# Comparison of Rain Gauge Network and Weather Radar Data: Case Study in Angra dos Reis, Brazil

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Case Study Area

^{2}semi-urbanized area with an estimated population of 210,171 inhabitants in 2021 [31], and it is located near an important nuclear power plant. The region is situated in the context of the geomorphological domain of the escarpments of Serra do Mar/Serra da Bocaina. The escarpments of Angra dos Reis are notable for having steep faces facing the ocean, alternating with embedded river valleys. The geology of the site is composed of igneous and metamorphic rocks of the Mesoproterozoic and Neoproterozoic ages, as well as orogenic and post-orogenic granites [32]. The city is crossed by torrential rivers with a torrential regime, grouping rivers into those that originate on the slopes of the Serra do Mar or on the top of the plateau and its tributaries, which flow into the Ilha Grande Bay [33].

#### 2.2. Rainfall Data

#### 2.2.1. Rain Gauge Data

#### 2.2.2. Radar Data

_{DP}(named PHIDP in Table 2) increases as the radar range is limited to rain below the melting layer and/or hot clouds at weather radar frequencies. The ${K}_{DP}$ estimated by this method always assumes a positive value. The methodology can only be applied to radar data with a constant range resolution, being considered a sophisticated processing technique by Ryzhkov and Zrnic [56].

^{−1}, and for tropical rainfall events, α is on average 0.028 deg

^{−1}. These results are similar to the values of α reported by Ryzhkov et al. [53], who used α values of 0.02–0.03 deg

^{−1}for high-quality rainfall estimates in most areas of Hurricane Irene and 0.008–0.015 deg

^{−1}for the Oklahoma flood case. In this study, we used 0.02 deg

^{−1}as the value of α, and $\mathsf{\beta}$ was set to 0.64884 according to Helmus and Collis [41], a value similar to that used by [53,62,63] (0.62). It is noteworthy that, in this study, the product generated from the reflectivity corrected by the attenuation [64] through the ZPHI methodology was used for comparative purposes with the reflectivity of the equipment under study without any correction. Figure 2 illustrates a comparison between Guaratiba’s radar reflectivity without (Figure 2a) and with the ZPHI-method correction (Figure 2b).

- Product 1: $R\left({Z}_{h},{K}_{DP}\right)$, Marshall–Palmer

- 2
- Product 2: $R\left({Z}_{h},{K}_{DP}\right)$, Morales

- 3
- Product 3: $R\left({Z}_{h},{K}_{DP}\right),$ Pluv

- 4
- Product 4: $R\left({Z}_{h},A\right),$ Marshall—Palmer

- 5
- Product 5: $R\left({Z}_{h},A\right),$ MoralesProduct 5 was obtained through the $Z$-$R$ relationship proposed by Morales Rodriguez [68] (similar to Product 2, with parameters $a$ = 378 and $b$ = 1.34 in Equation (1)) for low rainfall intensity ($\le 40\mathrm{dBZ}$) and the $R\left(A\right)$ relationship for higher rainfall intensity ($>40\mathrm{dBZ}$). Similar to Product 4, the $R\left(A\right)$ algorithm used by Ryzhkov et al. [53] and Wang et al. [61] was also used in this study.

- 6
- Product 6: $R\left({Z}_{h},A\right),$ PluvProduct 6 was also obtained through the $Z$-$R$ relationship for low rainfall intensity ($\le 40\mathrm{dBZ}$) and the $R\left(A\right)$ relationship for higher rainfall intensity ($>40\mathrm{dBZ}$). The $Z$-$R$ relationships were those used in Product 3. Similar to Product 4, the $R\left(A\right)$ algorithm used by Ryzhkov et al. [53] and Wang et al. [61] was also used in this study.$$R=0.196\xb7{10}^{0.1408\mathrm{dBZ}}for{Z}_{h1}\le 40\mathrm{dBZ},\phantom{\rule{0ex}{0ex}}or\phantom{\rule{0ex}{0ex}}R=4120\xb7{\left(A\right)}^{1.03}for{Z}_{h1}40\mathrm{dBZ}\phantom{\rule{0ex}{0ex}}\mathrm{a}\mathrm{n}\mathrm{d}$$$$R=0.0036\xb7{10}^{0.1487\mathrm{dBZ}}for{Z}_{h2}\le 40\mathrm{dBZ},\phantom{\rule{0ex}{0ex}}or\phantom{\rule{0ex}{0ex}}R=4120\xb7{\left(A\right)}^{1.03}for{Z}_{h2}40\mathrm{dBZ}$$

