Tritium Washout by Precipitation :

1

• Tritium Washout by Precipitation
• A Numerical Eulerian Stationary Model.
• Dimiter Atanassov
• National Institute of Meteorology and Hydrology
• 1784 Sofia, 66 Tzarigradsko Chaussee
• 4000 Plovdiv, 139 Rouski Str.
• Bulgaria
• Dimiter.Atanassov_at_meteo.bg
• Presented at IAEA EMRAS Tritium/C-14 Working
  Group
• 2007 Spring Meeting, Bucharest

2
Rain Scavenging of Tritiated Water Vapour A
Numerical Eulerian Stationary Model

• The study was conducted at the Center of
  Excellence of
• project
• IDRANAP
• (Inter-Disciplinary Research and Applications
• based on Nuclear and Atomic Physics)
• at National Institute of Physics and Nuclear
  Engineering
• "Horia Hulubei, Bucharest-Magurele, Romania
• Work package WP3
• The impact of tritium releases on environment and
  population,
• Coordinator Dan Galeriu
• supporting by the FP 5 of the European Commission

3
Rain Scavenging of Tritiated Water Vapour A
Numerical Eulerian Stationary Model

• Content
• Introduction - the present state of the HTO
  washout problem, intention of the present study
• Individual raindrop problem
• Modelling of HTO washout from the atmosphere
• Sensitivity analysis of the model
• Some results and analysis
• Conclusion - future development of the model

4
Rain Scavenging of HTO VapourIntroduction - the
present stateintention of the study
4

• The concept established by Jeremy M. Hales in
  1972 is the basis of almost all studies on
  washout of gaseous tritium (HTO) from the
  atmosphere. The concept is not substantially
  modified till today.
• At microphysical level, concerning the
  scavenging by individual raindrop, the present
  study will closely follow the Hales approach.
  The knowledge on this topic will be reviewed
  below, specifying exactly which assumptions will
  be accepted here.
• Concerning the HTO washout in a rain event,
  there are two peculiarities of the traditional
  approach, that will be reversed here.
• 1) Following Hales, all authors combine the
  washout model with a model for dispersion of the
  gaseous HTO in the atmosphere. Gaussian plume
  dispersion models are usually used, which allows
  analytic expressions for the washout output
  characteristics to be obtained. The present
  washout model will be formulated separately,
  without inclusion of a dispersion model. In this
  way, any kind of dispersion model, including the
  most advance ones could be used.

5
Rain Scavenging of HTO VapourIntroduction - the
present stateintention of the study
5
2) The traditional final goal of the HTO washout
studies is to determine some "universal"
coefficients (washout ratio and washout
coefficient). After have ones been established,
they are applied for description of the washout
process in more general models, as coefficients
in simple expressions, in order to determine the
washout output characteristics like downward flux
and concentration in the rain water. The problem
in this approach is that the mentioned
universal coefficients accumulate the
shortcomings of the Gaussian models. Second, any
attempt to determine the coefficients more
precisely, lead the necessity to considered them
as functions of height of the HTO source,
distance from it, atmospheric stability, air
temperature, etc, whish is usually insolvable
task in real situations.   A new, numerical
Eulerian approach, free from the mentioned above
shortcoming will be proposed in the present
study. The model will directly calculate the
demanded output characteristics, making needless
the mentioned above universal coefficients. The
washout coefficient is considered here in order
to express the present results in a conventional
way and for comparison with other studies.
6
Rain Scavenging of Tritiated Water Vapour A
Numerical Eulerian Stationary Model

• Content
• Introduction - the present state of the HTO
  washout problem, intention of the present study
• Individual raindrop problem
• Modelling of HTO washout from the atmosphere
• Sensitivity analysis of the model
• Some results and analysis
• Conclusion - future development of the model

7
Rain Scavenging of HTO individual raindrop
problem
HTO scavenging by individual raindrop
It is convenient to consider the scavenging
of gaseous HTO by an individual
raindrop as a consequence of two steps,
represented by the following equations
trough the drops surface
For the HTO flux

• liquid-phase step, and

• gas-phase step

One of the most significant peculiarities of the
Hales works is the combination
of the two steps, introducing an overall
mass-transfer coefficient
is gas-phase mole-fraction that would exist in
equilibrium with the liquid
where
mole-fraction -
8
Rain Scavenging of HTO individual raindrop
problem
HTO scavenging by individual raindrop
The advantages are that the problem becomes one
step problem and that the difficulty in
determining the interfacial pollutant
concentrations at the drop's surface is overcame.
The disadvantage is in definition of the overall
mass-transfer coefficient
The general relationship
in the special case where the system obeys
Henrys law, as the system water-HTO, reduces to
the following linear relationship
where
is the Henrys law constant.
The equilibrium relationships can be employed to
express the overall mass transfer
coefficient in terms of the
and
9
Rain Scavenging of HTO individual raindrop
problem
HTO scavenging by individual raindrop
The previously discussed equations for the flux
of HTO across the drops surface can be employed
to express the condensation/evaporation of
gaseous HTO to/from a raindrop by the following
equation
Here, following Ogram(1985), the mass of gaseous
and liquid HTO is expressed in
term of concentration instead of mole-fraction
is the time,
is
concentration of the liquid phase HTO in the
drop,
is concentration
of the gas phase HTO in the drops environment,
is the drops diameter,
10
Rain Scavenging of HTO individual raindrop
problem
10
Limiting situations - determination of the
Overall Mass-Transfer Coefficient

