# A Comparative Study of Statistical Methods for Daily Streamflow Estimation at Ungauged Basins in Turkey

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}) are used to evaluate the performance of the statistical methods. The results show that MDAR and ISW give improved performances compared to DAR to estimate daily streamflow for 7 out of 8 target stations in the Middle Euphrates Basin and for 4 out of 7 target stations in the Upper Euphrates Basin. Higher NSE values for both MDAR and ISW are mostly obtained with the three most physically similar donor stations in the Middle Euphrates Basin and with the two most physically similar donor stations in the Upper Euphrates Basin. The best statistical method for each target station exhibits slightly greater NSE when the smoothed data by the MA is used for all target stations in the Middle Euphrates Basin and for 6 out of 7 target stations in the Upper Euphrates Basin.

## 1. Introduction

## 2. Study Area and Data

#### 2.1. Study Area

^{2}, which is the largest basin of Turkey. It has also nearly 28.5% of the water potential of Turkey. As the biggest water source of the Euphrates-Tigris Basin, the Euphrates River is the longest and one of the most historically significant rivers of the Middle East. The total length of Euphrates is nearly 2800 km, and 40% of its length is in Turkey, 25% is in Syria, and 35% is in Iraq. The Euphrates River consists of two major tributaries, the Karasu River and the Murat River, which both originate in the Eastern Anatolia mountains of Turkey. These two rivers merge near the Keban Dam, which is one of the largest dams of Turkey. The Euphrates River Basin is subdivided into the Upper Euphrates, the Middle Euphrates, and the Lower Euphrates basins, which have some distinctive physical features. The water regime of the Euphrates River Basin depends heavily on winter rainfalls and spring snowmelt.

#### 2.2. Hydrological and Meteorological Data

^{2}whereas their elevations range between 852 and 1810 m above sea level. As shown by Table 2, drainage areas of the stations in the Upper Euphrates Basin vary between 233.2 and 15,562 km

^{2}whereas their elevations range between 840 and 1830 m above sea level.

## 3. Methods

#### 3.1. Statistical Information Transfer Methods

#### 3.1.1. Drainage Area Ratio (DAR) Method

#### 3.1.2. Multiple-Donor Stations Drainage Area Ratio (MDAR) Method

#### 3.1.3. Inverse Similarity Weighted (ISW) Method

^{3}/s/km

^{2}) at the target station and ${q}_{dono{r}_{i}}$ is the area normalized streamflow (m

^{3}/s/km

^{2}) at the donor station i. The weights ${w}_{i}$ based on physical similarity can be calculated for all donor stations using Equation (6). The sum of the weights assigned to each donor station is equal to 1.

#### 3.2. Selection of Donor Stations

#### 3.3. Data Preprocessing

#### 3.4. Evaluation Criteria

^{2}) between the estimated and observed streamflow values. NSE, RSR, PBIAS, and R

^{2}were calculated as follows:

^{2}) is the square of the correlation coefficient according to Pearson. The R

^{2}values range from 0 to 1, with higher values indicating better agreement between estimated and observed values. Generally, R

^{2}values greater than 0.5 are considered acceptable [47].

## 4. Results and Discussion

#### 4.1. Middle Euphrates Basin

^{2}) in the Middle Euphrates Basin and was determined as the most physically similar donor station for both D21A167 (250 km

^{2}) and E21A022 (5882.4 km

^{2}). Moreover, E21A002 has the largest drainage area (25,515.6 km

^{2}) in the Middle Euphrates Basin. Its drainage area is more than four times the next largest station. For all target stations other than D21A169 and E21A058, MDAR using of the three most physically donor stations produced better NSE values than that using the two most physically similar donor stations. For D21A169, the NSE value decreased from 0.852 to 0.595 when the three most physically similar donor stations were used instead of the two most physically similar donor stations (see Table 7). In case of the use of the three most physically similar donor stations, the third most physically similar donor station for D21A169 was determined as D21A167. The NSE value obtained for D21A169 using the DAR method and utilizing D21A167 was lower than the NSE values obtained from the other two donor stations (i.e., E21A058 and E21A077). The drainage area of the donor station D21A167 is very close to the target station D21A169. On the other hand, the drainage areas of the other two donor stations are much larger than D21A169. Hence, the weight of donor station D21A167 for streamflow estimation of D21A169 is significantly larger compared to the other two. Consequently, the NSE value obtained for D21A169 using MDAR with the three most physically similar donor stations is predominantly influenced by donor station D21A167. Similarly, for E21A058, the decrease in the NSE (i.e., from 0.894 to 0.839) was due to the same reason as for D21A169.

