As the ecological importance of gelatinous organisms becomes increasingly appreciated, so has the need for improved knowledge of their abundance and distribution. Acoustic backscattering measurements are routine for fisheries assessments but are not yet widely used to survey populations of gelatinous zooplankton. The use of acoustic backscattering techniques to understand the distribution and abundance of organisms requires an understanding of their target strength (TS). This study presents a framework for a sound scattering model for jellyfish based on the Distorted Wave Born Approximation that incorporates size, shape, and material properties of individual organisms. This model, with a full three-dimensional shape rendition, is applied to a common species of scyphomedusa (Chrysaora chesapeakei) and verified experimentally with broadband (52–90 and 93–161 kHz) laboratory TS measurements of live individuals. Cyclical changes in the organism's shape due to swimming kinematics were examined, as well as averages over swimming position and comparisons with scattering from simpler shapes. The model predicts overall backscattering levels and broad spectral behavior within <2 dB. Measured TS exhibits greater variability than is predicted by scaling the size of the organism in the scattering model, showing that density and sound speed vary among individuals.

Jellyfish populations and bloom occurrences have been observed to increase globally over the past several decades (Brotz , 2012; Duarte , 2013; Mills, 2001). This increase could be due in part to extra habitat for benthic jellyfish polyps associated with artificial structures in coastal areas (Duarte , 2013). It could also be due to other seasonal and anthropogenic factors that permit jellyfish to flourish in environments where other pelagic species are unable to sustain their populations (Richardson , 2009, and references therein), including overfished ecosystems (Lynam , 2006). However, there is little evidence to support claims that jellyfish blooms are exacerbated by anthropogenic stressors (Pitt , 2018), indicating a need to better understand and monitor their populations. Jellyfish abundance and biomass could be an indicator of ecosystem health and productivity, especially as their role in marine ecosystems as both predator and prey is becoming better understood (Pauly , 2009), as well as their impact on human activities like tourism, aquaculture, and power plant operations (Baliarsingh , 2020; Clinton , 2021; Zi , 2020).

While estimates of jellyfish biomass and distribution would permit a better understanding of their population dynamics, they are challenging to survey by traditional methods as their gelatinous bodies are either easily damaged by sampling nets or occur in such high abundance that they clog and burst the nets (Brierley , 2001). Optical sensing and aerial surveys provide other means for studying jellyfish in situ; however, the high attenuation of light in water permits a relatively small sampling volume, rendering optical methods inefficient and relatively uncertain for large-scale abundance estimates (Båmstedt , 2003; Graham , 2003; Houghton , 2006). Acoustic surveys provide a means of surveying jellyfish on a larger scale and have been used in multiple studies, in conjunction with other sampling methods such as trawls and video footage, to enumerate jellyfish and characterize their distributions (Alvarez Colombo , 2008; Båmstedt , 2003; Brierley , 2001; Graham , 2010; Kim , 2016; Yoon , 2019; Zi , 2020).

This investigation focused on modeling the acoustic target strength (TS) of a medusoid jellyfish (Cnidaria: Scyphozoa) and verifying the TS with controlled, broadband laboratory measurements. TS is a complex function of size, morphology, orientation, and material properties (i.e., the density and sound speed of an organism's tissue; see Stanton , 1994). Jellies are acoustically classified as fluid-like, weakly scattering organisms (Stanton, 1996), so the Distorted Wave Born Approximation (DWBA) was used to formulate the scattering model. An approximate three-dimensional (3-D) medusa shape was developed and digitized to calculate a medusa's predicted target strength. To reflect the diversity of different species of medusae as well as swimming-related cyclical changes in shape, the parameters of the model can be tuned to reflect various morphologies and material properties. This study presents data and modeling results obtained for live individuals of a species of sea nettle, Chrysaora chesapeakei, representing a common morphology of medusa.

A known TS for medusae is crucial for making accurate abundance estimates from measurements of volume scattering. Most acoustic studies on jellies have focused on measuring TS at multiple narrowband frequencies commonplace for fisheries applications. A broadly used method of measuring medusa TS is by analyzing in situ backscattering measurements, by detecting single targets (Alvarez Colombo , 2008; Brierley , 2004; Cimino , 2018; De Robertis and Taylor, 2014; Kim , 2016; Yoon , 2012) and/or by a combination of echo integration and trawls/video to obtain a relationship between echo intensity and numerical density (Båmstedt , 2003; Brierley , 2001). A handful of studies have obtained ex situ TS measurements in either a controlled laboratory setting or a semi-controlled open water enclosure (Hirose , 2005, 2009; Kang , 2014; Monger , 1998; Mutlu, 1996; Yoon , 2015; Yoon , 2010). Cyclical oscillations in TS of magnitudes up to 15 dB have been observed due to a medusa's swimming pulsations (Brierley , 2004); however, the use of narrowband signals limits the amount of information available related to variations in size and shape.

TS is determined by multiple animal parameters, so an accurate medusa scattering model is essential to verify and give predictive power to measurements. Few studies have attempted to model backscattering from medusae. The first medusa scattering model was developed by Monger (1998) and used a ray-based approximation to predict backscattering at broadside incidence. Their ellipsoid-based model shape was later reformulated into a DWBA-based model (Graham , 2010). Other studies employing DWBA-based scattering models utilized the outer shape of the medusa's bell, obtained from side-angle images, and assuming radial symmetry (Lee and Hwang, 2009; Shin , 2019; Yoon , 2019).

