# Analysis of the Landfill Leachate Treatment System Using Arima Models: A Case Study in a Megacity
## 3 Results and Discussion
### Untreated Leachate
The above also supported the selection of Cu, Pb, and Zn as possible HM indicators of the behaviour of the leachate untreated in this study. Figure 3a shows the HM indicators of untreated leachate on a diagram of two principal components, for better visualization. It was also observed that in each quadrant of the diagram an indicator HM was placed. [PERSON] and [PERSON] [50] also used these three HMs as indicators of the pollution degree of untreated leachate in active and closed landfills in Poland. Figure 2: [PERSON]’s correlation matrix between chemical characteristics of untreated leachate during the study period. The results of ARIMA modelling showed that the trend in HM concentrations was not to show a seasonal component: (p,d,q)(0,0,0). Namely, there was no annual cyclical behaviour in HM concentrations in untreated leachate (Table 2). Conversely, the model developed for the monthly MSW quantity disposed in the landfill showed a seasonal or cyclic component of one year: (p,d,q)(1,1,0). In this study, the results suggested that HM concentrations in untreated leachate did not follow the annual cycles observed in the MSW quantity disposed in the landfill. These differences in the temporal behaviour of HM concentrations in untreated leachate and in the MSW quantity disposed in the landfill were probably associated with the hydraulic retention time (HRT) of leachate in the transport system (pipeline) and pre-treatment (storage and homogenization ponds) under study. The results also showed that the BOD\({}_{5}\) and COD concentrations did not have an annual cyclic component, such as that observed for MSW quantity disposed in the landfill. Indeed, instead of the quantity of disposed MSW, the studies report the following factors  
Figure 3: Principal component diagram for the concentrations of HMs, BOD\({}_{5}\), and COD. (**a**) Untreated and (**b**) treated leachate. conditioning the leachate quantity and composition: landfill age, ambient air temperature, rainfall and permeability, depth, and temperature of the waste [51]. In relation to the concentrations of indicator HMs (Cu, Pb, and Zn), the findings showed that the term auto-regressive (AR) of the ARIMA models developed varied between 0-1 (Table 2). The other HMs under study had similar behaviour, except for As, which showed an AR = 2. These results suggested that the behaviour of HM concentrations in untreated leachate had a short memory. In other words, HM concentrations in untreated leachate were influenced by concentrations observed up to a month earlier. These results also suggested that the HRT of HMs in the leachate transport and pre-treatment system was probably up to one month, except for As, where the HRT was probably up to two months. There were studies that suggested a comprehensive increase in the HRT of untreated leachate to optimize the operation of treatment systems in the face of high pollutant concentrations. Specifically, it was suggested to extend the HRT of leachate in the waste cells and regulation ponds [52]. In relation to the organic matter content in untreated leachate, ARIMA analysis showed that memory was null (AR = 0). Namely, there were no influences from previous observations. On the other hand, the results showed that the moving average (MA) term of ARIMA models developed for indicator HM concentrations was equal to one (MA = 1). In other words, the results suggested short fluctuations in the indicator HM concentrations in