^{2}) of 0.91, which was higher than the R

^{2}values of 0.87 and 0.90 obtained by using the DAR and MDAR, respectively. The NSE values for these methods ranged from 0.814 to 0.907, and the best NSE value was achieved by ISW2. The best NSE performance for E21A058 was obtained using ISW2 with the three most physically similar donor stations.

#### 4.2. Upper Euphrates Basin

^{2}) of 0.94, which was higher than the R

^{2}values of 0.89 by using DAR. The NSE values for these methods ranged from 0.883 to 0.932, and the best NSE value was achieved by MDAR. The best NSE performance for E21A051 was obtained using MDAR with the two most physically similar donor stations.

## 5. Conclusions

^{2}between the observed and estimated daily streamflow. When the estimated daily streamflow values at the target station were obtained from the statistical methods using the observed (original) daily streamflow values at the donor station(s), they were compared to the observed (original) daily streamflow values at the target station. On the other hand, when the estimated daily streamflow values at the target station were obtained from the statistical methods using the observed-MA (smoothed) daily streamflow values at the donor station(s), they were compared to the observed-MA (smoothed) daily streamflow values at the target station. These two approaches were presented to estimate the daily streamflow values with and without MA. It is believed that the results will help decision makers choose the best one for their objectives.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**Comparison of daily streamflow estimated using DAR (top row), MDAR (mid row), and ISW2 (bottom row) with observed (original) daily streamflow at station E21A058 in the Middle Euphrates Basin.

**Figure 7.**Comparison of daily streamflow estimated using DAR-MA (top row), MDAR-MA (mid row), and ISW2-MA (bottom row) with observed-MA (smoothed) daily streamflow at station E21A058 in the Middle Euphrates Basin.

**Figure 8.**Comparison of daily streamflow estimated using DAR (top row), MDAR (mid row), and ISW1 (bottom row) with observed (original) daily streamflow at station E21A051 in the Upper Euphrates Basin.

**Figure 9.**Comparison of daily streamflow estimated using DAR-MA (top row), MDAR-MA (mid row), and ISW1-MA (bottom row) with observed-MA (smoothed) daily streamflow at station E21A051 in the Upper Euphrates Basin.

Station Number | Drainage Area (km^{2}) | Elevation (m) | Long-Term Mean (m^{3}/s) | Record Period (Years) |
---|---|---|---|---|

D21A167 | 250 | 1650 | 3.55 | 1986–2009 |

D21A169 | 276.1 | 1600 | 3.35 | 1986–2009 |

D21A213 | 65.3 | 1810 | 0.74 | 1986–2009 |

E21A002 | 25,515.6 | 852 | 239.82 | 1986–2009 |

E21A022 | 5882.4 | 1552 | 48.20 | 1986–2009 |

E21A058 | 1577.6 | 1310 | 18.91 | 1986–2009 |

E21A064 | 2232 | 990 | 32.97 | 1986–2009 |

E21A077 | 2995.3 | 1452 | 29.94 | 1986–2009 |

Station Number | Drainage Area (km^{2}) | Elevation (m) | Long-term Mean (m^{3}/s) | Record Period (Years) |
---|---|---|---|---|

