Inversion of Acoustic Zooplankton Measurement
for Adaptive Physical-Biological Ocean Forecast
by
Bertrand Renard
alumnus of Ecole Normale Superieure de Cachan,
Agr6gation in Civil Engineering, Technological and Energetical Equipments, 2001
Submitted to the Departments of Ocean Engineering and Material Science and Engineering
in Partial Fulfillment of the Requirements for the Degree of
Master of Science in Ocean Engineering
MASSACHUSETTS INSTiTUTE
OF TECHNOLOGY
at the
Massachusetts Institute of Technology
June 2003
AUG 2 5 2003
C 2003 Bertrand Renard
All rights reserved
LIBRAR IES
The author hereby grants MIT permission to reproduce and to
distribute publicly paper and electronic copies of this thesis document in whole or in part.
. ......
A u th or .................................................................................................
..................................
Bertrand Renard
Department of
aE
,003
Certified b y ............................................................................
Professor and Department Head,
Chairman, Dept Committee on Graduate Students, Graduat
d")
Accepted by ........................................................
,
I ',
,,
fik Schmidt
a Engineering,
dmissions Officer,
Thesis Supervisor
..........
Michael Triantafyllou
Professor of Ocean Engineering
Chairman, Departmental Committee on Graduate Studies
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This research is performed as part of the Poseidon project, at the Massachusetts Institute
of Technology department of Ocean Engineering, in cooperation with the Harvard
University department of Earth and Planetary Sciences. Funding for this research was
provided by:
The National Science Fundation (NSF), via
Information Technology Research (ITR),
A
and by
the US Department of Commerce (DOC), via
the National Oceanic and Atmospheric Administration (NOAA) and
the National Sea Grant program (Sea Grant) as part of the Poseidon project.
Principal Investigators:
Profs. Nicholas M. Patrikalakis and Henrik Schmidt,
Department of Ocean Engineering, Massachusetts Institute of Technology
and
Profs. Allan R. Robinson and Jim McCarthy,
Department of Earth and Planetary Science, Harvard University
kTeA2
2
Abstract
The Poseidon project is aimed at bringing multi disciplinary oceanographic data
together on an Information Technology backbone in real-time, for improved
understanding and forecasting. In this framework zooplankton acoustic backscatter is
needed for better biology understanding, and can in turn benefit from the input of
physical and biological models.
Zooplankton backscatter models are subdivided in three categories: fluid-like,
hard elastic shells, and gas bladder animals. Zooplankton species neither dominant in
number, size or biomass can overwhelm part of the acoustic target strength spectrum,
implying a necessary species-specific measurement. Furthermore, the too few high
frequencies sampled by available sonars leave the acoustic inversion widely
underdetermined.
Real data inversion from WHOI's BiomaperlI has provided plankton population
estimation comparable to what nets data and counting had recorded. Multiple species
acoustic inversion has been demonstrated with the fluid-like and the elastic-shelled
model.
Purely acoustic field data inversion would require unjustifiable assumptions and
lead to unbearable levels of uncertainty, which have always been reduced by cameras and
labor-intensive direct tows. While other methods remain necessary to validate large-scale
acoustic data, the Poseidon project's adaptive modeling, sampling, and the automatic
input of biological information as part of data assimilation could significantly reduce
acoustic uncertainty. Other issues addressed are acoustic inversion simulation behavior
with various target sizes, the inversion's probabilistic validation, multiple species
inversion, bubbles detection, application on WHIIG's BiomaperlI data, sources of error
and adaptive modeling.
Keywords
Zooplankton acoustics, bioacoustics, model inversion, adaptive sampling.
3
Foreword
I want to pay a special tribute to my parents for the best gift of all: life.
My warmest gratitude goes to my advisor who was always smiling and focused although
he had to squeeze me in his tight schedule as department head.
For their invaluable criticism, teaching and advice on my research I would like to thank
Dr. Andone Lavery, Dr. Tim Stanton, Dr. Peter Wiebe, Prof. James J. McCarthy, Dr. Van
Holliday, Prof. Nicholas Patrikalakis, Dr. Pierre Lermusiaux, Dr. Constantinos
Evangelinos, Dr. Michele Zanolin, Gareth Lawson, Luiz Souza, Joshua Wilson, Patricia
Moreno, Ding Wang and Da Guo.
For their help and support: Sabina Rataj, Geoffrey Fox, Kathy de Zengotita, Eda Daniel
and Mary Mullowney
For their cheering support, allow me to mention my Ocean Engineering friends: Nick
(also known as Prof. Nicholas C. Makris), Dr. Purnima Ratilal, Dr. Monica Montanari,
Yi-san Lai, Irena Veljkovic, Wenyu Luo, Tianrun Chen, Hwee Min Charles Low,
Sunwoong Lee, Travis Poole, Joe Edwards, Andrea Kraay, Jennifer Watson, Ian Ingram;
The friends who helped me create the Club Francophone: Olivier Grunberg, Fr6d&ric
Latour, Yannick Foing, Geraldine Kim, Prof. Johann Sadock, Wesley Farfan;
and my other friends: Moshe Alamaro, Patricia Sampson, Raihan Khan, Dr. Pavel
Hradecky, Adam Saffer, Todd Garvin, Oliver Pfeil.
4
Table of content
ABSTRACT.......................................................................................................................
3
Key w o rds .....................................................................................................................
3
FO REW O RD ....................................................................................................................
4
INTRO DU CTIO N .......................................................................................................
7
1.
9
ZOOPLANKTON ACOUSTICS BACKGROUND ..........................................
1.1
CHALLENGES OF ZOOPLANKTON BIOMASS ASSESSMENT ...................................
9
1.11
Introduction..................................................................................................
9
1.12
Net tows......................................................................................................
10
1.13
Video camera counting .............................................................................
11
CHARACTERISTICS OF ACOUSTIC BACKSCATTER .............................................
12
1.2
1.21
Zooplankton ...............................................................................................
12
1.22
Acoustic sensors.........................................................................................
14
1.23
Relevant acoustical-biologicalparameters...............................................
16
1.3
2.
ACOUSTIC BACKSCATTER OF BIOLOGICAL TARGETS: .........................................
18
1.31
Fluid-like animals......................................................................................
19
1.32
Hard elastic shelled and gas bladderedanimals.......................................
22
1.33
Backscatter addition and considerations..................................................
23
M ETH OD S ..............................................................................................................
2.1
FROM TARGET TO BACKSCATTER: MEASUREMENT MODELS ............................
25
25
2.11
Empiricalmethods ....................................................................................
25
2.12
Model-based methods ...............................................................................
26
2.13
Acoustics adaptive modeling.......................................................................
27
2.2
THE COMPUTATIONAL MEASUREMENT MODEL ...................................................
28
2.21
Physical basis.............................................................................................
28
2.22
Geometry of the instrumentalsonars........................................................
29
2.23
Towing method and data presentation......................................................
31
2.3
ACOUSTIC INVERSION ........................................................................................
34
2.31
Least squaresminimum norm inversion ...................................................
34
2.32
Newton polynomials implementation........................................................
35
2.33
Multiple models inversion........................................................................
36
5
3.
RESU LTS ................................................................................................................
3.1
3.11
Fluid-like animals: euphausiids, copepods, krill.......................................
37
37
3.12
Standarddeviation robustness..................................................................
40
3.13
Plankton radius andpolynom ial order influence ......................................
42
SINGLE SPECIES SIMULATION ..........................................................................
3.2
3.21
M ULTIPLE SPECIES SIMULATION.......................................................................
Euphausiids-pteropods...............................................................................
45
3.22
Influence of relativeprecision ...................................................................
47
3.3
N OISY FIELD DATA INVERSION ........................................................................
3.31 Data inversion setup .................................................................................
4.
37
45
49
49
3 .3 2
R esult.............................................................................................................
50
3.33
Populationsize distributioncheck.............................................................
52
DISCU SSIO N ........................................................................................................
4.1
BACKSCATTER ERROR MODELS........................................................................
54
54
4.11
Multiple targets interference and Dopplerdispersion...............................
54
4.12
Bubbles, sand and internalwaves.............................................................
55
4.13
Other sources of error...............................................................................
56
A DAPTIVITY.....................................................................................................
57
4.21
Body of water .............................................................................................
58
4.22
Physics ........................................................................................................
59
4.23
Biology ..........................................................................................................
60
4.2
4.31
Computationalmethod assessment...........................................................
62
62
4.32
Poseidon backbone connection..................................................................
63
4.33
Measurement strategy and applications....................................................
64
4.3
FUTURE W ORK ................................................................................................
C O NCLU SIO N ...............................................................................................................
65
BIBLIO G R A PH Y ...........................................................................................................
66
6
Introduction
Understanding the oceans and their biodiversity is critical to sustaining their
ecology and immense global economic value, yet our knowledge of such an important
topic is very limited and divided in separate fields. A new goal for oceanographers is to
perform real-time interdisciplinary ocean prediction. The monitoring of physical,
acoustical, chemical and biological parameters will allow scientific progress and better
ocean
management.
The Poseidon project
is designed
as an
interdisciplinary
communication tool to improve scientific understanding. Progress is expected in the
information technology backbone of the Poseidon project. Motivation for this research
also includes strategic knowledge of bioluminescence at the surface and other side-effect
plants and animals may have on the ocean water, with applications in pollution control,
outfalls,
spills,
harmful
containment,
algal blooms
resource
exploitation
and
management, particularly fisheries, and oil platforms application. Physical and Biological
modeling will benefit from data assimilation and the adaptivity of sampling and
modeling. The holy grail of this research is to forecast physical and biological parameters
using these three very important tools as the artificial intelligence of the system: data
assimilation, the real-time melding of new observation into predictive dynamical models;
adaptive modeling, modifying or replacing the models as some state variables change;
and adaptive sampling, which consists of observing at the right place and time to help
reduce uncertainties.
These combined tools are intended to help the different fields of interest exchange
information and could lead to an enhanced scientific productivity. For this research
project a patch of coastal ocean in the bay of Maine has been chosen for its importance
and the availability of previous research data in the area. Indeed Georges Bank serves as
breeding grounds for many species of north Atlantic fish. Zooplankton is an essential link
in the food chain, as feed for larvae, fish and even the largest marine mammals (whales).
