SONAR PERFORMANCE PREDICTIONS INCORPORATING
ENVIRONMENTAL VARIABILITY
PHILIP ABBOT AND IRA DYER1
Ocean Acoustical Services and Instrumentation Systems (OASIS), Inc.,
5 Militia Drive, Lexington, MA 02421, USA
E-mail: [email protected]
Perfect spatial/temporal knowledge of the ocean environment is rarely available for
evaluation of sonar performance. Instead, performance prediction is often done with
acoustic models assuming idealized inputs. The current capability of many such models
is superb; realistic inputs, however, often are not available, and this is the central focus
of the present paper. The prediction of sonar performance using a probability density
function (PDF) based on environmental variability is presented. The PDF describes the
distribution of the predictive capability of an acoustic model with respect to
measurements of actual performance and, therefore, represents the uncertainty in one's
ability to model the actual performance of the system. The PDF accounts for the
inherent variability of the environment not contained in the model inputs, and is a useful
probabilistic description of the environment’s intrinsic variability. As examples, two
littoral transmission loss data sets are invoked, and other passive sonar inputs are
assumed, from which curves of predictive probability of detection (PPD) versus range
are presented.
1
Introduction
Sonar performance predictions typically are based on a set of assumptions that attempt to
describe the oceanography, bottom and sea surface conditions of the environment under
consideration. Perfect spatial and temporal knowledge of the ocean environment at all its
relevant acoustic scales is rarely available, however. Thus, performance is often
predicted with idealized environmental inputs (e.g. direction-independent sound speed
profiles, or horizontally isotropic bottom properties, etc.). While the current state of
many acoustic models, such as those for transmission loss (TL), is excellent, realistic
environmental inputs at all the important acoustic scales often are not available.
The central focus of this paper is the prediction of sonar performance using a
probability density function (PDF) based on environmental variability. These
environmental PDFs are discussed generally in the next section and are suggested as a
useful way to predict performance, albeit probabilistically. This approach is not new
[e.g., 1–3], but the growing availability of relevant ocean acoustics data makes its
adoption practical.
In this paper we use PDFs for the 1- and 2-way transmission losses (TL) measured in
the East China Sea (ECS) and Sea of Japan (SOJ) during the summertime, with
downward refracting sound speed profiles. These provide predictive probability of
1
Also, MIT Department of Ocean Engineering, Cambridge, MA 02139
611
N.G. Pace and F.B. Jensen (eds.), Impact of Littoral Environmental Variability on Acoustic Predictions and
Sonar Performance, 611-618.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
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detection examples for a simulated system operating in the ECS and SOJ during summerlike conditions.
2
Description of predictive probability of detection based on
environmental variability
Figure 1 illustrates conceptually sonar performance prediction, and how environmental
uncertainty is incorporated into what we call “predictive probability of detection”, or
PPD. The environmental PDF shown in the figure is, for a given environment, derived in
our studies comparing model predictions with acoustic data. The PDF is a best fit to
histogramatic differences between the data and the acoustic model, with inputs idealized
as the predictor elects, and is typically represented as an n-th degree-of-freedom (dof)
Chi-squared probability density function. This PDF represents the uncertainty in the
computational modeling process, which typically can be made small, and the inherent
variability of the environment not contained in the model inputs, which typically is larger.
Figure 1. Illustration of probabilistic system performance prediction and Predictive Probability of
Detection (PPD) vs. range using system-based environmental PDF which incorporates
environmental uncertainty.
Figure 1 is applied by calculating, with a model of choice, the signal-to-noise ratio
(SNR) for an active or passive system, as a function of range. The system-based
environmental PDF is anchored by setting its mean to the SNR, at each range. Of course,
the PDF must be based on the same calculation model. Then, at each range, the area
under the PDF above the detection threshold level is computed, and the resulting
integrand is the PPD (i.e., the probability that the SNR is greater than or equal to the
threshold). In the example, the environmental PDFs are shown at range increments of 5
km with the range of the integrals (as set by the threshold level) shown in red. At the
bottom of the plot is the resulting PPD, which is close to unity at close-in ranges and
slowly decreases as the range increases.
SONAR PREDICTIONS AND ENVIRONMENTAL VARIABILITY
613
The PPD shown in Fig. 1 is a prediction of the system performance versus range, and
the uncertainties in the model estimate due to environmental variability are accounted for
in this function. Rather than use a single range value (e.g. “range-of-the-day” or “rangeof-the-moment”), the PPD provides the system operator with a probabilistic
representation of the system performance as a function of range. This distribution of
ranges is, at least to first order, independent of the acoustic model used, coupled with a
data-based statistical description of the uncertainties. The operator can thus use this
information to operate the system more effectively, and can make more informed
decisions on search, risk, expenditure of assets and assumptions of covertness.
With use of a sonar system example in Sect. 5, the foregoing method is generalized
to include non-environmental origins of variability. The resulting method considers both
environmental and non-environmental origins, so that the effects of each on the system
can be directly compared.
