 Open Access
 Authors : Alain Didier Simo, Mathias Fonteh Fru
 Paper ID : IJERTV12IS060131
 Volume & Issue : Volume 12, Issue 06 (June 2023)
 Published (First Online): 29062023
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Numerical modeling of glyphosate transfer to underground water: Application to the Djuttitsa watershed in the Bamboutos mountain, WestCameroon
1* 1* 1
Alain Didier SIMO
, Mathias FONTEH FRU
Department of Agricultural Engineering, Faculty of Agronomy and Agricultural Sciences, University of Dschang, P.O Box 222 Dschang, Cameroon

INTRODUCTION
The world population increases at an alarming rate, with about 52% of this population expected to be found in urban areas in 2025. Africa has the highest population growth rate in the world, estimated as 2,55% each year from 2010 to 2015. By 2050, Africa is expected to represent about four quarter of the worlds population estimated as 1,3 billion inhabitants (AFD, 2014). Therefore, modern agricultural practices become an important challenge for food security (Abass et al., 2016). To increase food yield, Africa is faced by an excessive usage of pesticides without respect of recommended doses and frequency of application (white and Bunn, 2017). Soil and water pollution are direct consequences of this, with levels more than the authorised levels of 0.1 and 0.5 for maximal concentration of an individual pesticide and the total of all pesticides in water (Sousa et al., 2018). This shift from normal concentrations can induce severe consequences on population health (cancers, infertility, developmental abnormalities, neurotoxicity) (Huang et al., 2018). Pesticides intoxication is estimated at about 1 to 5 million cases per year in the world, with about 220 000 deaths each year. Developing countries use only 25% of the pesticides produced in the world but they account for 99% of deaths in the world due to pesticides poisoning especially in rural areas. To follow the evolution of pesticides in the soil and evaluate the risk of pollution, researchers have developed some numerical transfer models. However, the use of these models remains difficult in SubSaharan Africa due to insufficient data and inability to get some parameters. In this study, we therefore developed a 1D numerical model which was tested to study the glyphosate transfer at the watershed of Djuttitsa in West region of Cameroon. Their validation was done after statistical comparison of
concentrations obtained from the model to those from the laboratory.

MATERIALS AND METHODS

Presentation of the study site

For this study, Djuttitsa area was selected due to intensive agriculture with high use of pesticides. Predominant crops cultivated in this area are irish potatoes, cabbages and carottes. It is situated on the southern flank of the Bamboutos mountain in the West Region of Cameroon between latitude 5Â°24 and 5Â°45 North, and between longitude 10Â°2 and 10Â°40 (Figure 1).
Figure 1: Location of the study site

Mathematical modelling
Basic equations which were used by this model are: convectiondispersion equation which controls the transport of pesticides in the soil and Richards equation which controls water flow in the soil.

The convectiondispersion equation

Presentation
It is given by the equation (1) and subjected to constraint (2)
, ( ) – 0 ( ) 1 , – – ,
{ ( ) ( )
( ) ( )
(1)
( )
(2)
C = pollutant concentration in the soil in mol. l1
Kd = transfer coefficient between solid and liquid phase
D = dispersion coefficient = soil density in g.cm3
= water content in g.(cm3)1
Co = Pesticide initial concentration in mol. l1

Resolution using the finite volume method
The mesh admissible of – , is defined by a family ( ) , N such that
] [ , and a family ( ) such that :
with ( ) , i=1 , , N and
* +
Considering the time step. Let ,
n and ( )
By integrating equation on each control volume
of the mesh we have:
The flux : ( ) is approximated by :
By replacing in the previous scheme, we obtain the numerical scheme for the resolution of the convectiondispersion equation


Richards equation and resolution

Presentation
The Richards equation in 1D which governs water movement in the soil is given by equation (3) and subjected to constraints (4) and (5)
( ) , ( ) . /
( ) ( )
( ) ( )
{ ( ) ( )
(3)
Where K is the hydraulic conductivity: This describes the capacity of the soil to transfer water content for a given quantity of water.
is the relative pressure compared to the atmospheric pressure of water expressed in water height.
Z is the vertical axis positively oriented toward the down part.
The resolution of Richards equation in a saturated zone needs the knowledge of two others
hydrodynamic functions : ( ) ( )
The functions ( ) ( ) are defined
empirically by :
( )
( )
[( ) ( ) ]( )
{
. /
( )
( ) , ( ) –
( )
We choose upwind approximation of and so that :
et
Flux approximation.
The flux : ( )
{ , ( ) –
( )
These different parameters represent:
water content at natural saturation, hydraulic conductivity at saturation,
parameters related to soil structure,
the inflexion point of the retention curve
( ) defined by :
( )
,
( ) –
(2.4)

