FORECASTING THE WATER QUALITY INDEX USING THE SEASONAL AUTOREGRESSIVE MOVING AVERAGE MODEL AND THE PROPHET MODEL

Abstract

Surface water quality (WQ) often exhibits strong seasonal and long-term trends influenced by both natural processes and human activity. Accurate WQ forecasting is vital for ecosystem protection, public health, and environmental management, but irregular data collection challenges conventional models like SARIMA, which assume evenly spaced observations. The objectives of this study are to compute the Weighted Arithmetic Water Quality Index (WAWQI) from irregularly collected physicochemical WQ parameters between March 2009 and September 2017 from 20 monitoring sites along the River Thames, to develop SARIMA models for WAWQI forecasting using regularly spaced time series constructed from the observed data, to implement the Prophet forecasting model to handle irregularly sampled WAWQI data while capturing trend and seasonality, to assess and compare the predictive performance of both models using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE), and to provide model selection recommendations for environmental monitoring applications with irregular sampling intervals. SARIMA models cannot be fitted to irregular data. Therefore, to fit the SARIMA model, missing values were linearly interpolated to create a regularly spaced time series. The Prophet model can be used for irregular data without interpolation. Time series data were split into 80% training and 20% testing sets. RMSE captures large errors, MAE shows average error, and MAPE allows relative comparison across sites. Results revealed consistent seasonality in WQ across most locations. Both models performed relatively well. However, Prophet outperformed SARIMA in terms of MAPE (0.02–0.3%) compared to SARIMA's 2–11%, indicating superior relative accuracy. However, SARIMA performed slightly better in terms of RMSE and MAE, particularly at sites with denser data. Therefore, comparisons should be interpreted with caution, as Prophet's higher RMSE and MAE at sparsely sampled sites highlight its reliance on raw, irregular data without interpolation. These findings underscore the importance of aligning model selection with specific forecasting objectives. SARIMA performs well with stable, regularly spaced data, whereas Prophet offers greater flexibility for handling nonlinear trends and irregular sampling. This study provides practical guidance for environmental analysts in selecting forecasting models that best align with their data characteristics and policy goals.