# Analysis of the Landfill Leachate Treatment System Using Arima Models: A Case Study in a Megacity
## 3 Results and Discussion
### Untreated Leachate
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Model**} & \multicolumn{1}{c}{**T \({}^{a}\)**} & \multicolumn{1}{c}{**R\({}^{2}\)**} & \multicolumn{1}{c}{**RMSE \({}^{b}\)**} & \multicolumn{1}{c}{**MAPE \({}^{c}\)**} & \multicolumn{1}{c}{**MAE \({}^{d}\)**} & \multicolumn{1}{c}{**Ljung-Box (Q)**} & \multicolumn{1}{c}{**BIC \({}^{e}\)**} \\ \hline \multicolumn{10}{c}{Untreated leachate} \\ BOD\({}_{5}\) & (0,1,1)(0,0,0) & NT & 0.863 & 1993 & 220 & 1369 & 0.294 & 15.2 \\ COD & (0,1,1)(0,0,0) & NT & 0.847 & 3302 & 24.5 & 2183 & 0.095 & 16.2 \\ NH\({}_{4}\) & (1,0,3)(1,0,1) & NT & 0.337 & 237 & 5.55 & 145.6 & 0.102 & 11.1 \\ Cd & (1,0,1)(0,0,1) & NL & 0.245 & 0.019 & 36.0 & 0.006 & 0.064 & \(-\)7.80 \\ Zn & (1,1,1)(0,0,0) & NL & 0.371 & 0.524 & 38.7 & 0.288 & 0.052 & \(-\)1.22 \\ Hg & (0,0,1)(0,0,0) & NL & 0.031 & 0.041 & 249 & 0.011 & 0.796 & \(-\)6.30 \\ As & (2,0,0)(0,0,0) & NL & 0.245 & 0.026 & 349 & 0.017 & 0.667 & \(-\)7.16 \\ Cu & (0,1,1)(0,0,0) & NL & 0.347 & 2.43 & 43.7 & 0.224 & 0.981 & 1.80 \\ Fe & (1,0,1)(0,0,0) & NL & 0.203 & 896 & 163 & 86.66 & 0.358 & 13.6 \\ Pb & (1,0,1)(0,0,0) & NL & 0.334 & 0.669 & 63.3 & 0.125 & 0.795 & \(-\)0.708 \\ Co & (0,0,2)(0,0,0) & NL & 0.105 & 0.062 & 31.0 & 0.030 & 0.278 & \(-\)5.45 \\ Cr & (1,0,0)(0,0,0) & SR & 0.291 & 0.303 & 95.5 & 0.196 & 0.153 & \(-\)2.32 \\ Ni & (1,0,0)(0,0,0) & SR & 0.329 & 0.159 & 24.1 & 0.097 & 0.145 & \(-\)3.60 \\ pH & (1,0,0)(0,0,0) & NT & 0.445 & 0.228 & 1.90 & 0.158 & 0.291 & \(-\)2.88 \\ \hline \multicolumn{10}{c}{Treated leachate} \\ BOD\({}_{5}\) & (0,0,4)(0,0,0) & NL & 0.514 & 613 & 112 & 296.2 & 0.051 & 12.9 \\ COD & (1,0,2)(0,0,1) & SR & 0.654 & 951 & 77.2 & 452.4 & 0.744 & 13.8 \\ NH\({}_{4}\) & (0,1,0)(0,0,0) & NT & 0.660 & 322 & 87.6 & 182.1 & 0.881 & 11.6 \\ Cd & (1,1)(0,0,0) & NL & 0.690 & 0.004 & 14.1 & 0.002 & 0.326 & \(-\)10.8 \\ Zn & (0,0,2)(0,0,0) & NL & 0.389 & 0.176 & 33.5 & 0.119 & 0.163 & \(-\)3.37 \\ Hg & (0,1,1)(0,0,0) & NL & 0.334 & 0.004 & 79.4 & 0.002 & 0.790 & \(-\)11.0 \\ As & (0,1,1)(0,0,0) & NL & 0.147 & 0.015 & 168 & 0.010 & 0.153 & \(-\)8.40 \\ Cu & (0,1,1)(0,0,0) & NT & 0.914 & 0.020 & 28.2 & 0.011 & 0.302 & \(-\)7.78 \\ Fe & (1,0,1)(0,0,0) & NL & 0.398 & 5.17 & 42.3 & 3.015 & 0.365 & 3.38 \\ Pb & (0,1,1)(0,0,0) & SR & 0.378 & 0.052 & 35.4 & 0.028 & 0.959 & \(-\)5.87 \\ Co & (0,1,1)(1,0,1) & NL & 0.553 & 0.019 & 18.9 & 0.012 & 0.797 & \(-\)7.79 \\ Cr & (1,0,2)(0,0,0) & NL & 0.389 & 0.187 & 34.1 & 0.119 & 0.975 & \(-\)3.22 \\ Ni & (1,0,1)(0,0,0) & NT & 0.365 & 0.095 & 27.1 & 0.069 & 0.736 & \(-\)4.60 \\ pH & (1,0,0)(0,0,0) & NT & 0.556 & 0.309 & 2.74 & 0.221 & 0.879 & \(-\)2.28 \\ \hline \hline \end{tabular} Note: \({}^{a}\) T = Transformation, NT = No transformation, NL = Natural log, and SR = Square root; \({}^{b}\) RMSE = Root mean square error; \({}^{c}\) MAPE = Mean absolute percentage error; \({}^{d}\) MAE = Mean absolute error; and \({}^{e}\) BIC = Normalized Bayesian Information Criterion. A constant was not included in the ARIMA models when differentiation was applied.  
\end{table} 
Table 2: ARIMA models for the chemical parameters of untreated and treated leachate. untreated leachate. These fluctuations in HM concentrations were probably up to one month. The other HMs under study also tended to show short fluctuations from the magnitude of their term MA, between 0-2 consecutive months (Table 2), except for Cd, which showed a variation of 11 consecutive months (MA = 11). In this study, the findings suggested Cd to be the HM with the greatest concentration variation in untreated leachate. Indeed, this suggested a greater occurrence of outliers in Cd concentration during the study period. The HMs with the least variation in concentration were As, Cr, and Ni (MA = 0), followed by Cu, Pb, Zn, Hg, and Fe (MA = 1). These variations were relative to the average concentration of each parameter during the study period. Additionally, this difference in the term MA from the developed models also suggested that there were more difficult HMs to homogenize in untreated leachate ponds.