Resolution using the finite volume method
Given ( ) , the mesh admissible of the domain , . That is [ ] where the family ( ) such that :
With ( ) , i=1 ,
, N and
where
by replacing by its value in the relation (4), we have:
( ) with
,
We suppose that for all and the middle of the class . We then have,
and
where
* +



Determination of pedological parameters
Given ( ) discrete unknowns that
Granulometric analysis were done using the
pipette Robinson method to determine the soil
is
( ). We integrate equation (3.1) on
texture of the area. Water content was determined
the control volume and we obtain :
using the thermogravimetric , – method as well as
the bulk density , – and absorption coefficient
(2)
( ( ) )
( ( )
, . The hydraulic conductivity was recorded
using the permeameter method based on Darcys
law , . The soil organic carbon was determined
(2) becomes : . ( )
. ( ) / ( ) ( ) ( )
/ ( )
using the titration method , .
The percentage of organic matter is determined
using equation 6.
% OM =% CO x 1.724.
where ( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
Given an approximation of the flux
. ( ) / ( )
We have on
and on
(6)

Laboratory determination of glyphosate experimental concentrations
At the start, a glyphosate solution of molar mass 360 g/l was used. 100 ml of glyphosate was mixed with 15l of water, giving a ratio of 7 l for 1 l of water. The molar concentration obtained was 14,9×103 mol/l. The next step was the collection of nonpolluted soil samples at the study site. A solution of 50 ml glyphosate previously prepared was then introduced in a graduated biuret and the nozzle opened for glyphosate to be distributed in soil samples found in a cylinder under (kodel et al., 2001). The filtrate was collected at 10 min interval
Where
with et
( )
for 80 minutes and for each horizon. The experiment was repeated three times for a same horizon and time i order to reduce errors and the average of the 3 experiments was calculated and
From the principle of continuity of flux, there is an
equality between the two flux
recorded as the pesticide concentration. The absorbance of the solution was read at wavelength of 258 nm using a UVvisible spectrophotometer.
After obtaining the absorbance values, the Beer Lambert law was used to deduce corresponding concentrations. The BeerLambert law is given as:
(7)
= absorbance
= length of the cuve
= Molar extinction coefficient in
= Molar concentration of colored substances in mol.l1
Where and are the concentrations measured and estimated respectively. n is the total
number of measurement performed.
The KolmogorovSmirnov test was used to assess the normality of collected data using SPSS software.
The performance of each horizon was evaluated by calculating the efficiency according to Marin Benito et al., (2014).

Statistical analysis
To validate the developed model, four statistical
( )
( )
(10)
tests were made: The KolmogorovSmirnov test to check the normality of the values of the experimental concentrations and those simulated by the model. The ttest was used to compare values of experimental and simulated concentrations for the same horizon and at the same time; the standard mean error (SME) and absolute mean error (AME). The standard mean error (SME) which quantifies the gap between experimental concentrations and simulated concentrations was calculated using the following formula
( )
(8)
The absolute mean (AME or bias) error has been calculated as the ratio between the absolute error
: Observed value
: Mean of
: Simulated values
: Number of observations
The performance of the model was evaluated by calculating the average performance of all horizons.
3 Results
3.1 Numerical resolution of convection dispersion equation by finite volume method
The resolution of the convectiondispersion equation and Richards equation in 1D dimension using the finite volume method presented in the methodology lead us to the following numerical solution.
(difference between simulated concentrations and experimental concentrations) and the experimental
( ) ( )
( )
Horizo ns(cm) 

0 – 1 0 
1 0 – 2 0 
2 0 – 3 0 
3040 
4 0 – 5 0 
5 0 – 6 0 
6 0 – 7 0 
7 0 – 8 0 
8 0 – 9 0 
9 0 – 1 0 0 

Cla y% 
3 
5 
5 
3 
7 
9 
6 
3 
8 
9 
Silt % 
1 0 
1 4 
8 
8 
2 0 
1 9 
1 8 
1 7 
1 1 
1 0 
Sa nd % 
8 7 
8 1 
8 7 
89 
7 3 
7 2 
7 6 
8 0 
8 1 
8 1 
( )
( )
{
According to [9] the previous numerical scheme is
stable and converges towards the solution of continuous problem (1).

