Why t_tide prediction is offseted?

Hi, i'm trying to use t_tide_v1.4beta using matlab R2016a in 2 ways like in t_tide example but the result of the harmonic constants is not similar and the prediction is not similar between prediction also offseted to the observation data. Help me please. Herewith the code and the data that I use.

Code:

clear
clc

%format LONGG
%load t_example
% load data excel
data = readtable('D:\Test\T_Tide\t_tide_v1.4beta\kmna_wnan.xlsx');

time_axis = datetime(data.waktu);

data_time = datenum(time_axis);
obs_value = data.ukuran;

% Analisis Harminik
%---------------------------------------------------------------------------

% Way 1
% analisys
[NAME,FREQ,TIDECON,XOUT] = t_tide(obs_value,'interval',1,'start',data_time(1),'latitude',-3.66295,'synthesis',1);
% prediction
YOUT=t_predic(data_time,NAME,FREQ,TIDECON,'latitude',-3.66295,'synthesis',1);

% Way 2
% analisys
[HarKons,XOUT2]=t_tide(obs_value,'interval',1,'start',data_time(1),'latitude',-3.66295,'rayleigh',1,'synthesis',1);
% prediction
%    YOUT=T_PREDIC(TIM,TIDESTRUC,...)
YOUTHarKons1=t_predic(data_time,HarKons,'latitude',-3.66295,'synthesis',1);
YOUTHarKons2=t_predic(data_time,HarKons);

%% visualisasi
figure(1)
plot(time_axis,obs_value,'b','LineWidth',1.5); hold on
plot(time_axis,XOUT,'r--','LineWidth',1.5); hold on
plot(time_axis,YOUT,'c.','LineWidth',1.5); hold on
plot(time_axis,YOUTHarKons1,'kx','LineWidth',1.5); hold on
plot(time_axis,YOUTHarKons2,'ko','LineWidth',1.5); hold on
title('Tidal Elevation','FontSize',14,'fontWeight','b')
legend({'obs_value', 'XOUT', 'YOUT', 'YOUTHarKons1', 'YOUTHarKons2'},'FontSize', 10, 'FontWeight', 'bold', 'Location', 'northeastoutside');
xlabel('Time','FontSize',14,'FontWeight','b')
ylabel('Elevation (m)','FontSize',14,'FontWeight','b')
% Format sumbu X agar menampilkan tanggal/waktu
% datetick('x', 'dd/mm/yyyy HH:MM:ss', 'keepticks', 'keeplimits')
grid on

Tidal graph obs_value and prediction:

Data:

Answer 1

[William Rose]

@Ghani,

The predictions from t_tide do not include a DC (i.e. zero-frequency) term. Therefore the t_tide predictions have zero mean value, since they are a sum of sinusoids with non-zero frequency. You can see this in the original article by the authors of t_tide, here. Compare panels A and B of Figure 1 in the article. The data to be fitted, in panel A, has non-zero mean value. The prediction in panel B has mean value equal to zero.

You can compute the mean value of your sample data, then add it to the t_tide prediction, so that the t_tide prediction better. If you publish this, explain what you have done. Or you can subtract the mean value from your signal before you plot it, so that it corresponds to the t_tide prediction.

Good luck with your research.

[Ghani]

Thank you for the reply William. After read your answer and some browsing for the video tutorial, I relize that the prediction of the t_tide indeed located in the zero mean value not around the observation data. And I look in the command window there is displayed x0 that represent the mean value. In the t_tide.m file x0 are as a part of the coef matrix and it writen as z0. And what I do it to make this z0 variable and value are usable is modify the function argument from 4 arguments to 5 arguments, so the z0 wiil be appeared in the workspace window and can be used for prediction computation.

from this ==> function [nameu,fu,tidecon,xout]=t_tide(xin,varargin)

to this ==> function [nameu,fu,tidecon,xout,z0]=t_tide(xin,varargin)

The Way 1 script become:

[NAME, FREQ, TIDECON, XOUT_raw, MSL_val] = t_tide(obs_value, 'interval', 1, 'start', data_time(1), 'latitude', -3.66295, 'synthesis', 1);

XOUT = XOUT_raw + MSL_val;

The prediction XOUT now at the same mean value with the obs data. But, I still couldn't found the way for the function that using 2 arguments [TIDESTRUC,XOUT]=T_TIDE(XIN) in Way 2. When I modified it to 3 arguments by added the z0 variable as the 3rd argument the result is the same result of tidecon in the Way 1.

