# Extreme Gradient Boosting Model for Rain Retrieval using Radar Reflectivity from Various Elevation Angles

^{*}

## Abstract

**:**

## 1. Introduction

^{1.6}where Z is in mm

^{6}/m

^{3}and R is in mm/h) converts radar reflectivity into rainfall rate. Numerous studies have analyzed and explored radar reflectivity-based rainfall estimations [10,11,12,13,14,15,16,17]. For example, Borga et al. [18] used high-resolution radar rainfall fields and space–time distributed hydrological models to evaluate the rainfall runoff during storm floods. Gabella et al. [19] used radar reflectivity to improve the accuracy of rainfall estimations in complex terrains. Seo and Breidenbach [20] used rain gauge measurements to correct nonuniform spatial deviations in radar rainfall parameters in real time. Libertino et al. [21] developed a quasi-real-time procedure for an adaptive (in space and time) estimation of the Z–R relationship. Tang and Matyas [22] presented a methodology to forecast a tropical cyclone rainfall distribution up to 8 h into the future using a high-resolution Doppler radar reflectivity mosaic in a large analytical domain. Chen et al. [23] reported the vertical structures of raindrop size distribution features and quantitative precipitation estimation parameters of two main synoptic systems, typhoons and meiyu/baiu fronts, based on summer observations with a ground-based impact disdrometer and a vertically pointing radar.

## 2. Study Area and Data

#### 2.1. Radar Reflectivity

#### 2.2. Ground Observations

#### 2.3. Dataset Definitions

**Z**}, ground meteorological attributes {

**G**}, and rainfall {

**R**}. The {

**Z**} dataset contained radar reflectivity from all elevation angles, and the mathematical expression was {

**Z**}={Z

_{i}}

_{I}

_{=1,9}, where i represents the radar elevation angles in the VCP21 system (i is from 1 to 9 representing the elevation angles at 0.5, 1.4, 2.4, 3.4, 4.3, 6.0, 9.9, 14.6, and 19.5°, respectively). {

**G**} contained meteorological attributes filtered through correlation analyses, expressed mathematically as {

**G**}={G

_{k}}

_{k}

_{=1,6}, where k represents the meteorological attributes (for Chenggong station, k is from 1 to 6 representing TX01, RH01, WD05, PP01, PP02, and SS02, respectively; and for Lanyu station, k is from 1 to 7 representing PS01, PS02, TX01, RH01, WD05, PP01, and PP02, respectively). {

**R**} was the rainfall dataset.

## 3. Case Design and Algorithms

- Case 1 used radar reflectivity {
**Z**} to retrieve rainfall rate. This case used radar reflectivity from every elevation angle as the model input to establish separate models. For example, the radar reflectivity from an elevation angle of 0.5° formulates ML-based rainfall retrieval models (namely subcase 1.1). That is, R = f_{1}(Z_{1}), where f_{1}() can be an ML-based model or the MP formula. Because there were nine elevation angles, nine models were established (i.e., subcases 1.1 to 1.9). An additional model, subcase 1.10, featured a specific model that used radar reflectivity of all elevation angles; that is, R = f_{2}({Z_{i}}_{i}_{=1,9}), where f_{2}() represents using ML-based models. - Case 2 used meteorological attributes {G
_{k}}_{k}_{=1,6}of weather stations to retrieve rainfall rate; that is, R = f_{3}({G_{k}}_{k}_{=1,6}), where f_{3}() represents using ML-based models. - Case 3 combined reflectivity intensity {
**Z**} and meteorological attributes {**G**} to retrieve rainfall rate. Nine elevation angles (Z_{1}to Z_{9}) separately combined with {G_{k}}_{k}_{=1,6}can build nine models (i.e., subcases 3.1 to 3.9). For example, for subcase 3.2, R = f_{4}(Z_{2}, {G_{k}}_{k}_{=1,6}), where f_{4}() represents ML-based models. An additional model, subcase 3.10, featured a specific model that combined meteorological attributes with the radar reflectivity of all elevation angles; that is, R = f_{5}({Z_{i}}_{i}_{=1,9}, {G_{k}}_{k}_{=1,6}), where f_{5}() represents using ML-based models.