Characteristics of the soil
Results from the granulometric analysis of the soil are presented in Table 1. Based on the USDA textual triangle, these results shows that the soil is a sandy loam soil.
concentration for each horizon.
( )
(9)
Table 1: Results of granulometric analysis
Table 2 presents the physicochemical properties of soil samples used in this study.
Depht (cm)
Residual water content
( )
Saturated water content
( )
Absorption coefficient
Density
010
0.77
0.64
1.20
0.35
1020
0.57
0.52
1.10
0.28
2030
0.62
0.60
1.04
0.32
3040
0.38
0.37
1 .03
0.19
4050
0.45
0.59
0.77
0.26
5060
0.28
0.50
0.56
0.19
6070
0.44
0.50
0.88
0.24
7080
0.51
0.57
0.91
0.28
8090
0.48
0.58
0.83
0.27
90100
0.45
0.54
0.78
0.25
Table 2: The physical and chemical properties of soil samples
Table 3: Experimental concentrations of glyphosate obtained in filtrate (mol.l1)
Time (min)
Horizons (cm)
010
1020
2030
3040
4050
10
0,00487
0,00520
0,00367
0,00450
0,00520
20
0,00421
0,00483
0,00331
0,00421
0,00466
30
0,00302
0,00413
0,00290
0,00383
0,00447
40
0,00190
0,00343
0,00225
0,00322
0,00402
50
0,00223
0,00323
0,00176
0,00312
0,00235
60
0,00173
0,00283
0,00163
0,00287
0,00323
70
0,00144
0,00212
0,00134
0,00237
0,00283
80
0,00110
0,00183
0,00103
0,00212
0,00246
Time (min)
Horizon(cm)
5060
6070
7080
8090
90100
10
0,00603
0,00533
0,00543
0,00520
0,00433
20
0,00563
0,00513
0,00513
0,00503
0,00402
30
0,00513
0,00483
0,00483
0,00473
0,00354
40
0,00488
0,00440
0,00433
0,00383
0,00323
50
0,00467
0,00390
0,00412
0,00412
0,00283
60
0,00412
0,0035
0,00383
0,00277
0,00246
70
0,00390
0,00323
0,00353
0,00235
0,00223
80
0,00323
0,00274
0,00313
0,00223
0,00178
b) Simulated concentrations
Table 4 below presents the simulated values of different concentrations as a function of time
Table 4: Simulated concentrations obtained by the
Depht
ConductivitÃ© hydraulique Ã saturation
( ) en
CO%
OM%
PH
010
1,79
7,5
12,93
4,8
1020
1,80
7,29
12,56
4,2
2030
1,80
7,64
13,18
4,3
3040
1,79
7,43
12,81
4,5
4050
1,79
5,93
10,22
4,7
5060
1,79
4,79
8,25
4,7
6070
1,78
4,07
7,02
4,9
7080
1,79
3,64
6,28
5,2
8090
90100
1,78
1,77
3,79
3,76
6,53
6,32
5,4
5,1
1
model (mol.l )
Time (min)
Horizons (cm)
010
1020
2030
3040
4050
10
0,00557
0,00537
0,00385
0,00475
0,00555
20
0,00487
0,00511
0,00346
0,00437
0,00505
30
0,00321
0,00453
0,00312
0,00410
0,00483
40
0,00280
0,00408
0,00267
0,00367
0,00420
50
0,00252
0,00355
0,00222
0,00352
0,00367
60
0,00207
0,00313
0,00190
0,00323
0,00340
70
0,00183
0,00242
0,00153
0,00283
0,00307
80
0,00153
0,00220
0,00124
0,00245
0,00269
Time (min)
Horizon(cm)
5060
6070
7080
8090
90100
10
0,00615
0,00576
0,00585
0,00576
0,00445
20
0,00593
0,00547
0,00557
0,00532
0,00420
30
0,00547
0,00520
0,00517
0,00483
0,00376
40
0,00520
0,00483
0,00487
0,00394
0,00356
50
0,00480
0,00431
0,00454
0,00384
0,00311
60
0,00440
0,00380
0,00417
0,00333
0,00290
70
0,00407
0,00340
0,00370
0,00285
0,00272
80
0,00369
0,00303
0,00340
0,00245
0,00232

