Modeling of methane oxidation in landfill cover soil using an artificial neural network

Abstract

Knowing the fraction of methane (CH₄) oxidized in landfill cover soils is an important step in estimating the total CH₄ emissions from any landfill. Predicting CH₄ oxidation in landfill cover soils is a difficult task because it is controlled by a number of biological and environmental factors. This study proposes an artificial neural network (ANN) approach using feedforward backpropagation to predict CH₄ oxidation in landfill cover soil in relation to air temperature, soil moisture content, oxygen (O₂) concentration at a depth of 10 cm in cover soil, and CH₄ concentration at the bottom of cover soil. The optimum ANN model giving the lowest mean square error (MSE) was configured from three layers, with 12 and 9 neurons at the first and the second hidden layers, respectively, log-sigmoid (logsig) transfer function at the hidden and output layers, and the Levenberg-Marquardt training algorithm. This study revealed that the ANN oxidation model can predict CH₄ oxidation with a MSE of 0.0082, a coefficient of determination (R ²) between the measured and predicted outputs of up to 0.937, and a model efficiency (E) of 0.8978. To conclude, further developments of the proposed ANN model are required to generalize and apply the model to other landfills with different cover soil properties.

Implications:

To date, no attempts have been made to predict the percent of CH₄ oxidation within landfill cover soils using an ANN. This paper presents modeling of CH₄ oxidation in landfill cover soil using ANN based on field measurements data under tropical climate conditions in Malaysia. The proposed ANN oxidation model can be used to predict the percentage of CH₄ oxidation from other landfills with similar climate conditions, cover soil texture, and other properties. The predicted value of CH₄ oxidation can be used in conjunction with the Intergovernmental Panel on Climate Change (IPCC) First Order Decay (FOD) model by landfill operators to accurately estimate total CH₄ emission and how much it contributes to global warming.

Introduction

Microbial methane (CH₄) oxidation in landfill cover soils provides a mean of controlling CH₄ emissions (Huber-Humer, 2004; Huber-Humer et al., 2008; Stern et al., 2007). It is facilitated by a group of methanotrophic bacteria that live in landfill cover soil and have the ability to oxidize CH₄ using migrated atmospheric oxygen (O₂) under natural conditions to produce carbon dioxide (CO₂), water (H₂O), and microbial biomass, as shown in eq 1.

(1)

CH₄ oxidation values differ in landfill cover soils due to several factors that affect the oxidation process. A value of 0–10% oxidation is recommended by the Intergovernmental Panel on Climate Change (IPCC) guidelines for national greenhouse gas (GHG) inventories. However, laboratory and field studies indicate that CH₄ oxidation capacity lies between 0% and 100% (Jugnia et al., 2008). Therefore, it is important to understand the factors that control CH₄ oxidation in landfill cover soils to model CH₄ oxidation and subsequently achieve reductions in GHG emissions.

Several factors affect CH₄ oxidation in landfill cover soils. The most important factors reported in the literature were soil texture, organic matter, moisture content, temperature, pH, nutrients, O₂ concentration, and CH₄ concentration (Boeckx et al., 1996; Borjesson et al., 2001; Spokas and Bogner, 2011; Wilshusen et al., 2004). However, climate and season also have an impact on oxidation capacity. CH₄ oxidation is expected to be less in subarctic or highland regions due to colder temperatures, in subtropical regions due to the relatively dry conditions of cover soils, and in humid continental regions as a result of longer, colder winters, and more dry summers (Oonk, 2010). Several attempts to model CH₄ oxidation in landfill cover soils have previously been made. Most of the current models are analytical models based on fundamental scientific laws governing oxidation processes (De Visscher and Cleemput, 2003; Perera et al., 2002; Stein et al., 2001), whereas few models are based on an empirical statistical modeling approach (Albanna et al., 2007).