Acoustic scattering models based on simple shapes are useful for predicting the TS of biological organisms; however, oversimplification results in inaccuracies. Balancing ease of use and accuracy are the primary drivers for these physics-based scattering models. In this paper, we approximate the medusa shape with two partial spherical caps to construct the oral and aboral surfaces of the bell and vary the width-height aspect ratio to predict changes in TS from swimming pulsations. Much of the physics can be captured by accurately representing the outer boundaries of the organism, assuming small internal inhomogeneities are insignificant contributors to scattering.

Broadband techniques have been widely used for both laboratory and field measurements of organisms (Jones , 2009; Lavery , 2002; Lavery , 2010; Stanton, 1996). Previous work employing broadband signals to detect jellies took place in a laboratory setting and utilized a frequency band centered at 1 MHz (Vasile , 2016), a much shorter wavelength with higher attenuation than what is practical for field deployments. This study presents broadband backscattering measurements of individual medusae collected with a system suitable for field operations and frequency range used commonly for fisheries (52–161 kHz) and compares them with model predictions.

The echosounders used to collect TS measurements consisted of two Kongsberg Simrad split-beam, broadband, transducers (ES70-7CD and ES120-7CD), a Simrad Wide Band Transceiver (WBT) Tube (Simrad, Egersund, Norway), and a data acquisition laptop running Windows 10 with the Simrad EK80 software application (Simrad, Egersund, Norway) for data acquisition. The split-beam transducers allowed for the localization of a target in the beam and the correction of off-axis beam parameters as appropriate. A video camera (Sony SNC-VB770 with Sony SEL35F28Z lens, Sony, Tokyo, Japan) was mounted in a pressure housing adjacent to the transducers to collect coincident video and still images of the jellies. The Simrad EK80 data acquisition software for acoustic data and VLC media player for video footage collection were run simultaneously on the single data acquisition laptop to ensure that time was synced between the video and acoustics. A custom acoustical-optical data mounting platform was designed using an existing stainless steel frame (Lavery , 2010) and a laser-cut polyvinyl chloride (PVC) baseplate, where the two broadband transducers were mounted in a downward-looking orientation. The Simrad WBT Tube was attached vertically to the frame. The video camera and Tube were powered by the same power supply.

Experimental trials were conducted in August–September 2021 in a cylindrical test tank about 3 m wide and 3 m deep. The tank was filled with filtered seawater, and the temperature and salinity were measured to determine the sound speed of water in the tank. The data acquisition system was lowered into the tank via an overhead crane system.

A laboratory calibration was performed in August 2021. The echosounders were calibrated in the tank using a spherical, 38.1-mm-diameter, tungsten carbide with 6% cobalt standard target, which was tethered on a fishing line approximately 2.5 m below the transducers. The EK80 standard calibration software was used to collect data in all four sectors and the center of each split-beam transducer. Calibration curves for both transducers were calculated from the matched filter (MF) output following the method of Lavery (2017), and it was determined that the ES70 had a usable frequency band of 52–90 kHz and the ES120 had a usable band of 93–161 kHz.1 A consistent set of operational parameters for the echo sounders was used for the entire duration of this study (Table I). A calibration for the video camera was unnecessary and thus not performed.

TABLE I.

Operational parameters for the echosounders used in this study.

ES70-7CD ES120-7CD
Pulse duration (ms)  0.512  0.512 
Decimated sampling frequency (ms)  0.016  0.008 
Start frequency (kHz)  45  90 
End frequency (kHz)  90  170 
Power (W)  500  400 
Ping rate (Hz)  10  10 
ES70-7CD ES120-7CD
Pulse duration (ms)  0.512  0.512 
Decimated sampling frequency (ms)  0.016  0.008 
Start frequency (kHz)  45  90 
End frequency (kHz)  90  170 
Power (W)  500  400 
Ping rate (Hz)  10  10 

Experimental measurements of live medusae were performed in August–September 2021. Nine sea nettles (each referred to as “Jelly #”) were collected locally in Woods Hole, MA (41° 31′ 26.136″ N, 70° 40′ 15.821″ W). Buckets were used to scoop the medusae from beside a dock or from a boat. Because different species co-occur and identification is challenging (Bayha , 2017), we conducted DNA barcoding to confirm the identity of our specimens as Chrysaora chesapeakei.1 The medusae were stored in buckets of seawater for up to 2 days in the lab, though acoustical measurements were taken either the same day the medusae were collected or the following day. Care was taken throughout the experiment to keep them fully submerged in seawater until after TS measurements were collected to avoid trapping air bubbles, which can contaminate scattering measurements with their high acoustic impedance.

The medusae were too buoyant and motile to allow for free swimming measurements to be taken, so they were tethered in place, and measurements were collected on just one individual at a time while fixed near the center of each transducer beam. The tether consisted of a piece of fishing line, which was strung on a needle and threaded through the central oral-aboral axis of the medusa. A steel shackle was tied to the end of the line to weigh it down such that the medusa would be oriented aboral (bell top) side up. The aboral end of the line was tied to the bottom of a ∼2-m long loop of fishing line attached to the data acquisition system. Another piece of fishing line was tied to each side of the loop and was pulled and anchored to opposite sides of the tank, creating a wide “V” shape that acted as a barrier for the medusa as it pulsed upward (Fig. 1). This configuration of fishing lines and shackle allowed the medusa to remain stationary while pulsing and did not appear to affect its movements (Mm. 1), and the two side-anchor lines were used to manipulate the position of the medusa. A 2 × 2 piece of black PVC was placed on the bottom of the tank as a background for the medusa to enhance visibility in the video footage. Acoustic TS measurements were collected using the single target detection tool in EK80 to verify that the medusa was located within around 2.5 degrees of the center of the beam. Corresponding down-looking video footage was collected simultaneously. Measurements were collected continuously for ∼10 min per transducer while the medusa was pulsing at a rate of ∼0.6 Hz (verified from video footage) to ensure that a sufficient number of echoes were recorded for the different flexion states of the animal.