Effective food chain understanding and fisheries management requires wild stocks
monitoring, which is only possible with plankton biomass knowledge.
7
The framework of this research is the ITR-Poseidon project, intended to gain
multi disciplinary understanding of a coastal ocean patch. The goal of this research is to
provide the POseidon project with the adequate acoustic measurements of zooplankton.
The general framework of data assimilation in the Poseidon research must therefore be
grasped to see why certain choices are made.
The highlights of the Poseidon project can be summarized as interdisciplinary
ocean forecasting: In order to understand the complex coupled physics, biology and
acoustics of the oceans, oceanographers are driving research towards Ocean prediction,
analogous to atmospheric weather prediction but including biological and chemical as
well as physical features. Prediction has been initiated in the Harvard Ocean Prediction
System (HOPS), which provides ground material for this project. The ultimate goal is to
enable ocean prediction with real-time objective adaptive sampling, assimilation and
autonomous adaptive modeling.
The research will be based upon a series of Observation System Simulation
Experiments (OSSE), Adaptive Sampling and Adaptive Modeling in the distributed
digital environment, data driven simulations via data assimilation, simulation driven
adaptive sampling and modeling of the ocean, using distributed computing infrastructure
to integrate the disciplines and optimize the system, providing feedback from acoustics to
physical and biological oceanography, establishing interesting features, setting up
optimal attributes sets corresponding to features. The motivation and goals of this
research include automated adaptive modeling and sampling, increased scientific access,
communication and productivity, better understanding of physical biological and
acoustics phenomena, better ocean management.
8
1.
Zooplankton acoustics background
This chapter attempts to explain why acoustics and biology are inextricably tied
when dealing with zooplankton, and what are some of the challenges the researchers face
in this field, in order to have the understanding necessary to proceed with acoustics.
1.1
Challenges of zooplankton biomass assessment
Because the oceans represent the majority of our planets' surface, scientists have
tried to estimate in numbers what the productivity and biomass are at all levels of the
food chain. Although we would be satisfied with precise biomass assessments without
having all the insight into specific populations and behaviors, we will see that eventually
one cannot estimate the first goal without some understanding of the latter, whether as a
biologist or as an acoustician.
1.11
Introduction
Phytoplankton levels can be estimated with chlorophyll concentration at the
ocean's surface seen by satellites. Though this observation does not provide species
distinction or vertical distribution, it is a fast, easy and accurate means for primary
productivity assessment at the surface. In the case of zooplankton undetected by
satellites, animals must be approached closer with cameras, sonars and net tows. Because
electromagnetic waves are absorbed within meters underwater, and net tows do not result
in quantitative data on scales of horizontal patchiness without exceptional cost and
counting effort, if at all", acoustics is the most effective and practical means of sensing
or communicating on a large-scale.
Other types of measurements are still simultaneously performed to verify or
complete the acoustics measurement. Acoustic compression waves cannot strictly replace
electromagnetic waves for our purpose because zooplankton is mostly transparent to
9
these waves. It is however possible to know more about the internal structure, and species
recognition is a potential that researchers have been exploring for several decades. In the
quest for zooplankton biomass assessment, only size and species composition distinction
allow accurate acoustic data processing. Of course, size bins and species have the
potential to be used by more precise species-specific plankton growth biology models not
available at present.
Acoustic methods have therefore been called upon in the Poseidon project to
provide efficient plankton sensing. This purpose must comply with the constraints of the
Poseidon framework: Plankton estimation must include mean and variance values, for the
uncertainty is needed for successful assimilation in other models. Acoustics models
benefit in turn from physical information on the environment. The nowcast resulting from
the assimilation taking into account biology models and a priori information is expected
to gain precision by constraining the models or limiting the number of variables.
1.12
Nettows
Nets and pumps are the common practical means for direct zooplankton sampling.
Systems to open and close nets can divide a watercolumn sample into a few separate
samples integrated over complementary depths. Patchiness in plants and animals at sea
has lead biologists to use either uniform sampling or stratified sampling." The samples
obtained are prepared, processed according to probabilistic laws and observed under a
microscope.
In fact, the validity of acoustics measurements can only be compared to other
means of direct plankton sampling. These include camera snapshots and net tows. Net
avoidance by zooplankton proven from the different measurements with or without
sunshine brings a strong bias. Larger nets were tried, up to 1 0m 2 but with the same
avoidance as smaller nets. This led to the belief that the larger zooplanktons with sight
and fast swimming capabilities were starting to move away as far as 6m ahead of the net.
Other solutions tried to reduce net avoidance include higher towing velocities, but with
the side effect of crushing some of the animals in the nets.
10
Further inquiries may include acoustic and visual stimuli provided by an
advancing net opening. A wide surface of openings with or without nets could contribute
to preventing plankton to escape or obtaining known patterns of escape routes.
In comparison with the effective diameter of a wind turbine, a reduced volume
sampled model, with an effective sampled surface smaller than the real surface of the net
opening is will not provide an easy answer because avoidance depends on the specie
(ability to see) and size. Avoidance applies naturally to camera systems as well.
1.13 Video camera counting
The Video Plankton Recorder used at Woods Hole Oceanographic Institution
(WHOI) consists of a video camera and a strobe light aimed toward each other.
Zooplankton shadows in the field of view of the video system are sent up to the towing
vessel. The VPR is part of the Biomaper II detailed further in this thesis.
Sampling has always been limited by ship time and processing resources instead
of the number of samples necessary to determine spatial or temporal variability." Again,
the validity of acoustics measurements depends on other means of direct plankton
sampling. But whether camera snapshots or net tows are used, computer-automated
species naming only has an 80% effectiveness, and even when the count is done by
biology staff with 100% effectiveness, after hours of qualified biologist time spent on
visualizing the snapshots or microscope slides, a large number of unrecognizable
specimens and body parts end up in the column "unknown".
Avoidance of nets is believed to occur because of visual stimuli. Evidence of this
comes from the strong avoidance in daylight, while nighttime measurements provide
much more biomass present in the water column. The new promising technology is
flashing. The blinding of plankton in the area in front of nets or cameras would hopefully
prevent the animals to avoid the net, but could have the unexpected effect of attracting
instead of repulsing.
Axial and side sampling at various distances from the axes of flashes may provide
valuable information about the effectiveness of the blinding attempt.
11
1.2
Characteristicsof acousticbackscatter
Biological ocean acoustics were used early after WWII, but focus was on larger
animals. Species distinction has remained the holy grail of plankton acoustics. Not only is
it needed for better biology understanding, but a certain level of distinction among
zooplanktons is also necessary to interpret the acoustic backscatter measurements at all.
The two main parameters of the acoustic backscatter are acoustic brightness and
color. Brightness is the strength of scattering back toward the sound source, measured in
dB. Color determines the variation of brightness with frequency, and gives the "central"
or main frequency of the backscatter spectrum. Both of these features can be viewed in a
graph plotting the Target Strength response as a function of frequency: this is the
backscatter spectrum of a single specie and size class.
More information is available from the raw acoustic data:
Doppler is the change in frequency between the sent and received signal, which is
due to relative motion between source/receiver and target. This effect can only be used
when frequencies used are separated enough compared to the target velocity, which is the
case for plankton acoustics where only few frequencies have been used on any single
measurement device. Observations of swimming speeds within migrating layers were
reported by Heywood (1996).
Imaging is possible when sending narrow beams to obtain angular resolution
rather than average brightness information over a solid angle. Even with just one angle
sampled, single animal distinction is possible at close range from the transducer.
1.21
Zooplankton
Plankton designates the ocean life forms that are carried by the currents; this
broad category is subdivided in phytoplankton, the primary producers on most of the
planet's surface, and zooplankton, both herbivores and carnivores. Phytoplankton may
have buoyancy control, and many zooplankton species have propulsion means for
12
grazing, but not sufficient to escape ocean currents long enough for a horizontal
migration.
Daily movements
are an
for
important phenomenon
the
zooplankton.
Phytoplankton migrates vertically as a direct response to sunlight, or finds itself trapped
in dense layers at the pycnocline, strongest density gradient often a few tens of meter
below the surface. Most zooplankton species will graze at night in the photic zone (upper
twenty to fifty meters), and migrate to greater depths during the day to avoid visual
predation by fish, and especially if they don't use visual cues to find prey. A few species
reverse their daily migration and spend the night deeper than the day, which reduces the
risk of being eaten by the non-visual predators.
Export
N
Heterotrophic
roKaryotes
Viruses
Cell debris
LOOP
Grazers
Dissolved
organic
organic
InnuL trients
N,) P, Fe...
matter
Primary producers
figl: The ocean lower trophic level food web, source Jim McCarthy, Harvard
The most abundant zooplankton species in the bay of Maine on the northeast
coast of North America are Euphausiids and Copepods. Their body is exclusively made
of flesh with a light outer skin, they typically account for 80% of the biomass.
...
.
...........
...
17 N _
fig2: Euphausiids and Copepods respectively, source: Tim Stanton, WHOI
13
1.22 Acoustic sensors
The Acoustic Doppler Current Profilers (ADCP) has become a routine instrument
for physical oceanographers as ships mounted or moored instruments. Their benefits are
high sensivity and digital recording, but with neither angular and temporal resolution nor
stable calibration. (Temporal resolution is necessary to separate objects at different
distances.)
TAPS Tracor Acoustic Profiling System is the acronym for a family of
instruments manufactured by TRACOR to study the size and extent of populations of
very small marine life. The TAPS
sensors can be used in several modes,
including a "cast" mode, wherein the
instrument is lowered through the
water column from a ship, making
measurements as it goes down and
again as it is retrieved. This is the
mode used when the TAPS is used on
a CTD (Conductivity, Temperature
and Depth) instrument.
fig3&4: source: Van Holliday, TRACOR
In
another
mode
of
deployment, the TAPS can be used on
r
net systems such as the MOCNESS
(Multiple
Opening
Environmental
Closing
Sampling
Net
System).
Sampling operations, MOCNESS tows
are
1.1 "
r
made
according
to
standard
MARMAP procedures, (i.e., oblique
Transducer
from surface to within five meters of
bottom or to a maximum depth of 200m while maintaining a constant wire angle
throughout the tow.
