# Tidal prediction 
The tidal prediction is calculted for harmonic coefficient for each tidal constituent as :

$
\eta_{tides}(t) = Re\left( \sum^{n=M2, S2...} f_n(t) A_ne^{i\left(\omega_nt + u_n(t) -\phi_n\right)} \right)
$

with $A$ the amplitude, $\omega$ the tidal pulsation and $\phi$ the phase lag. $f$ are and $u$ are the amplitude and phase nodal corrections.

## Time series from atlas 
To predict the tidal signal at specific locations from atlases or [model harmonic analyses](#models-harmonics), use the [predictor](../../tidal-processing/predictor.md) command.

Fist you need a locations.dat file with all the wanted loactions:
```bash
number of locations
 lon lat
 lon lat
 lon lat
 ...
```
For example:
```bash
6 
 -45.309906 2.587339
 -45.202062 3.810184
 -44.544542 3.466784
 -44.422247 2.818729
 -44.422247 2.818729
 -46.000000 0.500000
```
Then, compute the prediction:

```bash
fes=/ecola/share/data/tides/FES2022/

predictor -p locations.dat \
          -s "2021/08/01 00:00:00.000" -f "2025/01/01 00:00:00.000" \
          -g $fes/mesh-FES2022.nc \
          -a $fes/DOI/WAVE.FES2022.nc \
          -v Ha Hg \
          -w M2 S2 
```

*TIPS: is doing the interpolation calculation only once for each location so it is better to ask for all the wanted tidal constituent at once.*

The predictions will be stored the files "predictions.dat", an ASCII table with one column for each location:
1. Time [days since the begining of prediction]
2. Day [YYYY-MM-DD]
3. Hour [HH:MM:SS]
4. Location 1
5. Location 2
6. ...