• gas-phase limiting situation
• The transport of liquid HTO within the drop is
  due by circulation of the liquid water inside
  (convection) and by molecular diffusion. For a
  drop falling in the real atmosphere, the
  convection motion inside are stimulated by the
  friction with the air, and the HTO is mixed up so
  rapidly that the liquid-phase mass-transfer
  coefficient becomes large enough (kx?) and the
  overall mass-transfer coefficient K ky. In this
  case the condensation of the HTO will be governed
  by the availability of the gas-phase HTO in the
  air.
• stagnant drop case
• If there is no convection and the diffusion is
  the sole mechanism for transport, the mixing
  inside the drop is weak. Then, there exists a
  thin surface layer whit high liquid HTO pollutant
  concentrations, which are in equilibrium with the
  outside gas-phase HTO. In this case the
  stagnation in the inside drop mixing will govern
  the condensation.

11
Rain Scavenging of HTO individual raindrop
problem
11
HTO scavenging by individual raindrop
Limiting situations - determination of the
Overall Mass-Transfer Coefficient
The case of stagnant drop, represents the slowest
rate of mass-transfer possible. The gas-phase
limiting case, represents the most intensive rate
of mass-transfer possible. These, therefore,
provide lower and upper limits for washout
behavior. All atmospheric washout behavior
should fall somewhere between these two limits.
Hales (1972a,b) and his coworkers Dana et al.
(1978) always considered the two limiting cases,
gas-phase limiting and stagnant drop case. The
next authors (Ogram (1985), Abrol (1990), Belot
(1998)) considered only the more likely in the
atmosphere gas-phase limiting case. The
gas-phase limiting case will be the only case
considered in the present study.
12
Rain Scavenging of HTO individual raindrop
problem
Determination of the Overall Mass-Transfer
Coefficient
Following Bird et al.(1960), Hales and all next
authors determine the gas-phase mass-transfer
coefficients by the following semi-empirical
expression, referred to as the Froessling
equation
and
where
are Reynolds and Schmidt numbers,
is gas phase
diffusion coefficient of HTO,
is kinematic viscosity of the air,
is the drops velocity.
Finally, the HTO concentration in the drop turns
to be a function of the following parameters
13
Rain Scavenging of HTO individual raindrop
problem
Empirical formulas for raindrops downfall
velocity
Common assumptions in the literature dedicated
to HTO washout 1) Changes of the drops size
during the downfall is not taken into account
2) The drops velocity does not change during its
downfall 3) drops are falling down strictly in
vertical direction
a191, b0.0158, n1.754 for d lt 0.015cm.
1) Best (1950)
a932, b0.0885, n1.174 for d gt 0.015cm.
after Belot(1998)
2) Best (1980)
a958, b0.177, n1.174 for all d.
after Ogram(1985)
3) Kesler (1969)
after Ogram(1985)
after Ogram(1985)
4) Hales (1973)
14
Rain Scavenging of HTO individual raindrop
problem
Fig.2.1 Raindrops downfall velocity as a
function of drops diameter, according to
different authors
15
Rain Scavenging of HTO individual raindrop
problem
Fig. 2.2. Time for passing through a 10m layer,
according to the different drops downfall
velocity formulas
16
Rain Scavenging of HTO individual raindrop
problem
Fig. 2.2. Time for passing through a 10m layer,
according to the different drops downfall
velocity formulas
17
Rain Scavenging of HTO individual raindrop
problem
Solution of the individual raindrop problem
The basic equation for condensation / evaporation
of HTO to / from the raindrop is an ordinary
linear differential equation of the following
type and it solution is
If
and diameter
are constant to time , the solution reduces to
where
is the concentration at the initial moment
tends to the equilibrium concentration
The drops concentration
condensation is going on
If
evaporation is going on.
if
18
Rain Scavenging of HTO individual raindrop
problem
Fig.2.6 Non-dimensional liquid HTO
concentration in raindrops of different
diameters as a function of time T 150C, p850
hPa.
19
Rain Scavenging of HTO individual raindrop
problem
Fig.2.8. Sensitivity to temperature
non-dimensional HTO concentration in raindrops
of diameter 0.02 and 0.9cm, as a function of
time, for temperatures T 0, 15, and 300C
p850hPa. The concentration curve for d0.4cm
and T 150C is also presented.
20
Rain Scavenging of HTO individual raindrop
problem
Fig.2.7. Sensitivity to atmospheric pressure
non-dimensional HTO concentration in raindrops
of different diameter, as a function of time T
150C, p850 and 100hPa. The short vertical
lines mark the time, which is necessary a drop
with the corresponding diameter to pass through a
10m vertical layer. according to the downfall
velocity formula of Best1
21
Rain Scavenging of HTO HTO condensation at
microphysical level
Drop size distribution (DSD)
Drop size distribution number of drops
per unit space volume which diameter
is within interval of unit
length around
.
1) Marshall-Palmer (MP)
0.08
after Ogram(1985)

