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Abstract
Acquisition of entomological data with high-frequency lidar is an emerging research field in rapid development. The technique offers very high numbers of observations per time unit, suitable for statistical models. In this work, we use a near-infrared Scheimpflug lidar with a sampling frequency of 3.5 kHz to assess the activity of free flying organisms. In-situ measurements were done during the rainy season in Ivory Coast, and hierarchical cluster analysis was used to quantify the amount of unique modulation signatures. Here we propose a method to estimate the number of observed species within a certain air volume for a given time span. This paves the way for rapid in-situ biodiversity assessment in accordance with recent priorities for protection of pollinator diversity during global changes.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Apart from daily and seasonal dynamics, weather and climate phenomena are known to influence insect populations, behavior and activity [1,2]. As a result of these dynamics, it is challenging to obtain a representative inventory of the insect population [3]. Moreover, inaccurate abundance estimates cause an excessive use of pesticides which is harmful to the ecosystems. Insecticides and in particular neonicotinoid-based pesticides have been shown [4–6] to reduce biodiversity of natural pollinators with implications for the pollination of a long list of crops. Insecticides could also affect other beneficial insects and biomarkers of climate change [7,8]. For minimal and strategic use of pesticides in agricultural plantations, and for the purpose of estimating the impact of pesticides and climate change on the insect biodiversity, it is important to develop instrumentation and statistical methods to provide rapid assessment of insect diversity in-situ. One of the major challenges is to assess and control insect activity and population dynamics in agricultural plantations. Current entomological trapping methods to acquire insect samples are time-consuming [9]. To overcome this shortcoming, different technologies have been developed for insect monitoring, such as entomological radar [10] and lidar [11,12]. Low-cost instrumentation based on passive remote sensing spectroscopy have also been developed [13–15]. Recently, the Scheimpflug lidar technique [16] was developed to investigate aerofauna. In this work, we used a Scheimpflug lidar system with multivariate analysis methods to classify insects by their wing-beat modulation and evaluate their numbers.
2. Material and methods
2.1 Site, instrumentation and data acquisition
We used an entomological Scheimpflug lidar of similar configuration as in previous reports [17–20]. The instrument used in this study was placed in the laboratory, second floor at 6°56’26.4’’N 5°13’28.7’’ W, see Fig. 1. A refractive telescope (f = 500 mm, ø102 mm) was used to expand the light transmitted by a 3.2 W multimode laser diode with a center wavelength of 808 nm. The beam was transmitted across the landscape and terminated on a board covered with black neoprene foam (1.8% diffuse reflectance at 808 nm). At the termination, the laser spot was 20 cm wide and 1 cm high. The board was fixed at a height of 6 m to a tree located 514 m from the lidar system (6°53’30.1’’N 5°13’13.4’’W). Backscattered light was collected with a Newtonian telescope (f = 800 mm, ø200 mm) and focused onto a CMOS line sensor with 2048 pixels (14 × 200 µm2 pixel size) and a 16-bit dynamic span. An RG780 absorption filter and a 3 nm FWHM band pass filter centered at 808 nm was used to suppress background light. The receiving and expanding telescopes were mounted with a separation distance of 814 mm on a baseline attached to a tripod. The CMOS sensor was tilted at an angle of 45° relative to the optical axis of the receiver telescope. The laser diode and the CMOS sensor were connected to a combined time multiplexer and laser driver. This module allowed the laser to be transmitted either in modulated mode or in continuous mode. In modulated mode, a strobe signal was sent from the detector to a multiplexer which alternately switched the laser on and off for odd and even sensor line exposures. The sensor line rate was 3.5 kHz, implying that the background signal and the backscattered signal were sampled at 1.75 kHz each, enabling online background subtraction. The laser beam and the linear camera were aligned on the black neoprene sheet. The use of the black termination prevented detector saturation and minimized stray light from interfering with the monitored air transect. The acquired data was stored in files spanning 10 seconds, each containing 35000 lines exposures.
Fig. 1. (a) Aerial photograph of the measurement location. Light is transmitted from the lidar on second floor of a building, 6 m above ground, and terminated in a neoprene target mounted in a tree 514 m from the lidar system. (b) Photograph of the Scheimpflug lidar and its components. The line sensor in the Newtonian receiver is tilted 45° off the optical axis to fulfill the Scheimpflug criterion and achieve infinite focal depth. (c) Near infrared photograph through the monitor telescope. The termination- and atmospheric trace of the invisible beam is displayed. The vegetation background is bright in the near infrared wavelength regime.