The artificial neural network (ANN) is an empirical modeling approach that can determine relationships between different sets of data and is capable of solving problems where statistical models are insufficient (Zhou, 2003). ANN is defined by Abrahart (2004) as “structures which forecast and predict through pattern matching and comparison.” The ANN has been used in many fields to perform complex functions, such as pattern recognition, classification, vision, control systems, and prediction (Zilouchian, 2001). In prediction modeling, the ANN takes a set of inputs and produces one or more outputs. This task is accomplished by teaching the ANN, based on a set of input/output data that assists the ANN in obtaining knowledge on system dynamics and uses this knowledge to predict a system output for any given input (Zhou, 2003; Zilouchian, 2001). The ANN modeling technique is not comprehensive, as it cannot simulate processes outside the input variables domain. Therefore, a large number of experimental data are required, which may be site or case specific, for providing a viable predicting tool.

To date, no attempts have been made to predict the percent of CH₄ oxidation within landfill cover soils using an ANN, but many applications of ANN modeling in the field of environmental engineering exist. In the field of wastewater treatment, Hamed et al. (2004) developed an ANN model to predict wastewater performance in a treatment plant, whereas Elmolla et al. (2010) used a three-layer ANN to model chemical oxygen demand (COD) removal from wastewater. However, Tashaouie et al. (2012) developed an ANN model for predicting filter efficiency in the removal of turbidity from a municipal water treatment plant. Onkal-Engin et al. (2005) determined the relationship between sewage odor and biological oxygen demand (BOD) using an ANN, and Kardam et al. (2010) developed a two-layer ANN model to predict the removal efficiency of cadmium(II) ions from an aqueous solution using shelled Moringa oleifera seed powder. In the field of landfill gas (LFG) concentration and emission, Ozkaya et al. (2007) developed an ANN model to predict the CH₄ fraction in LFG using conventional leachate parameters such as pH, alkalinity, COD, sulfate, conductivity, chloride concentration, and waste temperature, whereas Li et al. (2011) developed an ANN model for predicting temperature, and CH₄, CO₂, and O₂ concentrations at several gas collection wells at a large landfill in southern California, USA. Karacan (2008) developed an ANN-based methodology to predict the ventilation of CH₄ emissions from longwall mines and Al-Quraishi and Shokir (2011) provided two models for predicting natural gas viscosity and density using independent input variables of gas pressure and temperature. In the geotechnical field, Zhao et al. (2009) used an ANN model to predict soil texture (sand, clay, and silt) based on soil attribute parameters.

The present study developed an ANN model to estimate the percentage of CH₄ oxidized in landfill cover soil, to enhance the determination of total CH₄ emissions from a landfill using IPCC First Order Decay (FOD) model. Several variables, such as average air temperature (°C), average soil temperature (°C) at a 10-cm depth of cover soil, average volumetric soil moisture content over soil depths (% v/v), CH₄ concentration (% v/v) underlying the bottom of soil cover, and O₂ concentration (% v/v) at a 10-cm depth of cover soil, were tested to select the main variables. The ANN modeling outputs were compared with the measured data.

Materials and Methods

Site description

The Sungai Sedu open dump landfill was used to gather the data required to model CH₄ oxidation. The Sungai Sedu open dump landfill is located in Kuala Langat, Selangor, Malaysia (2°50′39″N and 101°31′01″E) and is adjacent to the Sungai Sedu River (Figure 1). The landfill has a total area of 5.5 ha and receives approximately 340 tons per day of domestic and nonhazardous industrial waste. The total amount of waste disposed of in the landfill was estimated to be 1,613,300 tons. The landfill was operated and managed by Alam Flora Sdn. Bhd, and since 2010, the landfill has been full and not in use.

Figure 1. Aerial view of the Sungai Sedu landfill indicating the location of the study area and monitoring stations.

In the present study, measurements were gathered at the inactive part of the landfill, from cell number 5 (Figure 1). Cell number 5 consists of waste between 2 and 12 years old; the cell started receiving waste in 1998 and closed in 2008. The waste depth of the cell is approximately 34 m. The cell is covered by approximately 10 to 30 cm of poorly graded sand, which functions as an interim soil layer. The vegetation was not well established at some parts of the cell at the time of the study, whereas other parts were covered with grasses and herbs. The cell was not lined and at the time of the study, there was no gas collection system, and thus the waste gases directly escaped through the cover soil and were released into the atmosphere.