3
Environmental PDFs for 1-way and 2-way TL in East China Sea
Operational acoustics experiments were recently conducted over the frequency range of
25 to 800 Hz in the ECS, in water depth of about 100 m, during downward refracting
conditions [4,5]. The TL data were obtained from broadband explosive Signal
Underwater Sound (SUS) sources, and omnidirectional hydrophone sonobuoys. The
tests were conducted in directions approximately normal and parallel to the bathymetric
contours. In all directions, the TL was observed to be generally low. During the tests, the
sound speed profiles were downward refracting, with thermocline temporal variations
caused by internal tides.
A state-of-the-art TL model was adopted, based on environmental idealizations
typical of operational forecasting. The bottom bathymetry and geoacoustic inputs were
based on data atlases, the latter assuming a horizontally isotropic sedimentary layer. The
comparison between the model and measurements results in the histogram shown in Fig.
2. This is a histogram of the differences between the propagation model and the
measured TL data, the latter aggregated over all ranges (≤ 40 km) and encompassing four
transmission runs with up to three independent measurement paths per run. The data
shown are in an octave band, centered at 400 Hz (282 Hz bandwidth) and integrated over
640 ms. The histogram is described by the mean difference µ = –1.0 dB and the standard
deviation of the differences σ = 2.0 dB. A chi-square density (parameterized by n = 14
dof) is selected to represent the histogram. This is the 1-way TL environmental PDF and
it quantifies the differences between predictions of the model and the truth of the data,
caused by the stochastic variability of the environment. It illustrates our statistical
approach for portrayal of environmental uncertainties that are not captured by a
predictive tool restricted to idealized inputs. It was argued in [4] that the primary cause
of the TL uncertainties are bottom complexities associated with the variability of the
bottom, at spatial scales presumably not resolved in the historical geological data bases.
Recently, the 2-way TL environmental PDF was measured from a towed array
system operating in the ECS, also during an operational experiment. During these tests,
the acoustic conditions consisted of a broadband sound source, and a known target, with
a total 2-way travel distance of 70 km. The location was about 100 km southwest of the
1-way measurement site, and deployed similarly near the ECS shelf-break, under similar
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downward refracting sound speed profiles, but twenty-four months later. The
transmission paths were primarily in the direction parallel to the bathymetry contours.
With use of the same processing as in the 1-way experiment, the resulting histogram and
Chi-square fit (8 dof) are shown in Fig. 3. Here the data have statistics with µ = 0 and σ
= 2.5 dB.
Figure 2. ECS 1-way TL environmental PDF fit to histogram measured at omniphone, 400 Hz,
BW = 282 Hz, T = 640 ms, R ≤ 40 km, µ = -1.0 dB, σ = 2.0 dB [1].
Figure 3. ECS 2-way TL environmental PDF fit to histogram measured at towed array, 400 Hz,
BW = 282 Hz, T = 640 ms, R = 70 km, µ = 0, σ = 2.5 dB.
We assume that the PDF from the out-going (source-to-target) and in-coming (targetto-receiver) TL are random variables and statistically independent. Then, the 2-way PDF
SONAR PREDICTIONS AND ENVIRONMENTAL VARIABILITY
615
will be the convolution of the out-going and in-coming PDFs [6]. In Fig. 4, the
convolution of the 1-way PDF (from Fig. 2) with itself is compared with the 2-way TL
PDF (from Fig. 3), and these agree remarkably well. This implies that the differences in
the PDF from one nearby site, or from one summertime period, to another in the ECS are
not large.
TL measurements with a towed array could result in wider PDFs if out-of-plane
scattering is prevalent in the propagation paths. The results shown in Fig. 4 suggest that
out-of-plane scattering are not important in this environment.
Figure 4. ECS 2-way TL environmental PDF (Fig. 3) comparison with 1-way TL (Fig. 2)
convolution, 400 Hz, T = 640 ms, BW = 282 Hz.
4
Environmental PDF for 1-way TL in the Sea of Japan
Similar operational acoustic experiments were conducted off the Coast of Korea, in the
Sea of Japan (SOJ) in shallow to intermediate water depths, along the shelf and slope [7],
in downward refracting conditions. The sources were SUS and the receivers were
standard sonobuoys. These tests were conducted over varying bottom depths and slopes,
in directions approximately normal and parallel to the bathymetric contours, with a
processing method identical to that described for the ECS tests. Two different source
depths were included. Measured TLs were quite high (especially relative to ECS), and
were dependent on the direction of propagation. The TL was largest for the up-slope
direction (source-to-receiver), for both shallow (18 m) and deep (200 m) sources. The TL
was smallest for the cross-slope direction (parallel to the bathymetric contours), and
intermediate for the down-slope direction; both these latter tests used shallow sources.
We concluded that the bottom conditions, including bathymetry and geoacoustic
properties, varied widely within the test area, causing large differences between the TL
model predictions and the measured data. We also showed that sound speed variability in
the water column had a comparatively weak effect on the TL.