#### 2.2.3. Rainfall Events Studied

#### 2.3. Statistical Methods

- The Root-Mean-Square Error $\left(RMSE\right)$ between actual and predicted time series:$$RMSE\left(A,B\right)=\sqrt{\frac{1}{N}{{\displaystyle \sum}}_{i}{\left({A}_{i}-{B}_{i}\right)}^{2}},$$
- The Pearson correction coefficient ($Corr\in \left[-1,1\right]$) estimates the strength and direction of the linear relationship between time series:$$Corr\left(A,B\right)=\frac{{{\displaystyle \sum}}_{i}\left[\left({A}_{i}-{\overline{A}}_{i}\right)\left({B}_{i}-{\overline{B}}_{i}\right)\right]}{\sqrt{{{\displaystyle \sum}}_{i}{\left({A}_{i}-{\overline{A}}_{i}\right)}^{2}}\sqrt{{{\displaystyle \sum}}_{i}{\left({B}_{i}-{\overline{B}}_{i}\right)}^{2}}},$$
- The Nash–Sutcliffe efficiency $\left(Nash\in (-\infty ,1]\right)$ measures how well the outputs of a model reproduce observations against a model that uses only the average of the observed data:$$Nash\left(A,B\right)=1-\frac{{{\displaystyle \sum}}_{i}{\left({B}_{i}-{A}_{i}\right)}^{2}}{{{\displaystyle \sum}}_{i}{\left({B}_{i}-{\overline{B}}_{i}\right)}^{2}}.$$
- The mean absolute error $\left(MAE\right)$ between actual and predicted time series:$$MAE\left(A,B\right)=\frac{1}{N}{{\displaystyle \sum}}_{i}\left|{A}_{i}-{B}_{i}\right|.$$

## 3. Results

#### 3.1. Rain Gauge Data vs. Estimated Rainfall Radar Dara from Reflectivity ${Z}_{h1}$

#### 3.2. Rain Gauge Data vs. Estimated Rainfall Radar Data from Reflectivity ${Z}_{h2}$

## 4. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Locations of the rain gauge network of the municipality of Angra dos Reis (RJ) and of Guaratiba’s S-band radar in the state of Rio de Janeiro, Brazil.

**Figure 2.**Illustration of different products of Guaratiba’s S-band radar reflectivity (

**a**) without ZPHI-method correction and (

**b**) with the reflectivity corrected by the ZPHI methodology.

**Figure 3.**Different regressions developed in this work between Guaratiba’s S-band radar data and rain gauge measurements: (

**a**) method of least squares applied to ${Z}_{h1}$ (radar reflectivity without ZPHI-method correction); (

**b**) method of least squares applied to ${Z}_{h2}$ (radar reflectivity corrected by ZPHI methodology).

**Figure 4.**Total accumulated precipitation comparisons for Events 1, 2, 3, 4, and 5 between rain gauge results and Guaratiba’s six S-band radar products using ${Z}_{h1}$ at radar pixels where rain gauges are located.

**Figure 5.**Statistical indices (RMSE, Pearson correction coefficient, Nash–Sutcliffe efficiency, and mean absolute error) of the comparisons for Events 1, 2, 3, 4, and 5 between rain gauge results and Guaratiba’s six S-band radar products using ${Z}_{h1}$ at radar pixels where rain gauges are located.

**Figure 6.**Total accumulated precipitation comparisons for Events 1, 2, 3, 4, and 5 between rain gauge results and Guaratiba’s six S-band radar products using ${Z}_{h2}$ at radar pixels where rain gauges are located.

**Figure 7.**Statistical indices (RMSE, Pearson correction coefficient, Nash–Sutcliffe efficiency, and mean absolute error) of the comparisons for Events 1, 2, 3, 4, and 5 between rain gauge results and Guaratiba’s six S-band radar products using ${Z}_{h2}$ at radar pixels where rain gauges are located.

ID | Station Name | Lat | Lon |
---|---|---|---|

P1 | Angra dos Reis | −22.9785 | −44.2958 |

P2 | Areal | −22.9820 | −44.2920 |

P3 | Ariró | −22.9020 | −44.3320 |

P4 | BNH | −22.9920 | −44.2410 |

P5 | Bracuí | −22.9330 | −44.3870 |

P6 | Camorim | −22.9980 | −44.2640 |

P7 | Camorim Pequeno | −23.0050 | −44.2790 |

P8 | Enseada | −22.9870 | −44.3200 |

P9 | Frade | −22.9660 | −44.4400 |

P10 | Itanema | −22.9230 | −44.3590 |

P11 | Manbucaba | −22.9510 | −44.5650 |

P12 | Mombaça | −23.0170 | −44.2910 |

P13 | Monsuaba | −23.0100 | −44.2220 |

P14 | Monsuaba 2 | −22.9870 | −44.2180 |

P15 | Parque do Belém | −22.9604 | −44.2941 |

P16 | Parque Perequê | −23.0140 | −44.5330 |

P17 | Ponta Leste | −23.0520 | −44.2430 |

P18 | Pontal | −22.9480 | −44.3290 |

P19 | Portogalo | −23.0370 | −44.1950 |

P20 | Praia Brava | −23.0050 | −44.4800 |

P21 | Praia da Chacara | −23.0000 | −44.3050 |

P22 | Praia das Goiabas | −23.0240 | −44.5120 |

P23 | Praia de Araçatiba | −23.1550 | −44.3270 |

P24 | Praia de Bananal | −23.1090 | −44.2480 |

P25 | Praia de Garatucaia | −23.0370 | −44.1770 |

P26 | Praia Sitio Forte | −23.1370 | −44.2820 |

P27 | São Bento | −23.0120 | −44.3220 |

P28 | Serra d’Água | −22.8890 | −44.2780 |

P29 | Vila do Abraão | −23.1390 | −44.1690 |

P30 | Vila Velha | −23.0240 | −44.3490 |

**Table 2.**Characteristics of dual-polarization S-band Doppler weather radars located in the State of Rio de Janeiro, Brazil, operated by INEA.

