YoMaHa'07:
Velocity data assessed from trajectories of Argo floats
at parking level and at the sea surface
Konstantin V. Lebedev,
Hiroshi Yoshinari, Nikolai A. Maximenko, and Peter W. Hacker

IPRC Technical Note No.4(2)June 12, 2007

Konstantin V. Lebedev, Hiroshi Yoshinari, Nikolai A. Maximenko, and Peter W.
Hacker, 2007: YoMaHa’07: Velocity data assessed from trajectories of Argo floats
at parking level and at the sea surface, IPRC Technical Note No. 4(2), June 12, 2007.

Abstract

This variant of technical paper accompanies the release of public dataset YoMaHa'07 (theupdate of YoMaHa’05) and provides a brief description of its structure and thetechniques used for its preparation. The dataset contains estimates of velocities of deepand surface currents obtained using data of the trajectories from Argo floats. It includes
data from 4284 floats stored in nine Data Assembly Centers (DAC’s) worldwide andabout 297,000 values of velocity. This is a 41% increase in the number of floats and 78%
increase in the amount of data compared to YoMaHa’05. The data span the period from
August 04, 1997 through May 15, 2007. Surface velocities are linearly regressed fromfloat coordinates fixed by the ARGOS satellites. Deep velocities are estimates from floats
displacements during each submerged phase of the cycle. Both surface and deep
velocities are accompanied by error estimates, which are typically an order of magnitude
smaller than velocity values. The paper describes data distribution in space, time andbetween the DAC’s as well as probability distributions of programmed float parametersand statistics of their displacements. Possible application of the dataset is illustrated on
the example of the ensemble-mean velocity field.

iTable of content

1.

Introduction……………………………………………………………………1
1.1 What is Argo?.………………………………………………………………1
1.2

Argo data flow………...……………………………………………………1

1.3. Float design and data format………………………………………………...1
2.

YoMaHa'07 dataset…………………………………………………………...22.1. Argo array description and problems with data at DAC’s………..………..2
2.2. Characteristics of YoMaHa'07 dataset……………………………………....3
2.3. Applications………………………………………………………………...82.4. Format of YoMaHa'07 dataset……………………………………………..10

3.

Acknowledgments……………………………………………………………13

4.

Appendices…………………………………………………………………...134.1. Appendix A. Error assessment of deep velocity due to vertical shear ofhorizontal flow……………………………………………………………..13
4.2. Appendix B. Assessment of surface velocity and its error………………….14

5.

References……………………………………………………………………15

6.

Contacts………………………………………………………………………16

7.

Copyright…………………………………………………………………….16ii

1. Introduction
1.1. What is Argo?
Argo is an international program providing a nearreal-time assessment of the state of global ocean froman array of autonomous profiling floats. Program
began in 2000 and the number of active floats grows

fast having reached 2852 floats by the time of thiswriting. Their positions are shown in Figure 1. Whenthe array will reach the target number of 3000, it will
be providing data on a roughly 3° global grid.

Figure 1. Distribution of active Argo floats (the floats that have delivered data within the last 30 days)on June 8, 2007 (image downloaded from http://www.argo.ucsd.edu/FrAbout_Argo.html )1.2. Argo data flow
The array consists of coordinated regional
deployments and is made up of 25 different
countries’ contributions. The U.S. contribution isabout 50% of the global array. Raw data are publicly
available in near real-time via the Global
Telecommunications System. 24 hours later, realtime quality controlled trajectory data are stored atnine national/regional Data Assembly Centers(DAC’s), which also provide ultimately corrected
profile data with a few months delay. The data also
include pre-Argo floats of similar design. Two
GDAC’s (global DAC’s), USGODAE andIFREMER, manage global Argo dataset compiled offolders-images of the nine DAC’s. In the U.S.A., theftp gate to the data is
http://www.usgodae.org/ftp/outgoing/argo/ .