FIG. 1.

Schematic of experimental setup. The video camera and WBT Tube are connected to a power supply and the data acquisition laptop is located on a nearby lab bench. A medusa was tethered on a single strand of monofilament line, which was weighed down by a shackle. The line containing the medusa was tied to the bottom of a loop of line, which was tied to the data acquisition system. An additional piece of line was tied to each side of the loop and pulled and anchored to the sides of the tank to create a wide “V” that stopped the medusa from moving upward as it pulsed. The anchored lines were repositioned as necessary around the tank to center the medusa under each transducer. A rectangular sheet of opaque black PVC was placed at the bottom of the tank to serve as a high-contrast background for video footage.

FIG. 1.

Schematic of experimental setup. The video camera and WBT Tube are connected to a power supply and the data acquisition laptop is located on a nearby lab bench. A medusa was tethered on a single strand of monofilament line, which was weighed down by a shackle. The line containing the medusa was tied to the bottom of a loop of line, which was tied to the data acquisition system. An additional piece of line was tied to each side of the loop and pulled and anchored to the sides of the tank to create a wide “V” that stopped the medusa from moving upward as it pulsed. The anchored lines were repositioned as necessary around the tank to center the medusa under each transducer. A rectangular sheet of opaque black PVC was placed at the bottom of the tank to serve as a high-contrast background for video footage.

Close modal
Mm. 1.

Example footage of a tethered, pulsing medusa in the test tank. This is a file of type “mp4” (18.6 Mb).

Mm. 1.

Example footage of a tethered, pulsing medusa in the test tank. This is a file of type “mp4” (18.6 Mb).

Close modal

The fineness ratio (ratio of bell height to bell diameter) was used to determine the relative dimensions of the medusa scattering model shape and was assumed to be consistent across all individual C. chesapeakei. A handheld GoPro was used to film a single medusa swimming, and frames where the organism was in its fully expanded and fully contracted positions were then imported to a photogrammetry software (ImageJ) and used to measure the diameter of the base of the bell and the height from the base to top of the bell for both swimming positions. This process was performed over a couple of swimming cycles and the average fineness ratios for each position were used to create the expanded and contracted medusa model shapes.

Size and material property measurements of the captured medusae were collected after acoustical measurements (Table II). For Jellies #4–#9, after acoustical measurements were collected, each medusa was removed from its tether, placed on a flat surface so its bell was fully expanded, and photographed next to a measuring tape. The photographs were imported to ImageJ and, because most of the individuals had an oval shape, the effective diameter was determined by averaging the major and minor axis lengths. The medusae were then transferred to the lab, where they were scooped out of their buckets with a soup ladle and drained of excess water, then placed flat in a clear container where they were photographed from the side with a ruler for scale. The images were imported to ImageJ and the bell thickness was measured digitally. The organisms were then weighed on a digital balance and transferred to a graduated cylinder to measure their volume, from which their tissue density was calculated. For Jellies #1–#3, bell thickness was estimated using the best fit curve for thickness vs diameter measured for Jellies #6–#9.

TABLE II.

Size and material property parameters obtained for live jellies used in this study. The term “ka” refers to the product of the product of the insonifying wavenumber, k, and the medusa's effective radius, a.

Jelly # Diameter (cm) Thickness (cm) Frequency where ka = 1 (kHz) g h a
11.6  1.7b  4.2  —  1.026 
11.7  1.8b  4.2  —  1.007 
14.1  1.3  3.5  1.045  1.031 
9.7  1.8  5.0  0.861  1.009 
11.8  2.2  4.1  1.016  1.007 
9.9  1.9  4.9  1.001  1.004 
11.9  1.7  4.1  1.156  1.007 
Jelly # Diameter (cm) Thickness (cm) Frequency where ka = 1 (kHz) g h a
11.6  1.7b  4.2  —  1.026 
11.7  1.8b  4.2  —  1.007 
14.1  1.3  3.5  1.045  1.031 
9.7  1.8  5.0  0.861  1.009 
11.8  2.2  4.1  1.016  1.007 
9.9  1.9  4.9  1.001  1.004 
11.9  1.7  4.1  1.156  1.007 
a

Estimated by minimizing the sum of squares of the residuals between the measured and predicted TS over a range of values of h for other species of scyphomedusae (Table III).

b

Estimated value using thickness vs diameter best fit curve of other jellies.

A small clipping of tissue was taken for DNA barcoding,1 and the medusae were then archived in a –80 °C freezer. Out of the nine individuals caught and measured, only seven were used in the analyses presented because Jelly #2 was damaged and Jelly #5 was contaminated with an air bubble under its bell during the acoustic measurements.

Raw voltage data from the transducers were pulse compressed (Lavery , 2010) and output as calibrated echograms. The pulse compressed data were averaged ping-by-ping over a 0.5-m interval containing the echo from the medusa and plotted as a function of time so that cyclical variations in TS were visible [Fig. 2(b)]. It was determined by cross-referencing time stamps in the acoustic data with video footage that peaks in the TS corresponded to the medusa's expanded position; smaller peaks (“subpeaks”) were assumed to correlate with the contracted position [Fig. 2(a)]. Peaks and subpeaks across ∼500 pings per individual were identified and converted to frequency spectra via the Fast Fourier Transform (FFT) of the corresponding pulse-compressed pings [Fig. 2(c)]. FFT window lengths varied from 0.1 to 0.6 m depending on the duration of the medusa's echo in each frequency band, the timing of echoes from the sides of the tank, and the distance from the shackle weight below. For the expanded and contracted swimming positions, the calculated spectra, TS(f), were averaged in linear space to obtain a mean measured spectrum for comparison to model results.

