# An Evaluation of À Trous-Based Record Extension Techniques for Water Quality Record Extension

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## Abstract

**:**

## 1. Introduction

- It generates extended records with an underestimated variance [4,9,10,11,12]. Producing extended records with underestimated variance results from a bias in the estimation of extreme values, which as a result produces a bias in the estimation of exceedance and non-exceedance probabilities [4,5]. For WQ management generally and particularly for WQ assessment, high percentiles and extreme values are critical for evaluating whether WQ is within accepted limits or standards [13].

## 2. Materials and Methods

#### 2.1. Ordinary Least Squares Regression (OLS)

#### 2.2. Maintenance of Variance Extension Techniques (MOVE)

#### 2.3. Kendall–Theil Robust Line (KTRL & KTRL2)

#### 2.4. Robust Line of Organic Correlation (RLOC)

#### 2.5. Wavelet Transform

## 3. Empirical Experiment

## 4. Results and Discussion

_{1}= 90), and the WT-MOVE1 provided more precise results for small sizes (e.g., 60 records). Higher accuracy of the extended records’ standard deviation provided by the MOVE3 and MOVE4 approaches than the MOVE1 and MOVE2 is noted. This is attributed to the main difference between those techniques, where MOVE3 and MOVE4 were developed for small-size samples, unlike MOVE1 and MOVE2, which are based on population parameters. These results are in agreement with the results obtained by [10,27], where the four MOVE techniques were compared using streamflow and WQ data, respectively. This indicates the usefulness of the MOVE3 and MOVE4 for such small period of WQ records. The better accuracy provided by the KTRL2, RLOC, WT-KTRL2, and WT-RLOC approaches is due to the advantage of being insensitive to the existence of outliers and the ability to maintain variance of the extended records. These results are in agreement with results obtained by [27,28], which showed the better accuracy and precision provided by the KTRL2 and RLOC compared to MOVE techniques in the presence of outliers. For the extended records’ standard deviation, the WT data preprocessing step smooths the raw data into an approximation component that minimizes the influence of extreme values, which affects the extended records’ variance more than their mean value.

_{1}= 60 and 70) or the second least accuracy and precision for n

_{1}= 80 or 90.

## 5. Conclusions and Recommendations

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**The BIAS and RMSE results for the extended Na records for four different periods of concurrent records = 60; 70; 80; and 90.

**Figure 4.**The BIAS and RMSE results for the extended Na records mean value for four different periods of concurrent records = 60; 70; 80; and 90.

**Figure 5.**The BIAS and RMSE results for the extended Na records standard deviation for four different concurrent sizes = 60; 70; 80; and 90.

**Figure 8.**The BIAS (

**a**) and RMSE (

**b**) results for the extended Na records’ low percentiles for n

_{1}= 60 and 90.

**Figure 9.**The BIAS (

**a**) and RMSE (

**b**) results for the extended Na records’ high percentiles for n

_{1}= 60 and 90.

Monitoring Locations | Minimum | Maximum | Mean | St. Deviation | Skewness | |||||
---|---|---|---|---|---|---|---|---|---|---|

Na | TDS | Na | TDS | Na | TDS | Na | TDS | Na | TDS | |

(mg/l) | ||||||||||

WE01 | 1.13 | 203.00 | 16.79 | 1411.00 | 4.14 | 667.99 | 1.96 | 179.36 | 2.84 | 0.61 |

WE02 | 1.20 | 216.00 | 58.71 | 4155.61 | 21.45 | 2138.95 | 10.40 | 772.74 | 0.52 | 0.16 |

WE03 | 1.16 | 213.00 | 68.02 | 4734.70 | 9.17 | 1118.71 | 6.57 | 450.35 | 6.38 | 4.46 |

WE05 | 0.31 | 232.00 | 33.05 | 2978.05 | 6.31 | 950.24 | 3.09 | 266.01 | 5.61 | 3.43 |

WE06 | 1.09 | 197.00 | 16.96 | 1602.07 | 7.01 | 946.12 | 2.51 | 207.51 | 1.31 | 0.43 |

WE07 | 1.13 | 210.00 | 37.71 | 3737.00 | 9.47 | 1141.43 | 6.14 | 514.64 | 2.66 | 2.97 |

WE08 | 3.00 | 562.00 | 62.41 | 6390.00 | 23.73 | 2313.47 | 14.24 | 1153.32 | 0.66 | 0.64 |

WE10 | 1.00 | 259.00 | 11.61 | 1426.00 | 5.70 | 835.95 | 1.88 | 168.32 | 0.86 | 0.41 |

WE11 | 3.52 | 642.00 | 44.53 | 3556.00 | 6.78 | 913.38 | 4.14 | 306.54 | 6.86 | 6.20 |

WE21 | 1.27 | 232.00 | 43.88 | 3624.00 | 17.36 | 1774.25 | 7.91 | 577.39 | 0.98 | 0.82 |

Monitoring Locations | p Value | |
---|---|---|

Na | TDS | |

WE01 | 3.35 × 10^{−91} | 1.80 × 10^{−102} |

WE02 | 6.03 × 10^{−99} | 1.80 × 10^{−102} |

WE03 | 5.76 × 10^{−96} | 1.80 × 10^{−102} |

WE05 | 4.71 × 10^{−94} | 1.80 × 10^{−102} |

WE06 | 3.19 × 10^{−99} | 1.80 × 10^{−102} |

WE07 | 6.58 × 10^{−99} | 1.80 × 10^{−102} |

WE08 | 3.40 × 10^{−102} | 1.80 × 10^{−102} |

WE10 | 8.20 × 10^{−97} | 1.80 × 10^{−102} |

WE21 | 6.03 × 10^{−99} | 1.80 × 10^{−102} |

WE11 | 2.00 × 10^{−102} | 1.80 × 10^{−102} |

WE21 | 6.03 × 10^{−99} | 1.80 × 10^{−102} |

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**MDPI and ACS Style**

Anwar, S.; Khalil, B.; Seddik, M.; Eltahan, A.; Saadi, A.E.
An Evaluation of À Trous-Based Record Extension Techniques for Water Quality Record Extension. *Water* **2022**, *14*, 2264.
https://doi.org/10.3390/w14142264

**AMA Style**

Anwar S, Khalil B, Seddik M, Eltahan A, Saadi AE.
An Evaluation of À Trous-Based Record Extension Techniques for Water Quality Record Extension. *Water*. 2022; 14(14):2264.
https://doi.org/10.3390/w14142264

**Chicago/Turabian Style**

Anwar, Samah, Bahaa Khalil, Mohamed Seddik, Abdelhamid Eltahan, and Aiman El Saadi.
2022. "An Evaluation of À Trous-Based Record Extension Techniques for Water Quality Record Extension" *Water* 14, no. 14: 2264.
https://doi.org/10.3390/w14142264