# Rainfall Detection and Rainfall Rate Estimation Using Microwave Attenuation

^{1}

^{2}

^{*}

## Abstract

**:**

^{−1}), and the rainfall rate, R (mm h

^{−1}), were established and cross-validated by estimating the path-averaged rainfall rate. The mean bias of the path-averaged rainfall rate, as compared to the rainfall rate from ground rain gauges, was between −3 and 1 mm h

^{−1}. The improved accuracy of rainfall detection led to the improved accuracy of the path-averaged rainfall rate. Hence, it was confirmed that microwave links, used for broadcasting and media communications, can identify rainy or dry periods (rain spells or dry spells) in a way comparable to rain detectors and provide high time-resolution rainfall rates in real time.

## 1. Introduction

^{2}), the resulting estimated rainfall rate would be inaccurate, particularly for lower-resolution radars. Another source of error could be the changing nature of rainfall over time, with convective and stratiform rainfall occasionally. Bright band contamination and radar calibration errors could be other contributing factors in rainfall estimation errors from weather radar systems [4,5].

## 2. Materials

#### 2.1. Experimental Site

^{−1}) during three days from 27 July to 29 July 2011 [30].

#### 2.2. Rain Gauges and Rain Detectors

^{−1}) using a moving average.

#### 2.3. Weather Radar

#### 2.4. Microwave Links

^{−1}) by an equation of the form:

^{−1}).

#### 2.5. Rainfall Cases

^{−1}) because the bucket needs time to be filled. Classification schemes of precipitation type generally depend on rainfall rate or radar reflectivity because of a lack of detailed dynamic and microphysical information in time and space. Simple classification schemes (those that threshold the radar reflectivity and rainfall rate) were used to separate convective rainfall (≥40 dBZ or ≥10 mm h

^{−1}) from stratiform rainfall (<40 dBZ or <10 mm h

^{−1}) [4]. The rainfall cases (Cases 1, 4, 6, 7, 8, and 10) show rapid spatial and temporal variations with spatial heterogeneity.

## 3. Methods

#### 3.1. Classification of Rain and Dry Spells

_{W}is the number of ${\mathrm{A}}_{\mathrm{tot}}$ within ${\mathrm{W}}_{\mathrm{t}}$. While, as previously mentioned, ${\mathrm{A}}_{\mathrm{clear}}$ is generally determined using the 24-h period prior to the start of a rain event, it may also be determined by considering climate characteristics [16]. Barthès and Mallet [26] performed calculations using different window sizes centered on the current time, ranging from 100 s to 1 h, to test their ability to discriminate between rain spells and dry spells. Kaufmann and Rieckermann [36] use forward-backward-looking windows with ${\mathrm{W}}_{\mathrm{t}}$ (15, 30, 120 min). In this study, when the autocorrelation of ${\mathrm{A}}_{\mathrm{tot}}$ was 0.65 or more, the characteristics of the rainfall cell were determined to be the same, and the corresponding 90 min were used as ${\mathrm{W}}_{\mathrm{t}}$. Leijnse et al. [23] have investigated independently the length and time scales of rainfall by computing the autocorrelation function of rainfall rate for each time step. Since ${\mathrm{A}}_{\mathrm{tot}}\left(\mathrm{t}\right)$ is nonstationary, there is no convergence between the local standard deviations $\mathsf{\sigma}\left(\mathrm{t}\right)={\left(\mathrm{Var}\left[{\mathrm{A}}_{\mathrm{tot}}\left(\mathrm{t}\right)\right]\right)}^{1/2}$ of ${\mathrm{A}}_{\mathrm{tot}}$ and ${\mathrm{S}}_{{\mathrm{W}}_{\mathrm{t}}}$ [16]. The local variability of ${\mathrm{S}}_{{\mathrm{W}}_{\mathrm{t}}}$ is small during clear skies and increases with rainfall; hence, an appropriate threshold (${\sigma}_{0}$) is needed to determine the rainfall detection. This threshold can be determined using a rain gauge or a rain detector around the microwave link. To calculate ${\mathrm{A}}_{\mathrm{clear}}\left(\mathrm{t}\right)$, the appropriate ${\mathrm{W}}_{\mathrm{t}}$ related to the variability characteristics of rainfall should be selected. If ${\mathrm{W}}_{\mathrm{t}}$ is too short, rainfall is difficult to distinguish due to the small attenuation differences between ${\mathrm{A}}_{\mathrm{clear}}\left(\mathrm{t}\right)$ and attenuation caused by a low rainfall rate. Conversely, if ${\mathrm{W}}_{\mathrm{t}}$ is too large, the ${\mathrm{A}}_{\mathrm{tot}}$ during clear skies is difficult to distinguish. If ${\mathrm{A}}_{\mathrm{tot}}$ values are available for several months, ${\sigma}_{0}$ can be calculated using the climatological basis that rain spells are short in most regions. For example, Schleiss and Berne [16] used threshold values $({\sigma}_{0})$ from 0.05 to 0.15, which is the annual average period of rainfall in Paris, France. Due to the multifractal properties of rainfall, rain characteristics are related to the scale considered. Rainfall dynamics, due to coupling with atmospheric turbulence, can be statistically described by scale-invariant processes. Interactions occurring between energy fluxes and neighboring scales may be conserved from large to small scales [37]. Scale dependency is due to rain intermittency and the multifractal properties of rainfall. Verrier et al. [38] investigated the scaling properties of the rainfall process and reported that multiscaling regimes should be distinguished, i.e., 3 days to 30 min (interevent variability) and 15 min to 15 s (internal variability) with different universal multifractals. In this study, the seasonal differences in rainy periods were significant; hence, ${\sigma}_{0}$ was applied from 0.009 to 0.09. When ${\mathrm{W}}_{\mathrm{t}}$ is determined, ${\sigma}_{0}$ is determined, and the rainfall detection is determined using Equation (5) at intervals of 1 min:

