thermodynamicsm. d. eastin we need to understand the environment around a moist air parcel in order...
TRANSCRIPT
![Page 1: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/1.jpg)
Thermodynamics M. D. Eastin
We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the atmosphere
Here we investigate parameters that describe the large-scale environment
Hydrostatics
![Page 2: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/2.jpg)
Thermodynamics M. D. Eastin
Outline:
Review of the Atmospheric Vertical Structure
Hydrostatic Equation
Geopotential Height Application
Hypsometric Equation Applications Layer Thickness Heights of Isobaric Surfaces Reduction of Surface Pressure to Sea Level
Hydrostatics
![Page 3: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/3.jpg)
Thermodynamics M. D. Eastin
Pressure:
• Measures the force per unit area exerted by the weight of all the moist air lying above that height• Decreases with increasing height
Density:
• Mass per unit volume• Decreases with increasing height
Temperature (or Virtual Temperature):
• Related to density and pressure via the Ideal Gas Law for moist air
• Decreases with increasing height
Review of Atmospheric Vertical Structure
vdTRp ρ
z(km)
Tv(K) p(mb)
0
Tropopause12
151013
-60200
![Page 4: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/4.jpg)
Thermodynamics M. D. Eastin
Balance of Forces:
• Consider a vertical column of air
• The mass of air between heights z and z+dz is ρdz and defines a slab of air in the atmosphere
• The downward force acting on this slab is due to the mass of the air above and gravity (g) pulling the mass downward
• The upward force acting on this slab is due to the change in pressure through the slab
Hydrostatic Equation
dzgF
dpF
![Page 5: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/5.jpg)
Thermodynamics M. D. Eastin
Balance of Forces:
• The upward and downward forces must balance (Newton’s laws)
• Simply re-arrange and we arrive at the hydrostatic equation:
Hydrostatic Equation
dzgdp
FF
gdz
dp
![Page 6: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/6.jpg)
Thermodynamics M. D. Eastin
Application:
• Represents a balanced state between the downward directed gravitational force and the upward directed pressure gradient force
• Valid for large horizontal scales (> 1000 km; synoptic) in our atmosphere• Implies no vertical motion occurs on these large scales
The large-scale environment of a moist air parcel is in hydrostatic balance and does not move up or down
Note: Hydrostatic balance is NOT valid for small horizontal scales (i.e. themoist air parcel moving through a thunderstorm)
Hydrostatic Equation
![Page 7: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/7.jpg)
Thermodynamics M. D. Eastin
Definition:
• The geopotential (Φ) at any point in the Earth’s atmosphere is the amount of work that must be done against the gravitational field to raise a mass of 1 kg from sea-level to that height.
• Accounts for the change in gravity (g) with height
Geopotential Height
z
0dzg
Height Gravity z (km) g (m s-2)
0 9.81 1 9.80 10 9.77 100 9.50
dzgd
![Page 8: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/8.jpg)
Thermodynamics M. D. Eastin
Definition:
• The geopotential height (Z) is the actual height normalized by the globally averaged acceleration due to gravity at the Earth’s surface (g0 = 9.81 m s-2), and is defined by:
• Used as the vertical coordinate in most atmospheric applications in which energy plays an important role (i.e. just about everything)• Lucky for us → g ≈ g0 in the troposphere
Geopotential Height
0g
ΦZ
Height Geopotential Height Gravity z (km) Z (km) g (m s-2)
0 0.00 9.81 1 1.00 9.80 10 9.99 9.77 100 98.47 9.50
![Page 9: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/9.jpg)