2) Sekhorn-Srivastava (SS)
after Ogram(1985)
0.07
3) Best (B)


after Belot(1998)
where
is the total (non "spectral")
cm,

volumetric liquid water contain of air.
In the all formulas the rainfall rate
mm.h-1 36000 ml.cm-2.s-1 is the sole input
parameter determining the DSD.
22
Rain Scavenging of HTO HTO condensation at
microphysical level
Fig.3.1. Drop size distribution (DSD) for the
rainfall rate of 0.5 and 30 mm/h, according
different authors
23
Rain Scavenging of HTO HTO condensation at
microphysical level
Rain Characteristics
Assuming the drops are spherical, the spectral
volumetric liquid water content in the air
cm3.cm-3.cm-1ml.cm-3.cm-1 and the total over
the spectrum one cm3.cm-3ml.cm-3, by
definition are



The spectral volumetric liquid water flux
cm3.cm-2.s-1.cm-1ml.cm-2.s-1.cm-1 and the
total over the spectrum one cm3.cm-2.s-1ml.cm-
2.s-1 could be calculated in the following way



24
Rain Scavenging of HTO HTO condensation at
microphysical level
24
Rain Characteristics - normalization procedure
The total rainfall rate appears in the
calculations as an argument through the empirical
formulas for DSD. In the model's applications,
the rainfall rate will be taken from the
observations. When is necessary to underline
this, the rainfall rate will be denoted as
- "measured" total rainfall rate. Because
the formulas for drops downfall velocity and DSD
are, in principle, non-coincidence empirical
formulas, the calculated rainfall rate could not
equal the "measured" rainfall rate, appearing as
an argument in the mentioned formulas. In this
way, the calculated spectral liquid water content
of the air and the spectral rainfall rate do not
correspond to the measurements, in sense that
integral of the spectral rainfall rate over the
spectrum, i.e. does not equal the
measured value
.
The values of
, calculated from the previous formulas, should
be corrected,
and
normalized to the measurements by the following
way



If
are used, the calculated value
and
will equal the measured value
.
This procedure represents a normalization to the
input data. Its effect will be discussed below.
25
Rain Scavenging of HTO HTO condensation at
microphysical level
Fig.3.2. Spectral volumetric liquid water content
of the air, according to different DSD formulas,
in case of rainfall rate of 0.5 and 30 mm/h.
26
Rain Scavenging of HTO HTO condensation at
microphysical level
Fig.3.3. Spectral rainfall rate, according to
different DSD formulas and drops downfall
velocity formula of Best1, in case of total
rainfall rate of 0.5 and 30 mm/h.
27
Rain Scavenging of Tritiated Water Vapour A
Numerical Eulerian Stationary Model

• Content
• Introduction - the present state of the HTO
  washout problem, intention of the present study
• Individual raindrop problem
• Modelling of HTO washout from the atmosphere
• Sensitivity analysis of the model
• Some results and analysis
• Conclusion - future development of the model

28
Rain Scavenging of HTO Modelling of HTO washout
from the atmosphere
28
Assumptions and input data, concerning the rain
phenomenon

• Common assumptions, concerning rain phenomenon
• the raindrops are spherical and their size
  remains constant during the downfall ,
• the drops are falling down in vertical
  direction with a constant to time velocity ,
• there exists a level , that is suggested to be
  the level from which all the raindrops
• start their downfall, usually, it is assumed
  to be the cloud's bottom ,
• the raindrop spectrum is known, and is not
  changing with height ,
• the processes are stationary the rain
  spectral characteristics, the geometry of the
  rain cloud, the geometry of the gaseous HTO cloud
  are not changing, during the typical time for
  which the smallest raindrops are falling down
  from the rainfall top level to the ground
  surface.
• The listed assumptions make possible
• - the surface rainfall rate and the rainfall top
  level to be the only needed input data,
• - the HTO washout models to be developed as
  1-dimensional vertical models.
•  
• In the reality, satisfaction of most of these
  assumptions is not likely. Nevertheless, they are
  used in HTO washout studies and will be used
  here, because any refusal of some of them would
  lead necessity of
• - inclusion of a cloud model (water condensation,
  raindrop growth, in-cloud streams)
• - additional input information

