# Radar Estimation of Intense Rainfall Rates through Adaptive Calibration of the Z-R Relation

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## Abstract

**:**

## 1. Introduction

## 2. The Adaptive in Time and Space Estimation Technique (ATS)

#### 2.1. Definition of the Time Domain

#### 2.2. Definition of the Spatial Domains and Parameters Estimation

#### 2.3. Calibration Procedure

## 3. Application

#### 3.1. Case Study

**Figure 2.**Orography of the study area and locations of “Bric della Croce” radar and rain gauge network.

#### 3.2. Definition of the Set of Events and Estimation of the Static Coefficients

ID | Convective events | ID | Stratiform events |
---|---|---|---|

1 | 27/07/2003 | 9 | 31/10-01/11/2003 |

2 | 02/08/2005 | 10 | 25/10-02/11/2004 |

3 | 20/08/2005 | 11 | 15/04-17/04/2004 |

4 | 06/07/2006 | 12 | 06/09-12/09/2005 |

5 | 12/07/2006 | 13 | 14/09-15/09/2006 |

6 | 08/08/2007 | 14 | 01/05-04/05/2007 |

7 | 30/08/2007 | 15 | 25/05-28/05/2007 |

8 | 29/05/2008 | 16 | 28/10-06/11/2008 |

17 | 01/12-04/12/2003 | ||

18 | 16/12-17/12/2008 |

**Table 2.**Number of invalid radar records divided by the total number of records for each event (${n}_{inv}$).

Event | n_{inv} | Event | n_{inv} |
---|---|---|---|

1 | 0.254 | 9 | 0.001 |

2 | 0.003 | 10 | 0.004 |

3 | 0.003 | 11 | 0.005 |

4 | 0.004 | 12 | 0.051 |

5 | 0.003 | 13 | 0.003 |

6 | 0.461 | 14 | 0.003 |

7 | 0.002 | 15 | 0.073 |

8 | 0.050 | 16 | 0.011 |

**Figure 3.**Comparison between observed precipitation ${R}_{cum}$ and rainfall estimated with the regional formula ${\widehat{R}}_{cum}$ for the event occurred on 10/31-11/1/2003 at the event scale. (The grey scale refers to rain gauge distance from radar in km).

#### 3.3. Calibration of the ATS Technique

Event | Mean (dbZ) | Std (dbZ) | Event | Mean (dbZ) | Std (dbZ) |
---|---|---|---|---|---|

1 | −2.06 | 6.51 | 9 | 20.94 | 6.96 |

2 | 14.94 | 7.52 | 10 | 11.77 | 10.74 |

3 | 9.55 | 10.70 | 11 | 11.88 | 9.85 |

4 | 5.17 | 11.51 | 12 | 5.59 | 9.55 |

5 | 2.16 | 8.66 | 13 | 16.73 | 7.99 |

6 | 2.58 | 9.97 | 14 | 9.78 | 10.38 |

7 | 4.45 | 9.54 | 15 | 9.71 | 8.36 |

8 | 19.73 | 8.17 | 16 | 17.70 | 6.30 |

**Figure 4.**Pattern of the ${\overline{I}}_{3}$ index into the parameter space q-N (

**a**) for all the selected events, (

**b**) for convective only, (

**c**) and for stratiform only events. $q=0$ implies the application of the methodology without any threshold. The green dots indicate the location of the minima.

## 4. Results and Discussion

**Figure 5.**Comparison between the coefficients of determination obtained with the Joss-Waldvogel formula, the regional formula, the methodology proposed in [26] and the ATS technique (

**a**) at the event scale and (

**b**) at the hourly scale. Correlation coefficient ${R}^{2}$ falling outside the range (0,1) have not been reported. (

**c**) reports the comparison between the BIAS obtained with the four above-mentioned methodologies at the event scale.

**Figure 6.**Comparison between observed precipitation and rainfall estimated with the regional formula (top graphs) and with the ATS technique (bottom graphs). The comparison is made at the event scale for event 15 (column

**a**) and 13 (column

**b**). Comparison in (column

**c**) refers to event 3 at the hourly scale. (The grey scale refers to the distance from radar, in km).

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## A. Determination of a regional Z-R static relationship

**Figure A1.**(

**a**) Ellipse of the absolute error (greyscale ellipses, mm) into the parameter space $a-b$. Grey dots represent the sub-minimum area; (

**b**) Values of the BIAS (greyscale dots) and location of the minimum of the absolute error (+), of the BIAS (o) and of ${I}_{3}$ index (*) into the sub-minimum space for one of the selected events.

**Figure A2.**Optimal (a-b) values of the Z-R relation for each single event (grey symbols, according to event type), for the different event categories (black rhombus and cross) and for the whole set of events (black dot).

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**MDPI and ACS Style**

Libertino, A.; Allamano, P.; Claps, P.; Cremonini, R.; Laio, F.
Radar Estimation of Intense Rainfall Rates through Adaptive Calibration of the *Z-R* Relation. *Atmosphere* **2015**, *6*, 1559-1577.
https://doi.org/10.3390/atmos6101559

**AMA Style**

Libertino A, Allamano P, Claps P, Cremonini R, Laio F.
Radar Estimation of Intense Rainfall Rates through Adaptive Calibration of the *Z-R* Relation. *Atmosphere*. 2015; 6(10):1559-1577.
https://doi.org/10.3390/atmos6101559

**Chicago/Turabian Style**

Libertino, Andrea, Paola Allamano, Pierluigi Claps, Roberto Cremonini, and Francesco Laio.
2015. "Radar Estimation of Intense Rainfall Rates through Adaptive Calibration of the *Z-R* Relation" *Atmosphere* 6, no. 10: 1559-1577.
https://doi.org/10.3390/atmos6101559