# Flash-Flood Forecasting in an Andean Mountain Catchment—Development of a Step-Wise Methodology Based on the Random Forest Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Study Area and Dataset

## 3. RF Technique

^{®}[39]. The main functions, attributes and methods employed can be found in http://scikit-learn.org.

#### 3.1. Algorithm

- (i)
- Construct each one of the decision tree models based on a random selection of a number of bootstrap samples (n_ estimators parameter) drawn with (or without) replacement from the training dataset. Each bootstrap is composed by a different subset (roughly two-thirds) of the dataset, in a process known as out-of-bag (OOB) [19]. The OBB technique aims to get unbiased estimates of the regression as well as to get estimates of the importance of the variables used for the tree construction process [40].
- (ii)
- Determine a number of features (max_ features parameter) to perform the best split decision from the total number of predictor variables of the dataset (n_ features). The condition max_ features < n_ features ensures the nonexistence of duplicated DTs in the forest. Consequently, by assuring variety, the problem of over-fitting is avoided. Ref. [20] recommends $max\_features=\sqrt{\mathit{n}\_\mathit{features}}$, for regression problems.
- (iii)
- Split each node of each decision tree into two descendant nodes by using the best split criteria. The calculation of the best splits are chosen based on the mean squared error ($MSE$) for regression problems. The minimum number of samples required to split a node is controlled by the min_ samples_ split parameter.
- (iv)
- Grow n_ trees as much as possible (largest extent) by repeating steps 1 to 3 until a number of nodes have been reached. The optimal number of trees is reached when the $OO{B}_{error}$ stops decreasing. The depth of each tree is controlled by the max_ depth and the min_ samples_ leaf parameters; where min_ samples_ leaf is the minimum number of samples required to be at a leaf node. This is aimed to reduce the structural complexity of the models in what is called pruning criteria [22].
- (v)
- Determine the prediction as the mean response from all regression trees [20].

#### 3.2. Determination of Model Hyper-Parameters

#### 3.3. Input Data Composition

## 4. Model Evaluation

#### 4.1. Goodness-of-Fit Statistics

#### Graphical Analysis

#### 4.2. Feature Selection Analysis

## 5. Step-Wise Methodology

## 6. Results and Discussion

#### 6.1. Determination of the Number of Discharge and Precipitation Lags

#### 6.2. Base Model: Discharge Lags as the Sole Input

#### 6.3. Precipitation Lags as Additional Inputs

#### 6.4. Feature Selection

#### 6.5. Graphical Analysis

#### 6.6. Forecasting Models of 8, 12, 18 and 24 h

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ML | Machine learning |

RF | Random forest |

ANN | Artificial neural network |

SVM | Super vector machine |

ME | Mean error |

MSE | Mean square error |

NSE | Nash-Sutcliffe efficiency |

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**Figure 1.**Location of the Tomebamba catchment at Matadero-Sayausí outlet in the Andean cordillera of Ecuador, South America (UTM coordinates).

**Figure 2.**Precipitation (averaged for Toreadora, Virgen and Chirimachay stations) and discharge hourly time series for the study period (January 2015 to July 2017). Note the horizontal red dashed line at a discharge of 50 m${}^{3}$/s (historical indicator of a flood event).

**Figure 3.**Scheme of the step-wise methodology for developing precipitation-runoff forecasting models.

**Figure 4.**(

**a**) Autocorrelation function (ACF) and (

**b**) Partial autocorrelation function (PACF) of the Matadero-Sayausí discharge series. Gray hatch indicates the 95% confidence band.

**Figure 5.**Pearson cross-correlation comparison between the Toreadora (3955 m.a.s.l.), Virgen (3626 m.a.s.l.) and Chirimachay (3298 m.a.s.l.) precipitation stations and the Matadero-Sayausí (2693 m.a.s.l.) discharge station. Note the horizontal line at a cross-correlation of 0.20.

**Figure 6.**Feature relative importance of the 4-h discharge forecasting model B. Darkest bars indicate the features selected for a reduced version of the input (model C).

**Figure 7.**Model results of the parsimonious 4-h discharge forecasting (model C) (

**a**) Training period, from January-2015 to July-2016. (

**b**). Validation period, from July-2016 to July-2017.

**Figure 8.**(

**a**) Empirical extreme value distribution of peak flows; (

**b**) Comparison of nearly independent peak flow maxima.

**Figure 9.**(

**a**) Empirical extreme value distribution of peak flows, and (

**b**) Comparison of cumulative flow volumes for forecasting models of 4, 8, 12, 18 and 24 h.

**Figure 10.**Comparison of nearly independent peak flow maxima for forecasting models of 4, 8, 12, 18 and 24 h.

Hyper-Parameter | Values |
---|---|

n_estimators * | 50–700 |

max_features | ’auto’, ‘sqrt’ and ‘log2’ |

min_samples_split | 2, 5 and 10 |

min_samples_leaf | 1, 2 and 4 |

max_depth * | 10–700 |

**Table 2.**Input data composition and model efficiencies for forecasting models and their parsimonious versions for prediction horizons of 4, 8, 12, 18 and 24 h.

Forecast Horizon | Discharge | Toreadora | Virgen | Chirimachay | Total | NSE | NSE |
---|---|---|---|---|---|---|---|

[h] | Lags | Lags | Lags | Lags | Features | Training | Validation |

4 | 8 | 24 | 10 | 15 | 60 | 0.954 | 0.758 |

4 * | 8 | 9 | 9 | 9 | 38 | 0.972 | 0.761 |

8 | 8 | 32 | 19 | 23 | 85 | 0.868 | 0.581 |

8 * | 8 | 15 | 15 | 15 | 56 | 0.867 | 0.580 |

12 | 8 | 36 | 23 | 27 | 98 | 0.828 | 0.506 |

12 * | 8 | 18 | 18 | 18 | 65 | 0.829 | 0.503 |

18 | 8 | 42 | 29 | 33 | 115 | 0.772 | 0.442 |

18 * | 8 | 21 | 21 | 21 | 74 | 0.771 | 0.439 |

24 | 15 | 48 | 35 | 39 | 140 | 0.772 | 0.385 |

24 * | 15 | 21 | 21 | 21 | 81 | 0.767 | 0.384 |

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**MDPI and ACS Style**

Muñoz, P.; Orellana-Alvear, J.; Willems, P.; Célleri, R.
Flash-Flood Forecasting in an Andean Mountain Catchment—Development of a Step-Wise Methodology Based on the Random Forest Algorithm. *Water* **2018**, *10*, 1519.
https://doi.org/10.3390/w10111519

**AMA Style**

Muñoz P, Orellana-Alvear J, Willems P, Célleri R.
Flash-Flood Forecasting in an Andean Mountain Catchment—Development of a Step-Wise Methodology Based on the Random Forest Algorithm. *Water*. 2018; 10(11):1519.
https://doi.org/10.3390/w10111519

**Chicago/Turabian Style**

Muñoz, Paul, Johanna Orellana-Alvear, Patrick Willems, and Rolando Célleri.
2018. "Flash-Flood Forecasting in an Andean Mountain Catchment—Development of a Step-Wise Methodology Based on the Random Forest Algorithm" *Water* 10, no. 11: 1519.
https://doi.org/10.3390/w10111519