1.3. Float design and data format
There are three main types of Argo floats (APEX,SOLO and PROVOR) and at least six other types thatdiffer in nuances. Common among all the floats isthat they are able to change their buoyancy bypumping water in and out of an external bladder andare designed to spend most of their lifetime on somepre-selected isobaric surface (so-called, parking
pressure). During the ascent, the float measures andstores a CTD profile that is transmitted to ARGOS
satellite when the float reaches the sea surface. Samesatellite detects coordinates of the float as long as thelatter drifts at the sea surface. The floats thus work incycles. Schematic of a typical cycle is shown in1

Figure 2. The n-th cycle starts (a time Tndive ) when afloat begins to descend from the sea surface to theparking level (which it reaches by time Tnbeg ). As arule just before the beginning of the ascent, a float
dives (at time Tnend ) to a slightly larger depth. As it
surfaces at Tnsurf , it starts transmitting data. It stays at
the sea surface long enough to insure that ARGOS
satellites will receive the information. Transmissions
stop with the beginning of the next, n+1-th cycle at
Tn+1dive. Tnfirst and Tnlast indicate in Figure 2 first andlast transmissions, respectively, received (fixed) bysatellite during the n-th cycle of the float. As a rule
more than two transmissions are received.

Figure 2. Time-depth schematic of a float cycle. Red dots mark satellite fixes of the float at the sea surface.
Data from the float are stored in files of four different
types: meta, profile, trajectory and technical files.
“Meta” file contains pre-programmed information on
the float cycles. Data of individual CTD-profiles are
stored in the “profile” files (one per a cycle) and canbe used just like ship-borne CTD data. At present,
profile data is the most heavily used output of the
Argo program. Trajectory (“traj”) file contains
information on three-dimensional movement of thefloat. It basically consists of a set of coordinates ofthe float during its transmissions from the sea surface
and, in some instances, recorded pressure during the“parked” phase of the cycle. By itself, description of
the float trajectory in the “traj”-file is largely
incomplete. Typical duration of the cycle is 10 days
and, to ensure successful reception of data, a typicalstay at the sea surface is between 12 and 24 hours. In
most cases, a float is programmed to repeat the same
cycle. However, in some instances parking pressure
was programmed to vary cycle to cycle. Cycle
duration and parking pressure also change as the float
deteriorates and as it moves from one water mass tothe other [e.g., Park et al., 2005b].

This work is an attempt to extract information on surface and deep velocities using simple assumptions inapplication to Lagrangian part of the Argo floats. To the best of our knowledge this is the first suchdatabase utilizing data stored in all Argo DAC’s and covering the whole World Ocean.

2. YoMaHa'07 dataset
2.1. Argo array description and problems with data at DAC’s
We started at
http://www.usgodae.org/ftp/outgoing/argo/ and havedownloaded all data available at all nine DAC’s on
May 16, 2007. It included data of 4284 floats ranging
from August 04, 1997 through May 15, 2007. Data
from individual floats received from different DAC’s

2

were converted into same format and merged. This
procedure was complicated by differences between
processing techniques and actual formats of“trajectory” data in different DAC’s. In addition, anumber of apparent errors have been found in thequality-controlled data. These include:- Time inversion/duplication
In some trajectory files the timeline is not monotonic.
This is due to the errors in the time values, not amatter of the order of lines in the file. At time of
YoMaHa’05, this problem was most serious in thedata of INCOIS, but similar problems (mostly
duplicates) were also detected in data of all DAC’sand in 14% of all cycles. In this database we flag
- Coordinate spikes
In a number of cases large jumps in float
coordinates were detected. In simple cases,
corrections have been made by comparing withcycles with time problem and will address the
problem more adequately in future. In addition,
problem appeared in the recent version of INCOIS
files containing wrong julian time. When possible,
we used old, better, version of the problematic files
and notified the DAC about the error.

the “profile” files. BODC DAC has been notified
about the problem in their data and corrected
files were submitted to BODC.

2.2. Characteristics of Yomaha'07 dataset
Dataset Yomaha'07 contains data of 4284 floats
stored in the DAC’s. Total number of cycles in
YoMaHa'07 is 296974, 290247 of which provided
estimates of velocity at a float’s parking depth,
294201 provided estimates of surface current and
287474 provided both deep and surface velocities
during the same cycle.
As shown in Figure 3, the DAC at AOML contains
52% of the Argo float data and AOML, CORIOLIS
and JMA together provide about 84%. However,
Figure 4 illustrates that smaller datasets of the six
other DAC’s are important in a number of regions.
Figure 3. Number of floats and their cycles stored at
individual DAC’s and included into YoMaHa'07
dataset.

Figure 4. Data distribution between the Argo DAC’s. Shown are locations of velocity estimates at parking
depth gathered in YoMaHa'07.

3

Figure 5. Monthly number of the float cycles stored
in YoMaHa'07. Red line marks the end of the period
covered by YoMaHa’05.