Experimental procedure

To provide data for modeling CH₄ oxidation from the Sungai Sedu landfill, four monitoring locations in a square portion with an area of approximately 1000 m² were chosen randomly, as shown in Figure 1. CH₄ and CO₂ emissions on the surface and soil gas concentration profiles at those locations were measured between 9:00 and 11:00 a.m. twice per month from September 2010 to June 2011. Furthermore, two of the four monitoring stations were selected randomly for temporal sampling once per month in the morning (8:00–10:00 a.m.), at noon (12:00–2:00 p.m.), and during the afternoon (3:00–5:00 p.m.) over the monitoring period.

A square static flux chamber was constructed and used to measure the CH₄ and CO₂ emissions followed Abushammala et al. (2012) (Figure 2). Soil gas at each monitoring station was trapped by preinstalled stainless steel tubes, in accordance with the method by Kiese and Butterbach-Bahl (2002), and collected using 10-mL gas-tight syringes for direct analysis. The concentrations of three main soil gases were measured: CH₄, CO₂, and O₂. The combination of surface CH₄ and CO₂ emissions and soil gas concentration profiles was used to estimate the percentage of CH₄ oxidized in the soil cover, in accordance with the method by Christophersen et al. (2001). The gas analyses were performed on a Varian Micro-GC (CP-4900; Varian, Inc., Australia) gas chromatograph (Abushammala et al., 2012). Helium gas (99.999%) was used as the carrier gas for the thermal conductivity detector (TCD) at a pressure of 80 psi. Further details of the Micro-GC are shown in Table 1. Each gas sample was analyzed at least twice, and the average was determined. The gas components from each sample were detected in a typical 1.5 min and automatically integrated using the Galaxie software.

Figure 2. Measurements setup at each monitoring station.

Table 1. Micro-GC parameters for gas determination

Gas Chromatography	Varian Micro-GC CP4900
Column	MS5Å 10 m	PPQ, 10 m
Detector	TCD ^a	TCD
Oven temperature (°C)	80	40
Column head pressure (kPa)	150	150
Carrier and reference gas	Helium	Helium
Detection of	O2	CH4 and CO2
Note: ^aThermal conductivity detector.

For modeling of CH₄ oxidation using ANN, the following parameters were measured simultaneously with CH₄ and CO₂ emissions and soil gas profiles at each monitoring station: soil temperature at a 10-cm depth, air temperature, and volumetric soil water content. Each parameter was measured at least twice and the average was determined.

Analytical methods

Air temperature was measured using Skymaster (Great Falls, Virginia, USA) SM-28 and Speedtech instruments. The soil temperature at a depth of 10 cm was measured using a thermometer dual channel, type K, Monarch 306, connected with two K wire thermocouple probes (Monarch Instrument, Amherst, New Hampshire, USA) (Figure 2). An integrated profile probe (PR2) connected to a moisture meter (HH2) was used to measure the soil volumetric moisture content profile. The PR2 probe was inserted into preinstalled access tubes, and measurements were taken at different depths (Figure 2). A soil sieve analysis of particle density, moisture content, bulk density, pH, and organic matter was conducted following the method by Head (1992) and was previously presented (Abushammala et al., 2013).

ANN modeling

Data sets (121 experimental sets) obtained from our previous study of field investigations of the Sungai Sedu landfill (Abushammala et al., 2013) were used to develop the ANN oxidation model. As an initial step, the data sets were normalized and then divided into an input matrix and target matrix. CH₄ oxidation (%) was used as a target. To find the appropriate input parameters for developing the ANN oxidation model, an initial ANN structure with two hidden layers comprising 15 and 10 neurons for the first and the second layers, respectively, was used to evaluate the performance of combinations of measured variables (Karacan, 2008). The measured variables were p ₁ (soil temperature), p ₂ (air temperature), p ₃ (soil moisture content), p ₄ (CH₄ concentration at the bottom of the cover soil), and p ₅ (O₂ concentration at a 10-cm depth of cover soil). The entire data set was first randomized to prevent bias and to construct representative sections of the data set for the training and testing phases. Subsequently, the whole data set was divided into 100 exemplars (83%) for training data and 21 exemplars (17%) for the testing phase.

