A. S. Franco
IOUSP, Brazil


In 1988 it was published our first paper on Tidal Analysis of Long Series: (Franco & Harari, 1988). The paper showed how 1014 constituents of tides could be separated through the analysis of tidal time series with a nodal cycle span. The analysis was worked out in a Borrough 6900 computer during 6 minutes giving excellent results.

Again in 1988 it was done a full use of the algorithm to have a good insight of the micro structure of the tide at Cananéia (SP) harbour. The result of such analysis was submitted to the Conference on Tidal Hydrodynamics held at Gaithersburg, Martyland USA (Franco & Harari, 1991). Many interesting conclusions were taken about the satellites of the main astronomical and the shallow-waters constituents.

Several constituents of the fourth power of the lunar parallax were isolated. In fact, constituents such as M3 which very large (about 7 cm) at Cananéia, merge with other important constituents to generate shallow-water ones.

Since Huthnance showed that the third diurnal constituents were enhanced by some kind of organ pipe resonance, we concluded from the analysis that there was also a third diurnal constituent, which we called F3 (0.74 cm), probably enhanced by the same effect.

In 1991 we submitted a paper to the meeting of the IUGG, held in Vienna, showing that the harmonic constants of the long period constituents Sa and Ssa separated through the usual harmonic analysis of daily values of the MSL, were not constants (Franco & Harari). A considerable drift, both in amplitude and phase, for which we have not a scientific explanation, was identified.

The use of micro computers

From some years up to now we have worked with no interruption in writing software for micro computer to analyse and predicting tides. I believe that the "pack" I have prepared with 8 programs for such purposes and to solve some correlate programs is a very useful one as several foreign institutions are using the mentioned "pack".

This was a considerable stimulus to write a program to work out long series analysis with micro computers. In fact, such program should give an opportunity to people make tidal analyses at home with a very low cost.

It must be kept in mind that the IBM PC 386 DX, with the mathematical coprocessor is a very powerful machine which can be used to effect quickly very heavy computations. Then I started to try to write a new program to be used in these machines. This program is now ready and can be used to effect the same analysis as in the old Burroughs 6900 computer.

The running time is about 6 and a half minutes.

In that analysis the series is split into several subseries of 2 hours . 10 x 2 hours is equal to 18,69 Julian years, nearly equal to the nodal cycle (18,61). Thus the basis of the analysis of long series is the combination of 10 FFT analyses of 2 hours (Franco E& Harari, 1988).

However, the program was generalised in order to work out analyses of any number of subseries of that number of larger or equal the satellites can be separated. But if the number is less than 7 only the main constituents can be separated.

I believe that this summary is sufficient to give an idea of how powerful is the program.


I think that the above description of the method is sufficient to have an idea of the method of analysis and the software for modern PCs. A paper with more complete description of that program was just submitted to the International Hydrographic Bureau to be published in the I.H. Review.


I am very much in debted to Prof. A. R. de Mesquita and Dr J. Harari for their kind revision of this text and for the use of the excellent data of the Instituto Oceanográfico of the University of São Paulo. The program was tested with these data.


Franco, A. S. dos & Harari, J. 1988. Tidal analysis of long series. International Hydrographic Review, Monaco, LXV (1).

Franco, A. S. dos & Harari, J. 1991. A tidal analysis with a nodal cycle resolution level. Tidal Hydrodynamics . Edited by Bruce B. Parker. John Wiley & Sons.

Franco, A. S. dos & Harari, J. 1993. On the stability of long series tidal analysis. International Hydrographic Review, Monaco, LXX (1).