1. MET 61 1 MET 61 Introduction to Meteorology MET 61 Introduction to Meteorology - Lecture 4 “Heat in the atmosphere” Dr. Eugene Cordero San Jose State University W&H: Chap 3, Pg 74-84 Ahrens: Chapter 4 Class Outline: Sensible and latent heat First law of thermodynamics

2. MET 61 2 MET 61 Introduction to Meteorology Thermodynamic Diagram Green Dry Adiabats Red Moist Adiabats Yellow Saturation Mixing Ratio

3. MET 61 3 MET 61 Introduction to Meteorology Sensible heat Is related to the energy exchange that can be measured by a temperature change: C p =specific heat at constant pressure C p =C pd (1+0.84r); r=water vapor mixing ratio

4. MET 61 4 MET 61 Introduction to Meteorology Sensible heat Is related to the energy exchange that can be measured by a temperature change: C p =specific heat at constant pressure C p =C pd (1+0.84w); w=water vapor mixing ratio

5. MET 61 5 MET 61 Introduction to Meteorology Latent Heat Latent heat is the energy exchanged during a phase change (I.e. liquid to vapor etc.) Heat exchanged without a temperature change.

6. MET 61 6 MET 61 Introduction to Meteorology Latent Heat Latent heat is the energy exchanged during a phase change (I.e. liquid to vapor etc.) Heat exchanged without a temperature change.

7. MET 61 7 MET 61 Introduction to Meteorology Latent Heat The heat energy required to change water from one state to another (e.g. water from a vapor to a solid). evaporationLatent heat of evaporation : condensationLatent heat of condensation

8. MET 61 8 MET 61 Introduction to Meteorology Latent Heat The heat energy required to change water from one state to another (e.g. water from a vapor to a solid). evaporationLatent heat of evaporation : condensationLatent heat of condensation Heat lost by environment Heat given to environment

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12. MET 61 12 MET 61 Introduction to Meteorology 1 st law of thermodynamics Relates the change in internal energy with the heat added and the work done by the body U, q and w are defined as per unit mass du- internal energy (proportional to motion of molecules) dq- increment of heat added dw- work done by the body

13. MET 61 13 MET 61 Introduction to Meteorology 1 st law of thermodynamics Relates the change in internal energy with the heat added and the work done by the body U, q and w are defined as per unit mass du- internal energy (proportional to motion of molecules) dq- increment of heat added dw- work done by the body

14. MET 61 14 MET 61 Introduction to Meteorology 1 st law of thermo Work: related to a force acting on an object to cause a displacement. Basically, the temperature of a parcel changes when heat is added (dq) or when work is done (dw) Alternate form:

15. MET 61 15 MET 61 Introduction to Meteorology 1 st law of thermo Work: related to a force acting on an object to cause a displacement. Basically, the temperature of a parcel changes when heat is added (dq) or when work is done (dw) Alternate form:

16. MET 61 16 MET 61 Introduction to Meteorology Water Vapor The amount of water vapor present in the air can be expressed in a variety of ways: Mixing Ratio: Where m v is the mass of water vapor; m d is the mass of dry air: Units for r are typically given in: (g of water vapor/ kg of air) If there is no condensation or evaporation, then the mixing ratio of an air parcel is a conserved quantity. Note: symbol r is also commonly used for the mixing ratio

17. MET 61 17 MET 61 Introduction to Meteorology Water Vapor The amount of water vapor present in the air can be expressed in a variety of ways: Mixing Ratio: Where m v is the mass of water vapor; m d is the mass of dry air: Units for w are typically given in: (g of water vapor/ kg of air) Typical values; 1-5 g/kg midlatitudes and up to 20 g/kg in the tropics If there is no condensation or evaporation, then the mixing ratio of an air parcel is a conserved quantity. Note: symbol r is also commonly used for the mixing ratio

18. MET 61 18 MET 61 Introduction to Meteorology Saturation Vapor Pressure The saturation vapor pressure is defined as the maximum amount of water vapor necessary to keep moist air in equilibrium with a surface of pure water or ice. Consider a box containing air and water. If the box is initially dry, the water will evaporate and the water vapor pressure in the air will increase. Eventually, an equilibrium will be reached where evaporation and condensation are equal. At this point, the air is ‘saturated’ and the vapor pressure, e=e s. The saturation vapor pressure: e s =e s (T)

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21. MET 61 21 MET 61 Introduction to Meteorology Saturation Vapor Pressure The Clausius-Clapeyron equation describes the relationship between the saturation vapor pressure and temperature. You may see the derivation of this expression later in the course or further courses. For now, the relationship is: Where e 0 =6.11 hPa, T 0 = 273°K and L represents the latent heat of vaporization (L v= = 2.453 × 10 6 J/kg) or the latent heat of deposition (L d =2.8 x 10 6 J/kg).

22. MET 61 22 MET 61 Introduction to Meteorology Saturation Vapor Pressure The Clausius-Clapeyron equation describes the relationship between the saturation vapor pressure and temperature. You may see the derivation of this expression later in the course or further courses. For now, the relationship is: Where e 0 =6.11 hPa, T 0 = 273°K and L represents the latent heat of vaporization (L v= = 2.453 × 10 6 J/kg) or the latent heat of deposition (L d =2.8 x 10 6 J/kg).

23. MET 61 23 MET 61 Introduction to Meteorology The Clausius-Clapeyron equation Example problem: What is the saturation vapor pressure when the temperature is 30° C?

