Wave measurements from SAR¶

This notebook is from Salman Khan and Emilio Echevarria, there is a great presentation about how they use synthetic aperture radar here.

Frequency spectra conversion¶

We will now convert directional wavenumber spectra to frequency spectra using deep water assumptions: efth - spectral variance density - units m2.s.deg-1

# compute efth
dset_WA_ws = dset_WA.assign(efth = s1_compute_efth(dset_WA))

Plot some wave statistics derived from directional frequency spectra:¶

swell significant height
mean period - Tm02
mean wave direction

Note

A directional wave spectrum describes how the wave energy (more specifically, the variance spectral density) is distributed over frequencies (or wavenumbers) and directions. For a detailed description of wave spectra, its uses and applications, and the transformations from wavenumber to frequency spectra, see: Holthuijsen, L. (2007). Waves in Oceanic and Coastal Waters. Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9780511618536

It is very common to describe the wave climate with integrated (also called bulk) wave parameters, instead of with a directional wave spectra. These parameters represent average conditions of the wave climate.

# plot stats
# hs
fig = plt.figure(figsize = (7.5, 3))
ax = plt.subplot(111)
dset_WA_ws.spec.hs(tail = True).plot(ax = ax)
plt.title('Swell significant wave height')
plt.grid(linestyle = 'dashed')

# tm02
fig = plt.figure(figsize = (7.5, 3))
ax = plt.subplot(111)
dset_WA_ws.spec.tm02().plot(ax = ax)
plt.title('Mean period - Tm02')
plt.grid(linestyle = 'dashed')

# dm
fig = plt.figure(figsize = (7.5, 3))
ax = plt.subplot(111)
dset_WA_ws.spec.dm().plot(ax = ax)
plt.ylabel('Mean wave to direction $(^\circ)$')
plt.title('Mean wave direction')
plt.grid(linestyle = 'dashed')
plt.show()

Visualise directional frequency spectra:¶

1st directional spectra
all directional spectra
all omni-directional spectra

# plot 1st directional spectra
cmap = cmap_wavespectra(n = 64)
qcs = (dset_WA_ws
       .isel(time = 0)
       .spec
       .plot
       .contourf(cmap = cmap,
                 as_period = True, 
                 as_log10 = False, 
                 show_direction_label = True,
                 levels = cmap.N,
                 figsize = (7.5, 7.5),
                 robuts = True))
angle_labels = ['N', 'NE', 'E', 'SE', 'S', 'SW', '','NW']
qcs.ax.set_rlabel_position(180 + 45)
qcs.ax.set_ylim(0, 30)#set_rmax(30)
qcs.ax.set_thetagrids(angles = range(0, 360, 45),
                      labels = angle_labels)

(<a list of 16 Line2D ticklines objects>,
 [Text(0.0, 0, 'N'),
  Text(0.7853981633974483, 0, 'NE'),
  Text(1.5707963267948966, 0, 'E'),
  Text(2.356194490192345, 0, 'SE'),
  Text(3.141592653589793, 0, 'S'),
  Text(3.9269908169872414, 0, 'SW'),
  Text(4.71238898038469, 0, ''),
  Text(5.497787143782138, 0, 'NW')])

## plot all directional spectra
ncols = 4
fg = (dset_WA_ws
      .efth
      .spec
      .plot
      .contourf(col = "time", col_wrap = ncols, cmap = cmap,
                as_period = True, as_log10 = False, 
                show_direction_label = True, levels = cmap.N,
                robuts = True, size = 3, aspect = 1))
angle_labels = ['N', 'NE', 'E', 'SE', 'S', 'SW', 'W','NW']        
for i, ax in enumerate(fg.axes.flat):
    ax.set_rlabel_position(180 + 45)
    ax.set_ylim(0, 30)#set_rmax(30)
    ax.set_thetagrids(angles = range(0, 360, 45),
                      labels = angle_labels)
fg.set_titles(pad = 15)
fg.set_ylabels('Wave period [s]', labelpad = 20)
fg.set_xlabels('Wave to direction [$^\circ$]', labelpad = 0)
fg.cbar.set_label('Variance density [$m^2 s deg{-1}$]', labelpad = 10)

