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To assess the groundwater vulnerability due to leaching of chemicals, the groundwater system in the unsaturated zone is characterized by conceptual models that are further extended and refined with more detailed mathematical models to understand the governing physical processes in detail. However, due to lack of data and uncertainty level, an intermediate transition through index based models is researched. The attenuation factor (AF) approach, which works under the assumption that the chemicals degrade following a first-order kinetics and determines the fraction of the chemicals that goes to groundwater table, is one of the index based models that has been widely used due to its simplicity. Therefore, the objective of this paper is to review the research works done using the AF approach, to outline the future research needs. Furthermore, the mathematical implementation of the AF approach and the associated uncertainty levels is explained through an example and MATLAB source code.

Chemical fate and transport models are used to assess groundwater vulnerability due to leaching. There are three types of models. They are index based models, processed based models, and statistical based models. The index based models which exclude important processes and are conceptual are used for preliminary investigations, as they are not data intensive. Due to its simplicity, the index based models are useful specifically in relative vulnerability assessments based on relative or reference chemicals whose leaching behaviors are known from field/experimental/modeling studies [

AF, which ranges between 0 and 1, is defined as the fraction of the pesticide that goes to groundwater table (GWT). For example, referring to

In AF approach, as shown in

where M, M_{0}, t and K are mass leaching past the zone, mass entering the zone, the travel time and the first-order degradation coefficient, respectively. Assuming that_{2}) is given by Equation (2’’’’).

where

Considering that the total travel time (T) is approximately equal to

where d, ϑ, q, t_{1/2}, ρ, f, and K are depth to groundwater table (m), moisture content at field capacity, recharge rate or average water flow rate through soil (m/day), half-life time of the applied pesticide (days), bulk density (kg/m^{3}), faction of organic carbon content, and soil organic carbon sorption coefficient (m^{3}/kg), respectively.

With the analysis of available data, [

VOCs are a group of chemicals with high vapor pressures, which can cause public health risk. Ki and Ray [

where^{2}/day),dimensionless Henry’s constant, thickness of stagnant boundary layer above ground surface (m), and air-filled porosity, respectively.

Though the index based models are the simplest in assessing the groundwater vulnerability due to leaching of chemicals, the index based models are associated with input uncertainties such as uncertainties in soil properties (e.g., θ and ρ), climate (e.g., q), and pesticide properties (e.g., t_{1/2}). Therefore, there is a need to associate an error band on AF. As per [

where

Loague et al. [

The concept of reference chemicals are introduced for the purpose of relative vulnerability assessments. The reference chemicals are the pesticides whose leaching behaviors are known under local conditions based on field/experimental/modeling studies, and that have sufficiently different mean AFRs and low standard deviations [

The reference chemicals are used to categorize the pesticides as “leachers” or “nonleachers”. To illustrate the method of categorization using the concept of reference chemicals, few chemicals with the associated AFR values in Rhodic Eutrustox soil are placed in

The midpoint between these two points (i.e., between −1 and 1) becomes the origin of the normalized axis, and the distance between the origin and either of the two normalized means is assigned one unit in the normalized axis [

Chemical Name | AFR | Remarks | Normalized AFR |
---|---|---|---|

DBCP | 3.12 | Reference chemical as leacher | −1 |

Diuron | 6.03 | Reference chemical as non-leacher | +1 |

Anilazine | 11.63 | These chemicals are categorized as “leachers” or “nonleachers” based on the reference chemicals. | +4.83 |

Dicamba | 1.92 | −1.82 | |

Ametryn | 5.49 | 0.62 |

found to be

ing the AFR value. Then for any chemical of interest that need to be categorized based on reference chemicals, its means and standard deviations are converted to normalized scale. For example, as shown in

normalized mean of Anilazine is

normalized standard deviations) for the chemicals. As shown in

The classification of the selected chemicals (i.e., Ametryn, Dicamba, and Anailazine) with respect to the reference chemicals (i.e., DBCP and Diuron) is shown in

Though AF approach is an index based model, the accurate prediction of AF heavily relies on some site specific data. As reported in the literature [

Mathematical models are used to understand the complex phenomena. Therefore, the determination of model parameters that are most influential on model results is one of the important phases in model development. Oftentimes, the parameters that are most influential are identified through a sensitive analysis.

Based on a sensitive analysis of parameters using Latin-Hypercube-One-factor-At-a-Time (LH-OAT) method, [_{1/2}. For this study, the samples are obtained from 10 equiprobable intervals in a 11-dimensional parameter space for a loop of 10,000 iterations. This study also concludes that the AF approach is least sensitive to parameters such as ϑ and ρ.