The initial ANN type was feedforward. The supervised backpropagation is the most popular training method (Abrahart, 2004; Rene and Saidutta, 2008) and, therefore, was used for training the initial ANN using the Levenberg-Marquardt training algorithm (trainlm). The training process between both input and expected output was repeated until the performance error decreased to an acceptable level and the internal connection weights were modified in response to the computed error. For a single iteration, the error is calculated and the summed errors from overall neurons are divided by the size of data used in the training process to estimate average MSE (Figure 3). The log-sigmoid transfer function (logsig) was selected at the hidden and output layers, as it is the most common type of the transfer function used to construct neural networks (Mjalli et al., 2007) and is commonly used in backpropagation networks (Bishop, 1995). The momentum factor of 0.92 was constant.

Figure 3. The ANN iterative procedure.

To evaluate the performance of the initial models, the mean square errors (MSE), coefficient of determination (R ²), and model efficiency (E) were noted during the testing phase. The model efficiency was estimated using eq 2 (Singh and Panda, 2011):

(2)

where N is the number of data points in the testing phase, M_i is the measured value, P_i is the estimated value, and is the mean of measured values. The model provided the smallest MSE and greatest R ² and E values, and its input variables were selected as the effective input variables for estimating CH₄ oxidation (%). Next, the optimum backpropagation training algorithm and the optimum number of neurons in the hidden layers were investigated to improve the estimation performance of CH₄ oxidation. The MSE, R ², and E values were noted in the test phase to select the best model.

Results and Discussion

Selection of effective input variables

This section presents the results of initial modeling to find the effective input variables for the final ANN oxidation model. The combination between variables was subsequently changed to determine which input variables produced the smallest MSE and highest R ² and E values in the testing phase. Table 2 summarizes the performance of the combination of variables used in the initial models in the testing phase.

Table 2. Evaluation of variable efficiency in estimating CH₄ oxidation

Model Number	Variable Combinations	MSE	R ^2	E	Epoch	Best Linear Equation
1	p 1 + p 2	0.1717	0.075	−1.1419 ^b	1615	0.390x + 22.14
2	p 1 + p 3	0.0503	0.598	0.3728	167	0.986x + 2.205
3	p 1 + p 4	0.1377	0.209	−0.7169	634	0.633x + 5.437
4	p 1 + p 5	0.1345	0.250	−0.6771	1329	0.752x + 13.11
5	p 2 + p 3	0.0633	0.557	0.2107	325	0.838x − 5.984
6	p 2 + p 4	0.1424	0.170	−0.7756	171	0.579x + 24.23
7	p 2 + p 5	0.1045	0.362	−0.3030	405	0.874x + 7.806
8	p 3 + p 4 ^a	0.0252	0.785	0.6858	507	1.086x − 3.184
9	p 3 + p 5	0.0277	0.766	0.6546	384	1.059x − 5.906
10	p 4 + p 5	0.0552	0.444	0.3117	1146	0.709x + 9.885
11	p 1 + p 2 + p 3	0.0428	0.697	0.4663	256	1.118x − 6.632
12	p 1 + p 2 + p 4	0.1048	0.314	−0.3067	312	0.766x + 5.059
13	p 1 + p 2 + p 5	0.0462	0.704	0.4239	60	1.081x + 5.007
14	p 1 + p 3 + p 4	0.0353	0.707	0.5599	144	1.025x − 5.414
15	p 1 + p 3 + p 5	0.0263	0.789	0.6721	90	1.064x + 2.306
16	p 1 + p 4 + p 5	0.0549	0.503	0.3155	129	0.832x + 5.236
17	p 2 + p 3 + p 4	0.0591	0.525	0.2636	176	0.914x + 6.262
18	p 2 + p 3 + p 5	0.0411	0.593	0.4878	69	0.809x + 2.120
19	p 3 + p 4 + p 5 ^a	0.0189	0.821	0.7643	87	1.045x + 0.429
20	p 1 + p 2 + p 3 + p 4	0.0265	0.784	0.6696	75	1.091x − 6.752
21	p 1 + p 2 + p 3 + p 5	0.0366	0.678	0.5428	48	0.946x + 8.231
22	p 1 + p 2 + p 4 + p 5	0.0470	0.602	0.4143	78	0.896x − 2.620
23	p 1 + p 3 + p 4 + p 5	0.0174	0.820	0.7835	88	1.018x − 0.145
24	p 2 + p 3 + p 4 + p 5 ^a	0.0146	0.828	0.8177	38	0.953x + 3.056
25	p 1 + p 2 + p 3 + p 4 + p 5 ^a	0.0267	0.779	0.6731	50	1.074x − 6.492
Notes: ^aBest variables group performance;
^bNegative value indicated model failure.