D21A001 | 233.2 | 1830 | 2.75 | 1986–2009 |

D21A193 | 518.1 | 1000 | 6.31 | 1986–2009 |

E21A033 | 3284.8 | 875 | 89.38 | 1986–2009 |

E21A051 | 8185.6 | 1355 | 60.23 | 1986–2009 |

E21A054 | 2886 | 1675 | 19.68 | 1986–2009 |

E21A056 | 15,562 | 865 | 153.57 | 1986–2009 |

E21A066 | 5430 | 840 | 78.26 | 1986–2009 |

Physical Characteristics | Maximum | Minimum | Mean |
---|---|---|---|

Drainage Area (km^{2}) | 25,515.6 | 65.3 | 4849.3 |

Elevation (m) | 1810 | 852 | 1402 |

Annual Mean Total Precipitation (mm) | 939.50 | 431.20 | 679.68 |

Annual Mean Temperature (°F) | 53.60 | 42.26 | 47.29 |

Basin Slope (%) | 2.69 | 0.19 | 1.21 |

Channel Length (km) | 565.11 | 14.75 | 142.27 |

Latitude (°) | 39.54 | 38.69 | 39.19 |

Longitude (°) | 42.78 | 39.93 | 41.58 |

Physical Characteristics | Maximum | Minimum | Mean |
---|---|---|---|

Drainage Area (km^{2}) | 15,562 | 233.2 | 5157.1 |

Elevation (m) | 1830 | 840 | 1205.7 |

Annual Mean Total Precipitation (mm) | 840.17 | 374.90 | 524.15 |

Annual Mean Temperature (°F) | 56.48 | 42.26 | 48.52 |

Basin Slope (%) | 2.82 | 0.16 | 0.96 |

Channel Length (km) | 381.60 | 25.10 | 161.19 |

Latitude (°) | 40.11 | 38.86 | 39.44 |

Longitude (°) | 41.39 | 38.41 | 39.79 |

**Table 5.**Performance ratings of the Nash–Sutcliffe efficiency (NSE) and percent bias (PBIAS) statistics for daily streamflow.

Performance Rating | NSE | abs(PBIAS) % |
---|---|---|

Very good | NSE ≥ 0.7 | abs(PBIAS) ≤ 25 |

Good | 0.5 ≤ NSE < 0.7 | 25 < abs(PBIAS) ≤ 50 |

Satisfactory | 0.3 ≤ NSE < 0.5 | 50 < abs(PBIAS) ≤ 70 |

Unsatisfactory | NSE < 0.3 | abs(PBIAS) > 70 |

Target Station | Donor Station | ||||||
---|---|---|---|---|---|---|---|

1st | 2nd | 3rd | 4th | 5th | 6th | 7th | |

D21A167 | D21A213 | D21A169 | E21A022 | E21A058 | E21A077 | E21A064 | E21A002 |

D21A169 | E21A058 | E21A077 | D21A167 | D21A213 | E21A022 | E21A064 | E21A002 |

D21A213 | D21A167 | E21A022 | D21A169 | E21A058 | E21A077 | E21A064 | E21A002 |

E21A002 | E21A064 | E21A058 | E21A077 | E21A022 | D21A169 | D21A167 | D21A213 |

E21A022 | D21A213 | E21A077 | D21A167 | E21A058 | D21A169 | E21A064 | E21A002 |

E21A058 | E21A077 | D21A169 | E21A064 | E21A022 | D21A167 | D21A213 | E21A002 |

E21A064 | E21A058 | E21A077 | D21A169 | E21A002 | E21A022 | D21A167 | D21A213 |

E21A077 | E21A058 | D21A169 | E21A022 | E21A064 | D21A213 | D21A167 | E21A002 |

**Table 7.**NSE values for the drainage area ratio (DAR) and multiple-donor stations drainage area ratio (MDAR) methods in the Middle Euphrates Basin.

Target Station | The Geographically Nearest Donor Station | The Most Physically Similar Donor Station | Two Most Physically Similar Donor Stations | Three Most Physically Similar Donor Stations |
---|---|---|---|---|

DAR | DAR | MDAR | MDAR | |

D21A167 | 0.313 | −0.187 | 0.312 | 0.316 |

D21A169 | 0.581 | 0.850 | 0.852 | 0.595 |

D21A213 | 0.718 | 0.354 | 0.369 | 0.608 |

E21A002 | −0.171 | −0.171 | 0.433 | 0.729 |

E21A022 | −0.205 | −0.205 | 0.622 | 0.718 |

E21A058 | 0.826 | 0.814 | 0.894 | 0.839 |

E21A064 | 0.649 | 0.724 | 0.694 | 0.706 |

E21A077 | 0.300 | 0.647 | 0.651 | 0.781 |

**Table 8.**NSE values for the inverse similarity weighted (ISW) with powers of 1, 2, and 3 in the Middle Euphrates Basin.