#### 3.1. Algorithms

- 1.
- REG

_{1},…x

_{r}), r is the number of variables, assuming that the linear regression relationship between y and x is as follows:

_{0}+ β

_{1}x

_{1}+ …+ β

_{r}x

_{r}+ ε

_{0}, β

_{1}, and β

_{r}are regression coefficients, and ε is the random error. In this study, rainfall was estimated with datasets {

**Z**} and {

**G**} using linear regression.

- 2.
- SVR

_{1}, y

_{1}),…, (x

_{i}, y

_{i}), with x as the input characteristic and y representing the characteristic’s corresponding regression value. SVR’s mathematical representation is similar to the following regression formula:

**w**·

**x**+ b,

**w**∈ R

^{d}, b ∈ R

_{i}) and truth value y

_{i}is very small, then the predictive value f(x) can be accurately derived after inputting property

**x**, and weight

**w**is the hyperplane sought in SVR.

- 3.
- XGBoost

_{1},P

_{2},…}.

_{m}is the parameter of the mth regression tree, and β

_{m}is the weight of the same tree in the prediction function.

_{m}and β

_{m}can be expressed as follows:

#### 3.2. Programming Tools

#### 3.3. Performance Criteria

## 4. Modeling

#### 4.1. Parameter Calibration

#### 4.2. Model Performance

## 5. Evaluation and Discussion

## 6. Simulations

## 7. Conclusions

- In the process of building the rainfall-retrieval models, combining radar reflectivity with ground meteorological attributes (Case 3) achieved superior rainfall-retrieval results compared with only inputting radar reflectivity (Case 1) or only ground meteorological attributes (Case 2).
- When the experimental station radar elevation angles were evaluated, radar reflectivity at an elevation angle of 6.0° combined with ground meteorological attributes were the optimal input variables for rainfall retrieval at Chenggong station; at Lanyu station, the optimal input variables were radar reflectivity at an elevation angle of 4.3° combined with ground meteorological attributes.
- Simulation results of the testing typhoons (Nanmadol in 2011, Tembin in 2012, Matmo in 2014, and Nepartak in 2016) demonstrated that Lanyu station exhibited smaller error index values in model retrieval than Chenggong station. This study speculated that this is because Lanyu station is situated on the ocean, where a typhoon circulation encounters little to no topographical interference to affect its structure when passing; as a result, the radar reflectivity signals are better reflected off the variations (gradients) of water vapor and possibly rain. By contrast, Chenggong station is affected by rapid changes in typhoon circulation and structure when a typhoon circulation encounters land and the Coastal Mountain Range and the Central Mountain Range, resulting in greater fluctuations in radar reflectivity signals. As a result, the Chenggong station retrieval models were worse at predicting rainfall than those at Lanyu station.
- In terms of model errors, the XGBoost model at both Chenggong and Lanyu stations exhibited smaller error indices than the MP, REG, and SVR models (including absolute errors (MAE and RMSE) and relative errors (rMAE and rRMSE)). In terms of efficiency performance during retrievals, Lanyu station’s XGBoost model had the highest efficiency coefficient (0.903), and Chenggong station’s XGBoost model had the second highest (0.885).

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Historical tracks of typhoons during 2008–2017: (

**a**) Fung-Wong, (

**b**) Fanapi, (

**c**) Nanmadol, (

**d**) Tembin, (

**e**) Usagi, (

**f**) Matmo, (

**g**) Fung-Wong, (

**h**) Soudelor, (

**i**) Goni, (

**j**) Nepartak, (

**k**) Meranti, (

**l**) Megi, (

**m**) Nesat, and (

**n**) Hato.

**Figure 3.**Schematics of radar reflectivity parameters of range and range_step. (The example is the reflectivity mosaic of Typhoon Matmo at 2014/07/22 1600 UTC; scanning modes in plan position indicator. The mosaic was produced by the Central Weather Bureau (CWB). The dBZ values of 0−30 km from radar center are using the reflectivity from an elevation angle of 6.0°, the dBZ values of 30−180 km are using the average reflectivity from elevation angles between 1.4° and 4.3°, and the dBZ values of greater than 180 km are using the reflectivity from elevation angle of 0.5° [52]).

