12
The Effect of Raindrops on Interfacial Turbulence
and Air-Water Gas Transfer
Satoru Komori, Naohisa Takagaki, Rina Saiki, Naoya Suzuki and Kenji
Tanno
Department of Mechanical Engineering and Science and Advanced Research
Institute of Fluid Science and Engineering
Kyoto University, Kyoto 606-8501, Japan
[email protected]
Abstract The effects of impinging raindrops on both turbulence below the airwater interface and CO2 transfer across the air-water interface are discussed using laboratory measurements by Takagaki and Komori [1]. The measurements
of CO2 absorption rate and turbulence quantities in an open-channel flow show
that impinging raindrops enhance both turbulent mixing near the free surface on
the liquid side and CO2 transfer across the air-water interface, and that the mass
transfer velocity due to impinging raindrops is well correlated with the mean
vertical momentum flux of raindrops. The reason why the mass transfer velocity
is well correlated by the mean vertical momentum flux is explained by showing
the instantaneous velocity vectors induced by a falling single droplet. Further, in
order to clarify the effects of rainfall on the global and local CO2 transfer across
the air-sea interface, the mean annual net air-sea CO2 flux was estimated using
both the daily precipitation data set and the empirical correlation [1] between the
mass transfer velocity and mean vertical momentum flux. The rainfall effects are
also compared with wind shear effects. The results show that rainfall effects are
significant for the local CO2 budget between atmosphere and ocean in equatorial
and mid-latitude regions, but are not so important for global budget, compared
to the wind shear effect.
12.1 Introduction
Numerical predictions of the CO2 exchange rate across the air-sea interface are so sensitive to the air-sea CO2 transfer velocity that uncertainty
in the CO2 air-sea exchange rate may lead to uncertainty in future predictions of the global carbon budget. It is, therefore, of great importance to
investigate all the fluid-mechanical factors that control the CO2 transfer
across the air-sea interface in precisely estimating the CO2 exchange rate
across the air-sea interface. The effects of wind shear on the air-sea CO2
transfer have been investigated as the most important factor in previous
C.S. Garbe, R.A. Handler, B. Jähne (eds.): Transport at the Air Sea Interface
pp. 169-179, 2007, © Springer-Verlag Berlin, Heidelberg 2007
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studies [2, 3, 4, 5, 6] and some empirical equations based on the relation
between the mass transfer velocity and wind speed have been proposed.
However, there exist other control factors that have not been well investigated.
One such control factor is rainfall, which is expected to promote CO2
transfer across the air-sea interface [7, 8]. Ho et al. [8] showed that the
mean kinetic energy flux of raindrops, KEF , is a main parameter for determining the effects of rainfall on the CO2 transfer across the air-water
interface. Here, KEF is defined as
KEF = 0.5ρRvp2 ,
(12.1)
where ρ is the density, R the rain rate and vp the impinging velocity of
raindrops. On the other hand, Takagaki and Komori [1] measured the mass
transfer velocity by changing the impinging velocity of raindrops, vp , and
they concluded that the mean kinetic energy flux KEF is not always the
predominant parameter and the mean vertical momentum flux of raindrops, MF , is the most suitable parameter. Here, MF is defined as
MF = ρRvp .
(12.2)
However, it has not been clarified why MF is a more suitable rain parameter than KEF .
Impinging raindrops on the air-water interface enhance the turbulence
below the interface and the enhancement of turbulence results in promotion of the CO2 transfer. However, previous studies have not investigated
whether the rainfall effect on local or global air-sea CO2 exchange is really significant, compared to the wind shear effect. In addition to this mass
transfer due to the impingement of raindrops on the air-sea interface, raindrops themselves absorb CO2 while falling. Direct numerical simulations
by Sugioka and Komori [9] have suggested that the CO2 concentration inside a raindrop reaches equilibrium before the raindrop impinges on the
air-sea interface. It is, therefore, of interest to estimate the total rainfall
effects including both CO2 transfer across the air-sea interface and CO2
absorption into raindrops through the raindrop surface by using the empirical relation between kLR and MF , and precipitation data.
The purpose of this paper is to investigate the precise relation between
rainfall and air-water CO2 transfer and to estimate the rainfall effect on
the air-sea CO2 transfer.