The initial modeling indicated that “model 8” was the best model, as it produced the smallest MSE (0.0252) and the greatest R ² (0.785) and E (0.6858) compared with other models in the group of two variables. In the group of three variables, “model 19” achieved the smallest MSE compared with other models in the same group and “model 8,” with an MSE of 0.0189, an R ² of 0.821 and an E of 0.7643. In the group of four variables, “model 24” was the best model, producing the lowest MSE and highest R ² compared with other models in the same group as well as with the other group models, including the group of five variables. In a test of “model 24,” an MSE of 0.0146, R ² of 0.828, and E of 0.8177 were achieved. “Model 24” had the lowest MSE in the testing phase of the groups of two, three, and five variables up to 42%, 22.8%, and 45.3%, respectively. Similarly, R ² and E values improved from 0.785 to 0.828 and from 0.6858 to 0.8177, respectively. Thus, the “model 24” variables were the most effective inputs among other variables in the other groups. Subsequently, the air temperature (°C), average volumetric soil moisture content over soil depths (% v/v), CH₄ concentration (% v/v) underlying bottom of soil cover, and O₂ concentration (% v/v) at a 10-cm depth of cover soil were selected as the input variables for the CH₄ oxidation ANN model. Table 3 shows the descriptive statistics of the experimental data of these input variables as well as the CH₄ oxidation values.

Table 3. Summary of descriptive statistics of the experimental data

Parameter	Air Temperature (°C)	Average Soil Moisture (% v/v)	CH4 Concentration Underlying Cover Soil (% v/v)	O2 Concentration at 10 cm Depth of Cover Soil (% v/v)	CH4 Oxidation (%)
n	121	121	121	121	121
Maximum	42.9	76.3	62.7	15.5	97.9
Minimum	24.6	24.7	11.4	0.31	0.12
Mean	32.5	53.8	44.9	6.4	48.2
s	4.12	14.08	11.76	4.70	28.59

Selection of backpropagation training algorithm

After selecting the “model 24” input parameters, 10 backpropagation training algorithms were used to determine the best training algorithm for the gathered data. For all algorithms, a three-layered approach with a log-sigmoid transfer function (logsig) at hidden layers and an output layer was used. In addition, 15 and 10 neurons were used in the first and the second hidden layers, respectively, as initial values for all backpropagation algorithms. The momentum was a constant 0.92 for all the algorithms used. The testing phase results with different backpropagation training algorithms are provided in Table 4. Compared with other backpropagation algorithms, Levenberg-Marquardt (trainlm) was the best algorithm, producing the lowest MSE, and was associated with the highest R ² and E values in the testing phase. Using the Levenberg-Marquardt algorithm resulted in a decrease of up to 27.3% of the MSE produced compared with using the Powell-Beale conjugate gradient algorithm, which was the algorithm that produced the second lowest MSE (Table 4). Subsequently, the Levenberg-Marquardt algorithm was considered for training the final ANN oxidation model.

Table 4. Comparison of backpropagation algorithms

Backpropagation Algorithms	Function	MSE	R ^2	E	Best Linear Equation
Levenberg-Marquardt backpropagation^a	trainlm	0.0146	0.828	0.8177	0.953x + 3.056
Scaled conjugate gradient backpropagation	trainscg	0.0211	0.740	0.7369	0.852x + 6.622
BFGS quasi-Newton backpropagation	trainbfg	0.1006	0.375	−0.2544	0.879x + 8.296
One step secant backpropagation	trainoss	0.0305	0.722	0.6197	1.017x + 0.324
Batch gradient descent	traingd	0.0355	0.707	0.5573	0.722x + 5.556
Variable learning rate backpropagation	traingdx	0.0323	0.863	0.5973	1.317x − 7.843
Batch gradient descent with momentum	traingdm	0.0425	0.611	0.4700	0.679x + 4.360
Fletcher-Reeves conjugate backpropagation	traincgf	0.0540	0.448	0.3267	0.710x + 13.79
Polak-Ribière conjugate gradient backpropagation	traincgp	0.0482	0.517	0.3990	0.795x + 8.816
Powell-Beale conjugate gradient backpropagation	traincgb	0.0201	0.804	0.7494	0.951x + 7.319
Note: ^aBest training algorithm.