Figure 5 shows the growing number of cycles
available for velocity estimates. Annual coverage ofthe World Ocean with the data is presented in
Figure 6.

Figure 6. Annual distribution of Argo velocity estimates in YoMaHa'07.

Figure 7. Number of cycles in 10-dbar intervals of the float parking pressure. Red dashed lines separate
four layers selected for Figure 8.

4

As seen in Figure 7, the majority of the data in YoMaHa'07 came from the floats programmed for theparking pressure 1000 dbar (63% of total data volume), 2000 dbar (12%) and 1500 dbar (14%). Horizontal
distribution of Argo floats in different layers is shown in Figure 8.

Figure 8. Distribution of Yomaha'07 deep velocity data in four layers shown in Fig.7.

Figure 9a. Probability density function (PDF) of
float cycle lengths stored in YoMaHa'07.
Average value is 9.5 days, 85% of values lie
between 8.9 and 11.5 days.

Figure 9b. PDF of duration of float stay at thesea surface. Average value is 10.1 hours.

Figure 9c. PDF of float stay under water.
Average value is 9.1 days.

5

Figure 10a. PDF of displacement during one
cycle. Mean value is 45.4 km.

Figure 10b. PDF of displacement at the sea
surface. Mean is 9.7 km.

Figure 10c. PDF of the number of transmissions
received by ARGOS satellite from the float
during its stay at the surface during one cycle.
Mean is 10.8 fixes.

Figure 10d. PDF of the float displacement
while submerged. Mean is 41.0 km.

As follows from Figures 9 and 10, a typical float included into the YaMaHa’07 dataset most probably is
programmed for a 10-day cycle with 8-hour duration of the surface phase. During one cycle the float moves
over the distance about 15 km, most of which it makes underwater. Displacements at the sea surface,during which the float will most likely send eight successful messages to the satellite, is approximately 4
km. As all variables, whose probability distributions are shown in Figures 9 and 10, are essentially positive,
their statistics are naturally skewed toward larger values, so that mean values exceed corresponding mostprobable ones by a factor of 1.2-2.5.
Of particular importance are statistics of velocities
that are the essence of this dataset. Probability
density function of velocity estimates at parking level
shown in Figure 11a has its maximum around 2 cm/s.
The weakness of deep currents makes their velocity
estimates sensitive to many known and unknown
errors. Unlike trajectories of SOFAR or RAFOS

6

floats, trajectories of Argo floats are essentially threedimensional. During ascending/descending phases of
the cycle floats are subject to effect of not only
vertically sheared geostrophic currents, but also
Ekman currents, inertial oscillations and otherprocesses specific to the upper ocean (e.g., Park et al.
[2004, 2005a]). Given the complexity of thesituation, certain optimism comes from Figure 11b,
which shows that simple estimates of velocity error
have most probable value of 0.25 cm/s and mean 0.53
cm/s. An order of magnitude difference between thevelocity and its error allows sensible quantitative
estimates even when a preliminary, simple technique

is employed. According to Figure 11c, most probablerelative error of the velocity at parking pressure (i.e.,error-to-velocity ratio) is 0.03 (3%), 54% of deep
velocity data have relative error less than 10% and97.6% of the data have velocity error smaller thanvelocity value.

Figure 11a. PDF of deep velocity. Mean is 5.5
cm/s.

Figure 11b. PDF of error of estimate of deep
velocity due to baroclinicity (as described inAppendix B). Mean is 0.53 cm/s.

Figure 11c. PDF of relative velocity error (in %)at the parking depth (blue bars and left y-axis)
and cumulative probability (in %, red line andright y-axis).

As shown in Figure 12 most probable surface
velocity is about 20 cm/s and its mean value is 28.2
cm/s. Probability of surface velocity error peaks at
1.9 cm/s and the mean error value is 2.9 cm/s.
Similarly to deep velocities, surface velocities exceed
their errors by an order of magnitude. Higher-order

7

techniques [Park et al., 2005a] may further improvethe confidence of the surface velocity data.
According to Figure 12c, most probable relative
error of the velocity at the sea surface is 0.06(6%), 45% of surface velocity data have relative
error less than 10% and 98.8% of the data havevelocity error smaller than velocity value.

Figure 12b. PDF of error of estimate of surface
velocity. Mean is 2.9 cm/s.