12.2 Experiments
Figure 12.1 shows the open channel and water-velocity measuring system used here. The open flume was 7.6m long, 0.5m wide and 0.2m deep.
12 The Effects of Raindrops on Air-Water Gas Transfer
171
Rain chamber
Open channel
Figure 12.1. Experimental apparatus and measuring system [1].
The flume was filled with tap water. The flow depth in the open channel ranged from 0.06 to 0.17m, and the open-channel flow was fully developed. The cross-sectional mean velocity, Uave , ranged from 0.056 to
0.164m/s, and the Reynolds number based on the hydraulic radius and
Uave ranged from 22700 to 31700. Turbulence quantities were measured
using a laser Doppler velocimeter (LDV).
In order to conduct CO2 absorption experiments, a closed rain chamber
was set on the free surface in an open-channel flow. The rain chamber
was 1.00m long and 0.40m wide, and the chamber height was changed
from 0.38 to 1.20m. Uniform raindrops were generated in the closed rain
chamber by using many uniform needles mounted at the rooftop of the
chamber, i.e., at the bottom of a head water tank. By changing needle
diameter and tap water level in the head tank, the droplet diameter, dr ,
was varied from 2.1 to 5.7mm. The height of the rain chamber was changed
to several values, 0.38, 0.49, 1.09 and 1.20m, to obtain a spread of a factor
of 2 in raindrop velocity. The impinging raindrop velocity was measured
by a high-speed video system; it ranged from 2.37 to 4.69m/s. The rain
rate R ranged from 1 to 435mm/h.
Pure CO2 was injected into the rain chamber at atmospheric pressure,
and the CO2 absorption rate was measured using a soap-film meter. The
absorption rates due to both original turbulent motion in an open-channel
flow and falling of raindrops before impinging on the free surface were
subtracted from the absorption rate measured by the soap-film meter [1].
From the measured CO2 flux per unit area at the air-water interface, the
mass transfer velocity (mass transfer coefficient on the liquid side) due to
impinging raindrops, kLR , was estimated and kLR was normalized to the
mass transfer velocity for fresh water at 20◦ C. The details of the experiments are described in Takagaki and Komori [1].
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Figure 12.2. Relation between mass transfer velocity kLR due to impinging raindrops and mean vertical momentum flux MF [1].
12.3 Results and Discussion
12.3.1 Mass Transfer Velocity
Figure 12.2 shows the relation between the mass transfer velocity kLR due
to impinging raindrops and the mean vertical momentum flux MF defined
by Equation (12.2).
It is found that the mass transfer velocity kLR is well correlated with
MF . Takagaki and Komori [1] have confirmed that this relation holds for
various rain rates, raindrop diameters, impinging raindrop velocities and
horizontal distances between raindrops. Furthermore, Takagaki and Komori [1] showed that kLR normalized by the Schmidt number for 3.5wt%
salt water is the same between two open channel flows filled with fresh
water and 3.5wt% salt water.
On the other hand, Ho et al. [8] concluded that the mean kinetic energy
flux of raindrops KEF defined by Equation (12.1) is a main parameter for
determining the rainfall effect on gas transfer. However, Ho et al. [8] measured kLR without significantly changing the impinging velocity. In fact,
we could not find a good correlation between kLR and KEF for different
impinging velocities [1]. This suggests that MF is more appropriate as a
rainfall parameter for representing air-water CO2 transfer due to imping-
12 The Effects of Raindrops on Air-Water Gas Transfer
173
Figure 12.3. Instantaneous velocity vectors at 400ms after the impingement of
a single raindrop with the diameter of dr =2.2mm and impinging velocity of
vp =3.5m/s.
ing raindrops than KEF . In order to find the reason why MF is a significant rainfall parameter, we measured the instantaneous velocity vectors
around an impinging raindrop with the diameter of dr =2.2mm and impinging velocity of vp =3.5m/s by means of a Particle Image Velocimeter
(PIV). Figure 12.3 shows the instantaneous velocity vectors at 400ms after
the impingement of a single raindrop. It is found that surface renewal eddies are generated behind the impinging raindrop. Considering that the
surface renewal motions responsible for the mass transfer are generated
by exchanging momentum with falling raindrops, we can easily understand that the vertical momentum flux should be relevant to the mass
transfer.