Target Station | Two Most Physically Similar Donor Stations | Three Most Physically Similar Donor Stations | ||||
---|---|---|---|---|---|---|

ISW1 | ISW2 | ISW3 | ISW1 | ISW2 | ISW3 | |

D21A167 | 0.136 | 0.060 | −0.009 | 0.317 | 0.184 | 0.065 |

D21A169 | 0.844 | 0.849 | 0.852 | 0.816 | 0.825 | 0.833 |

D21A213 | 0.501 | 0.463 | 0.429 | 0.608 | 0.556 | 0.502 |

E21A002 | 0.418 | 0.396 | 0.374 | 0.696 | 0.664 | 0.630 |

E21A022 | 0.432 | 0.375 | 0.316 | 0.636 | 0.591 | 0.535 |

E21A058 | 0.893 | 0.892 | 0.892 | 0.904 | 0.907 | 0.906 |

E21A064 | 0.696 | 0.701 | 0.706 | 0.712 | 0.713 | 0.714 |

E21A077 | 0.641 | 0.651 | 0.656 | 0.774 | 0.743 | 0.716 |

**Table 9.**Performance evaluation of the best statistical method without the moving average (MA) for each target station in the Middle Euphrates Basin.

Target Station | Method | NSE | RSR | PBIAS |
---|---|---|---|---|

D21A167 | ISW1 | 0.317 ^{3} | 0.827 | 23.265 ^{1} |

D21A169 | ISW3 | 0.852 ^{1} | 0.385 | 6.459 ^{1} |

D21A213 | ISW1 | 0.608 ^{2} | 0.626 | −6.122 ^{1} |

E21A002 | MDAR | 0.729 ^{1} | 0.520 | −30.114 ^{2} |

E21A022 | MDAR | 0.718 ^{1} | 0.531 | −39.089 ^{2} |

E21A058 | ISW2 | 0.907 ^{1} | 0.304 | 3.123 ^{1} |

E21A064 | DAR | 0.724 ^{1} | 0.525 | 18.865 ^{1} |

E21A077 | MDAR | 0.781 ^{1} | 0.468 | −11.015 ^{1} |

^{1}Very good,

^{2}good,

^{3}satisfactory, and

^{4}unsatisfactory.

**Table 10.**Performance evaluation of the best statistical method with the MA for each target station in the Middle Euphrates Basin.

Target Station | Method | NSE | RSR | PBIAS |
---|---|---|---|---|

D21A167 | ISW1-MA | 0.326 ^{3} | 0.821 | 23.265 ^{1} |

D21A169 | ISW3-MA | 0.876 ^{1} | 0.352 | 6.459 ^{1} |

D21A213 | ISW1-MA | 0.618 ^{2} | 0.618 | −6.122 ^{1} |

E21A002 | MDAR-MA | 0.767 ^{1} | 0.483 | −30.114 ^{2} |

E21A022 | MDAR-MA | 0.725 ^{1} | 0.524 | −39.089 ^{2} |

E21A058 | ISW2-MA | 0.921 ^{1} | 0.282 | 3.123 ^{1} |

E21A064 | DAR-MA | 0.744 ^{1} | 0.506 | 18.865 ^{1} |

E21A077 | MDAR-MA | 0.817 ^{1} | 0.428 | −11.015 ^{1} |

^{1}Very good,

^{2}good,

^{3}satisfactory, and

^{4}unsatisfactory.

Target Station | Donor Station | |||||
---|---|---|---|---|---|---|

1st | 2nd | 3rd | 4th | 5th | 6th | |

D21A001 | E21A054 | E21A051 | D21A193 | E21A033 | E21A033 | E21A066 |

D21A193 | E21A033 | E21A066 | E21A056 | E21A051 | E21A051 | E21A054 |

E21A033 | E21A066 | D21A193 | E21A051 | E21A056 | E21A056 | D21A001 |

E21A051 | E21A054 | E21A056 | E21A066 | E21A033 | E21A033 | D21A193 |

E21A054 | E21A051 | D21A001 | E21A033 | E21A056 | E21A056 | D21A193 |

E21A056 | E21A051 | E21A066 | E21A033 | D21A193 | D21A193 | D21A001 |

E21A066 | E21A033 | E21A051 | E21A056 | D21A193 | D21A193 | D21A001 |

Target Station | The Geographically Nearest Donor Station | The Most Physically Similar Donor Station | Two Most Physically Similar Donor Stations | Three Most Physically Similar Donor Stations |
---|---|---|---|---|

