Page 1 of 11
_______________________________________ DATE:
5/13/2021
5/13/2021
5/13/2021
5/13/2021
DATE: _________
California Department of Pesticide Regulation
Environmental Monitoring Branch
1001 I Street, Sacramento, CA 95814-4015
SOP Number: METH009.02
Previous SOP: METH009.01
STANDARD OPERATING PROCEDURE
Calculation of Pesticide Half-life from a Terrestrial Field Dissipation Study
KEY WORDS
Linear regression, TFD, mass, first order decay, half-life
APPROVALS
Original signed by
APPROVED BY: _________
Joy Dias
Environmental Monitoring Branch, Environmental Program Manager
Original signed by
APPROVED BY: _______________________________________ DATE: _________
Tiffany Kocis
Environmental Monitoring Branch, Senior Environmental Scientist
Original signed by
APPROVED BY: ______________________________________ DATE: __________
Vaneet Aggarwal, Ph.D.
Environmental Monitoring Branch, Environmental Scientist (QA Officer)
Original signed by
PREPARED BY: _______________________________________
Rick Bergin
Environmental Monitoring Branch, Senior Environmental Scientist
Environmental Monitoring Branch organization and personnel, such as management,
senior scientist, quality assurance officer, project leader, etc., are defined and discussed
in Standard Operating Procedure (SOP) ADMN002.
Previous Authors: Chang-Sook Lee Peoples, Murray Clayton, Lisa Ross, Ph.D.
California Department of Pesticide Regulation SOP Number: METH009.02
Environmental Monitoring Branch Previous SOP: METH009.01
1001 I Street, Sacramento, CA 95814-4015 Page 2 of 11
STANDARD OPERATING PROCEDURE
Calculation of Pesticide Half-life from a Terrestrial Field Dissipation Study
= 

ln
(
)
= ln
(
)

1.0 INTRODUCTION
For pesticide products being registered in California, the Department of Pesticide
Regulation (DPR) characterizes various physical-chemical properties of the
products’ active ingredients (A.I.s). Terrestrial field dissipation (TFD) half-life is one
property that is characterized. The half-life of a substance is defined as the time it
takes for a substance to decrease its amount by half. Of the various methods for
determining a half-life of an A.I., DPR has adopted the method described by Fossen
(2006). However, a lack of specificity in data preparation prior to the half-life
calculation has resulted in inconsistency in the determination of TFD half-life values.
Current DPR procedure, as specified by Fossen (2006), utilizes the first order decay
function:
Eq. 1
Where:
Y = amount of pesticide at time=t [mg/m
2
]
A = initial amount of pesticide [mg/m
2
]
k = dissipation rate constant [days
-1
]
t = time [days]
Note that k is taken to be positive and Eq. 1 explicitly uses a negative sign in order
to represent the loss rate. The remaining problem is to find k, the dissipation rate
constant. In order to find k, perform a natural log transformation on Eq. 1, which
yields:
Eq. 2
A linear regression of ln(Y) on t can now be used to estimate k (Eq. 2). With an
estimate for k, the half-life (days) can be calculated by setting Y=0.5A in Eq. 1 and
then solving for t. After taking the natural log of both sides, and rearranging, the
result is Eq. 4. Eq. 4 is then used to estimate the TFD half-life of the pesticide.
California Department of Pesticide Regulation SOP Number: METH009.02
Environmental Monitoring Branch Previous SOP: METH009.01
1001 I Street, Sacramento, CA 95814-4015 Page 3 of 11
STANDARD OPERATING PROCEDURE
Calculation of Pesticide Half-life from a Terrestrial Field Dissipation Study
1.2.1 DAFT - Days After Final Treatment: the time interval between sampling
event and date of pesticide application.
1.2.2 LOQ - Limit of Quantification: the lowest concentration of a substance
that a method of analysis can reliably quantify.
1.2.3 LOD - Limit of Detection: the lowest concentration of a substance that a
method of analysis can reliably detect.
1.2.4 ND - Nondetect: no pesticide residue was found in an analyzed soil
sample above the LOD.
