Thermocline Tracking Based on Peak-Gradient
Detection by an Autonomous Underwater Vehicle
Yanwu Zhang, James G. Bellingham, Michael Godin, John P. Ryan, Robert S. McEwen, Brian Kieft,
Brett Hobson, and Thomas Hoover
Abstract—Thermoclines play a key role in ocean circulation,
marine ecology, and underwater acoustics. In oceanographic
surveys, it is often desirable to detect the thermocline and
track its spatio-temporal variation. Mobility of an autonomous
underwater vehicle (AUV) makes it an efficient platform for thermocline tracking. In this paper, we present a fully autonomous
algorithm for detecting and tracking the thermocline by an AUV.
The key is detection of the peak gradient of temperature. We have
tested the algorithm by post-processing data from a previous
Dorado AUV survey over the northern Monterey Bay shelf. We
are in preparation for field tests of the algorithm on the newly
developed long-range AUV Tethys.
Index Terms—Autonomous underwater vehicle (AUV), peakgradient detection, thermocline.
I. I NTRODUCTION
On a vertical profile of temperature, where temperature
changes most rapidly (i.e., the temperature gradient is maximum) is called the thermocline [1]. Thermoclines play a
key role in ocean circulation, marine ecology, and underwater
acoustics. In oceanographic surveys, it is often desirable to
detect the thermocline and track its spatio-temporal variation.
For studying internal tidal waves in Monterey Bay, CA [2],
the first and second authors developed a method of using
an autonomous underwater vehicle (AUV) to closely track
the vertical displacement of the thermocline. The vehicle was
first deployed for a short mission to measure the vertical
temperature profile, and then recovered for a quick review
of the measured profile. Based on the temperature profile,
we set a narrow temperature envelope (upper and lower
temperature bounds) around the thermocline, and commanded
the vehicle to run within the temperature envelope, thereby
closely tracking the thermocline. This method was not fully
autonomous because it required human intervention with data
analysis from a preliminary survey in order to set temperature
bounds for thermocline tracking.
In some other experiments that used AUVs for thermocline
tracking [3], [4], human intervention was required to define a
pre-set threshold of the temperature gradient. Cruz et al. [5]
took an important step forward: a temperature gradient threshold was still required, but it was determined in real time instead
of pre-set. When the AUV ran on a sawtooth (i.e., yo-yo)
trajectory (in the vertical dimension), a temperature gradient
threshold for the thermocline was defined based on the vehicle’s temperature measurements and a temperature profile
All authors are with the Monterey Bay Aquarium Research Institute, 7700
Sandholdt Road, Moss Landing, CA 95039. Email of the corresponding author
Yanwu Zhang: [email protected]
978-1-4244-4333-8/10/$25.00 ©2010 IEEE
model. Using this threshold, on the succeeding yo-yo profile,
the vehicle determined whether it had entered or departed
from the thermocline layer, and accordingly altered its attitude
(diving or climbing) to stay close to the thermocline.
In this paper, we present a fully autonomous algorithm for
detecting and tracking the thermocline by an AUV. Different
from the algorithm in [5], our algorithm does not require
any temperature gradient threshold, and no temperature profile
modeling is required either. The key to our method is detection
of the peak gradient of temperature, as described in Section II.
We test the algorithm by post-processing data from a previous
Dorado AUV survey over the northern Monterey Bay shelf
during the fall of 2009, as presented in Section III. The next
step is to field-test the algorithm on the newly developed longrange AUV Tethys [6], as discussed in Section IV.
II. A T HERMOCLINE D ETECTION AND T RACKING
M ETHOD BASED ON P EAK -G RADIENT D ETECTION
The crux of thermocline detection is detection of the peak
gradient of temperature. For peak detection, we employ the
approach of slope tracking, drawing upon our development
experience with a separate algorithm for capturing peaks in a
thin biological layer [7]. The key components of our algorithm
are elaborated upon in the following subsections.
A. Averaging temperature in Depth Bins
Temperature gradient dT
dz is the derivative of temperature
T as a function of depth z. The differentiation amplifies
measurement noise. To mitigate this effect, we divide the
water column into a number of depth bins, and average the
AUV’s temperature measurements in each bin. The averaged
temperature T̄ is used for calculating the temperate gradient:
T̄ (n) − T̄ (n − 1)
(1)
Δz
where Δz is the depth bin size, and n is the depth bin index.
