Irradiance vs US Annual Mean Temperatures

50

50.5

51

51.5

52

52.5

53

53.5

54

54.5

55

1895

1900

1905

1910

1915

1920

1925

1930

1935

1940

1945

1950

1955

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

1363

1363.5

1364

1364.5

1365

1365.5

1366

1366.5

1367

1367.5

1368

US Annual Mean Temp

Solar Irradiance

Poly. (Solar Irradiance)

Poly. (US Annual Mean Temp)

• 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. • Hathaway (NASA) says “Solar Cycle 25, which peaks in the year 2022, should be one of the weakest ever observed”• Very weak solar cycles have been historically associated with cold periods, even mini-ice-ages

Active cycle periods

17001700 1800 1800 1900 1900 20002000

Quieter cycle periods

11 year solar cycles themselves vary in their strength 11 year solar cycles themselves vary in their strength on a longer term with cycles of 80 and 200 yearson a longer term with cycles of 80 and 200 years

Gleissberg CycleGleissberg Cycle

Cyclical Factors - OceansCyclical Factors - Oceans• Multi-decadal cycles in the ocean

temperature patterns in both Pacific and Atlantic

– Pacific Decadal Oscillation– Atlantic Multidecadal Oscillation

• They have a major influence on temperatures over adjacent land areas and the frequency and strength of storms

Pacific Decadal Oscillation (5 Year)

-1

-0.5

0

0.5

1

1.5

1952

1956

1960

1964

1968

1972

1976

1980

1984

1988

1992

1996

2000

Cold 1947-1977

Warm 1978 -

Atlantic Multidecadal Oscillation (5 year)

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

1952

1956

1960

1964

1968

1972

1976

1980

1984

1988

1992

1996

2000Warm 1930-1963 Warm 1995-

Cold 1964-1994

Positive PDO favors warm Alaska and more El Ninos

Pacific Decadal Pacific Decadal OscillationsOscillations

El Ninos

El Nino

La Nina

We can see the warming effects of El Nino and the cooling effects of La Nina in the global temperatures since 1979

Correlation of +0.49

What about these extensive global cooling events?

Atlantic Multidecadal Atlantic Multidecadal OscillationOscillation

Annual Atlantic MultiDecadal Oscillation (AMO)

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

1856

1861

1866

1871

1876

1881

1886

1891

1896

1901

1906

1911

1916

1921

1926

1931

1936

1941

1946

1951

1956

1961

1966

1971

1976

1981

1986

1991

1996

2001

2006

Stratospheric Volcanic Aerosol (NASS GISS Aerosol Optical Thickness)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

1850

1860

1870

1880

1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

St. HelensEl Chichon

PinatuboCerro 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

SantaMaria

Global cooling after major eruptions quite clear

Lowest levels ofhigh atmospherevolcanic aerosols since records began allowed more solar heating since 2000

Long term climate changes Long term climate changes

• Rotation of theEarth every 24 h leadsto days and nights;T1=24 h• Revolution of theEarth every 365 daysleads to seasons;T2=365 days=1 year• Solar CycleT3=11 – 12 years• Precession of theEquinoxesT4=23,000 years• Tilt of the Earth’s axisT5=41,000 years

0 20 40 60 800

0.2

0.4

0.6

0.8

1

0 20 40 60 801

0.5

0

0.5

1

x

0 20 40 60 801

0.5

0

0.5

1

x

0 20 40 60 800.5

0

0.5

1

1.5

2

x

0 20 40 60 801

0.5

0

0.5

1

x

0 20 40 60 801

0.50

0.51

1.52

2.5

x

Periodic Patterns in Nature and its Graphical Representation

DCBxAy )sin(

Daily variations – Days and Nights Period = T = 24 hr

Daily, monthly, and yearly variations - three periods T1= 24 hr, T2= 90 days, T3= 365 days

Time Series Analysis

Maximum

Minimum

Mean or Average

Range

More complicated behaviors are indicators of hidden dynamical processes to be studied

Slopes, Trigonometric Functions, Average Values, and Global WarmingSlopes, Trigonometric Functions, Average Values, and Global Warming

It is worth to notice the periodicity (24 hrs) of these peaks; however itis 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

Slopes, Trigonometric Functions, Average Values, and Global WarmingSlopes, Trigonometric Functions, Average Values, and Global Warming

200

00

00

0

)(

)(

)(

)()()(

atTtT

atTtT

TtT

tTtSinTtT M

Trigonometric Interpolation

Case 1: The free term To is a constant

Case 2: The free term To is a linear function of time

Case 3: The free term To is a quadratic function of time

f

i

dttTTave

)(

1 Climate is all about the value of this Integral, known as the average value

Weather is all about the values of theseFunctions at some moments of time, known as the time series

Slopes, Trigonometric Functions, Average Values, and Global WarmingSlopes, Trigonometric Functions, Average Values, and Global Warming

0 20 40 60 80 100

2

4

6

8

10

0 20 40 60 80 100

2

4

6

8

10

12

0 20 40 60 80 100

2.5

5

7.5

10

12.5

15

17.5

2200

00

00

0

001.05)(

03.05)(

5)(

)()()(

tatTtT

tatTtT

TtT

tTtSinTtT M

It is worth to notice how the trigonometric function oscillates around the main value

function To(t).

