Plot Tide Form Factor

This (notebook) demonstrates plotting tidal form factors for classifying tides

Daily tidal form factors for determining the dominant species of a region using the classifications from Courtier (1938). The dominant species classifications do have limitations as pointed out by Amin (1986)
Monthly tidal form factors for semi-diurnal species from Byun and Hart

OTIS format tidal solutions provided by Oregon State University and ESR

Global Tide Model (GOT) solutions provided by Richard Ray at GSFC

https://earth.gsfc.nasa.gov/geo/data/ocean-tide-models

Finite Element Solution (FES) provided by AVISO

https://www.aviso.altimetry.fr/en/data/products/auxiliary-products/global-tide-fes.html

Python Dependencies

Program Dependencies

crs.py: Coordinate Reference System (CRS) routines
io.model.py: retrieves tide model parameters for named tide models
io.OTIS.py: extract tidal harmonic constants from OTIS tide models
io.ATLAS.py: extract tidal harmonic constants from ATLAS netcdf models
io.GOT.py: extract tidal harmonic constants from GOT tide models
io.FES.py: extract tidal harmonic constants from FES tide models

This notebook uses Jupyter widgets to set parameters for calculating the tidal maps.

Load modules

import numpy as np
import matplotlib
matplotlib.rcParams['axes.linewidth'] = 2.0
import matplotlib.pyplot as plt
import matplotlib.colors as colors
import cartopy.crs as ccrs
import ipywidgets

# import tide programs
import pyTMD.io
import pyTMD.tools

# autoreload
%load_ext autoreload
%autoreload 2

Set parameters for program

Model directory
Tide model

# available model list
model_list = sorted(pyTMD.io.model.ocean_elevation())
# display widgets for setting directory and model
TMDwidgets = pyTMD.tools.widgets()
TMDwidgets.model.options = model_list
TMDwidgets.model.value = 'GOT4.10'
TMDwidgets.VBox([
    TMDwidgets.directory,
    TMDwidgets.model,
    TMDwidgets.compress
])

Setup tide model parameters

# get model parameters
model = pyTMD.io.model(TMDwidgets.directory.value,
    compressed=TMDwidgets.compress.value
   ).elevation(TMDwidgets.model.value)

Setup coordinates for calculating tides

# create a global image
xlimits = [-180,180]
ylimits = [-90, 90]
spacing = [0.25, 0.25]
# x and y coordinates
x = np.arange(xlimits[0],xlimits[1]+spacing[0],spacing[0])
y = np.arange(ylimits[0],ylimits[1]+spacing[1],spacing[1])
xgrid,ygrid = np.meshgrid(x,y)
# x and y dimensions
nx = int((xlimits[1]-xlimits[0])/spacing[0])+1
ny = int((ylimits[1]-ylimits[0])/spacing[1])+1
# flatten latitude and longitude to arrays
lon,lat =  xgrid.flatten(), ygrid.flatten()

Calculate tidal amplitudes and phases

# read tidal constants and interpolate to grid points
if model.format in ('OTIS','ATLAS-compact','TMD3'):
    amp,ph,D,c = pyTMD.io.OTIS.extract_constants(lon, lat, model.grid_file,
        model.model_file, model.projection, type=model.type, crop=True,
        method='spline', grid=model.file_format)
elif (model.format == 'ATLAS-netcdf'):
    amp,ph,D,c = pyTMD.io.ATLAS.extract_constants(lon, lat, model.grid_file,
        model.model_file, type=model.type, crop=True, method='spline',
        scale=model.scale, compressed=model.compressed)
elif model.format in ('GOT-ascii', 'GOT-netcdf'):
    amp,ph,c = pyTMD.io.GOT.extract_constants(lon, lat, model.model_file,
        grid=model.file_format, crop=True, method='spline',
        scale=model.scale, compressed=model.compressed)
elif (model.format == 'FES-netcdf'):
    amp,ph = pyTMD.io.FES.extract_constants(lon, lat, model.model_file,
        type=model.type, version=model.version, crop=True,
        method='spline', scale=model.scale, compressed=model.compressed)
    c = model.constituents