2.1.1 TFD Study
2.2.1 Computer program capable of performing a regression using least
squares methodology (SAS, Minitab, etc.)
3.1.1 Convert all concentrations to mg/kg (ppm), if they are not already
reported as such.
3.1.1.1 Concentrations must be reported on a dry soil-weight basis. See
SOP METH006.00 for more information (Segawa, 2008).
3.1.1.2 If numeric estimates between LOD and LOQ are not provided, a
value equivalent to 1/2(LOD+LOQ) will be used as a substitute; this
value is halfway between the LOD and LOQ.
3.1.1.3 If the residue in a soil core is below the LOD, then treat it as zero.
3.1.2 Convert all soil core segment lengths into meters. A 6 in. long segment
is equivalent to 0.1524 m.
1.1 Purpose
The purpose of this document is to standardize the calculation of a TFD half-
life, using a first-order decay function.
1.2 Definitions
2.0 MATERIALS
2.1 Documents
2.2 Software
3.0 PROCEDURES
3.1 Unit Conversions
California Department of Pesticide Regulation
Environmental Monitoring Branch
1001 I Street, Sacramento, CA 95814-4015
SOP Number: METH009.02
Previous SOP: METH009.01
Page 4 of 11
STANDARD OPERATING PROCEDURE
Calculation of Pesticide Half-life from a Terrestrial Field Dissipation Study
3.1.3 Convert residue data from a mass per dry soil-weight basis to a mass
per surface area basis for each segment in the soil column; mg/kg to
mg/m
2
. See Eq. 3.
3.2.1 At each sampling event in the TFD study, sum all residue mass in the
soil column.
3.2.2 Determine the natural log of the total residue mass of the soil column at
each sampling event.
3.2.2.1 If a study has multiple replications during each sampling event, see
section 5.1: Field Subdivided into Blocks.
3.3.1 Perform linear regression on the natural log-transformed residues. The
natural log-transformed total residue mass is the y-axis variable and the
corresponding sampling event, as DAFT, is the x-axis variable.
3.3.1.1 Record the p-value of the regression slope and indicate its
significance at p ≤ 0.05.
3.3.1.2 The coefficient of the predictor variable Slope in Fig. 1 (-0.00609) is
the slope of the regression line and is equal to k, the dissipation
rate constant.
3.2 Data Aggregation
3.3 Linear Regression
Figure 1. Regression performed with statistical software. Data used in this regression is located in Table
2, column "Average In."
California Department of Pesticide Regulation
Environmental Monitoring Branch
1001 I Street, Sacramento, CA 95814-4015
SOP Number: METH009.02
Previous SOP: METH009.01
Page 5 of 11
STANDARD OPERATING PROCEDURE
Calculation of Pesticide Half-life from a Terrestrial Field Dissipation Study
3.3.1.3 The R-Squared value in Fig.1 is 0.96. Values approaching 1.0
indicate a better fit to the regression model.
3.3.1.4 The p-value for the slope should be equal to or less than 0.05,
indicating a statistically significant regression, and giving
confidence in the model.
3.3.2 Convert the rate constant into a half-life value. The units are consistent
with those used for the x-axis variable and are typically in days. See
Eq. 4.
4.1.1 Convert from concentration to mass per area.
=
M = mass of pesticide residue on an area basis [mg/m
2
]
C = concentration of pesticide residue [mg/kg] (ppm by dry weight)
ρ = bulk density of soil segment [kg/dm
3
] = [g/cm
3
]
l = length of soil segment [m]
F = scaling factor, 1000 [dm
3
/m
3
]
(.)
/
=
t
1/2
= half-life of pesticide [days]
k = dissipation rate constant [days
-1
]
4.0 CALCULATIONS
4.1 Preliminary Calculations
This conversion addresses problems associated with calculating half-lives on
a concentration basis by accounting for the in-field variation of bulk density
and differences in soil segment length between samples. Pesticide residues in
each soil segment are converted from a concentration value to a mass per
surface area value.