^{−1}).

#### 3.2. Weighted Rainfall Rate

^{−1}) is related to the inverse distance within a radius of influence with respect to each transmitting and receiving antenna, we obtain the following [39]:

## 4. Results and Discussion

#### 4.1. Detection of Rain and Dry Spells

#### 4.2. Path-Averaged Rainfall Rate

^{−1}or more to establish the R-k relationship. Verrier et al. [5] applied a threshold at R = 0.1 mm h

^{−1}(at a maximum 15-s resolution) to eliminate small rainfall rates that would not be observed by most instruments (radars and rain gauges) and demonstrated the existence of multifractal properties over specific scaling regimes. In this study, each power-law R-k relationship was established when the rainfall rate was ≥1 mm h

^{−1}at all rain gauges around each microwave link. Of the 10 rain cases, 7 cases were used for establishing the R-k relationships, and the remaining 3 cases (Cases 4, 7, and 10 in May) were used for the validation set approach.

^{−1}, and in Case 7, where the maximum rain gauge rainfall rate was 40 mm h

^{−1}or more. The path-averaged rainfall rates calculated using the R-k relationship in Cases 4 and 7 were compared with the weighted rainfall rates (Figure 10). Case 4 had a correlation coefficient of 0.9, an root mean square error (RMSE) of 1.5 mm h

^{−1}, and a mean bias of −0.5 mm h

^{−1}. Furthermore, Case 7 had a correlation coefficient of 0.9, an RMSE of 2.1 mm h

^{−1}, and a mean bias of −0.2 mm h

^{−1}. Leijnse et al. [23] stated that the time and length scales of rain events are very important variables to know for the dependence of errors on microwave link length. If the typical length scale of rainfall events is much shorter than the microwave link, the relationship between specific attenuation and rainfall rate will have to be very close to linear in order to provide an accurate path-averaged rainfall rate; however, if the variation in rainfall rate is small along an entire microwave link, this requirement of near-linearity is much less strict. Leijnse et al. [35] reported that uncertainties about the retrieval relations decrease when scatter decreases due to averaging of the spatially variable DSDs for longer microwave links. Leijnse et al. [23] stated that if most of the variation in rainfall occurs within a microwave link (i.e., if the microwave link is much longer than the typical length scale of rainfall cases), then the relation between rainfall rate and specific attenuation will have to be very close to linear. The typical spatial scales are relatively distributed in ranges below 8 km; the typical temporal scales are mostly below 20 min [23]. The microwave link lengths used in this study are very long, except for those at WM and MW (Table 5). The high power resolution (0.01 dBm) of the microwave total path attenuation can capture the dynamics of the considered rainfall.

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Location of the research area (Seoul metropolitan area) in Korea. Lines represent microwave links, and triangle symbols indicate the automatic weather stations.

**Figure 2.**Average of total path attenuation ${\overline{\mathrm{A}}}_{{\mathrm{W}}_{\mathrm{t}}}(\mathrm{black}\text{}\mathrm{solid}\text{}\mathrm{line})$ of eight microwave links ((

**a**) MW link, (

**b**) MB link, (

**c**) WM link, (

**d**) GH link, (

**e**) HM link, (

**f**) HG link, (

**g**) MG link, (

**h**) MH link) during Case 6; the rain spell (top gray bars) recorded by the rain detector and the rainfall (bottom black bars) recorded by the rain gauge.

