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CHAPTER 2. VERTICAL STRUCTURE OF THE ATMOSPHEREPowerPoint Presentation

CHAPTER 2. VERTICAL STRUCTURE OF THE ATMOSPHERE

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vacuum. h. A. B. CHAPTER 2. VERTICAL STRUCTURE OF THE ATMOSPHERE. Measurement of atmospheric pressure with the mercury barometer:. Atmospheric pressure P = P A = P B = r Hg gh. Mean sea-level pressure: P = 1.013x10 5 Pa = 1013 hPa

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h

A

B

CHAPTER 2. VERTICAL STRUCTURE OF THE ATMOSPHEREMeasurement of atmospheric pressure with the mercury barometer:

Atmospheric pressure P = PA = PB = rHggh

Mean sea-level pressure:

P = 1.013x105 Pa = 1013 hPa

= 1013 mb

= 1 atm

= 760 mm Hg (torr)

“SEA LEVEL” PRESSURE MAP (2/5/13, 13Z)

weather.unisys.com

SEA-LEVEL PRESSURE CAN’T VARY OVER MORE THAN A NARROW RANGE: 1013 ± 50 hPa

Consider a pressure gradient at sea level operating on an elementary air parcel dxdydz:

P(x)

P(x+dx)

Pressure-gradient force

Vertical area

dydz

Acceleration

For DP = 10 hPa over Dx = 100 km, g ~ 10-2 m s-2 a 100 km/h wind in 3 h!

Effect of wind is to transport air to area of lower pressure a dampen DP

On mountains, however, the surface pressure is lower, and the pressure-gradient force along the Earth surface is balanced by gravity:

P(z+Dz)

P-gradient

- This is why weather maps show “sea level” isobars even over land; the fictitious “sea-level” pressure assumes an air column to be present between the surface and sea level

gravity

P(z)

MASS RANGE: 1013 ± 50 hPama OF THE ATMOSPHERE

Mean pressure at Earth's surface:

984 hPa

Radius of Earth:

6380 km

Total number of moles of air in atmosphere:

Mol. wt. of air: 29 g mole-1 = 0.029 kg mole-1

CLAUSIUS-CLAPEYRON EQUATION: RANGE: 1013 ± 50 hPaPH2O, SAT = f(T)

A = 6.11 hPa

B = - 5310 K

To = 273 K

PH2O,SAT (hPa)

T (K)

VERTICAL PROFILES OF PRESSURE AND TEMPERATURE RANGE: 1013 ± 50 hPaMean values for 30oN, March

Stratopause

Tropopause

Barometric law (variation of pressure with altitude) RANGE: 1013 ± 50 hPa

- Consider elementary slab of atmosphere:

P(z+dz)

P(z)

hydrostatic

equation

unit area

Ideal gas law:

Assume T = constant, integrate:

Barometric law

Application of barometric law: the sea-breeze effect RANGE: 1013 ± 50 hPa

CHAPTER 3: SIMPLE MODELS RANGE: 1013 ± 50 hPa

The atmospheric evolution of a species X is given by the continuity equation

deposition

emission

transport

(flux divergence;

U is wind vector)

local change in concentration

with time

chemical production and loss

(depends on concentrations

of other species)

This equation cannot be solved exactly e need to construct model (simplified representation of complex system)

Improve model, characterize its error

Design observational system to test model

Design model; make assumptions needed

to simplify equations and make them solvable

Evaluate model with observations

Define problem of interest

Apply model:

make hypotheses, predictions

Atmospheric “box”; RANGE: 1013 ± 50 hPa

spatial distribution of X within box is not resolved

ONE-BOX MODELChemical

production

Chemical

loss

Inflow Fin

Outflow Fout

X

L

P

D

E

Deposition

Emission

Lifetimes add in parallel:

Loss rate constants add in series:

NO RANGE: 1013 ± 50 hPa2 emitted by combustion, has atmospheric lifetime ~ 1 day:strong gradients away from source regions

Satellite observations of NO2 columns

CO emitted by combustion, has atmospheric lifetime ~ 2 months:mixing around latitude bands

Satellite observations

CO months:2 emitted by combustion, has atmospheric lifetime ~ 100 years:global mixing

Assimilated observations

SPECIAL CASE: months:SPECIES WITH CONSTANT SOURCE, 1st ORDER SINK

Steady state solution (dm/dt = 0)

Initial condition m(0)

Characteristic time t = 1/k for

- reaching steady state
- decay of initial condition

If S, k are constant over t >> t, then dm/dt g0 and mg S/k: quasi steady state

TWO-BOX MODEL months:defines spatial gradient between two domains

F12

m2

m1

F21

Mass balance equations:

(similar equation for dm2/dt)

If mass exchange between boxes is first-order:

e system of two coupled ODEs (or algebraic equations if system is assumed to be at steady state)

LATITUDINAL GRADIENT OF CO months:2 , 2000-2012

Illustrates long time scale for interhemispheric exchange;

use 2-box model to constrain CO2 sources/sinks in each hemisphere

http://www.esrl.noaa.gov/gmd/ccgg/globalview/

EULERIAN months:RESEARCH MODELS SOLVE MASS BALANCE EQUATION IN 3-D ASSEMBLAGE OF GRIDBOXES

The mass balance equation is then the finite-difference approximation of the continuity equation.

Solve continuity equation for individual gridboxes

- Models can presently afford
~ 106 gridboxes

- In global models, this implies a horizontal resolution of 100-500 km in horizontal and ~ 1 km in vertical
- Drawbacks: “numerical diffusion”, computational expense

IN EULERIAN APPROACH, DESCRIBING THE EVOLUTION OF A POLLUTION PLUME REQUIRES A LARGE NUMBER OF GRIDBOXES

Fire plumes over

southern California,

25 Oct. 2003

A Lagrangian “puff” model offers a much simpler alternative

PUFF MODEL: FOLLOW AIR PARCEL MOVING WITH WIND POLLUTION PLUME REQUIRES A LARGE NUMBER OF GRIDBOXES

CX(x, t)

In the moving puff,

wind

CX(xo, to)

…no transport terms! (they’re implicit in the trajectory)

Application to the chemical evolution of an isolated pollution plume:

CX,b

CX

In pollution plume,

COLUMN MODEL FOR TRANSPORT ACROSS URBAN AIRSHED POLLUTION PLUME REQUIRES A LARGE NUMBER OF GRIDBOXES

Temperature inversion

(defines “mixing depth”)

Emission E

In column moving across city,

CX

x

0

L

LAGRANGIAN POLLUTION PLUME REQUIRES A LARGE NUMBER OF GRIDBOXES RESEARCH MODELS FOLLOW LARGE NUMBERS OF INDIVIDUAL “PUFFS”

C(x, to+Dt)

Individual puff trajectories

over time Dt

ADVANTAGES OVER EULERIAN MODELS:

- Computational performance (focus puffs on region of interest)
- No numerical diffusion
DISADVANTAGES:

- Can’t handle mixing between puffs a can’t handle nonlinear processes
- Spatial coverage by puffs may be inadequate

C(x, to)

Concentration field at time t defined by n puffs

LAGRANGIAN RECEPTOR-ORIENTED MODELING POLLUTION PLUME REQUIRES A LARGE NUMBER OF GRIDBOXES

Run Lagrangian model backward from receptor location,

with points released at receptor location only

backward in time

- Efficient cost-effective quantification of source influence distribution on receptor (“footprint”)

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