Quantifying insect migration across Bohai strait using weather radar

: Weather radars provide continuous recording over extensive spatial coverage, which is valuable for biologists who observe and study biological activities over a wide range of temporal and spatial scales. Through the interpretation of weather radar observations, powerful biological inferences can be obtained. However, when it comes to certain biological problems, such as the determination of biological parameters related to airborne biological densities, weather radar data needs to be processed based on certain assumptions before. This article analyses and calculates the impact of the phenomenon of migratory insects gathering into layers on the interpretation of weather radar data and develops a biomass estimation method with known bio- spatial distribution characteristics. Quantitative research was conducted on the situation of migrating insects across the Bohai Bay in the autumn of 2012.


Introduction
The use of weather radar for large-scale observation of airborne organisms is of great scientific significance, including epidemic control, natural protection, flight safety, and crop disaster forecasting [1].
As early as half a century ago in 1945 and 1955, researchers discovered that radars can observe birds [2] and insects [3]. In 1965, when Doppler radar was used for aerial observations, clearair dot angel echoes were found and the occurrence and activity of these discrete point targets were fixed on a regular basis [4]. Then, in 1969, Hardy et al. classified the cause of Doppler radar clear-air echoes, and believed that the scattering echoes produced by insects and birds occupy the major part of the clear-air echoes [5]. After 1979, Riley et al. began to complete preliminary work on the quantitative investigation of radar detection [6]. Later, Drake began designing a dedicated insect detection radar, which laid the basic working model of the entomological radar [7]. Beginning in 1985, Mueller et al. began the dual-polarised observation of insects [8] and concluded that the clear-air echoes observed by CHILL radar in the evening of mid-June was produced by insects [9]. Gauthreaux et al. performed curve fitting on the reflectivity factor observed by the weather radar and the bird migration rate, and obtained a cubic quantitative estimation model [10].
Zrnic uses a dual polarised radar to quantitatively observe the dual polarisation measurements of insects and birds, such as Z DR , δ, and ρ hv . The US began to use the weather radar network to study birds in 2000. Combined with radiosonde data, the weather radar's reflectivity factor and radial velocity data were used to analyse the large-scale migration of birds [11]. Since 2005, the quality control method for weather radar data has been gradually moved from nonprecipitation echoes removal to specific research on the extraction, classification, and quantification of biological information [12,13].
Gasteren et al. first conducted a regression analysis of the reflectivity factor measured by the weather radar and the bird density, and obtained the linear relationship between the bird density VID and the radar reflectivity factor VIR observed by the weather radar [14]. Buler et al. considered the influence of the weather radar beam propagation model on the reflectivity measurements, and fitted a regression analysis with the ground bird density to improve the estimation accuracy [15]. Dokter et al. derived the relationship between the radar reflectivity factor and the average bird density and the average radar cross section (RCS) [16]. Chilson et al. established a framework for estimating airborne biological densities using weather radars, and the simulation results showed that the error in estimating biomass using weather radars is small enough to quantify biological populations [17]. The use of weather radar for large-scale phenology research has achieved initial results [18][19][20].
In this paper, the effect of insect migration stratification characteristics on weather radar detection is analysed, and the formula for estimating the biomass under non-uniform beam filling is given. Using the weather radar data from Yantai station, a quantitative study of the aerial migrating insects over sea in autumn was carried out, and statistics were made on the total amount of migratory organisms and the characteristics of time of flight.

Radar data processing
Weather radar can provide base data products such as radar reflectivity factor Z, radial velocity V, and velocity spectrum width W, as well as retrieved products. For quantitative observations, the base data products with an angular resolution of 1° are used. The reflectivity factor range resolution is 1 km, and radial velocity and spectral width range resolutions are 250 m. Weather radar base data products include biological echoes, meteorological echoes, ground clutter, sea clutter, anomalously propagated echoes, and other types of radar echoes. Quantification of migratory organisms using weather radar data requires processing of radar data to extract biological echoes.
Dokter's method [16] has been able to better remove meteorological echoes and ship clutter. Based on this method, we have adjusted the parameters for radar data in China and added morphological processing procedure to smooth the edges of radar images.

