presentation slides for chapter 20 of fundamentals of atmospheric modeling 2 nd edition
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Presentation Slides for Chapter 20 of Fundamentals of Atmospheric Modeling 2 nd Edition. Mark Z. Jacobson Department of Civil & Environmental Engineering Stanford University Stanford, CA 94305-4020 [email protected] March 10, 2005. Particle Sedimentation. - PowerPoint PPT PresentationTRANSCRIPT
Presentation Slides for
Chapter 20of
Fundamentals of Atmospheric Modeling 2nd Edition
Mark Z. JacobsonDepartment of Civil & Environmental Engineering
Stanford UniversityStanford, CA [email protected]
March 10, 2005
Particle Sedimentation
Fig. 20.1
Drag
Gravity
Vertical forces acting on a particle
Drag and Gravitational ForcesDrag during Stokes flow (20.1)
Where particle radius > mean free path of air molecule (e.g., 68 nm) but small enough so its inertial force < viscous force.
Drag during slip flow (20.2)Particle radius < mean free path of an air molecule
FD =6πri ηaVf,i
FD =6πri ηaVf,i
Gi=
6πriηaVf,i
1+Kna,i ′ A + ′ B exp− ′ C Kna,i−1
( )⎡ ⎣
⎤ ⎦
Kna,i =λari
Knudsen number of particle in air
Particle Sedimentation
Equate gravity with drag to estimate fall speed (20.4)
Small particlesLess resistance to motion ---> diffusion and fall speed enhanced at small particle sizes
Large particlesFall speed decreases due to physical properties effect --> need to correct fall speed for large particles
Vf,iest=
2ri2 ρp−ρa( )g
9ηaGi
Gravitational force (20.3)
FG =43
πri3 ρp −ρa( )g
Estimated Reynolds NumberEstimate Reynolds number from estimated fall speed. (20.4)
Recalculate Reynolds number for three flow regimes
• slip flow around a rigid sphere ( «1-20 m diameter)
• continuum flow around a rigid sphere (20 m - 1 mm)
• continuum flow around equilibrium-shaped drop (1-5 mm)
Reiest=
2riVf,iest
νa
Final Reynolds Number (20.6)
Parameters affected by physical properties (e.g., temperature, density, viscosity, surface tension, gravity) (20.7)
Reifinal=
2riVf,iest νa Rei
est<0.01
Gi expB0 +B1X +B2X2 +...( ) 0.01<Reiest<300
NP16Gi expE0+E1Y +E2Y2+...( ) Rei
est>300
⎧
⎨
⎪ ⎪ ⎪
⎩
⎪ ⎪ ⎪
X =ln32ri
3 ρp −ρa( )ρag
3ηa2
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥
Y =ln43
N BoNP16⎡
⎣ ⎢ ⎤ ⎦ ⎥
Physical Properties CorrectionPhysical property number (20.8)
Bond number (20.8)
Final fall speed from final Reynolds number (20.9)
N p =σw/a
3 ρa2
ηa4 ρp −ρa( )g
N Bo=4ri
2 ρp−ρa( )g
σw/a
Vf,i =Vf,ifinal=
Reifinalνa2ri
Sedimentation Times
Table 20.2
Time for a particle (or gas molecule for the smallest size) to fall 1 km in the atmosphere due to sedimentation
Diameter
(m)
Time to Fall 1 km
Diameter
(m)
Time to Fall 1 km
0.0005 9630 y 4 23 d
0.02 226 y 5 14.5 d
0.1 36 y 10 3.6 d
0.5 3.2 y 20 23 h
1 326 d 100 1.1 h
2 89 d 1000 4 m
3 41 d 5000 1.8 m
Dry DepositionDry deposition