FIG. 2.

(a) Calibrated MF output of echoes from Jelly #6 in the expanded and contracted bell positions at 70 kHz. (b) Time series of averaged backscattering strength for Jelly #6, averaged from 1.5–2 m range in log space to aid in peak finding by enhancing differences between expanded and contracted positions. “Peaks” where the medusa's bell was expanded, and “Subpeaks” where the bell was contracted, are indicated with black and gray dots, respectively. (c) TS(f) spectra for the 52–90 kHz band for the expanded and contracted bell position, calculated from individual pings corresponding to the “Peaks” and “Subpeaks” identified in (b).

FIG. 2.

(a) Calibrated MF output of echoes from Jelly #6 in the expanded and contracted bell positions at 70 kHz. (b) Time series of averaged backscattering strength for Jelly #6, averaged from 1.5–2 m range in log space to aid in peak finding by enhancing differences between expanded and contracted positions. “Peaks” where the medusa's bell was expanded, and “Subpeaks” where the bell was contracted, are indicated with black and gray dots, respectively. (c) TS(f) spectra for the 52–90 kHz band for the expanded and contracted bell position, calculated from individual pings corresponding to the “Peaks” and “Subpeaks” identified in (b).

Close modal
The scattering amplitude of an organism is a complex function of its size, shape, orientation, and material properties (density, ρ, and sound speed, c), as well as the incident wavelength. In cases where the organism's material properties are close to those of the surrounding medium, its scattering in the far field can be modeled using the Born approximation (Morse and Ingard, 1986). For the backscattering case (i.e., the present study), scattered energy is represented by the backscattering amplitude, f b s, given by
f b s = k 1 2 4 π V ( γ κ γ ρ ) e 2 i k 2 i · r d V ,
(1)
where V is the volume of the organism's body k 1 is the acoustic wavenumber of the incident wave ( k = 2 π / λ, where λ is the incident wavelength), k 2 i is the incident wave vector evaluated inside the volume, and r is the position vector for any volume element d V . The material properties of the organism are reflected in the terms γ κ = ( κ 2 κ 1 ) / κ 1 = ( 1 g h 2 / ) g h 2 and γ ρ = ( ρ 2 ρ 1 ) / ρ 2 = ( 1 g ) / g, where κ 1 = 1 / ( ρ 1 c 1 2 ) and κ 2 = 1 / ( ρ 2 c 2 2 ) are the compressibility of the surrounding medium's and organism's body, respectively; g = ρ 2 / ρ 1 and h = c 2 / c 1 are the density and sound speed contrasts. The material properties of the medusae in this study were assumed to be uniform, so these terms are constants and factored out of the integral. The evaluation of the volume integral over the wavenumber inside the organism ( k 2 i rather than k 1 i) is a modification of the Born Approximation referred to as the DWBA (Stanton , 1998).
Throughout this work, the far-field backscattered energy is expressed as the TS, given by
TS = 10 log f b s 2 ,
(2)
which has units of decibels (dB) relative to 1 m2 (Urick, 1983). To compare scattering from multiple individuals, assuming similar morphologies and proportions, the TS was normalized by the unit area of the medusa's bell and thus expressed by the reduced target strength (RTS), given by
RTS = 10 log f b s 2 π a 2 = 10 log f b s 2 10 log π a 2 .
(3)
The RTS is plotted against the product of the acoustic wavenumber and bell radius, “ka,” a dimensionless quantity representing the ratio of the characteristic size of an organism to the insonifying wavelength. The presentation of RTS as a function of ka allows for a direct comparison of physical scattering processes irrespective of the actual target size or frequency used.
As part of the development of a novel scattering model shape to represent a medusa, DWBA models for simpler shapes were considered to determine what geometrical aspects would be important to the overall scattering behavior of the medusa. For shapes with certain symmetries, Eq. (1) may be evaluated analytically or semi-analytically assuming homogeneous material properties and following the approach of Stanton and Chu (2000) to obtain an exact solution. Variations of weakly scattering spheres and finite cylinders were considered, as their solutions have been used as benchmarks for other scattering models for organisms (Jech , 2015). Evaluating Eq. (1) over a spherical geometry yields the closed-form backscattering amplitude of a fluid sphere,
f b s , sphere = 1 8 k 1 γ κ γ ρ * [ 2 k 2 i a cos 2 k 2 i a + sin 2 k 2 i a ] .
(4)
A hemisphere consisting of one rounded face and one flat face was also derived. Evaluating Eq. (1) over half a sphere with an incident insonifying wave normal to the flat face of the hemisphere leads to the closed-form backscattering amplitude,
f b s , hemisphere = k 1 4 i γ κ γ ρ * a 2 2 + 1 4 k 2 i 2 + e i 2 k 2 i a a i 2 k 2 i 1 4 k 2 i 2 .
(5)
Finally, a thick disk or “puck” shape with two flat faces was considered. The puck is treated mathematically as an axially symmetric cylinder, so the result obtained by Stanton (1998) was simplified for an end-on incident insonifying wave to obtain the backscattering amplitude,
f b s , puck = k 1 a 4 ( γ κ γ ρ ) L / 2 L / 2 e i 2 k 2 i l d l ,
(6)
where the integral is evaluated computationally over the length of the cylinder, L. Comparisons between these three scattering models and the medusa model developed in this paper are discussed in the following section.

