# Forecasting the Ensemble Hydrograph of the Reservoir Inflow based on Post-Processed TIGGE Precipitation Forecasts in a Coupled Atmospheric-Hydrological System

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Material and Methods

#### 2.1. Research Methodology

#### 2.2. Case Study and Data

^{2}, the average height is 1976 m, and the long-term mean annual rainfall is 784 mm. The flow data from the Taleh-Zang hydrometric station, located upstream of the reservoir, was applied to forecast ensemble inflow into the reservoir [37]. Over the past several decades, flood occurrence in the study area has caused huge damage [38]. Accordingly, six flood events were selected during 2013–2019. Table 1 illustrates the peak discharge during flood events, cumulative precipitation, and duration of the events. It is worth noting that these events were selected based on the date of the annual peak discharge.

#### 2.3. Post-Processing Ensemble Precipitation Forecasts

#### 2.3.1. Multi-Model Ensemble System by the WA-WLSR Model

#### 2.3.2. Multi-Model Ensemble System by the GMDH Model

#### 2.4. HBV Hydrological Model

_{0}and Q

_{1}), while the lower zone has only one outlet (Q

_{2}). These zones are coupled together by constant percolation (perc). After the water level exceeds a threshold limit (L) in the upper zone, runoff is rapidly triggered at the upper part of the upper zone (Q

_{0}). The parameters K

_{0}, K

_{1}, and K

_{2}are used to control runoff associated with the response functions of the upper and lower zones [52]. The HBV model applies the triangular weight function (MAXBAS) which is used for routing the runoff at the outlet [52,53]. The HBV model’s parameters and their range are shown in Table 3.

#### 2.5. Goodness-of-Fit Metrics

## 3. Results and Discussion

#### 3.1. Correction of Ensemble Precipitation Forecasts

#### 3.2. Multi-Model Ensemble Forecasts

#### 3.3. Ensemble Reservoir Inflow Forecasting

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Schematic of the HBV model with main equations [41].

**Figure 5.**The percentage of variations in improving the forecast skill of the NWP models based on post-processing approaches.

**Figure 6.**ROC diagrams for raw and post-processed ensemble precipitation forecasts: (

**a**) 2.5 mm (

**b**) 10 mm.

**Figure 9.**Ensemble reservoir inflow during flood events for the calibration stage. Black lines: observed inflow hydrograph; blue lines: the deterministic inflow forecast based on observed precipitation; grey lines: ensemble inflow forecasts simulated by post-processed EPFs containing all ensemble members; red lines: ensemble-mean of all members.

**Figure 11.**Model’s performance distribution over the members of ensemble reservoir inflow at the validation stage based on (

**a**) NSE and (

**b**) MARE criteria.

Event No | Date of Events | Peak Discharge (m^{3}/s) | Time (h) | Precipitation Depth (mm) |
---|---|---|---|---|

1 | 29.01.2013 | 633 | 48 | 31.33 |

2 | 24.03.2017 | 1307 | 72 | 37.93 |

3 | 25.02.2018 | 622 | 72 | 19.67 |

4 | 01.04.2019 | 5222 | 48 | 104.39 |

5 | 28.12.2016 | 1037 | 84 | 101.26 |

6 | 18.02.2018 | 665 | 72 | 48.8 |

Center | Forecast Length (Day) | Model Resolution (lon × lat) | Number of Ensemble Members | Base Time (UTC) |
---|---|---|---|---|

NCEP | 16 | 1.00° × 1.00° | 20 | 00/06/12/18 |

UKMO | 15 | 0.83° × 0.56° | 23 | 00/12 |

KMA | 10 | 1.00° × 1.00° | 24 | 00/12 |

Sub-Models | Parameters | Description of the Parameters | Range |
---|---|---|---|

Snow | Tr | Temperature threshold above which precipitation is liquid [°C] | 0–2 |

Ts | Temperature threshold below which precipitation is solid [°C] | −2–0 | |

Tm | Temperature threshold above which snowmelt starts [°C] | −2–2 | |

DDF | Degree-day factor determines the speed of the snow melting [mm/°C/day] | 1–5 | |

SCF | Factor for correcting snow measurements [-] | 1–1.6 | |

Soil moisture | FC | Field capacity- maximum soil moisture storage [mm] | 100–250 |

Lp | A limit for potential evapotranspiration [-] | 0.5–1 | |

BETA | Coefficient influencing the amount of water caused by soil moisture and the upper reservoir [-] | 0.1–2.5 | |