More noisy measurements require a larger Δz. Setting of Δz
will be discussed in Section IV.
T empGrad(n) =
B. Peak-Gradient Detection
We run the AUV on a yo-yo trajectory in the vertical
dimension. On each descent or ascent leg, the AUV detects
the peak of the temperature gradient. We define a state variable [8] ST empGrad , and two other variables T empGradmax
and T empGradmin for storing the maximum and minimum
temperature gradient values. The definitions of the states are
as follows,
If T empGrad(n) > T empGradmax ,
set ST empGrad (n) to 1,
to ascent or conversely). Since it takes a little time for the AUV
to change attitude, the vehicle will overshoot by some distance
before making the turn. This will further enlarge the AUV’s
depth envelope.
III. T EST BY P OST-P ROCESSING OF P REVIOUS AUV
F IELD DATA
and update T empGradmax by T empGrad(n).
and update T empGradmin by T empGrad(n).
A temperature gradient peak is detected when ST empGrad
flips from 1 to 0 (i.e., the slope changes from being positive
to being negative). Note that the peak detection comes with
a delay because the sign flipping of ST empGrad lags behind
the peak by one depth bin index. Assuming the AUV is
descending, if the sign of ST empGrad flips from 1 to 0 at
depth bin n, the peak gradient is actually at depth bin n−1. To
account for this one-bin delay, the AUV saves the temperature
gradient at the preceding depth bin. On each descent or
ascent leg, the vehicle may encounter more than one local
peak-gradient of temperature. A higher peak will overwrite
a preceding lower peak, such that only the strongest peak is
saved. Note that peak-gradient detection is for each descent
or ascent leg. At the start of the next ascent or descent leg,
peak-gradient detection starts anew.
C. Thermocline Tracking
Using the same state tracking method expressed by Equation (2), the AUV tracks its own attitude by a state variable for
depth SDEP (SDEP = 1: descending; SDEP = 0: ascending).
For example, when SDEP changes from 1 to 0 (i.e., the AUV
flips from descending to ascending), the vehicle knows that it
has reached the end of a descent leg and is about to make a
turn onto an ascent leg.
On each descent or ascent leg, the vehicle detects the peakgradient of temperature and saves the corresponding depth
(i.e., the thermocline depth). At the end of each descent or
ascent leg, the vehicle sets the target depth for the upcoming
leg based on the latest thermocline depth as follows,
A. Thermocline Detection
We test the algorithm by post-processing data from a
Dorado AUV survey over the northern Monterey Bay shelf on
7 October 2009 [7]. A section of the data is shown in Figure 1.
The AUV’s sawtooth trajectory (in the vertical dimension) is
shown in the lower panel. The measured temperature is shown
by the black line in the upper panel. We set the depth bin
size to 1 m (see Section IV for an explanation), and the binaveraged temperature is shown by the magenta line.
Temperature gradient calculated by Equation (1) is shown
in the middle panel. Using our peak detection algorithm, the
peak gradients are detected as marked by the red circles. The
corresponding depths are marked in the lower panel. The green
line shows simulated thermocline tracking to be described in
the following subsection.
Dorado AUV mission starting from 10/7 14:14 (PDT), 2009.
13.5
Temp (°C)
If T empGrad(n) < T empGradmin ,
set ST empGrad (n) to 0,
13
12.5
12
11.5
1.405
1.41
1.415
1.42
1.425
1.43
1.435
1.44
1.445
4
Raw
Averaged over 1−m depth−bin
Peak of temperature gradient detected
0.4
Temp grad (°C/m)
(2)
x 10
0.2
0
−0.2
−0.4
1.405
1.41
1.415
1.42
1.425
1.43
1.435
1.44
1.445
4
DEPthermocline + DEPextension
DEPthermocline − DEPextension
x 10
Dorado Depth (m)
for descent
Simulated thermocline tracking by Tethys AUV
DEPtarget =
0
for ascent
5
(3)
where DEPthermocline is the thermocline depth, and
10
DEPextension is an extension depth. For an upcoming de15
scent leg, the vehicle targets a depth that is deeper than
DEPthermocline by DEPextension ; for an upcoming as20
cent leg, the vehicle targets a depth that is shallower than
25
DEPthermocline by DEPextension . We set this extension
1.405
1.41
1.415
1.42
1.425
1.43
1.435
1.44
1.445
4
Time (seconds)
depth to let the AUV cover a larger depth range, for two
x 10
reasons: i. to capture the true peak (rather than a local
1.