12.3.2 Estimation of Air-Sea CO2 Flux
The CO2 flux across the air-sea interface was estimated by
FR = kLR Ss ∆pCO2 ,
(12.3)
where kLR is the mass transfer velocity due to an impinging raindrop, Ss is
the solubility of CO2 in sea water and ∆pCO2 is the partial pressure difference between atmosphere and ocean. kLR (m/s) is given by the following
best-fit curves [1] shown in Figure 12.2:
kLR = 0.00135MF
kLR = 0.00035MF
0.7
for
0 < MF < 0.0111,
for
0.0111 ≤ MF ,
(12.4)
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Figure 12.4. Relation between rainfall time tR and CO2 flux normalized by the
full day rainfall flux for tR =24hr.
where MF (kg/ms2 ) is given by Equation (12.2). The mean vertical momentum flux MF cannot be explicitly determined for unsteady natural rainfall.
In order to overcome this problem we derived a relationship between MF
and the rain rate in a natural environment, Rn (mm/h), by using the raindrop size distribution [10] and the terminal velocity of the droplets [11]:
1.09
MF = 1.29 × 10−3 Rn
.
(12.5)
The same method was used by Ho et al. [11] to calculate KEF . Time
records of global rain rate Rn are required to estimate the air-sea CO2 flux
from this MF . However, such global data of temporal Rn are not available
except for some local observing stations with buoys. Therefore, we were
forced to use the GPCP (Global Precipitation Climatology Project) OneDegree Daily Precipitation Data Set (World Climate Research Program [13],
Huffman et al. [14]) and we estimated Rn from the daily rain rate, Rday ,
by using the following method. When rain is assumed to continue for tR
hours, Rn is given by Rday /tR and the daily CO2 flux due to the impinging
raindrops can be calculated by integrating FR in Equation (12.3) over the
time period tR . Figure 12.4 shows the CO2 flux FR against tR . Here, FR is
normalized by the flux FR24 for tR =24hr and the best-fit curve for each
Rday is overlapped with the bold solid line from each intersection point.
From the flux curves for each Rday , we chose the value of tR to give the
12 The Effects of Raindrops on Air-Water Gas Transfer
175
o
60 N
30oN
0
o
30oS
60oS
0o
−1.5
60oE
−1
120oE
−0.5
180oW
120oW
0
0.5
60oW
1
−9 x 10−9
x 10
a
0o
1.5
2
[mol/(m s)]
o
60 N
30oN
0
o
30oS
60oS
0
o
−1.5
o
60 E
−1
o
120 E
−0.5
o
o
180 W
120 W
0
0.5
o
60 W
1
−9 x 10−9
x 10
b
0
o
1.5
2
[mol/(m s)]
o
60 N
30oN
0
o
30oS
60oS
0o
−1.5
c
60oE
−1
120oE
−0.5
180oW
120oW
0
0.5
60oW
0o
1
x 10
−7 x 10−7
1.5
2
[mol/(m s)]
Figure 12.5. For 2001, the mean annual net air-sea CO2 flux due to impinging
raindrops, raindrop absorption and wind shear in a, b and c respectively.
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maximum CO2 flux FR . By applying this maximum CO2 flux method, we
computed the global CO2 flux due to impinging raindrops.
It is, however, uncertain how much error will be caused by this maximum flux method. Therefore, we compared the rainfall CO2 flux based on
the data base of daily rain rate Rday with that based on temporal data base
of 10 minutes rain rate R10min , observed at 28 locations in the tropical
region. The data are provided as the TAO (Tropical Atmosphere Ocean)
buoy array data set provided by NOAA/PMEL (National Oceanic and Atmospheric Administration / Pacific Marine Environmental Laboratory). The
comparison showed that the present maximum flux method based on the
daily rain data base overestimates the CO2 flux due to impinging raindrops by about 10%, compared to the flux based on the 10 minute data
base. Here, we neglect this overestimation in the following discussion of
the global effects of the rainfall.