Certain symmetries (e.g., sphere, cylinder) give rise to a closed-form or reduced dimensionality integral expression for the DWBA formulation of f b s. These analytical or semi-analytical solutions are convenient when it is reasonable to approximate the geometry of the organism with a simpler shape (e.g., Stanton , 1998). One must be cautious when making shape approximations, as over-approximating the shape of an organism could result in a loss of important scattering physics characteristics of that organism. For our target jellyfish species C. chesapeakei, an approximate medusa shape was created by stacking two partial spherical caps with different curvature, resulting in a radially symmetric volume with two interfaces [Fig. 3(a)]. The curvature of the faces was adjusted depending on the swimming position while conserving total volume. Scattering from the oral arms and tentacles was assumed to be negligible at the frequencies used in this study, so these appendages were not included in the model shape.

FIG. 3.

(a) Scattering geometry used in the medusa scattering model. The z ̂ axis runs through the center of the bell. The bell is radially symmetric in the x ̂ y ̂ ( ϕ) plane and the circular curves outline a two-dimensional cross section in a constant ϕ plane. Broadside incidence corresponds to θ = 0 °, β = 90 °, and β = 270 °. (b) Size parameters for expanded (upper) and contracted (lower) bell positions. Each arc forming the top/bottom (aboral/oral) face of the bell is a spherical cap.

FIG. 3.

(a) Scattering geometry used in the medusa scattering model. The z ̂ axis runs through the center of the bell. The bell is radially symmetric in the x ̂ y ̂ ( ϕ) plane and the circular curves outline a two-dimensional cross section in a constant ϕ plane. Broadside incidence corresponds to θ = 0 °, β = 90 °, and β = 270 °. (b) Size parameters for expanded (upper) and contracted (lower) bell positions. Each arc forming the top/bottom (aboral/oral) face of the bell is a spherical cap.

Close modal

Because it has been observed that medusa TS varies cyclically with its swimming pulsations (Brierley , 2004), the shape of the model was tuned to reflect the width/height ( W / H top) ratio, or fineness ratio, of the medusa's bell [Fig. 3(b)]. The mean fineness ratios for C. chesapeakei in its fully expanded and fully contracted positions (3.012 and 1.705, respectively) were obtained from side-angle video footage of a single individual swimming in the test tank, as well as the ratio of widths between the expanded and contracted positions ( W e / W c = 1.303, obtained from video footage). All individuals of the same species were assumed to exhibit the same fineness ratios.

The subscript “e” and superscript “(e)” refer to the medusa's fully expanded position, while “c” and “(c)” refer to the contracted position. For this study, the medusa's expanded bell diameter, W e, and bell thickness, t e, were measured directly, and the expanded fineness ratio and geometry of the shape were then used to estimate the heights of the top and bottom faces of the stacked spherical caps, H top ( e ) and H bot e. From these values, the radius of curvature for each face was calculated and used to obtain the volume of the bell. The bell volume, contracted fineness ratio, and W e / W c ratio were then used to calculate the remaining size parameters for its fully contracted position (see the  Appendix). For each swimming position, a numerically integrable 3-D model was constructed in matlab1 as a 3-D binary matrix with a pixel size of W e / 200, which could then be implemented in Eq. (1) to compute f b s.

Following the approach of Lavery (2002) for predicting backscattering from krill, and because the live medusa TS measurements were averaged across multiple pings over multiple swimming cycles, the medusa scattering model was averaged over a normal distribution of bell thickness with the mean equal to the bell thickness measured from images and standard deviation set at 16% of the measured thickness. This standard deviation was selected after examining the relationship between the measured bell diameter and thickness, and then calculating the standard deviation of the residuals between the thickness predicted by this relationship and the actual measured thickness values.

Density measurements were averaged across Jellies #4–#9 (no density measurements were taken for Jellies #1–#3) to obtain an average value of the density contrast, g, for the scattering model. Measurements of the sound speed inside the medusae were not taken during the present study, so the sound speed contrast, h, was estimated for each individual by calculating the sum of squares of the residuals between the measured TS and predicted TS from a single realization of the scattering model at the measured bell thickness using a range of values of h previously measured for other species of scyphomedusae (Table III). The h value corresponding to the minimum of the sum of squares was obtained from each individual and were averaged to obtain a mean h of 1.013.

TABLE III.

Material properties measured for scyphomedusae.

Species g h Reference
Aurelia aurita  0.9808  1.0005  Kang (2012)   
0.989  1.0001  Hirose (2009)   
Cyanea nozakii  1.073  1.038  Hirose (2009)   
Nemopilema nomurai  1.004  1.0008  Hirose (2009)   
Cyanea capillata  1.009  1.0004  Warren and Smith (2007)   
Chysaora chesapeakei  1.0028a  1.013b  This study 
Species g h Reference
Aurelia aurita  0.9808  1.0005  Kang (2012)   
0.989  1.0001  Hirose (2009)   
Cyanea nozakii  1.073  1.038  Hirose (2009)   
Nemopilema nomurai  1.004  1.0008  Hirose (2009)   
Cyanea capillata  1.009  1.0004  Warren and Smith (2007)   
Chysaora chesapeakei  1.0028a  1.013b  This study 
a

Average.

b

Average estimate.

To examine the potential utility of this medusa scattering model for field-based volume scattering measurements of dense populations of medusae swimming randomly, the model was additionally averaged over a uniform distribution of fineness ratios ranging from fully expanded to fully contracted swimming positions and compared with measured TS across ∼500 consecutive pings per individual. No averages were performed over swimming orientation because it was not a variable in the present study; however, orientation dependence of scattering from medusae should be considered in future work. Following standard practice at the frequencies used in this study, only single scattering was assumed.