Thermocline detection using data from Dorado AUV Mission
maximum) of temperature gradient; ii. to allow for variation of Fig.
2009.280.00. For details of the green line in the lower panel, see Figure 2.
the thermocline depth over distance. Once the vehicle reaches
the target depth, it starts to flip attitude (to change from descent
B. Simulated Thermocline Tracking by a Tethys AUV
Simulated thermocline tracking by Tethys AUV, using Dorado AUV Mission 2009.280.00 data.
8
IV. D ISCUSSIONS AND N EXT-S TEP W ORK
Depth bin size Δz (in Equation (1)) is selected for a balance
between noise rejection and depth resolution in calculating
temperature gradient. If the bin size is set too small, temperature noise may cause a large error in temperature gradient that
leads to a wrong thermocline depth. If it is set too large, depth
resolution will be too coarse. In Figure 3, we compare the
calculated temperature gradients using three different values of
depth bin size: 0.5 m, 1 m, and 2 m. We define a dimensionless
“spikiness” of temperature gradient by
E abs(T empGradP eaks)
(4)
SPT empGrad =
std(T empGrad)
where E abs(T empGradP eaks) is the average height (absolute value) of the gradient peaks, and std(T empGrad) is
the standard deviation of the whole gradient.
SPT empGrad is a measure of the abruptness of the gradient
peaks against the background gradient. A high SPT empGrad is
an indication of erroneous gradient due to noise in temperature
measurements. In Figure 3, SPT empGrad = 4.8, 2.3, and 1.9
9
Detected thermocline depth
Target depth for next profile
10
2m
11
AUV Depth (m)
We are in preparation for field tests of the presented
algorithm on the newly developed long-range AUV Tethys [6].
In this section, we present a simulation of thermocline tracking
based on control dynamics of the Tethys AUV, but still using
the Dorado AUV Mission 2009.280.00 data. The Tethys AUV
has a length of 2.3 m and a diameter of 0.3 m (i.e., 12 inches)
at the midsection. The propeller-driven vehicle can run at two
speeds: 1 m/s and 0.5 m/s. Propulsion power consumption is
minimized through a careful design of a low-drag body and a
high-efficiency propulsion system [9]. In addition, by using a
buoyancy engine, the vehicle is capable of trimming to neutral
buoyancy and drifting in a lower power mode. The Tethys
AUV combines the merits of propeller-driven and buoyancydriven vehicles.
We run the Tethys AUV software [10] to simulate thermocline tracking, using a section of the Dorado AUV Mission
2009.280.00 data (corresponding to Figure 1). The result is
shown in Figure 2. On a descent or ascent leg, the vehicle
detects the thermocline, and accordingly sets the target depth
for the upcoming leg. For example, the fourth red circle in
Figure 2 marks the detected thermocline depth (11.1 m) on an
ascent leg. By Equation (3), the target depth (green triangle)
of the upcoming descent leg is set to 11.1 m + 2 m = 13.1 m,
where 2 m is the extension depth. On the descent leg, on the
way to the target depth, the vehicle detects the thermocline
at 11.8-m depth, and accordingly sets the target depth for the
upcoming ascent leg to 11.8 m−2 m = 9.8 m. When the AUV
reaches the target depth on this descent leg, it transitions to
the next state, i.e., an ascent leg. Since it takes a little time
to complete the attitude change, the vehicle overshoots by
about 1.5 m. In this simulation, the Tethys AUV tracks the
thermocline by roughly ±3.5m. As compared in the lower
panel in Figure 1, the Tethys AUV’s thermocline-tracking
depth envelope is less than half of the Dorado’s original depth
envelope.
12
2m
13
14
15
16
17
1.405
1.41
1.415
1.42
1.425
1.43
1.435
Time (seconds)
1.44
1.445
4
x 10
Fig. 2. Simulated thermocline tracking by the Tethys AUV, using data from
Dorado AUV Mission 2009.280.00 (the same as in Figure 1). The simulated
track is also shown in the lower panel in Figure 1.
for depth bin size of 0.5 m, 1 m, and 2 m, respectively. We
consider 1-m bin size as providing a good balance between
robustness and resolution of temperature gradient. In future
improvement of the algorithm, depth bin size should be set
adaptively instead of being pre-set.