Figure 12a. PDF of surface velocity. Mean is28.2 cm/s.

Figure 12c. PDF of relative velocity error (in %)at the sea surface (blue bars and left y-axis) andcumulative probability (in %, red line and righty-axis).

2.3. Applications
To illustrate possible application of data in YoMaHa,
we calculated mean velocity based on the previous
version YoMaHa’05, both in the deep and at the sea
surface, by averaging data in bins of size 3°x3°. For
deep velocities we used all data with parking pressurelarger than 750 dbar and deep velocity error smaller
than 2 cm/s. For surface velocities we used all datawith the surface velocity error less than 15 cm/s.
Figure 13 shows surface circulation pattern similar tothe one observed with surface drifters [Maximenko

8

and Niiler, 2005]. Deep currents in Figure 13b are
extraordinarily strong in the Antarctic Circumpolar
Current and contain a number of peculiar structures
emerging from the generally noisy patches. The latterstructures are beyond the scope of this dataset
documentation and are a subject of our future study.
At present it is not clear whether the noise is due todata distribution, related to mesoscale eddies or aconsequence of errors in our data and methods.

Figure 13. Argo velocity statistics in 3°x 3° bins estimated from YoMaHa’05. Left column is for parking
level, right is for sea surface. Rows are number of cycles falling into the bin (top, a,e), mean zonal (b,f) andmeridional (c,g) velocity components, and magnitude of mean velocity (bottom, d,h). Units of velocities are
cm/s. Deep velocities with the error larger than 2 cm/s and surface velocities with the error larger than 15
cm/s are disregarded.

92.4. Format of YoMaHa'07 dataset
YoMaHa'07 dataset is a set of velocity estimatesat random times and locations. The techniquethat we employed was targeted at flow velocity
assessment at the float parking pressure and,independently, at the sea surface. However, tomake the comparison between surface and deep
currents simpler, we sorted all the data according
to the float number and the cycle number.

The dataset consists of nine files:- yomaha070612.dat- yomaha2wmo_070612.dat- DACs_060227.txt- float_types_070612.txt- MeanVpark3x3_060227.dat- MeanVsurf3x3_060227.dat- Copyright_070612.txt- YoMaHa070612.pdf- Sample_060227.f

2.4.1. File yomaha070612.dat is an ASCII file containing 28 following columns (same as
YoMaHa’05).
Columns 1-8 contain three-dimensional coordinates, time, components and errors of the deep float
velocity.
1-2. Coordinates (longitude Xndeep and latitude Yndeep)of location where deep velocity is estimated. These
coordinates are averages between last fixed float
position (Xn-1last , Yn-1last) at the sea surface during
previous cycle (stored in columns 16-17) and first fix(Xnfirst , Ynfirst)in the current cycle (stored in columns
19-20).
I.e., [X,Y] ndeep = ( [X,Y] n-1last + [X,Y] nfirst)/2 .
3. “Parking” pressure Zpark (dbars) for this cycle. Thisvalue is a pre-programmed value stored in the“meta”-file.
4. Julian time Tndeep (days) relative to 2000-01-01
00:00 UTC. (Adding 18262 will convert it into more
traditional Julian time relative to 1950-01-01 00:00

UTC.) This value is an average between the Julian
time of the last fix during the previous cycle (Tn-1last
stored in column 18) and the first fix in the current
cycle (Tnfirst stored in column 21). I.e., Tndeep = ( Tnn1last + T first)/2 .
5-6. Estimate of eastward and northward componentsof the deep velocity (Undeep , Vndeep) (cm/s) at Zpark
calculated from the float displacement from
[X,Y] n-1last to [X,Y] nfirst for time Tnfirst - Tn-1last.
7-8. Estimates of the errors of components of deep
velocity (εUndeep , εVndeep) (cm/s) due to a vertical shearof horizontal flow obtained as described in Appendix
A.

Columns 9-15 contain horizontal coordinates, time, components and errors of the float velocity at the sea
surface. Velocity is estimated using linear regression of all surface fixes for the cycle. Details are given in
Appendix B.
9-10. Coordinates (longitude Xnsurf and latitude Ynsurf)of location where surface velocity is estimated.
11. Julian time Tnsurf (days) relative to 2000-01-01
00:00 UTC when surface velocity is estimated.