2.2 Event extraction and calibration
An algorithm was used to extract insect signals from the raw data files [21]. In the first step, the background signal, Ioff (r, t), was identified through linear interpolation of the time slots when the laser was turned off. Ioff (r, t) was subtracted from the backscattered signal Ion (r, t), yielding a 2D time-range intensity map, I(r, t). The lidar sensitivity varies with range, and therefore a range-dependent intensity threshold for finding signals corresponding to insect observations was set according to Eq. (1). The threshold was based on the static median signal from the air, Imedian(r), and the interquartile range, IIQR(r), of the signal in each range pixel in a data file. The IQR has units of intensity counts and reflects the symmetric Gaussian read-out noise amplitude (3.5 IQR = 1 noise amplitude). In this study, we chose to consider observations deviating from static signal by at least a factor of Trsh = 5 IQRs, alternatively a minimum 1.43 signal-to-noise ratio (SNR).
Intensities exceeding the threshold were extracted and further evaluated as insect observations (Fig. 2). The distance or range to an insect, r, was obtained by Eq. (2), derived from the geometrical design of the instrument and the constraints of the Scheimpflug condition and the Hinge rule [17]. The Scheimpflug lidar principle is illustrated in Fig. 3.
Fig. 2. Statistical representation of a ten second data file. For every range pixel the temporal minimum, median, maximum and resulting detection threshold is shown. The median value is insensitive to short and high-intensity occurrences such as insects flying through the beam, and represents the reflectance of the air between the lidar system and the termination. The signal spikes exceeding the threshold are interpreted as insects flying through the beam, and further evaluated.
Fig. 3. Illustration of the Scheimpflug principle. Despite the large aperture, a sharply focused image along the entire laser beam can be obtained when the lens plane is tilted and intersects with the object plane and the image plane of the sensor. The sensor is tilted with an angle θ=45° relative to the lens plane. The separation distance between transmitter and receiver is L = 814 mm and the swing angle of the lens is φ≈1°.
Fig. 4. (a) Time-range map of a presumed male Anopheline mosquito observed moving through the lidar transect after sunset. (b) Optical Cross Section (OCS) time series of the observed insect, obtained by integrating the intensities in (a). The oscillatory component arises from light reflected in the insect wings, and the non-oscillatory contribution comes from the body. The transit time, Δt, corresponds to the time the insect spent in the laser beam. This particular insect flapped its wings with a wing-beat frequency f0 = 679 Hz.
The known distance and reflectance of the black termination was used to calibrate the backscatter optical cross section of insects (Fig. 4), σinsect, according to Eq. (3). For more information, see [22]. A total of 11965 insect observations were found in the raw data and parameterized.
PJ Pixel position from the optical axis on the sensor plane (m)
J Pixel index (#)
f Receiver focal length (m)
L Separation distance between the receiver and the transmitter (m)
θ Sensor tilt angle (°)
φ Swing angle (°)
σterm Known optical cross section of the black neoprene termination target (mm2)
Iinsect Insect signal (16 bit)
Istatic Static signal from homogeneous atmosphere (16 bit)
rinsect Detection distance of the observed insect (m)
rterm Termination distance of the beam (m)
2.3 Modulation spectra, unsupervised clustering and classification processing
The transit time, Δt, i.e. the amount of time each observed insect remained in the probe volume, was obtained. A threshold was set to include observations with 23 ms transit times or longer. This corresponded to signals with at least 40 times samples and included 80% of the observations. A frequency vector with 40 bins was defined, evenly spaced between the lowest observable frequency during a 23 ms transit (43 Hz) and the highest observable frequency defined by the Nyquist frequency (875 Hz). The modulation power in these frequency bins was calculated and auto-normalized for all observations using Welch’s method [23,24], see selected examples in Fig. 5.
Fig. 5. Optical cross sections and modulation power of free flying insects. (ace) Examples of time series obtained from insects flying through the laser beam. Peaks correspond to specular reflexes in the insect wing membranes and appear periodically due to the insects flapping their wings. (bde) Power spectra of the time series in ace, with the modulation power calculated at 40 frequencies bins. Insects species were sorted according to the similarity of the modulation spectra using hierarchical clustering. To classify the 11965 observations, the Euclidean distance between combinations of observations in the 40-dimensional parameter space of auto-normalized and logarithmized modulation power was calculated.
