# A Sustainable Early Warning System Using Rolling Forecasts Based on ANN and Golden Ratio Optimization Methods to Accurately Predict Real-Time Water Levels and Flash Flood

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## Abstract

**:**

## 1. Introduction

#### 1.1. Background

#### 1.2. Literature Review

#### 1.3. Contributions

- Developing a novel rolling forecast model for flash-floods-based ANN technique equipped with an early warning system based on the weather forecast data and real-time measurements of water level in the street drainage system (downtown/Amman). The proposed EFWS in this paper aims to support decision makers by providing them with reliable and accurate information and warning about any possible flood events. Furthermore, the EFWS will provide accurate forecasts with efficient lead-time to reduce any damages due to flash floods.
- This paper develops an ANN using a new optimization method, called the Golden Ratio Optimization Method (GROM) technique, to estimate the water level over one day ahead during flash flood events. The result of the new forecast model (ANN based on GROM) will be compared to the literature, the traditional ANN model.
- This article examines the impact of using different exogenous variables on the ANN forecast and investigate the optimal ANN structure for forecasting the flash flood in Jordan.
- Developing a rolling ANN forecast model to treat the stochasticity of weather forecast data and improve the prediction accuracy of the flash flood in Jordan compared to fixed point forecast models.

#### 1.4. Outline of Paper

## 2. Methodology

## 3. EFWS System Modeling and Study Area

#### 3.1. Study Area and the Water Drainage System

#### 3.2. Real-Time Measurement Model

#### 3.3. Flood Warning System

## 4. Rolling ANN Forecast Model Optimized by GROM

#### 4.1. ANN Forecast Model for ESWS Optimized by GROM

- Traditional ANN model: this proposed model is a feedforward ANN model trained by one of the most common methods called Levenberg-Marquard and the neuron activated by a sigmoid function. This traditional ANN model has been widely used in the literature with stochastic targets [24].
- ANN forecast model optimized by Golden Ratio Optimization Method (GROM) algorithm [33]: the feedforward ANN model will use the GROM algorithm to handle the learning process and achieve the optimal performance in ANN.

#### 4.1.1. Implementation of ANN Models (Traditional and GROM Models)

- Inputs variables: initially, the following variables (adding water level at a time, $\Delta \widehat{L}$ (t), and real-time measurement for the water level, $L$ $\left(t-10\right)$ have been carefully selected as the main input variables, where they are directly connected to calculate the future water level. In order to improve the forecast model performance and select more suitable input variables, the previous time steps from 10 min until one hour, the previous day water level at the same time, previous day data of daily rain intensity and temperature are tested in this work as external variables.
- Output variables: the future water level, $\widehat{H}\left(t\right),$ over the next day with 10 min time resolution.
- Data processing: weather conditions data has been collected over three years from 2017 to 2019. These data sets are divided into training (60%), validation (10%) and testing data sets (30%). In general, the training set is the largest data set, and it is used to fit the parameters of the model, train the forecast model and find the patterns. The training set needs to be large enough to represent the data characteristics. This data set is mainly used to select the potential models. Then the validation set is used to try and find the best of these by training each of the model parameters in the training set and then testing the errors for forecasts in the validation set. The validation set is used as a final performance check for the trained network before testing the model with around 10% of the training set. The reason for this structure is to avoid a specific good forecast on the training set which turns out to be inaccurate in the test set. In addition, this way aims to avoid “overfitting” by selecting a forecast that is over-trained on the training set. Finally, the testing set is used to provide an unbiased evaluation of the final forecast model and is typically 10% to 30% of the training set.
- The number of hidden layers and neurons: to optimally select the number of hidden layers and neurons for the ANN in EFW, different number of hidden layers (1 to 5) and different number of hidden neurons (10 to 50) has been tested.
- Training and learning algorithm: Levenberg-Marquardt and GROM algorithms are used and tested.
- The stopping criteria: in case there are no improvements in the accuracy.