Removal of gas molecules or particles from the air when they stick to or react with a surface
Gas dry deposition speed (20.10)
Particle dry deposition speed (20.11)
Vd,gas= Ra+Rb +Rs( )−1
Vd,part,i = Ra +Rb+RaRbVf,i( )−1
+Vf,i
Dry Deposition Resistances
Fig. 20.2
zr
Ra
Rb
Rs
Dry Deposition ResistancesAerodynamic resistance (20.12)
Resistance to diffusion in laminar sublayer (20.14)
Particle and gas Schmidt numbers, Prandtl number (15.36)
Ra =
φhdzzz0,q
zr∫ku*
Rb =lnz0,mz0,q
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
Sc Pr( )2 3
ku*
Scpi =νaDpi
Scq =νaDq
Pr =ηacp,m
κa
Surface ResistanceSurface resistance due to biological interactions (20.15)
Stomatal resistance (20.16)Resistance to entering openings in leaf surfaces
Leaf mesophyll resistance (20.17)Resistance to dissolving in or reacting with water within leaves
Rs =1
Rstom+Rmeso+
1Rcut
+1
Rconv+Rexp+
1Rcanp+Rsoil
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
−1
Rstom,q =Rmin1+200
Sf +0.1
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
2⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥
400
Ta,c 40−Ta,c( )
DvDq
Rmeso,q =Hq
*
3000+100f0,q
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
−1
Surface ResistanceResistance to deposition on leaf cuticles (waxy surface) (20.18)
Resistance to buoyant convection in canopy (20.19)
Resistance to deposition on bark, exposed surfaces (20.20)
Rconv=1001+1000
Sf +10
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
11+1000st
Rsurf,q =10−5Hq
*
Rsurf,SO2+
f0,qRsurf,O3
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
−1
Rcut=Rcut,dry,q =Rcut,0 10−5Hq* + f0,q( )
−1
Surface ResistanceIn-canopy resistance (20.21)
Accounts for canopy leaf density
One-sided leaf area index (LT)Integrate foliage area density from surface to height hc
Foliage area densityArea of plant surface per unit volume of space. Thus, the leaf-area index measures canopy area density
Rcanp=bchcLT
u*
Resistance to deposition on soil and leaf litter at ground (20.22)
Rsoil,q =10−5Hq
*
Rsoil,SO2
+f0,q
Rsoil,O3
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
−1
Dry Deposition, Sedimentation Speeds
Fig. 20.3
10
-6
10
-4
10
-2
10
0
10
2
10
4
0.01 0.1 1 10 100 1000
Speed (cm s
-1
)
Particle diameter ( )m
-Dry deposition
speed without
sedimentation
Sedimentation speed
-Total dry deposition
speed
Spe
ed (
cm/s
)
Several Parameters Versus Size
Fig. 20.4
10
-11
10
-7
10
-3
10
1
10
5
0.01 0.1 1 10 100 1000
Particle diameter ( )m
Knudsen
number
- ( Total dry deposition speed cm s
-1
)
Reynolds
number
(Diffusion coefficient cm
2
s
-1
)
Gas Dry Deposition Speeds
Fig. 20.5a,b
10
-3
10
-2
10
-1
10
0
10
1
0 10 20 30 40 50
10 g/mol, 10 m/s
130 g/mol, 10 m/s
10 g/mol, 0 m/s
130 g/mol, 0 m/s
Dry deposition speed (cm s
-1
)
Surface resistance (s cm
-1
)
(a) z0,m=3 m
Dry
dep
osit
ion
spee
