# Successive-Station Streamflow Prediction and Precipitation Uncertainty Analysis in the Zarrineh River Basin Using a Machine Learning Technique

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{2}, is the largest lake in Iran and accounts for 7% of the country’s surface water [4]. Zarrineh River (ZR) basin is the largest and most crucial sub-basin of the LU basin, providing more than 41% (i.e., 1271 MCM) of the environmental flow into LU [3]. ZR is situated to the southeast of Lake Urmia and covers an area of about 12,025 km

^{2}with a length of around 300 km, as depicted in Figure 1 [41]. However, the lake surface area has drastically decreased to one-tenth, to 500 km, with the volume of half a billion cubic meters due to the unconventional use of available water and climate changes [2,3]. The Boukan Dam is the largest and most significant dam operating in the ZR basin with a live storage capacity of 650 MCM, storing water for drinking, agricultural, and industrial uses [42]. The average annual precipitation over the basin for the last four decades was 352 mm, which classifies the region as semi-arid with a Mediterranean climate.

## 3. Data Collection

## 4. Model Description

#### 4.1. Gated Recurrent Unit (GRU) Cell Structure

_{t−1}(h

^{′}

_{t−1}) is transferred to the up-to-date time step from the earlier one. More state data from the prior time step is produced by the greater number of update gates. The reset gate is applied to determine the degree to which the information from the previous state is forgotten. The lesser the reset gate, the more state information is forgotten. The update equations in the GRU cell structure are computed as per Equations (1)–(4):

#### 4.2. GLUE Theory

## 5. Methodology

#### 5.1. GRU Model Development

_{1}and S

_{2}consider all the features, except the current station’s streamflow with zero- and one-month lag times, respectively. However, S

_{3}, S

_{4}, and S

_{5}structures contain all the input variables with two- to four-month lag times. A total of five model structures were used to simulate all hydrometric stations, except for the first station (Safakhaneh station), which does not include the streamflow from the upstream station.

_{o}and Q

_{s}are the observed and estimated streamflow at time t, correspondingly.

#### 5.2. Data Normalization

_{i}and X

_{norm}denote the raw and normalized data, correspondingly. X

_{max}and X

_{min}represent the maximum and minimum of raw dataset, respectively.

#### 5.3. Model Evaluation Criteria

^{2}) (Equation (8)), which has a range of [0, 1], represents the linear relation between the observed and predicted data. The prediction model shows more reliable results if the value of R

^{2}is closer to 1. The root mean square error (RMSE) (Equation (9)) evaluates the magnitude of the difference between the observed and predicted values. The closer the value of RMSE to 0, the higher the accuracy of the prediction.

#### 5.4. Bias Correction Method

_{BC}is the bias-corrected GCM output, T

_{RAW}is the raw GCM output for the historical or future period, T

_{REF}is the GCM output from the historical reference period, and ${\sigma}_{T,REF}$ and ${\sigma}_{o,REF}$ are the standard deviation of GCM output and the standard deviation of reference observations from the reference period, respectively.

#### 5.5. Quantification of Input Data Uncertainty Using GLUE

## 6. Results

#### 6.1. Evaluation of GRU Networks

_{3}model structure. The GRU network might reach sub-optimal solutions using a random start point. Therefore, ten identical runs were performed for each structure, and the final model was selected based on the replication with the best performance in the testing period.

^{2}, and RMSE in the validation and testing phases to obtain high and comparable performance and avoid model overfitting. The S

_{1}structure with no lag time shows the poorest performance among the other models in that station. However, introducing antecedent streamflow of the station and a one-month lag time of other input parameters in the S

_{2}model increases the model performance significantly compared to the S

_{1}structure. The S

_{2}, S

_{3}, S

_{4}, and S

_{5}model structures have the same input variables with a one- to four-month lag time. All the available climate data with various lag times were considered in the model structures to obtain the best combination of these inputs and their period. In addition, lag times were chosen in order to analyze how temporal variations in inputs affect the results.

_{5}model, which showed lower results than the S4 model. This indicates that the model’s performance declines when complicating the model with excessive inputs. Overall, the S4 structure shows the best performance among the other models, with NSE, R

^{2}, and RMSE of 0.75, 0.78, and 5.7, respectively, in the testing phase. While the streamflow of an upstream station is not considered in the model structures of this station, the downstream stations of the Safakhaneh benefit from the upstream streamflow. The monthly inflow to the Boukan dam was predicted using five structures, in which S1 presents inferior performance compared to the other models. However, applying the station’s streamflow and various lag times substantially improves the statistical criteria of the model. The S

_{5}structure with all the input variables and a four-month lag time shows the best output results, with NSE, R

^{2}, and RMSE of 0.85, 0.86, and 20.7, respectively.