Eq. 3
Where
4.2 Conversion of Rate Constant to Half-life
Eq. 4
Where
California Department of Pesticide Regulation SOP Number: METH009.02
Environmental Monitoring Branch Previous SOP: METH009.01
1001 I Street, Sacramento, CA 95814-4015 Page 6 of 11
STANDARD OPERATING PROCEDURE
Calculation of Pesticide Half-life from a Terrestrial Field Dissipation Study
5.1.1 Studies often divide the field into different blocks and report the
resulting residues from each block separately. Ensure residue mass is
summed from soil columns within the block at each sampling time, not
amongst the blocks (Table 1).
5.1.2 At each sampling time, the summed residue mass in each soil column
of each block must be log-transformed individually (Table 2). If the
study has 4 blocks, then there are 4 values per sampling event to log-
transform.
5.0 STUDY-SPECIFIC CONSIDERATIONS
5.1 Field Subdivided into Blocks
Table 1. Aggregation of residues [mg/m2] by block. In this table, concentrations have already been
converted to mass per unit area using Eq.3.
DAFT
Block A
Block B
Block C
Block D
0-6”
6-12”
Sum
0-6”
6-12”
12-18”
Sum
0-6”
6-12”
12-18”
Sum
0-6”
6-12”
12-18”
Sum
0 159.7 159.7 154.5 154.5 127.3 127.3 158.5 158.5
3 125.8 125.8 86.5 86.5 120.9 120.9 174.7 2.4 177.1
7 158 158 104.6 104.6 112.9 112.9 89.3 89.3
14 92.6 92.6 67 67 92.1 92.1 56 56
21 91.4 91.4 83.2 83.2 98 98 71.8 2.7 74.5
28 82.5 3.3 85.8 103.3 103.3 66.4 66.4 72.3 72.3
59 79.5 2.3 81.8 52.3 52.3 56.2 8.7 64.9 45.3 4.3 49.6
89 44.9 6.3 51.2 37.3 4.4 41.7 42.2 6.3 48.5 41.8 5.5 47.3
119 23.8 8.2 2.1 34.1 28 4.3 32.3 45.2 4.8 50 34.4 6 40.4
150 31.7 5.8 37.5 25.3 7.6 32.9 32.3 5.2 37.5 24.6 24.6
180 21.7 5 26.7 23.8 5.7 29.5 23.2 3.5 26.7 24.4 4 28.4
243 27.2 7.2 34.4 17.5 6.4 23.9 20.2 4.5 3.6 28.3 12.7
6.8 2.9 22.4
300 16 5.5 2.8 24.3 17.7 5 2.8 25.5 16.5 6.1 22.6 12.7 2.6 15.3
361 11.7 2.3 14 10.7 10.7 15.7 2 17.7 13.2 13.2
421 7.9 7.9 5.5 5.5 9.7 2.9 12.6 7 7
486 4 4 4.2 4.2 10.8 10.8 3.8 3.8
539 3 3 2.5 2.5 3 3 5.7 5.7
California Department of Pesticide Regulation SOP Number: METH009.02
Environmental Monitoring Branch Previous SOP: METH009.01
1001 I Street, Sacramento, CA 95814-4015 Page 7 of 11
STANDARD OPERATING PROCEDURE
Calculation of Pesticide Half-life from a Terrestrial Field Dissipation Study
5.1.3 Average the natural log-transformed residues of all blocks to get only
one value for each sampling time. The bold values in Table 2, in the
column labeled “Average ln”, are regressed against DAFT in the first
column of Table 2. For blocks with nondetects, see section 5.2.
5.2.1 For studies with multiple blocks, ensure that all the blocks have total
residue concentrations ending at the same final sampling time. If the
blocks have total residue concentrations ending at different sampling
times, then follow the procedure below. This should occur before
converting residue concentrations to a mass per area.
5.2.1.1 First, identify the block or blocks with the last measurable residue
concentrations. This will dictate the number of sampling times to be
used in the determination of the half-life.
5.2.1.2 Next, replace earlier nondetects (NDs) in the remaining blocks with
residue concentrations (see below) until all the blocks end at the
same final sampling time. Assign ½ LOD for the first (earliest) ND,
¼ LOD for the next ND, 1/8 LOD for the next ND, etc.
