Physical Oceanography, Vol. 19, No. 6, 2009
ANALYSIS OF OBSERVATIONS AND METHODS FOR CALCULATING
HYDROPHYSICAL FIELDS IN THE OCEAN
A METHOD OF ESTIMATION OF THE RESULTS OF RECONSTRUCTION OF
THE TRAJECTORIES OF DRIFTING BUOYS
A. P. Tolstosheev
A method for the estimation of the results of reconstruction of the trajectories of drifting buoys is
proposed. It is based on the comparison of the estimates of power spectral densities for the com-
ponents of current velocity computed according to three data sets: the data set of the coordinates
of a drifting buoy with a built-in GPS receiver, the data set of coordinates formed on the basis of
the first set but with data missing and observational errors corresponding to the actual trajectory
measurements by the Argos satellite location and data collection system by the Doppler method,
and the data set of coordinates obtained as a result of interpolation of the second set. As an ex-
ample, we consider the procedure of realization of the proposed method and demonstrate the ef-
ficiency of its application for the improvement of the reliability of reconstruction of the trajecto-
ries of drifting buoys.
Despite the undoubted efficiency of application of the autonomous Lagrangian drifting buoys for the inves-
tigation of the surface currents in the Black Sea [1–3], the problem of increasing the accuracy of reconstruction
of the trajectories of drifters according to the data of the Argos satellite location and data-collection system ob-
tained by using the Doppler method (“Doppler” data) remains quite urgent. The analysis of the data of more
than 70 buoys launched in the Black Sea in 1999–2007 shows that, in addition to the error of the method, the re-
liability of the results of reconstruction of their trajectories is strongly affected by the nonuniformity of time in-
tervals between the locations. The histograms of the time intervals between the successive locations plotted ac-
cording to the data corresponding to some of these buoys launched in the Black Sea in 2001–2006 are presented
1. These estimates were obtained by using the data of drifters with the longest periods of Lagrangian drift
(i.e., drift with attached underwater drogue). As follows from Fig.
1, the time intervals between coordinate read-
ings do not exceed
cases. At the same time, these series may contain intervals with data
missing for up to
h. This is mainly explained by the natural fluctuations of the characteristics of the channels
of satellite communication and the number of servicing satellites. In seldom cases, due to the specific features of
data delivery to the users, one can also encounter longer periods of data missing. Clearly, the direct application
of these time series of buoy locations can lead to serious errors in the results of analysis, especially in the case of
reconstruction of relatively high-frequency transport processes in the surface waters.
The method traditionally used for the reconstruction of the trajectories of drifting buoys  is based on the
linear interpolation of the primary data. However, the results of its application are reduced to the possibility of
filling the time intervals with missing information by the data reflecting, with a certain degree of accuracy, the
actual trajectory of a buoy only in the case of its rectilinear drift.
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol, Ukraine.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
23–32, November–December, 2009. Original article submitted August
14, 2008, revision submitted November 7, 2008.
358 0928-5105/09/1906–0358 © 2009 Springer Science+Business Media, Inc.