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The 1-way TL environmental PDFs were not derived in [7], but are here. Five TL
runs in an octave at 400 Hz are used, each encompassing up to four independent paths
per run. These were compared with the same state-of-the-art TL model as used with the
ECS data, with inputs based on measured range-dependent sound speed profiles, and on
atlases covering range-dependent bottom depths and geoacoustic bottom data.
Differences between the TL predictions and data are shown as a histogram in Fig. 5, in
which the five TL measurement runs have been demeaned and aggregated. The resulting
1-way TL environmental PDF, with a Chi-square fit with 8 dof, has σ = 5.9 dB,
significantly larger than the 2.0 dB found for the ECS.
Figure 5. SOJ 1-way TL environmental PDF fit to histogram measured at omniphone, 400 Hz,
BW =282 Hz , T = 640 ms, µ = 0, σ = 5.9 dB (model and measurements given in Ref. [7]).
5
Probability of detection; ECS and SOJ predicted performance
In Fig. 6, we show predictive probability of detection (PPD) curves for a simulated
broadband passive sonar operating in the ECS and SOJ environments described in the
foregoing. The simulated system operates in the 400 Hz octave band and integrates for
640 ms. (Passive systems analyze signals and noise over much narrower frequency bands
and integrate for much longer time periods, but we simplify here in order to match the
conditions of the existing data sets). We assume the system’s Figure-of-Merit (FOM) =
65 dB, as defined in [6] for a passive system. For each environment, we use two PDFs
in the prediction, one consisting of the 1-way TL environmental PDF, the other being a
System-Based PDF as discussed in Sect. 2. The latter includes the ambient noise and the
source level, in addition to the 1-way TL environmental PDFs. We further: i) take the
ambient noise PDF as approximately normal, with σ = 0.4 dB [8], and ii) assume the
source level PDF to be a log-normal density with σ = 3 dB2. The 1-way TL
2
While reasonable, we have no physical basis for this particular assumption on source level, but
we use it for illustrative purposes.
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617
environmental PDF is convolved with the ambient noise PDF and the source level PDF to
result in the system-based PDF used in the simulation.
Figure 6. Predictive probability of detection (PPD) vs. range, for simulated passive system
operating in the ECS and SOJ (downward refracting sound speed conditions) for FOM = 65 dB,
400 Hz, BW=282 Hz, T=640 ms. Discontinuities in PPD are caused by discontinuities in the
underlying predicted TL curves versus range.
Figure 6 illustrates that all classes of variability affect the PPD. Their origins could
be environmental (as in TL, ambient noise and, by extension, reverberation) or, nonenvironmental (as in source level and, by extension, target strength, sonar self-noise,
array uncertainties, recognition-differential, and the like). Variability controls the slope of
PPD versus range in Fig. 6; the larger its total σ, the larger the slope. To be sure, the
slope is not a straight line over the entire PPD interval, its shape being controlled near its
0/1 limits by the tails of the component PDFs. Nonetheless, the slope provides an
operator with a basis for trading the gradual range-dependence of detection probability
with mission desiderata.
Where PPD is small (but not zero) in Fig. 6, the range at a fixed PPD is shown to
increase for larger σ. The relative increase for the ECS and SOJ examples is about the
same; such increases can also be important in meeting mission desiderata.
The range at which PPD = 0.5 for the two examples, is, in contrast, governed by their
respective range-dependent parameters (as in the TL mean and, by extension, in the
reverberation mean). Poor mean transmission in the SOJ leads to smaller predicted
detection ranges, while good transmission in the ECS leads to larger ranges which, of
course, makes the mean TL a dominant effect. That is, variability is important in
performance prediction, but the means are more so.
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Summary and conclusions
Predictive Probability of Detection curves have been shown for a simulated passive
system operating under a large time-bandwidth product in ECS and SOJ summertime
environments. These curves show significant differences of sonar system operation for
the two locations, with simulated detection ranges much greater in ECS. The means of
the relevant sonar equation terms retain their dominant role in performance, and
variability around the means causes the detection probability to spread in range. The
predicted spreads appear to be realistic. Named simply as slopes in Sect. 5, these spreads
potentially could provide additional detection insights for sonar operators.
The PPD method appears to be useful for incorporating environmental uncertainty
into predictions of sonar system performance. Of course, the non-environmental origins
of variability must also be considered. Because reasonable judgements can not be made a
priori as to which of the two classes is more important, both environmental and nonenvironmental origins should be considered simultaneously in the PPD method. For
example, a passive sonar with a significantly smaller time-bandwidth product than the one
illustrated here, will have significantly wider TL and ambient noise PDFs, which could
make non-environmental uncertainties moot. Further, narrower beamwidths can also
result in wider PDFs for the environmental origins of variability.
Acknowledgements
We thank OASIS personnel Chris Emerson and Stephen Celuzza for helping with the
data reduction and analyses. The ECS and SOJ omniphone data were acquired from
Dave Volak at NAWC. The work is sponsored by ONR in the Uncertainty Program.
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