**Figure 6.**Parameter C verification results for SVR models in Cases 1–3: (

**a**–

**c**) Chenggong station at a radar elevation angle of 6.0°; and (

**d**–

**f**) Lanyu station at a radar angle of 4.3°.

**Figure 7.**XGBoost model verification results for Cases 1–3 of Chenggong station at a radar elevation angle of 6.0°: (

**a**–

**c**) learning rate; (

**d**–

**f**) min_child_weight and max_depth.

**Figure 8.**XGBoost model verification results for Cases 1–3 of Lanyu station at a radar angle of 4.3°: (

**a**–

**c**) learning rate; (

**d**–

**f**) min_child_weight and max_depth.

**Figure 9.**Root mean square error (RMSE) verification results for every retrieval model and case: (

**a**) Chenggong station; (

**b**) Lanyu station.

**Figure 10.**Comparison of RMSE for Cases 2 and 3 in the XGBoost model: (

**a**) Chenggong station; (

**b**) Lanyu station.

**Figure 12.**Retrieval results for the top four major typhoons: (

**a**) Chenggong station at an elevation angle of 6.0° under Case 3; (

**b**) Lanyu station at an elevation angle of 4.3° under Case 3.

**Figure 13.**Performance comparison of Chenggong and Lanyu stations: (

**a**) mean absolute error (MAE), (

**b**) relative mean absolute error (rMAE), (

**c**) RMSE, (

**d**) relative root mean square error (rRMSE), and (

**e**) efficiency coefficient (CE).

Typhoon | Duration | Rain (mm) | Intensity | Typhoon | Duration | Rain (mm) | Intensity |
---|---|---|---|---|---|---|---|

Fung-Wong | 2008/7/27−28 | 173 | Moderate | Soudelor | 2015/8/7−09 | 159 | Moderate |

Fanapi | 2010/9/19−20 | 273 | Moderate | Goni | 2015/8/21−22 | 140 | Severe |

Nanmadol | 2011/8/27−30 | 360 | Severe | Nepartak | 2016/7/7−10 | 399 | Severe |

Tembin | 2012/8/23−28 | 459 | Moderate | Meranti | 2016 9/13~09/15 | 310 | Severe |

Usagi | 2013/9/21−23 | 314 | Severe | Megi | 2016/9/26−29 | 67 | Moderate |

Matmo | 2014/7/21−23 | 394 | Moderate | Nesat | 2017/7/29−31 | 112 | Moderate |

Fung-Wong | 2014/9/19−21 | 231 | Mild | Hato | 2017/8/21−23 | 200 | Moderate |

Attribute (Unit) | Notation | Attribute (Unit) | Notation |
---|---|---|---|

Ground air pressure (hPa) | PS01 | Ground vapor pressure (hPa) | RH02 |

Air pressure at sea level (hPa) | PS02 | Surface wind speed (maximum 10-min mean, | WD01 |

Ground temperature (°C) | TX01 | 10 m above the surface) (m/s) | |

Ground dew point temperature (°C) | TX05 | Wind direction of WD01 (deg) | WD02 |

Ground relative humidity (%) | RH01 | Maximum instantaneous wind speed (m/s) | WD05 |

Ground global solar radiation (MJ/m^{2}) | SS02 | Wind direction of WD05 (deg) | WD06 |

Rainfall duration within 1 h (h) | PP02 | Precipitation (mm/h) | PP01 |

**Table 3.**Statistical values of the employed data attributes. The collection time ranges from 2008 to 2017 (including 14 typhoon events). The sampling frequency is one hour and a total of 2339 records were collected.