Runoff response | perc | Constant percolation rate from the upper to the bottom reservoir [mm] | 0.5–4 |

L | Threshold storage state for initiating very fast surface runoff [mm] | 10–60 | |

K_{0} | The recession coefficients associated with the surface (K_{0}), sub-surface (K_{1}), and base flow (K_{2}) [-] | 1–5 | |

K_{1} | 5–30 | ||

K_{2} | 30–120 | ||

Maxbas | The parameter for runoff routing [-] | 1–6 |

Goodness-of-Fit Metrics | Equation | Description | Best Fit/Poorest Fit |
---|---|---|---|

Nash-Sutcliffe Efficiency | $NSE=1-\frac{\sum {\left(O-F\right)}^{2}}{\sum {\left(O-\overline{O}\right)}^{2}}$ | Measure of the relative magnitude of the residual variance compared with the observed data variance | 1/−∞ |

Kling-Gupta Efficiency | $KGE=1-\sqrt{{(1-r)}^{2}{(1-\beta )}^{2}{(1-\gamma )}^{2}}$ | A function of correlation, bias, and variability to ensure that the bias and variability ratios are not cross-correlated | 1/−∞ |

Pearson coefficient | $r=\frac{\sum \left(O-\overline{O}\right)\left(F-\overline{F}\right)}{\sqrt{{\left(O-\overline{O}\right)}^{2}}\sqrt{{\left(F-\overline{F}\right)}^{2}}}$ | The capability of a linear relationship between observed and forecasted data | 1/−1 |

Normalized Root Mean Square Error | $NRMSE=\frac{\sqrt{\frac{1}{N}\sum {\left(O-F\right)}^{2}}}{\stackrel{-}{O}}$ | The difference between observed and forecasted data | 0/ |

Mean Absolute Error | $MAE=\frac{1}{N}\sum \left|O-F\right|$ | The difference between observed and forecasted data | 0/ |

Mean Absolute Relative Error | $MARE=\frac{1}{N}\sum \frac{\left|O-F\right|}{O}$ | The difference between observed and forecasted data | 0/ |

Model’s Efficiency | The Range of Goodness-of-Fit Criteria | |
---|---|---|

Very good | NSE, KGE > 0.75 | MARE < 0.5 |

Good | 0.65 < NSE, KGE < 0.75 | 0.5 < MARE < 0.6 |

Acceptable | 0.5 < NSE, KGE < 0.65 | 0.6 < MARE < 0.7 |

Unsatisfactory | NSE < 0.5 | MARE > 0.7 |

Observed | Occurrence | Non-Occurrence | Total | |
---|---|---|---|---|

Forecasted | ||||

Alarm | H | FA | A | |

No-Alarm | MA | CN | A’ | |

Total | O | O’ | N |

NWP Models | Linear Regression Models | Goodness-of-Fit Metrics | |||
---|---|---|---|---|---|

Train | Test | ||||

NSE | MAE | NSE | MAE | ||

NCEP | ${P}_{O}=-0.184+1.191{P}_{r}$ | 0.531 | 2.838 | 0.651 | 2.108 |

KMA | ${P}_{O}=-0.933+1.205{P}_{r}$ | 0.518 | 3.115 | 0.51 | 2.725 |

UKMO | ${P}_{O}=0.038+0.841{P}_{r}$ | 0.473 | 2.704 | 0.462 | 2.671 |

NWP Models | Power Regression Models | Goodness-of-Fit Metrics | |||
---|---|---|---|---|---|

Train | Test | ||||

NSE | MAE | NSE | MAE | ||

NCEP | ${P}_{O}=1.021{{P}_{r}}^{1.059}$ | 0.532 | 2.816 | 0.651 | 2.107 |

KMA | ${P}_{O}=0.485{{P}_{r}}^{1.35}$ | 0.53 | 2.972 | 0.5 | 2.658 |

UKMO | ${P}_{O}=1.032{{P}_{r}}^{0.914}$ | 0.541 | 2.701 | 0.513 | 2.682 |

Goodness-of-Fit Metrics | NCEP | KMA | UKMO | ||||||
---|---|---|---|---|---|---|---|---|---|

Raw | Corrected-PRM | The Percentage of Variations | Raw | Corrected-PRM | The Percentage of Variations | Raw | Corrected-PRM | The Percentage of Variations | |