The TAPS has been deployed on a Sea Soar towed body in the Arabian Sea and
on Georges Bank. When used on the Sea Soar body, the TAPS collects data in a "to-yo"
14
fashion, a mix of the towed and cast modes of deployment. Typically, the Sea Soar is
used for data collection when broad scale information is desired for a large area. The
TAPS is in a constant improvement process, with an increase in the number of
frequencies.
The
Biomaper-JI
(BIOlogical,
Multi-frequency
Acoustical,
Physical
and
Environmental Recorder) is a multi-sensing device. The acoustic transducers transmit
volume backscattering data at five frequencies (43, 120, 200, 420 and 1000 kHz). The
system multiplexes through its 10 transducers (5 pointing upwards, 5 pointing
downwards), and achieves a ping-rate of -0.3pings/s. The Biomaper is towed up and
down in the water column.
Tow
Cable
Environmental
Sensors
Acoustic
transducers
VPR
Bio-Optical
Sensors
Fiber Optics
Telemetry
Housing
Shock
Mounts
Welded
Aluminum
Frame
Digital
Echo Sounder
fig5: the BIOMAPER II, source: Peter Wiebe, WHOI
The Biomaper was designed as a multidisciplinary sensor because the complexity
of zooplankton sensing requires to involve as much knowledge as we can: Physical
properties of the water are hence recorded as the Biomaper II is towed up and down to
15
sample all parts of the watercolumn. All the data collected by the Biomaper is sent in real
time to its towing vessel through the cable.
Researchers at WHOI are already considering the design of a future third
generation of multidisciplinary sampling device, the Biomaper III and are studying the
features and characteristics it may have.
Fixed mooring site buoys were used one decade ago with two frequencies to
observe acoustic backscatter as a function of time, both by Holliday (TRACOR) and
Wiebe (WHOI). Records of wind, cloud cover, sea state plus echo sounder records at 3m
complete the measurements of the ancillary collection program." While it can be
interesting to see a daily or weekly evolution, the measurement is too localized to be
meaningful in itself. The very nature of the Poseidon project, where data is assimilated, is
likely to give a new meaning to isolated measurements because maps of physical ocean
properties will ensure that local measurement results are extrapolated at the right
geographic scale. These measurements could provide, at a more affordable price, an
efficient way to implement adaptive sampling as a fixed or drifting solution: one form of
adaptive sampling consists in selecting a criterion to grade the relative significance of a
measurement locations with respect to the performance and uncertainty of sonar
performance. Sufficiently slow and large scale areas of similar properties could be
efficiently sampled with just a few devices The decision to select moored or drifting
devices depends primarily on the on the typical behavior of the bodies of water.
1.23 Relevant acoustical-biological parameters
Species: The acoustic scattering signature of an animal depends on its physical
makeup, morphology, and orientation. Models distinguish three kinds of zooplankton
morphology:
" fluid-like animals,
*
animals with hard elastic shells and
" animals with gas inclusions.
Size, or more precisely animal radius or length, is a major factor. Empirical
formulas give one from the other, and the aspect ratio, ratio of length over width is often
16
used.
In figure 6, we can see that life forms occupy the whole range of sizes. While
vireo-, bacterio- and myco-plankton do not contribute significantly to biomass, the
phytoplankton can be measured by satellite and is at the lowest range of possible acoustic
measurement. Protozoans are scavengers that belong to the microbial loop below
zooplankton in the food chain. The zooplankton we are interested to detect is for the large
part mesoplankton with size order of fractions of or few millimeters. The concentration of
zooplankton is the number of animals per cubic meter [m 3]. Other ways to quantify
plankton exist, such as total dry weight, area or volume per unit volume. All are speciesspecific.
MESO
FEMTO PICO NANO MICRO
70
t.000- 0402 uv 2.0 urn 20 8M 700 Um
PLANKTON
02 -20
m
_20__con
MM
2-7 0
NEKTON
MACRC MEGA
200cm
2. - 1
200 CM
IDM1
CM
2-20
2-
M
2-20
VIRIoPLANKTON
eACTERIOPLANKTON
-
MYCO
PLANKTON
-
PHY TO
PLANKTON
PROTOZOANS
METAZOANS
NE KTON
~
i
I
=j
16*
10
70
-i
L L
-I-
SIZE
-r
I
10
SZ
163
10-2
16-0
70
7I
(m)
fig6: plankton life forms and size ranges, source Jim McCarthy, Harvard
Frequency: without any Doppler effect, the backscatter from a group of animals
occurs at exactly the same frequency as that of the signal sent by the active sonar. The
strength of the return signal depends heavily on this frequency. The acoustic frequency
signature or backscatter spectrum is the main feature used for the recognition of
populations of different species. For mesoplankton a few mm long, the corresponding
acoustic frequencies used by the Biomaper II are in the hundreds of kHz, much higher
17
than what off-the-shelf fishing sonars can offer. Size bins are used for the inversion.
Labsorption/ 2
f
43kHz
33mm
500m
120kHz
11mm
150m
200kHz
7.2mm
I00m
420kHz
3.4mm
50m
1MHz
1.4mm
15m
fig7: BiomaperII sampling frequencies
5
and corresponding absorption lengths l/e.
2
Orientation: the orientation or orientation probability distribution is a key factor in
the TS of elongated animals, simply because the acoustic beam pattern of any elongated
object has a strong angle dependence.
The calibration of the instrument at sea in real conditions is subject to the
reliability and precision of the net tows or cameras sampling methods. Even if the
quantity and size distribution we have in the other sampling methods are biased, the
knowledge of what species are present at all is valuable a priori information that allows to
choose the right acoustics model.
1.3
Acousticbackscatterof biologicaltargets:
In order to measure zooplankton densities and species, we must first understand
the acoustic response of the plankters to an incident (plane) pressure wave. For each
category of species and size, the Target Strength (TS) must be known as a function of
frequency f and sound speed c. All other relevant parameters such as sunlight (for
migration and plankton body properties), oxygen (for backscatter and plankton
migration), flows and temperatures will enter the game through adaptivity. Zooplankton
studies are based on their anatomical similarities, leading to the distinction of three major
groups from an acoustics perspective:
18
"
fluid-like (Decapod shrimps, Euphausiids, Salps),
*
hard elastic shelled (Gastropods) and
" gas-bearing (Siphonophores) animals. 19
Fluid-like animals have been modeled as homogeneous bent cylinders with a
density and sound speed ratio between body fluid and surrounding waters. Hard elastic
shelled animals behave like monopoles with waves traveling in and along the shell. Gas
bladder animals feature a strong resonance in frequency.
1.31
Fluid-like animals
The fluid-like animals are essentially composed of flesh. Density and sound speed
contrasts generate the physical gradients responsible for the backscatter. These contrasts
are in fact corrected (increased values) to take into account the soft outer shell. Secondary
parameters controlling the backscatter are acoustic frequency, size 11 , shape, orientation
and roughness. The fluid-like animals were first transformed by the models into fluid
spheres (Anderson 1950), then a directional term was added (Greenlaw, 1977) as well as
empirical factors for mean tilt angle and tilt angle distribution (Kristensen and Dalen,
1986). Recent theoretical developments by Stanton showed that the radius of curvature of
the animals (1989) and the mean and standard deviation of the angle of incidence (1993)
have an important effect on the scattering characteristics of fluid elastic cylinders. The
latest models include studies of the small-scale roughness of the shell.
Fluid-like animals are the most abundant zooplankton kind; this model is
sufficient for small crustaceans including Euphausiids and copepods. 8
Models available for fluid-like animals are either approximate or defined for a
particular species geometry; these models are still subject to active research. It is
important to mention that such models were built on theoretical scattering properties and
using mostly preserved zooplankton in the laboratory instead of live animals; their
accuracy depends critically upon two parameters that have to be either measured or
estimated: the contrasts in sound speed and density between the scatterer and the
surrounding water. These parameters are naturally species-dependant; furthermore they
are tied to lipids levels and are subject to annual, seasonal and daily cycles. The
19
calibration of any acoustic measurement is subject to the reliability and precision of net
tows sampling methods in real conditions at sea.
Equation (1) is Stanton's model based on theoretical scattering from bent
It corresponds to the backscatter from just one animal but with averaged
orientation. The backscatter depends mainly on the size and size ratios, acoustic
cylinders
.
frequency and reflection coefficient through density and sound speed contrast.
TS
=1
l0og 0.08 R
2
19,
-exp
8; 2 f'a's2
-c
x cos
4f.a
(c
2
04
(7r.f a / c + 0.4)))
j
(1)
where we have:
R: plane/interface reflection coefficient
f: acoustic frequency [Hz]
L: plankton class average length = D
0 .134
[m]
fr2m
D: plankton radius =0.095+0.134L [m]
PO: L/D, twice the aspect ratio
s: standard deviation of length [m]
c: sound velocity [m/s]
In figure 8, the Target Strength (TS) plotted as a separate function of frequency
and radius is a high-pass filter for both variables. Physically, low frequencies cannot
detect the presence of the too small animals. The deep nulls correspond to multiple
reflections inside one target hit at broadside. This plot corresponds to TS from just one
individual, but averaged over all angles. Model parameters give the choice between a
Gaussian or uniform probability distribution of size within a chosen standard deviation.
Which means in fact this TS is a random variable and the model an expected value.
20
Ak
T2.
c 10
10
10pa
10
10
,plank
Ion radius a
acoustic frequency f
102
fig8: Gaussian-length randomly-oriented fluid-like scattering model
plotted as a 2D-function of the radius a[m] and the frequency
-4(
-
-50
V
-c
Th
C
ci~
L.
-60
70F
(I)
I-
-80
H
-90
-10C
0
0.5
1.5
ka
1
fqHz] 24
2
2.5
3
fig9: Stanton's' fluid-like reduced TS for multiple individual plankters12
21
In this second plot of the same model, we see the "deep nulls" are smoothed and
disappear when scattering is averaged over many individuals. This plot is more typical of
acoustics, with the product ka = 27r a -wave number times radius- on the X-axis.
Model assumptions include uniform and unique fluid body properties, with
corrected sound-speed and density ratios. The targets are supposed to be randomly
oriented, which is slightly inconsistent with the knowledge of daily migrations and has
been observed to be non-random 5 . Linear addition of the backscatter contributions from
all targets without shadowing is also assumed.
Backscatter from elongated cylinder-like animals is much stronger at broadside,
where the modeling of the scattering is more precise; therefore the contribution from less
predictable end fire backscatter is less relevant which contributes to the overall excellent
results the fluid-like model has proven to offer.