Parameter | Dual-Polarization S-Band Doppler Radar |
---|---|

Transmitter | 2.8 GHz |

Pulse Repetition Frequency (PRF) | 600 Hz |

Pulse width | 1μsec |

Pulse Repetition Time (PRT) | 1.67 ms |

Peak power | $\ge $750 kW |

Antenna gain, horizontal and vertical | 45 dB |

Antenna aperture | 8.5 |

Beam width horizontal and vertical | 1° |

Polarimetric mode | STSR ¹ |

Nyquist Velocity | 48.195 m/s |

Number of samples used to compute moments | 60 |

Radar Receiver Bandwidth | 1 MHz |

Radar Transmit Power Horizontal and Vertical Channel | 800 watts |

Scan mode | Plan Position Indicator (PPI) |

Radial range | 250 km |

Radar fields ^{2} | UH, UV, DBZH, DBZV, ZDR, RHOHV, PHIDP, NCPH, NCPV, SNRHC, SNRVC, VELH, VELV, WIDTHH, WIDTHV, CCORH, CCORV |

^{2}UH is Unfiltered Reflectivity Factor H, UV is Unfiltered Reflectivity Factor V, DBZH is Equivalent Reflectivity Factor H, DBZV is Equivalent Reflectivity Factor V, ZDR is Log Differential Reflectivity H-V, RHOHV is Cross-Correlation Ratio H-V, PHIDP is Differential Phase H-V, NCPH is Normalized Coherent Power H, NCPV is Normalized Coherent Power V, SNRHC is Signal-to-Noise Ratio Co-polar H, SNRVC is Signal-to-Noise Ratio Co-polar V, VELH is Radial Velocity H, VELV is Radial Velocity V, WIDTHH is Doppler Spectrum Width H, WIDTHV is Doppler Spectrum Width V, and CCORH is Clutter Correction H, CCORV is Clutter Correction V.

**Table 3.**Rainfall events, the number of rain gauges used in each event, the rain gauges’ and radar’s temporal resolutions, and the number of radar time steps per event.

Event ID | Event Duration | Number of Rain Gauge Stations | Rain Gauges’ Temporal Resolution | Radar’s Temporal Resolution and Number of Time Steps |
---|---|---|---|---|

Event 1 | 14 December 2016 (00:00:00 UTC-3)–18 December 2016 (23:50:00 UTC-3) | 29 ^{1} | 10 min | 10 min (720) |

Event 2 | 21 January 2017 (00:00:00 UTC-3)–23 January 2017 (23:50:00 UTC-3) | 27 ^{2} | 10 min | 10 min (227) |

Event 3 | 13 March 2017 (00:00:00 UTC-3)–18 March 2017 (23:50:00 UTC-3) | 27 ^{3} | 10 min | 10 min (720) |

Event 4 | 12 December 2017 (00:00:00 UTC-3)–13 December 2017 (23:55:00 UTC-3) | 28 ^{4} | 10 min | 5 min (275) |

Event 5 | 3 July 2018 (00:00:00 UTC-3)–4 July 2018 (23:55:00 UTC-3) | 22 ^{5} | 10 min | 5 min (201) |

^{1}There were no data from rain gauge P1.

^{2}There were no data from rain gauges P1, P11, and P29.

^{3}There were no data from rain gauges P11, P23, and P29.

^{4}There were no data from rain gauges P4 and P23.

^{5}There were no data from rain gauges P1, P4, P7, P12, P18, P19, P23, and P28.

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## Share and Cite

**MDPI and ACS Style**

Silva, E.J.R.d.; Alves, C.N.; Campos, P.C.d.O.; Oliveira, R.A.A.C.e.; Marques, M.E.S.; Amorim, J.C.C.; Paz, I. Comparison of Rain Gauge Network and Weather Radar Data: Case Study in Angra dos Reis, Brazil. *Water* **2022**, *14*, 3944.
https://doi.org/10.3390/w14233944

**AMA Style**

Silva EJRd, Alves CN, Campos PCdO, Oliveira RAACe, Marques MES, Amorim JCC, Paz I. Comparison of Rain Gauge Network and Weather Radar Data: Case Study in Angra dos Reis, Brazil. *Water*. 2022; 14(23):3944.
https://doi.org/10.3390/w14233944

**Chicago/Turabian Style**

Silva, Elton John Robaina da, Camila Nascimento Alves, Priscila Celebrini de Oliveira Campos, Raquel Aparecida Abrahão Costa e Oliveira, Maria Esther Soares Marques, José Carlos Cesar Amorim, and Igor Paz. 2022. "Comparison of Rain Gauge Network and Weather Radar Data: Case Study in Angra dos Reis, Brazil" *Water* 14, no. 23: 3944.
https://doi.org/10.3390/w14233944