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QUESTIONS

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2. Torricelli used mercury for his barometer, but a column barometer could be ... level, with mercury rfluid= 13.6 g ... Natural Surface: terrestrial and marine ... – PowerPoint PPT presentation

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Title: QUESTIONS


1
QUESTIONS
  • The definition of "1 atmosphere" is 1013 hPa, the
    average atmospheric pressure at sea level. But
    when we computed the mass of the atmosphere, we
    used a mean atmospheric pressure of 984 hPa. Why?
  • Torricelli used mercury for his barometer, but a
    column barometer could be constructed using any
    fluid, with the height of the column measuring
    atmospheric pressure given by h P/rfluidg
  • At sea level, with mercury rfluid 13.6 g cm-3 e
    h 76 cm
  • with water rfluid 1.0
    g cm-3 e h 1013 cm
  • Now what about using air as a fluid?
  • with air rfluid 1.2 kg m-3 e h 8.6
    km
  • which means that the atmosphere should extend
    only to 8.6 km, with
  • vacuum above! WHAT IS THE FLAW IN THIS
    REASONING?

2
CHAPTER 3 SIMPLE MODELS
The atmospheric evolution of a species X is given
by the continuity equation
deposition
transport (flux divergence U is wind vector)
emission
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
3
TYPES OF SOURCES
Natural Surface terrestrial and marine highly
variable in space and time, influenced by season,
T, pH, nutrients eg. oceanic sources estimated
by measuring local supersaturation in water and
using a model for gas-exchange across interface
f(T, wind velocity.) Natural In situ eg.
lightning (NOx) N2? NOx, volcanoes (SO2,
aerosols) ? generally smaller than surface
sources on global scale but important b/c
material is injected into middle/upper
troposphere where lifetimes are
longer Anthropogenic Surface eg. mobile,
industry, fires ? good inventories for
combustion products (CO, NOx, SO2) for US and
EU Anthropogenic In situ eg. aircraft, tall
stacks Secondary sources tropospheric
photochemistry Injection from the stratosphere
transport of products of UV dissociation (NOx,
O3) transported into troposphere (strongest at
midlatitudes, important source of NOx in the UT)
4
TYPES OF SINKS
  • Wet Deposition falling hydrometeors (rain, snow,
    sleet) carry trace species to the surface
  • in-cloud nucleation (depending on solubility)
  • scavenging (depends on size, chemical
    composition)
  • Soluble and reactive trace gases are more readily
    removed
  • Generally assume that depletion is proportional
    to the conc (1st order loss)
  • Dry Deposition gravitational settling turbulent
    transport
  • particles gt 20 µm ? gravity (sedimentation)
  • particles lt 1 µm ? diffusion
  • ? rates depend on reactivity of gas, turbulent
    transport, stomatal resistance and together
    define a deposition velocity (vd)
  • In situ removal
  • chain-terminating rxn OH?HO2? ? H2O O2
  • change of phase SO2 ? SO42- (gas ? dissolved
    salt)

Typical values vd Particles0.1-1 cm/s Gases
vary with srf and chemical nature (eg. 1 cm/s for
SO2)
5
RESISTANCE MODEL FOR DRY DEPOSITION
Deposition Flux
Fd -vdC
Vd deposition velocity (m/s) C concentration
Use a resistance analogy, where rTvd-1
C3
For gases at steady state can relate overall flux
to the concentration differences and resistances
across the layers
0
0
Aerodynamic resistance ra
C2
Quasi-laminar layer resistance rb
C1
Canopy resistance rc
C00
For particles, assume that canopy resistance is
zero (so now C10), and need to include particle
settling (settling velocityvs) which operates in
parallel with existing resistances. End result
Reference Seinfeld Pandis, Chap 19
6
ONE-BOX MODEL
Atmospheric box spatial distribution of X
within box is not resolved
Chemical production
Chemical loss
Inflow Fin
Outflow Fout
X
L
P
D
E
Flux units usually mass/time/area
Deposition
Emission
(turnover time)
Lifetimes add in parallel
(because fluxes add linearly)
Loss rate constants add in series
7
ASIDE LIFETIME VS RADIOACTIVE HALF-LIFE
Both express characteristic times of decay, what
is the relationship?
½ life
8
EXAMPLE GLOBAL BOX MODEL FOR CO2 reservoirs in
PgC, flows in Pg C yr-1
atmospheric content (mid 80s) 730 Pg C of
CO2 annual exchange land 120 Pg C yr-1 annual
exchange ocean 90 Pg C yr-1
(now 816 PgCO2)
Human Perturbation
IPCC 2001
9
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 gtgt t, then dm/dt g 0
and mg S/k "steady state"
10
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)
11
Illustrates long time scale for interhemispheric
exchange can use 2-box model to place
constraints on sources/sinks in each hemisphere
12
TWO-BOX MODEL(with loss)
mo m1m2
T
Q
m1
m2
S1
S2
Lifetimes
If at steady state sinkssources, so can also
write
Now if define aT/Q, then can say that
Maximum a is 1 (all material from reservoir 1 is
transferred to reservoir 2), and therefore
turnover time for combined reservoir is the sum
of turnover times for individual reservoirs. For
other values of a, the turnover time of the
combined reservoir is reduced.
13
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

14
EULERIAN MODEL EXAMPLE
Summertime Surface Ozone Simulation
Here the continuity equation is solved for each
2?x2.5? grid box. They are inherently assumed to
be well-mixed
Fiore et al., 2002
15
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
16
PUFF MODEL FOLLOW AIR PARCEL MOVING WITH WIND
X(x, t)
In the moving puff,
wind
X(xo, to)
no transport terms! (theyre implicit in the
trajectory)
Application to the chemical evolution of an
isolated pollution plume
Xb
X
In pollution plume,
17
COLUMN MODEL FOR TRANSPORT ACROSS URBAN AIRSHED
Temperature inversion (defines mixing depth)
Emission E
In column moving across city,
Solution
X
x
L
0
18
LAGRANGIAN RESEARCH MODELS FOLLOW LARGE NUMBERS
OF INDIVIDUAL PUFFS
C(x, toDt)
Individual puff trajectories over time Dt
  • ADVANTAGES OVER EULERIAN MODELS
  • Computational performance (focus puffs on region
    of interest)
  • No numerical diffusion
  • DISADVANTAGES
  • Cant handle mixing between puffs a cant
    handle nonlinear processes
  • Spatial coverage by puffs may be inadequate

C(x, to)
Concentration field at time t defined by n puffs
19
FLEXPART A LAGRANGIAN MODEL
Retroplume (20 days) Trinidad Head, Bermuda
x Emissions Map (NOx)
Region of Influence
But no chemistry, deposition, convection here
Cooper et al., 2005
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