1.32
Hard elastic shelled and gas bladdered animals
The scattering behavior of "small" animals with hard elastic shells is that of an
acoustic monopole when ka<l. 19 Straightforward expressions are available for a larger
radius of the shell, but only when turning the shell of the animal into a dense fluid sphere.
While a species-specific expression can be explicitly written with the assumption
that the dominant scattering takes place with specular reflection at the shell-water
interface, in fact other physical processes take place that can neither be neglected nor
easily modeled: Processes within the shell, the internal fluid and the closely surrounding
water account for a large part of the total backscattered energy. Stanton et al. (1998)
suggested a new model including flexural Lamb waves propagating in the shell, and
Frantz waves propagating within the surrounding fluid along the shell, and resulting in
harmonics of round-the-shell propagation.
Animals with gas inclusions produce backscatter both from their bubble and from
their tissues. The gas inclusion has by far the strongest acoustic response to an incident
wave: all other scattering mechanisms account for 5dB less backscatter power than the
22
bubble-reflected wave. This difference is large enough to look upon other effects as
secondary; nonetheless tissue response has also been modeled.
The gas sphere, filled with very low density and sound velocity fluid, is subject to
a resonance that augments the scattering significantly when ka<1. For most cases, the
combination of bubble size and swimming depth causes the resonance to be below
50kHz." The bubble is somewhat spherical and always modeled as such, but its real
shape can modify the equivalent radius measured because it alters the cross-section as
well as the angle of incidence of the pressure wave on a significant percentage of the
bubble. Random orientation of multiple animals contributes to reduce this default when
averaging.
1.33
Backscatter addition and considerations
As a conclusion to this section 1.3, it must be stated that TS is only proportional
to animal concentration for a given species, size and acoustic frequency. TS is very
frequency-sensitive and acoustic backscatter may be dominated for a single frequency by
animals neither dominant in number, volume, area, weight nor length.18 This makes it
quite difficult to directly link the echo energy to the biomass of the animals.1 4
As a result, attempts for single frequency devices to correlate backscatter with any
single geometric quantification of plankton have met with little success, and research
doesn't have the choice but to work on multi-frequency species differentiation.
Now that the basis for acoustic inversion has been laid, assessing the presence of
different species is needed. Figure 10 shows the relative scattering strength of the major
species and physical phenomena relevant to high acoustic frequencies.
23
Swim-bladdered fish
-20-
,
-
-30
IS
Siphonophore
-70
Copepod
0-
100 -
T-microstructure
Krill
11 1-12
10
S-microstructure
3
10
10
4
10
a
10
10
10a
1
Frequency (Hz)
fig 10: the most important biological and physical
ocean acoustics scatterers, source: Andone Lavery, WHOI
Siphonophore and swim bladdered fish display a narrow peak of scattering: the
resonance of a gas bladder. We recognize Pteropod, Copepod and Krill (= Euphausiid) as
high-pass fluid-like plankton. Notice that the smaller Copepod tend to have weaker
acoustic response to insonification, and must be clearly identified in order to assess
accurately the biomass. The only way to assess size and biomass among fluid-like
animals is by finding the value of ka where the asymptotes cross.
Temperature and salinity microstructure represent significant noise, especially the
latter one, which provides a TS above that of fluid-like animals for frequencies below
1MHz. This noise is a problem especially is it prevents a clear detection of the acoustic
transition between Rayleigh and geometric scattering - rising and horizontal asymptots
for fluid-like scatterers. Information about currents and inhomogeneities of the bodies of
water available through data assimilation may prove to be very helpful in that regard.
24
2.
Methods
2.1
From target to backscatter: measurement models
The models or forward models allow acousticians to predict TS from information
on the target. The measurement models must tackle the inverse problem: how to obtain
information on the plankton population from the acoustic TS 18? The use of a model-based
method allows for physical interpretation and improvement of the inverse technique.
Moreover, it allows us to take advantage of adaptive modeling with the use of
computational resources.
The simplest inversions have been achieved in geographic locations and seasons
where and when one targeted specie could be so widely dominant that models did not
have to worry much about species differentiation. Even in these simple conditions, the
goal of the studies is to measure both abundance and animal length distribution, two or
more unknown parameters that require the use of multi-frequencies devices.
2.11
Empirical methods
Determination of animal length leading to species differentiation has been
achieved with relatively little effort in areas of low species diversity. Madureiras et al.
(1993) used two frequency observations, 38 and 120 kHz. By plotting the mean volume
scatter at frequency one against frequency two, it was possible to distinguish three areas
for three present species. Visual comparison with the same plots constructed from the
Stanton et al. model offered population estimation. Brierley et al. (1998) used the
technique to consider a range of five species using three measuring frequencies and
discriminant function analysis for automated classification. Agreement between the
classification and net observations had about 75% concordance.
Of course this visual methods do not work as soon as the number of frequencies
exceeds three, and the trend is to augment the number of transducers and measuring
frequencies in an effort to better recognize the different scattering groups present. Note
25
that because of pricing and designing challenges, even the most comprehensive
multidisciplinary zooplankton sensing devices only have half a dozen sensors, while
TAPS, the only commercially available off-the shelf tool possesses two frequencies.
Biomass assessment from concentration and length distribution is then achieved
by turning all animals into spheres of equivalent volume. The analysis of the biomass
spectrum has been measured in Equivalent Spherical Radius where all animals were
assumed to be fluid-like and spherically shaped.
Whatever the method used, contributions from each individual within a
population, and from each population add up linearly. This approximation is quite
reasonable given the weakness of the scattering, hence eliminating cross-scattering return
in practice. The acoustic backscatter cross section is therefore assumed to be linear
relative to concentration and population type and class.
2.12
Model-based methods
The simplest model inversion comes for fluid-like animals with two frequencies
and the formula (2):
a4
=2(r
(2)
-R
where:
a is the equivalent spherical radius representative of the fluid animal's size,
r is the ratio of frequencies fHI/fLo, and
R the ratio of scattering cross-sections THI/ALOa can be turned into the length L using a=0.095+0.134L
This inversion model has three clear advantages: first, it is explicit, which makes
it possible to plot and interpret physically. Second, the error models are easily obtained
for the parameters appearing in the formula. The third advantage of this particular model
using two frequencies is that it cancels out all empirical constants present in the true
frequency-dependant model.
As can be seen in figure 10, the backscatter spectrum from the three main types of
animal has a different shape. In tens and hundreds of Hertz, gas-bearing, fluid-like and
26
elastic-shelled animals are predicted by the models to respectively have a linear behavior
above resonance, a cosine with null spacing of 130 to 370 kHz, and a cosine with null
spacing between 60 and 100 Hz spectra. Martin et al. introduced two classifiers based on
the physical scattering models1 8 :
The Model Parameterization Classifier (MPC) first correlated the receiver echo
spectrum against the bladder model.1 8 If the sum of the square of the residuals was less
than a determined value, the echo was classed as being from a gas bladder animal. If not,
correlation with the fluid-like model spectrum was performed and so on.' 8
The Empirical Orthogonal Function Classifier (EOFC) is another computational
method for species recognition that uses the eigenvector and eigenvalues of the
covariance matrix to find the dominant mode.1 8 Both techniques proved themselves
worthy with single targets within a laboratory tank but the sonar and transducers need
improvements before they can be used for real time in situ classification.
2.13 Acoustics adaptive modeling
The acoustics inversion is an attempt to reverse the scattering process and guess
from the backscatter spectrum what the zooplankton population, or most explicitly
population size and species distribution, initially was.
In reaching this goal, we must keep in mind how this measurement fits into the
big picture of data assimilation and adaptivity at the heart of the ITR-Poseidon research
project. The acoustics inversion provides a result, expected value of zooplankton size and
species distribution, and an estimation of the error of this inversion, just as important as
the result itself because any model or sample estimate must come along with an
uncertainty level to allow data assimilation, and because adaptive sampling will be aimed
at reducing this uncertainty by adjusting the real-time sensing tools in any possible way.
27
Assimilation and adaptivity
Uncertainty
Adaptive
sampling
Target strength
spectrum
Acoustics
inversion
Population
distribution
Data
assimilation
Adaptive
modeling
Physical and Biological metadata
figi 1: a graphical summary of the roles of assimilation
and adaptivity with plankton acoustics
In turn, information stored in the interdisciplinary database will contribute to
improve acoustics methods directly and indirectly. Direct improvement happens by
providing up-to-date physical and biological propagation and scattering coefficients as
well as the appropriate model to be used. Indirect improvement has a role to play when
the assimilation of acoustical and biological information with their respective error
estimations will converge to provide the end user with a unique information expected to
be the best of both worlds.
2.2
The computationalmeasurement model
2.21 Physical basis
It is assumed at backscatter from different targets simply adds up at the receiver.
We have the relation a(f) = N x o(f1 ), where
28
-(fi) is the total scattering cross-section
for the given frequency fi,
-(f
1 ) is the cross-section of a single individual and Ni the
number of animals per m 3
The population of animals is then broken down into classes, each class having a
narrow range of radius (centered on aj) and a unique behavior c(f 1 ,a 1 ) at the frequency
fi. A typical size class is distributed for all simulations evenly on a log scale between .05
and 5mm.22 The total backscatter for the diverse population adds up with one or multiple
frequencies to:
a(f )=Za(f , ak)xNk (3)
k
Utoti
=
a(fk,aI)xNI
k
(4)
I
Classes are not just different classes of radius, but can also represent different
species. Different classes must have a different TS behavior on the studied frequencies,
otherwise the matrix is singular and the inversion cannot be performed.
The model itself is provided by Stanton and allows species separation. This
method is only valid for weakly scattering bodies, which is the case here, and is valid for
all angles of orientation. 8 One of the approximation also assumes that material properties
are uniform inside the animal, which explains why the measured average properties are
not the best for the scattering inversion, and why the degree of variability
(inhomogeneities) is also a key issue.8 Assumptions on the L/a ratio and the probability
distribution in size around the center of the size bin are also required and hidden in the
explicit formulation given in Stanton's equation (l)model.