Optimization of neuron numbers

Optimization of neural network neuron numbers is an important task in developing the best ANN model. Therefore, the optimum network neuron numbers were investigated in the current study to improve the estimation performance of the ANN oxidation model. The number of hidden layers chosen was two, as it was during the initial ANN structure. The Levenberg-Marquardt backpropagation training algorithm was used for training different ANN models with different neuron numbers at the first and second hidden layers. The log-sigmoid transfer function was used at the hidden layers and the output layer during the training phase, whereas the value of momentum was a constant of 0.92.

In the first stage, neuron numbers in the first hidden layer varied from 10 to 20, whereas neuron numbers in the second hidden layer were kept constant at 10. The optimal number of neurons in the first hidden layer was chosen based on the smallest MSE and highest R ² and E values in the testing phase. In the second stage, the optimum number of neurons in the first hidden layer, selected during the first stage, was kept constant, whereas the number of neurons in the second hidden layer varied and ranged from 2 to 12. Thus, the optimum number of neurons in the second hidden layer that were associated with the smallest MSE and highest R ² and E values in the testing phase were selected. Table 5 and Table 6 show the performance of different models with varying neuron numbers between the two hidden layers. The best model performance, according to minimum MSE and greatest R ² and E values in the testing phase, are highlighted in Table 5 and Table 6.

Table 5. Performance of different models tested in ANN with a varying number of neurons in the first hidden layer and a constant number of neurons in the second hidden layer

Model	MSE	R ^2	E	Epoch	Best Linear Equation
[10 10 1]	0.0298	0.685	0.6284	47	0.900x + 1.917
[11 10 1]	0.0214	0.753	0.7332	50	0.906x + 5.428
[12 10 1]^a	0.0090	0.882	0.8878	75	0.888x + 4.013
[13 10 1]	0.0132	0.827	0.8354	56	0.821x + 8.268
[14 10 1]	0.0122	0.878	0.8479	48	1.085x − 1.958
[15 10 1]	0.0146	0.828	0.8180	38	0.953x + 3.056
[16 10 1]	0.0107	0.860	0.8666	50	0.837x + 7.234
[17 10 1]	0.0216	0.743	0.7307	60	0.836x + 10.10
[18 10 1]	0.0157	0.836	0.8043	53	1.013x + 1.242
[19 10 1]	0.0246	0.746	0.6933	44	0.915x − 0.991
[20 10 1]	0.0201	0.800	0.7494	41	1.025x − 0.771
Note: ^aBest model.

Table 6. Performance of different models tested in ANN with a constant number of neurons in the first hidden layer and a varying number of neurons in the second hidden layer

Model	MSE	R ^2	E	Epoch	Best Linear Equation
[12 2 1]	0.0554	0.579	0.3092	207	0.910x + 12.64
[12 3 1]	0.0411	0.608	0.4875	1170	0.889x + 8.067
[12 4 1]	0.0353	0.703	0.5598	128	1.029x + 1.913
[12 5 1]	0.0317	0.718	0.6047	111	0.927x + 10.07
[12 6 1]	0.0271	0.752	0.6621	123	1.036x-0.974
[12 7 1]	0.0225	0.747	0.7195	127	0.920x + 2.212
[12 8 1]	0.0237	0.735	0.7045	115	0.879x + 8.585
[12 9 1]^a	0.0082	0.937	0.8978	143	1.095x − 2.892
[12 10 1]	0.0090	0.882	0.8878	75	0.888x + 4.013
[12 11 1]	0.0219	0.774	0.7269	54	0.945x + 6.306
[12 12 1]	0.0197	0.794	0.7544	60	0.969x − 1.731
Note: ^aBest model.