Station | Attribute (Unit) | Min-Max | Mean | St. Dev. |
---|---|---|---|---|

Chenggong | Ground temperature, TX01 (°C) | 23.8−33.8 | 27.1 | 1.83 |

Ground relative humidity, RH01 (%) | 48−100 | 83.7 | 9.82 | |

Maximum instantaneous wind speed, WD05 (m/s) | 1.6−49.2 | 12.6 | 7.50 | |

Precipitation, PP01 (mm/h) | 0−66 | 3.41 | 6.96 | |

Rainfall duration within 1 h, PP02 (h) | 0−1 | 0.47 | 0.46 | |

Ground global solar radiation, SS02 (MJ/m^{2}) | 0−3.95 | 0.37 | 0.79 | |

Lanyu | Ground air pressure, PS01 (hPa) | 927.7−975.5 | 962.4 | 7.21 |

Air pressure at sea level, PS02 (hPa) | 963.1−1012.5 | 998.9 | 7.47 | |

Ground temperature, TX01 (°C) | 21.9−28.8 | 25.0 | 1.07 | |

Ground relative humidity, RH01 (%) | 71−100 | 92.1 | 6.12 | |

Maximum instantaneous wind speed, WD05 (m/s) | 2.3−71.3 | 24.8 | 12 | |

Precipitation, PP01 (mm/h) | 0−63 | 2.2 | 5.6 | |

Rainfall duration within 1 h, PP02 (h) | 0−1 | 0.34 | 0.42 |

Station | Chenggong | Lanyu | ||||
---|---|---|---|---|---|---|

Parameter | Learning Rate | Min_Child_Weight | Max_Depth | Learning Rate | Min_Child_Weight | Max_Depth |

Case 1 | 0.3 | 1 | 3 | 0.2 | 3 | 7 |

Case 2 | 0.2 | 1 | 7 | 0.2 | 2 | 10 |

Case 3 | 0.4 | 3 | 9 | 0.3 | 1 | 11 |

Angle | Chenggong Station | Lanyu Station | ||
---|---|---|---|---|

Optimal Model Case | RMSE (mm/h) | Optimal Model Case | RMSE (mm/h) | |

0.5° | XGBoost with Case 3 | 2.827 | XGBoost with Case 3 | 2.391 |

1.4° | XGBoost with Case 3 | 2.750 | XGBoost with Case 3 | 2.102 |

2.4° | XGBoost with Case 3 | 2.832 | XGBoost with Case 3 | 2.087 |

3.4° | XGBoost with Case 3 | 2.782 | XGBoost with Case 3 | 2.227 |

4.3° | XGBoost with Case 3 | 2.636 | XGBoost with Case 3 | 2.016 |

6.0° | XGBoost with Case 3 | 2.520 | XGBoost with Case 3 | 2.289 |

9.9° | XGBoost with Case 3 | 2.584 | XGBoost with Case 3 | 2.093 |

14.6° | XGBoost with Case 3 | 2.649 | XGBoost with Case 3 | 2.802 |

19.5° | XGBoost with Case 3 | 2.761 | XGBoost with Case 3 | 2.532 |

All | XGBoost with Case 3 | 2.723 | XGBoost with Case 3 | 3.050 |

Average of all subcases | 2.706 | Average of all subcases | 2.359 |

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## Share and Cite

**MDPI and ACS Style**

Wei, C.-C.; Hsu, C.-C.
Extreme Gradient Boosting Model for Rain Retrieval using Radar Reflectivity from Various Elevation Angles. *Remote Sens.* **2020**, *12*, 2203.
https://doi.org/10.3390/rs12142203

**AMA Style**

Wei C-C, Hsu C-C.
Extreme Gradient Boosting Model for Rain Retrieval using Radar Reflectivity from Various Elevation Angles. *Remote Sensing*. 2020; 12(14):2203.
https://doi.org/10.3390/rs12142203

**Chicago/Turabian Style**

Wei, Chih-Chiang, and Chen-Chia Hsu.
2020. "Extreme Gradient Boosting Model for Rain Retrieval using Radar Reflectivity from Various Elevation Angles" *Remote Sensing* 12, no. 14: 2203.
https://doi.org/10.3390/rs12142203