Statistical modeling of river water quality index

Water quality index (WQI) is a unitless number that indicates overall water quality at a specific time and location using several important water quality variables. In Malaysia, general WQI which is based on water quality expert opinion has been introduced by the Department of Environment (DOE) to describe the status of a specific location at identified rivers. The accuracy of DOE-WQI measured by the experts is assessed using four important phases namely variables selection, weights determination, variables transformation and variables aggregation, i.e. WQI calculation. However, the experts opinion approach is found to be the most subjective in nature. On determining weights in WQI development, new statistical methodologies were introduced in this study to enhance the current Malaysian DOE-WQI. The Langat River in Selangor was chosen as the location is significantly altered due to several environmental issues. In this study, several descriptive models as well as Bayesian models have been introduced based on a data-driven approach. To enable comparison between models, water quality variables in the Malaysian DOE-WQI calculation was employed. For the descriptive models, 17 Principal Component Analysis (PCA) models had been applied to five selected monitoring stations and four PCA models were found to have similar patterns with the existing DOE-WQI. The models are the PC Standardization, i.e. based on Minimum-Maximum approach known as D1 and D5 as well as the Model E1 and E2 which are based on the re-weighting of the eigenvector elements from two different approaches. The findings also showed that using the relative importance based on relative rank of the first PCA eigenvector elements provided an alternative way to calculate the PCA-WQI, as described in Model E2. Similar approach was conducted using standard deviation of the data for all stations as described in Model E3 and each station separately in Model E4. The results showed that the new weights based on the relative ranks of the standard deviation for Model E3 and Model E4 had contributed well in the new WQI calculations. Both new models are simpler, consistent, stable, comparable and reliable. Furthermore, new Simultaneous-WQI (S-WQI) model in Bayesian approach for each station was introduced to improve WQI estimates. Several potential Bayesian models were considered and the best Bayesian model was selected based on two certain criteria, i.e. Deviance Information Criteria (DIC) values and monitoring convergence. S-WQI can be estimated accurately using a general form of Bayesian model with further constraint in the variance of sub-index pH, SIpH, i.e. the natural water quality characteristic for each station. New parameters from the best Bayesian model were used to re-calculate weights in WQI calculation. Based on the new WQI calculation using the Bayesian knowledge, narrower ranges for each individual observation at all stations were found, indicating better estimates of DOE-WQI. Several interesting further research were also discussed in order to provide WQI researchers better understanding on the benefits and limitations of the different indices.

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