Rainfall Measurement by Commercial Microwave Links

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This entry is adapted from the peer-reviewed paper 10.3390/s22124395

As one of the most critical elements in the hydrological cycle, real-time and accurate rainfall measurement is of great significance to flood and drought disaster risk assessment and early warning. Using commercial microwave links (CMLs) to conduct rainfall measure is a promising solution due to the advantages of high spatial resolution, low implementation cost, near-surface measurement, and so on.

wireless cellular networks microwave links rainfall machine learning remote sensing

1. Introduction

Rainfall is one of the major driving forces in the hydrological cycle of the land area. Natural disasters caused by rainfall, such as flash flood, debris flows, landslides, and urban waterlogging, have been damaging people’s lives and property over the years ^[1]. On 20 July 2021, floods and secondary disasters caused by torrential rain had a negative impact on 14.786 million people in Zhengzhou, China, with a direct economic loss of 120.06 billion yuan ^[2]. Therefore, developing rapid and accurate rainfall information acquisition technologies is extremely urgent and important to achieve precise flood risk assessment and enhance the public safety response capability. Meanwhile, rainfall is one of the most critical climate factors to determine crop growth, and accurate precipitation information can substantially improve crop yield ^[3]. In addition, rainfall information is also an important reference index for reservoir operations, urban water supply, irrigation planning, and other forms of water resource management ^[4]. However, due to the high spatial and temporal dynamics of rainfall, it is still challenging to accurately monitor and measure rainfall in real time ^[5]^[6].

Rain gauges (RGs), weather radars, and satellite remote sensing are the three main rainfall measurement methods at present. RG is a point measurement tool with limited density, low spatial resolution, and relatively high construction and maintenance costs. Radar observation of rainfall emits electromagnetic waves into the sky. These electromagnetic waves are reflected by clouds and returned to a ground receiver. Rainfall information is then estimated by comparing the original and returned electromagnetic waves ^[7]. This method measures the water volume in the clouds, which could be quite different from the rainfall amount on the ground. In addition, this method can be easily affected by ground obstacles at a low elevation angle ^[8]. Satellite rainfall measurement, on the other hand, has a global scale, but the resolution is relatively coarse in terms of small spatial and temporal scales. Moreover, its accuracy is significantly affected by the density of clouds, and the time lag is high ^[9].

In the recent years, many countries such as Israel, the Netherlands, France, Germany, the Czech Republic, Switzerland, Italy, and China have adopted commercial microwave links (CMLs) in wireless cellular networks (WCNs) to retrieve the regional rainfall information. The measurement accuracy and ability of capturing the spatial and temporal dynamics of rainfall for the CML method have been verified through a variety of simulations and experiments. The CMLs that have already been deployed in WCNs to achieve fronthaul/backhaul communications among base stations can be considered as a widely distributed environmental monitoring sensor network. Since CMLs were originally designed for the communications purpose and environment sensing is just a by-product, the network of CMLs is also called an opportunistic wireless sensor network (OWSN) ^[10]. The IMT-2030 (6G) Promotion Group released a research report on the integration of communications and sensing technology in September 2021 ^[11], which points out that the communications and sensing capabilities will finally achieve the integration and symbiosis in the future 6G wireless networks. According to the statistics of the Industry and Information Technology Ministry, the number of 5G base stations in China has already exceeded one million in 2021. The increasing number of the deployed base stations and microwave links provides great opportunities and supports to develop CML-based rainfall measurement technology ^[12]^[13]^[14]. Table 1 provides the comparisons of the existing rainfall measurement methods.

Table 1. Comparisons of conventional and CML-based rainfall measurement techniques.

Techniques	Advantages	Disadvantages
Rain Gauge	High accuracy	Point measurement; low spatial resolution; high capital and operational cost; difficult to deploy in mountainous areas
Weather Radar	Broad spatial coverage of up to 300 km	Low accuracy in near-surface measurement; easy to be affected by ground obstacles at a low elevation angle
Satellite	Global scale	Coarse resolution for small spatial and temporal scales; affected by clouds; high time lag
Commercial Microwave Links	Path-integrated and near-surface measurements; high spatial and temporal resolution; no additional capital cost	Hard to acquire CML data; relatively high complexity for data processing