The results in Table 5 show that the 12 neurons in the first hidden layer produced smaller MSE and higher R ² and E values compared with other models. However, the results in Table 6 show that the 9 neurons in the second hidden layer produced smaller MSE and higher R ² and E values in contrast to other models. Therefore, 12 and 9 neurons were selected as the best number of neurons in the first and second hidden layers, respectively. Figure 4 shows the optimized ANN structure for estimating CH₄ oxidation, whereas Figure 5 shows the linear regression between the measured CH₄ oxidation and the ANN model outputs in the training phase. The optimum ANN training process took 143 epochs (Table 6) to reach the error goal (10⁻⁶). The MSE in the training phase was 7.0766 × 10⁻⁷, and the R ² and E values were 1 (Figure 5). Figure 6 shows the training MSE with respect to epochs of the selected model.

Figure 4. Optimized ANN structure.

Figure 5. ANN performance during the training phase.

Figure 6. A plot of the training MSE with respect to epochs of the selected model.

The targets of oxidation in the test data set were compared and plotted with the estimated values using the ANN model in Figure 4. The comparison between the target data and the estimated values in the testing phase is shown in Figure 7. Although the target data exhibited large variations, it was obvious that the ANN model outputs were reasonable and mimicked the target data. Figure 8 shows the linear regression between the ANN model outputs and the corresponding targets in the testing phase, and the outputs appear to track the targets reasonably well. The figure contains the best linear equation y = 1.095x − 2.892, with an R ² of 0.937. The R ² value found in this study was relatively higher than those reported in the literature; a coefficient of determination of 0.92 for prediction of CH₄ emission ventilation from longwall mines (Karacan, 2008), 0.90 for prediction of the CH₄ fraction of LFG (Ozkaya et al., 2007), 0.90 for prediction of the quantitative characteristics of water bodies (Palani et al., 2008), and 0.90 for prediction of performance of a wastewater treatment plant (Nasr et al., 2012). However, some previous studies achieved R ² values up to 0.99 (Elmolla et al., 2010; Oguz et al., 2008; Salari et al., 2005). The relatively low values of R ² and E of the ANN oxidation model obtained by this study might be attributed to data noise, due to the small sample size of the data set.

Figure 7. ANN estimated and measured CH₄ oxidation data.

Figure 8. Scatter plot of measured CH₄ oxidation and ANN estimated of the testing data.

The proposed ANN oxidation model can be used to estimate the percentage of CH₄ oxidation from other landfills with similar climate conditions, and cover soil texture and other properties in which the data were collected. Therefore, further field investigations and data collection of CH₄ oxidation and the inputs from different cover soil properties are required for developments and enhancements of the proposed ANN oxidation model to apply the model to other landfills. Furthermore, the ANN oxidation model can be incorporated with the IPCC 2006 First Order Decay (FOD) model to accurately estimate total CH₄ emissions from landfill surfaces.

Conclusions

This study presents estimation of CH₄ oxidation (%) in landfill cover soil by considering environmental factors, such as air temperature, soil moisture content, and O₂ and CH₄concentrations at the top and bottom of cover soil, respectively. These selected environmental factors were the result of initial modeling and were determined to be the most effective parameters producing the smallest MSE and highest coefficient of determination in estimating CH₄ oxidation. The optimum ANN configuration giving the smallest MSE was a three-layer backpropagation, with 12 and 9 neurons at the first and the second hidden layers, respectively. The Levenberg-Marquardt backpropagation training algorithm was the best algorithm, producing the smallest MSE compared with other training algorithms. The results of this study indicated a small MSE (0.0082), a relatively high coefficient of determination (R ²) between the measured and estimated values, reaching up to 0.937, and a relatively high model efficiency (E) of 0.8978.

In conclusion, the ANN oxidation model provides an effective tool for estimating percent of CH₄ oxidation in landfill cover soil with similar properties of that where the data had been collected and with the same range of experimental data that were used to train the model. However, the model cannot be used with different cover soil properties or input values outside the range of the trained data.

Acknowledgment

The authors gratefully acknowledge the Alam Flora Company staff for their assistance with this research and Tuwati B. Tuwati for his assistance with field sampling.

Funding

This work was financed by Universiti Kebangsaan Malaysia (UKM) under research grant UKM-GUP-ASPL-08-06-208.