_{4}model composed of all the input variables and a three-month lag time. The evaluation criteria for the S

_{4}model are 0.98, 0.99, and 8.2 for NSE, R

^{2}, and RMSE, respectively, demonstrating the most accurate model. The most critical station in the Zarrineh River basin is the outlet station, i.e., Nezamabad, which yields the outflow to Lake Urmia. The model illustrates satisfactory output results in all the structures with the highest model performance in the S

_{3}model, with NSE, R

^{2}, and RMSE of 0.87, 0.88, and 18.3, respectively. Thus, the GRU network shows a significant capability to predict the successive-station monthly streamflow of the basin, particularly at the outlet station contributing to the Lake Urmia inflow.

^{2}in each station. Although the model shows some inconsistencies at high flows at the Safakhaneh station and Boukan dam, they performed reasonably for the low- and medium-range flows. The GRU model generally performed significantly for all the flows at the Qezkorpi and Nezamabad stations. Various climate data, the land use, and the location of stations are responsible for the inconsistency in the results for the same model structure in different stations. The results demonstrate that the model performed better for downstream stations compared to the upstream stations considering that the calibrated river flow reaches the downstream stations.

#### 6.2. Uncertainty

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Zarrineh River basin: Part (

**A**) shows the location map of the Zarrineh River basin in the northwest of Iran and part (

**B**) shows the Zarrineh River basin and its rivers network along with hydrometric and meteorological stations 1–4.

**Figure 6.**Comparison of observed and predicted streamflow for (

**a**) Safakhaneh, (

**b**) Boukan dam, (

**c**) Qezkorpi, (

**d**) Nezamabad stations.

**Figure 7.**Uncertainty interval (95 PPU) of input data for (

**a**) Safakhaneh, (

**b**) Boukan dam, (

**c**) Qezkorpi, (

**d**) Nezamabad; the gray area is the uncertainty interval and the dots are observations.

Name | Model Structure |
---|---|

S_{1} | ${Q}^{t}=f({Q}_{us}^{t},{P}^{t},{T}_{max}^{t},{T}_{min}^{t},{T}_{avg}^{t})$ |

S_{2} | ${Q}^{t}=f\left({Q}_{us}^{t-1},{Q}_{us}^{t},{Q}^{t-1},{P}^{t-1},{P}^{t},{T}_{max}^{t-1},{T}_{max}^{t},{T}_{min}^{t-1},{T}_{min}^{t},{T}_{avg}^{t-1},{T}_{avg}^{t}\right)$ |

S_{3} | ${Q}^{t}=f({Q}_{us}^{t-2},{Q}_{us}^{t-1},{Q}_{us}^{t},{Q}^{t-2},{Q}^{t-1},{P}^{t-2},{P}^{t-1},{P}^{t},{T}_{max}^{t-2},{T}_{max}^{t-1},{T}_{max}^{t}$ ${T}_{min}^{t-2},{T}_{min}^{t-1},{T}_{min}^{t},{T}_{avg}^{t-2},{T}_{avg}^{t-1},{T}_{avg}^{t})$ |

S_{4} | ${Q}^{t}=f({Q}_{us}^{t-3},{Q}_{us}^{t-2},{Q}_{us}^{t-1},{Q}_{us}^{t},{Q}^{t-3},{Q}^{t-2},{Q}^{t-1},{P}^{t-3},{P}^{t-2},{P}^{t-1},{P}^{t},{T}_{max}^{t-3}$ ${T}_{max}^{t-2},{T}_{max}^{t-1},{T}_{max}^{t},{T}_{min}^{t-3},{T}_{min}^{t-2},{T}_{min}^{t-1},{T}_{min}^{t},{T}_{avg}^{t-3},{T}_{avg}^{t-2},{T}_{avg}^{t-1},{T}_{avg}^{t})$ |

S_{5} | ${Q}^{t}=f({Q}_{us}^{t-4},{Q}_{us}^{t-3},{Q}_{us}^{t-2},{Q}_{us}^{t-1},{Q}_{us}^{t},{Q}^{t-4},{Q}^{t-3},{Q}^{t-2},{Q}^{t-1},{P}^{t-4},{P}^{t-3},$ ${P}^{t-2},{P}^{t-1},{P}^{t},{T}_{max}^{t-4},{T}_{max}^{t-3},{T}_{max}^{t-2},{T}_{max}^{t-1},{T}_{max}^{t},{T}_{min}^{t-4},{T}_{min}^{t-3},{T}_{min}^{t-2},$ ${T}_{min}^{t-1},{T}_{min}^{t},{T}_{avg}^{t-4},{T}_{avg}^{t-3},{T}_{avg}^{t-2},{T}_{avg}^{t-1},{T}_{avg}^{t})$ |

**Table 2.**Performance of GRU-based streamflow forecasting models for five station structures in the Zarrineh River basin with varying monthly lag time.

