Term Paper: MSE 515 — Thermodynamics of Materials
Professor Jim Adams

Stochastic Mathematical Modeling of Thermodynamics
of Global Warming Related to Greenhouse Effects

by Avi Singhal

Outline

  1. Abstract
  2. Introduction
    1. Thermodynamical Aspects
    2. Greenhouse Effects
    3. Energy Changes
    4. Receding Ice Caps
  3. Mathematical Model / Deterministic Models
    1. Simple Model of Global Warming
      1. Radiation from Sun
      2. Re-radiation from Earth
      3. Heat Capacity
  4. Discussion on Stochastic Modeling
  5. Future Trends of Temperature Changes
  6. Discussion
  7. Conclusions
  8. References

Global Warming

Term Paper for MSE 515 – Thermodynamics of Materials
Professor Adams – Spring 2000

by Avinash C. Singhal
Science and Engineering Materials Program
Arizona State University
Tempe, Arizona

Summary

Currently there is considerable interest in the phenomena of global warming. There have been many international meetings with the heads of the states from various countries during the past 15 years. Many agencies including NOAA – National Oceanographic and Atmospheric Administration are carefully maintaining temperature records at key locations throughout the world. The latest records seem to show that the global temperature has risen by half a degree in Centigrade during the past decade. Although people are concerned about global warming, the rise in temperature is only half a degree it does not lead to a major concern until one looks at the receding boundaries of the polar caps. During the same ten-year periods, the ice caps at both poles have melted by more than 1,000 each.

Lets examine a simple analogy. If one takes a flask with water and begins to heat it, the temperature will rapidly rise. On the other hand if several ice cubes are placed in the flask and the heat is applied, the temperature will not rise so rapidly but will begin to melt the ice. It is clear that the half-degree rise in the global temperature in the presence of polar caps will be significantly different once all the ice at the caps has melted.

Many researchers attribute this phenomena of the global temperature including El Nino effects attributed to the long term change in the jet stream as caused by the continuous rise of the Himalayas and the formation of the Tibetan plateau. It is well known that the Indian subcontinental plate is continuously moving northward and is being restrained by the Euro-Asia plate thus causing the rise in the Himalayas. Researchers from MIT and the University of California Berkeley have conducted many experimental and field studies to correlate the change in the heights of the Himalayas with the change in the jet stream and the consequent change in the weather, rain, and temperature patterns.

Introduction

The global temperature record shows an average warming of about 1°F over the past century. This warming has been recorded in both the northern and southern hemispheres, and over the oceans, with some areas substantially warmer and others actually cooler. The ten warmest years have occurred since 1983, with seven of them since 1990. Recent evidence shows the 20th century is the warmest over the last 1,000 years, the 1990s the warmest decade, and 1998 the single warmest year of the past millennium.

Many factors, both natural and human, do indeed affect the temperature of our planet, which varies constantly on time scales of hours to centuries. Changes in the atmosphere, oceans and land surface affect our planet's temperature. Gradual changes in Earth's orbit around the sun (which in turn change how sunlight hits our planet) are thought to be the key pacemaker for the comings and goings of past ice ages. The sun's energy can also vary over time.

Large volcanic eruptions can cool the planet for a few years by spewing out particles that block out some sunlight. Even some of our own pollutants, like sulfur dioxide that contributes to acid rain, have a similar cooling effect. And finally, the depletion of our ozone layer – caused by our release of chlorofluorocarbons – has led to cooling of the upper atmosphere. Scientists think these cooling effects have been masking some of the global warming.

Nevertheless, it appears the buildup of greenhouse gases in our atmosphere is at least partially responsible for the observed warming. And over the 21st century and beyond, the ongoing accumulation of greenhouse gases may be the dominant climatic influence.

The Greenhouse Effect

Energy from the sun drives the earth’s weather and climate, and heats the earth’s surface; in turn, the earth radiates energy back into space. Atmospheric greenhouse gases (water vapor, carbon dioxide, and other gases) trap some of the outgoing energy, retaining heat somewhat like the glass panels of a greenhouse.

Without this natural "greenhouse effect," temperatures would be much lower than they are now, and life as known today would not be possible. Instead, thanks to greenhouse gases, the earth’s average temperature is a more hospitable 60°F. However, problems may arise when the atmospheric concentration of greenhouse gases increases.

Since the beginning of the industrial revolution, atmospheric concentrations of carbon dioxide have increased nearly 30%, methane concentrations have more than doubled, and nitrous oxide concentrations have risen by about 15%. These increases have enhanced the heat-trapping capability of the earth’s atmosphere. Sulfate aerosols, a common air pollutant, cool the atmosphere by reflecting light back into space, however, sulfates are short-lived in the atmosphere and vary regionally.