In WCNs, in order to monitor the quality of service (QoS) of a CML, the network system always regularly monitors and records the transmission and received power of the signal in the CML for every, for example, 15 min. That is, a huge amount of CML attenuation data is already available and can be used to retrieve real-time rainfall intensity. However, there are many factors leading to the signal attenuation during the propagation, and it is nontrivial to extract the rain-induced attenuation from these attenuation data. This is because, first, microwave link attenuation data contain many spatio-temporal variations and uncertainties, which are not only related to path length, frequency, polarization, and other attributes of microwave links ^[15], but also affected by external factors such as temperature, humidity, atmospheric composition, and so on; second, rainfall is a highly spatio-temporal dependent event ^[16], and it is relatively complex and difficult to establish the model between rain-induced attenuation and rainfall intensity. Considering the problems mentioned above, data-driven methods such as machine learning have been proposed to facilitate CML-based rainfall measurement. Machine learning is a new way to solve interdisciplinary issues and the problems which are difficult to simulate their processes ^[17]. In particular, deep learning (DL) has been proven to be an important tool to exploit the power of big data (BD) by capturing high-dimensional and multi-modal data distribution, and extracting spatio-temporal features of data in order to understand the internal data logic and whole physical process ^[18].

Rainfall measured by the CML network has a broad application prospect in both densely populated cities and remote mountainous areas. Although current studies have made significant contributions on the technological aspects, there are very few review articles about this technique. One study ^[1] reviews the existing technologies and challenges of CML-based precipitation monitoring from a signal processing prospective, which includes calibration, detection, estimation, classification and separation, assimilation, and reconstruction. Another ^[19] divides the CML-based measurement studies into four groups and points out that the biggest challenge is the capitalization of CML data. Overviews of the history, theory, challenges, and opportunities toward CML-based rainfall monitoring technique are given by refs. ^[5]^[10]. The former focuses on the background introduction and continental-scale rainfall monitoring, while the latter emphasizes the issues of wet antenna attenuation and abnormal signal fluctuations. Studies related to terrestrial microwave rain attenuation measurement from 2010 to 2020 are investigated by ^[20]

2. The Principle and Theory of Rainfall Measurement by CML

2.1. Basic Principle

Wireless communications use electromagnetic waves, which can propagate in free space, to carry data. Microwave refers to the electromagnetic wave with 300 MHz–300 GHz frequency, i.e., 1 mm–1 m wavelength. Microwave can be further divided into decimeter wave, centimeter wave, and millimeter wave. Normally, round directional antennas have stronger beam focusing characteristics than rectangular omnidirectional antennas. The communication link between two such directional antennas is called a microwave backhaul link, or microwave link for short. As shown in Figure 1, when the microwave propagates through the rain area, the transmitting power will be attenuated due to the scattering and absorption by raindrops ^[21]^[22]. This type of microwave attenuation is called rain-induced attenuation, and the relative loss of power per unit path length is called specific attenuation, denoted as k (dB/km). Recommendation ITU-R P.838-3 ^[23] gives the relationship between the specific attenuation k and rain rate, denoted as R (mm/h), as follows:

k = a R^{b},

where the coefficients a and b are functions of microwave signal frequency, polarization, and raindrop size distribution (DSD). In addition to rain-induced attenuation, non-rain factors, such as free space path loss, atmospheric attenuation and multipath effect, can also lead to microwave link attenuation. Therefore, the rain-induced attenuation can only be obtained by eliminating the non-rainfall induced attenuation from the total attenuation. CML-based rainfall measurement has the advantages of path-integrated measurement, high spatial density, less human intervention, low implementation cost, and true reflection of near-surface rainfall and thus can be used as an effective substitution or supplement to traditional rainfall measurement methods, such as RGs, weather radar, and satellite ^[20]^[24]^[25]. In addition, CML-based measurement can estimate not only rainfall, but also water vapor, solid particles, fog, snow, sleet, hail, and so on ^[26]^[27]^[28]^[29].

Figure 1. Basic operating principle of CML-based rainfall measurement.

2.2. Mathematical Models

The amount of signal attenuation, denoted as

A_{t o t}

(dB), is obtained by subtracting the received power from the transmitting power. Here,

A_{t o t}

comprises three types of attenuations, i.e., baseline attenuation

A_{b a s e l i n e}

(dB), path-integrated rain attenuation

A_{r a i n}

(dB), and wet antenna attenuation

A_{W A A}

(dB). That is,

A_{t o t} = A_{b a s e l i n e} + A_{r a i n} + A_{W A A} .

2.2.1. Baseline Attenuation

A_{b a s e l i n e}

is usually determined by the attenuation value in a time interval right before a rainfall event and mainly consists of free space path loss

A_{b f}

(dB) and atmospheric attenuation

A_{g a s}

(dB), i.e.,

A_{b a s e l i n e} = A_{b f} + A_{g a s} .