An important step in cluster analysis is evaluating the appropriate number of clusters. Many decision criteria have been devised based on knowledge of the data structure and partitioning [25–28]. In the present study, the number of clusters was evaluated using an efficient knee point detection method [29], called the L-method. The L-method was applied to the Euclidean merging distances, y, between the pairs of the most distinct auto-normalized and logarithmized modulation power spectra in the clusters (Fig. 6). Each point was presumed to be a possible knee. A pair of linear fits, $\hat{y}$, to the left and right of each possible knee point was created (Fig. 6(a)). The root-mean-square error to the left and right of each knee point, rmseL and rmseR, were calculated according to equation Eq. (4). The linear pair that minimized the total root-mean-square error, RMSET, (Eq. (5)) was selected [30,31], corresponding to the appropriate number of clusters (α). The maximum number of clusters (β) was set to 100.
Fig. 6. (a) Merge distance as a function of number of clusters. This graph shows a decision boundary of the number of appropriate clusters. The maximum number of clusters was arbitrarily set to 100. (b) The best number of clusters is given by the minimum value of the total RMSET. In this study the number of appropriate clusters was 12.
After selecting the number of clusters, the calculated power spectra of all observed insects were sorted into 12 groups based on similarity of their modulation spectra using hierarchical clustering. The 12 groups are displayed in Fig. 7.
Fig. 7. Dendrogram of the 12 clusters, showing the resemblance between them. For example, clusters C8 and C9 are most similar because the height of the link that joins them is the smallest. The size of the colored circles reflects the number of observations assigned to each cluster.
Figure 8 displays the 12 centroid spectra of the dendrogram branches presented in Fig. 7. Centroids of the power spectra and insect size distributions were obtained for each cluster, and the wing beat frequency (WBF) of each centroid is also indicated when applicable. The WBF is not clearly discernable in clusters C7-C12. These clusters may correspond to larger organisms with WBFs below the lowest observable frequency (43 Hz), which is limited by insect transit times. The apparent uneven spacing between tones in C3 and C5 are due to frequency folding in the Nyquist frequency (875 Hz). This is a sampling artifact which would not appear if the sample rate was higher. Folded tones can be superimposed on top of lower tones, or in some cases appear in the reverse order.
Fig. 8. Centroid spectra of the 12 clusters. The average body cross section of the clustered insects is indicated by BS in all subfigures. N denotes the number of observed insects in each cluster. Diamonds indicate the fundamental tones in each centroid power spectrum. This can give clues on the insect species identity. For example, in cluster C3 and C5, the fundamental tones are respectively 330 Hz and 433 Hz, and are presumably female mosquitoes. The second harmonics are indicated by the plus sign and the third harmonics by crosses. The gray lines indicate the within-group interquartile range.
The activity level in time and space of all clusters is shown in Fig. 9. Though most clusters exhibit peak activity in relation to sunset (∼18:50 local time), distinct patterns can be observed for several clusters.
Fig. 9. 2D time-range histograms of insect cluster activity during the evening. The time scale is the same for the subfigures associated to each cluster. Sunset activity of insects is seen along the probe volume of the beam.
3. Conclusion
We have demonstrated a method of unsupervised classification of insect lidar targets in-situ. During a limited time interval, we were able to evaluate the number of unique modulation signatures in the data set. We used the L-method, or knee test, to estimate the appropriate number of insect classes. Although simplistic, the knee-test is a relatively well-known method, and we consider this an important first step towards developing an in-situ method for insect diversity assessment. For the testing time of 3 hours we counted 11965 insects in a probe volume of approximately 2 m3. The L-method knee test estimated 12 unique modulation signatures. We expect the actual number of insect species present in the probe volume to be much higher than 12, which could be evaluated with traps or truck-mounted sweep-net drives in future studies. Other information criteria than the L-method may yield a different number of clusters. However, we do expect such numbers to reflect the diversity of insect species. This test demonstrates the possibility to assess the number of unique insect species in-situ, and therefore paves the way for a rapid objective metric of biodiversity without the biases and demanding assessment by a broad range of insect traps. The properties of the insect clusters, such as the optical cross section and wing-beat frequency with associated overtone spectra provide clues on the species identity of the counted groups. Topographic preferences in detection distance and time preferences of different clusters may provide enough information for qualified species estimation based on known behavior and information on prevalent species in the area. Information on timing and location of insects may also be used improve strategic pest management and thus contribute to pollinator survival.
Funding
Uppsala Universitet; Vetenskapsrådet.
Acknowledgments
The authors would like to thank Elin Malmqvist and Alexandra Andersson from Lund University for technical assistance in Yamoussoukro, Ivory Coast. We also extend our thanks all the members of the laboratory in Ivory Coast for their assistance.
Disclosures
The authors declare no conflicts of interest.
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