2.22 Geometry of the instrumental sonars
The Biomaper II used at WHOI and in this thesis sends pings upward and
downward at five frequencies. The sound is not sent continuously but as a series of pulses
every third of a second. The time integration of the signal returned over small At provides
a separate layered measurement of the watercolumn and it's layered zooplankton
population in 1.5 or 2m heights. Absorption is taken into account linearly as a function of
distance. An extinction length occurs as close as 15m (half traveling length) for the
highest frequency (1MHz) and can be calculated when linear absorption added to the
29
weak backscatter reflection reaches a certain threshold.
The absorption a=a(z) could be a function of z if a better approximation than a
constant is needed, especially to take into account the intensity loss for a wave traveling
through dense plankton layers.
The integrated beam pattern, intrinsic to the geometries of the source and receiver (piston
and disc), is part of the calibration constant used in the codes processing the Biomaper's
raw data. This constant also includes calibration from basin experimentation. With
measurement data, compensation must but be made for the dependence of the system
acoustic response on depth."
Source and receiver beampatterns are part of the hidden Biomaper calibrations.
Because these beampatterns have very strong directivity with their narrow cones
geometry, a plane wave assumption in the insonified region is a fair assumption. The
half-power beam-width is 1.5' for all Biomaper frequencies except at 43 kHz where it is
3'. The spherical wavefront is assumed to be plane with the condition 4r2
AR, hence
the scattering models created for plane waves are applicable and the horizontal layers
sampled separately.
The lowest frequency of the Biomaper was designed (diameter and power) to
function at 38kHz. It turns out that 43kHz provide a much better dynamic pressure
resonance; therefore the transducer is now used at this higher frequency. This illustrates
why broadband sonar cannot be used in plankton acoustics: these weak scatterers reflect
sound poorly and the high frequencies are absorbed within tens of meters at the hundredsof-Hertz high frequencies, so a lot of power - as much as reasonable and technically
feasible - is sent with a resonance at a very few number of frequencies. Because the
resonance depends on the geometry of the transducers, one specific transducer must be
designed for each frequency sampled.
In principle, horizontal beaming reduces the risk of coherent or specular reflection
from a pycnocline 2, but it is more practical to do vertical plankton abundance
measurement for two reasons: The vertical concentration profile provides at once values
that can be extrapolated up to hundreds of meters around. Secondly, towing an
instrumental device is more practical than having to stop regularly for vertical
measurements at sea.
30
In the near field, the raw acoustic data allows to count individual targets when
they are sufficiently separated by their travel time. But this possibility remains a dim
prospect compared to the huge task of biomass assessment on the entire column.
2.23 Towing method and data presentation
The BIOMAPER-II acoustic data used in this thesis were collected on May 28,
2001, in Laubeuf Fjord, which is an extension of Marguerite Bay. The latter is found on
the west side of the Western Antarctic Peninsula, and is the study area of the Southern
Ocean GLOBEC program.
path
plankton
beam
fig 12: behavior pattern of the Biomaper II when towed
The data is presented ping by ping, with date, latitude, longitude, frequency,
starting depth, ending depth and depth intervals information for each row of data.
At 43 and 120 kHz, data were collected in 1.5m bins (i.e. integrated over depth
interval of 1.5m). At 200 and 420 kHz, depth bins were im in size. This experimental
data was chosen for its monospecies layer of plankton clearly observed. Although the
Biomaper possesses a transducer at 1 MHz, this latter malfunctioned during that
experiment which leaves us with data from four usable frequencies. It is but one
illustration of the difficulties and impediments occurring when conducting field
experimentation. While lines correspond to pings, columns of data give volume
31
backscattering measurements at the starting depth, depth interval by depth interval. For
example it means at 120 kHz that the first data column gives volume scattering
measurements from 1-2.5m, then from 2.5-4m, etc. Similarly, at 200 kHz, the first
column shows 1-2m, the second 2-3m, etc. Data was only collected as far as extinction
length permits, depending on frequency, above and below the Biomaper that was towed
at linearly varying depth. Data is therefore not available for locations either within the
very near field of the system or at ranges greater than those reached by the transducers.
Data were thresholded for system noise, integrated over three pings and the
dynamic range of the system was -100 to -40 dB. Measurements less than 1*1010 were
automatically set to zero. The 43 kHz transducers have a nominal half-power beam-width
of 3 degrees, while all other transducers have half-power beam-widths of 1.5 degrees
which is sufficiently narrow to apply the plane wave assumptions used by the scattering
models.
32
Laubeuf Fjord measurements at 43, 120, 200 and 400 kHz
-
-40
100
-50
-
300
-60
-
-
200
400
147.85
147.9
147.95
148
148.05
148.1
148.15
148.2
100
200
300
(I-
400
147.85
147.9
147.95
148
148.05
148.1
148.15
-70-
148.2
-:A
100
200
80
300
400
500
147.85
147.9
147.95
148
148.05
148.1
148.15
148.2
-90-
100
300
400
145
1100
500
147.85
147.9
147.95
148
148.05
148.1
148.15
148.2
fig 13: TS measurements at four frequencies, source: BiomaperII, WHOI
We can clearly observe recurrent measurements between the depths of 50 and
loom, where net collections were 95% krill (Euphausiid, a kind of shrimp). The two
deeper measurements are attributable to fishes. The very surface layer -first 20m- gives
very strong TS certainly because of bubbles and significant surface waves mixing, but
also possibly because of the bio-diversity and -density occurring at the surface. The
biological acoustic response close to the surface is probably related to small pelagic
fishes as well as larvae and plankton.
33
The ping-by-ping measurement solution provides a record of the range through
time gone by since the last ping, but maximizing the number of measurements through a
maximal number of pings with the best intentions can be inadequate: in some cases of flat
ocean floor and mirror-like ocean surface, too many reflections on the surface and the
bottom have led to arrivals posterior to a second ping. This creates "shadow" or "ghost"
measurements that have to be diagnosed on the spot in order to change ping separation
and obtain usable data during the rest of the cruise. The scientists can augment ping time
separation to avoid these cross-measurement between pings whenever they are identified.
2.3
Acousticinversion
2.31
Least squares minimum norm inversion
Zooplankton has been accurately modeled, allowing an acoustic scattering
prediction given a known population. We want to solve the inverse problem: going from
the measurement of the TS at a set of frequencies back to the plankton population. Once
we achieve that reconstruction, we can feed the result and its uncertainty for data
assimilation. The uncertainty of the estimate is also useful to perform adaptive sampling.
Physical and biological information should be fed to the model or inverse model for
adaptive modeling, the real time adaptation of models and model parameters.
The acoustics inversion therefore must be designed from the beginning to make
possible or facilitate the use of adaptive modeling, sampling and data assimilation. The
principle of the reconstruction is to use the forward model we know and perform a
computational inversion. This is achieved by equating the measured TS to a TS made of
the model applied to the unknown population we are looking for.
TS
measured()
=
TS(f;,ai) * Nreconstructed (5)
Instead of numbers (concentration, in other words number of zooplankters per m3
or 1 000m 3) at different size classes, the population is chosen to be a Newton nested
34
polynomial (7), subdivided into a Vandermonde matrix R with arbitrary radii values and
an unknown coefficients vector C. A few matrix transpositions and inversions provide the
unknown coefficients according to a method of least squares and minimum norm solution
(8). Nreconstructed is modeled as a Newton polynomial.
TSmeasured(f) )=TS*R *C (6)
r
TSmeasure
(fi
2
r,2
...
(1K
)=TS*1
C =((TS * R) T * (TS* R
* (TS * R) T * Ntrue
(8)
This is a very common inversion method; it can be efficiently implemented with
software and provides a least square minimal norm inversion on an orthogonal basis of
solutions (hence the unicity and minimal norm proof).
2.32 Newton polynomials implementation
The polynomial modeling, subdividing the population values in each size bin,
comparable to a bar chart, by a polynomial function, allows us to have more size bins
than inversion unknowns, and will force the population to be somewhat smoothly, or at
least continuously varying, which can be expected from a natural population distribution.
Practically it means less unknown coefficients in the unknown C vector, and/or more size
classes available.
Newton nested polynomials are convenient to use in computational methods
because of the recurrent loop present in the nested property. The Vandermonde matrix R
displaying increasing powers of the arbitrary coefficients ri can be inversed at will as long
as none of the ri is null.
35
2.33 Multiple species inversion
The inversion principle can be extended to several species in the following way:
The target strength model matrix is now made of two or more models side by side, and
the population becomes a superposition of population matrices. These populations can
simply be of one or more values; they can also be subdivided into a polynomial
construction, allowing to use more size classes than the number of unknown polynomial
coefficients. The inversion principle and matrix calculus then obeys the same rules.
TS
measured(f)
=
TS(fJ, a 1)* N
(5)
,econstr,,,ed
The TS model is decomposed into appropriate species
=[Ts,
TSS2]*
LNSI
(9)
The species are made of single or multiple values whenever Rsi is unity or the
identity matrix, but can in the more general case be polynomials
=[TsSI
TSs 2 ]*
sI
Ls]
(10)
Following this parallel combination of two different scattering models, the same
inversion (8) applies.
C = ((TS * R) T * (TS * R))' * (TS * R) T * Ntr,, (8)
Because the active sonar measurements are a superposition of all backscatter
response, at all frequencies, a variety of physical and biological ocean sound scatterers
apply and the right models have to be chosen. The frequency separation is automatic and
the Doppler effects are ignored, but the appropriate choice of models is a crucial decision
where adaptive modeling applies.
36
Results
3.
3.1
Single species simulation
3.11
Fluid-like animals: euphausiids, copepods, krill
This is an example of reconstruction: a simulated population (blue) is measured
without noise; the reconstruction is plotted (dashed green) as a polynomial of lower
degree. The 50 size classes are spread in a logarithmic scale, with widths of the order of
0.1mm. The Y-axis shows the number of individuals in the volume insonified, say the
1m3 unit volume and you obtain a concentration of plankton. One hundred (100)
measuring frequencies and fifty size bins are used in these simulations.
