## 4 Experimental Studies
### Results and Comparative Analysis
Among the seven results, the window sizes 14, 15, 19 and 20 were wrong. The largest proportion of window sizes was 19, and its proportion value was 25%; the smallest proportion of window sizes was 14, and its proportion value 2.5%. When \(i=0.6n\), six optimal window sizes were calculated, which were 15, 16, 17, 18, 19 and 20. The largest proportion of window sizes was 17, and its proportion value was 30%; the smallest proportion of window sizes was 20, and its proportion value was 2.5%. When \(i=0.7n\), six optimal window sizes were calculated, which were 15, 16, 17, 18, 19 and 20. The largest proportion of window sizes was 18, and its proportion value was 32.5%; the smallest proportion of window sizes was 20, and its proportion value was 2.5%. When \(i=0.8n\), four optimal window sizes were calculated, which were 16, 17, 18 and 19. The largest proportion of window sizes was 18, and its proportion value was 37.5%; the smallest proportion of window sizes was 16, and its proportion value was 17.5%. Figure 3: Histogram of the rate of computation time increase under different sampling scales. Figure 4b also shows the following regular pattern, and in the calculation results, the correct results and the incorrect results exist together. The results of the incorrect window sizes were near the optimal window sizes. In view of this regular pattern, we gathered statistics on the outlier detection rate corresponding to the optimal window sizes, the suboptimal window sizes and the worst window sizes, and the results are shown in Table 5. It can be seen from this table that the suboptimal window sizes were generally distributed near the optimal window sizes. The difference between the outlier detection rates of the suboptimal window sizes and the optimal window sizes was very small, while the difference between the worst window sizes and the optimal window sizes was obvious. Taking EC and Chl-a time series data as examples, the outlier detection results under the optimal window size sliding detection conditions are shown in Figure 5. This shows that the combination of sliding windows and Dixon detection criteria can well detect the outliers of observation data. The reconstructed observation time series of water quality factors only dealt with the outlier data, while the normal values in the series were effectively preserved, and the features of the original observation data were retained to a great extent. Figure 4: Statistical characteristics of Monte Carlo Search Method (MCSM) and Full Time Series Sliding Search Method (FTSSSM) results under different sampling scales. (**a**) The red line indicates the outlier detection rate of FTSSSM under different window sizes; the blue–black line indicates the outlier detection rate of MCSM under different window sizes with a sampling scale of \(i=0.5n\), and the blue–black shadow is the standard deviation area of 40 test results; the green line indicates the outlier detection rate of MCSM under different window sizes with a sampling scale of \(i=0.6n\), and the green shadow is the standard deviation area of 40 test results; the blue line indicates the outlier detection rate of MCSM under different window sizes with a sampling scale of \(i=0.7n\), and the blue shadow is the standard deviation area of 40 test results; the brown line indicates the outlier detection rate of MCSM under different window sizes with a sampling scale of \(i=0.8n\), and the brown shadow is the standard deviation area of 40 test results. (**b**) The results and percentage distribution of optimal window under different sampling scales.