<<nfTides>> An experimental alogirthm to implement a parametric tidal frequency analysis of time series by robustly fitting the four complex Admiralty basis functions M2A, S2A, K1A and O1A to the time series while also implementing an optional signal drift removal algorithm.

Admirality basis functions M2A and S2A represent the semi-diurnal tidal variations, and K1A and O1A the diurnal tidal variations. In contrast to Fourier or harmonic-based tidal analyses, which decompose the time series into a sum of stationary (non-time variant) sinusoidal basis functions, the Admirality M2A, S2A, K1A and O1A basis functions are non-stationary and pseudo-sinusoidal. These represent a more compact form of the 20 most important Harmonic Method components as follows (where each of the Admiralty basis functions represents a condensed combination of anywhere from 3 to 7 harmonic components) [Table from Admiralty Tidal Handbook, No. 3, published by the UK Hydrographic Office]:

Admiralty Method Component     Harmonic Method Component       Period (hours)      Relative Magnitude Within Group
                     M2A                                               2N2                                   12.90                          0.02534
                                                                           mu2                                   12.87                          0.03057
                                                                             N2                                    12.66                         0.19146
                                                                           eta2                                   12.63                          0.03636
                                                                             M2                                   12.42                          1.00000
                                                                    lambda2                                   12.22                          0.00738
                                                                              L2                                   12.19                          0.02827

                     S2A                                                 T2                                    12.02                          0.05861
                                                                             S2                                    12.00                         1.00000
                                                                             K2                                    11.97                          0.27215
                    K1A                                                  pi1                                    24.13                         0.01939
                                                                             P1                                    24.06                         0.33093
                                                                             K1                                    23.94                         1.00000
                                                                           phi1                                    23.81                         0.01424
                                                                              J1                                    23.09                         0.05591
                   O1A                                                 2Q1                                    28.02                        0.02534
                                                                       sigma1                                    27.84                       0.03056
                                                                              Q1                                    26.87                       0.19146
                                                                            rho1                                    26.73                       0.03637
                                                                              O1                                    25.83                       1.00000

The parameters calculated by <<nfTides>> are the amplitudes (H1, H2, H3, H4) and phase-lags (g1, g2, g3, g4) that are applied to each of the four basis functions (M2A, S2A, K1A, O1A) that minimize the misfit between the original time series and a time series generated from the four basis functions (after the original time series has either first had its mean value or a Bayesian drift term removed from it).

The four complex-valued Admiralty basis functions are published annually by the UK Hydrographic Office, in the "Admiralty Tide Tables" under "Tidal Angles and Factors". In this table they appear as daily values of the functions F_j(t) and phi_j(t), valid at 00h00 UT, where the tidal part of the time series, f(t) is taken to by the superposition of the four basis functions: f(t) = Sum from j=1,4 of H_j F_j(t) cos (phi_j(t)-g_j) + e(t), where e(t) is the uncorrelated noise, F and phi are the amplitude and phase, and H_j and g_j are the basis functions. In this representation, F_j(t) and phi_j(t) are the temporal modulations in amplitude and phase of the basis functions necessary to represent the original time series.

<<nfTides>> reads in the daily values for the Admiralty basis functions from a file "admirality.in" which must be present in the installation directory. The default version of this file, as distributed with the source code, has basis functions defined for each day in 1988 through the beginning of January 2000. The extent of the valid time window for the basis functions is easily extended by referring to the latest Adminralty Tide Tables publication, as referenced above. The format of "admiralty.in" is as follows:

             column 1            column 2           column 3         columns 4,...,11
             YYYY                  MM                 DD               integer angles and tidal factors

where YYYY is the year, MM is the month, DD is the day of month, a factor of 1.12 would be written as 112, and angles are in integer degrees. IT IS ESSENTIAL TO NOTE THAT ALL DATES/TIMES ARE IN UNIVERSAL TIME (GMT). If time series time stamps are not in UT, the analysis will be invalid.

 <<nfTides>> interpolates the basis functions between the published day values.

 Input file format:

<<nfTides>> requires only one input file - containing the time series to be analyzed. A simple text (ASCII) file format is used. The input file must have no header, and 7 columns separated by white spaces:

             column 1           column 2          column 3          column 4          column 5         column 6        column 7

              YYYY                    MM                    DD                    HH                    MM                   SS               time series

where YYYY is the year, MM is the months, DD is the day, HH is the hour, MM is the minute, SS is the seconds, and "time series" is the value of the time series at that time.

TO REPEAT - IT IS ESSENTIAL THAT ALL DATES/TIMES IN THE INPUT FILES BE PROVIDED IN UNIVERSAL TIME (UT/GMT), OTHERWISE THE ANALYSIS WILL BE INVALID! All phase delays reported by <<nfTides>> are relative to UT, i.e. hours from the prime meridian at Greenwich, UK. Understanding this is critically important to interpreting the results of <<nfTides>>, since the phase delay from 0 degrees longitude is the way in which one can distinguish between ocean and earth tidal modulation.