Deposition

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Deposition is a process where compounds in air come down and stay in the soil or water. This page is a method about estimating deposition of different compounds.

Question

How to estimate deposition for different compounds?

Answer

Default key: UcK5o1jtjD3DMLT5 [2]

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library(OpasnetUtils)

# deposition: Function for estimating airborne compound deposition to soil or water.
# Result is given as kg/m^2 as a function of distance from the sorce.
# emission: amount of emission during a defined time period (in kg)
# rate: deposition rate (in kg/m)
# distance: how far is the deposition estimated from the suorce (default: 10000 m).
# hitpoint: it is assumed that the compound travels some distance in air before hitting the ground, i.e. deposition = 0 if distance < hitpoint.
deposition <- function(emission, rate, distance = 10000, hitpoint = 50) {
	distance <- 1:distance
	out <- data.frame(
		Distance = distance,
		Deposition = ifelse(distance < hitpoint, 0, rate * emission * exp(- rate * (distance - hitpoint)) / (2 * pi * distance))
	)
	plot(out)
	return(out)
}

objects.put(deposition)
cat("Function initiated. Save the page address key for further use.\n")

#example:
a <- deposition(emission = 1, rate = 0.01, hitpoint = 50)

Rationale

If there is no need to consider atmospheric chemistry, it can be assumed that everything that goes into the air eventually comes down. The question is: what is the geographical distribution of the deposition around the source?

For screening purposes, we can assume that the wind rose is a circle (especially if averaged over long periods of time), although in many places this is not true. However, meteorological information is not easily available and usable, and then the alternative is to not estimate anything. Therefore, a robust assumption is better than no estimate.

Many compounds of interest are naturally occurring compounds in small concentrations (such as metals), and many living organisms have developed some tolerance against exposure to these compounds. Therefore, if the exposure is very low (e.g. much smaller than natural background), we can assume that a very small deposition does not cause such increases in environmental concentrations that it would have any human or ecological impact. Thus, the critical question is this: what is the area where the deposition causes biologically significant increases in concentrations and thus exposures?

It is important to notice that if the deposition is very quick, the compound deposits near the source in high amounts, causing high exposures to very small area and small number of individuals. On the other hand, if the deposition is very low, the compound deposits in a very large area and a large number of individuals are exposed to biologically insignificant amounts. Therefore, there seems to be somewhere in between a deposition rate that causes the maximal health impact. What that deposition rate is, depends on the total emission, the threshold of biologically significant exposure, and the population distribution.

We can assume constant deposition rate as a function of distance from source, which results in exponential reduction of the compound in air:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M_r = M_0 * e^{-k r}}

where M is the mass of compound (in kg) in air when it has traveled distance r, and k is a deposition rate constant. This will result in deposition rate S (in kg/m²):

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S_r = \frac{-D(M_0 * e^{-k r})}{2 \pi r} = \frac{k M_0 e^{-k r}}{2 \pi r},}

which is the negative derivative of the mass in the air at distance r, divided by the circumference of a circle centered around the source at that distance. Time is not involved in the equation, because we are observing the situation integrated over a proper time period.

This results in a robust equation with only two parameters, deposition rate k and emission M₀ (and the emission is assumed to be known).

EUSES

In calculating the deposition flux, the emissions from the two sources (direct and STP) are summed. ^[1]

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle DEPtotal = (Elocal_{air} + Estp_{air})(Fass_{aer}*DEPstd_{aer} + (1-Fass_{aer}) DEPstd_{gas} } (682)

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle DEPtotal_{ann} = DEPtotal \frac{Temission}{365} } (682)

Symbol	Description	Unit	Status
Input
Elocal_air	local direct emission rate to air during emission episode	[kgc.d-1]	O
Estp_air	local indirect emission to air from STP during episode	[kgc.d-1]	O
Fass_aer	fraction of chemical bound to aerosol	[-]	O
DEPstd_aer	standard deposition flux of aerosol-bound compounds at source strength of 1 kg.d-1	[kgc.m-2.d-1]	D 0.01 mg /m² /d ^[2]
DEPstd_gas	deposition flux of gaseous compounds as function of Henry's Law coefficient, at source strength of 1 kg.d-1	[kgc.m-2.d-1]	D ?? mg /m² /d ^[2]
Temission	number of days per year that emission occurs	[d.yr-1]	O
Output
DEPtotal	total deposition flux during emission episode	[kgc.m-2.d-1]	O
DEPtotal_ann	annual average total deposition flux	[kgc.m-2.d-1]	O

The S, D, O or P classification of a parameter indicates the status:

S Parameter must be present in the input data set for the calculation to be executed (there is no method implemented in the system to estimate this parameter; no default value is set).
D Parameter has a standard default value (most defaults can be changed by the user). Defaults are presented in the sub-module, where they are used in separate tables. Sets of changed default values can be saved.
U This parameter is ‘unspecified’, no default value is set.
O Parameter is output from another calculation (most output parameters can be overwritten by the user with alternative data).
P Parameter value can be chosen from a 'pick-list' with values.
c Default or output parameter is closed and cannot be changed by the user.
* An asterisk is added when a parameter can be set to a different value on the regional and continental spatial scale.

Mixing depths of compounds: 0.1 m in grassland soil, 0.2 m in agricultural soil.^[3]

References

↑ EUSES model 2.1, documentation: Chapter 3, "Model Calculations", page 296 [1]
↑ ^2.0 ^2.1 default value from EUSES model 2.1.2, assuming 1 kg /d emission and 2.78E-04 mg /m³ air concentration.
↑ default value from EUSES model 2.1.2

Related files

[1] EUSES model 2.1, documentation: Chapter 3, "Model Calculations", page 296 [1]

[eusesdefault-2] 2.0 ^2.1 default value from EUSES model 2.1.2, assuming 1 kg /d emission and 2.78E-04 mg /m³ air concentration.

[3] ult value from EUSES model 2.1.2

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