**Figure 3.**Spatial distributions of the radar composite rainfall rate at (

**a**) 04:10 LST on 15 June 2016, (

**b**) 07:20 LST on 15 June 2016, (

**c**) 09:40 LST on 15 June 2016, (

**d**) 12:10 LST on 15 June 2016 during Case 6.

**Figure 4.**Average of total path attenuation ${\overline{\mathrm{A}}}_{{\mathrm{W}}_{\mathrm{t}}}$ (black solid line) and the test statistic for the local variation in total path attenuation ${\mathrm{S}}_{{\mathrm{W}}_{\mathrm{t}}}$ (gray solid line) variations according to the change in window size ${\mathrm{W}}_{\mathrm{t}}$ ((

**a**) 60 min and (

**b**) 90 min) at the MH link for Case 4.

**Figure 5.**Rainfall detection according to (

**a**) threshold ${\mathsf{\sigma}}_{0}$ and (

**b**) window size ${\mathrm{W}}_{\mathrm{t}}$ at all links for Case 4.

**Figure 6.**${\overline{\mathrm{A}}}_{{\mathrm{W}}_{\mathrm{t}}}$ (black solid line) and ${\mathrm{S}}_{{\mathrm{W}}_{\mathrm{t}}}$ (gray solid line) variations according to the power resolution ((

**a**) 1 dBm and (

**b**) 0.01 dBm) at the MH link for Case 2.

**Figure 7.**For the 10 rainfall cases, (

**a**) rainfall detection rate, (

**b**) dry detection rate, (

**c**) dry detection rate during rainfall, and (

**d**) rainfall detection rate during dry spells.

**Figure 8.**Rainfall measured by the rain gauges of 36 AWS for Case 6 and the rain spell recorded by the rain detectors.

**Figure 9.**Specific attenuation versus weighted rainfall rate calculated by the Inverse Distance Weighting (IDW) method for microwave links ((

**a**) MW link, (

**b**) MB link, (

**c**) WM link, (

**d**) GH link, (

**e**) HM link, (

**f**) HG link, (

**g**) MG link, (

**h**) MH link) with frequencies ranging from 6 to 8 GHz and time resolutions of 1 min. The black solid lines represent the corresponding fitted power-law R-k relationships. The gray solid lines indicate the International Telecommunication Union (ITU)-RP.838-8 power-law R-k relationships.

**Figure 10.**(

**a**) Path-averaged rainfall rate with the weighted rainfall rate for the MH link for (

**a**) Case 4 and (

**b**) Case 7. Temporal variations of path-averaged rainfall rate and weighted rainfall rate for the MH link for (

**c**) Case 4 and (

**d**) Case 7.

**Figure 11.**(

**a**) Correlation coefficients and (

**b**) bias of the path-averaged rainfall rate to the weighted rainfall rate for all eight microwave links for Cases 4, 7, and 10.

Link Name | Receiving Antenna | Transmitting Antenna | Frequency (GHz) | Nearest AWS | Power (dBm) | Link Length (km) |
---|---|---|---|---|---|---|

HG | Heyhwa | Geomdan | 8.06 | 419 | 29 | 21.1 |

GH | Geomdan | Heyhwa | 7.75 | 413 | 29 | 21.1 |

WM | Woomyeon | Manggyeong | 6.32 | 401 | 29 | 5.7 |

MW | Manggyeong | Woomyeon | 6.06 | 401 | 29 | 5.7 |

MH | Manggyeong | Heyhwa | 8.26 | 401 | 30 | 17.6 |

HM | Heyhwa | Manggyeong | 7.95 | 421 | 30 | 17.6 |

MB | Manggyeong | Gobong | 6.23 | 425 | 30 | 37.4 |

MG | Manggyeong | Geomdan | 8.1 | 572 | 29 | 13.4 |

**Table 2.**Rainfall amounts and rain spells recorded for 10 cases at five rain gauges installed near the microwave links.

Case | Type of Rainfall Rate | Maximum Radar Rainfall Rate (mm h^{−1}) | Total Rainfall (mm) | Rain spell from Rain Gauge (min) | Rain spell from Rain Detector (min) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

401 | 413 | 419 | 425 | 401 | 413 | 419 | 425 | 401 | 413 | 419 | 425 | |||

1 | convective | 25 | 53 | 56 | 44 | 73 | 106 | 111 | 88 | 145 | 1383 | 966 | 1213 | 1372 |

2 | stratiform | 9 | 9 | 10 | 13 | 8 | 17 | 19 | 26 | 16 | 305 | 214 | 565 | 395 |

3 | stratiform | 5 | 14 | 14 | 6 | 16 | 28 | 27 | 12 | 32 | 621 | 456 | 318 | 666 |

