met 61 1 met 61 introduction to meteorology met 61 introduction to meteorology - lecture 2 “the...

MET 61

1 MET 61 Introduction to MET 61 Introduction to MeteorologyMeteorology

MET 61 Introduction to Meteorology - Lecture 2

“The atmosphere (II)”

Dr. Eugene CorderoSan Jose State University

W&H Chapter 1

Class Outline:

ThermodynamicsHydrostatic balanceHypsometric equation

Functions of the AtmosphereFunctions of the Atmosphere

What is the structure of the atmosphere?What is the structure of the atmosphere?

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Discussion QuestionsDiscussion 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

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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

Unit: 1018 g

Permanent gases

Variablegases

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ThermodynamicsThermodynamics

• 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.

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ThermodynamicsThermodynamics

• The thermodynamic state of the atmosphere can be described by three variables:– ________________– ________________– ________________

Pressure

Density

Temperature

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• 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

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PressurePressure

Measured in Measured in

millibars (mb) or millibars (mb) or

hPa (hecto pascals)hPa (hecto pascals)

inches of mercuryinches of mercury

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Air PressureAir 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)

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Pressure measured Pressure measured via a:via a:Barometer Barometer

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Pressure (I)Pressure (I)• What does pressure represent physically?

• How does atmospheric pressure change

with height?

pHzepp 0

– p0 is average sea level pressure

– Hp is the pressure scale height (~ 7km)

– Assumption is that temperature is

constant within that layer.

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Scale HeightScale Height• The scale height is proportional to the

average temperature in a layer:

0g

TRH

• R- gas constant for dry air (287 J K-1kg-1)• g – gravitational acceleration (9.8 m s-2)

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Question 1Question 1Question:

• What is the pressure at 10km?

• At what altitude is the pressure 50% of the

surface value?

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Atmospheric Pressure and Atmospheric Pressure and DensityDensity

• 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.

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DensityDensity• What does density represent physically?

• How does atmospheric density change with height?

ρHz0eρρ

0 is average sea level pressure

– H is the density scale height (~8km)

– Assuming temperature constant

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TemperatureTemperature• What does temperature represent

physically?

• How does atmospheric temperature change with height?

2vamT w– a is a constant

– mw is the molecular weight

– v is the average molecular speed

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Equation of StateEquation of State• Ideal Gas Law; relates the thermodynamic

states of a gas

ρRTP

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.

p-Pressure (Pa)p-Pressure (Pa)

- density (kg m- density (kg m-3-3))

R - Gas Constant for dry air R - Gas Constant for dry air (287 J K(287 J K-1-1 kg kg-1-1))

T - Temperature (K)T - Temperature (K)

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Hydrostatic Balance (I)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

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Hydrostatic Balance (I)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.

ρgdz

dp

p+p

p

z

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Hydrostatic Balance (II)Hydrostatic Balance (II)• Hydro – fluids• Static – balance

• Atmosphere is nearly always in hydrostatic balance.

• Exceptions are in severe weather conditions - “non-hydrostatic”

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Hypsometric EquationHypsometric 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

2

112 lnZ

p

pT

g

RZ d

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Question 2Question 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.

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Principle forcesPrinciple forces

Q: What drives the weather in the atmosphere?Q: What drives the weather in the atmosphere?

Q: What causes the weather to change?Q: What causes the weather to change?

We will develop a foundation for answering these questions We will develop a foundation for answering these questions through understanding the predominant forces in the through understanding the predominant forces in the atmosphere, namely:atmosphere, namely:

• pressure and pressure gradients, pressure and pressure gradients, • gravitygravity• rotation of the earthrotation of the earth• friction friction

TodayToday

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Pressure ChangesPressure Changes

• Caused byCaused by– Temperature or density changesTemperature 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 weatherHigh pressure: clear skies/fine weather– Low pressure: cloudy skies/changeable weatherLow pressure: cloudy skies/changeable weather

Why is this?Why is this?

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Pressure (II)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.

met 61 1 met 61 introduction to meteorology met 61 introduction to meteorology - lecture 2 “the...

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