Dynamic Climatology: Basis in Mathematics and Physics

List of Tables.

Preface.

Part I: The Field of Dynamic Climatology: .

Part II: Mathematics:.

1. Geometry.

2. Differential Calculus.

3. Partial Derivatives.

4. Integral Calculus.

5. Development of Calculus.

6. Vectors.

7. The Exponential and Complex Numbers.

8. Finite Differences.

9. Comment.

Part III: Statistics:.

10. Data.

11. One Variable Descriptive Statistics.

12. Two Variables.

13. Dependence.

14. Dependence for More Than One Variable.

15. Comment.

Part IV: Mechanics:.

16. Newton's Definitions and Laws.

17. Base Units.

18. Derived Units.

19. Discussion.

Part V: Thermodynamics:.

20. Definitions.

21. The Equation of State - The Macroscopic Approach.

22. Atmospheric Composition.

23. Heat.

24. The First Law of Thermodynamics.

25. The Carnot Cycle.

26. Dry Adiabats and Potential Temperature.

27. The Second Law of Thermodynamics.

28. Water.

29. Discussion.

Part VI: Radiation: .

30. Early Work.

31. Quanta.

32. Definitions of Laws of Radiation.

33. Applications to the Earth.

34. Comment.

Part VII: Atmospheric Equations:.

35. The Nature of Fluids.

36. Continuity - Conservation of Mass.

37. Molecular Viscosity.

38. The Stress Tenor.

39. Navier-Stokes Equations.

40. Turbulent Eddy Viscosity.

41. The Vector Equation of Motion.

42. General Coordinates.

43. Some Simple Solutions.

44. Fluid Rotation.

45. The Equation Set.

46. Comment.

Part VIII: Observed Angular Momentum and Energy: .

47. Perspective.

48. Angular Momentum.

49. The Partition of Energy.

50. The Lorenz Model of Energy Flow.

51. Heat Budget.

52. Water Budget.

53. Conversion between Scales of Motion.

54. The General Circulation.

Part IX: Towards an Explanation of Climate: .

55. The Problem.

56. Numerical Modeling.

57. Climate Modeling.

Part X: Concluding Remarks:.

58. Power Notation.

59. Constants.

60. Conversions.

61. World Data.

Index.