#### 4.1.2. ANN Forecast Model Based on GROM Algorithm

#### 4.2. The Forecast Model Evaluation

- Evaluating different exogenous variables and ANN structure parameters to determine the optimal parameters for the ANN models
- Overall comparisons are presented for the traditional ANN and ANN optimized by GROM.
- Evaluating the significance of using the rolling forecasts compared to a fixed model.

## 5. Results and Discussion

#### 5.1. Risk Knowledge and Flood Warning System

- The EFWS generates daily and hourly reports (excel sheets) and dialog box warning (lights and sound) in the workstation (control center). This data and information will be available for the decision-maker and government to make necessary decisions and actions.
- The EFWS model will send an email notification to selected emails by control center holder such as private and government stockholders and emergency team.
- To increase the awareness of the flash flood risk among communities, the EFWS model will post a warning message on Twitter if the estimated water level in orange or red zones.

#### 5.2. Effect of Exogenous Variables and Model Parameters on Forecast Models

- Input exogenous variables: adding water level at time t, $\Delta \widehat{L}$ (t), and real-time measurement for the water level, $L$ $\left(t-10\right)$
- Hidden layers: two layers.
- Hidden neurons in each layer: 10 neurons.
- Rolling forecasts.

#### 5.3. Traditional ANN Model and ANN Forecast Model Optimized by GROM

- Input exogenous variables: adding water level at time t, $\Delta \widehat{L}$ (t), and real-time measurement for the water level, $L\left(t-10\right)$ and ${\mathrm{A}}_{1}$ (the previous time steps from 20 min until one hour)
- Hidden layers: two layers.
- Hidden neurons in each layer: 20 neurons.

#### 5.4. Evaluating the Significance of Using the Rolling Forecasts Compared to a Fixed Model

#### 5.5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**(

**a**) Simulation for a street area with the drainage system. (

**b**) Simulation for the drainage system in the street. (

**c**) The real-time measuring system (ultrasonic sensor) located at the top of the water drainage system.

**Figure 9.**An example database from the ultrasonic sensor with the Arduino system via ThingSpeak cloud.

Equipment | Specifications |
---|---|

Arduino microcontroller (ATMega328) | Input: Voltage: 5~12 V, current: 50 mA, Temp range: −40 °C to 80 °C |

Ultrasonic Sensor (HC-SR04) | Input: Voltage: 3.3~5 V, Distance range: 2 cm–400 cm |

GPRS/3G/4G module | Input power: Voltage: 5 V, Output: SMS texts |

Solar panel | O/P: 6 V, Power: 3 W, Current: 300 mA |

Battery lead acid | Voltage: 6 V, Cpacity: 12 Ah. |

Step | Description |
---|---|

1 | Estimate the 10 min adding water level, $\Delta \widehat{L}$, for one day ahead using the weather forecast data, the water drainage flow and maximum discharge of the drainage channel data. |

2 | Collect the real-time water level measurements $L$ at time $\left(t-10\right)$. |

3 | Generate a flash flood (water level) prediction profile), $\hat{H}$, for one day ahead with 10 min resolution by ANN forecast model. The details of forecast model will be discussed in Section 4.1. |

4 | Collect and feed all updated data (water level measurements and forecast error) back to the forecast model to reforecast the water level. |

Step | Description |
---|---|

1 | Create an initialization population for the learning parameters in the ANN forecast model. |

2 | Calculate the mean value of the population. |

3 | Calculate the objective function (forecast error), as fitness term, for all and mean populations. To achieve convergence within minimum time, if the fitness value of the mean solution is better than the worst solution, the worst solution will be replaced by the mean solution. |

4 | Create a random solution vector in the population to determine the new searching step angle and movement using the golden ratio method. This process aims to move the searching towards the best solution area. |

5 | Compare the fitness value of the new random solution and the mean solution. This comparison aims to create a random searching and increase the ability of to search the whole solution of the fitness function and achieve the global solution. |

6 | The optimal solution for the ANN parameters will achieve the minimum fitness value. |

