This post is the result of an online conversation about tidal ellipses and how to compute them in Python. We will be using the same data from previous posts.

In [2]:

import pandas as pd
from datetime import datetime

fname = './data/15t30717.3f1'
cols = ['j', 'u', 'v', 'temp', 'sal', 'y', 'mn', 'd', 'h', 'mi']


df = pd.read_table(fname , delim_whitespace=True, names=cols)
dates = [datetime(*x) for x in
         zip(df['y'], df['mn'], df['d'], df['h'], df['mi'])]
df.index = dates
df.drop(['y', 'mn', 'd', 'h', 'mi', 'j'], axis=1, inplace=True)
df.head()

Out[2]:

	u	v	temp	sal
1993-07-18 03:00:00	11.7	-1.3	28.3	29.2
1993-07-18 04:00:00	12.3	-4.5	28.1	29.4
1993-07-18 05:00:00	9.6	-5.3	27.6	31.0
1993-07-18 06:00:00	7.6	-2.3	27.2	32.4
1993-07-18 07:00:00	10.6	-2.0	27.2	32.5

And now we can compute the tidal analysis using utide.

In [3]:

from utide._solve import solve
from matplotlib.dates import date2num


time = date2num(df.index.to_pydatetime())

kw = dict(lat=32, cnstit='auto', notrend=True, rmin=0.95, method='ols',
          nodiagn=True, linci=True, conf_int=True)

coef = solve(time, df['u'].values, df['v'].values, **kw)

solve: 
matrix prep ... 
Solution ...
conf. int vls... 
Done.

The two cells below just clean the results a little bit and show a table with the ellipse parameters.

In [4]:

import numpy as np


frq = coef['aux']['frq']
for k, v in coef.items():
    if not isinstance(v, np.ndarray) or v.shape < frq.shape:
        del coef[k]

In [5]:

df = pd.DataFrame.from_dict(coef)
df['frq'] = frq

index = [s.strip() for s in df['name']]
df['name'] = index

df = df.set_index('name').sort(['Lsmaj', 'Lsmin'], ascending=False)

df.head()

Out[5]:

	Lsmaj	Lsmaj_ci	Lsmin	Lsmin_ci	g	g_ci	theta	theta_ci	frq
name
MM	10.025156	1.330969	-1.472702	1.598556	357.242244	8.045043	28.903073	9.227543	0.001512
O1	4.120147	1.011807	-3.293878	0.175315	149.042548	39.399034	170.177282	31.926241	0.038731
MSF	3.638211	1.087993	-1.875688	0.567645	348.262650	23.515309	151.782141	17.031935	0.002822
K1	2.570776	1.049644	-1.988055	0.177977	87.852104	58.807203	9.605010	46.156704	0.041781
J1	2.115125	0.334725	-1.994584	0.944709	32.351296	232.821085	70.504177	243.696261	0.043293

For the figure we can use the Python translation of Zhigang Xu's tidal_ellipse MATLAB tools.

In [6]:

MM = df.ix['MM']
SEMA, SEMI = MM['Lsmaj'], MM['Lsmin']
PHA, INC = MM['g'], MM['theta']
ECC = SEMI / SEMA

And here is the plot!

In [7]:

import tidal_ellipse

tidal_ellipse.do_the_plot(SEMA, ECC, INC, PHA)

In [8]:

HTML(html)

Out[8]:

This post was written as an IPython notebook. It is available for download or as a static html.

python4oceanographers by Filipe Fernandes is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at https://ocefpaf.github.io/.

python4oceanographers

Turning ripples into waves

Plotting tidal ellipse with Utide

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