29
Rain Scavenging of HTO Modelling of HTO washout
from the atmosphere
29
The models construction meteorological and HTO
input data

• Meteorological data input
• vertical profiles of the atmospheric pressure
  and atmospheric temperature.
• Gas HTO data input
• the present model needs the profile of the
  gaseous HTO over the considered site.
• The traditional HTO washout studies incorporate
  Gausian dispersion models. The HTO profile is
  calculated by the Gausian model, the input data
  for which are the HTO emission rate and the
  parameters for the HTO source its height,
  distance to it,
• The models construction
• A modern HTO atmospheric transport modelling
  system should consist at least of the following
  models a model describing the dispersion of
  gaseous HTO in the space, dry deposition and wet
  deposition (washout) models, and a meteorological
  preprocessor, ensuring the necessary
  meteorological input for the mentioned models.
  The present washout model is constructed as a
  subroutine of a such transport modelling system.
  The washout model takes the gaseous HTO profile
  from the dispersion model, calculates the
  washout, and returns the gaseous HTO profile,
  corrected by the scavenged HTO by the rainfall.
  This exchange between the dispersion and the
  washout models takes place at each time step,
  over each horizontal grid cell (point).

30
Rain Scavenging of HTO Modelling of HTO washout
from the atmosphere
30
HTO washout calculations - numerical scheme
The domain of the model is between the soil
surface and the level Hrain from which the drops
start their downfall. The uniform vertical grid
is defined. At the top level Hrainz(N) we assume
the liquid HTO into the raindrops is in
equilibrium with the surrounding gaseous HTO
CNCequil. The basic equation (1) is applied
layer by layer downward the level Hrain,
separately for all drop size intervals. All
parameters in equation (1) are assumed constant
within a grid layer. This makes possible the
analytic solution (2) to be applied to a drop for
the time it is passing through the grid layer.

(1)
(2)

31
Rain Scavenging of HTO Modelling of HTO washout
from the atmosphere
31

• HTO washout calculations - numerical scheme

Before to apply (2) to a drop with diameter d in
layer i, its passing time t is determined,
according to the accepted formula for drops'
downfall velocity. The concentration C(d,i),
calculated for this drop, after it has spent time
t in the i-th layer, is used as initial condition
for the next i-1-st layer. The calculations for
the last 1-st layer, the layer above the ground,
give the spectral mass concentration of liquid
HTO in raindrops at the surface C(d,1).
32
Rain Scavenging of HTO Modelling of HTO washout
from the atmosphere
HTO washout output characteristics
Spectral and total mass concentration of liquid
HTO in the air, i.e. mass of liquid HTO per
unit space volume are
g.cm-3
g.cm-3 .cm-1


Total mass concentration of liquid HTO in liquid
water in the air, i.e. the total mass of liquid
HTO per unit volume of water in the air is
g.cm-3 g.ml-1


Spectral and total mass flux of liquid HTO, i.e.
spectral and total mass of liquid HTO
passing through unit surface area perpendicular
to
per unit time are

g.cm-2.s 1 .cm 1
g.cm-2.s 1


If the flux
of liquid HTO at the ground surface is divided to
the rainfall rate
, the result
is the mass concentration of liquid HTO in the
falling rainwater
g.cm-3 g.ml-1

33
Rain Scavenging of HTO Modelling of HTO washout
from the atmosphere
HTO washout output characteristics
Mass concentration of liquid HTO in liquid water
in the air
Mass concentration of liquid HTO in the falling
rainwater




The differences obtained by model calculation
will be shown later. The difference is expected
to be detected in measurements by the following
different technics
Pumping
Passive sampling
34
Rain Scavenging of HTO Modelling of HTO washout
from the atmosphere
34
HTO washout output characteristics
Washout ratio
Washout coefficient
, s-1 ,



The washout ratio and washout coefficient are
invented as universal characteristics of the
washout process. After they have ones been
determined in theoretical studies, they are used
to determine , and .
Usually, they are coefficients in simple formulas
like that

,
,

• Some comments
• The shortcomings of the washout ratio is obvious
  - only the surface is taken into account.
• The washout coefficient approach is most useful
  when the scavenging process can be considered
  irreversible. In case of HTO, irreversible
  conditions would only be expected to hold at very
  short travel distance. At longer travel distances
  a washout coefficient, based on irreversible
  scavenging, may significantly overestimate plum
  depletion. The true washout coefficient will
  therefore be a parameter that is a function of
  downwind distance- Ogram(1985).
• Hales(1972) suggested to overcome the problem by
  redefining the washout coefficient in term of a
  reversible process.
• Belot (1998) introduced a reversible washout
  coefficient and considered it as a function of
  downwind distance and sources height.