As underscored in the literature [

widely used to compare the outcome of AF approach.

STANMOD is designed to analyze solute transport in soils using analytical solutions of convection-dispersion solute transport equation [_{1/2}, ρ, f, and K) used in STANMOD are the same as in AF approach. Some of the parameters such as chemical properties (e.g., K and t_{1/2}) come from an in-built database that is taken from [

On the other hand, HYDRUS-1D is an interactive model for simulating one-dimensional water flow, heat transport, and solute movement in variably saturated soils (i.e., between the groundwater surface and the ground water table). In HYDRUS-1D, the water flow is modeled by Richards’ equation. The solute movement and heat transport are modeled through Fickian-based advection-dispersion equation [

In this section, the computation of AF approach is explained by selecting a soil in the state of Hawaii. The statistical properties of the soil and the chemical (i.e., Diuron) are placed in

Based on the values of the parameters presented in

As discussed previously, in AF approach, the inputs are associated with uncertainties. The uncertainty levels of the inputs are represented through the given standard deviations (

Soil Taxonomic Category | ||||||||
---|---|---|---|---|---|---|---|---|

Mean | SD | Mean | SD | Mean | SD | Mean | SD | |

Soil No 8(Order) | 687 | 248 | 0.41 | 0.1 | 0.09 | 0.05 | 0.383 | 0.276 |

^{*}SD: Standard Deviation; d = 0.5 m ± 0.25 m; t_{1/2} = 27.5 days ± 43.8 days; q = 0.001 m/day ± 0.0005 m/day.^{ }

The computed value of

MATLAB® is a high-level language and an interactive environment for numerical computation, visualization, and programming. More than a million engineers and scientists in industry and academia use MATLAB to analyze data, develop algorithms, and create models and applications [

In the given source code, within the mainFunction(), few global variables are declared to store the input data for the AF approach. The input data is read from a user specified spreadsheet. The input data has the mean and the standard deviation of the variables (e.g., d, ϑ, q, t_{1/2}, ρ, f, and K) that are used in the AF approach as explained in Section 2.0. The assignments of the global variables are carried out within the function named assignVariables(). Having assigned the variables, the computation of AF and RF are performed by calling the function named computeAFRF(). To compute the standard deviations of AF and RF, two functions namely computeSDAF() and computeSDRF() are called within the mainFunction(). These functions are used to compute the CV values, as discussed in Section 5.0, for each of the variables (e.g., d, ϑ, q, t_{1/2}, ρ, f, and K) that are used in the AF approach. The final outcomes (i.e., values of AF, RF, and standard deviations of AF and RF) of the simulation are stored in a spreadsheet that can be visualized using one of the GIS software.

%Declaration of global variables

%Reading from a worksheet

%Calling of functions

function mainFunction()

global AFData RF AF SDRF SDAF;

global Density SDDensity f SDf Theta SDTheta K SDK q SDq Halflife SDHalflife d SDd;

AFData = readtable('afinput.xlsx','Sheet','parameters');

assignVariables();

computeAFRF();

computeSDRF();

computeSDAF();

writeOutput(RF,SDRF,AF,SDAF,'afoutput.xlsx');

displayGraph(RF,SDRF)

end

%Assignment of variables

function assignVariables()

global AFData;

global Density SDDensity f SDf Theta SDTheta K SDK q SDq Halflife SDHalflife d SDd;

Density = AFData{:,{'Density'}};

SDDensity=AFData{:,{'SDDensity'}};

f=AFData{:,{'f'}};

SDf=AFData{:,{'SDf'}};

Theta=AFData{:,{'Theta'}};

SDTheta=AFData{:,{'SDTheta'}};

K=AFData{:,{'K'}};

SDK=AFData{:,{'SDK'}};

q=AFData{:,{'q'}};

SDq=AFData{:,{'SDq'}};

Halflife=AFData{:,{'Halflife'}};

SDHalflife=AFData{:,{'SDHalflife'}};

d=AFData{:,{'d'}};

SDd=AFData{:,{'SDd'}};

end

%Computation of AF and RF

functioncomputeAFRF()

global RF AF ;

global Density SDDensity f SDf Theta SDTheta K SDK q SDq Halflife SDHalflife d SDd;

