An abnormal phenomenon in entropy weight method in the dynamic evaluation of water quality index

The entropy weighting model (EWM) is widely used for evaluating the water quality index (WQI). Weights are assigned by EWM according to the degree of differentiation of the indicators. The higher the discrimination degree of the pollutant is, the larger its weight is. Through a counterexample, an abnormal phenomenon in EWM during the dynamic evaluation of WQI is revealed. In this counterexample, the water quality condition at three monitoring sites is evaluated based on the permanganate index (CODMn), ammonia nitrogen (NH3-N), and total phosphorus (TP). The observation data from each sampling point shows a continuous deterioration. However, from the weight parameters generated by EWM, the WQI results of these three monitoring sites continuously improve from 50.74, 50.74, and 55.20 to 63.33, 61.20, and 61.82, respectively. This abnormal phenomenon is discussed. The evaluation results of WQI, in which EWM is used to assign weights, may probably be contrary to the actual change in the pollutants. The abnormal phenomenon is due to the continuous deteriorating process. The discrimination degrees of clean indices become higher, and the discrimination degrees of heavy pollution indices become lower. The main contribution of this study is to reveal the distortion of EWM in the weighting process, which ensures the rationality of the dynamic evaluation of water quality evaluation. To avoid this abnormal phenomenon, the dynamic trend of pollutants should be analyzed or predicted before weighting.