Fate in the Environment and Long-Range Atmospheric Transport of the Organophosphorus Insecticide, Chlorpyrifos and Its Oxon - Reviews of Environmental Contamination and Toxicology - page 48

The rate of change of mass M in the parcel is given by the following
relationships ( 7 ):

dV C
dt

´

=- ´´ + ´´

VCk
H

dM
dt

æ
ç

ö
÷ =

VCk

M

(7)

R

Integration from an initial mass M 0 gives the relationship ( 8 ):

æ
ç

k
H

ö
÷

æ
ç

ö
÷ ´

M

- k + t

R

MM = (8)

0

If a constant wind velocity U m h −1 is assumed, t can be replaced by L

U , where
L is distance in m. The CTD (m) is defined as L when the group in the exponent is

−1.0, i.e., CTD is:

U

(9)

k
H

æ
ç

ö
÷

k +

M

R

The corresponding characteristic travel time (CTT, expressed in h) is:

1

(10)

k
H

æ
ç

ö
÷

k +

M

R

This time has the advantage that it applies regardless of the assumed wind
velocity. When L equals CTD or CTT equals:

1 C

C

(11)

- 1

,and is e

k
H

æ
ç

ö
÷

k +

M 0

R

or 0.368 and 63.2% of the mass is lost by transformation and net deposition. A com-
plication arises when describing the behavior of CPY in that some of the deposited
CPY re-evaporates. The actual CTD is thus somewhat longer than that calculated,
but, for CPY, this is a relatively small quantity. In practice, this complication is read-
ily addressed by calculating the CTD by an alternative, but equivalent method,
which has become standard in LRT calculations. This is done by use of a multi-
media, mass balance model to calculate the steady-state mass of chemical in the
atmosphere of an evaluative environment which contains water and soil compart-
ments. The only emission is to air and no advective losses from air are included;
thus, the only losses from air are degrading reactions and net deposition processes,
i.e., deposition and absorption less volatilization. Since the rate of input to air is