Table 2. Transformation and averaging of data. For example, 5.07 is the transformed sum from Block A of
Table 1 at DAFT = 0, 5.07 = ln(159.7).
DAFT
ln(Block A)
ln( Block B)
ln(Block C)
ln(Block D)
Average ln
0
5.07
5.04
4.85
5.07
5.01
3
4.83
4.46
4.79
5.18
4.82
7
5.06
4.65
4.73
4.49
4.73
14
4.53
4.20
4.52
4.03
4.32
21
4.52
4.42
4.58
4.31
4.46
28
4.45
4.64
4.20
4.28
4.39
59
4.40
3.96
4.17
3.90
4.11
89
3.94
3.73
3.88
3.86
3.85
119
3.53
3.48
3.91
3.70
3.65
150
3.62
3.49
3.62
3.20
3.49
180
3.28
3.38
3.28
3.35
3.33
243
3.54
3.17
3.34
3.11
3.29
300
3.19
3.24
3.12
2.73
3.07
361
2.64
2.37
2.87
2.58
2.62
421
2.07
1.70
2.53
1.95
2.06
486
1.39
1.44
2.38
1.34
1.63
539
1.10
0.92
1.10
1.74
1.21
5.2 Nondetects and Uneven Sampling Times (“1/2 LOD Rule”)
California Department of Pesticide Regulation SOP Number: METH009.02
Environmental Monitoring Branch Previous SOP: METH009.01
1001 I Street, Sacramento, CA 95814-4015 Page 8 of 11
STANDARD OPERATING PROCEDURE
Calculation of Pesticide Half-life from a Terrestrial Field Dissipation Study
5.2.1.3 Table 3 shows the raw data as presented by the registrant. Table 4
shows the raw data transformed by the “1/2 LOD Rule” (LOD=1
ppm). Block B has the last measurable residue detection (DAFT
30). Blocks A and C have successive fractions of the LOD added to
the 0-6” column until they have the same number of data points as
Block B, all ending at DAFT 30. The “-” in Table 3 denotes a zero
for purposes of summation. Then resume following this SOP at
section 3.1 to complete the regression.
Table 3. Raw data from registrant [ppm].
DAFT
Block A
Block B
Block C
0-6”
6-12”
12-18”
0-6”
6-12”
12-18”
0-6”
6-12”
12-18”
0
35
ND
ND
37
ND
ND
40
ND
ND
1
30
1
ND
29
3
ND
25
7
ND
2
15
4
ND
12
5
1
10
4
1
5
10
3
1
7
2
2
6
2
1
10
5
1
ND
7
ND
1
2
1
ND
20
2
ND
ND
2
1
ND
ND
ND
ND
30
ND
ND
ND
1
ND
ND
ND
ND
ND
50
ND
ND
ND
ND
ND
ND
ND
ND
ND
70
ND
ND
ND
ND
ND
ND
ND
ND
ND
Table 4. Data after the "1/2 LOD Rule" is applied [ppm]. Gray highlighted cells indicate where the “1/2
LOD Rule” has been applied.
DAFT
Block A
Block B
Block C
0-6”
6-12”
12-18”
0-6”
6-12”
12-18”
0-6”
6-12”
12-18”
0
35
-
-
37
-
-
40
-
-
1
30
1
-
29
3
-
25
7
-
2
15
4
-
12
5
1
10
4
1
5
10
3
1
7
2
2
6
2
1
10
5
1
-
7
-
1
2
1
-
20
2
-
-
2
1
-
0.5
-
-
30
0.5
-
-
1
-
-
0.25
-
-
50
-
-
-
-
-
-
-
-
-
70
-
-
-
-
-
-
-
-
-
California Department of Pesticide Regulation
Environmental Monitoring Branch
1001 I Street, Sacramento, CA 95814-4015
SOP Number: METH009.02
Previous SOP: METH009.01
Page 9 of 11
STANDARD OPERATING PROCEDURE
Calculation of Pesticide Half-life from a Terrestrial Field Dissipation Study
5.3 Biphasic Degradation
5.3.1 It sometimes appears that dissipation proceeds at two different rates
over the course of a study: often an initial fast rate followed by a slow
rate.
