# Analysis of the Landfill Leachate Treatment System Using Arima Models: A Case Study in a Megacity
## 3 Results and Discussion
### Treated leachate
The findings of ARIMA modelling in treated leachate showed that HM concentrations did not have a seasonal component: (p,d,q)(0,0,0). In other words, there was no annual cyclical component in the HM concentrations of treated leachate (Table 2), except for Co, which showed a one-year cycle in its concentrations: (p,d,q)(1,0,1). This annual cycle was also observed for MSW disposed in the landfill. In general, the results suggested that the HM concentrations in treated leachate depended mainly on the treatment plant operation rather than on the MSW quantity disposed in the landfill. The findings also suggested a similar seasonal trend between HM concentrations in treated and untreated leachate. Namely, there was no evidence of a seasonal component in the HM concentrations before and after the leachate treatment plant under study, except for Cd and Co in untreated and treated leachate, respectively. In relation to the HM concentrations indicators of the leachate treatment plant (Fe and Ni), the results showed ARIMA models with a term AR = 1. The Cr also showed similar results (Table 2). Moreover, Fe (7.78 mg/L), Cr (0.455 mg/L), and Ni (0.390 m/L) were the  
Figure 4: [PERSON]’s correlation matrix between chemical characteristics of treated leachate during the study period. HMs which tended to show the highest concentrations in the treated leachate (Table 1). Thus, the findings suggested that concentrations of these HMs were influenced by the concentrations observed during the month immediately preceding. Namely, the removal of these HMs at the leachate treatment plant was possibly conditioned by operations performed over a one-month period. This was also probably influenced by the high concentrations observed at the inlet of the leachate treatment plant: Fe = 97.2 mg/L, Cr = 0.717 mg/L, and Ni = 0.488 m/L. On average, [PERSON] and [PERSON] [56] also reported that the HMs with the highest concentrations in leachate prior to treatment were Fe (200-1000 mg/L), Ni (0.050-2.0 mg/L), and Cr (0.020-1.0 mg/L). Additionally, it was observed that the AR terms of ARIMA models developed for concentrations of Fe, Cr, and Ni in treated and untreated leachate were similar (AR = 1). The Cd also showed a similar trend. In this way, the results suggested that the treatment plant did not have the ability to change the ARIMA temporal structure of these HMs (decrease in the term AR), possibly due to its high inlet concentrations (Figure 5). This also suggested a decrease in the removal efficiency of these HMs by the leachate treatment plant under study. The removal efficiencies of Fe, Cr, Ni, and Cd observed at the leachate treatment plant during the study period were 52.4%, 33.5%, 12.8%, and 17.0%, respectively (Table 1). Overall, the removal rates of all HMs in the leachate treatment plant were low (average = 26.1%). Figure S1 shows a scatter plot for the observed and simulated (ARIMA) values of Fe and Ni concentrations in untreated and treated leachate during the study period. In relation to the organic matter content in the treated leachate, ARIMA analysis showed that the memory for the BOD\({}_{5}\) concentrations was null. Namely, there was no influence from the previous months' concentrations during the treatment plant operation. The previous trend was probably as this parameter depended on controlled conditions to ensure optimal treatment of leachate, which could be related to the mud age and mass load of the extended-aeration treatment system used. On average, BOD\({}_{5}\) removal efficiency was 86.3% during the study period (Table 1). Nevertheless, for the COD concentration, the memory was one month. In other words, during the treatment plant operation, there was influence of the COD concentrations observed up to one month earlier. This trend may have been associated with a high content of inorganic matter in the leachate to be treated, which could reduce the removal efficiency of the treatment plant [52]. On average, the removal efficiency of COD during the study period was 63.8%.