4 | convective | 20 | 45 | 42 | 42 | 55 | 89 | 84 | 83 | 110 | 764 | 557 | 676 | 730 |

5 | stratiform | 8 | 31 | 31 | 36 | 42 | 61 | 62 | 71 | 83 | 644 | 525 | 635 | 626 |

6 | convective | 20 | 35 | 30 | 18 | 36 | 63 | 59 | 33 | 67 | 447 | 268 | 461 | 450 |

7 | convective | 50 | 115 | 119 | 57 | 134 | 180 | 238 | 109 | 206 | 1006 | 554 | 1076 | 967 |

8 | convective | 50 | 138 | 155 | 124 | 154 | 244 | 255 | 196 | 254 | 1764 | 820 | 1033 | 1509 |

9 | stratiform | 7 | 47 | 48 | 31 | 64 | 93 | 95 | 62 | 126 | 1092 | 472 | 843 | 1371 |

10 | convective | 80 | 23 | 38 | 33 | 33 | 39 | 44 | 50 | 56 | 332 | 137 | 254 | 386 |

Case | ${\mathbf{W}}_{\mathbf{t}}$ | Data Resolution | ${\mathsf{\sigma}}_{0}$ | Rain Detector | ${\mathbf{A}}_{\mathbf{rain}-\mathbf{induced}}$ | RR (%) | DD (%) | RD (%) | DR (%) |
---|---|---|---|---|---|---|---|---|---|

4 | 60 min | 0.01 dB | 0.09 | 764 | 526 | 68.8 | 97.8 | 28.9 | 0.4 |

90 min | 725 | 97.9 | 93.6 | 2.1 | 4.6 |

Case | Data Resolution | ${\mathbf{W}}_{\mathbf{t}}$ | ${\mathsf{\sigma}}_{0}$ | Rain Detector | ${\mathbf{A}}_{\mathbf{rain}-\mathbf{induced}}$ | RR (%) | DD (%) | RD (%) | DR (%) |
---|---|---|---|---|---|---|---|---|---|

2 | 1 dB | 90 min | 0.09 | 305 | 134 | 43.9 | 97.7 | 56.1 | 0.8 |

0.01 dB | 248 | 81.3 | 88.3 | 18.7 | 10.2 |

Link Name | Frequency (GHz) | Polarization | Path Length (km) | R-k Relationships | ITU-R P.838-8 R-k Relationships |
---|---|---|---|---|---|

GH | 7.75 | H | 21.1 | $\mathrm{k}=0.0087\text{}{\mathrm{R}}^{1.063}$ | $\mathrm{k}=0.001915\text{}{\mathrm{R}}^{1.4810}$ |

HG | 8.06 | H | 21.1 | $\mathrm{k}=0.01\text{}{\mathrm{R}}^{1.1}$ | $\mathrm{k}=0.004115\text{}{\mathrm{R}}^{1.3905}$ |

MG | 8.1 | H | 13.4 | $\mathrm{k}=0.012\text{}{\mathrm{R}}^{1.1}$ | |

WM | 6.32 | V | 5.7 | $\mathrm{k}=0.018\text{}{\mathrm{R}}^{1.15}$ | $\mathrm{k}=0.0004878\text{}{\mathrm{R}}^{1.5728}$ |

MW | 6.06 | V | 5.7 | $\mathrm{k}=0.017\text{}{\mathrm{R}}^{1.12}$ | |

MB | 6.23 | V | 37.4 | $\mathrm{k}=0.003\text{}{\mathrm{R}}^{1.2}$ | |

MH | 8.26 | V | 17.6 | $\mathrm{k}=0.015\text{}{\mathrm{R}}^{1.1}$ | $\mathrm{k}=0.003450\text{}{\mathrm{R}}^{1.3797}$ |

HM | 7.95 | V | 17.6 | $\mathrm{k}=0.0095\text{}{\mathrm{R}}^{1.2}$ | $\mathrm{k}=0.001425\text{}{\mathrm{R}}^{1.4745}$ |

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Kim, M.-S.; Kwon, B.H.
Rainfall Detection and Rainfall Rate Estimation Using Microwave Attenuation. *Atmosphere* **2018**, *9*, 287.
https://doi.org/10.3390/atmos9080287

**AMA Style**

Kim M-S, Kwon BH.
Rainfall Detection and Rainfall Rate Estimation Using Microwave Attenuation. *Atmosphere*. 2018; 9(8):287.
https://doi.org/10.3390/atmos9080287

**Chicago/Turabian Style**

Kim, Min-Seong, and Byung Hyuk Kwon.
2018. "Rainfall Detection and Rainfall Rate Estimation Using Microwave Attenuation" *Atmosphere* 9, no. 8: 287.
https://doi.org/10.3390/atmos9080287