165
7-
160
/
/
.1'~
N
155
0
ii
/
145
/
/
150
140
/
0
135
1
2
2
3
3
4
4
5
5
6
6
plankton radius [in]X103
figl4: simulated random degree 10 polynomial population (blue),
and degree 4 polynomial inversion (dashed green)
37
comparative given vs reconstructed concentration of euphasiids
160
\
140
120S100
U
20
C
~40
-
80
20
0.5
1
2
1.5
radius [m]
3
2.5
X 10i
figl 5: other inversion example and the distribution of errors between
the given random population and the reconstruction from a perfect measurement
This other reconstruction hints that the precision may be weaker for smaller radii
of zooplankton. Indeed the physics of the scattering provides stronger TS in the
geometrical acoustics zone (larger ka) while the Rayleigh scattering zone is a high pass
and drops quickly as ka becomes smaller. The difference in polynomial degree is here
obviously also an error factor.
38
Repartition of mean normalized errors
for a hundred randon populations reconstructions
30
25
0
201[
0
0
C 15 [
0
E
10 [-
C
-
5
0-L
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
mean error
fig16: mean errors for a hundred inversions
The center of gravity of these mean errors is at 12.6%. The number of inversions
with mean errors above 25% is less than 10%, with the highest concentration of mean
errors between 5% and 10%.
39
3.12 Standard deviation robustness
A test of standard deviation provides us with valuable insight about the transfer
function that turns the probability densities of measurements into probability densities of
the corresponding numerical inversion. The error is an essential component of
assimilation therefore model and inversion error must be quantified.
To test the inversion and how it affects variance systematically, a uniform
population simulator was chosen with mean 100 individuals in each of fifty size classes,
and a Gaussian distribution of standard deviation (Y= 20. All the following plots in
section 3.1 provide animal concentration in each size bins vs. radius in mm.
After a perfect "measurement" of the fiction population at a hundred (100)
frequencies ranging from 10 kHz to 1MHz, the population is approximated by a degree
ten polynomial:
Example of random population and its reconstruction
200
150 1
100
01
-50
0
1
2
3
4
5
figl7: example of random population used for standard deviation test
40
6
standard deviation of true population
200
1501
1--I-I_
- 100 1
0
-50'
0
1
2
3
4
5
6
7
x 103
figl8: true population abundance distribution
per volume of water in each size bin for variance test inversion
Standard deviation after inversion
200
*1~
-
150
8
-
100
---
50
(4~4
0
-50
0
1
3
2
4
5
Fluid-like zooplankton size bins [mnm]
6
7
figl9: standard deviation of 200 realizations of reconstructed polynomial populations
41
After 200 realizations, we observe in figure 19 that the reconstruction does not
bring bias. The important question to tackle is where the standard deviation envelope
shape comes from.
3.13 Plankton radius and polynomial order influence
In order to clearly determine whether the standard deviation observed after 200
realizations is indeed the transfer function of the computational acoustics inversion for
uncertainty, and what part of the error can be attributed to the physics, the choice of
polynomial simplification or the inversion mechanics, a much broader range of plankton
radii size bins is used, and different degrees for the polynomial are examined in figures
20 and 21.
First, we can observe that the inversion is very poor on the edges as can be seen
for a= 10 m, which can be linked to the absence of constraints for the polynomials past
the edges. The inversion itself is reliable except for the loose ends: polynomials are free
on the edges and lead the standard deviation to excessive limits. This skyrocketing
uncertainty moves with a choice of broader radii from 6*10- in fig19 to 102 in fig20 and
finds itself always shifted to the outer edges of the inversion.
The central structure of the standard deviation in figures 19, 20 and 21 -nodes and
antinodes- is clearly related to the order of the polynomial: The number and height of the
bumps in the general envelope of the standard deviations correspond to polynomial
patterns, 2 central maxima in figure 20, 4 in figure 21 while physical scattering reduces
precision as for small radii (small ka) and the matrix inversion is unreliable close to the
chosen window extremities. Note that the number of nodes observed is expected to be
(N-1) if N is the inversion size polynomial degree.
Because
ak = exp log(amax
the
scale
radius
(ami
*
,-
used
for
these
simulations
is
logarithmic
+log(ami)] for the kth radius out of n, the width of the
error bar tops is also logarithmic, which creates a misleading graphical effect.
42
standard deviation of degree 4 reconstructed population
250
200
150
100
-
50
0
-50
-10010
10
10 2
fig20: degree four wide radius range inversion
standard deviation of degree 6 reconstructed population
300
250
200
150
100
50
.501 4
10
-k
--
---
L -
-
I
-
.
.
.
.
.
1
4
10*3
fig21: degree six wide radius range inversion
43
6
.
0+102
Figure 22 is an example of simulation with very broad radii in order to observe
what happens for small and large radii. The two curves are almost superposed for
a 2 x 10- while they diverge more and more rapidly as the radius becomes smaller.
wide size range fluid-like reconstruction
90
/
/
/
/
85-
75
70[
true
reconstructed
601 4
.
.
a
I
,1.
.
i.
1
-
65
102
101
plankton equivalent radius
fig22: wide radii range inversion; observe the divergence of the curves as a decreases.
The physics of the TS make the inversion better for larger plankton radii:
zooplankton smaller than .5 or 1mm has a weak scattering strength compared to larger
animals, and acoustical sampling uncertainty rises under this threshold.
Fifty measuring frequencies were used on the simulated reconstructions, with just
1 kind of zooplankton, while high frequency acoustic sonars used by researchers offer at
most 6 frequencies. Because some model parameters need to be fine-tuned and if more
species are present in the water, the inversion is much underdetermined in the real world.
44
3.2
Multiple species simulation
3.21
Euphausiids-pteropods co-inversion
Gas-bearing and elastic-shelled animals, even when not in great number must be
detected simultaneously with the fluid-like plankters to lessen the noise they represent. 19
The assessment of their small number and biomass may be of little interest because
irrelevant compared to the often overwhelming biomass of euphausiids and copepods, but
their effect on backscatter can be significant at some frequencies.
Elastic-shelled animals are here used for the simultaneous inversion with the more
common fluid-like zooplankton type. The two species have separate TS models and
different size ranges.
TS
measuredf1
=
S
T
SS2]*
10
j
RS2_
(10)
*
.Cs2_
From the numerical inversion method in paragraph 2.33, R is chosen to have 250
columns. In this first presentation of a double inversion, Csi attributed to fluid-like
animals has 200 parameters, while 50 are attributed to elastic-shelled bearers.
We obviously get as a result a much more precise inversion on the species that
was given 4 /5th of the inversion equations.
45
200 coefficients fluid-like co-inversion
-80
-90
-100
-110
-120
-130
I
I-
-150
/
-
/
/
-140
-160
17k
*,/
.5
1
1.5
2
2.5
x 10
fig23: fluid-like acoustics co-inversion with 200 equations
50 parameters elastic-shelled co-inversion
150
1 001F
/ /
/
50 1N
0 1-
/1
/
N
-
-50
I
I
3
4
-inn i
0
1
2
5
6
X10
fig24: twin elastic-shelled co-inversion with a complementary 50 equations
46
3.22 Influence of relative precision
It would only seem natural to expect that the ratio reversion for the number of
unknowns attributed to each species in figures 23 and.24 vs. figures 25 and 26 would
reverse the quality of the inversion. An examination of this assumption in the figures 25
and 26 doesn't quite offer this picture:
The fluid-like reconstruction has lost precision, but without transferring this lost
information to the elastic-shelled animals. A possible explanation can consist in the fact
that the elastic-shelled inversion does not depend critically upon the number of equations,
while the fluid-like animals reconstruction does.
Another attempt to interpret this unexpected result would be to claim that the
parameter reduction and lower quality of the fluid-like inversion has a significant
negative impact on the precision of the elastic-shelled inversion. The reciprocity does not
hold true. The fact that both inversions are inextricably tied in the simultaneous inversion
can certainly account for some crossing uncertainty: the total spectrum measured is made
of categories in size and species. If one category is underestimated, the other categories
will share the missing TS according to their TS spectrum.
47
50 coefficients fluid-like co-inversion
320
300
280
260
N
-
-
240
\
200
-
---
_
-
-
220
180
160
140
11
.5
1
2
1.5
3
25
'
x1
fig25: fluid-like acoustics co-inversion with 50 equations
200 parameters elastic-shelled co-inversion
1wJ
100
50
0
-50
-100
. .....
-150
-200
-250
-300
1
2
3
6
4
x 10
fig26: twin elastic-shelled co-inversion with 200 equations
48
3.3
Noisy field data inversion
The purpose of this section is to experiment the acoustic inversion developed and
simulated previously on field data collected by WHOI's Biomaper II. In particular, the
acoustic inversion aim is to see what response to noise and bubbles could be brought.
Would a double- or multiple-model inversion with a model for bubbles or noise help?
3.31
Data inversion setup
Data were thresholded for system noise, and the dynamic range of the system was
-100 to -40 dB. Measurements less than le-10 were automatically set to zero. None of
these data were corrected for calibration offsets, nor were they cleaned up from nearsurface measurement. This means that echoes from the bottom and surface bubble layers
have not been edited out, and some of the data (at 43 kHz in particular) are somewhat
noisy.
From paragraph 2.23 fig 13, data at the single depth of 75m is extracted in order
to perform the inversion on data where the actual species composition and size
distribution have been recorded by means other than acoustics.
The x-axis, ranging from zero to two thousand, is the number of pings. Pings
occur every AT = 1/3rd of a second for all frequencies. (One frequency cannot disturb
measurement at another frequency because they are sufficiently separated.) Because the
pings are averaged three by three, and for the vessel moving at V = 4knots = 8kmh-1 , the
distance between the measurements plotted is:
Ax=VxAT=
8000 3
x-2.22m
3600 3
The total scale of the sampling used is 4.5km long and the horizontal patchiness
on the order of a few hundreds of meters.
49
75m depth data cut
10
+ 43kHz
-- 120kHz
200kHz
420kHz
10
ILiI
1017
+/
i
I
I
a
+4
+
+
4A ++
+
0
200
400
600
+
+
BOO
1000
1200
1400
+
++
1600
1800
2000
fig27: 2000 multifrequency measurements at 75m depth
3.32 Result
An inversion is now performed at this depth using Stanton's fluid-like averagelength average-orientation bent cylinder with Euphausiids parameters.
50
75m deep Antartica fluid-like inversion
x 10-2.5
2
IE
(DJ
E
0
4500
3375
1010-125
1125
Fluir-liike krill rrii
rml
102
0
I
Iea
d
l
=
stance aong0 e ]~ t tL l-L l
k
fig28: fluid-like inversion on 75m deep data track
The inversion has been limited to a narrow radii size range because of the low
number of frequencies sampled, in an effort to limit the number of unknowns.