Free-space path loss $A_{b f}$ . The free-space path loss is the loss of signal strength when a signal propagates through free space. Free-space path loss $A_{b f}$ increases as the distance between the transmitter and the receiver increases. According to Recommendation ITU-R P.525-4 ^[30], when the distance between antennas is much larger than the electromagnetic wavelength $λ$ , the path loss of electromagnetic wave in free space is only related to the frequency and distance, as shown in Equation (4):

$A_{b f} = 20 l o g (4 π L / λ) = 32.4 + 20 l o g f + 20 l o g L,$

where f (MHz) is carrier frequency and L (km) is the distance between the transmitter and the receiver.
Atmospheric attenuation $A_{g a s}$ . When electromagnetic waves propagate through the atmosphere, they will be attenuated by the absorption, reflection, and scattering of water vapor, fog, solid particles, oxygen, nitrogen, carbon dioxide, and other substances in the atmosphere. According to Recommendation ITU-R P.676-12 ^[31], the specific gaseous attenuation of a microwave link, denoted as $k_{g a s}$ (dB/km), can be estimated by

$k_{g a s} = k_{o} + k_{w} = 0.1820 f (N_{o x y g e n}^{″} (f) + N_{w a t e r v a p o r}^{″} (f)),$

where $k_{o}$ and $k_{w}$ (dB/km) are the specific attenuation caused by dry air (oxygen, nitrogen, etc.) and water vapor, respectively, and $N_{o x y g e n}^{″}$ and $N_{w a t e r v a p o u r}^{″}$ are the imaginary parts of the frequency-dependent complex refractivities. Then, the atmospheric attenuation of a microwave link can be estimated by

$A_{g a s} = \int_{0}^{L} k_{g a s} (l) d l .$

2.2.2. Path-Integrated Rain Attenuation

According to refs. ^[5]^[10]^[19], path-integrated rain attenuation

A_{r a i n}

in Equation (2) basically is a function of the specific attenuation k, which can be calculated based on Equation (1), that is,

A_{r a i n} = \int_{0}^{L} k (l) d l = \int_{0}^{L} a R {(l)}^{b} d l \overset{b \approx 1}{=} a {\bar{R}}^{b} L,

where R (mm/h) is the path-average rain rate. The attenuation caused by rainfall and the average rain rate are linearly correlated if b≈ 1. Other than Equation (1), the values of the rain rate R and the specific attenuation k can be estimated based on DSD refer to ^[32]^[33], i.e.,

R = 6 \times 10^{- 4} π \int_{D} v (D) D^{3} N (D) d D,

k = \frac{1}{l n (10)} \int_{D} C e x t (D, f) N (D) d D,

where D is the raindrop diameter in mm,

N (D)

is the DSD’s number concentration per diameter in mm⁻¹m⁻³,

v (D)

is the rain droplet final velocity in m/s, and

C e x t (D, f)

is the extinction cross section at frequency f in m², which describes the attenuation of the signal at frequency f by each raindrop. The dependence of

C e x t (D, f)

and

v (D) D^{1}

on raindrop diameter D is very similar, especially in the frequency range from 20 GHz to 35 GHz ^[5].

2.2.3. Wet Antenna Attenuation (WAA)

WAA (

A_{W A A}

) refers to the signal attenuation due to the water film attached to the radome during the rainfall, and it will last for a period of time until the water on the radome evaporates. Because

A_{b a s e l i n e}

is determined prior to the rainfall event, WAA is generally not included in

A_{b a s e l i n e}

. Usually, WAA is assumed as a constant value (1–2 dB) or determined by the RSL time series of the link and its surrounding links in the previous time, and the time probability distribution function of WAA can also be estimated by data-driven algorithms.

2.3. Example Demonstration

Figure 2 shows the relationship between the total attenuation of the CML and the rainfall intensity measured by RG. The simulation data come from an open access dataset ^[34], which contains the signal power total loss collected from six E-band (71–76 GHz and 81–86 GHz) CMLs and the rainfall intensity collected from four RGs in Prague, Czech Republic. The data from one CML of the six and one RG, which is nearest to the selected link midpoint, to generate the signal level time series of 24 h (23 August 2018 19:39–24 August 2018 19:39) with a time resolution of 1 min. It can be seen that there is a clear correlation between CML power total loss and rainfall intensity, and even very low intensity rainfall can be perceived by the CML measurement, because the E-band CML is more sensitive to rainfall than other used frequency bands (roughly from 10 to 50 GHz) at present ^[35]^[36].

Figure 2. Correlation between CML power total loss and rainfall intensity.