Calculate tidal form factors

Courtier form factor: Ratios between major diurnal tides and major semi-diurnal tides

F: < 0.25: Semi-diurnal
F: 0.25 - 1.5: Mixed predominantly semi-diurnal
F: 1.5 - 3.0: Mixed predominantly diurnal
F: > 3.0: Diurnal

Byut-Hart form factor: Ratios between semi-diurnal tides for monthly tidal envelopes

E: < 0.8: Spring-Neap
E: 0.8 - 1.0: Mixed predominantly Spring-Neap
E: 1.0 - 1.15: Mixed predominantly Perigean-Apogean
E: > 2.0: Perigean-Apogean

TMDwidgets.form_factor = ipywidgets.Dropdown(
    options=['Courtier','Byun-Hart'],
    value='Courtier',
    description='Factor:',
    disabled=False,
    style=TMDwidgets.style,
)
display(TMDwidgets.form_factor)

# find constituents for tidal form factors
k1 = c.index('k1')
o1 = c.index('o1')
m2 = c.index('m2')
s2 = c.index('s2')
n2 = c.index('n2')
# select form factor
if TMDwidgets.form_factor.value == 'Courtier':
    # tidal form factor from Courtier
    factor = np.reshape((amp[:,k1] + amp[:,o1])/(amp[:,m2] + amp[:,s2]), (ny,nx))
    boundary = np.array([0.0, 0.25, 1.5, 3.0, 5.0])
    ticklabels = ['Semi-Diurnal', 'Mixed SD', 'Mixed D', 'Diurnal']
    longname = 'Tide Species Classification'
elif TMDwidgets.form_factor.value == 'Byun-Hart':
    # semi-diurnal form factor from Byun and Hart
    factor = np.reshape((amp[:,m2] + amp[:,n2])/(amp[:,m2] + amp[:,s2]), (ny,nx))
    boundary = np.array([0.0, 0.8, 1.0, 1.15, 2.0])
    ticklabels = ['Spring-Neap', 'Mixed S-N', 'Mixed P-A', 'Perigean-Apogean']
    longname = 'Semi-Diurnal Classification'
# calculate ticks for labels
ticks = 0.5*(boundary[1:] + boundary[:-1])

Create plot of tidal form factors

# cartopy transform for Equirectangular Projection
projection = ccrs.PlateCarree()
# create figure axis
fig, ax = plt.subplots(num=1, figsize=(5.5,3.5),
    subplot_kw=dict(projection=projection))
# create boundary norm
norm = colors.BoundaryNorm(boundary, ncolors=256)
# plot tidal form factor
extent = (xlimits[0],xlimits[1],ylimits[0],ylimits[1])
im = ax.imshow(factor, interpolation='nearest',
    norm=norm, cmap='plasma', transform=projection,
    extent=extent, origin='lower')
# add high resolution cartopy coastlines
ax.coastlines('10m')

# Add colorbar and adjust size
# pad = distance from main plot axis
# extend = add extension triangles to upper and lower bounds
# options: neither, both, min, max
# shrink = percent size of colorbar
# aspect = lengthXwidth aspect of colorbar
cbar = plt.colorbar(im, ax=ax, extend='neither',
    extendfrac=0.0375, orientation='horizontal', pad=0.025,
    shrink=0.90, aspect=22, drawedges=False)
# rasterized colorbar to remove lines
cbar.solids.set_rasterized(True)
# Add label to the colorbar
cbar.ax.set_title(longname, fontsize=13,
    rotation=0, y=-2.0, va='top')
# Set the tick levels for the colorbar
cbar.set_ticks(ticks=ticks, labels=ticklabels)

# axis = equal
ax.set_aspect('equal', adjustable='box')
# set x and y limits
ax.set_xlim(xlimits)
ax.set_ylim(ylimits)

# no ticks on the x and y axes
ax.get_xaxis().set_ticks([])
ax.get_yaxis().set_ticks([])
# stronger linewidth on frame
ax.spines['geo'].set_linewidth(2.0)
ax.spines['geo'].set_capstyle('projecting')

# adjust subplot within figure
fig.subplots_adjust(left=0.02,right=0.98,bottom=0.05,top=0.98)
# show the plot
plt.show()