Error in callback <function flush_figures at 0x7f7ff6b0c8c8> (for post_execute):

---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
/usr/share/miniconda/envs/coast/lib/python3.6/site-packages/ipykernel/pylab/backend_inline.py in flush_figures()
    118         # ignore the tracking, just draw and close all figures
    119         try:
--> 120             return show(True)
    121         except Exception as e:
    122             # safely show traceback if in IPython, else raise

/usr/share/miniconda/envs/coast/lib/python3.6/site-packages/ipykernel/pylab/backend_inline.py in show(close, block)
     40             display(
     41                 figure_manager.canvas.figure,
---> 42                 metadata=_fetch_figure_metadata(figure_manager.canvas.figure)
     43             )
     44     finally:

/usr/share/miniconda/envs/coast/lib/python3.6/site-packages/IPython/core/display.py in display(include, exclude, metadata, transient, display_id, *objs, **kwargs)
    311             publish_display_data(data=obj, metadata=metadata, **kwargs)
    312         else:
--> 313             format_dict, md_dict = format(obj, include=include, exclude=exclude)
    314             if not format_dict:
    315                 # nothing to display (e.g. _ipython_display_ took over)

/usr/share/miniconda/envs/coast/lib/python3.6/site-packages/IPython/core/formatters.py in format(self, obj, include, exclude)
    178             md = None
    179             try:
--> 180                 data = formatter(obj)
    181             except:
    182                 # FIXME: log the exception

<decorator-gen-9> in __call__(self, obj)

/usr/share/miniconda/envs/coast/lib/python3.6/site-packages/IPython/core/formatters.py in catch_format_error(method, self, *args, **kwargs)
    222     """show traceback on failed format call"""
    223     try:
--> 224         r = method(self, *args, **kwargs)
    225     except NotImplementedError:
    226         # don't warn on NotImplementedErrors

/usr/share/miniconda/envs/coast/lib/python3.6/site-packages/IPython/core/formatters.py in __call__(self, obj)
    339                 pass
    340             else:
--> 341                 return printer(obj)
    342             # Finally look for special method names
    343             method = get_real_method(obj, self.print_method)

/usr/share/miniconda/envs/coast/lib/python3.6/site-packages/IPython/core/pylabtools.py in <lambda>(fig)
    252         jpg_formatter.for_type(Figure, lambda fig: print_figure(fig, 'jpg', **kwargs))
    253     if 'svg' in formats:
--> 254         svg_formatter.for_type(Figure, lambda fig: print_figure(fig, 'svg', **kwargs))
    255     if 'pdf' in formats:
    256         pdf_formatter.for_type(Figure, lambda fig: print_figure(fig, 'pdf', **kwargs))

/usr/share/miniconda/envs/coast/lib/python3.6/site-packages/IPython/core/pylabtools.py in print_figure(fig, fmt, bbox_inches, **kwargs)
    130         FigureCanvasBase(fig)
    131 
--> 132     fig.canvas.print_figure(bytes_io, **kw)
    133     data = bytes_io.getvalue()
    134     if fmt == 'svg':

/usr/share/miniconda/envs/coast/lib/python3.6/site-packages/matplotlib/backend_bases.py in print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2194 
   2195                     bbox_inches = self.figure.get_tightbbox(
-> 2196                         renderer, bbox_extra_artists=bbox_extra_artists)
   2197                     if pad_inches is None:
   2198                         pad_inches = rcParams['savefig.pad_inches']

/usr/share/miniconda/envs/coast/lib/python3.6/site-packages/matplotlib/figure.py in get_tightbbox(self, renderer, bbox_extra_artists)
   2504 
   2505         for a in artists:
-> 2506             bbox = a.get_tightbbox(renderer)
   2507             if bbox is not None and (bbox.width != 0 or bbox.height != 0):
   2508                 bb.append(bbox)

