GLOBAL WARMINGIN MATHEMATICAL

ASPECTS

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ACKNOWLEDGEMENTWe would like to express our special thanks of gratitude to our teacher Ms. Jasbir Kaur who gave us the golden opportunity to do this wonderful project on the topic Global Warming(in mathematical aspects),which also helped us in doing a lot of Research and we came to know about so many new things we are really thankful to them.Secondly we would also like to thank our parents and friends who helped me a lot in finalizing this project within the limited time frame.

CONTENTGLOBAL WARMINGWHERE IS GLOBAL WARMING GOING?OBSERVED TEMP. CHANGESHOW GLOBAL WARMING WORKS?GREENHOUSE EFFECTTHE (ATMOSPHERIC)GREENHOUSE EFFECTATMOSPHERIC CO2 MATHEMATICAL EQUATIONS ON GLOBAL WARMINGWITHOUT GREENHOUSE EFFECTGLACIERS AND MOUNTAIN ARE SLOWLY MELTINGWHAT CAN WE DO TO STOP IT?

GLOBAL WARMINGGlobal warming is the unequivocal and continuing rise in the average temperature of Earth's climate system.Since 1971, 90% of the warming has occurred in the oceans.  Despite the oceans' dominant role in energy storage, the term "global warming" is also used to refer to increases in average temperature of the air and sea at Earth's surface. Since the early 20th century, the global air and sea surface temperature has increased about 0.8 °C (1.4 °F), with about two-thirds of the increase occurring since 1980.Each of the last three decades has been successively warmer at the Earth's surface than any preceding decade since 1850.

OBSERVED TEMP CHANGESThe Earth's average surface temperature rose by 0.74±0.18 °C over the period 1906–2005. The rate of warming over the last half of that period was almost double that for the period as a whole (0.13±0.03 °C per decade, versus 0.07±0.02 °C per decade). The urban heat island effect is very small, estimated to account for less than 0.002 °C of warming per decade since 1900 . Temperatures in the lower troposphere have increased between 0.13 and 0.22 °C (0.22 and 0.4 °F) per decade since 1979, according to satellite temperature measurements. Climate proxies show the temperature to have been relatively stable over the one or two thousand years before 1850, with regionally varying fluctuations such as the Medieval Warm Period and the Little Ice Age.

How Global Warming Works

Fossil fuels (coal, oil, natural gas)

Carbon Dioxide (CO2)

The Sun’s energy passes through the car’s windshield.

This energy (heat) is trapped inside the car and cannot pass back through the windshield, causing the inside of the car to warm up.

Greenhouse Effect

The (Atmospheric) Greenhouse Effect

• Examples of greenhouse gases: H2O, CO2, CH4, CFC.

• Currently, CO2 is the main suspect of causing the global warming

since the 20th century because combustion of fossil fuel naturally

injects CO2 into the atmosphere and it has increased dramatically since last century.

Remember this chart?

Why it happens?C + O2 = CO2

Burning carbon-containing fossil fuels produces carbon dioxide

Atmospheric Carbon DioxideThis chart shows a steady increase of CO2 concentration in the last five decades. Although this chart is based on Mauna Loa’s data, the same trend has been found in many other places.

Atmospheric CO2 (1958-2004)Parametric Analysis / Inferential

• It is best characterized by the 3-par. Weibull, and its cumulative form is given by

• Scale

• Shape• • Location• X: Atmospheric CO2

• Thus, we can obtain, E[X], Var[X], S.D[X], Confidence limits, etc.

Trend Analysis: Determine If Atmospheric CO2 Depends on Time

• The where gamma function

• Consider• Best Fit

• Thus, F(x) as a function of time, is

• Using this result we can obtain projections with a desired degree of confidence, ten, twenty, fifty years from now.

South Pole and Barrow, Alaska, show the same trend as Hawaii

The CO2 Emissions Model

• ARIMA(1,1,2)×(1,1,1)12

• After expanding the model and inserting the coefficients, we have

The degree of warming will not be uniform everywherehigher latitudes are more sensitive

Total Atmospheric CO2E CO2 emission (fossil fuel

combustion)C1 Gas fuels

C2 Liquid fuel

C3 Solid fuel

C4 Gas flares

C5 Cement production

D Deforestation and destruction D1 deforestation

D2 destruction of biomass

D3 destruction of soil carbon

R Terrestrial plant respiration Only one variable

S Respiration S1 respiration from soils

S2 respiration from decomposers

O the flux from oceans to atmosphere Only one variable

P terrestrial photosynthesis Only one variable

A the flux from atmosphere to oceans Only one variable

B burial of organic carbon and limestone carbon

B1 the burial of organic carbon

B2 burial of limestone carbon

Differential Equation of Atmospheric CO2

8 Contributable Variables

E CO2 emission (fossil fuel combustion)

D Deforestation and destruction

R Terrestrial plant respiration

S Respiration

O the flux from oceans to atmosphere

P terrestrial photosynthesis

A the flux from atmosphere to oceans

B burial of organic carbon and limestone carbon

MORE AND MORE

Fossil Fuels ARE BURNED

Slowly melting

Of course the physical environmental change will lead to changes in the biosphere – including our society.

The Arctic Ocean could be ice-free in summer by 2040.

(U.S National Center for Atmospheric Research, 2006)2000

2040

Melting Sea Ice

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

As the temperature of oceans rise, so will the probability of more frequent and stronger hurricanes.

Warmer waters and more hurricanes

Increased probability and intensity of droughts and heat

waves

WHAT CAN WE DO TO STOP IT?

Ways to stop/control global warming

REDUCE USE

Plastic bags and cups do not decompose so harmful to environment

Paper bags and cups are eco friendly and easily decomposable 

Reduce the usage of cars for short distances

Walk /use cycles for short distances 

Avoid turning up the air conditioner. Instead dress lightly or use a fan.

Keep rooms cool by closing the Blinds, shades, or curtains.

Avoid turning up the air conditioner. Instead dress lightly or use a fan.

Keep rooms cool by closing the Blinds, shades, or curtains.

Turn off the lights when you leave. Turn off the lights when you leave.

Conserve electricity! DO NOT leave appliances on standby .

Conserve electricity! DO NOT leave appliances on standby .