35
Rain Scavenging of HTO Modelling of HTO washout
from the atmosphere
HTO washout output characteristics - summary

• Two types of outputs can be distinguished
• Absolute characteristics
• liquid HTO concentration in the water in the
  air g.ml-1 ,
• liquid HTO concentration in the rainfall
  g.ml-1 , and the
• downward flux of liquid HTO
  g.cm-2.s 1.
• Relative characteristics
• like washout ratio
• washout coefficient s 1.

The present model is designed to be used for
direct calculation of the absolute
characteristics the washout coefficient will be
considered below only in order to discuss the
washout coefficient concept.
36
Rain Scavenging of Tritiated Water Vapour A
Numerical Eulerian Stationary Model

• Content
• Introduction - the present state of the HTO
  washout problem, intention of the present study
• Individual raindrop problem
• Modelling of HTO washout from the atmosphere
• Sensitivity analysis of the model
• Some results and analysis
• Conclusion - future development of the model

37
Rain Scavenging of HTO Sensitivity analysis
Typical variability of the factors governing the
washout process
Local sensitivity criterion
If
is an output characteristic of the washout model,
depending on the parameters
the quantity
100

will be used below as an assessment criterion for
the local sensitivity of to the parameter
.
38
Rain Scavenging of HTO Sensitivity analysis
38

• Calculation of will be performed many times
  for the same values , , for
  different values of where
  the lasts will take the values, formulas and
  profiles from the previous table.
• It is easy to prove, that the criterion
  will have the same value for , for
  and
• for they are considered at
  ones in the following sensitivity analysis. The
  sensitivity of is considered
  separately.
• A simple Gaussian plum dispersion model is used
  only in order to generate profiles at
  10 distances from the source, from 100m to
  33000m. The source is at 60m height, the
  emission rate is 1000g.s-1, the wind speed is
  10m.s-1 and the atmospheric stability is neutral.
  The sensitivity to the distance from the source
  could be considered as a sensitivity to the
  profile and magnitude of the gaseous HTO close
  to the source, the vertical gradient of
  is significant, while far away from the source,
  tends to a constant of small
  magnitude.

39
Rain Scavenging of HTO Sensitivity analysis
Sensitivity analysis
Sensitivity to DSD. The result of criterion S,
maximum by absolute value with respect to the
distance to the source is presented. The
temperature is constant to z , equal to 150C.

Sensitivity to the temperature - The value of
criterion S is calculated for temperatures of
00C and 150C for the different DSDs, rain rates
and downfall velocity formulas.

40
Rain Scavenging of HTO Sensitivity analysis
40
Summary of the sensitivity analysis

• To the numerical parameters
• Consideration of raindrops which diameter is
  smaller then 0.02cm changes the washout outputs
  les then 1. dRmin 0.02cm is used as a lower
  limit of integration.
• An increase of the vertical grid step dz from 2m
  to 10m changes the values of Cc, Cf and J by
  -18 from its value in case of dz2m the value
  of Wc is changed by about 3. An increase of dz
  from 2m to 20m changes the values of Cc , Cf and
  J by -86 from its value in case of dz2m the
  value of Wc is changed by about 9. These
  assessments are the maximum ones for variation of
  temperature, pressure, DSD, drops downfall
  velocity in their ranges set in the table. They
  are obtained at a distance of 100m downwind the
  source. At a distance of 400m and more, the all
  assessments are less then 1. A vertical grid
  step dz10m could be recommended as appropriate
  one.
• Omission of the normalization procedure lead an
  error in J and Wc determination which magnitude
  is up to 62 (in case of R30.0mm.h-1, vz
  according to Best and DSD of SS). The procedure
  does not affect Cf, as the effect on J and R is
  compensated. The conclusion is that in any case
  the normalization procedure must be applied.

41
Rain Scavenging of HTO Sensitivity analysis
41
Summary of the sensitivity analysis

• To the atmospheric and rain parameters
• Sensitivity to drop size distribution. The
  value of the criterion S varies from less then 1
  (between DSD of SS and MP, in case of R3mm.h-1,
  vz according to Kesler) up to 72 for ACc
  (between DSD of B and MP, in case of R30mm.h-1,
  vz according to Best) and 69 for A Cf , J and
  Wc (between DSD of B and MP, in case of
  R30mm.h-1, vz according to Best).
• Sensitivity to drops downfall velocity. The
  maximum value of the criterion S is 8 (in case
  of R3mm.h-1, DSD of MP and SS).
• Sensitivity to the temperature. The value of
  the criterion S varies from 13 (in case of
  R30mm.h-1, vz according to Best) up to 62 for
  ACc (in case of DSD of MP, R0.5mm.h-1, vz
  according to Best) and 54 for A Cf , J and Wc
  (in case of DSD of MP, R0.5mm.h-1, vz according
  to Kesler).
• The effect caused by typical variations in
  atmospheric pressure is less the 2.
• Comment
• The influence of the rain parameters and the
  temperature on the washout process is
  significant. Unlike the temperature which is
  usually well known, the rain parameters are
  difficult to be established precisely.