Why are greenhouse gas concentrations increasing? Scientists generally believe that the combustion of fossil fuels and other human activities are the primary reason for the increased concentration of carbon dioxide. Plant respiration and the decomposition of organic matter release more than 10 times the CO2 released by human activities; but these releases have always been in balance with the carbon dioxide absorbed by plant photosynthesis. What has changed in the last few hundred years is the additional release of carbon dioxide by human activities. Energy burned to run cars and trucks, heat homes and businesses, and power factories is responsible for about 80% of society's carbon dioxide emissions, about 25% of U.S. methane emissions, and about 20% of global nitrous oxide emissions. Increased agriculture, deforestation, landfills, industrial production, and mining also contribute a significant share of emissions. In 1994, the United States emitted about one-fifth of total global greenhouse gases.

Estimating future emissions is difficult, because it depends on demographic, economic, technological, policy, and institutional developments. Several emissions scenarios have been developed based on differing projections of these underlying factors. For example, by 2100, in the absence of emissions control policies, carbon dioxide concentrations are projected to be 30-150% higher than today’s levels.

What Are Greenhouse Gases?

Some greenhouse gases occur naturally in the atmosphere, while others result from human activities. Naturally occurring greenhouse gases include water vapor, carbon dioxide, methane, nitrous oxide, and ozone. Certain human activities, however, add to the levels of most of these naturally occurring gases:

Carbon dioxide is released to the atmosphere when solid waste, fossil fuels (oil, natural gas, and coal), and wood and wood products are burned.

Methane is emitted during the production and transport of coal, natural gas, and oil. Methane emissions also result from the decomposition of organic wastes in municipal solid waste landfills, and the raising of livestock.

Nitrous oxide is emitted during agricultural and industrial activities, as well as during combustion of solid waste and fossil fuels.

Greenhouse gases that are not naturally occurring include byproducts of foam production, refrigeration, and air conditioning called chlorofluorocarbons (CFCs), as well as hydrofluorocarbons (HFCs) and perfluorocarbons (PFCs) generated by industrial processes.

Each greenhouse gas differs in its ability to absorb heat in the atmosphere. HFCs and PFCs are the most heat-absorbent. Methane traps over 21 times more heat than carbon dioxide, and nitrous oxide absorbs 270 times more heat than carbon dioxide. Often, estimates of greenhouse gas emissions are presented in units of millions of metric tons of carbon equivalents (MMTCE), which weights each gas by its GWP value, or Global Warming Potential.

Global Warming Potentials

Gases in the atmosphere can contribute to the greenhouse effect both directly and indirectly. Direct effects occur when the gas itself is a greenhouse gas; indirect radiative forcing occurs when chemical transformations of the original gas produce a gas or gases that are greenhouse gases, or when a gas influences the atmospheric lifetimes of other gases. The concept of a Global Warming Potential (GWP) has been developed to compare the ability of each greenhouse gas to trap heat in the atmosphere relative to another gas. Carbon dioxide was chosen as the reference gas to be consistent with IPCC guidelines.

Global Warming Potentials are not provided for the criteria pollutants CO, NOx, NMVOCs, and SO2 because there is no agreed upon method to estimate the contribution of gases that indirectly affect radiative forcing to climate change (IPCC 1996).

All gases in this inventory are presented in units of million metric tons of carbon equivalents (MMTCE). Carbon comprises 12/44ths of carbon dioxide by weight. In order to convert emissions reported in teragrams (Tg) of greenhouse gas to MMTCE, the following equation was used:

The GWP of a greenhouse gas is the ratio of global warming, or radiative forcing (both direct and indirect), from one unit mass of a greenhouse gas to that of one unit mass of carbon dioxide over a period of time. While any time period can be selected, the 100 year GWPs recommended by the IPCC and employed by the United States for policy making and reporting purposes were used in this report (IPCC 1996). A tabulation of GWPs is given below in Table 1 : Global Warming Potentials (100 year).

Table 1 : Global Warming Potentials (100 year)

Gas

GWP

Carbon dioxide (CO2)

1

Methane (CH4)*

21

Nitrous oxide (N2O)

310

HFC-23

11,700

HFC-125

2,800

HFC-134a

1,300

HFC-143a

3,800

HFC-152a

140

HFC-227ea

2,900

HFC-236fa

6,300

HFC-4310mee

1,300

CF4

6,500

C2F6

9,200

C4F10

7,000

C6F14

7,400

SF6

23,900

Source: (IPCC 1996).
* The methane GWP includes the direct effects and those indirect effects due to the production of tropospheric ozone and stratospheric water vapor. The indirect effect due to the production of CO
2 is not included.

Conclusions and Recommendation

The receding shoreline of the ice at the two polar caps is a serious thermodynamic and global concern. A mere half degree change of the global temperature with the presence of polar caps does not seem alarming enough but the rate of shoreline recess is indeed very alarming. Funding should be requested to perform research work related to reduction of the heat sources causing the global warming and the recession of the polar ice caps.


References

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