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MET 61 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 1 MET 61 Introduction to Meteorology Functions of the Atmosphere What is the structure of the atmosphere? MET 61 3 MET 61 Introduction to Meteorology MET 61 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 4 MET 61 Introduction to Meteorology Principal Atmospheric Gases GAS MASS Nitrogen 3870 (78%) Oxygen 1185 (21%) Argon 67 (1%) Water Vapor 17 (0.3%) CO2 3 (0.06%) TOTAL 5140 MET 61 Permanent gases Variable gases Unit: 1018 g 6 MET 61 Introduction to Meteorology MET 61 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. 8 MET 61 Introduction to Meteorology MET 61 Thermodynamics • The thermodynamic state of the atmosphere can be described by three variables: Pressure – ________________ Density – ________________ Temperature – ________________ 10 MET 61 Introduction to Meteorology Lapse Rate MET 61 • 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 MET 61 Introduction to Meteorology 12 Pressure MET 61 Measured in millibars (mb) or hPa (hecto pascals) inches of mercury 13 MET 61 Introduction to Meteorology MET 61 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/m2 (N-Newton is Kg m/s2) 15 MET 61 Introduction to Meteorology MET 61 16 MET 61 Introduction to Meteorology MET 61 Pressure measured via a: Barometer 18 MET 61 Introduction to Meteorology MET 61 Pressure (I) • What does pressure represent physically? • How does atmospheric pressure change with height? p p0e z H p – p0 is average sea level pressure – Hp is the pressure scale height (~ 7km) – Assumption is that temperature is constant within that layer. MET 61 Introduction to Meteorology 20 MET 61 Scale Height • The scale height is proportional to the average temperature in a layer: RT H g0 • R- gas constant for dry air (287 J K-1kg-1) • g – gravitational acceleration (9.8 m s-2) 22 MET 61 Introduction to Meteorology MET 61 Question 1 Question: • What is the pressure at 10km? • At what altitude is the pressure 50% of the surface value? 23 MET 61 Introduction to Meteorology MET 61 24 MET 61 Introduction to Meteorology MET 61 25 MET 61 Introduction to Meteorology Atmospheric Pressure and Density MET 61 • Density and Pressure related… • Density refers to number of air molecules per volume – Units are given in Kg/m3 • Pressure refers to the ‘weight’ of the atmosphere above. 27 MET 61 Introduction to Meteorology MET 61 Density • What does density represent physically? • How does atmospheric density change with height? ρ ρ0e z Hρ – 0 is average sea level pressure – H is the density scale height (~8km) – Assuming temperature constant 29 MET 61 Introduction to Meteorology MET 61 Temperature • What does temperature represent physically? • How does atmospheric temperature change with height? T amw v 2 – a is a constant – mw is the molecular weight – v is the average molecular speed 31 MET 61 Introduction to Meteorology MET 61 Equation of State • Ideal Gas Law; relates the thermodynamic states of a gas p-Pressure (Pa) P ρRT - density (kg m-3) R - Gas Constant for dry air (287 J K-1 kg-1) T - Temperature (K) For moist air one can use the virtual temperature; Tv=T(1+0.61r) r- water vapor mixing ratio Virtual temperatures allows for the use of R for dry air in ideal gas law. 33 MET 61 Introduction to Meteorology MET 61 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 34 MET 61 Introduction to Meteorology MET 61 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 z dp dz ρg p+p 36 MET 61 Introduction to Meteorology MET 61 Hydrostatic Balance (II) • Hydro – fluids • Static – balance • Atmosphere is nearly always in hydrostatic balance. • Exceptions are in severe weather conditions - “non-hydrostatic” 37 MET 61 Introduction to Meteorology MET 61 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; zt (m) = thickness between two pressure levels Rd p1 Z 2 Z1 T ln g p2 39 MET 61 Introduction to Meteorology MET 61 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. 40 MET 61 Introduction to Meteorology Principle forces MET 61 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, gravity rotation of the earth friction Today 42 MET 61 Introduction to Meteorology Pressure Changes MET 61 • Caused by – Temperature or density changes • Determines the direction and speed of winds • Can help explain general circulation of atmosphere. • General guidelines: – High pressure: clear skies/fine weather – Low pressure: cloudy skies/changeable weather Why is this? 44 MET 61 Introduction to Meteorology MET 61 45 MET 61 Introduction to Meteorology MET 61 46 MET 61 Introduction to Meteorology MET 61 47 MET 61 Introduction to Meteorology MET 61 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. 48 MET 61 Introduction to Meteorology