42
Rain Scavenging of Tritiated Water Vapour A
Numerical Eulerian Stationary Model

• Content
• Introduction - the present state of the HTO
  washout problem, intention of the present study
• Individual raindrop problem
• Modelling of HTO washout from the atmosphere
• Sensitivity analysis of the model
• Some results and analysis
• Conclusion - future development of the model

43
Rain Scavenging of HTO Some results and analysis
43
Model application
A part of the parameters considered in the
sensitivity analysis, after being once fixed,
will be not varied in the models application.
What will vary is the rainfall rate, the profile
of the gaseous HTO and the temperature profile.
The Marshall-Palmer DSD and the Bests formula
for drops' downfall velocity are used in the
following considerations. Six Cg(z)
distributions have been manually determined and
the model has been run with them instead to use
the Gaussian dispersion model. The value of Cg
is constant with z in the first three
profiles, but the magnitudes of Cg are too
different 1.0e-6, 1.0e-9 and 1.0e-21 g.cm-3,
correspondingly for profiles ?1,2,3. In the
case of the next 3 profiles, profiles ?4,5,6, the
amount of gaseous HTO in a vertical column is
one and the same 0.6997e-5 g.cm-2, but their
vertical distribution is quite different.
Fig.5.1
profile ? 4
profile ? 5
profile ? 6
44
Rain Scavenging of HTO Some results and analysis
Spectral view of the washout process
Fig.5.2 Changes of HTO concentration into the
raindrops of different diameter (0.02, 0.075,
0.25cm) during their downfall, for case of the
gaseous HTO profile ?5 and for two constant to z
temperatures of 150C and 00C. The rainfall rate
is 3mm.h-1, the DSD is according to
Marshall-Palmer, the downfall velocity is
according to Best.

45
Rain Scavenging of HTO Some results and analysis
45
Spectral view of the washout process

• The equilibrium concentration is bigger and the
  drops can accumulate more HTO in the case of
  lower temperatures (compare the equilibrium
  curves - bolt). However, the processes of
  condensation and evaporation of HTO to and from
  the drops are more intensive in higher
  temperatures.
• - During the downfall of the smallest drops
  (0.02cm), the HTO concentration in them follows
  closely the equilibrium curve in the case of 150C
  and lags behind it in the case of 00C.
• - The HTO concentration into the drops of
  diameter 0.075cm reaches close values (3.59e-05
  g.ml-1 and 4.06e-05 g.ml-1, for the cases 150C
  and 00C, correspondingly) around the bottom of
  the HTO gaseous layer, but below that layer, the
  lose of HTO by evaporation is more intensive in
  the case of 150C.
• - For the big raindrops, the considered layer of
  gaseous HTO is obviously too thin and these drops
  accumulate a small part of the tritium they can
  accumulate.
• A change of the thickness or the position of the
  gaseous HTO layer can change the results
  substantially.

46
Rain Scavenging of HTO Some results and analysis
46
Typical behaviour of the washout outputs -
constant gaseous HTO profile
Fig.5.3 Washout characteristics for Cg 1.0e-6
g.cm-3const (profile ?1), as a function of
rainfall rate ( 0.5, 3.0, 30 mm.h-1), for
temperatures 0 0C, 15 0C and 30 0C .

The results for the two other cases of
Cg(z)const just scale with Cg the bigger
amount of the gaseous tritium in the atmosphere
leads higher concentrations Cc, Cf and higher
flux J the washout coefficient remains the same.
Comments on the results The interesting
conclusion from these examples is that the both
concentrations Cc and Cf are almost independent
on the rainfall rate R (Fig.5.3 a,b). The flux
and the washout coefficient are increasing
linearly with the increasing of R in logarithmic
axes (c,d).
47
Rain Scavenging of HTO Some results and analysis
Typical behaviour of the washout outputs
Fig.5.4. Washout characteristics as a function
of rainfall rate (0.5, 3. , 30. mm.h-1), for
Cg(z) profiles ?4,5,6 with equable column HTO
amount 0.7g/cm2 for 0,15,300C.
a) HTO concentration in the water in the
air Cc g/ml b) HTO concentration
in rainfall Cf g/ml
48
Rain Scavenging of HTO Some results and analysis
48
Comments on the results

• Now, when Cg(z) is not a constant, the
  concentrations CC and Cf depend in a complex way
  on the rainfall rate R, on the Cg(z) profile and
  on the temperature. The both concentrations CC
  and Cf are decreasing with increasing of R for
  temperature of 00C, in different degree for the
  different Cg(z) profiles. For temperature of
  300C, CC and Cf are also decreasing with the
  increasing of R for profile ?4, but for elevated
  gaseous tritium clouds (profile ?5), they are
  weakly increasing with the increasing of R. For
  the profile ?6 and temperature of 300C, CC and Cf
  depend weekly and indeterminately on R, similarly
  to the case of Cg(z) const, but for
  temperature of 00C and 150C they are decreasing
  with increasing of R.
• For all cases, the lower temperatures lead higher
  concentrations CC and Cf, higher flux J and
  washout coefficient WC. For the concentrations
  this effect is more significant for smaller
  rainfall rate R than for a bigger one. For the
  flux J and WC, the effect is more significant for
  bigger rainfall than for a smaller rain rate.

