# Combing Random Forest and Least Square Support Vector Regression for Improving Extreme Rainfall Downscaling

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data Set

^{8}m

^{3}. Its upstream catchment (Figure 1) has an area of 763 km

^{2}, and the basin ground elevation varies from 209 to 2609 meters. The average annual rainfall of the catchment is around 2250 mm.

## 3. Methods

#### 3.1. Proposed Approach

#### 3.1.1. Approach Type-I

#### 3.1.2. Approach Type-II

#### 3.1.3. Approach Type-III

#### 3.2. Linear Discriminant Analysis

_{1}, x

_{2},…, x

_{n}).

_{0}, a

_{1}, a

_{2},…, a

_{n}) are calibrated from the training data of predictors and a predefined class label (for example, +1 and −1) of the predictand. The linear discriminant function L is then used to predict the class of a new predictand according to the estimated class label. In the current study, LDA was performed by the “fitcdiscr” function provided by MathWorks.

#### 3.3. Random Forest

#### 3.4. Least Square-Support Vector Machine

_{i}(predictors: climate variables) and output y

_{i}(predictand: local rainfall). According to the LS-SVR method, the nonlinear LS-SVR function can be expressed as

_{i}is the training error for x

_{i}.

_{i}and w as

## 4. Results and Discussion

#### 4.1. Rainfall-State Classification

#### 4.2. Regression for Rainfall-Amount

#### 4.3. Discussion

## 5. Conclusions and Future Work

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Shih-Men Reservoir basin (Source: [41]).

**Figure 6.**Quantile–quantile (Q–Q) plot of downscaling daily rainfalls during the calibration period (1964–1999).

Station Name | Station Code | Location | Elevation (m) | Areal Weight | |
---|---|---|---|---|---|

