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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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chapter 2 vertical structure of the atmosphere

vacuum

h

A

B

CHAPTER 2. VERTICAL STRUCTURE OF THE ATMOSPHERE

Measurement 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 can t vary over more than a narrow range 1013 50 hpa
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 m a of the atmosphere
MASS ma 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

slide5

CLAUSIUS-CLAPEYRON EQUATION: PH2O, SAT = f(T)

A = 6.11 hPa

B = - 5310 K

To = 273 K

PH2O,SAT (hPa)

T (K)

barometric law variation of pressure with altitude
Barometric law (variation of pressure with altitude)
  • Consider elementary slab of atmosphere:

P(z+dz)

P(z)

hydrostatic

equation

unit area

Ideal gas law:

Assume T = constant, integrate:

Barometric law

chapter 3 simple models
CHAPTER 3: SIMPLE MODELS

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

one box model

Atmospheric “box”;

spatial distribution of X within box is not resolved

ONE-BOX MODEL

Chemical

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 2 emitted by combustion has atmospheric lifetime 1 day strong gradients away from source regions
NO2 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
CO emitted by combustion, has atmospheric lifetime ~ 2 months:mixing around latitude bands

Satellite observations

co 2 emitted by combustion has atmospheric lifetime 100 years global mixing
CO2 emitted by combustion, has atmospheric lifetime ~ 100 years:global mixing

Assimilated observations

special case species with constant source 1 st order sink
SPECIAL CASE: 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 defines spatial gradient between two domains
TWO-BOX MODELdefines 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)

slide17

LATITUDINAL GRADIENT OF CO2 , 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 research models solve mass balance equation in 3 d assemblage of gridboxes
EULERIAN 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
slide19
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
PUFF MODEL: FOLLOW AIR PARCEL MOVING WITH WIND

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
COLUMN MODEL FOR TRANSPORT ACROSS URBAN AIRSHED

Temperature inversion

(defines “mixing depth”)

Emission E

In column moving across city,

CX

x

0

L

lagrangian research models follow large numbers of individual puffs
LAGRANGIAN 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
LAGRANGIAN RECEPTOR-ORIENTED MODELING

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”)