## 2 Dixon Quality Control Method  
Natural water quality monitoring data in time series has the characteristics of being multi-dimensional and covering long time scales. The quality control and outlier detection of time series are critical for the quality control of environmental monitoring time series data considering the effect of hydrometeors, the electromagnetic environment, and water organisms on the process of data acquisition in addition to the complex natural environment and high monitoring cost. The control means of data quality are mainly realized through regular sensor calibration and maintenance, while the conventional parallel observation experiments in data quality control are usually difficult to achieve. In this context, [PERSON] et al. [27] proposed a new detection method by integrating the difference analysis and Dixon detection criteria to account for the outliers in the time observation series of marine water elements. The core assumptions of this method for the quality control of environmental monitoring time series data are as follows:  
1. In a short period of time, environmental monitoring factors have similar physical and chemical properties;
2. the monitoring value in a short time window has the same significance as the parallel repeated observation experiment in outlier detection;
3. the time series of environmental monitoring that needs quality control treatment should meet the assumption of stationarity. How can we meet the requirements of sequence stability? In this method, the first-order or multi-order difference method is used for processing, and the Augmented Dickey-Fuller (ADF) stability test [28; 29] is selected to test the stability of the difference time series. For a sequence that does not meet the stability test, the high-order difference transformation is needed to realize the stability of the sequence. Figure 1 is the time sequence diagram and the first-order difference sequence diagram of the original observation values of the experimental data selected in this paper (including the water chlorophyll-a concentration and electronic conductivity). The ADF detection results of the first-order difference sequence meet the test hypothesis of stability. Dixon detection is one of the most commonly used methods for data quality control. It was proposed by the mathematician [PERSON] in 1950 [30; 31; 32] and is a method performed without estimating the mean value and standard deviation. It is used to identify the gross error according to the order difference of measurement data in size order. It is commonly used in consistency testing and in the removal of outlier testing of parallel test measurement data. Here, the parallel observation test is used instead of the statistical window size of the continuous difference sequence; the test calculation method is as follows:  
First, sort a set of \(w\) differential sequences \(\Delta y\) (\(t+1\)), \(\Delta y\) (\(t+2\)),..., \(\Delta y\) (\(t+w\)) into \(\Delta y\) (\(t+1\))', \(\Delta y\) (\(t+2\))',..., \(\Delta y\) (\(t+w\))' from lowest to highest; \(t\) is a certain time of time series, \(w\) is a statistical inspection window. Figure 1: Original time series curve and first-order difference series curve of automatic environmental monitoring data. (**a**): The original time series data of the observation series; (**b**): the first-order differential time series data of the observation series. The blue line is the time series data of chlorophyll a concentration observation; the brown line is the time series data of water conductivity observation. Second, consider the lowest and highest value in the ranked data sequence as the questionable values. Identify the lowest or highest value as outliers according to the formula in Table 1.  
After calculating the value of \(Q\), the threshold \(Q_{\alpha}\) is read from Table 2 according to the selected significance level \(\alpha\) and sliding window size \(w\).