Experimental and simulated glyphosate concentrations obtained
a) Experimental concentrations
After polluting the soil samples with glyphosate and collecting the filtrates every 10 minutes. The spectrophotometer analysis gave the concentrations in mol.l1 of glyphosate at each horizon. The result is presented in table 3
Figures 2 to 7 show the simulated and experimental curves of the evolution of glyphosate for each horizon of the study area.
Figure 2: Simulated and experimental curve of the evolution of glyphosate at horizon of 4050 cm
Figure 3: Simulated and experimental curve of the evolution of paraquat at horizon of 5060 cm
Figure 4: Simulated and experimental curve of the evolution of glyphosate at horizon of 6070 cm
Figure 5: Simulated and experimental curve of the evolution of glyphosate at horizon of 7080 cm
Figure 6: Simulated and experimental curve of the evolution of glyphosate at horizon of 8090 cm
Figure 7: Simulated and experimental curve of the evolution of paraquat at horizon of 90100 cm
c) Error chart
Figure 12 shows the mean errors of simulated and experimental concentrations of the evolution of glyphosate.
Figure 8: Error chart of simulated and experimental concentrations of glyphosate
3.5 Statistical analysis
The normality test performed was the Kolmogorov test to verify if the data respects the normal law. Results of this test are presented in tables 5 and 6 below for the two cases: simulated and experimental data. Results show that simulated and experimental data respect the normal law at 10% critical value (P0.1). So the comparison test (t test) between simulated and experimental concentrations can be done followed by the test on the difference between the simulated and experimental concentrations. Table 6 presents a summary of results from statistical analysis comparing the differences between the values simulated by the model and those from the laboratory experiment.
Parameters 

6070 
7080 
8090 
90100 

Normal Mean Parameters 
0.003322 5 
0.003018 8 
0.002862 5 
0.002650 0 
Std.Deviatio n 
0.001397 5 
0.000932 6 
0.000987 4 
0.001067 0 
Most Extreme Differences 
0.159 
0.146 
0.140 
0.157 
Positive 
0.159 
0.138 
0.140 
0.157 
Negative 
0.127 
0.146 
0.139 
0.125 
Test Statistic 
0.159 
0.146 
0.140 
0.157 
Table 6: KolmogorovSmirnov test for experimental data
Paramete rs 
Horizons (cm) 

010 
1020 
2030 
3040 
4050 

Normal Me Parameters 
0.0036 950 
0.0043 063 
0.0034 850 
0.0029 588 
0.0028 488 
Std.Devia tion 
0.0012 876 
0.0011 360 
0.0014 652 
0.0005 122 
0.0011 318 
Most Extre Absolute D 
0.164 
0.178 
0.196 
0.195 
0.202 
Positive 
0.164 
0.149 
0.196 
0.150 
0.202 
Negative 
0.128 
0.178 
0.151 
0.195 
0.139 
Test Statistic 
0.164 
0.178 
0.196 
0.195 
0.202 
Parameters Horizons (cm)
5060 6070 7080 8090 90100
Normal Me 
0.00284 
0.0028 
0.0032 
0.0032 
0.0032 
Parameters 
25 
925 
488 
413 
063 
Std.Devi 
0.0010 
0.0010 
0.0010 
0.0010 
0.0011 
ation 
630 
961 
727 
012 
432 
Most Extre 
0.188 
0.150 
0.130 
0.125 
0.202 
Absolute D 

Positive 
0.188 
0.150 
0.127 
0.125 
0.202 
Negative 
0.152 
0.132 
0.130 
0.122 
0.118 
Test 
0.188 
0.150 
0.130 
0.125 
0.202 
Statistic
Clearances 
Horizons (cm) 

010 
1020 
2030 
3040 
4050 

MAPE(%) 
12,62 
10,88 
9,53 
9,41 
6,88 
RMSE 
0,00014 
0,00015 
0,00020 
0,00010 
0,00010 
Table 7: Values of SME and AME
MAPE RMS
Table 8: KolmogorovSmirnov test for simulated data
Clearances 
Horizons (cm) 