NSE | 0.53 | 0.55 | +4 | 0.51 | 0.52 | +2 | 0.51 | 0.54 | +6 |

KGE | 0.54 | 0.65 | +20 | 0.53 | 0.65 | +23 | 0.56 | 0.58 | +4 |

Pearson correlation | 0.74 | 0.74 | 0 | 0.72 | 0.72 | 0 | 0.72 | 0.75 | +4 |

NRMSE | 0.82 | 0.8 | −2 | 0.85 | 0.83 | −2.3 | 0.81 | 0.71 | −12 |

MAE | 2.57 | 2.18 | −15 | 2.85 | 2.62 | −8 | 2.78 | 2.21 | −20 |

Goodness-of-Fit Metrics | GMDH | WA-WLSR | ||
---|---|---|---|---|

Train Data | Test Data | All Data | ||

NSE | 0.68 | 0.65 | 0.68 | 0.76 |

KGE | 0.75 | 0.68 | 0.73 | 0.73 |

Pearson correlation | 0.82 | 0.83 | 0.82 | 0.88 |

NRMSE | 0.63 | 0.64 | 0.65 | 0.58 |

MAE | 2.15 | 2.18 | 2.11 | 2.02 |

**Table 11.**The goodness-of-fit metrics used for the HBV model to simulate ensemble reservoir inflow in the calibration stage.

Goodness-of-Fit Metrics | Modeling Approach | Flood Events | |||
---|---|---|---|---|---|

Event 1 | Event 2 | Event 3 | Event 4 | ||

NSE | Ensemble members | 0.93 | 0.82 | 0.92 | 0.79 |

Ensemble-mean | 0.97 | 0.88 | 0.97 | 0.81 | |

Deterministic forecasts | 0.9 | 0.81 | 0.86 | 0.79 | |

KGE | Ensemble members | 0.92 | 0.83 | 0.88 | 0.7 |

Ensemble-mean | 0.97 | 0.89 | 0.94 | 0.71 | |

Deterministic forecasts | 0.89 | 0.7 | 0.83 | 0.68 | |

MARE | Ensemble members | 0.14 | 0.12 | 0.14 | 0.65 |

Ensemble-mean | 0.11 | 0.09 | 0.08 | 0.63 | |

Deterministic forecasts | 0.17 | 0.11 | 0.24 | 0.78 |

**Table 12.**The goodness-of-fit metrics used for the HBV model to simulate ensemble reservoir inflow in the validation stage.

Goodness-of-Fit Metrics | Modeling Approach | Flood Events | |
---|---|---|---|

Event 5 | Event 6 | ||

NSE | Ensemble members | 0.65 | 0.74 |

Ensemble-mean | 0.74 | 0.79 | |

Deterministic forecasts | 0.6 | 0.73 | |

KGE | Ensemble members | 0.78 | 0.71 |

Ensemble-mean | 0.87 | 0.73 | |

Deterministic forecasts | 0.75 | 0.63 | |

MARE | Ensemble members | 0.35 | 0.53 |

Ensemble-mean | 0.3 | 0.47 | |

Deterministic forecasts | 0.34 | 0.54 |

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**MDPI and ACS Style**

Tanhapour, M.; Soltani, J.; Malekmohammadi, B.; Hlavcova, K.; Kohnova, S.; Petrakova, Z.; Lotfi, S.
Forecasting the Ensemble Hydrograph of the Reservoir Inflow based on Post-Processed TIGGE Precipitation Forecasts in a Coupled Atmospheric-Hydrological System. *Water* **2023**, *15*, 887.
https://doi.org/10.3390/w15050887

**AMA Style**

Tanhapour M, Soltani J, Malekmohammadi B, Hlavcova K, Kohnova S, Petrakova Z, Lotfi S.
Forecasting the Ensemble Hydrograph of the Reservoir Inflow based on Post-Processed TIGGE Precipitation Forecasts in a Coupled Atmospheric-Hydrological System. *Water*. 2023; 15(5):887.
https://doi.org/10.3390/w15050887

**Chicago/Turabian Style**

Tanhapour, Mitra, Jaber Soltani, Bahram Malekmohammadi, Kamila Hlavcova, Silvia Kohnova, Zora Petrakova, and Saeed Lotfi.
2023. "Forecasting the Ensemble Hydrograph of the Reservoir Inflow based on Post-Processed TIGGE Precipitation Forecasts in a Coupled Atmospheric-Hydrological System" *Water* 15, no. 5: 887.
https://doi.org/10.3390/w15050887