12-13. Estimate of eastward and northward
components of velocity (Unsurf , Vnsurf) (cm/s) at
the sea surface.
14-15. Estimates of the errors of components ofsurface velocity (εUnsurf , εVnsurf) (cm/s) obtained as
described in Appendix B.

Auxiliary float and cycle data are in columns 16-27.
16-18. Coordinates (Xn-1last , Yn-1last) and Julian time
Tn-1last (relative to 2000-01-01 00:00 UTC) of the last
fix at the sea surface during the previous cycle.

1019-21. Coordinates (Xnfirst , Ynfirst) and Julian time
Tnfirst (relative to 2000-01-01 00:00 UTC)of the first
fix at the sea surface during the current cycle.

22-24. Coordinates (Xnlast , Ynlast) and Julian time Tnlast(relative to 2000-01-01 00:00 UTC)of the last fix at
the sea surface during the current cycle.
25. Number of surface fixes Nnfix during the current
cycle.
26. Float ID. To unify data of all DAC’s we recounted all the floats. Correspondence between our
float ID’s and WMO float ID’s used by the DAC’s isdescribed in our fileyomaha2wmo.dat
27. Cycle number. We adopted cycle numbersrecorded in data of the DAC’s.
28. Time inversion/duplication flag Ft. Ft = 1 if at
least one duplicate or inversion of time is found in
the sequence containing last fix from the previous
cycle and all fixes from the current cycle. Otherwise,
Ft =0.

Missing cycles
Our float ID number increases monotonicallythroughout yomaha070612.dat from 1 to 4284, andcycle number increases monotonically within data ofeach float. However, not all cycles are recorded, only
the cycles, data from which allowed an estimate of atleast one (deep or surface) velocity.

Missing values- Julian times, Tndeep , Tnsurf , Tn-1last , Tnfirst , andTnlast (columns 4, 11, 18, 21 and 24):
-999.999- parking pressure, Zpark (column 3): -999.9- velocity components, Undeep , Vndeep , Unsurf , andVnsurf (columns 5, 6, 12, and 13): -999.99- velocity errors, εUndeep , εVndeep , εUnsurf , andεVnsurf (columns 7, 8, 14, and 15): -999.99

The following values are used to mask missing
values:- longitudes, Xndeep , Xnsurf , Xn-1last , Xnfirst , and Xnlast(columns 1, 9, 16, 19 and 22):-999.9999- latitudes, Yndeep , Ynsurf , Yn-1last , Ynfirst , and Ynlast(columns 2, 10, 17, 20 and 23): -99.9999

2.4.2. File yomaha2wmo_070612.dat catalogs the float information included into YoMaHa'07
dataset.
This ASCII file contains four columns:
1. Serial YoMaHa'07 number of the float (varies from1 through 4284).
2. WMO float ID.

3. DAC where float data are stored (from 1 through9).
4. Float type (from 0 through 9).

2.4.3. File DACs_060227.txt describes the notations of the DAC’s names, which are as follows:
1. AOML (USA)
2. CORIOLIS (France)
3. JMA (Japan)
4. BODC (UK)
5. MEDS (Canada)

6. INCOIS (India)
7. KMA (Korea)
8. CSIRO (Australia)
9. CSIO (China)

112.4.4. File float_types_070612.txt describes the notations of the float types, which are as follows:

1. APEX
6. PALACE
2. SOLO
7. NINJA
3. PROVOR
8. NEMO
4. R1
9. ALACE
5. MARTEC
0. METOCEAN** Float 2524 (WMO ID 5900474), whose data are stored in CORIOLIS, has no float type specified in themeta-file. We guessed its type to be METOCEAN based on types of other CORIOLIS floats with close ID
numbers.
2.4.5. File MeanVpark3x3_060227.dat contains mean velocity values at the parking pressurelarger than 750 dbar averaged throughout the data offile yomaha05.dat within 3°x3° bins. Excluded are
only data with error larger than 2 cm/s. File is an
ASCII file containing the following five columns:

1. longitude and2. latitude of the center of the bin
3. zonal and4. meridional components of the mean velocity
5. number of data in the bin used for the average.

Left column of Figure 13 illustrates the data of MeanVpark3x3.dat.
2.4.6. File MeanVsurf3x3_060227.dat contains mean velocity values at the sea surface
averaged throughout the data of file yomaha05.dat
within 3°x3° bins. Excluded are only data with error
larger than 15 cm/s. File is an ASCII file containing
the following five columns:

1. longitude and2. latitude of the center of the bin
3. zonal and4. meridional components of the mean velocity
5. number of data in the bin used for the average.