5060 
6070 
7080 
8090 
90100 

(%) 
18,07 
13,82 
6,09 
12,18 
18,29 
E 0,00016 0,00015 0,00008 0,00013 0,00020
Paramete rs 
Depht (cm) 

010 
1020 
2030 
3040 
4050 

Normal Me Parameters 
0.0033 013 
0.0038 825 
0.0035 638 
0.0026 738 
0.0031 038 
Std.Devia tion 
0.0013 918 
0.0012 162 
0.0088 019 
0.0004 833 
0.0014 325 
Most Extre Absolute D 
0.162 
0.142 
0.144 
0.144 
0.166 
Positive 
0.162 
0.138 
0.125 
0.109 
0.166 
Negative 
0.128 
0.142 
0.144 
0.144 
0.138 
Test Statistic 
0.162 
0.142 
0.144 
0.144 
0.166 
The ttest which compares the mean values of the simulated and experimental concentrations shows that 4 values have a significant difference at the
10% level ( ), 8 have a significant
difference at the 5% level (p0.05), 63 have a
highly significant difference at the 1% level (p0.01) and 4 values show a nonsignificant difference (NS).
3.6. Performance of the model
The MarinBenito formula (10) presented above was used to calculate the performance of the model to describe the evolution of the paraquat in the soil. Table 7 below presents the performance of each horizon.
Table 9: Efficiency of the model for each horizon
Dept h(c m) 
0 – 1 0 
1 0 – 2 0 
2 0 – 3 0 
3 0 – 4 0 
4 0 – 5 0 
5 0 – 6 0 
6 0 – 7 0 
7 0 – 8 0 
8 0 – 9 0 
9 0 – 1 0 0 
Effic ienc y 
0, 9 5 
0, 9 7 
0, 9 2 
0, 9 8 
0, 9 4 
0, 9 3 
0, 9 7 
0, 9 8 
0, 9 7 
0, 9 4 
The performance of the model was evaluated by calculating the average performance of all horizons.
4. Graphical interface of the model
Figure 13 shows the graphical interface of the developed model, where the user insert values or required parameters and click on the button
Â« Exe Â» to obtain simulated data of different concentrations of pesticides over soil ranges of 10 cm.
Figure 9: Graphical interface of the model
4. Discussion and conclusion
Most of the existing models take into account several phenomena such as absorption/desorption, degradation, hypodermic flow and infiltration to describe the transfer of pesticides in soils. This increases the number of parameters and data to be
used , . The model developed in this study
focused on infiltration and the parameters taken into
account were the bulk density, the soil/water partition coefficient, the water content and the hydraulic conductivity. The better approximation of the developed model would be due to the discretization technique used, the choice of constant horizons and the dimension of the model. Most of the existing models have been developed with an unstructured mesh that respects the natural stratification of the soil.
The KolmogorovSmirnov statistical test performed showed that the simulated and experimental values followed a normal distribution at the 10% threshold with a standard deviation of less than 0.01 in both cases. This shows a homogeneity in the values obtained which would be due to the best experimental measurement conditions and the good quality of the simulated values
Eighty glyphosate concentration values were simulated by the model for each soil horizon and at regular time intervals of 10 min for 80 min and 80 paraquat concentration values were obtained experimentally in the laboratory at the same horizons and at the same times. These 160 values were compared 2 to 2 for the same horizonand at the same time. It results that: 5 had a significant difference at the 10% level (p0.1). 9 have a significant difference at the 5% level (p0.05). 62 have a highly significant difference at the 1 level % (p0.01) and 4 values show a nonsignificant difference (NS). The best comparison results were obtained for pairs of values where the difference was nonsignificant (NS) and the worst comparisons were obtained with pairs where the p value was smallest (p0.01). Nonsignificant differences were obtained on the 1020. 4050 and 7080 horizons. respectively. after 20. 70. 70 and 80 minutes of flow.
These finding shows that the model used underestimates the values actually obtained in the laboratory, which could be due to the fact that climatic data were not taken into account in the construction of the model. The differences between the experimental values and those simulated by the model increase over time for the same horizon. On the other hand, the average of the deviations shows that it varies from one horizon to another. However, all the mean values of MAE remain very low 30%, a threshold for which a model is considered acceptable [16]. Likewise, the mean standard error (MSE) values are well below unity, further
confirming the quality and precision of the used model.
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