[William Rose]

@Ghani,

It sounds like you have solved your problem with your Way 1 method.

I am not sure why your Way 2 method is not giving you the results you want.

I do not like to modify function t_tide(), because it I did not write t_tide(), so I do not fully understand it, and it interacts with other functions that are part of the t_tide package. Any changes I make could have unexpected effects. Therefore I do not modify t_tide(). I do want the predictions to look like the data, so I compute the mean of the good data points (excluding NaNs) and I add the mean to xout when plotting the results. The example below, which is runnable in thre Matlab Answers window, shows this. Scroll to bottom to see the plot of measured and predicted tide data.

load('data2share');
% Vector elev is from satellite data, and includes NaNs.
% tInterval is the time between satellite passes.
%% Identify missing points
gd=find(~isnan(elev));  % indices of good points
%% Compute mean
meanElev=mean(elev(gd));  % mean of observations

Next: analyze the data.

% Analyze tide components
unzip('tide3')                          % reference data used by t_tide
[tidestruc,xout]=t_tide(elev,...
       'interval',tInterval, ...        % sampling interval
       'error','wboot');                % CI from white noise model

   number of standard constituents used: 68
   Points used: 277 of 280.
   percent of var residual after lsqfit/var original: 44.00 %
   Phases at central time
   Using nonlinear bootstrapped error estimates
   Generating prediction without nodal corrections, SNR is 2.000000
   percent of var residual after synthesis/var original: 70.30 %
-----------------------------------
date: 04-Jan-2026
nobs = 280,  ngood = 277,  record length (days) = 2776.38
rayleigh criterion = 1.0
Phases at central time

x0= -7.55, x trend= 0

var(x)= 0.18876   var(xp)= 0.068388   var(xres)= 0.1327
percent var predicted/var original= 36.2 %