5.3.2 DPR policy will be to use all of the data when performing the linear
regression, unless there is a good reason to omit some data points.
This provides a consistent way to compare the dissipation rates of
different pesticides. A good reason to omit data points would be
something going wrong with the experiment itself.
5.4 Multiple Applications
5.4.1 If multiple pesticide applications are made to a TFD study, then linear
regression should only be conducted on residue data measured after
the final pesticide application.
5.4.1.1 Example: Pesticide in a TFD study is applied 3 times at 30 day
intervals to the same site. The DAFT starts after the third
application.
5.4.1.2 Note in any write-up or summary that multiple applications to a site
occurred during the TFD study.
5.5 Missing Data for Mass Conversion
5.5.1 Missing bulk density data
5.5.1.1 Sometimes soil bulk density is omitted from TFD reports, making it
impossible to convert pesticide concentration values into mass per
surface area values.
5.5.1.2 Soil bulk density can be estimated from soil texture, organic matter
content, and the degree of soil compaction by utilizing the empirical
equations from Saxton and Rawls (2006). These equations are in
the “Soil Water Characteristics” calculator, published by the NRCS
(2016), which can be used to estimate soil bulk density.
5.5.1.3 TFD turf studies often omit bulk density data for the thatch layer.
However, pesticide concentrations can be converted to a mass per
surface area basis if the study provides the weight and the surface
area of the thatch sample. See Eq. 5.
California Department of Pesticide Regulation SOP Number: METH009.02
Environmental Monitoring Branch Previous SOP: METH009.01
1001 I Street, Sacramento, CA 95814-4015 Page 10 of 11
STANDARD OPERATING PROCEDURE
Calculation of Pesticide Half-life from a Terrestrial Field Dissipation Study
∗
=
5.5.1.3.1 Eq 5.
M = mass of pesticide residue on an area basis [mg/m2]
C = concentration of pesticide residue in thatch [mg/kg]
W = weight of thatch [kg]
A = Area of thatch [m2]
Where
5.5.1.3.2 If all descriptive information on the thatch layer is missing,
then you may use the thatch parameters from the PRZM turf
scenarios (USEPA, 2014): bulk density = 0.37 g/cm
3
and turf
thickness = 2 cm.
California Department of Pesticide Regulation SOP Number: METH009.02
Environmental Monitoring Branch Previous SOP: METH009.01
1001 I Street, Sacramento, CA 95814-4015 Page 11 of 11
STANDARD OPERATING PROCEDURE
Calculation of Pesticide Half-life from a Terrestrial Field Dissipation Study
6.0 REFERENCES
Contact [email protected]ov for references not currently available on the web.
Fossen, M. 2006. “2006 Revision: Documentation of Procedures for Filling Out
PESTCHEM Data Coding Sheets.” Environmental Monitoring Branch,
California Department of Pesticide Regulation, Sacramento, CA.
Saxton, K. and Rawls, W. 2006. “Soil Water Characteristic Estimates by Texture
and Organic Matter for Hydrologic Solutions.” Soil Sci. Soc. Am. J. 70:1569–
1578.
Segawa, R. 2008. “Calculating Pesticide Concentration in Dry and Wet Soil. SOP
METH006.00. Environmental Monitoring Branch, Environmental Monitoring
Branch, California Department of Pesticide Regulation, Sacramento, CA.
NRCS, 2016. “SPAW Hydrology and Water Budgeting, Soil Water Characteristics.”
Natural Resources Conservation Service, United States Department of
Agriculture. Available at:
https://www.nrcs.usda.gov/wps/portal/nrcs/detailfull/national/water/
manage/drainage/?cid=stelprdb1045331 (verifie d April 28, 2021).
USEPA. 2014. Pesticide Root Zone Model v. 5. Center for Exposure Assessment
Modeling, National Exposure Research Laboratory - Ecosystems Research
Division, Office of Research and Development, United States Environmental
Protection Agency, Athens, Georgia.