DEPextension in Equation (3) is to let the AUV cover a
sufficient depth range. If it is set too small, the vehicle may
be fooled by a local maximum of temperature gradient and
miss the true peak-gradient, or the vehicle cannot catch up
with a fast variation of thermocline depth over distance. If it
is set too large, the vehicle’s depth envelope will be unnecessarily thick, resulting in less accurate thermocline tracking.
Instead of being set to a fixed value, DEPextension should be
adaptively set depending on the measured temperature profile
and the spatial variation of the thermocline depth. We will
accordingly improve the algorithm. We are now in preparation
for field tests of the presented algorithm on the Tethys AUV
in Monterey Bay.
ACKNOWLEDGMENT
This work was supported by the David and Lucile Packard
Foundation.
R EFERENCES
[1] G. L. Pickard and W. J. Emery, Descriptive Physical Oceanography: An
Introduction, 5th ed. New York, NY: Pergamon Press, 1990.
[2] F. Cazenave, “Internal waves over the continental shelf in south
Monterey Bay,” Master’s thesis, Moss Landing Marine Laboratories,
California State University, May 2008.
[3] H. C. Woithe and U. Kremer, “A programming architecture for smart
autonomous underwater vehicles,” in Proc. IEEE International Conference on Intelligent Robots and Systems, St. Louis, MO, October 2009,
pp. 1–6.
[4] D. Wang, P. F. J. Lermusiaux, P. J. Haley, D. Eickstedt, W. G. Leslie,
and H. Schmidt, “Acoustically focused adaptive sampling and on-board
routing for marine rapid environmental assessment,” Journal of Marine
Systems, vol. 78, pp. S393–S407, 2009.
Temp grad (°C/m)
Depth bin size = 0.5 m. Spikiness of temperature gradient = 4.8
Peak of temperature gradient
0.5
0
−0.5
1.405
1.41
1.415
1.42
1.425
1.43
1.435
1.44
1.445
4
x 10
Temp grad (°C/m)
Depth bin size = 1 m. Spikiness of temperature gradient = 2.3
0.5
0
−0.5
1.405
1.41
1.415
1.42
1.425
1.43
1.435
1.44
1.445
4
x 10
Temp grad (°C/m)
Depth bin size = 2 m. Spikiness of temperature gradient = 1.9
0.5
0
−0.5
1.405
1.41
1.415
1.42
1.425
1.43
1.435
1.44
1.445
Time (seconds)
Fig. 3. Calculated temperature gradient using different values of depth bin
size, for the same data section of Dorado AUV Mission 2009.280.00 as in
Figure 1.
[5] N. Cruz and A. C. Matos, “Reactive AUV motion for thermocline
tracking,” Proc. IEEE Oceans’10, pp. 1–6, Sydney, Australia, May 2010.
[6] J. G. Bellingham, B. Hobson, M. A. Godin, B. Kieft, J. Erikson,
R. McEwen, C. Kecy, Y. Zhang, T. Hoover, and E. Mellinger, “A small,
long-range AUV with flexible speed and payload,” Ocean Sciences
Meeting, Abstract MT15A-14, Portland, OR, February 2010.
[7] Y. Zhang, R. S. McEwen, J. P. Ryan, and J. G. Bellingham, “An adaptive
triggering method for capturing peak samples in a thin phytoplankton
layer by an autonomous underwater vehicle,” IEEE Journal of Oceanic
Engineering, revision under review.
[8] V. T. Jordanov, D. L. Hall, and M. Kastner, “Digital peak detector with
noise threshold,” Proc. IEEE Nuclear Science Symposium, vol. 1, pp.
140–142, November 2002, Norfolk, VA.
[9] J. G. Bellingham, Y. Zhang, J. E. Kerwin, J. Erikson, B. Hobson,
B. Kieft, M. Godin, R. McEwen, T. Hoover, J. Paul, A. Hamilton,
J. Franklin, and A. Banka, “Efficient propulsion for the Tethys longrange autonomous underwater vehicle,” IEEE AUV 2010, Monterey, CA,
September 2010, to be presented.
[10] M. A. Godin, J. G. Bellingham, B. Kieft, and R. McEwen, “Scripting
language for state configured layered control of the Tethys long range
autonomous underwater vehicle,” MTS/IEEE Oceans’10, Seattle, WA,
October 2010, to be presented.
4
x 10