Scattering predicted by the stacked spherical cap medusa model is considerably lower than that of the volume-equivalent sphere, hemisphere, and puck (Fig. 4). Scattering from the hemisphere and puck increases with frequency due to the presence of flat faces, which intercept an increasing proportion of incident energy with decreasing wavelength. Curved faces, on the other hand, direct a greater proportion of scattered energy away from the receiver, resulting in relatively flat scattering spectra as exhibited by the sphere and medusa (stacked spherical caps) models.

FIG. 4.

Predicted TS spectra for Jelly #6 for a single realization in both fully expanded and fully contracted swimming positions (expanded case has deep nulls) and an average of predicted TS over a normal distribution of bell thicknesses (mean 1.8 cm, standard deviation 0.29 cm) for both positions. Dashed black curve represents TS predicted over an average of thickness, plus an average over a uniform distribution of swimming positions ranging from fully expanded to fully contracted. TS spectra for a sphere, hemisphere, and puck (thick disk) shape have been averaged over the volume-equivalent size distributions. The thickness of the puck shape is set to equal that of the medusa model and its corresponding radius is obtained from volume conservation.

FIG. 4.

Predicted TS spectra for Jelly #6 for a single realization in both fully expanded and fully contracted swimming positions (expanded case has deep nulls) and an average of predicted TS over a normal distribution of bell thicknesses (mean 1.8 cm, standard deviation 0.29 cm) for both positions. Dashed black curve represents TS predicted over an average of thickness, plus an average over a uniform distribution of swimming positions ranging from fully expanded to fully contracted. TS spectra for a sphere, hemisphere, and puck (thick disk) shape have been averaged over the volume-equivalent size distributions. The thickness of the puck shape is set to equal that of the medusa model and its corresponding radius is obtained from volume conservation.

Close modal

In general, the medusa model predicts stronger scattering from the expanded position than from the contracted position. The TS spectrum peaks at the Rayleigh-geometric scattering transition (∼18–22 kHz) and evens out in the geometric regime apart from null structure. Averaging over bell thickness has the effect of smoothing out some of the null structure in the model output, especially for the medusa's contracted position (Fig. 4). Additionally, averaging over a range of swimming positions further smooths the spectral null structure.

Although orientation dependence was not investigated experimentally in this study, the medusa scattering model predicts that scattering levels are dependent on the angle of incidence and that this relationship changes depending on the medusa's swimming position (Fig. 5). In the expanded position, scattering levels are relatively even up to incident angles ∼18 degrees off broadside and drop off steeply at increasing angles. Scattering from the contracted position is maximized around 40 degrees off broadside and does not drop off at higher angles other than at nulls. Scattering from the expanded position is stronger than the contracted position near broadside, from ∼30–60 degrees off broadside, both swimming positions exhibit similar scattering strengths. Above ∼60 degrees off broadside, the contracted position exhibits stronger scattering.

FIG. 5.

Predicted orientation dependence (TS vs θ) for Jelly #6 over single model realizations (i.e., no averaging) of both its expanded and contracted positions. TS was calculated at 70 and 120 kHz, the nominal center frequencies of the transducers used in the experimental portion of this study.

FIG. 5.

Predicted orientation dependence (TS vs θ) for Jelly #6 over single model realizations (i.e., no averaging) of both its expanded and contracted positions. TS was calculated at 70 and 120 kHz, the nominal center frequencies of the transducers used in the experimental portion of this study.

Close modal

Backscattering from seven individuals was measured in the present study. Despite all individuals being C. chesapeakei, RTS varied among individuals (Fig. 6), likely driven by variability in their material properties. While the density contrast, g, was measured directly in this study, the value of h was inferred from the best fit between the model and data. Average scattering levels predicted and measured in this investigation are well within the range of values in the literature for other species of scyphomedusae (Table III), suggesting that the values of g and h obtained in this study for C. chesapeakei (Table II) are reasonable and consistent with the material properties of other species of a similar body type (Fig. 7). However, there is still a high degree of variability between species and individuals.

FIG. 6.

Comparison between model prediction and data for reduced TS vs frequency for all medusae measured, including both expanded and contracted swimming positions. Model has been averaged over a normal distribution of thicknesses; data have been averaged over pings identified as “Peaks” and “Subpeaks,” as described in Sec. III. Breaks in the data occur between the 70 kHz and 120 kHz bands.

FIG. 6.

Comparison between model prediction and data for reduced TS vs frequency for all medusae measured, including both expanded and contracted swimming positions. Model has been averaged over a normal distribution of thicknesses; data have been averaged over pings identified as “Peaks” and “Subpeaks,” as described in Sec. III. Breaks in the data occur between the 70 kHz and 120 kHz bands.

Close modal
FIG. 7.

Comparison between predicted TS vs frequency averaged across all seven live medusae (black curve) and model output averaged across all seven medusae (gray curve). Shaded region indicates a range of predicted possible scattering levels based on published values of h for other species (Table III).

FIG. 7.

Comparison between predicted TS vs frequency averaged across all seven live medusae (black curve) and model output averaged across all seven medusae (gray curve). Shaded region indicates a range of predicted possible scattering levels based on published values of h for other species (Table III).

Close modal

Measured scattering from both the expanded and contracted swimming positions was similar, with scattering from the contracted position slightly lower in most cases (Fig 6). With the model averaged over thickness, position-dependent behavior of the scattering spectrum agreed better in the 70-kHz frequency band, especially for Jelly #6 [Fig. 6(d)]. Overall scattering levels were similar to those predicted by the model.

