mkep4 ss11 12 gas transfer
Post on 07-Jul-2018
218 Views
Preview:
TRANSCRIPT
-
8/18/2019 MKEP4 SS11 12 Gas Transfer
1/21
1
Master Course „Environmental Physics“ (MKEP4)
http://www.iup.uni-heidelberg.de/institut/studium/lehre/MKEP4/
12. Gas and Heat Transfer
between Air and Water
Summer Term 2011
Werner Aeschbach-Hertig
Institut für Umweltphysik
Lecture Program of MKEP4
Part 1: Introduction and Fundamentals (4 sessions)1. Introduction to Environmental Physics and the Earth System
2. Global energy balance and structure of the atmosphere
3. Stratification and convection in air and water
4. Trans ort rocesses
Part 2: Geophysical Fluid Dynamics (7 sessions)5. Introduction to Geophysical Fluid Dynamics
6. Navier-Stokes equation and geostrophic approximation
7. Geostrophic Flow and Vorticity
8. Turbulence
9. Turbulent transport and flow near boundaries10. Global circulation of the atmosphere
11. Global circulation of the ocean
Part 3: Other Compartments and Fields (4 sessions)12. Gas and heat transfer between air and water
13. Freshwater systems
14. Soil and Groundwater 15. The cryosphere
2
-
8/18/2019 MKEP4 SS11 12 Gas Transfer
2/21
2
Contents of Today's Lecture
Gas and heat transfer between air and water
• Heat exchange
Change of ocean heat content and temperature
• Gas solubility (Henry's law)
• Gas exchange: Stagnant laminar film model
Transfer velocity: Dependence on diffusion, Schmidt-no., wind
• Evaporation
3
Heat and Gas Exchange (Transfer)
Wind-wave facility at IUP
4
-
8/18/2019 MKEP4 SS11 12 Gas Transfer
3/21
3
Processes at the Air/Water Interface
http://www.whoi.edu/ooi_cgsn/page.do?pid=532785
Processes of Heat Transfer
The total heat flux Q tot [W/m2] from water (ocean, lakes, etc.) into
the atmosphere (upward) can be divided into 5 contributions:
net SW LWA LWW S LQ Q Q Q Q Q
thermal radiation
of the atmosphereconvection
sensible heat
6
(long wave, IR)
thermal radiation
of the water
(long wave, IR)
evaporation
(latent heat)
solar radiation
(short wave, VIS)
-
8/18/2019 MKEP4 SS11 12 Gas Transfer
4/21
4
0SW SW SWQ 1 Q 1 0.65B
Radiative Heat Fluxes
Solar radiation (short wave):
reflectivit of clear sk cloud cover
Parameterisations to estimate the radiative terms:
4LWA LW A AQ 1 T
17
water in SW
radiation
fraction
Long wave atmospheric radiation:
reflectivity of water
(in LW (IR), ≈0.03)
emissivity of
atmosphere
Parameterisation
= 5.67∙10‐8 W m‐2 K‐4
Stefan‐Boltzmann constant
2 A
A A1.24 1 0.17BT
4WLWW WQ T Long wave water radiation:
of emissivity A
:
emissivity of water (≈ 0.97)
water vapour
pressure in air
7
Non-Radiative Heat Fluxes
S air p S 10 W AQ c c u T T Convection:
latent heat of evap
cL, cS ≈ 0.001:
bulk transfer coefficients
for vapor and heat,
stabilit ‐de endent
specific heat of airwind
velocity
transfer
coefficients
L air e L 10 s W AQ L c u q T q Evaporation:
specific humidity of air
saturation specific humidity at TW
q = ρv / ρair= e / (RvTρair)
Estimate of latent flux:
w
E P Adt
eL e w
L dmQ L P
A dt
For P = 1 m/a: Q L = 71 W/m2
8
-
8/18/2019 MKEP4 SS11 12 Gas Transfer
5/21
5
Ocean – Atmosphere Heat Fluxes
Q LW = Q LWA + Q LWW
Marshall and Plumb, 2008 9
Seasonal Heat Fluxes
in a Lake
• Long-wave terms
(thermal radiation of air
and water) are largest
Q LWA
Q SW
contributions, but nearly
cancel
• Net effect in IR is a heatloss of the water
• Sensible heat flux is
u wards heat loss of
Q S
Q L
Q net
water) most of the time,
as usually TW > T A
• Net flux: Upwards in
winter, downwards in
summer
Q LWW
10
-
8/18/2019 MKEP4 SS11 12 Gas Transfer
6/21
6
Annual Mean Net Upward Heat Flux
Marshall and Plumb, 2008 11
Change of the Ocean Heat Content
Development of heat content of the upper ocean
1955 to 2003
Heat uptake of different compartments between
1955 and 1998 (in 1022 J)
from Levitus et al., 2005, Geophys. Res. Lett. 32, doi:10.1029/2004GL021592
These data are outdated due to recent corrections to ocean temperature data series ‐ see next slide.