A minimum of 30 years it is needed tomake a conclusion about a warming Climate. It is worth to notice also, how short Cold intervals may coexist with awarming trend.

Climate

The average weather patterns for an area over a longperiod 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

N

xx

N

ii

1

It is determined by

and

Which are influenced by

And affects

Systems and Complex SystemsSystems and Complex Systems

Key Components of most systems

• Inputs of things such as matter, energy, or information into the system.• Flows, or throughputs, of matter, energy, or information within the system at certain rates.• Stores, or storage areas, within a system where energy, matter, or information can accumulate for various lengths of time before being released.• Outputs of certain forms of matter, energy, or information that flow out of the system into

sinks in the environment.

InputsOutputs

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

Hurricanes

Tropical Storms

MesoscaleConvective

Systems

“Long”Waves

Small – ScaleMotions

(Turbulence)

Land / SeaBreezes

Thunderstorms

High / Low Pressure

“Short”Waves

Tornadoes

secondsto

minutes

minutesto

hours

hoursto

days

daysto

weeks

weeksto

months

0.000001 km 1 km 10 km 100 km 1000 km 10000 km

Microscale Mesoscale Synoptic Scale

Tem

por

al S

cale

s

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 forscales larger than those previously analyzed.

Strong Dynamical Instabilitiesknown as Chaos, restrict thepredictability of models…

Statistical Analysis

Statistical Analysis of Time Series Data Statistical Analysis of Time Series Data

Descriptive Statistics

Finding of average values of weatherparameters whose time series is available. We will get:• Normals == averages over 30 years• Standard deviations == anomalies• Medians and Modes• Distribution of outcomes

Fourier Analysis

Search for periodicities in theTime series…a very important information, since it will provideclues about the internal dynamics• Trigonometric functions• Wavelet functions• Power spectra• Filtering and smoothing• Singular spectrum analysis• Noise• Detrending and prewithening

Correlation Analysis

Establish functionalrelationships betweendifferent weather sets:• Canonical correlationAnalysis (CCA)• Multiple Discriminant Analysis (MDA)• Cluster Analysis

Feedback networks of interconnectedinteracting subsystems within the climaticGraph – a very useful mathematical techniquefor complex systems.

Sea level rise due to Greenland ice loss. Source: Rignot and

Kanagaratnam, 2006.

BS in MathematicsPREREQUISITE 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

Feature Range (English)

Accuracy (English)

Range(Metric)

Accuracy(Metric)

Temperature -55F – 150F +/- 1F -45C – 60C +/- 0.5C

Relative Humidity 0 – 100% +/- 2% 0 – 100% +/- 2%

Wind Speed 0 – 125 mph +/- 2 mph 0 – 275 kph +/- 4 kph

Wind Direction 0 – 360 deg +/- 3 deg 0 – 360 deg +/- 3 deg

Barometric Pressure 28 – 32” Hg +/- 0.05”Hg 900 – 1100 mbar +/- 5 mbar

Rainfall Unlimited +/- 2% Unlimited +/- 2%

Light Intensity 0 – 100% N/A 0 – 100% N/A

Auxiliary Temperature -55F – 150F +/- 2F -45C – 60C +/- 1C

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.

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.

Ongoing research project # 1: The effect of Climate and Weather Ongoing research project # 1: The effect of Climate and Weather Variability on Hurricane DynamicsVariability on Hurricane Dynamics

Hurricane’s Science

Ongoing research project # 2: Asthma – Weather connectionOngoing research project # 2: Asthma – Weather connectionAir Quality and Respiratory disorders: Modeling asthma attacks considering the environmental triggers, the mechanics of lung functioning, immune response and genetic factors.

Asthma Statistics Worldwide: A brief overview# of people diagnosed: more than 150 MEurope: the # of cases has doubledUSA: the # of cases has increased more than 60%India: between 15 and 20 MAfrica: between 11 and 18% population# of deaths yearly: around 180,000Miami Dade County – 7.1% Middle and HS children were reported with asthmaThe # of hospitalizations due to asthma has doubled.The # 1 cause of school absences and 35 % of parents missed work

Urban Heat Island EffectMan is likely playing a role in climate change through urbanization and land use changes competing with greenhouse Gases and cycles of Nature

• In cities, vertical walls, steel and concrete absorb the sun’s heat and are slow to cool at night

• Nights may be 10 or more degrees warmer in and near cities than in rural areas some nights

• Temperatures measured in cities increase as they grow.

Mesoscopic immune description of an asthma episodeA 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 Th2 patterns whereas T cells from non atopic, non-asthmatic individuals show the opposing Th1 (interferon-γ and IL2) pattern of cytokine secretion

Science & Mathematics Fellows Program• Start Date: August 2008 - 30 freshmen & 30 juniors who transfer with an AA.• Qualified students may receive financial aid and academic scholarships.• Research based in state of the art Science & Technology facility.

The question is…The question is…

Can we cross the Can we cross the bridge?bridge?