When averaged over both bell thickness and a uniform distribution of swimming positions, scattering levels predicted by the model agreed well with the data to within <2 dB except around nulls in the data (Fig. 8). In general, averages over swimming position smoothed out much of the null structure present in single realizations and thickness-averaged model predictions.

FIG. 8.

Comparison between model and data for TS vs frequency for Jelly #6, averaged over swimming position. Model output was averaged over a normal distribution of thickness and a uniform distribution of swimming position (i.e., fineness ratio) ranging from fully expanded to fully contracted. Data output has been averaged over all pings in a 50-s interval, capturing the full range of swimming positions. Roll-off below 102 kHz is due to the presence of a null in the data at the low end of the 120 kHz frequency band.

FIG. 8.

Comparison between model and data for TS vs frequency for Jelly #6, averaged over swimming position. Model output was averaged over a normal distribution of thickness and a uniform distribution of swimming position (i.e., fineness ratio) ranging from fully expanded to fully contracted. Data output has been averaged over all pings in a 50-s interval, capturing the full range of swimming positions. Roll-off below 102 kHz is due to the presence of a null in the data at the low end of the 120 kHz frequency band.

Close modal

A primary finding of the modeling portion of this study is that the spectral behavior of broadband scattering is significantly impacted by the position of its bell during its swimming pulsations, and this is supported particularly by observed scattering in the 70 kHz band. Furthermore, scattering levels are higher overall in the bell's expanded position than its contracted position. This makes sense because the greater curvature in the bell in its contracted state would direct a greater proportion of scattered energy away from the direction of the receiver. Swimming-dependent scattering behavior in the data were more pronounced in the 70 kHz band than in the 120 kHz band, possibly because smaller wavelengths are more sensitive to roughness and fine-scale structure inside the medusa's bell, and their scattering processes are consequently more complex than scattering of larger wavelengths, which are less impacted by small-scale contributions. On the other hand, higher frequencies would be more sensitive to the curvature of the top face of the bell, complicating the interpretation. Investigation of swimming pulsation effects on scattering in the Rayleigh regime would require use of frequencies lower than those used commonly for oceanographic applications (Table II).

Another finding from this study is that there is a prominent peak in the modeled TS as the scattering regime transitions from Rayleigh to geometric, around 20 kHz (a bit higher for the expanded swimming position and lower for the contracted position due to the contracted bell being thicker than the expanded bell). This corresponds to a wavelength of ∼7.5 cm, or a quarter wavelength of ∼1.9 cm. This is close to the measured thickness of the live medusa's bell (Table II), and where the first peak in TS would be expected to occur due to constructive interference between reflections off the aboral and oral (i.e., top and bottom, respectively) faces of the bell. The range of frequencies used in this study was too high to verify this result experimentally; future studies might add 18 and 38 kHz transducers to capture this peak, especially as these frequencies are routine for fisheries applications. A larger test tank would be needed for lower frequencies to remain in the far-field and minimize interference from the surface and sides of the tank.

The average TS of C. chesapeakei measured in this study is well within previously observed (narrowband) scattering levels for scyphomedusae (Fig. 9). It is important to note that RTS— essentially a measure of scattering strength per unit projected surface area of the bell—varies vastly between studies, indicating that more subtle differences in species shape and material properties could have significant impacts on scattering levels. Material properties are encapsulated in density and sound speed contrasts ( g and h, respectively), which need to be determined experimentally. Measurements of g may be obtained using commonplace laboratory equipment, though with some uncertainty; h is more difficult to measure directly and requires a specialized lab setup to measure the speed of sound through animal tissue. Observed variability in scattering strength highlights the need for species-specific measurements of these parameters, and potentially more complex representations that account for variation in material properties between different types of tissues in a single organism.

FIG. 9.

Reduced TS vs ka data from this study (averaged over all seven live medusae) and previous studies on other species. Because physical properties vary between species, data points are colored by genus to aid in comparison. Notably, species belonging to the genus Chrysaora are in blue for comparison with the results of the present study.

FIG. 9.

Reduced TS vs ka data from this study (averaged over all seven live medusae) and previous studies on other species. Because physical properties vary between species, data points are colored by genus to aid in comparison. Notably, species belonging to the genus Chrysaora are in blue for comparison with the results of the present study.

Close modal

Within this study, a wide range of TS levels were measured across individual medusae (Fig. 6), even after normalizing for size. This shows that individuals even within a single species might vary in their material properties, and/or that C. chesapeakei vary in their body proportions. The material and morphological properties of C. chesapeakei may also change throughout the life cycle as individuals grow and mature (Bayha , 2017). A larger sample size would be needed to investigate both potential sources in TS variability between individuals. Compared to TS measurements for species of the same genus (Chrysaora; blue in Fig. 9), the average measurements presented in this study agree well, especially with the published measurements for Chrysaora melanaster (De Robertis and Taylor, 2014), suggesting that a single model might be used to represent more than one species within a limited scope, provided that the model is averaged over thickness and swimming position.

As mentioned above, the measurements presented in this study were taken at frequencies in the geometric scattering regime of these medusae. Thus, one cannot expect that TS will scale linearly with body size and consequently cannot directly infer biomass from backscattering measurements at these frequencies. The frequency dependence of TS must be known in order to obtain quantitative estimates from volume scattering from a population of medusae, and future studies should consider the effects of size and maturity of medusae on TS.