/usr/share/miniconda/envs/coast/lib/python3.6/site-packages/matplotlib/artist.py in get_tightbbox(self, renderer)
    284             if clip_path is not None and bbox is not None:
    285                 clip_path = clip_path.get_fully_transformed_path()
--> 286                 bbox = Bbox.intersection(bbox, clip_path.get_extents())
    287         return bbox
    288 

/usr/share/miniconda/envs/coast/lib/python3.6/site-packages/matplotlib/path.py in get_extents(self, transform, **kwargs)
    597             for curve, code in self.iter_bezier(**kwargs):
    598                 # places where the derivative is zero can be extrema
--> 599                 _, dzeros = curve.axis_aligned_extrema()
    600                 # as can the ends of the curve
    601                 xys.append(curve([0, *dzeros, 1]))

/usr/share/miniconda/envs/coast/lib/python3.6/site-packages/matplotlib/bezier.py in axis_aligned_extrema(self)
    296         roots = []
    297         for i, pi in enumerate(dCj.T):
--> 298             r = np.roots(pi[::-1])
    299             roots.append(r)
    300             dims.append(np.full_like(r, i))

<__array_function__ internals> in roots(*args, **kwargs)

/usr/share/miniconda/envs/coast/lib/python3.6/site-packages/numpy/lib/polynomial.py in roots(p)
    241         A = diag(NX.ones((N-2,), p.dtype), -1)
    242         A[0,:] = -p[1:] / p[0]
--> 243         roots = eigvals(A)
    244     else:
    245         roots = NX.array([])

<__array_function__ internals> in eigvals(*args, **kwargs)

/usr/share/miniconda/envs/coast/lib/python3.6/site-packages/numpy/linalg/linalg.py in eigvals(a)
   1067         _raise_linalgerror_eigenvalues_nonconvergence)
   1068     signature = 'D->D' if isComplexType(t) else 'd->D'
-> 1069     w = _umath_linalg.eigvals(a, signature=signature, extobj=extobj)
   1070 
   1071     if not isComplexType(t):

KeyboardInterrupt: 

# plot all omni-directional spectra
ncols = 4
fg = dset_WA_ws.spec.oned().plot.line(col = 'time', col_wrap = ncols)
fg.set_axis_labels(y_var = 'var. spec. density ($m^2s/deg$)')
for i, ax in enumerate(fg.axes.flat):
    ax.grid(True)

Visualise directional frequency spectra swell partitions:¶

paritions of first directional spectrum
partitions of all directional spectra

# plot partitions for 1st 2d spectrum
fig = plot_part(dset_WA_ws.EKTH_PART.isel(TIME = 0))

# plot partitions for all 2d spectra
fig = plot_part(dset_WA_ws.EKTH_PART)

Plot some primary swell wave statistics:¶

# plot primary swell stats
# swell height
fig = plt.figure(figsize = (7.5, 3))
ax = plt.subplot(111)
dset_WA_ws.HS_PART.isel(PARTITION = 0).plot()
plt.title('Primary swell significant height') 
plt.grid(linestyle = 'dashed')

# direction at spectral peak
fig = plt.figure(figsize = (7.5, 3))
ax = plt.subplot(111)
dset_WA_ws.DP_PART.isel(PARTITION = 0).plot()
plt.title('Primary swell peak direction') 
plt.grid(linestyle = 'dashed')

# wavelength at spectral peak
fig = plt.figure(figsize = (7.5, 3))
ax = plt.subplot(111)
dset_WA_ws.WP_PART.isel(PARTITION = 0).plot()
plt.title('Primary swell peak wavelength') 
plt.grid(linestyle = 'dashed')

Coastal Processes, Environments & Systems

Wave measurements from SAR¶

About Sentinel-1 Ocean Surface Wave Measurements¶

Imported Python packages¶

Daily along-track measurements¶

Auxialliary variables¶