24. MET 61 24 MET 61 Introduction to Meteorology The Clausius-Clapeyron equation Example problem: What is the saturation vapor pressure when the temperature is 30° C? Answer: Convert temperature to Kelvins, 30° C = 303 K ln(E s /6.11) = (2.453×10 6 J/kg/461 J/kg)(1/273 - 1/303) E s = (e 1.92 )(6.11) = 42.1 hPa

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26. MET 61 26 MET 61 Introduction to Meteorology Saturation Mixing Ratio The saturation mixing ratio, with respect to water is defined as the ratio of the mass of saturated water vapor, m vs, to the mass of dry air, m d. We can express the saturation mixing ratio in terms of pressure as: Where  vs ' is the partial density of water vapor required to saturate air and  d ' is the partial density of dry air.

27. MET 61 27 MET 61 Introduction to Meteorology Saturation Mixing Ratio The saturation mixing ratio, with respect to water is defined as the ratio of the mass of saturated water vapor, m vs, to the mass of dry air, m d. We can express the saturation mixing ratio in terms of pressure as: Where  vs ' is the partial density of water vapor required to saturate air and  d ' is the partial density of dry air.

28. MET 61 28 MET 61 Introduction to Meteorology Saturation Mixing Ratio The above equation can be further simplified as: For typical values of temperatures in the Earth’s atmosphere, p>>e s, and thus Thus, w s =w s (T,P)

29. MET 61 29 MET 61 Introduction to Meteorology Saturation Mixing Ratio The above equation can be further simplified as: For typical values of temperatures in the Earth’s atmosphere, p>>e s, and thus Thus, w s =w s (T,P)

30. MET 61 30 MET 61 Introduction to Meteorology Relative Humidity The relative humidity is generally the ratio of the amount of water vapor in the air compared to the maximum amount of water the air can hold. RH is a function of temperature:

31. MET 61 31 MET 61 Introduction to Meteorology Relative Humidity The relative humidity is generally the ratio of the amount of water vapor in the air compared to the maximum amount of water the air can hold. RH is a function of temperature:

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33. MET 61 33 MET 61 Introduction to Meteorology Dew Point The dew point temperature, T d, is the temperature air must be cooled at constant pressure for the air to become saturated. Or, this is the temperature where the actual mixing ratio and the saturation mixing ratio are equal. Dewpoint is a good measure of the amount of water in the air. The Clausius-Clapeyron can be used to determine the dew point. If you know the saturation vapor pressure, e s, and T d =T and solve for T d, giving:

34. MET 61 34 MET 61 Introduction to Meteorology Dew Point The dew point temperature, T d, is the temperature air must be cooled at constant pressure for the air to become saturated. Or, this is the temperature where the actual mixing ratio and the saturation mixing ratio are equal. Dewpoint is a good measure of the amount of water in the air. T d ~ 20°C uncomfortable T d > 24 °C very uncomfortable! The Clausius-Clapeyron can be used to determine the dew point. If you know the saturation vapor pressure, e s, and T d =T and solve for T d, giving:

35. MET 61 35 MET 61 Introduction to Meteorology Lifting Condensation Level The lifting condensation level (LCL) defines the level where a moist parcel lifted adiabatically will become saturated. Because dry air must be lifted further to reach the LCL than moist air, the LCL height serves as another measure of the amount of water vapor in the air. During the lifting of a parcel, one often assumes that: - the mixing ratio, r, of the parcel is conserved. - the potential temperature of the parcel is conserved. At the LCL, the mixing ratio, r and the saturation mixing ratio, r s are equal. One often uses a pseudoadiabatic chart to find the LCL. However, there is a relationship:

36. MET 61 36 MET 61 Introduction to Meteorology Lifting Condensation Level The lifting condensation level (LCL) defines the level where a moist parcel lifted adiabatically will become saturated. Because dry air must be lifted further to reach the LCL than moist air, the LCL height serves as another measure of the amount of water vapor in the air. During the lifting of a parcel, one often assumes that: - the mixing ratio, w, of the parcel is conserved. - the potential temperature of the parcel is conserved. At the LCL, the mixing ratio, w and the saturation mixing ratio, w s are equal. One often uses a pseudoadiabatic chart to find the LCL. However, there is a relationship: LCL=125m (T-T d ) in ºC

37. MET 61 37 MET 61 Introduction to Meteorology Thermodynamic Diagram Green Dry Adiabats Red Moist Adiabats Yellow Saturation Mixing Ratio

38. MET 61 38 MET 61 Introduction to Meteorology Activity 3 (Due Feb 14 th ) 1.Show that for adiabatic motions, increases in temperatures are accompanied by decreases in geopotential. 2.Derive an expression for the dry adiabatic lapse rate. 3.Plot out the vertical distribution of potential temperature between the surface and 10hPa. 4.Exercise 3.42 5.Exercise 3.46 6.Exercise 3.47

39. MET 61 39 MET 61 Introduction to Meteorology Questions 1.Calculate the density of water vapor which exerts a pressure of 9 mb at 20°C. 2.Determine the virtual temperature of moist air at 30 °C which has a mixing ratio of 20 g/kg. 3.Air at 1000hPa and 18 °C has a mixing ratio of 6g/kg. What is the relative humidity and dew point? 4.In (3), determine the LCL using the given relationship between dew point and temperature.

40. MET 61 40 MET 61 Introduction to Meteorology Polar air: Air temp: -2°C (28 ° F) Dew point: -2 ° C(28 ° F)

41. MET 61 41 MET 61 Introduction to Meteorology Desert air: Air temp: 35°C (95°F) Dew point: 5°C (41°F) Which has higher relative humidity? Which has higher water vapor content?

42. MET 61 42 MET 61 Introduction to Meteorology Quiz #2: Part A 1.Describe what the saturation vapor pressure represents. 1.Explain how temperature and relative humidity are related.