The model predicted that at incident angles near broadside, TS predictions were relatively stable, but TS fell off steeply off-broadside in the expanded swimming position. Both the expanded and contracted positions exhibited deep null structures in their orientation dependence. Given uncertainties in the swimming orientation of medusae in the field, it is important that future studies experimentally examine the effect of orientation on scattering strength and include averages over orientation in model predictions when orientation cannot be directly observed. Assuming all medusae in a swarm do not pulse in sync and are thus in random swimming positions at a given moment, it is also critical that model predictions for field-based studies incorporate averages over swimming positions.

In summary, a scattering model for medusae has been developed based on the DWBA and an approximate medusa bell shape formed by two stacked spherical caps and a homogeneous volume. This model was applied to a species of sea nettle, C. chesapeakei, representing a common morphology of scyphomedusae. Controlled, broadband TS measurements of live individuals were obtained and compared to model predictions averaged over bell thickness. Overall scattering levels agreed reasonably between the model and data. Both the model and data exhibited differences in spectral scattering behavior depending on changes in bell shape throughout the medusa's swimming pulsations, with scattering levels maximized in the bell's fully expanded state. When averaged over swimming position, TS measurements and TS predictions were in good agreement, indicating that the medusa model more accurately captures the relevant scattering physics than the simpler models based on canonical shapes. Even though the sphere, hemisphere, and puck shapes are significantly less computationally expensive than the full 3-D DWBA model, these shapes resulted in prediction errors of up to ∼30 dB at the frequencies used in this study, while the DWBA model more closely described the scattering levels observed in the experimental measurements.

There remains uncertainty in the material properties of C. chesapeakei, as its sound speed was not measured directly in this study. Backscattering strength of live medusae measured in this experiment exhibited a high degree of variability between individuals, suggesting that there may not be such thing as a “one size fits all” medusa scattering model. This highlights the importance of averaging model predictions to reflect natural variability in the field. Averages could be fine-tuned in a future field-based study by collecting measurements of bell size parameters in addition to backscattering when C. chesapeakei is abundant in the late summer.

One of the main advantages of the model presented here is that it can be easily tuned to reflect the size, shape, and material properties of other species. The DWBA framework is a powerful tool for developing scattering models for gelatinous organisms. Further development on this and similar models is a crucial step toward being able to quantify jellies rapidly and remotely in the ocean, both for ecosystem monitoring purposes and for gaining a better understanding of the global distribution of gelatinous biomass.

This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. 1745302; the Woods Hole Oceanographic Institution's Ocean Ventures Fund; and the Woods Hole Oceanographic Institution's Ocean Twilight Zone project, funded as part of the Audacious Project at TED. The authors would like to thank Bob Petitt and Kaitlyn Tradd for their help with the design and implementation of the acoustic-optical data acquisition system; Bill Grossman and Scott Loranger for catching medusae; Sarah Stover for assisting with DNA barcoding; Rick Galat for facilitating test tank usage; and Jessie Terray for help running the scattering experiment. The authors would also like to thank the anonymous reviewers of this manuscript for their thoughtful suggestions. The authors have no conflicts of interest with this research to disclose. The data that support the findings of this study are available from the corresponding author upon reasonable request.

In the following formulations, the subscript “e” and superscript (e) refer to the bell's expanded position; the subscript “c” and superscript (c) indicates that the bell is in a contracted state. The expanded bell diameter ( W e) and vertical thickness ( t e) were the only size parameters measured directly in this study. Other parameters necessary for constructing the stacked spherical caps model shape and a range of contracted positions were derived and calculated using geometric formulas, assuming the bell volume is conserved (Fig. 3). Recall that the expanded bell height, H top ( e ), is obtained from W e via the fineness ratio f ratio e = W e / H top e. Then, the height of the bottom face, H bot e = H top ( e ) t e. From there, the radii of curvature for the top and bottom faces, r top and r bot, respectively, follow as
r top = H top e 2 + W e 2 8 H top e ; r bot = H bot e 2 + W e 2 8 H bot e .
(A1)
The volumes of the spherical caps forming the top and bottom faces of the expanded bell, V top e and V bot e, are then calculated; the difference between them is the total volume of the jelly's bell, V 0,
V top e = π 6 H top e 3 W e 2 2 + H top e 2 ,
(A2)
V bot e = π 6 H bot e 3 W e 2 2 + H bot e 2 ,
(A3)
V 0 = V top V bot ,
(A4)
where V 0 is a conserved quantity across all swimming positions. From this foundation, size parameters may be obtained for another fineness ratio, f ratio c = W c / H top c. Ideally, W c is obtained from the ratio W ratio = W e / W c determined by visual data of the jelly's swimming pulsations. In hypothetical cases, such as for swimming-averaged model predictions, W ratio is assumed to scale linearly with f ratio. From these ratios, size parameters for the contracted top face can be obtained as
W c = W e / W ratio ,
(A5)
H top c = W c / f ratio c ,
(A6)
V top c = π 6 H top c 3 W c 2 2 + H top c 2 .
(A7)
Then, volume conservation may be used to obtain a cubic polynomial,
V 0 = V top c V bot c = V top c π 6 H bot c 3 W c 2 2 + H bot c 2 ,
(A8)
which can be solved for H bot c computationally. Finally, the thickness of the contracted bell is obtained as
t c = H top c H bot c ,
(A9)
and the contracted bell shape can be digitally constructed and integrated via the DWBA formulation.
1

See supplementary material at https://www.scitation.org/doi/suppl/10.1121/10.0019577 for calibration curves indicating usable frequency bands; for information regarding the DNA barcoding results; for medusa DWBA model matlab code.

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