3. Development of Rainfall Measurement Based on CML

In the middle of the 20th century, it was found that rainfall had a significant impact on the attenuation of electromagnetic waves, especially high-frequency electromagnetic waves, and it was proposed that the attenuation of electromagnetic waves could be used to retrieve rainfall intensity ^[37]. At the end of the 20th century, the implementation of the Tropical Rainfall Measuring Mission (TRMM) project has promoted a series of experiments to retrieve DSD by using dedicated dual-frequency links ^[38]. However, it is not realistic to deploy such a network of microwave links just for rain measurement in a large area. Fortunately, since the beginning of the 21st century, with the rapid growth number of mobile phone users, a variety of wireless base stations and microwave links have been widely deployed to build seamless WCNs. This forms the infrastructure foundation of the CML-based rainfall monitoring networks to timely observe rainfall with high temporal and spatial resolution. Each microwave link between two base stations is equivalent to a sensor node. Moreover, for the typical frequencies used by CML in WCNs, the coefficient b in Equation (1) is very close to 1, which means that there is a good linear relationship between rain-induced attenuation and rainfall intensity. In 2006, Messer et al. ^[39] used CML-RSL data to retrieve the rainfall intensity in Israel for the first time. In 2013, Overeem et al. ^[40] used an unprecedented number of more than 2400 CMLs to reconstruct the rainfall map for the entirety of the Netherlands (35,500 km²). Subsequently, countries around the world established research teams and tried to explore the potential of CML in the field of environmental monitoring. Table 2 summarizes the countries that have achieved rainfall measurement by CML in chronological order.

Table 2. Countries that have used CML to measure rainfall.

CML Data
Authors (Year)	Country	Frequency (GHz)	Link Number	Length (km)	Temporal	Quantization Level (dB)	Remarks
Messer et al. (2006) ^[39]	Israel	—	—	—	15 min	—	The correlation between rainfall intensity measured by CML and RG is 0.86 for a 15 min interval and 0.9 for an hourly interval.
Leijnse et al. (2007) ^[41]	The Netherlands	38	2	7.75, 6.72	15 min	1	Eight rainfall events are evaluated, and the results are consistent with the rainfall retrieved from RGs and C-band radar.
Schleiss et al. (2010) ^[42]	France	26, 19	4	3.7, 3.7, 7.1, 2.4	30s, 6s	1	A wet and dry weather classification method is proposed, which can identify 92% of all rainy periods and 93% of the total rain amount.
Chwala et al. (2012) ^[43]	Germany	15, 18.7, 23	5	17.4, 10.2, 4, 17.1, 10.4	selectable	<0.05	A new algorithm based on short-time Fourier transform (STFT) is proposed for the wet/dry classification. The correlation reaches 0.81 for the link-gauge comparison.
Bianchi et al. (2013) ^[44]	Switzerland	23, 38, 58	14	0.3–8.4	5 min	0.1 or 1	RGs, weather radar and CMLs are combined to estimate the intensity and temporal distribution of rainfall more accurately.
Fencl et al. (2013) ^[45]	Czech Republic	38	14	—	—	—	CML networks can better capture the spatio-temporal rainfall dynamics, especially in heavy rain, and thus improve pipe flow prediction.
Doumounia et al. (2014) ^[46]	Burkina Faso	7	1	29	1s	1	95% of the rainy days are detected by CML measurement, and the correlation with the RGs data series is 0.8.
D’Amico et al. (2016) ^[47]	Italy	25	3	average of 6	—	—	Tomographic technique was applied to reconstruct 2-D fields of rainfall accumulation, and the link density and topology affect the accuracy of the reconstruction algorithm.
Rios Gaona et al. (2018) ^[48]	Brazil	above 15	145	shorter than 20	—	0.1	As compared to RGs, CML-based measurement can better capture the city-average rainfall dynamics.
Sohail Afzal et al. (2018) ^[49]	Pakistan	38	35	0.5–2.5	15 min	—	The correlation coefficient value between rainfall intensity measured by CMLs and RGs is as high as 0.97.
Jacoby et al. (2020) ^[50]	Sweden	14–39	17	1.5–7	10 s	—	Using long short-term memory (LSTM) to learn from previous attenuation values is sufficient to generate accurate attenuation predictions.
Song et al. (2021) ^[51]	China	15–23	8	0.55–1.08	1 min	0.1	The correlation coefficient values between the rain rate measured by CMLs and RGs are all higher than 0.77, and the highest coefficient is over 0.9.
Pudashin et al. (2021) ^[52]	Australia	10–40	144	0.2–57	15 min	0.1	Using two types of datasets collected by different sampling strategies (maximum/minimum RSL and average RSL) to retrieve rainfall, the results show that the maximum/minimum RSL data are better than average in terms of the statistics, i.e., root mean square error (RMSE), bias, and coefficient of variation (CV).

"—" represents that the content is not mentioned in the literature.

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Subjects: Remote Sensing

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Zhihua Li

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Entry Collection: Environmental Sciences

Update Date: 29 Jun 2022

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