Right column of Figure 13 illustrates the data of MeanVsurf3x3.dat.
2.4.7. File Copyright_070612.txt describes conditions of use of the dataset YoMaHa'07.
This file must always be in the same directory as file yomaha070612.dat.
2.4.8. File YoMaHa070612.pdf is a pdf copy of this June 12, 2007 version of the technical note.
2.4.9. File Sample_060227.f is a Fortran script illustrating how to access the data stored in YoMaHa'07
files.
2.4.10. File Update_log.txt is a new file added to the dataset to document changes in YoMaHa andrelease of auxiliary files.

123. Acknowledgments
This work was supported by the NOAA, NASA and Japan Agency for Marine-Earth Science andTechnology (JAMSTEC) through individual and institutional grants at the International Pacific ResearchCenter (IPRC) within the School of Ocean and Earth Science and Technology (SOEST) at the University of
Hawaii.
These data were collected and made freely available by the International Argo Project and the national
programs that contribute to it. (http://www.argo.ucsd.edu, http://argo.jcommops.org). Argo is a pilot
program of the Global Ocean Observing System.
The authors thank Sharon DeCarlo (APDRC/IPRC) for her valuable technical help.
The picture on the cover page was compiled using images downloaded from scuba.dvdesign.com and theArgo website.

4. Appendices4.1. Appendix A. Error assessment of deep velocity due to vertical shear of horizontal flow
We estimate components of deep (Undeep , Vndeep) vector at every cycle of the float using its coordinates before it
dives and after it re-arrives at the sea surface as(Undeep , Vndeep) = ([X,Y] nfirst - [X,Y] n-1last ) / ( Tnfirst - Tn-1last)(A.1)

This does not account for the fact that velocity varies with depth. Simple estimate of the error of (A.1) due tothe vertical shear of horizontal flow can be obtained as follows.
Let’s adopt the following assumptions:- vertical shear of the horizontal velocity is constant in vertical for a given cycle;- rate V0 of ascent and descent of the float on corresponding phases of the cycle is constant and isapproximately equal to 10 cm/s [Webb, personal communication, 2004];- differences between last fix and diving times as well as between surface arrival and first fix times are
negligible (i.e., communication of the float with satellite is continuous while the former is at the sea
surface).
Then deviation of the velocity estimate (A.1) from the true deep velocity (undeep , vndeep) can be shown to beequal to(Undeep,Vndeep) - (undeep , vndeep) = ((Unsurf,Vnsurf) - (undeep , vndeep))/( Tnfirst - Tn-1last) · Zpark / V0 =(A.2)

= ((Unsurf,Vnsurf) - (Undeep , Vndeep)) · α / (1- α),(A.3)

where (Unsurf,Vnsurf) is velocity at the sea surface, Zpark is parking depth and α = Zpark / V0 /( Tnfirst - Tn-1last) isa ratio of ascend or descend time to the total time float stays underwater. We define the errors of deep
velocity as(εUndeep , εVndeep) = | (Undeep,Vndeep) - (undeep , vndeep) |(A.4)

and calculate it using (A.3). Remarkably, the error is proportional to the velocity shear and is defined byduration of the float’s vertical excursions. We do not use (A.3) to correct the error because our model is too
simplistic. It neither accounts for the real baroclinic structure of the ocean nor discriminates between the
Ekman currents, inertial oscillations and geostrophic circulation. In addition, some floats are programmed

13

to dive to the level deeper than the parking depth before starting their ascent. This may disturb our error
estimate, but is not critical as vertical shear of horizontal velocity is largest in the upper ocean.

4.2. Appendix B. Assessment of float surface velocity and its error
We adopt a linear regression least squares method to calculate the surface float velocity Vsurf and its standard
error. y here is a coordinate, t is time and data consist of N pairs of y-t values. Optimal velocity is then the slopeof the line minimizing the distance to the data [Weistein, 1999]
Vsurf = a =∑ yt − N yt
∑ t − nt
2

2

(B.1)

where ‘ t ’ and ‘ y ’ denote the mean of t and y, respectively.
Standard error εV surf of Vsurf isεV surf =SSyy − a ⋅ SSty
1
N −2
SStt