DAR | DAR | MDAR | MDAR | |

D21A001 | 0.619 | 0.619 | 0.630 | −0.328 |

D21A193 | 0.299 | −0.646 | −0.053 | 0.089 |

E21A033 | 0.446 | 0.446 | 0.377 | 0.319 |

E21A051 | 0.883 | 0.883 | 0.932 | 0.362 |

E21A054 | 0.159 | 0.885 | 0.585 | −5.128 |

E21A056 | −3.199 | 0.769 | 0.415 | −0.586 |

E21A066 | −0.067 | −0.067 | 0.698 | 0.732 |

Target Station | Two Most Physically Similar Donor Stations | Three Most Physically Similar Donor Stations | ||||
---|---|---|---|---|---|---|

ISW1 | ISW2 | ISW3 | ISW1 | ISW2 | ISW3 | |

D21A001 | 0.633 | 0.629 | 0.626 | 0.597 | 0.626 | 0.631 |

D21A193 | 0.015 | −0.085 | −0.185 | 0.307 | 0.217 | 0.108 |

E21A033 | 0.416 | 0.439 | 0.444 | 0.353 | 0.412 | 0.435 |

E21A051 | 0.931 | 0.928 | 0.921 | 0.811 | 0.877 | 0.905 |

E21A054 | 0.753 | 0.775 | 0.794 | 0.244 | 0.580 | 0.719 |

E21A056 | 0.404 | 0.541 | 0.640 | −0.788 | −0.306 | 0.083 |

E21A066 | 0.479 | 0.191 | 0.033 | 0.645 | 0.331 | 0.097 |

**Table 14.**Performance evaluation of the best statistical method without the MA for each target station in the Upper Euphrates Basin.

Target Station | Method | NSE | RSR | PBIAS |
---|---|---|---|---|

D21A001 | ISW1 | 0.633 ^{2} | 0.606 | 40.537 ^{2} |

D21A193 | ISW1 | 0.307 ^{3} | 0.832 | −51.370 ^{3} |

E21A033 | DAR | 0.446 ^{3} | 0.744 | 47.035 ^{2} |

E21A051 | MDAR | 0.932 ^{1} | 0.261 | −10.006 ^{1} |

E21A054 | DAR | 0.885 ^{1} | 0.339 | −7.892 ^{1} |

E21A056 | DAR | 0.769 ^{1} | 0.480 | 25.436 ^{2} |

E21A066 | MDAR | 0.732 ^{1} | 0.518 | −22.121 ^{1} |

^{1}Very good,

^{2}good,

^{3}satisfactory, and

^{4}unsatisfactory.

**Table 15.**Performance evaluation of the best statistical method with the MA for each target station in the Upper Euphrates Basin.

Target Station | Method | NSE | RSR | PBIAS |
---|---|---|---|---|

D21A001 | ISW1-MA | 0.646 ^{2} | 0.595 | 40.537 ^{2} |

D21A193 | ISW1-MA | 0.305 ^{3} | 0.834 | −51.371 ^{3} |

E21A033 | DAR-MA | 0.453 ^{3} | 0.740 | 47.035 ^{2} |

E21A051 | MDAR-MA | 0.939 ^{1} | 0.248 | −10.006 ^{1} |

E21A054 | DAR-MA | 0.897 ^{1} | 0.322 | −7.892 ^{1} |

E21A056 | DAR-MA | 0.780 ^{1} | 0.469 | 25.436 ^{2} |

E21A066 | MDAR-MA | 0.749 ^{1} | 0.501 | −22.120 ^{1} |

^{1}Very good,

^{2}good,

^{3}satisfactory, and

^{4}unsatisfactory.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yilmaz, M.U.; Onoz, B.
A Comparative Study of Statistical Methods for Daily Streamflow Estimation at Ungauged Basins in Turkey. *Water* **2020**, *12*, 459.
https://doi.org/10.3390/w12020459

**AMA Style**

Yilmaz MU, Onoz B.
A Comparative Study of Statistical Methods for Daily Streamflow Estimation at Ungauged Basins in Turkey. *Water*. 2020; 12(2):459.
https://doi.org/10.3390/w12020459

**Chicago/Turabian Style**

Yilmaz, Mustafa Utku, and Bihrat Onoz.
2020. "A Comparative Study of Statistical Methods for Daily Streamflow Estimation at Ungauged Basins in Turkey" *Water* 12, no. 2: 459.
https://doi.org/10.3390/w12020459