Biological quantification
Chilson et al. [17] conducted a detailed theoretical derivation of aerial biomass estimation using weather radar reflectivity factors. For the case of single scatter located at a distance r (m) from a monostatic radar, the received power P r (W) is given by a simplified the radar equation: where P t (W) is the transmit power of the radar, G is the gain of the antenna, λ (m) is the wavelength of the radio waves, and σ (m 2 ) is the RCS of the scatter. The Gaussian shape one-way beam weighting function of the antenna is where θ 1 and ϕ 1 are the one-way half-power (3 dB) beamwidths in the horizontal and vertical planes, respectively. For pulsed Doppler weather radar, the matched filter has a range-weighting effect. The one-way range weighting function can be written as Here r is the range from the radar antenna to the scatter, σ r = 0.35Δr and Δr = cτ/2, with c being the electromagnetic wave propagation speed through the atmosphere and τ is the duration of the transmitted wave. The quantity Δr is referred to as the range resolution. Therefore, the radar echo power of a single migrating creature in the air can be expressed as For migrating insects dispersed in the air, it can be simply assumed that the total echo power can be written as A radar sampling volume produced by the beam and range weighting functions given by (2) and (4), can be expressed as According to Probert-Jones [21], when the scatterer uniformly fills the beam in the horizontal and vertical beam directions, the integral of the sampling volume can be written as The distribution of organisms in the height direction during longdistance migration is not uniformly, and it cannot be considered to fill up the radar beam when located far from the radar. Therefore, it is necessary to calculate and analyse the non-uniformly distributed beam filling. This is depicted in Fig. 1.
Generally, migratory organisms have the most suitable height to migrate, and it can be assumed that the height interval is h min to h max , and the angles corresponding to the main beam directions are t 1 and t 2 , respectively. Then the integral of the sampling volume in (7) can be written as In the standard atmosphere, combined with the 4/3 Earth radius model, the relationship between the radar beam irradiation height and the irradiation angle is In the formula, a e = 4a/3, it can be derived that After the bio-altitude distribution is known, according to (11), the corresponding elevation angles at different distances are calculated, and the difference between the corresponding elevation angle and the antenna elevation angle is t 1 and t 2 . Combining (11), the result of (7) can be written as V bio = 0.35 2π πr 0 2 θ 1 ϕ 1 Δr 16ln 2 × erf 2t 2 2ln 2 ϕ 1 − erf 2t 1 2ln 2 ϕ 1 .
When the scatters are widely distributed, (12) degenerates to the form of (8).
During weather radar observations, the echo power is converted into radar reflectivity factors that can reflect the meteorological conditions. The weather radar equation can be written as: wherein, P r represents the radar receiving power, P t represents the radar transmitting power, Δr is the range resolution, G is the antenna gain, θ and ϕ represent the horizontal and vertical beam width, λ represents the radar wavelength, K represents the coefficient related to the complex refractive index, and Z is the equivalent reflectivity factor, r 0 represents the distance from the radar. This equation does not include the power loss of receiver's filter. The meaning of Z is under Rayleigh scattering condition (πD/λ ≤ 0.13), the sum of the sixth power of the diameter of all raindrops in a unit volume, the unit is mm 6 /m 3 , that is Radar reflectivity η is defined as the sum of backscattered cross sections per unit volume. The reflectivity factor Z reported by weather radar When considering the relationship between the backscattering cross section of small spherical particles and particle diameter under the assumption of Rayleigh scattering, we can get For biological observations, there are usually dominant populations. It can be considered that the average RCS is σ, and the spatial number density is N bio , then we get That is, the radar reflectivity η can be calculated by the radar reflectivity factor Z observed by the weather radar, and the biological spatial average density N bio can be calculated by combining the biological average radar RCS. After removing non-biological echoes such as meteorological echoes from weather radars, the radar reflectivity of the radar observations can reflect the airborne biological density. Combined with the radar sampling volume, the total airborne biomass in the radar observational airspace can be statistically obtained.
Firstly, after the radar echoes are extracted by biological echoes, biological echoes are obtained. For the characteristics of over-sea migrating insects, only the echoes of the radar scan above the sea and the islands are selected for quantitative estimation in order to avoid the possible existence of other types of echoes such as superreflection, ground clutter etc. which may not be removed by the biological echo extraction algorithm in radar echoes over terrestrial regions.
According to (15), the radar reflectivity factor Z is converted into radar reflectivity η, combined with the typical RCS information of the migratory species, and in combination with (16), the radar reflectivity η can be further transformed into the corresponding area's aerial biological density N bio . Then according to (12), the radar beam sampling volume at different distances can be calculated, and the calculated volume and the corresponding area's aerial biological density can be correspondingly multiplied to obtain the number of airborne organisms.

Results
China is located in a typical East Asian monsoon climate zone, providing a stable wind-temperature background field for pests moving across regions. After >60 years of systemic studies, the seasonal migration patterns of migratory pests in China have been clarified. The 'horseshoe-shaped' topographic structure that is surrounded by mountains on three sides and southwards in the northeast region has made the flat Bohai Gulf Channel the most important insect migration channel in northern China.
The night observation data of Yantai station weather radar at the end of August and early September 2012, during the outbreak of armyworm 2012, were statistically analysed, and quantitative estimations were made using the methods described in this article. Yantai weather radar station is located in the north of Shandong Peninsula. The detection range can cover the Bohai Strait. A series of islands dominated by Beihuangcheng Island in the north of the strait are important habitats for long-distance migration of insects. The radar observation geometry is shown in Fig. 2.
By observing the original reflectivity factor data at Yantai from 30th August to 6th September 2012, a large number of radar echoes in line with the characteristics of night migrating organism echoes were found. The typical situation is from the evening of 4 September to the early morning of the following day, a large number of biological echoes from the Liaodong Peninsula to the Shandong Peninsula can be observed, as shown in Fig. 3.
For this phenomenon, quantitative analysis was conducted using the method described above. According to the observations of Feng et al. [22] (Fig. 4b), it is believed that the height distribution ranges from 300 to 1000 m. The measured RCS of 130 mg armyworm in the S-band was −55.39 dBsm (0.0289 cm 2 ). The subsequent quantitative analysis assumed that the average body weight of the armyworm was 130 mg, and the RCS was similar to that measured in the laboratory. The quantitative analysis result was shown in Fig. 4.
It can be seen that the night-time migration of insects peaks from 7 pm to 3 am. The number of insects migrated crossing the Bohai Bay reached 40 million in the evening and the total mass Similar to 4th September, the insects migration peak was also between 7 pm and 3 am, with the peak number of insects across the Bohai Bay over 22 million, and the total mass over 3 tons.

Conclusion
Based on the theoretical derivation and analysis of weather radar biological detection, this paper analyses the biological quantitative methods of weather radar observations in the case of non-uniform beam filling. In the case of armyworm outbreak migration in the fall of 2012, typical date observations were verified. The results show that this method can estimate the number of migratory insects, total mass, and migration intensity over time.

Acknowledgments
This work was supported by the National Natural Science Foundation of China under Grant no. 31727901.