* Reading Assignments:

All sections

7. Hydrostatic Equilibrium

7.1 Effective gravity

• Radial gravitation by the planet’s mass

• Centrifugal acceleration due to rotation of the reference frame

• Anisotropic contributions

srr zekgg 2

7.2 Geopotential and Geopotential height

* Geopotential

is the specific work performed against gravity to displacea unit mass of air parcel from the sea level to a height of Z.

Zdzg

0

* Geopotential height

ZgdzZ

08.9

1

8.9

is nearly identical to geometric height, but has different physicalmeaning.

7.3 Hypsometric equation

1

212 ln

p

pHzzz

g

TRH

2

1

2

1

ln

ln

p

p

p

p

pd

pTdT

7.4 Stratification of environment

The environmental lapse rate:

dz

dT

* Layer of constant lapse rate

dz

zdTzTzT s

)(,)(

g

R

s

s

p

pTz 1

* Isothermal Layer

sTconstzT )(

p

p

g

RTz ss ln

* Layer of Homogeneous Density

sconstz )(

g

ppz

s

s

1.One meteorology station is located at 250 m above the sea level. When it measures the pressure and temperature at 982 hPa and -12oC, another station has the pressure and temperature at 975 hPa and -14oC. What is the height of the this station above the sea level?

2. One of the weather map is the 1000-500 mb thickness map. The contour lines represent the distance between these two pressure surfaces. a) Use the hydrostatic equation to derive a relationship between the 1000-500mb thickness and the average temperature in the layer of 1000-500mb.

b) The 1000-500 mb thickness is predicted to increase from 5280m to 5460m at a given station. Assuming that the lapse rate remains constant, what change in surface temperature would you predicted? (Assume the amount of moisture in the air does not change.)

3. A moist air parcel initially is at 500 m. Due to the advection, the pressure of this air parcel decreases 20 mb. Find if there is cloud forming during this process. Assuming the process is adiabatic; the vapor pressure of the air parcel is 8 mb at 500m and remains constant. The vertical distribution of atmospheric pressure and temperature are

respectively, where P is in mb, T in K, and z in m.

,006.0280)(,1000)( 9000 zzTandezpz

7.5 Lagrangian Interpretation of stratification

7.5.1 Adiabatic Stratification

Describing the atmospheric stratification in terms of the behaviorof individual air parcels

The atmospheric potential temperature is uniformly distributedwith height,

The environmental lapse rate is constant and is equal to thedry adiabatic rate,

* For unsaturated moist air

constz )(

constd

7.5.2 Diabatic Stratification

0

Air parcels interact with the environment through the heat transfer when they move both horizontally and vertically.

When the atmospheric temperature increases with height,

the potential temperature increases with height.

0,0

0,0

dTq

dTq

Meteorology 341 Homework (7)1. Using the following sounding records, calculate the virtual temperature (Tv) and height correspond to each pressure level. The surface pressure, temperature and mixing ratio are 1008mb, 21.9 oC, and 9.6 gkg-1 , respectively.

P (mb) T (oC) q (gkg-1) Tv (K) z (m)1008 21.9 9.6 0 989 20.9 8.4 955 19.5 6.8 898 16.2 6.2

2. On a certain day, the atmosphere has a temperature T0 of 20oC and a pressurep0 of 1000 hPa at the surface (z0=0). The lapse rate is 0=6 K/km from the surface to 3 km altitude; 1=3 K/km from 3 km to 6 km altitude. Find the pressure p at an altitude of 5 km.

3. A moist air parcel initially is at 500 m. Due to the advection, the pressure of this air parcel decreases 20 mb. Find if there is cloud forming during this process. Assuming the process is adiabatic; the vapor pressure of the air parcel is 8 mb at500m and remains constant. The vertical distribution of atmospheric pressure and temperature are respectively.

4. Problem 7 on page 169

,006.0280)(,1000)( 9000 zzTandezpz