In figure 28 we observe recognize the same patchiness scale than in the raw data
shown in figure 27, on the order of hundreds of meters. The band of missing data
corresponds to the part where the Biomaper dived a little deeper. In this area the highest
frequency (420kHz) did not reach the 75m-deep layer and the inversion cannot be
performed.
The edges of the inversion, at a = 5 x 104 and a = 2 x 10-
witness the occurrence
of the highest peaks. As was demonstrated in paragraph 3.13, the inversion is not reliable
on the outer edges, in particular for a radius of 2mm. It looks like the sharpest peaks for
radii larger than 1.3* 10-3 belong to the outer layer where inversion cannot be trusted.
These concentration peaks should simply be ignored. Interesting features include the
width of the main peak of animal concentration. The shape of the size repartition is
certainly smoothed by the polynomial function.
51
3.33
Population size distribution check
The inversion examined in figure 28 is now averaged over the entire experimental
data, in an effort to compare the inversion result to net collection statistical estimates. We
can again discard the 2mm peak of plankton concentration as clarified in 3.13. Although
the inversion is only performed on a narrow radii range of optimal precision, the result is
displayed on the same scale as that of the biology counting plot. The inversion results
have been simply trimmed when turning negative, with no physical meaning.
Although animals larger than 30mm are very sparse, their contribution to the total
biomass is very significant. But echo from the larger Euphausiids -50mm- is much easier
to pick up; it does not require frequencies in the hundreds of kHz and could therefore be
detected with sensitive commercial fishing sonar.
52
Plankton length repartition from acoustics inversion
B
7
6
0:)5
C0
C0
4.
-0
E
2
1
01 0
0
10
10
-1
20
20
30
30
40
40
50
50
70
50
60
70
80
60
Krill(Euphausiid) size [mm]
fig29: 4500m average size-abundance distribution of computational inversion
Plankton length repartition in the 50 to 1D00m depth layer observed
BI
7
6
0E
34
U
21
1
01
0
10
20
30
40
s0
60
70
KriI (Euphausiid) size [mm]
fig30: population distribution from direct net collection,
statistical sampling and microscope observations
53
80
4.
Discussion
4.1
Backscatter error models
It is fair to say that the physical modeling precision is more than enough, but that
the errors and uncertainties regarding many influencing parameters don't allow good
measurement. The low number of frequencies is also a factor limiting the reliability of
acoustics inversion, because they are widely underdetermined.
4.11
Multiple targets interference and Doppler dispersion
All models assume the backscatter of the sum is the sum of the backscatters for
animals of same size and shape. This linearity assumption between acoustic backscatter
and animal concentration is justified as long as the concentration of targets is reasonably
low and the distribution sufficiently random.20 Why are the models and their linear
approximation good enough? The shadow zone behind any individual is negligible.
Multiple reflections are strongly attenuated because the reflection coefficient R12 appears
multiple times. The precision of the model is greater than that of the other zooplankton
assessment techniques necessary to calibrate the acoustic instruments.
The linear addition assumption is generally true for zooplankton found in
somewhat limited numbers in the temperate New England waters, even when swimming
in thin layers of much higher plankton and particulate matter concentration floating on a
pycnocline. On the contrary, this may be a source of error in tropical upwelling waters
where swarms of plankton animals densely aggregate near the surface or in thin layers.
As a matter of fact, the model for one animal is different from the model for
many, where the variance of animal size has a role to play.
A single fixed target provides a returned signal at the same frequency than the
incident one. For multiple targets, the mean return frequency only provides information
about the motion of the target as a whole. Since we don't expect the animals to behave as
54
a military squad, the relative motions will create dispersion in frequencies:
proportional to
Vmax
where
Vmax
dfmax is
is the maximum velocity of any animal in a motionless
flock. Hence in the general case Vmax is the maximum difference between the mean flock
velocity vector and the velocity of any individual animal in the flock.
The narrowband transducers of the Biomaper are not meant to be extremely
frequency sensitive and frequency shifts have been left aside in the data WHOI has
provided.
4.12 Bubbles, sand and internal waves
Bubbles are always present near the ocean surface. This phenomenon brings
strong bias to all measurements. Air bubbles contamination may affect measurements in
the highest water layer no deeper than 5m, where it can be a source of concern.' The
attitude adopted when faced with this extremely strong backscatter from non-biological
sources was to simply discard the data. Indeed, even if an acoustics inversion were using
physical models to unmask physical features from a surface layer measurement, the
likelihood of holding a quality inversion would still be low because of the extreme
diversity of life near the ocean-atmosphere interface. If the surface layer represents a
higher level of challenge, there is a bright side to the medal: it is also much easier to
observe and access by any other method.
On the continental shelf, sand can be suspended by the current and lifted in the
watercolumn. Acoustic high frequency sonars clearly pick up sand in their measurements
Sand and dissolved organic material suspended in the water column have been reported
to look like plankton. Data assimilation of currents and opacity of the water could help
automatically detect these abnormalities if three-dimensional knowledge of continental
shelf currents and upwelling provide hints on whether measurements are potentially a
sand storm or marine snow.
The animals are often in greater concentration near a moving isodensity surface
called internal wave, which is similar in form, but not directly related to surface waves."
Just like typical zooplankton patches, internal waves and solutions are characterized by
horizontal lengths of hundreds of meters and vertical lengths of a few meters. The thermo
55
cline and pycnocline, depths of strongest temperature and density gradients, have to be
closely watched because the change of density often captures some of the neutrally
buoyant plankton and attracts the rest of the marine plankton and life for feeding.
The thermal gradient is helpful to validate
TSzoopankton > TSgradient.
More generally,
noise from turbulence can be comparable to the TS of large zooplankton. This noise can
be successfully eliminated either with a broadband sonar (distinct behavior with broader
frequency range) or spectral analysis using properties like temporal variations in the
noise, or the fact that the noise's average doesn't have any spectral structure.
4.13 Other sources of error
It also appears in the literature that bio-acoustic measurements up to present date
had a fair precision as far as models, instruments and calibration were concerned. In fact,
all the methods used have had limited precision, but searchers pointed out that the
patchiness in time and space of the population being sampled doesn't allow
straightforward improvements of the measurements. In particular the TS has a stochastic
nature. 2 0 Some of the major concerns were due to unwanted species (fish schools etc.)
entering the measurement area sometimes for only part of the measurement, weather and
time effects on the comportment of the plankton, inconsistency of the plankton
population size through diurnal cycle etc. The vertical migration is well observed, but
total zooplankton biomass integrated over the watercolumn is consistently different
during day versus night times.
Assimilation of other parameters (physical and biological) may be an efficient
way to improve the measurement methods. The Poseidon project here has been
appropriately designed to promote interdisciplinary science and models improvements in
that regard. Bioacoustics measurements are indeed not limited by instruments or models,
but by the complexity of zooplankton behavior and interdisciplinary implications on
zooplankton. Assimilation is expected to tie critical bonds and obtain significant science
improvements.
Calibration is achieved with metal spheres used as reference targets, to produce a
well-defined echo, which leads to a calibration accuracy of about
56
5%20
The fluid-like animals model is extremely sensitive to slight changes in the
parameters g and h, because values of plankton body density and sound speed are close to
that of the oceanic water. As an example, altering the density contrast g from 1.035 to
1.04 is a 14% increase, significantly altering numerical outputs. Values of g reported in
the literature vary from 1.016 to 1.120, while the values of sound speed contrast h range
from 1.007 to 1.033.11
According to Peter Wiebe, "acoustics is great at measuring backscatter, but not
strictly zooplankton." This refers to the many physical features that are recorded by
acoustical measurements, and sometimes look like biological features. This category of
physical features includes solitons, internal waves and suspended sand or sediment.
Although acoustics is the only measure that samples large volumes fast, Dr.
Wiebe finds it difficult to confidently relate acoustic measurement to plankton biomass.
He believes progress can be made faster using the Video Plankton Recorder, because this
method is also automated and it provides direct counts and accurate sizes.
4.2
Adaptivity
Species identification will not be accomplished with acoustics alone, but cannot
be accomplished without acoustics. 2 0 All available information must be integrated in new
analytical procedures, which will make probabilistic statements regarding the specific
cause of the marks seen on echo sounders and sonars. 20
The objectives of Adaptive Sampling include dynamical "hotspots" sampling,
reduction of error variance, reduction of errors for tomorrow, maintaining accurate
forecast and accurate synoptic picture, optimization of the sampling as a function of
objectives and metrics, automation of the previous points, nonlinear and interdisciplinary
sampling impact study, reduction of error in analysis vs. in forecast, minimization of final
time errors vs. minimization of time-averaged errors, cost function minimization for the
three following: forecasted model errors (ESSE), forecasted significant dynamical events
(MS-EVA, pattern recognition) and maximum length of time an area can be left without
updating.
57
4.21
Body of water
Using data assimilation, the real-time melding of measurements and calculation
outputs, metadata can be created, for meaningful use and visualization of information.
Adaptive modeling consists in using these metadata and state variables evaluated in real
time to address the changing environment and adapt the model parameters or very nature
of the models used. Adaptive sampling closes the loop: given our knowledge of the ocean
patch that is monitored as a digital ocean, and given the uncertainties that our metadata
carry in space and time, a sampling strategy changing in real time as well can be carefully
thought in order to minimize the uncertainties.
Pumping double-checking or precise depth measurement can be made in an
adaptive manner, with a relatively small horizontal patchiness (ranges of hundreds of
meters instead of meters)".
The specificity of this research on plankton is to use the tools of adaptivity and
meta-data to benefit from interdisciplinary information. How do acoustics fit into the big
picture?
Physical water properties of Gulf Stream vs. cold upwelling northern waters must
be accounted for in the model parameters. These different bodies of water and the
pycnocline must be documented for sampling depth, vertical daily migrations and
extrapolation of the measurements on larger areas.
At least two distinct bodies of water coexist on Georges Bank: polar waters and
Gulf Stream waters. True enough, mixing is occurring between these bodies, but
practically the mixing is occurring with widths of small scale compared to the
mainstream and gyres of the two bodies. Practically, knowledge of the water body is
determined in 3D by the temperature and salinity.
