# Radar Quantitative Precipitation Estimation Algorithm Based on Precipitation Classification and Dynamical Z-R Relationship

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## Abstract

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^{1.4}(fixed Z-R), Optimization Processing (OP), Optimization processing of Dynamical Adjustments (ODA) and OCD were performed using various evaluation metrics. The results show that ODA and OCD can significantly reduce the error of QPE, with OCD being the best estimator, reaching a correlation coefficient (CC) of 0.7 and reducing mean absolute error (MAE) and root mean square error (RMSE) by 31% and 34%, respectively. OCD outperforms other algorithms in terms of MAE and RMSE for different rain rates (RR), and the various assessment metrics at hourly scales are also more concentrated in reasonable intervals. OP gives fair results at weaker rain rates (0.2 ≤ RR < 8 mm/h) but underestimates rainfall more incorrectly at stronger rain rates (8 mm/h ≤ RR). Both the OCD and ODA provide a more significant improvement in the estimation of the area and magnitude of strong rainfall, with the OCD providing a better description of the local characteristics of the rainfall distribution, further demonstrating the advantages of the ODA.

## 1. Introduction

^{6}·mm

^{−3}) and rain rates R (mm·h

^{−1}) [7]. Marshall and Palmer proposed in the 1940s to describe the distribution of the Drop Size Distribution (DSD) using the M-P distribution and gave the classical exponential relationship between radar reflectivity factor Z and rain rates R (Z = 300R

^{1.4}) [8]. In mainland China, the QPE system of the China New Generation Weather Radar (CINRAD) system also obeys this classical fixed Z-R relationship. The QPE of the WSR-88D radar system obeys a Z-R relationship of Z = 300R

^{1.4}in temperate regions and Z = 250R

^{1.2}in tropical regions [9,10]. However, Z-R relationships often produce different parameter values in different regional and climatic environments, so the choice of parameters in the Z-R relationship is a tremendous influence on the accuracy of the QPE [11,12,13].

## 2. Study Area and Data

#### 2.1. Study Area

#### 2.2. Data

## 3. Methodology

#### 3.1. Optimization Process (OP)

^{b}) is assumed, and a number of reflectivity factors in any hour are converted into radar-estimated rainfall Ri and integrated in time to obtain the hourly radar estimate Ri. Then, a Target Function (TF) is selected, the radar estimate Ri and rain gauge observation Gi at each point are substituted into the TF, and the parameters A and b in the Z-R relationship are adjusted by cycling. Finally, parameters A and b are optimal when the target discriminant function TF reaches its minimum value.

#### 3.2. Optimization Process of Dynamical Adjustment (ODA)

_{hour_average}) in 10 dBZ intervals. Then, a set of Z-R relationships for the different intervals is calculated by OP. Finally, this set of Z-R relationships is used to obtain radar rainfall estimates.

_{hour_average}) is calculated as follows:

#### 3.3. Optimization Process of Precipitation Classification and Dynamical Adjustments (OCD)

^{2}at any time, the radar-rain gauge data in that hour is identified as convective precipitation. Otherwise, it is stratocumulus precipitation.

^{2}[34], and n is the altitude layer of the radar data. Through the above operations, radar-rain gauge data under convective and stratiform rainfall types can be obtained. Then ODA is used to complete the dynamic adjustment and optimization processes for the two types of rainfall separately, and finally, a QPE algorithm combining the Optimization process of precipitation Classification and Dynamical adjustments (OCD) can be established.

#### 3.4. Evaluation Indicators

## 4. Results and Discussion

#### 4.1. Scatter Distribution of Inversion Results by Algorithms

#### 4.2. Evaluation Indicators Distribution of the Algorithms

#### 4.3. Performance of Algorithms under Different Rain Rates

#### 4.4. Case Analysis of Rainfall Event

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Spatial map showing the elevation of the study area, together with rain gauges and weather radar.

**Figure 3.**Scatter distribution of Rain Gauge Rainfall and different QPE algorithms, (

**a**) fixed Z-R, (

**b**) OP, (

**c**) ODA and (

**d**) OCD.

**Figure 4.**The distribution of the evaluation indicators for fixed Z-R, OP, ODA, and OCD at hourly scales, (

**a**) CC, (

**b**) BIAS, (

**c**) MAE, (

**d**) RMSE.

**Figure 6.**Time-by-time evolutionary characteristics of 4 QPE algorithms (rainfall event 5, rain gauge ID: 40505780), (

**a**) hourly, (

**b**) cumulant.

**Figure 7.**Time-by-time evolutionary characteristics of 4 QPE algorithms (rainfall event 5, rain gauge ID:40537250), (

**a**) hourly, (

**b**) cumulant.

**Figure 8.**Spatial distribution of rainfall in 22 July 2018, (

**a**) interpolation of rain gauge observations, (

**b**) fixed Z-R for radar, (

**c**) OP for radar, (

**d**) ODA for radar and (

**e**) OCD for radar.

Event | Date | Start Time | Duration (hours) | Max Rain Rates (mm/h) | Average Rain Rates (mm/h) | Type | Note |
---|---|---|---|---|---|---|---|

1 | 12 April 2018 | 5:00 | 14 | 13.4 | 1.25 | Stratiform | train |

2 | 19 April 2018 | 10:00 | 15 | 28.4 | 1.87 | Stratocumulus | train |

3 | 18 May 2018 | 17:00 | 8 | 8 | 1.21 | Stratiform | test |

4 | 30 June 2018 | 19:00 | 24 | 37.6 | 2.37 | Convective | train |

5 | 22 July 2018 | 11:00 | 29 | 53 | 4.83 | Convective | test |

6 | 15 August 2018 | 9:00 | 41 | 25.2 | 1.23 | Stratocumulus | train |

7 | 26 April 2019 | 11:00 | 7 | 27.6 | 2.04 | Stratocumulus | test |

8 | 18 June 2019 | 23:00 | 39 | 3.4 | 0.49 | Stratiform | test |

9 | 11 September 2019 | 23:00 | 22 | 5.6 | 1.58 | Stratiform | test |

10 | 18 September 2019 | 12:00 | 10 | 3 | 0.57 | Stratiform | train |

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**MDPI and ACS Style**

Peng, W.; Bao, S.; Yang, K.; Wei, J.; Zhu, X.; Qiao, Z.; Wang, Y.; Li, Q. Radar Quantitative Precipitation Estimation Algorithm Based on Precipitation Classification and Dynamical Z-R Relationship. *Water* **2022**, *14*, 3436.
https://doi.org/10.3390/w14213436

**AMA Style**

Peng W, Bao S, Yang K, Wei J, Zhu X, Qiao Z, Wang Y, Li Q. Radar Quantitative Precipitation Estimation Algorithm Based on Precipitation Classification and Dynamical Z-R Relationship. *Water*. 2022; 14(21):3436.
https://doi.org/10.3390/w14213436

**Chicago/Turabian Style**

Peng, Wang, Shuping Bao, Kan Yang, Jiahua Wei, Xudong Zhu, Zhen Qiao, Yongcan Wang, and Qiong Li. 2022. "Radar Quantitative Precipitation Estimation Algorithm Based on Precipitation Classification and Dynamical Z-R Relationship" *Water* 14, no. 21: 3436.
https://doi.org/10.3390/w14213436