Thermodynamics M. D. Eastin
Application:
• The geopotential height (Z) is the standard “height” parameter plotted on isobaric charts constructed from daily soundings:
Geopotential Height
500 mb
Geopotential heights (Z)are solid black contours(Ex: Z = 5790 meters)
Air temperatures (T) arered dashed contours(Ex: T = -11ºC)
Winds are shown as barbs
![Page 10: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/10.jpg)
Thermodynamics M. D. Eastin
Derivation:
• If we combine the Hydrostatic Equation with the Ideal Gas Law for moist air and the Geopotential Height, we can derive an equation that defines the thickness of a layer between two pressure levels in the atmosphere
1. Substitute the ideal gas law into the Hydrostatic Equation
Hypsometric Equation
gdz
dpvdTRp ρ
vdTR
gp-
dz
dp
![Page 11: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/11.jpg)
Thermodynamics M. D. Eastin
Derivation:
2. Re-arranging the equation and using the definition of geopotenital height:
3. Integrate this equation between two geopotential heights (Φ1 and Φ2) and the two corresponding pressures (p1 and p2), assuming Tv is constant in the layer
vdTR
gp-
dz
dp
p
dpTRgdzd vd
2
1
2
1 p
dpTRd vd
p
p
Hypsometric Equation
![Page 12: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/12.jpg)
Thermodynamics M. D. Eastin
Derivation:
4. Performing the integration:
5. Dividing both sides by the gravitational acceleration at the surface (g0):
2
1
2
1 p
dpTRd vd
p
p
1
2vd12 p
plnTRΦΦ
1
2
0
vd
0
1
0
2
p
pln
g
TR
g
Φ
g
Φ
Hypsometric Equation
![Page 13: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/13.jpg)
Thermodynamics M. D. Eastin
Derivation:
6. Using the definition of geopotential height:
Defines the geopotential thickness (Z2 – Z1) between any two pressure levels (p1 and p2) in the atmosphere.
1
2
0
vd
0
1
0
2
p
pln
g
TR
g
Φ
g
Φ
1
2
0
vd12 p
pln
g
TRZZ
Hypsometric Equation
HypsometricEquation
![Page 14: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/14.jpg)
Thermodynamics M. D. Eastin
Interpretation:
• The thickness of a layer between two pressure levels is proportional to the mean virtual temperature of that layer.
• If Tv increases, the air between the two pressure levels expands and the layer becomes thicker
• If Tv decreases, the air between the two pressure levels compresses and the layer becomes thinner
1
2
0
vd12 p
pln
g
TRZZ
Hypsometric Equation
Black solid lines are pressure surfaces
Hurricane (warm core) Mid-latitude Low (cold core)
![Page 15: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/15.jpg)
Thermodynamics M. D. Eastin
Interpretation:
Hypsometric Equation
Layer 1:
Layer 2:
p2
p1
p1
p2
Which layer has the warmest mean virtual temperature?
+Z
+Z
![Page 16: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/16.jpg)
Thermodynamics M. D. Eastin
Application: Computing the Thickness of a Layer
A sounding balloon launched last week at Greensboro, NC measured a mean temperature of 10ºC and a mean specific humidity of 6.0 g/kg between the 700 and 500 mb pressure levels. What is the geopotential thickness between these two pressure levels?
T = 10ºC = 283 Kq = 6.0 g/kg = 0.006
p1 = 700 mbp2 = 500 mb
g0 = 9.81 m/s2
Rd = 287 J /kg K
1. Compute the mean Tv → Tv = 284.16 K
2. Compute the layer thickness (Z2 – Z1) → Z2 – Z1 = 2797.2 m
Hypsometric Equation
1
2
0
vd12 p
pln
g
TRZZ
T0.61q)(1Tv
![Page 17: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/17.jpg)
Thermodynamics M. D. Eastin
Application: Computing the Height of a Pressure Surface
Last week the surface pressure measured at the Charlotte airport was 1024 mb with a mean temperature and specific humidity of 21ºC and 11 g/kg, respectively, below cloud base. Calculate the geopotential height of the 1000 mb pressure surface.
