Tidal Harmonic analysis, by finding the amplitude and the phase of each tidal component

In the exercise i have to find the amplitude and the phase at tidal component M2 annd S2, which M2 describes the sea surfase elevation because of the Moon and S2 due to the Sun, by coding some expression. Also, I have data of observed sea surface for one year and the length of timestep in 1 hour.

Tthe expression that I have to use is Am=(2/K)Σ(Xk'cos[(2pi/Tm)kΔt], Bm=(2/K)Σ(Xk'sin[(2pi/Tm)kΔt], the amplitude is equal to Hm^2=(Am^2)+(Bm^2)

what I know is:

Tm describes the period of each body rotation, for example for tidal component M2 is 12.42 hr.

Xk' describes the observed sea surface anomalies

K+1 is the number of observation or discrete hourly readings

Also what I have to consider is the tidal period Tm. What I know is that the length of analysed portion of the sea level time series is a multiple M of the tidal period for tk=M*Tm, tk is the total duration of the time series, tk=K*Δt where Δt is considered as 1 hr, describing the lenght of timestep.

My problem is that if I have to put the M somewhere in my expression, or I only take it into account finding the specific number of observations.

Btw I already coded, the scales of amplitude is okay but I don't find the results that i suppose to have.

Answer 1

[KSSV]

Refer these file exchange packages.

https://www.eoas.ubc.ca/~rich/

https://in.mathworks.com/matlabcentral/fileexchange/46523-utide-unified-tidal-analysis-and-prediction-functions

https://in.mathworks.com/matlabcentral/fileexchange/19099-tidal-fitting-toolbox

https://in.mathworks.com/matlabcentral/fileexchange/24217-world-tides

[Andriani Gl]

Hy! Thank you very much to share these files. I found what I wrote wrong. However for what I had to do, they don't actually help me, because I had to do something very simple as an exercice, not coding in a clear meaning of model.

Best,

Andriani.