1. MET 61 1 MET 61 Introduction to Meteorology MET 61 Introduction to Meteorology - Lecture 2 “The atmosphere (II)” Dr. Eugene Cordero San Jose State University W&H Chapter 1 Class Outline: Thermodynamics Hydrostatic balance Hypsometric equation

2. Functions of the Atmosphere What is the structure of the atmosphere?

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4. MET 61 4 MET 61 Introduction to Meteorology Discussion Questions What is the weight of the atmosphere? What is the altitude where 99% of the atmosphere exists below? What is the approximate temperature of the atmosphere at 5 km above the surface? How is the atmosphere different on the top of Mt. Everest compared to San Jose in terms of –Composition –Density –Pressure

5. MET 61 5 MET 61 Introduction to Meteorology Principal Atmospheric Gases GASMASS 3870 (75%) 1185 (23%) 67 (1%) 17 (0.3%) 3 (0.06%) TOTAL 5140 Unit: 10 18 g

6. MET 61 6 MET 61 Introduction to Meteorology Principal Atmospheric Gases GASMASS Nitrogen 3870 (78%) Oxygen 1185 (21%) Argon 67 (1%) Water Vapor 17 (0.3%) CO 2 3 (0.06%) TOTAL 5140 Unit: 10 18 g Permanent gases Variable gases

7. MET 61 7 MET 61 Introduction to Meteorology Thermodynamics Definition: Definition: The study of the processes that involve the transformation of heat into mechanical work, of mechanical work into heat, or the flow of heat from a hotter body to a colder body.

8. MET 61 8 MET 61 Introduction to Meteorology Thermodynamics Definition: The study of heat and its transformation into mechanical energy. Definition: The study of the processes that involve the transformation of heat into mechanical work, of mechanical work into heat, or the flow of heat from a hotter body to a colder body.

9. MET 61 9 MET 61 Introduction to Meteorology Thermodynamics The thermodynamic state of the atmosphere can be described by three variables: –________________

10. MET 61 10 MET 61 Introduction to Meteorology Thermodynamics The thermodynamic state of the atmosphere can be described by three variables: –________________ Pressure Density Temperature

11. MET 61 11 MET 61 Introduction to Meteorology Environmental lapse rate, . – Dry adiabatic lapse rate,  d – Moist adiabatic lapse rate,  s – – Lapse Rate

12. MET 61 12 MET 61 Introduction to Meteorology Environmental lapse rate, . –From radiosonde (sounding) Dry adiabatic lapse rate,  d –Constant (9.8°/1000m) Moist adiabatic lapse rate,  s –Varies with temperature/moisture –1°/1000m - 9°/1000m; typical = 6°/1000m Lapse Rate

13. MET 61 13 MET 61 Introduction to Meteorology Pressure  Measured in  millibars (mb) or  hPa (hecto pascals)  inches of mercury

14. MET 61 14 MET 61 Introduction to Meteorology Air Pressure The weight of the air about us. Pressure equals – Weight is the force exerted by gravity (g) on a unit mass The average pressure at sea level is about ~ ~ 14.70 pounds force per sq inch 1013 mb; 101.3 kPa or 1013 hPa ~ 29.9 in Hg Pa – N/m 2 (N-Newton is Kg m/s 2 )

15. MET 61 15 MET 61 Introduction to Meteorology Air Pressure The weight of the air about us. Pressure equals –a force over a given area (P = F/A) Weight is the force exerted by gravity (g) on a unit mass The average pressure at sea level is about ~ ~ 14.70 pounds force per sq inch 1013 mb; 101.3 kPa or 1013 hPa ~ 29.9 in Hg Pa – N/m 2 (N-Newton is Kg m/s 2 )

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17. MET 61 17 MET 61 Introduction to Meteorology  Pressure measured via a: 

18. MET 61 18 MET 61 Introduction to Meteorology  Pressure measured via a:  Barometer

19. MET 61 19 MET 61 Introduction to Meteorology Pressure (I) What does pressure represent physically? How does atmospheric pressure change with height? –p 0 is average sea level pressure –H p is the pressure scale height (~ 7km) –

20. MET 61 20 MET 61 Introduction to Meteorology Pressure (I) What does pressure represent physically? How does atmospheric pressure change with height? –p 0 is average sea level pressure –H p is the pressure scale height (~ 7km) –Assumption is that temperature is constant within that layer.

21. MET 61 21 MET 61 Introduction to Meteorology Scale Height The scale height is proportional to the average temperature in a layer: R- gas constant for dry air (287 J K -1 kg -1 ) g – gravitational acceleration (9.8)

22. MET 61 22 MET 61 Introduction to Meteorology Scale Height The scale height is proportional to the average temperature in a layer: R- gas constant for dry air (287 J K -1 kg -1 ) g – gravitational acceleration (9.8 m s -2 )

23. MET 61 23 MET 61 Introduction to Meteorology Question 1 Question: What is the pressure at 10km? At what altitude is the pressure 50% of the surface value?

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26. MET 61 26 MET 61 Introduction to Meteorology Atmospheric Pressure and Density Density and Pressure related… Density refers to number of air molecules per volume – Pressure refers to the ‘weight’ of the atmosphere above.

27. MET 61 27 MET 61 Introduction to Meteorology Atmospheric Pressure and Density Density and Pressure related… Density refers to number of air molecules per volume –Units are given in Kg/m 3 Pressure refers to the ‘weight’ of the atmosphere above.