Longitude (°E) | Latitude (°N) | ||||

Shih-Men | 21C050 | 121.23 | 24.81 | 255 | 0.018 |

Ba-Ling | 21C070 | 121.39 | 24.69 | 1220 | 0.075 |

Kao-Yi | 21C080 | 121.35 | 24.71 | 620 | 0.127 |

Ka-La-Ho | 21C090 | 121.39 | 24.64 | 1260 | 0.123 |

Chang-Hsing | 21C110 | 121.30 | 24.80 | 350 | 0.151 |

San-Kuang | 21C150 | 121.36 | 24.67 | 630 | 0.038 |

Hsiu-Luan | 21D140 | 121.28 | 24.62 | 840 | 0.045 |

Yu-Feng | 21D150 | 121.29 | 24.66 | 780 | 0.049 |

Hsin-Pai-Shih | 21D160 | 121.25 | 24.59 | 1620 | 0.115 |

Chen-His-Pao | 21D170 | 121.30 | 24.58 | 630 | 0.259 |

No. | Acronym | Predictor |
---|---|---|

1 | Mslp | Mean sea level pressure |

2 | p5_z | Vorticity at 500 hPa height |

3 | p8_z | Vorticity at 850 hPa height |

4 | p300 | 300 hPa geopotential height |

5 | p500 | 500 hPa geopotential height |

6 | p850 | 850 hPa geopotential height |

7 | p_f | Near surface geostrophic airflow velocity |

8 | p_z | Near surface vorticity |

9 | r500 | Relative humidity at 500 hPa height |

10 | r850 | Relative humidity at 850 hPa height |

11 | rhum | Near surface relative humidity |

12 | shum500 | 500 hPa specific humidity |

13 | Temp | Near surface air temperature |

14 | uas | Zonal surface wind speed |

15 | ua_700 | 700 hPa zonal wind speed |

16 | ua_850 | 850 hPa zonal wind speed |

17 | pr_wtr | Precipitable water |

18 | lftx | Surface lifted index |

19 | prec | Precipitation total |

20 | dswrf | Surface downwelling shortwave flux in air |

21 | dlwrf | Surface downwelling long flux in air |

22 | vas | Meridional surface wind speed |

23 | ta_700 | 700 hPa temperature |

24 | ta_850 | 850 hPa temperature |

25 | ta_925 | 925 hPa temperature |

26 | va_925 | 925 hPa meridional wind speed |

27 | uswrf | Surface upwelling shortwave flux in air |

28 | ulwrf | Surface upwelling longwave flux in air |

Type of Approach | LDA | RF | SVC | |||
---|---|---|---|---|---|---|

Wet Season | Dry Season | Wet Season | Dry Season | Wet Season | Dry Season | |

Type-I | 75.38 | 75.39 | 79.35 | 75.64 | 74.00 | 72.42 |

Type-II Step 1 ^{1} | 75.38 | 75.39 | 79.35 | 75.64 | 74.00 | 72.42 |

Type-II Step 2 | 95.26 | 97.62 | 95.31 | 98.33 | 93.06 | 96.83 |

Type-III | 66.72 | 68.85 | 74.46 | 69.71 | 69.44 | 68.63 |

^{1}Note: Step 1 in Approach Type-II is similar to Approach Type-I. LDA: linear discriminant analysis; RF: random forest; SVC: support vector classification.

Type of Approach | LDA | RF | SVC |
---|---|---|---|

Type-II Step 2 | 49.52 | 56.19 | 30.48 |

Type-III | 47.36 | 47.57 | 15.53 |

Season | Model | Penalty Term | Kernel Width |
---|---|---|---|

Wet | Approach Type-I for wet day | 4.62 | 6.27 |

Wet | Approach Type-II for non-extreme-rainfall day | 1.64 | 5.95 |

Wet | Approach Type-II for extreme-rainfall day | 78.50 | 1.12 |

Wet | Approach Type-III for non-extreme-rainfall day | 2.32 | 5.40 |

Wet | Approach Type-III for extreme-rainfall day | 73.65 | 1.05 |

Dry | Approach Type-I for wet day | 10.89 | 32.60 |

Dry | Approach Type-II for wet day | 11.14 | 31.23 |

Dry | Approach Type-III for wet day | 24.34 | 52.81 |

Statistics | Approach Type-I | Approach Type-II | Approach Type-III | Observation |
---|---|---|---|---|

Mean (mm) | 10.36 | 10.33 | 10.33 | 10.29 |

SD (mm) | 21.49 | 24.15 | 24.12 | 26.87 |

Skewness (mm) | 10.52 | 10.22 | 10.32 | 9.52 |

Statistics | Approach Type-I | Approach Type-II | Approach Type-III | Observation |
---|---|---|---|---|

Mean (mm) | 10.52 | 11.51 | 10.57 | 12.29 |

SD (mm) | 22.55 | 30.21 | 28.50 | 34.94 |

Skewness (mm) | 9.12 | 8.05 | 9.09 | 8.08 |

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## Share and Cite

**MDPI and ACS Style**

Pham, Q.B.; Yang, T.-C.; Kuo, C.-M.; Tseng, H.-W.; Yu, P.-S.
Combing Random Forest and Least Square Support Vector Regression for Improving Extreme Rainfall Downscaling. *Water* **2019**, *11*, 451.
https://doi.org/10.3390/w11030451

**AMA Style**

Pham QB, Yang T-C, Kuo C-M, Tseng H-W, Yu P-S.
Combing Random Forest and Least Square Support Vector Regression for Improving Extreme Rainfall Downscaling. *Water*. 2019; 11(3):451.
https://doi.org/10.3390/w11030451

**Chicago/Turabian Style**

Pham, Quoc Bao, Tao-Chang Yang, Chen-Min Kuo, Hung-Wei Tseng, and Pao-Shan Yu.
2019. "Combing Random Forest and Least Square Support Vector Regression for Improving Extreme Rainfall Downscaling" *Water* 11, no. 3: 451.
https://doi.org/10.3390/w11030451