12
-
8/18/2019 MKEP4 SS11 12 Gas Transfer
7/21
7
Change of the Ocean Heat Content
upper 700 m
old
Levitus et al., 2009. Geophys. Res.
Lett. 36: L07608,
doi:07610.01029/02008GL037155.
new
upper 700 m
upper 100 m
Domingues et al., 2008. Nature 453: 1090‐1093.
SST
http://www.nodc.noaa.gov/
OC5/3M_HEAT_CONTENT/
Trend global heat gain: 4.0∙1021 J/a = 1.3∙1014 W
AOcean = 3.6∙1014 m2
Imbalance: 0.35 W/m213
Imbalance of Global Radiation Budget
Hansen et al., 2005.
Science 308: 1431-1435.
Net radiative forcing in
2003 rel. to 1880:
Partly compensated by
warming of ~ 0.7 °C.
Global energy imbalance
in the year 2003:
+ 0.85 ± 0.15 W/m2
+ 1.80 ± 0.85 W/m2
14
Compare global energy
consumption in 2008:
4.7·1020 J/a = 1.5·1013 W
= 15 TW = 0.03 W/m2
(AEarth = 5.1∙1014 m2)
-
8/18/2019 MKEP4 SS11 12 Gas Transfer
8/21
8
Temperature Response of the Ocean
Simple box model (strictly applicable only to mixed surface layer):
Change of heat content Eth (resp. temperature T) of a well mixed
water body of volume V due to a heat flux Q through the surface A
Q A
th w wdE V c dT Ah c dT
thdE QAdt
w Ah c dT QAdt
V Th
w
dT 1 Q
dt h c
Eth
Example: Q net = 0.35 W/m2, h = 100 m: dT/dt = 0.026 K/a
(Note: cw = 4.18∙106 J m‐3 K‐1; 1 a = 3.15∙107 s) 15
Temperature Trends in the Ocean
IPCC, 4th Assessment Report, 2007 16
-
8/18/2019 MKEP4 SS11 12 Gas Transfer
9/21
9
Gases: Air/Water Solubility Equilibrium
Equilibrium:
different
concentrations
equal fluxes!
17
Gas Solubility in Water: Henry's Law
At equilibrium, the concentration cw of a gas in solution is propor‐
tional to its concentration cg (partial pressure p) in the gas phase:
KH: Henry coefficient ("constant")g H wc K c
If both concentrations molar (mol/L): KH dimensionless = K'HIn practice, many concentration units occur (mol/kg, mg/L, cm3STP/g, ….)
Conversion of units for cw in mol/L and p in atm via the ideal gas law:
gcn atm L pRT RTc K RT RTK
H wp cor
w wV mol c c
KH is the inverse of a solubility (large KH little gas dissolved)→ (Ostwald) solubility: L = 1/K'H (sometimes also defined as Henry const.)
w
g H
c 1L
c K
w
H
c 1
p K or
18
-
8/18/2019 MKEP4 SS11 12 Gas Transfer
10/21
10
Dependence of Solubi lity on T and S
KH (or L) is specific for each gas i and depends on temperature and salinity of the water: , ,H H iK K T S
Temperature epen ence o ows rom Van t Ho equat on:
H2
d lnK H
dT RT
H: Enthalpy change for dissolution(H = U + pV)
Integrated with const. H: H H 00
H 1 1K T K T exp
R T T
Salinity dependence ("salting out") described by Setschenow
relation:
k: Setschenow or salting coefficient
kSH HK T,S K T,0 e
19
Temperature Dependence of Solubil ities
0.9
1
0.6
0.7
0.8
He NeAr Kr
c i (
T ) / c i ( 0 ° C )
L i (
T ) / L
i ( 0 ° C )
0.4
.