The body of water can help predetermine plankton composition and physical
parameters. It is necessary for geographic adaptivity (right choice of measurement
locations in the area of study). The correlation of the body of water to nutrients,
temperature and the resulting plankton abundance at the surface has been strongly
reported and demonstrated.
58
4.22
Physics
The parameters g & h, density and sound speed ratios, may be partially provided
by the knowledge of the sampled water body, but must be more precisely actualized. This
adaptivity can ideally be continuous, with rates of modification well under a day, because
the parameters vary as a function of sunshine exposure. Seasonal and diurnal cycles
depend strongly on feed availability and physiological processes. We must note that the
averaged g and h values that the acoustical model calls for are not the ideal value to be
used, but the value must be somewhat larger, to better take into account the external
skeleton. We therefore speak of modified average density and sound speed contrasts.
Values of g and h can be chosen according to the cross-comparison between
acoustic measurements and sampling. When the measure has similar spectrum but with a
lower TS, it is probably not a problem of net avoidance from larger plankters but values
of g and h too low." Adaptivity of g & h parameters can ideally be continuous: these
parameters vary as a function of sunshine over time: seasonal and diurnal cycles
depending strongly on feed availability and physiological processes via lipid proportions.
The pycnocline and thermocline must be known to look for plankton layers sitting
on it and\or avoid specular or coherent reflection on it. Plankton is often concentrated on
small patches on top of the thermocline, with typical vertical range of less than 3m and
horizontal range from a few to 200m.
Plankton biomass is apparently much higher in well-mixed areas, especially near
the bottom, possibly because of sand resuspension.2 2 The validity of bioacoustics should
at this point be limited to areas where resuspended sediments are known to be absent
from the watercolumn.2 2 Physical knowledge of upwelling areas can contribute to
warning scientists when the sonar echoes are likely to originate from undesired physical
features in the watercolumn.
Adaptivity applied to physical features is aimed at automatically determining
features like upwelling, vortices, jet filaments, gradients, gyres, meanders, jets, velocitybased fronts, temperature-salinity fronts, shelf-slope fronts, eddies, streams, crests, tidal
phenomena, plumes, lenses, currents, meandering, circular fronts and facilitate adaptive
sampling. Adaptive modeling and sampling are ultimately meant to be automatic.
59
The full list of "interesting" features must be established and could welcome
additions as events of interest are added to the scope of research. The optimal attributes
sets corresponding to these features must be defined.
4.23 Biology
Further biological knowledge can be useful to either predetermine or compare
species composition when running models using a priori seasonal knowledge etc.
Higher frequencies lead to the measurement of phytoplankton and possibly a
significant response from particulate organic material. Phytoplankton represents noise
that must be taken into account in the measurement campaigns (location and height in the
water column) and could also be used in the model to be better subtracted, data
assimilation could also point out how much phytoplankton is affecting a zooplankton
remote sensing: Some of the large phytoplankters interact with zooplankton measurement
and could be subtracted to avoid redundancy with total chlorophyll seen by satellites. The
ratio of the phytoplankton population larger than, say, 1mm, can be modeled and it's TS
spectrum subtracted from acoustic sensing in each water body.
Fish behavior research has greatly improved our understanding of target strength
and why it is a highly variable feature. Much less is known at this point about plankton
behavior, but understanding of TS can be expected to improve in that regard.
In
particular, orientation is a scattering issue where biology understanding can provides and
improve significant information.
The orientation probability distribution of elongated fluid-like cylinders like
animals is a key parameter that is believed to vary during the day depending on plankton
behavior. Migration and feeding are behavior patterns likely to change the distribution of
zooplankton orientation.
Quantitative comparison of acoustically derived data to pump and net samples has
proven to be difficult (Costello et al. 1989). The sampling devices work on different
scales and collect data from different volumes of water.2 2 Plankton is perpetually in
motion: different water depth are carried by currents of different directions and velocities.
60
No plankton patch is uniform, stable or easily traceable in time. The complexity of the
coupled physics and biology of the ocean provide no small challenge and justify the
Poseidon projects' attempt to put artificial intelligence at work through adaptivity.
Arctic
Seasonal blooms:
2
A
producers
second
bloom
primary
is
usually
observed in temperate latitudes.
Temperate
Keep in mind that the abundance
of animals observed and reflected
A
in these curves is not the rate of
hh=
growth,
because
predation
pressure plays an important role as
Tropical
J
F
M
A
AIjae
M
J
J
z
A
S O
a population reducer.
N
D
Herbivores
Fig3 1: phytoplankton and zooplankton blooms, source: Jim McCarthy, Harvard
Finally, the season could provide valuable information on model parameter values
such as species present, expected average size, and sound velocity ratio that comes with
lipid contents. Meteorology is a strong factor in phytoplankton growth models, it should
directly or indirectly appear in the sampling strategy. The size range targeted depends on
the season with/without the presence of juveniles. The "season" can in fact be turned into
a state parameter separated from the actual date, because weather and primary
productivity may be early or late a couple of weeks from year to year.
61
4.3
Future work
4.31
Computational method assessment
This method has several advantages:
" Size classes and precision can be adapted at any moment depending on the rapidity
requirements, precision need and computing possibilities.
*
Only the forward model needs to be known; it can be modified, replaced or improved
just by modifying the corresponding coefficients in the backscatter cross-section
matrix.
" Measurements can be used instead of theoretical models: a limited number of
measured species-specific backscatter values can replace a physical model for
comparison purposes.
" Multiple models can be used simultaneously simply by adding or dropping size
classes with different characteristics. It is important to emphasize that this features is
necessary to take care of the real world superposed measurements and is a good way
to wipe out noise from unwanted species and physical features measurement. Again,
the inversion will only be able to separate the species as far as their backscatter
spectrum shape differs in the sampled frequencies.
Now comes the disadvantages side:
" The inversion is a black box
"
The error model is not theoretically and explicitly obtained, but has to come from
multiple inversions of virtual populations with known (Gaussian) probabilistic
repartitions.
In short, the computational inversion allows scalability in the model, the
computational power available and the precision we require (though the limitations here
are not in the computational power or in the model precision but in the measurements).
Measured or empirical values of TS can be used in lieu of formulas. We can make the
62
inversion simultaneously for a few species. On the inconvenience side, the inversion is
opaque and error models can only be guessed from multiple trials, without closed-form
formula.
4.32
Poseidon backbone connection
The adaptive physical-biological-acoustical modelling at the core of the Poseidon
project is to be designed after the already existing and effective Harvard Ocean
Prediction System (HOPS),
system of integrated software for multidisciplinary
oceanographic research. Accurate estimation of ocean fields in a timely and reliable
manner is the first step. HOPS data are stored in a NetCDF file. A palette file, contour
parameters file, coastline data file, isobath file, geosat track file, etc. are also needed.
HOPS Plotting packages can then visualize over two hundred fields by providing
contours of the desired fields at the given depth and time. Vector fields include
geostrophic velocity vectors, total velocity, zonal velocity, zonal geostrophic velocity and
meridional velocity. Scalar fields cover temperature, transport stream function, surface
heat flux, wind stress, surface pressure, velocity components, density, salinity,
zooplankton and chemical concentrations.
To present the results in a fashion easy to use remotely -over the internet- and
that can remains open to future adaptations, the NetCDF files format has been chosen:
useful and popular format to store large scientific data, it provides an interface for arrayoriented data access, a library with an implementation of the interface, (in Fortran or C
codes), and other interfaces that can be used by other tools (Java interface, toolboxes for
MATLAB-5). As a second step, the data can be transferred from NetCDF to ASCII
format, and finally Ncview can be used to get a quick look at the NetCDF data. NetCDF
files are array-oriented data that can be created, accessed and shared in a form that is selfdescribing {dimensions, variables, data} and portable.
The acoustic data will in the future need to draw physical and environmental
parameters from the NetCDF library, and provide its results in this form as well. Matlab
is a suitable tool compatible with, or at least convertible to the NetCDF file format.
63
4.33 Measurement strategy and applications
The Biomaper designed and custom-built at WHOI has proven to be an efficient
multi-disciplinary sampling device. While it is among the leading edge high-frequency
acoustics sensing devices, it is complicated to operate and must be towed by a vessel, an
expensive and manpower-hungry operation.
The Biomaper remains a reference for measurements and multidisciplinary
double-checking, but it also is meaningful to envision some simpler captors such as
moored or drifting bi-frequency sensors. The use of such sensors has been abandoned for
research operations in the last decade, but these sensors truly offer an opportunity for
automatic sensing. Depending on what the diagnosis of the bay of Massachusetts
uncertainties "hotspots" brings, such affordable sensors could be used in a more
automated fashion.
64
Conclusion
High frequency ocean acoustics measurements capture any sound velocity or
density contrast, ranging from sand, bubbles and internal waves to the shells, bubbles and
bodies of zooplankters. This type of measurement, fundamentally more efficient than any
other localized zooplankton-sampling tool, is also intrinsically tied to physical features in
the water column. The Poseidon project possesses in its very structure a possible response
to the challenges offered by interdisciplinary ocean science:
The pycnocline and thermocline are physical features that typically concentrate
plankton layers and can lead to specular or coherent pressure wave reflection. Mixing (of
nutrients as well as generation of small-scale sound velocity gradients), presence of sand
in upwelling plumes or bubbles in a surface layer, solitons and mutlireflections between a
peaceful sea and a flat sediment bottom are features likely to generate undesired sonar
echoes. The definition of the body of water sampled could provide estimates for sound
speed and density ratios g & h, further precised by sunshine exposure, seasonal, diurnal
and physiological models. Direct species sampling, plankton body lipid proportions and
average orientation of the plankton were also identified as valuable for adaptive
sampling.
Fifty measuring frequencies were used on simulated reconstructions, proven to
work with fluid-like or elastic-shelled kinds of zooplankton, while high frequency
acoustic sonars used by researchers offer at most 8 frequencies. Because some model
parameters need to be fine-tuned and if more species are present in the water, the
inversion is clearly underdetermined in the real world. Adaptive sampling will here play a
decisive role in helping refine the real-time parameters of the acoustics models, with a
priori biology information about species swimming and physics parameter values. Real
data inversion from WHOI's BiomaperII has provided plankton population estimation
comparable to what nets data and counting had recorded. Multiple species acoustic
inversion has been demonstrated with the fluid-like and the elastic-shelled model.
65
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