**Table 4.**The overall and daily MAPE forecast error for the traditional ANN with a different number of hidden layers.

Number of Hidden Layers | Overall MAPE | Mean of the Daily MAPE |
---|---|---|

1 | 3.2% | 3.0% |

2 (Model A) | 1.4% | 1.3% |

3 | 4.5% | 4.4% |

4 | 5.2% | 5.1% |

5 | 6.7% | 6.6% |

Number of Neurons | First Hidden Layer | |||||
---|---|---|---|---|---|---|

10 | 20 | 30 | 40 | 50 | ||

Second hidden layer | 10 | 1.3% | 1.5% | 2.2% | 2.9% | 3.3% |

20 | 1.2% | 1.1% | 2.3% | 2.2% | 3.1% | |

30 | 1.6% | 1.9% | 2.5% | 3.4% | 3.4% | |

40 | 2.1% | 1.6% | 2.9% | 3.7% | 4.2% | |

50 | 2.3% | 1.9% | 2.7% | 3.9% | 4.8% |

${\mathbf{A}}_{1}$ | ${\mathbf{A}}_{2}$ | ${\mathbf{A}}_{3}$ | ${\mathbf{A}}_{4}$ | |
---|---|---|---|---|

Description | the water level of previous time steps from 20 min until one hour | the previous day water level at the same time | the previous day data of daily rain intensity | the hourly temperature |

Unit | cm | cm | mm/hour | °C |

**Table 7.**The R-squared values for the relationship between H(t) and (${\mathrm{A}}_{1},\text{}{\mathrm{A}}_{2},\text{}{\mathrm{A}}_{3},\text{}{\mathrm{A}}_{4}$).

Correlated Variables | ${\mathbf{R}}^{2}$ |
---|---|

$H\left(t\right)\text{}\mathrm{vs}.\text{}{\mathrm{A}}_{1}$ | 93.7% |

$H\left(t\right)\text{}\mathrm{vs}.\text{}{\mathrm{A}}_{2}$ | 51.8% |

$H\left(t\right)\text{}\mathrm{vs}.\text{}{\mathrm{A}}_{3}$ | 35.1% |

$H\left(t\right)\text{}\mathrm{vs}.\text{}{\mathrm{A}}_{4}$ | 27.7% |

Daily MAPE | Overall RMSE | ||
---|---|---|---|

Traditional ANN | 1.0% | 0.8% | 17 cm |

ANN optimized by GROM | 0.6% | 0.5% | 7 cm |

ANN optimized by MPSO | 0.9% | 0.8% | 14 cm |

ANN optimized by TLBO | 0.7% | 0.6% | 10 cm |

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## Share and Cite

**MDPI and ACS Style**

Alasali, F.; Tawalbeh, R.; Ghanem, Z.; Mohammad, F.; Alghazzawi, M.
A Sustainable Early Warning System Using Rolling Forecasts Based on ANN and Golden Ratio Optimization Methods to Accurately Predict Real-Time Water Levels and Flash Flood. *Sensors* **2021**, *21*, 4598.
https://doi.org/10.3390/s21134598

**AMA Style**

Alasali F, Tawalbeh R, Ghanem Z, Mohammad F, Alghazzawi M.
A Sustainable Early Warning System Using Rolling Forecasts Based on ANN and Golden Ratio Optimization Methods to Accurately Predict Real-Time Water Levels and Flash Flood. *Sensors*. 2021; 21(13):4598.
https://doi.org/10.3390/s21134598

**Chicago/Turabian Style**

Alasali, Feras, Rula Tawalbeh, Zahra Ghanem, Fatima Mohammad, and Mohammad Alghazzawi.
2021. "A Sustainable Early Warning System Using Rolling Forecasts Based on ANN and Golden Ratio Optimization Methods to Accurately Predict Real-Time Water Levels and Flash Flood" *Sensors* 21, no. 13: 4598.
https://doi.org/10.3390/s21134598