0 5 10 15 20 25 30
e
N2
O2
T [°C]
20
-
8/18/2019 MKEP4 SS11 12 Gas Transfer
11/21
11
Salinity Dependence of Solubi lities
0.95
1
He NeAr Kr
0.8
0.85
0.9
Xe
N2
O2
c i (
S ) / c i (
0 )
L i (
T , S
) / L i (
T , 0
)
0.75
0 5 10 15 20 25 30 35 40
S [g/kg]
21
Atmospheric Equilibrium Concentrations
The equilibrium (or air saturation) concentration cs,i is the dissolved
concentration of gas i in equilibrium with moist (saturated) air:
c e x i: solubility of gas i in water, ,s a m s
cs depends on T, S and p:
,i atm s ip p e x
, , , ,i eq i s ic T S p T S p e T x
Atmospheric pressure p depends on altitude z: sz z
0p z p e
pi ,air: par a pressure o gas n mo s a r
p: total atmospheric pressure
es: saturation water vapour pressure
xi: mixing ratio of gas i in air
, . /2 2 2s O O s Oc p e x 10 6mg l
Examples O2, N2:
altitude z = 400 m, p = 0.95 atm
S = 0, T = 10°C, es = 0.012 atm
O2 = 53.7 mg l‐1 atm‐1, xO2 = 0.209 N2 = 23.1 mg l‐1 atm‐1, xN2 = 0.781 , . /2 2 2s N N s Nc p e x 17 1mg l
22
-
8/18/2019 MKEP4 SS11 12 Gas Transfer
12/21
12
Solubil ity and Equilibr ium of some Gases
Solubilities i in pure water (S = 0) for various temperatures in g l‐1
atm
‐1
:
, . /
2s COc 1 3 mg lxCO2 = 3.9∙10‐4
, . /
2s Nc 22 8 mg l
s,i
p = 1 atm, T = 0°C
xN2 = 0.781
, . /
2s Oc 14 4 mg lxO2 = 0.209
, . /s Ar c 0 89 mg lxAr = 9.3∙10‐3
23
Equilibrium, Saturation, Oversaturation
Equilibrium conc.: Equilibrium at local air pressure (water surface)
Saturation conc. (absolute): Maximum dissolved conc. at in situ
pressure (incl. phyd) before bubbles are formed
i toti p pOversaturation:
, ,i H i W ip K c
'tot 0p p gz z': water depth
Henry's law relates dissolved concentrations to partial pressures.
I t e sum o a part a pressures excee s t e externa pressure
(oversaturation), bubbles are formed and gas escapes.
Typical example: Methane bubbles rising from lake sediments.
-
8/18/2019 MKEP4 SS11 12 Gas Transfer
13/21
13
Gas Contents of some Volcanic Lakes
Lake Monoun, Cameroon Lake Kivu, Kongo/Ruanda
80 % Sat.
Schmid et al., 2005, G3, doi:10.1029/2004GC000892Halbwachs et al., 2004, Eos 85 (30): 281
Lake Nyos, Cameroon: Artificial Degassing of a Lake
Principle
-
8/18/2019 MKEP4 SS11 12 Gas Transfer
14/21
14
Lake Nyos, Cameroon: Artificial Degassing of a Lake
Halbwachs et al., 2004, Eos 85 (30): 281
Gas Transfer: Molecular Boundary Layer
Free atmosphere or open water: Efficient transport by turbulence
Near the boundary: Molecular‐viscous boundary layer
• laminar flow, no turbulence
• Transport only by molecular diffusion: "Resistance"
For heat and most gases, the water‐side boundary layer dominates
(most strongly restricts exchange): One‐layer model
Flux of gas i by molecular diffusion in water boundary layer:
ii i
dc j D
dz Di: molecular diffusion constant of gas i in water
ci: concentration of gas i in water
In steady state, j must be constant, thus dc/dz = constant
(linear concentration profile)28
-
8/18/2019 MKEP4 SS11 12 Gas Transfer
15/21
15
“ Stagnant Film” Model
z turbulent
cg, p
Air
Water
s g Hc p c K sc
molecular
C
c
turbulent
29
Transfer Velocity in the Film-Model
For gases with low solubility, the main transport resistance is on the
water side: 1‐Film model, water‐side control
Flux in the laminar film is determined by molecular diffusion
Dk
S Sc cdc j D D k c cdz
Transfer coefficient:
(D: Diffusion coefficient in water)
2L T L
kL T
Dependence of k on D: k D
Model parameter: Film thickness , which depends on strength of turbulence, e.g. expressed by friction velocity u* (related to u10)
k = transfer/exchange
velocity, piston velocity
30
-
8/18/2019 MKEP4 SS11 12 Gas Transfer
16/21
16
Friction Velocities in Air and Water
Friction velocity:
z u
2 2
10 D *u c u
2
* x zu v v Wind velocity:
air
water
u(z)
2xz W *w0 u
2 2xz air D 10 air *0 c u u
x
Shear stress continuous at z = 0 (conservation of momentum), thus:
31
air *w *air
w
u u
Measure of turbulence in the water,
dependent on wind velocity
Wind Veloci ty and Film Thickness
Typical exchange velocities k for some gases and correspon-
ding film thicknesses w for different wind velocities u10.