49
Rain Scavenging of HTO Some results and analysis
Typical behaviour of the washout outputs
Fig.5.4. Washout characteristics as a function
of rainfall rate (0.5, 3. , 30. mm.h-1), for
Cg(z) profiles ?4,5,6 with equable column HTO
amount 0.7g/cm2 for 0,15,300C.
c) HTO flux on the ground J
g/cm2.s linear y axis c) HTO flux on
the ground J g/cm2.s log y axis
50
Rain Scavenging of HTO Some results and analysis
Typical behaviour of the washout outputs
Fig.5.4. Washout characteristics as a function of
rainfall rate (0.5, 3. , 30. mm.h-1), for Cg(z)
profiles ?4,5,6 with equable column HTO amount
0.7g/cm2 for 0,15,300C.
d) Washout coefficient WC 1/s
linear y axis d) Washout coefficient
WC 1/s log y axis
51
Rain Scavenging of HTO Some results and analysis
51
Comments of the results
The dependence of J and WC on R is approximately
linear in logarithmic axes. However, if Cg is
function of z, unlike the cases of Cgconst, the
curve J(R) and WC(R) has different slope for
different temperatures and for different Cg(z)
profiles. Any attempt to define J or WC as a
simple function of R will lead up to a necessity
to define different functions for the different
temperatures and different Cg(z) profiles. In
case of incorporation of a Gaussian dispersion
model, the last means to J and WC as a functions
of height of the source, distance to it, as well
as a functions of atmospheric conditions. It
should be taken into account, that in case of
logarithmic y-axis, a comparison of the results
for different Cg profiles is risky. For example,
for R 0.5mm.h-1, the difference between the HTO
flux for temperature 00C and 300C is bigger for
profile ?4 (2.71e-10 g.sm-2.s-1), than for
profile ?5 (1.83e-10 g.sm-2.s-1), despite it
seems just opposite on the figure (Fig.5.4c -
logarithmic y-axis). By this reason, the HTO
flux and the washout coefficient is presented
twice on Fig.5.4c,d once in a linear y-axis and
second in a logarithmic y-axis. Obviously, the
processes are so complex, that any change of the
gaseous HTO layer thickness, a change of its
height, a change of temperatures can change the
tendencies and the results. In reality, the
gaseous tritium and the temperature could be
complex functions of z. A change of the rainfall
rate will, on the other hand, change the rain
spectral characteristics. The final effect from
such changes on the washout outputs is difficult
to be predicted without the help of a model.
52
Rain Scavenging of HTO Some results and analysis
52
Typical behaviour of the washout outputs
Fig.5.5. Washout characteristics for different
Cg(z) distributions ?1- 1.e-6, ?2 - 1.e-9, ?3
-1.e-21 g.cm-3 const profiles ?4,5,6 with
equable column HTO amount 0.7g/cm2, for
rainfall rate ( 0.5, 3.0, 30 mm.h-1),
temperature 15 0C.

The significance of the elevation and the shape
of the gaseous tritium cloud is obvious also from
Fig.5.5. The concentrations CC and Cf the flux
J are bigger when the cloud of gaseous HTO is
close to the ground (profile ?4), because when it
is high, the under layer evaporation causes a
decrease of their values. The both
concentrations CC and Cf are more sensitive to
the rainfall rate in case of surface gaseous HTO
cloud.
53
Rain Scavenging of HTO Some results and analysis
53
Typical behaviour of the washout outputs
Fig.5.5d is a good demonstration of advantages
and disadvantages of the washout coefficient
concept. If the gaseous HTO is distributed
homogeneously over z, the value of the washout
coefficient is one and the same, despite the big
difference in the amount of gaseous tritium in
the air. However, if the gaseous HTO is
distributed in different manner over z, even the
total amount of it is one and the same (profiles
?4,5,6), the values of WC are too different.
Fig.6 Washout coefficient for different Cg(z)
?1- 1.e-6, ?2 - 1.e-9, ?3 -1.e-21 g.cm-3 const
? 4,5,6 with equable HTO amount 0.7g/cm2,
for rainfall rate 3.0mm.h-1, for different
temperatures 0 0C, 15 0C, 30 0C.

