This notebook will be used to analyze the baroclinic tides over the CODAR region.
Background¶
Tidal anlaysis performed on hourly nowcast results from Nov 26, 2014- Apr 26, 2015.
The analysis used t_tide. Scripts are found in /data/nsoontie/MEOPAR/analysis/Nancy/currents/t_tide_analysis
For each grid point in the CODAR region, the baroclinic currents $u_{bc}, v_{bc}$ were calculated as
$u_{bc}= u - u_{depav}$, $v_{bc} = v - v_{depav}$
where $u, v$ are the full currents at that grid point and $u_{depav}$, $v_{depav}$ are the depth avergaed currents at that grid point. Depth averaging was performed over the entire water column.
A harmonic analysis to generate ellipse parameters for each grid point (x,y,z) was performed on $u_{bc}$ and $v_{bc}$.
import datetime
import matplotlib.pylab as plt
import matplotlib.colors as mcolors
import numpy as np
import scipy.io as sio
import netCDF4 as nc
from salishsea_tools.nowcast import (research_VENUS)
from salishsea_tools import viz_tools
import baroclinic
%matplotlib inline
import seaborn as sns
Load Data¶
data =sio.loadmat(
'/ocean/nsoontie/MEOPAR/TidalEllipseData/CODAR/CODAR_region_baroclinic_20141126_20150426_masked.mat')
datastruc = data['datastruc']
lats = datastruc['lats'][0,0]
lons = datastruc['lons'][0,0]
grid = nc.Dataset('/data/nsoontie/MEOPAR/NEMO-forcing/grid/bathy_meter_SalishSea2.nc')
SITES = research_VENUS.SITES['VENUS']
#Cyclical colormap
palette = sns.hls_palette(40, l=.6, s=0.8)
cmap1 = mcolors.ListedColormap(palette)
def plot_ellipse_params(dep, const, datastruc, maj_lim = [0,.5], min_lim = [-.25,.25], isobaths = [5,20]):
"""Plots the major, minor, phase and inclination of a constituent stored in datastruc."""
fig, axs = plt.subplots(2,2,figsize= (15,10))
lonax = [-123.7,-123]
latax= [48.8,49.3]
params = baroclinic.get_constituent(const, datastruc)
names = ['Major Axis', 'Minor Axis', 'Phase', 'Inclination']
units = ['(m/s)', '(m/s)', '(deg GMT)', '(deg CCW East)']
lims = [maj_lim, min_lim, [0,360], [0,180]]
depth = datastruc['depth'][0,0]
for param, name, unit, lim, ax in zip(params, names, units, lims, axs.flatten()):
if name =='Phase' or name =='Inclination':
cmap = cmap1
else:
cmap = 'jet'
mesh = ax.pcolormesh(lons, lats, param[:,:,dep], cmap=cmap, vmin=lim[0], vmax=lim[1])
cbar = plt.colorbar(mesh, ax=ax)
cbar.set_label('{} {}'.format(name, unit))
ax.set_title('{0} {1} at d = {2:.3g} m'.format(const, name, depth[dep][0]))
viz_tools.plot_coastline(ax, grid, coords = 'map')
for isobath in isobaths:
viz_tools.plot_coastline(ax, grid, coords = 'map', isobath = isobath,color = 'grey')
ax.set_xlim(lonax)
ax.set_ylim(latax)
ax.plot(SITES['Central']['lon'], SITES['Central']['lat'], 'ks', label='Central')
ax.plot(SITES['East']['lon'], SITES['East']['lat'], 'ko',label = 'East')
ax.legend(loc=0)
return fig
def plot_ellipse_errors(dep, const, datastruc):
"""Plots the major, minor, phase and inclination errors of a constituent stored in datastruc."""