gas exchange velocity k (m d-1)
Molecular diffusion coefficient D
at 25 °C (m2
s-1
)
Film thickness decreases with increasing wind speed.
Typical values are on the order of 100 m32
-
8/18/2019 MKEP4 SS11 12 Gas Transfer
17/21
17
Dependence of k on D: Schmidt Number
The stagnant film model is the simplest gas exchange model. More
complex models show different dependences of k on D:
n
To compare exchange of heat, momentum, and gases, the transfer
velocity is often parameterised by the so called Schmidt number:
Schmidt number: ScD
nk Sc with 1 2 n 1 Thus we get:
Measurements of k are often normalised to Sc = 600 (CO2 at 20°C)
33
Transfer Velocity in Different Regimes
nk Sc
1 2 n 1
smooth surface:
n = 2/3 (or n = 1)
rough surface:
Liss and Merlivat, 1986
n = 1/2
34
-
8/18/2019 MKEP4 SS11 12 Gas Transfer
18/21
18
Transfer Velocity and Wind Speed
Dependence of
k on
wind speed
wind speed, but how
exactly?
Frequently used
parametrisation:
2
10k u
Lab measurements
with fit curves
normalised to Sc = 600
35
Transfer Velocity and Wind Speed
Wanninkhof and Bliven 1991
Liss and Merlivat 1984
36
-
8/18/2019 MKEP4 SS11 12 Gas Transfer
19/21
19
Transfer Velocity and Wind Speed
Various models
37
Ocean – Atmosphere CO2 Flux
Based on 940.000 pCO2 measurements, assuming k u2. Balance: ‐ 1.6 ± 1 GtC/a. IPCC AR4, 2007 38
-
8/18/2019 MKEP4 SS11 12 Gas Transfer
20/21
20
Importance for CO2-Budget
39
Gas Exchange for Vapour: Evaporation
Water vapour saturation pressure as Henry‐equilibrium:
2H O s H wp e K c .
-1
w -1
1000 g L molc 55 55
M 18 g mol L
Vapour pressure p and "Henry coefficient" of water for different temperatures
o concen ra on gra en n wa er: vapora on s con ro e y a r‐s e m.
Sensible heat flux: Also air‐side controlled, flux given by th w j k c T
40
-
8/18/2019 MKEP4 SS11 12 Gas Transfer
21/21
Evaporation and Wind Speed
41
Summary
• Air/water heat transfer
– Radiative terms dominate, SW downward, IR terms nearly cancel
– Latent and sensible heat flux: upward, analogous to gas transfer
– Eva oration: Gas exchan e for water va our air-side controlled
• Solubility equilibrium for gases in water
– Henry's Law: Concentrations in both phases proportional
– Equilibrium concentration in water: cs(T,S,p)
• Air/water gas exchange
– Laminar boundary layer (usually water-side) transport resistance
– - = ,
– Schmidt number parameterisation: k Sc-n, ½ < n < 1
• Transfer velocity and wind speed
– strong but not exactly known relationship (e.g. k u2)
– important for correct estimation of ocean CO2 uptake
42
top related