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Product No. 99770 Supplementary Print Price: FREE with membership
 

Climate Change and the Daily Temperature Cycle (UMAP)

Robert M. Gethner


Mathematics Topic:
Differential Equations
Application Areas:
Geophysics, climate modeling
Prerequisites:
one-variable calculus; first-order differential equations

| ©1999 by COMAP, Inc. | The UMAP Journal 19.1 | 54 pages |


This module constructs differential equations models of the daily temperature cycle on atmosphere-free planets and on planets that have atmospheres. The models give some insight into the behavior, observed in recent decades, that nighttime lows have been increasing faster than daytime highs over the Earth's land surfaces.

Table of Contents:

INTRODUCTION

TEMPERATURE, ENERGY, AND POWER

RADIATION, FLUX, AND THE SOLAR CONSTANT

BLACKBODIES AND EFFECTIVE TEMPERATURE

TEMPERATURES ON AN AIRLESS PLANET
How Much Will the Temperature Rise?
How Long Until the Surface Reaches Equilibrium?
How Large Is the Dinurnal Temperature Range?

A MATHEMATICAL INTERLUDE
Solution of the Homogeneous Equation
Solution of the Inhomogeneous Equation

TEMPERATURES ON AN AIRLESS PLANET, CONTINUED
The Diurnal Temperature Range

EQUILIBRIUM TEMPERATUES ON A PLANET WITH AN ATMOSPHERE
Shortwave Power
Longwave Power
Nonradiative Power

DAILY TEMPERATURE CYCLE OF A PLANET WITH ATMOSPHERE

APPENDIX I. KIRCHOFF'S LAW

APPENDIX II. PHYSICAL CONSTANTS AND CONVERSIONS

APPENDIX III. GLOSSARY

ANSWERS AND SOLUTIONS TO SELECTED EXERCISES

REFERENCES

ACKNOWLEDGMENTS

ABOUT THE AUTHOR