d (c
m/s
)
10
-2
10
-1
10
0
10
1
0 10 20 30 40 50
10 g/mol, 10 m/s
130 g/mol, 10 m/s
10 g/mol, 0 m/s
130 g/mol, 0 m/s
Dry deposition speed (cm s
-1
)
Surface resistance (s cm
-1
)
(b) z0,m=0.01 m
Dry
dep
osit
ion
spee
d (c
m/s
)
Air-Sea FluxesChange in concentration of a gas at the air-sea interface (20.23)
Mole concentration of a gas (20.24)
Mole concentration of a gas dissolved in seawater (20.25)
Cq,t =Cq,t−h +hVd,gas,q
Δza
cq,T,t−h′ H q
−Cq,t−h⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
Cq =pq
R*T
cq,T =ρdwmq,T
Air-Sea FluxesDissolution and dissociation of carbon dioxide (20.26)
Dimensionless effective Henry’s constant (20.27)
Surface resistance of gas over the ocean (20.34)=chemical reactivity (1 for CO2; large for HCl)
Rs,q =1
αr,q ′ H qkw,q
CO2
(g) + H2
O(aq) H2
CO3
(aq) H+
+ HCO3
-
2H+
+ CO3
2-
HK
1K
2
′ H q =ρdwR*THqs 1+
K1,qs
mH+1+
K2,qs
mH+
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
Air-Sea FluxesAir-sea gas transfer speed (two parameterizations) (20.35,7)
Schmidt number ratio in water (20.36)Schmidt number is kinematic viscosity / diffusion coefficient
Srw,q =Scw,CO2,20oC
Scw,q,Ts,c
kw,q =0.31vh,10
2Srw,q12
3600
kw,q =1
3600
0.17vh,10Srw,q2 3 vh,10 ≤3.6 m s-1
0.612Srw,q23 + 2.85vh,10 −10.262( )Srw,q
12 3.6 m s-1<vh,10 ≤13 m s-1
0.612Srw,q23 + 5.9vh,10 −49.912( )Srw,q
12 13 m s-1<vh,10
⎧
⎨
⎪ ⎪
⎩
⎪ ⎪
Solution to Air-Sea Flux EquationsImplicit equation for atmosphere-ocean transfer (20.23)
Solution to gas concentration (20.39)
Cq,t =Cq,t−h +hVd,gas,q
Δza
cq,T,t′ H q
−Cq,t⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
Cq,t =
Cq,t−h +hVd,gas,q
Δza
cq,T,t′ H q
1+hVd,gas,q
Δza
Solution to Air-Sea Flux EquationsSubstitute into mass balance equation (20.40)
Solution to ocean concentration (20.41)
cq,T,tDl +Cq,tΔza =cq,T,t−hDl +Cq,t−hΔza
cq,T,t =
cq,T,t−h +hVd,gas,qCq,t−h
Dl1+
hVd,gas,qΔza
⎛
⎝ ⎜
⎞
⎠ ⎟
⎡
⎣ ⎢
⎤
⎦ ⎥
1+hVd,gas,q
Dl ′ H q1+
hVd,gas,qΔza
⎛
⎝ ⎜
⎞
⎠ ⎟
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
Stability TestAir-sea transfer plus chemistry of CO2 with time steps of 6 h to 1 y
7.4
7.6
7.8
8
8.2
0.01 0.1 1 10 100
6 h
1 d
10 d
100 d
1 y
pH
Year of simulation
(c)
pH
1-D Ocean, 2-Box Atmosphere Case
Ocean Chemistry System
Na+
Ca2+
Mg2+
K+
H+
Sr2+
Li+
NH4+
Cl-
Br-
OH-
HSO4-
HCO3-
CO32-
B(OH)4-
SiO(OH)3-
H 2PO4-
HPO42-
PO43-
HNO3-
H2O(aq)H2CO4(aq)H2SO4(aq)H3PO4(aq)HF(aq)H2S(aq)
CaCO3(s)& other solids
Chemicals treated in simulations discussed next
Modeled CO2(g) and Modeled v Measured Ocean pH 1751-2003
280
300
320
340
360
380
8.1
8.15
8.2
8.25
8.3
1750 1800 1850 1900 1950 2000
Data
Model
pH-500Tg-C/yBBemis
CO
2
mixing ratio (ppmv)
Surface ocean pH
Year
CO
2(g)
mix
ing
rati
o (p
pmv)
Surface ocean pH
Fig. 20.6
Modeled Ocean Profiles 1751; 2004
8 8.1 8.2 8.3
0
500
1000
1500
2000
1751
2004
pH
Depth (m)
(a)
Dep
th (
m)
1.9 2 2.1 2.2