28. MET 61 28 MET 61 Introduction to Meteorology Density What does density represent physically? How does atmospheric density change with height? –  0 is average sea level pressure –H  is the density scale height (~8km) –Assuming temperature constant

29. MET 61 29 MET 61 Introduction to Meteorology Density What does density represent physically? How does atmospheric density change with height? –  0 is average sea level pressure –H  is the density scale height (~8km) –Assuming temperature constant

30. MET 61 30 MET 61 Introduction to Meteorology Temperature What does temperature represent physically? How does atmospheric temperature change with height? –a is a constant –m w is the molecular weight –v is the average molecular speed

31. MET 61 31 MET 61 Introduction to Meteorology Temperature What does temperature represent physically? How does atmospheric temperature change with height? –a is a constant –m w is the molecular weight –v is the average molecular speed

32. MET 61 32 MET 61 Introduction to Meteorology Equation of State Ideal Gas Law; relates the thermodynamic states of a gas  For moist air one can use the virtual temperature; T v =T(1+0.61r) r- water vapor mixing ratio p-Pressure (Pa)  - density (kg m -3 ) R - Gas Constant for dry air (287 J K -1 kg -1 ) T - Temperature (K)

33. MET 61 33 MET 61 Introduction to Meteorology Equation of State Ideal Gas Law; relates the thermodynamic states of a gas  For moist air one can use the virtual temperature; T v =T(1+0.61r) r- water vapor mixing ratio Virtual temperatures allows for the use of R for dry air in ideal gas law. p-Pressure (Pa)  - density (kg m -3 ) R - Gas Constant for dry air (287 J K -1 kg -1 ) T - Temperature (K)

34. MET 61 34 MET 61 Introduction to Meteorology Hydrostatic Balance (I) Pressure gradient: the change in pressure with distance. Horizontal variations in air pressure are much less than the vertical ones. However, horizontal pressure differences drive our weather, while vertical pressure changes don’t exert as much influence

35. MET 61 35 MET 61 Introduction to Meteorology Hydrostatic Balance (II) Pressure decrease produces a vertical pressure gradient force. Vertical pressure gradient force is directed __________. Vertical pressure gradient force is balanced by gravity.

36. MET 61 36 MET 61 Introduction to Meteorology Hydrostatic Balance (I) Pressure decrease produces a vertical pressure gradient force. Vertical pressure gradient force is directed __________. Vertical pressure gradient force is balanced by gravity. p+  p p z

37. MET 61 37 MET 61 Introduction to Meteorology Hydrostatic Balance (II) Hydro – fluids Static – balance Atmosphere is nearly always in hydrostatic balance. Exceptions are in severe weather conditions - “non-hydrostatic”

38. MET 61 38 MET 61 Introduction to Meteorology Hypsometric Equation Combination of ideal gas law with hydrostatic balance. Relates atmospheric thickness with average temperature. Thickness of atmosphere relates to difference between two atmospheric layers; z t (m) = thickness between two pressure levels

39. MET 61 39 MET 61 Introduction to Meteorology Hypsometric Equation Combination of ideal gas law with hydrostatic balance. Relates atmospheric thickness with average temperature. Thickness of atmosphere relates to difference between two atmospheric layers; z t (m) = thickness between two pressure levels

40. MET 61 40 MET 61 Introduction to Meteorology Question 2 What is the thickness between 500hPa and 200hPa if the average temperature of the layer is 10F? Compare the average thickness at latitudes between 60N-70N with the thickness between 20N-30N.

41. MET 61 41 MET 61 Introduction to Meteorology Principle forces Q: What drives the weather in the atmosphere? Q: What causes the weather to change? We will develop a foundation for answering these questions through understanding the predominant forces in the atmosphere, namely:

42. MET 61 42 MET 61 Introduction to Meteorology Principle forces Q: What drives the weather in the atmosphere? Q: What causes the weather to change? We will develop a foundation for answering these questions through understanding the predominant forces in the atmosphere, namely: pressure and pressure gradients,pressure and pressure gradients, gravitygravity rotation of the earthrotation of the earth frictionfriction Today

43. MET 61 43 MET 61 Introduction to Meteorology Pressure Changes Caused byCaused by –Temperature or density changes Determine the direction and speed of windsDetermine the direction and speed of winds Can help explain general circulation of atmosphere.Can help explain general circulation of atmosphere. General guidelines:General guidelines: –High pressure: –Low pressure: Why is this?

44. MET 61 44 MET 61 Introduction to Meteorology Pressure Changes Caused byCaused by –Temperature or density changes Determines the direction and speed of windsDetermines the direction and speed of winds Can help explain general circulation of atmosphere.Can help explain general circulation of atmosphere. General guidelines:General guidelines: –High pressure: clear skies/fine weather –Low pressure: cloudy skies/changeable weather Why is this?

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48. MET 61 48 MET 61 Introduction to Meteorology Pressure (II) Pressure can be used as a vertical coordinate. Convenient as many instruments have pressure sensors Example questions: Compare the pressures at 5 km above sea level for average layer temperatures of 25C and 35C.

49. MET 61 49 MET 61 Introduction to Meteorology Pressure change with altitude Explain why the pressure at p1 is greater or less than p2? Explain what direction the pressure gradient force is directed at the earth’s surface. Explain why the atmosphere does not rush out to space. Question 3

50. MET 61 50 MET 61 Introduction to Meteorology Activity 2 Answer all questions, show all your work. And please write neatly. See Appendix ____ for suggestions on preparing homework. Due on Tuesday, Feb 7th. 4.The average surface pressure is around 14.7 lbs/in 2. What is this in hPa and mb? 5.Explain (in words) why pressure always decreases with increasing altitude. 6.What is the approximate temperature at 5 km in altitude? 7.Derive the hypsometric equation starting from hydrostatic balance. Show all steps and make sure you understand how this works. Hint: see today’s reading. 8.How much oxygen is there at the top of Mt. Everest compared to San Jose?