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Estimation of the average life span of Argo floats
Taiyo Kobayashi E-mail: taiyok@jamstec.go.jp
IORGC/JAMSTEC, Japan
Estimation of the average life span of Argo floats
Introduction
Estimation of average life span of float is very imporant for
the Argo Project, because it would directly determine the
number of floats deployed annually to maintain the observa-
tion network, or the total cost for the Project.
This study introduces the method to evaluate float life
span, survival analysis, and some estimations desuced from
the records of Argo databases.
Method
The life span of Argo float is deduced from the "survival
function" of Argo float. In this study, the function is esimated
by the Kaplan-Meier method, which is widely used in the
medical staticsics. An advantage of this method is that the
function can be calculated accurately by using only a small
sample set. The details of this method should be refered to
textbooks of medical statistics.
In this study, the float life span is defined by the average
of profile number measured by floats; the results would not
be affected by the difference of the observation cycles.
Words:
Survival function: a function of time for the rate of survivers.
Average life span: it is given by an integration of the survival
function with time.
Median survival time: it is the time when the survival
function loses 0.5.
Survival functions and average lifetimes of Argo float based on GDAC data
APEX
SOLO
PROVOR
All types
110
99
134
112
87+
90
64+
71
Ave. Med.
The long lifetime for APEX msut
be discounted: a dosen of Japa-
nese floats drifting much shallower
depth (400-600db) are super-long-
living, 270 cycles at their maximum.
Removing such the floats, the life-
time of APEX reduces to 120 cy-
cles.
PROVORs made by Martec (France) are widely used in the wrold. Most of PROVORs
deployed by Japan are manufacted by Metocean (Canada), and many of them were
short lived (see the results of JAMSTEC floats) probably because they were under de-
velopment. Removing 77 Metocean-PROVORs of Japan from GDAC data, the life span
of PROVOR is estimated as 70+ cycles.
Estimation of lifetime of the improved float
In actual estimation of the life span of the current floats
with the JAMSTEC data set, the current status of the floats
that died from the already fixed problems is adjusted from
"dead" to "unknown." Under the assumption that the causes
of float deaths are independent, the current float will die stati-
sitcally from causes other than the fixed problems.
The problem is simplified as follows:
A type of float has 4 fatal troubles (A, B, C, and D) to its
death potentially, and they are independent from each other
(see the left figure).
The touble B has been addressed, and improvments pre-
vent the float from its death from the trouble B. The other
troubles (A, C, and D) will occur to the float with the same
probabilities before the improvements. Thus, the survival
function of the float will be changed, and it is expected from
the existing infromation as that in the right figure.
7/8
5/8
7/16
Probability
of death
1/8
2/7
3/10
7/8
5/7
7/10
Probability
of survive
A
B
C
1/7
6/7
D
3/8
Accumulate probability
of survive
62.5%
43.75%
37.5%
Fatal troubles
7/8
7/8
49/80
1/8
0
3/10
7/8
1
7/10
A B
C
1/7
6/7
D
21/40
52.5%
61.25%
87.5%
Probability
of death
Probability
of survive
Fatal troubles
Accumulate probability
of survive
Before improvements
After improvements
Survival functions and average life spans of floats managed at JAMSTEC
All types
APEX
PROVOR
All types
APEX
PROVOR
Ave. Med.
80+
81
99+ 115
50
62
Num.
409
317
78
Shorter lifetime for PROVOR is attrib-
uted to its lower survivability just after
deployment (0-20 cycles) and its earlier
programmed death from battery con-
sumption (about 80 cycles).
Note that most of PROVOR floats
are manufacted by Metocean.
Expected life span of Argo floats currently used
At the beginning of the Argo, unexpect-
ed hardware failures caused many floats
to die prematurely. Some of these fail-
ures have been already fixed, and the life
spans of the Argo floats currently used
are expected to be much longer than the
above results based on the records in the
databases.
At JAMSTEC, causes of the float
deaths are identified by operational moni-
toring. Thus, using the JAMSTEC data-
base, the information of the failues which
had been addressed enables to estimate
the lifetime of the current Argo float.
Assumptions on float improvements
APEX
- Almost no death caused from the failure of
the Druck pressure sensor.
- No death caused from the premature con-
sumption of battery cells before the 65th cycle
(voluntarily determined).
- Grounding does not cause float death.
PROVOR (made by Metocean)
- Float dives to deep layer to continue its nor-
mal operation after emergent surfacing.
- Float works normally under the very cold con-
ditions such as those around the Antarctica.
At present, many APEX floats managed
at JAMSTEC continue their operation at
sea: the life span of APEX will be further
extended in the near future. It is anticipat-
ed that an actual life span of 128 cycles
(ca. 3.5 years) will be realized for the cur-
rent APEX floats, even under the severe
condition of the Argo standard.
APEX
Metocean-Provor
Ave.: 99+ 116+
Med.: 115 132+
Ave.: 50 54
Med.: 65 67
Data
Dataset of GDAC
Total number of floats is 2839, and many of them do not
follow the Argo standard. Current status of the float is
defiend by the following criteria:
Active: the last measurement is conducted within 60 days of
the date for analysis (March 1, 2006).
Dead: Data with the last profile measured before 60 days.
Unknown: The date of the last profile is "unknown". Kaplan-
Meier method uses such data in the similar way of "active"
data.
Database managed at JAMSTEC
Total number is 4** (APEX *** and PROVOR ***), and all
floats follow the Argo standard. Operational monitoring of
float behaviours/data at JAMSTEC enables to estimate the
lifetime of Argo float more accurately. Thus, more severe
criteria (the total number of normal CTD mesurements) are
used for the analysis on the JAMSTEC floats.
In this analysis, the status of float (active or dead) is
determined by float behaviours: the floats which can not
measure normal CTD profiles due to some troubles (e.g.,
drifting ashore, the Druck sensor problem) are considered
dead.
This study uses two datasets for analysis.
Summary
As of March 1, 2006
The average life spans (unit is cycle) estimated in this study is the followings:
Average and Median represent the average life span and the median survival time.
: One Metocean-PROVOR float deployed by Japan was not registered to GDAC
because it had been missing since its deployment.
Float type Average Median No. of floats Note
Including many floats not following the Argo standard.
All types
110
99
2839
APEX
134
112
1637
120
110
1626
Removal of 11 super-long-living Japanese APEX floats which
exceeding the 180th cycle.
PROVOR
64+
71
425
Including 20 floats of MARTEC.
70+
74
348
Removal of 77 Metocean-PROVOR floats deployed by Japan. SOLO
87+
90
720
All floats follows the Argo standard basically.
All types
82+
82
395
Including 317 APEX floats and 78 PROVOR floats.
APEX
99+
115
317
116+
132+
(317)
Estimation of the current APEX: To refrect the improvements of
failures which have been fixed.
PROVOR
50
62
78
Manufactured by Metocean.
54
67
(78)
To refrect the improvements of failures which have been fixed.
GDAC
JAMSTEC