Figure 12.5a shows the mean annual net air-sea CO2 flux due to impinging raindrops, FR . The values of FR were adjusted to correspond to
salinity and local temperature using the NCEP/NCAR (National Centers
for Environmental Prediction/National Center For Atmospheric Research)
reanalyzed data [15]. To determine kLR , we used the GPCP One-Degree
Daily Precipitation Data Set [13, 14] for a period of one year from 1 Jan. to
31 Dec. 2001. The data are obtained by combining the precipitation data
from SSM/I (Special Sensor Microwave/Imager), infrared (IR) sensor and
TOVS (TIROS Operational Vertical Sounder) satellite data. For the distribution of the partial pressure difference ∆pCO2 , the data base provided
by Takahashi et al. [16] was used. We assume that these ∆pCO2 data are
the same as in 2001. From Figure 12.5a, it is found that impinging raindrops promote CO2 transfer from ocean to atmosphere in the tropics and
from atmosphere to ocean in the mid-latitude region. In addition to CO2
transfer by impinging raindrops, there is CO2 absorption during the fall of
raindrops. According to direct numerical simulation of air and water flows
outside and inside a spherical droplet with mass transfer [9], the concentration field in a falling raindrop comes to equilibrium before impinging
on the ocean surface. Therefore CO2 flux due to raindrop absorption, FD ,
was given by
FD = Rn Sf (pCO2air ),
(12.6)
where Sf is the solubility of CO2 in fresh water and pCO2air is the partial
pressure of CO2 in the atmosphere. Figure 12.5b shows the mean annual
net air-sea CO2 flux due to the raindrop absorption, FD . High absorption
is seen in both equatorial and mid-latitude regions.
In order to compare these rainfall effects with the effect of wind shear,
we estimate the CO2 flux due to wind shear, FW , by using the mass transfer
velocity, kLW (m/s), proposed by Wanninkhof [3]:
2
kLW = 0.31U10
,
(12.7)
12 The Effects of Raindrops on Air-Water Gas Transfer
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Figure 12.6. Distribution of the zone integrated values of mean annual net air-sea
CO2 fluxes, FR , FD , FW and FR +FD against latitude.
where U10 (m/s) is the wind speed at 10m elevation from the ocean surface;
we used the NCEP/NCAR reanalyzed wind data. The mean annual net airsea CO2 flux due to the wind shear is shown in Figure 12.5c. Figure 12.6
shows the distributions of the zone integrated values of annual net airsea CO2 fluxes, FR , FD , FW and FR +FD against latitude. Compared to the
wind shear effect, the rainfall effect is not so large. The impinging effect
of raindrops is 2% of the wind shear effect at most in the tropics. The net
effects of FR +FD are 6% and 3% at most, compared to the wind shear effect
in the equatorial and mid-latitude region, respectively. On the other hand,
the contribution of rainfall is locally big in the tropical region near 140
degrees of longitude, as shown in Figure 12.7, and the values of FR /FW
and (FR +FD )/FW are about 7% and 35%, respectively.
Global air-sea CO2 fluxes for 2001 were computed; FW , FR , FD and
FR +FD corresponded to -1.81, -0.003, -0.09 and -0.093PgC/Year, respectively. This shows that the global effect of rainfall is less than 5%. The
above results also suggest that the rainfall effect on the CO2 flux should
be considered in terms of the local CO2 budget, but it can be neglected
for discussing the global CO2 budget.
12.4 Conclusions
The water below the free surface is mixed by impinging raindrops and
therefore, CO2 transfer across the air-water interface is promoted. The
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Figure 12.7. Longitudinal distribution of mean annual net air-sea CO2 fluxes, FR ,
FD , FW and FR +FD on the equator.
mass transfer velocity is determined by the mean vertical momentum flux
of raindrops. The rainfall effect is significant for the local CO2 budget
between atmosphere and ocean in equatorial and mid-latitude regions,
but not so important for discussing the global carbon budget.
Acknowledgement. This work was supported by the Ministry of Education, Science, Sports and Culture, Grant-in Aid (No.14102016). The part of the estimation
of the global carbon budget was supported by the Core Research for Evolutional
Science and Technology Program "Advanced Model Development and Simulations
for Disaster Countermeasures" of Japan Science and Technology Agency. The authors acknowledge Profs. W. McGillis and T. Takahashi for their provision of the
data sets of ∆pCO2 .
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