T = 21ºC = 294 Kq = 11.0 g/kg = 0.011
p1 = 1024 mbp2 = 1000 mb
Z1 = 0 m (at the surface)Z2 = ???
g0 = 9.81 m/s2
Rd = 287 J /kg K
1. Compute the mean Tv → Tv = 295.97 K
2. Compute the height of 1000 mb (Z2) → Z2 = 198.9 m
Hypsometric Equation
1
2
0
vd12 p
pln
g
TRZZ
T0.61q)(1Tv
![Page 18: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/18.jpg)
Thermodynamics M. D. Eastin
Application: Reduction of Pressure to Sea Level
• In mountainous regions, the difference in surface pressure from one observing station to the next is largely due to elevation changes
• In weather forecasting, we need to isolate that part of the pressure field that is due to the passage of weather systems (i.e., “Highs” and “Lows”)
• We do this by adjusting all observed surface pressures (psfc) to a common reference level → sea level (where Z = 0 m)
Hypsometric Equation
850 mb
600 mb
700 mb
400 mb
500 mb
Denver
Aspen
Kathmandu
![Page 19: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/19.jpg)
Thermodynamics M. D. Eastin
Application: Reduction of Pressure to Sea Level
Last week the surface pressure measured in Asheville, NC was 934 mb with a surface temperature and specific humidity of 14ºC and 8 g/kg, respectively. If the elevation of Asheville is 650 meters above sea level, compute the surface pressure reduced to sea level.
T = 14ºC = 287 Kq = 8.0 g/kg = 0.008
p1 = ??? (at sea level)p2 = 934 mb (at ground level)
Z1 = 0 m (sea level)Z2 = 650 m (ground elevation)
g0 = 9.81 m/s2
Rd = 287 J /kg K
1. Compute the surface Tv → Tv = 288.40 K2. Solve the hypsometric equation for p1 (at sea level)3. Compute the sea level pressure (p1) → p1 = 1009 mb
Hypsometric Equation
1
2
0
vd12 p
pln
g
TRZZ
T0.61q)(1Tv
![Page 20: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/20.jpg)
Thermodynamics M. D. Eastin
Application: Reduction of Pressure to Sea Level
• All pressures plotted on surface weather maps have been “reduced to sea level”
Hypsometric Equation
![Page 21: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/21.jpg)
Thermodynamics M. D. Eastin
In Class ActivityLayer Thickness:
Observations from yesterday’s Charleston, SC sounding:
Pressure (mb) Temperature (ºC) Specific Humidity (g/kg) 850 10.4 9.2 700 1.8 3.5
Compute the thickness of the 850-700 mb layer
Reduction of Pressure to Sea Level:
Observations from the Charlotte Airport: Z = 237 m (elevation above sea level) p = 983 mbT = 10.5ºCq = 15.6 g/kg
Compute the surface pressure reduced to sea level
Write your answers on a sheet of paper and turn in by the end of class…
![Page 22: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/22.jpg)
Thermodynamics M. D. Eastin
Summary:
• Review of the Atmospheric Vertical Structure
• Hydrostatic Equation
• Geopotential Height• Application
• Hypsometric Equation• Applications• Layer Thickness• Heights of Isobaric Surfaces• Reduction of Surface Pressure to Sea Level
Hydrostatics
![Page 23: ThermodynamicsM. D. Eastin We need to understand the environment around a moist air parcel in order to determine whether it will rise or sink through the](https://reader035.vdocuments.mx/reader035/viewer/2022062713/56649cbb5503460f9498398d/html5/thumbnails/23.jpg)
Thermodynamics M. D. Eastin
References
Houze, R. A. Jr., 1993: Cloud Dynamics, Academic Press, New York, 573 pp.
Markowski, P. M., and Y. Richardson, 2010: Mesoscale Meteorology in Midlatitudes, Wiley Publishing, 397 pp.
Petty, G. W., 2008: A First Course in Atmospheric Thermodynamics, Sundog Publishing, 336 pp.
Tsonis, A. A., 2007: An Introduction to Atmospheric Thermodynamics, Cambridge Press, 197 pp. Wallace, J. M., and P. V. Hobbs, 1977: Atmospheric Science: An Introductory Survey, Academic Press, New York, 467 pp.