0
500
1000
1500
2000
1751
2004
Total inorganic carbon (mmol/kg)
Depth (m)
(b)
Dep
th (
m)
0 5 10 15 20
0
500
1000
1500
2000
S-30 (1751)
S-30 (2004)
Tc
S-30 (ppth-mass) and T
c
(
o
C)
Depth (m)
(d)
Dep
th (
m)
Jacobson, JGR 2005
Modeled Ocean Profiles 2004; 2104 Under SRES A1B Emission Scenario
7.8 7.9 8 8.1 8.2
0
500
1000
1500
2000
2004
2104
pH
Depth (m)
(a)
1.9 2 2.1 2.2 2.3
0
500
1000
1500
2000
2004
2104
Total inorganic carbon (mmol/kg)
Depth (m)
(b)
Dep
th (
m)
Dep
th (
m)
Sensitivity of Future Results
300
400
500
600
700
800
900
7.8
7.9
8
8.1
8.2
2000 2020 2040 2060 2080 2100
T=292.25
T=289.25
T=286.25
pH
CO
2
mixing ratio (ppmv)
Surface ocean pH
Year
(b)
CO
2(g)
mix
ing
rati
o Surface ocean pH
To temperature (K)
300
400
500
600
700
800
900
7.8
7.9
8
8.1
8.2
2000 2020 2040 2060 2080 2100
u=1
u=3
u=5
CO
2
mixing ratio (ppmv)
Surface ocean pH
Year
(a)
Surface ocean pH
To wind speed (m/s)
CO
2(g)
mix
ing
rati
o
300
400
500
600
700
800
900
1000
7.7
7.8
7.9
8
8.1
8.2
2000 2020 2040 2060 2080 2100
D=0.00001
D=000063
D=0.0001
CO
2
mixing ratio (ppmv)
Surface ocean pH
Year
(c)
To mean oceandiffusion (m2/s)
CO
2(g)
mix
ing
rati
o Surface ocean pH
300
400
500
600
700
800
900
7.7
7.8
7.9
8
8.1
8.2
2000 2020 2040 2060 2080 2100
BB=0
BB=500
CO
2
mixing ratio (ppmv)
Surface ocean pH
Year
(d)
To biomass burningemission (Tg-C/yr)
CO
2(g)
mix
ing
rati
o Surface ocean pH
Sensitivity of Future Results
Effect of CO2(g) on Atmospheric Acids
10
-18
10
-16
10
-14
10
-12
10
-10
10
-8
10
-6
2000 2020 2040 2060 2080 2100
Ammonia x (-1)
Nitric acid
Hydrochloric acid
Sulfur dioxide
Mixing ratio (ppbv)
Year of simulation
Diff. between A1B base and today
(d)
Mix
ing
rati
o (p
pbv)
Assumes trace gases initialized but not emitted
Atmospheric NH3 Without and With Ocean Acidification
0
0.2
0.4
0.6
0.8
1
1.2
2000 2020 2040 2060 2080 2100
Current CO2, u=3
Future CO2, u=3
Current CO2, u=8
Future CO2, u=8
Mixing ratio (ppbv)
Year
NH3
Mix
ing
rati
o (p
pbv)
Assumes NH3 initialized and continuously emitted
Air-Sea Exchange Summary• Globally-averaged surface ocean pH may have decreased
from about 8.25 to 8.14 between 1751 and 2004
• Under the SREAS A1B emission scenario, pH may decrease to 7.85 by 2100, for an increase in the hydrogen ion by a factor of 2.5 from1751 to 2100.
• Ocean acidification may slightly increase concentrations of atmospheric acids and more significantly decrease those of bases, thereby affecting cloud and radiative properties and ocean nutrient availability.
Effect of Calcite and AragonitePrecipitation reaction forming calcite/aragonite (20.42)
Formation of solid when (20.43)
Molality of carbonate ion (20.44)
Ca2++CO32-CaCO3(s)
mCa2+mCO32−γ
Ca2+,CO23−
2 >Keq T( )
mCO32− =
cCO2,T
ρsw
K1,CO2K2,CO2
mH+mH++K1,CO2mH+ +K1,CO2
K2,CO2
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