RF=1+Density.*f.*K./Theta

AF=exp(-0.69.*d.*RF.*Theta./q./Halflife);

end

%Computation of standard deviation of RF

function computeSDRF()

globalAFData;

global SDRF;

global Density SDDensity f SDf Theta SDTheta K SDK q SDq Halflife SDHalflife d SDd;

CVTheta=-1.*Density.*f.*K./(Theta.^2).*SDTheta;

CVDensity=f.*K./Theta.*SDDensity;

CVf=Density.*K./Theta.*SDf;

CVK=Density.*f./Theta.*SDK;

SDRF=(CVTheta.^2+CVDensity.^2+CVf.^2+CVK.^2).^0.5

end

%Computation of standard deviation of AF

function computeSDAF()

global AFData;

global Density SDDensity f SDf Theta SDTheta K SDK q SDq Halflife SDHalflife d SDd;

global RF AF SDRF SDAF ;

CVd=(-0.69.*RF.*Theta./q./Halflife).*exp(-0.69.*d.*RF.*Theta./q./Halflife).*SDd;

CVRF=(-0.69.*d.*Theta./q./Halflife).*exp(-0.69.*d.*RF.*Theta./q./Halflife).*SDRF;

CVTheta_AF=(-0.69.*d.*RF./q./Halflife).*exp(-0.69.*d.*RF.*Theta./q./Halflife).*SDTheta;

CVHalflife=(0.69.*d.*RF.*Theta./q./(Halflife.^2)).*exp(-0.69.*d.*RF.*Theta./q./Halflife).*SDHalflife;

CVq=(0.69.*d.*RF.*Theta./(q.^2)./Halflife).*exp(-0.69.*d.*RF.*Theta./q./Halflife).*SDq;

SDAF=(CVd.^2+CVRF.^2+CVTheta_AF.^2+CVHalflife.^2+CVq.^2).^0.5;

end

%Write to a worksheet

function writeOutput(RF,SDRF,AF,SDAF,OutputFilename)

Output

writetable(OutputTable,OutputFilename,'Sheet',1)

end

%Display the graph

function displayGraph(RF,SDRF)

plot(1:3,RF,'g--O', 1:3,SDRF,'--*');

xlabel('Soil Taxonomy Order');

ylabel('RF or Standard Deviation of RF');

legend('RF','Standard Deviation of RF','Location', 'southeast');

end

Based on the reviewed papers, the following points are highlighted:

1) In AF approach, the groundwater recharge/average water flow rate through soil (q) requires a constant value. Therefore, it is unclear about the time scale (i.e., daily, monthly, or yearly) of the groundwater recharge. Moreover, with the current approach of AF with a constant value of groundwater recharge, it is not feasible to evaluate trends and strengths of attenuation of chemicals over time and space, which can help to determine if the pollutant levels have declined or increased with time in space.

2) A value of zero for RF implies that the applied pesticide is not lost due to sorption. In other words, at RF = 0, AF = 1. Thus, all the applied pesticide reaches the GWT regardless of half-life time of the applied pesticide.

3) In the literature, it has been concluded that the depth to GWT does not have an influence on the groundwater vulnerability assessment. Therefore, the uncertainty associated with the value of depth to GWT is set to zero. These conclusions may not be concrete in spatial context as well at a given location.

4) As per the definition of AF, it is expected to have x*AF mg at the groundwater table, if the AFs of two pesticides that are applied at a rate of x mg are the same. Under this scenario, the outlined classification system based on reference chemicals will not work. This is owing to the fact that the classification system based on reference chemicals does not consider the acceptable levels of the pesticides at the groundwater table.

5) [

6) In AF approach, recharge and depth to GWT are some of the most defining parameters [

7) The major driver of water-level changes in many highly stressed aquifers (e.g., high plain aquifer in the central United States) is irrigation pumping that is a function of metrological conditions such as precipitation and ET [

8) Sensitivity analysis on model parameters are carried out to determine the sensitive ranking of parameters sorted by the amount of influence each has on model results [

9) The first level of uncertainty arises from the mathematical representation of the underlying physical processes that define the system of interest. Though [

The authors would like to thank the Board of Regents, University of Nebraska-Lincoln, Lincoln, for providing the financial support to conduct this research. This research was conducted when author^{*} was a researcher at University of Nebraska-Lincoln, Lincoln.

SivarajahMylevaganam,ChittaranjanRay, (2016) The Assessment of Groundwater Vulnerability Due to Leaching of Chemicals: The Review of Attenuation Factor. Open Journal of Soil Science,06,9-20. doi: 10.4236/ojss.2016.61002