The washout coefficient depends significantly on
the temperature - Fig.6. That is way, if one
wishes to use the washout coefficient concept,
the coefficient WC should be a function of
temperature and the Cg(z) profile, except of the
rainfall rate.
54
Rain Scavenging of HTO Some results and analysis
Comparison of the presents model and analytic
solution Belot(1998)
Washout coefficient as a function of downwind
distance, according to the present numerical
model and according to the analytic solution of
Belot(1998) for different height of the gaseous
HTO source.
Source height H60m
H30m
H10m
Reasons for the differences - numerical
approximation - dependence of Henrys low
coefficient, gas phase diffusion coefficient of
HTO and kinematic viscosity of air on
temperature and atmospheric pressure. -
normalization procedure
55
Rain Scavenging of Tritiated Water Vapour A
Numerical Eulerian Stationary Model

• Content
• Introduction - the present state of the HTO
  washout problem, intention of the present study
• Individual raindrop problem
• Modelling of HTO washout from the atmosphere
• Sensitivity analysis of the model
• Some results and analysis
• Conclusion - future development of the model

56
Rain Scavenging of HTO Conclusion - future
development of the model
56
Conclusion The study follows the approach
established by Hales (1972a,b) concerning the
processes in an individual raindrop, but
concerning the washout process, some innovations
are made   1) A new, numerical Eulerian
approach to the washout process is proposed. The
corresponding model describes only the washout
process, without to consider the dispersion. The
model is designed to be used as a numerical
subroutine in general models dealing with HTO
problems. The present model can be combined with
any advance dispersion model. As a result, the
washout model becomes free from the non-inherent
duty to take into account the height of the
source, distance from it, etc., and these tasks
are forwarded to the dispersion model, which is
by idea constructed to deal with them.   2) In
the traditional studies, the goal is to determine
the relative characteristics like washout
coefficient and ratio. However, later in
applications, these characteristics are used as
coefficients in simple formulas in order to
determine the absolute washout characteristics
like HTO downward flux and concentration in the
rain water. The present model is constructed to
determine directly the absolute washout
characteristics.
57
Rain Scavenging of HTO Conclusion - future
development of the model
Conclusion Different rain drops size
distributions and downfall velocities formulas
have been considered. A sensitivity analysis to
all of them and to other models parameters has
been performed. The analysis established
recommendable values for some numerical
parameters and procedures. A vertical grid step
of 10m is an appropriate choice, especially close
to a HTO source. The calculated spectral liquid
water content in the air and the liquid water
flux have to be normalized to the measured
rainfall rate. The sensitivity analysis has also
shown that both the rain parameters and the
temperature are influencing significantly the
washout process. Unlike the temperature which is
usually well known, the rain parameters are
difficult to be established precisely, that could
make the model's outputs substantially wrong.  
58
Rain Scavenging of HTO Conclusion - future
development of the model
Conclusion   The washout coefficient WC can be
determined as a relatively simple function of the
rainfall rate R in case of constant vertical
distribution of the gaseous HTO Cg(z). However,
if Cg(z) is not constant, the relationship
between WC and R becomes dependent on Cg(z) ,
i.e. on the characteristics of the HTO source and
atmospheric conditions and the dependence on the
temperature becomes more complex. It is not easy
to define such a function even theoretically
what is more, in practice there could be more
then one HTO source and the temperature is
changing with height. Obviously, the washout
processes are too complex to be described
comprehensively by simple parametresations like
the washout coefficient concept. A proposed here
alternative is to use the present model,
determining directly HTO concentration in the
rainwater CC and Cf and HTO downward flux J.
Anyway, the washout coefficient is needed mainly
to determine exactly these characteristics. On
the other hand, the present model gives the
washout coefficient also, if anybody needs it,
but it will take realistic different values at
different sites at different moments.  
59
Rain Scavenging of HTO Conclusion - future
development of the model
Conclusion   The present study makes some steps
toward modernization of the HTO washout
simulations, however significant shortcomings
still remain. More of them are related to the
description of the cloud-rain processes the
assumption for stationarity of the processes, the
assumption that the raindrops are falling down
without changing their size and velocity are
unrealistic. The solution of these problems is
related with provision of a better input
information for the cloud-rain processes. The
all washout models for now, including the present
one, use only the rainfall rate as the sole input
data for the rain phenomena. Today is easy to
get much more information the radars seem to be
the most promising source of data. They are able
to ensure information for the cloud and rain
drops distribution in space and time, for their
spectrum and movements (sometimes the drops are
moving even upward). A substantial
reconstruction of the modeling approach will be
necessary in order the models to be able to
incorporate this information.
60
Rain Scavenging of HTO Conclusion - future
development of the model

• Future development of the model
• 1) Modification of the program code as a
  subroutine
• in order to be used in general HTO models.
• 2) Validation of the models results on field
  measurements.
• 3) Determination of site , climatic specific
  cloud-rain characteristics.
• 4) Extension of the model for cases of fog and
  snowfall.
• 5) Inclusion of the radar measurements as input
  data

61
ENDthank you for attention