(B.2)

where

SStt ≡ ∑ t 2 − N t , SSyy ≡ ∑ y 2 − N y , SSty ≡ ∑ ty − N t y
2

2

(B.3)

Zonal (meridional) component of surface float velocity and its error were calculated by substituting
properly scaled longitude (latitude) data to y in formula (B.1-3). Standard error here includes velocity
variations due to inertial oscillations. The latter have been found by Park et al. [2004] to be significantly
strong in the Japan/East Sea. However, our Figures 12 a-c illustrate that effect of inertial motions on global
velocity dataset is relatively small. Unaccounted in this approach is a slip of the float relative tosurrounding water under joint force of wind and waves. Similar effect directly measured with near-surface
drifters [Niiler et al., 1995] leads to sensible (a few cm/s) values of the slip under moderate (some m/s)
winds and can be even stronger for the Argo floats not having (unlike the drifters) the large drogue at 15m
depth.

14

4. References

Maximenko, N.A., and P.P. Niiler, 2005: Hybrid decade-mean global sea level with mesoscale resolution.
In N. Saxena (Ed.) Recent Advances in Marine Science and Technology, 2004, pp. 55-59. Honolulu:
PACON International.
Niiler, P. P., A. S. Sybrandy, K. Bi, P. M. Poulain, and D. Bitterman, 1995: Measurements of waterfollowing characteristics of Tristar and Holey-sock drifters. Deep-Sea Res., 42, 1951-1964.
Park, J. J., K. Kim, and W. R. Crawford, 2004: Inertial currents estimated from surface trajectories of
ARGO floats. Geophys. Res. Lett., 31, L13307, doi: 10.1029/2004GL020191.
Park, J. J., K. Kim, and B. A. King, 2005a: Global statistics of inertial motions. Geophys. Res. Lett., 32,
L14612, doi: 10.1029/2005GL023258.
Park, J. J., K. Kim, B. A. King, and S. C. Riser, 2005b: An advanced method to estimate deep currents
from profiling floats. J. Atmos. Oceanic Technol., 22, 1294-1304.
Weistein, E.W., 1999: The CRC concise encyclopedia of mathematics, Chapman & Hall/CRC, p.1047.

15

5. Contacts
Comments, questions regarding the YoMaHa'07 dataset and requests for the data can be directed to any of
the authors.
Konstantin Lebedev, Nikolai Maximenko, and Peter Hacker are affiliated at
IPRC/SOEST, University of Hawaii, 1680 East West Road, POST Bldg. #401, Honolulu, HI 96822-2327, USA
Hiroshi Yoshinari works at Physical Oceanography Section, Marine Productivity Division, National ResearchInstitute of Fisheries Science, Fisheries Research Agency, 2-12-4 Fukuura, Kanazawa-ku,
Yokohama 236-8648, Japan.
The authors can also be contacted by phone or e-mail at:
Konstantine V. Lebedev
Hiroshi Yoshinari
Nikolai A. Maximenko
Peter W. Hacker

E-mail: klebedev@soest.hawaii.edu
E-mail: hyy@affrc.go.jp
E-mail: nikolai@soest.hawaii.edu
E-mail: phacker@hawaii.edu

Tel.: 1 (808) 956-9710
Tel.: 81-45-788-7648
Tel.: 1 (808) 956-2584
Tel.: 1 (808) 956-9312

Fax at IPRC is 1 (808) 956-9425 and at NRIFS 81-45-788-5001.
Link to the YoMaHa’07 webpage at the Asia-Pacific Data-Research Center (APDRC) is throughhttp://apdrc.soest.hawaii.edu/projects/

6. Copyright
YaMaHa’07 dataset is open for free unrestricted use, copying and distribution. The dataset is a research
quality product. Errors reported to the authors by users will be published and corrected in the next update ofthe dataset.
Use of the data should be acknowledged in the following form:“This study used the data of YoMaHa’07 [Lebedev et al., 2007] dataset of velocities derived from Argo
float trajectories provided by APDRC/IPRC.”
Reference of this technical paper:
K. V. Lebedev, H. Yoshinari, N. A. Maximenko, and P. W. Hacker. YoMaHa’07: Velocity data assessedfrom trajectories of Argo floats at parking level and at the sea surface, IPRC Technical Note No. 4(2), June
12, 2007, 16p.
When copying data from YoMaHa’07, the copyright file “Copyright_070612.txt” must be also copied andkept in the same directory as the file “yomaha070612.dat”.

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