     tidal amplitude and phase with 95% CI estimates

tide   freq       amp     amp_err    pha    pha_err     snr
*SA   0.0001141    0.3660    0.048   271.49     7.53       59
 SSA  0.0002282    0.0319    0.045   135.94    87.23     0.51
 MSM  0.0013098    0.0634    0.046    22.45    44.41      1.9
*MM   0.0015122    0.0830    0.052   254.43    28.73      2.6
 MSF  0.0028219    0.0319    0.037   149.33    88.55     0.72
 MF   0.0030501    0.0521    0.046   213.28    56.41      1.3
*ALP1 0.0343966    0.0898    0.047   217.08    32.20      3.6
 2Q1  0.0357064    0.0249    0.035    89.68    87.66     0.52
 SIG1 0.0359087    0.0586    0.043   322.33    52.24      1.8
*Q1   0.0372185    0.0842    0.049   106.74    33.37      2.9
*RHO1 0.0374209    0.0615    0.043    86.51    45.56        2
 O1   0.0387307    0.0402    0.042   263.60    70.89     0.94
*TAU1 0.0389588    0.0758    0.049     1.45    36.87      2.4
*BET1 0.0400404    1.6590    0.050   182.22     1.66  1.1e+03
 NO1  0.0402686    0.0362    0.038   238.86    75.31      0.9
*CHI1 0.0404710    0.8147    0.046    26.76     2.82  3.2e+02
 PI1  0.0414385    0.0112    0.038   122.76   169.73    0.087
*P1   0.0415526    1.9927    0.045   348.48     1.36    2e+03
 S1   0.0416667    0.0483    0.044   102.07    54.76      1.2
 K1   0.0417807    0.0646    0.047   355.38    45.78      1.9
*PSI1 0.0418948    0.1604    0.051    89.28    17.41      9.9
 PHI1 0.0420089    0.0658    0.051    39.27    44.76      1.7
 THE1 0.0430905    0.0437    0.044   136.50    65.97        1
 J1   0.0432929    0.0384    0.043    87.30    75.89     0.79
 SO1  0.0446027    0.0471    0.044   227.46    56.43      1.2
 OO1  0.0448308    0.0480    0.044   347.13    59.22      1.2
*UPS1 0.0463430    0.2755    0.043   107.41     9.79       41
 OQ2  0.0759749    0.0071    0.034    75.49   201.44    0.043
 EPS2 0.0761773    0.0560    0.047    21.28    48.21      1.4
 2N2  0.0774871    0.0442    0.040   222.65    59.76      1.2
 MU2  0.0776895    0.0580    0.044    89.16    44.10      1.8
*N2   0.0789992    0.0802    0.042   358.04    35.22      3.6
*NU2  0.0792016    0.1147    0.042   184.14    23.38      7.4
*GAM2 0.0803090    2.0321    0.046   190.40     1.44  1.9e+03
 ALP2 0.0803973    0.0353    0.041   175.06    73.31     0.73
*M2   0.0805114    0.1229    0.049   243.11    21.14      6.2
 BET2 0.0806255    0.0530    0.042   346.67    44.96      1.6
 MKS2 0.0807396    0.0409    0.044   174.98    68.62     0.88
*LDA2 0.0818212    1.6516    0.049   356.29     1.63  1.1e+03
*L2   0.0820236    0.0764    0.043   121.30    39.60      3.2
 T2   0.0832193    0.0333    0.040    90.91    85.56      0.7
*S2   0.0833333    0.0834    0.043   300.44    32.90      3.8
*R2   0.0834474    0.1088    0.045   260.93    25.60      5.9
 K2   0.0835615    0.0692    0.054    62.98    39.12      1.7
 MSN2 0.0848455    0.0263    0.037   124.23    96.56     0.51
 ETA2 0.0850736    0.0375    0.044   197.33    81.17     0.74
 MO3  0.1192421    0.0328    0.040   159.09    85.07     0.68
 M3   0.1207671    0.0437    0.040    37.78    62.98      1.2
 SO3  0.1220640    0.0425    0.042   116.12    57.80        1
 MK3  0.1222921    0.0477    0.045   198.79    48.40      1.1
 SK3  0.1251141    0.0582    0.043   136.45    48.56      1.8
 MN4  0.1595106    0.0568    0.053   217.32    42.47      1.1
 M4   0.1610228    0.0297    0.030   271.71    81.48     0.95
*SN4  0.1623326    0.8247    0.052   204.25     3.40  2.6e+02
 MS4  0.1638447    0.0578    0.052   221.41    44.01      1.2
 MK4  0.1640729    0.0524    0.043   318.21    53.00      1.5
 S4   0.1666667    0.0288    0.039   120.59    81.82     0.55
 SK4  0.1668948    0.0561    0.047   280.52    49.21      1.4
*2MK5 0.2028035    0.0731    0.047   111.51    39.85      2.4
 2SK5 0.2084474    0.0341    0.040   334.61    77.63     0.74
 2MN6 0.2400221    0.0436    0.044    87.43    57.97     0.99
*M6   0.2415342    0.0683    0.043   104.37    42.06      2.5
*2MS6 0.2443561    0.0830    0.044    16.30    32.01      3.5
 2MK6 0.2445843    0.0337    0.037   210.47    84.14     0.82
 2SM6 0.2471781    0.0390    0.046    33.38    71.91      0.7
 MSK6 0.2474062    0.0300    0.044   166.65    77.45     0.47
 3MK7 0.2833149    0.0528    0.043   304.40    49.01      1.5
 M8   0.3220456    0.0586    0.046   317.17    47.34      1.6

Next: Plot results. Add meanElev to xout when plotting.

% Plot elevation versus time,  observed & fitted & residuals
figure;
plot(obsTime,elev,'-b.',...
     obsTime,xout+meanElev,'rx', obsTime,elev-(xout+meanElev),'-g+')
title([filename,': Elevation versus Time'],'Interp','none')
xlabel('Date'); ylabel('Elevation (m)')
grid on; legend('Observed','Fitted','Residual')