Training Phase | Validation Phase | Testing Phase | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Station | Structure | NSE | R^{2} | RMSE | NSE | R^{2} | RMSE | NSE | R^{2} | RMSE |

Safakhaneh (#1) | S_{1} | 0.34 | 0.35 | 13.9 | 0.49 | 0.34 | 15.1 | 0.46 | 0.29 | 12.3 |

S_{2} | 0.53 | 0.66 | 10.2 | 0.52 | 0.63 | 11.1 | 0.54 | 0.57 | 8.1 | |

S_{3} | 0.74 | 0.8 | 7.5 | 0.73 | 0.69 | 5.8 | 0.69 | 0.71 | 6.6 | |

S_{4} | 0.75 | 0.86 | 5.8 | 0.75 | 0.78 | 6.7 | 0.8 | 0.8 | 5.3 | |

S_{5} | 0.73 | 0.81 | 7.7 | 0.79 | 0.75 | 6.6 | 0.75 | 0.78 | 5.7 | |

Boukan dam (#2) | S_{1} | −7.9 | 0.79 | 23.4 | −10.8 | 0.82 | 27.4 | −12.6 | 0.85 | 20.7 |

S_{2} | 0.79 | 0.89 | 35.1 | 0.83 | 0.88 | 31.5 | 0.75 | 0.92 | 28.1 | |

S_{3} | 0.8 | 0.81 | 35.5 | 0.73 | 0.76 | 27.7 | 0.78 | 0.81 | 25.9 | |

S_{4} | 0.84 | 0.84 | 31.3 | 0.78 | 0.88 | 28.5 | 0.81 | 0.83 | 24.2 | |

S_{5} | 0.88 | 0.89 | 26.8 | 0.88 | 0.89 | 23.5 | 0.85 | 0.86 | 20.7 | |

Qezkorpi (#3) | S_{1} | 0.94 | 0.96 | 15.2 | 0.86 | 0.84 | 18.6 | 0.95 | 0.99 | 12.7 |

S_{2} | 0.93 | 0.96 | 19.2 | 0.93 | 0.95 | 16.5 | 0.94 | 0.99 | 13.4 | |

S_{3} | 0.95 | 0.96 | 15.9 | 0.92 | 0.94 | 11.4 | 0.96 | 0.99 | 10.2 | |

S_{4} | 0.96 | 0.96 | 15.1 | 0.97 | 0.98 | 7.6 | 0.98 | 0.99 | 8.2 | |

S_{5} | 0.94 | 0.95 | 18.7 | 0.91 | 0.94 | 14.1 | 0.94 | 0.99 | 12.6 | |

Nezamabad (#4) | S_{1} | 0.72 | 0.72 | 42.3 | 0.66 | 0.72 | 34.7 | 0.71 | 0.77 | 27.7 |

S_{2} | 0.81 | 0.85 | 34.8 | 0.84 | 0.87 | 26.3 | 0.79 | 0.82 | 23.7 | |

S_{3} | 0.95 | 0.95 | 18.1 | 0.85 | 0.89 | 17.6 | 0.87 | 0.88 | 18.3 | |

S_{4} | 0.94 | 0.94 | 18.7 | 0.89 | 0.93 | 22.4 | 0.85 | 0.88 | 19.8 | |

S_{5} | 0.84 | 0.87 | 31.7 | 0.84 | 0.87 | 24.4 | 0.82 | 0.83 | 21.3 |

Station Names | $\mathit{L}\left(\mathit{P}|\mathit{Q}\right)$ | p-Factor (%) | r-Factor |
---|---|---|---|

Safakhaneh | 86 | 78.5 | 0.53 |

Boukan dam | 89 | 89.3 | 0.57 |

Qezkorpi | 91 | 86.6 | 0.52 |

Nezam Abad | 85 | 61.6 | 0.47 |

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Nakhaei, M.; Ghazban, F.; Nakhaei, P.; Gheibi, M.; Wacławek, S.; Ahmadi, M. Successive-Station Streamflow Prediction and Precipitation Uncertainty Analysis in the Zarrineh River Basin Using a Machine Learning Technique. *Water* **2023**, *15*, 999.
https://doi.org/10.3390/w15050999

**AMA Style**

Nakhaei M, Ghazban F, Nakhaei P, Gheibi M, Wacławek S, Ahmadi M. Successive-Station Streamflow Prediction and Precipitation Uncertainty Analysis in the Zarrineh River Basin Using a Machine Learning Technique. *Water*. 2023; 15(5):999.
https://doi.org/10.3390/w15050999

**Chicago/Turabian Style**

Nakhaei, Mahdi, Fereydoun Ghazban, Pouria Nakhaei, Mohammad Gheibi, Stanisław Wacławek, and Mehdi Ahmadi. 2023. "Successive-Station Streamflow Prediction and Precipitation Uncertainty Analysis in the Zarrineh River Basin Using a Machine Learning Technique" *Water* 15, no. 5: 999.
https://doi.org/10.3390/w15050999