fig, axs = plt.subplots(2,2,figsize= (15,10))
lonax = [-123.7,-123]
latax= [48.8,49.3]
params = baroclinic.get_constituent_errors(const, datastruc)
names = ['Major Axis', 'Minor Axis', 'Phase', 'Inclination']
units = ['(m/s)', '(m/s)', '(deg)', '(deg)']
depth = datastruc['depth'][0,0]
cmap = 'hot'
for param, name, unit,ax in zip(params, names, units, axs.flatten()):
mesh = ax.pcolormesh(lons, lats, param[:,:,dep], cmap=cmap)
cbar = plt.colorbar(mesh, ax=ax)
cbar.set_label('{} {}'.format(name, unit))
ax.set_title('Error in {0} {1} at d = {2:.3g} m'.format(const, name, depth[dep][0]))
viz_tools.plot_coastline(ax, grid, coords = 'map')
viz_tools.plot_coastline(ax, grid, coords = 'map', isobath = 5,color = 'grey')
ax.set_xlim(lonax)
ax.set_ylim(latax)
ax.plot(SITES['Central']['lon'], SITES['Central']['lat'], 'ks', label='Central')
ax.plot(SITES['East']['lon'], SITES['East']['lat'], 'ko',label = 'East')
ax.legend(loc=0)
return fig
Surface M2¶
dep=0
fig = plot_ellipse_params(dep, 'M2', datastruc)
Major/Minor Axis¶
This is really neat! There is a large M2 internal tide amplitude on the banks. Some possible explainations:
- Internal tide generation as the currents move over the banks. If the flow is transcritcal then there can be very large waves forming at the generation site.
- Internal tide shoaling on the banks. If the internal tide was generated else where, it could steepen and shoal as it approaches the banks.
How can we know which mechanism is responsible for our large M2 baroclinic currents on the banks?
- Check the phase - does it match with the barotropic tide? If so, that could indicate the large amplitude is due to internal tide generation. I will do this in detail later
- Turn off the banks. Do we still get a large M2 signature? If so, that could indicate shoaling because the generation site is removed.
- Compare with the CODAR. My guess is they don't see this very large signature. Remember, our surface M2 at East is a lot bigger than the CODAR. The discrepancies could be due to how the model is representing the banks.
Phase/Inclination¶
I need to do something clever with the phase and inclination. The large discontinuities in phase are associated with inlincation 'flips' since there is a 180 degree ambiguity in the inclination.
Is there a systematic way to adjust the phase and inclincation so that they don't have sharp discontinuities?? Perhaps measure phase relative to the barotropic tide phase or full tide phase?
Notes¶
I did not remove the boundary layer from my depth averaging mainly because it wasn't easy to do this systematically for so many grid points. Could that contribute what we are seeing? My thinking is that if the water column is deep enough then the boundary layer won't have a big impact on the depth averaged currents. The large M2 amplitudes begin at about the 30 m isobath, which isn't exactly deep. So by not removing the boundary layer, I could be underestimating the depth averged currents and overestimating the baroclinic currents. It would be wortwhile to go back and look at the boundary layer thicnkess in this region.
Errors¶
fig = plot_ellipse_errors(dep, 'M2', datastruc)
There are some really large errors in the phase and inlincation. The major/minor seem ok though. But why is there larger error near the south-eastern edge?
K1 Surface¶
dep=0
fig = plot_ellipse_params(dep, 'K1', datastruc, maj_lim=[0,.25], min_lim = [-.1,.1])
K1 also has a relatively large baroclinic amplitude at the banks. I don't think this supports the shoaling theory becuse $\omega_{K1} < f$ and internal waves need $f < \omega < N$. So there cannot be an internal tide at the K1 frequency propagating through the domain and shoaling onto the banks.
Errors¶
fig = plot_ellipse_errors(dep, 'K1', datastruc)
M2 147m¶
In the baroclinic profiles at the Central nodes, there was a spike in M2 currents at 150m depth. Let's look at the depth.
dep=28
fig = plot_ellipse_params(dep, 'M2', datastruc, maj_lim = [0,.2], min_lim = [-.1,.1])
K1 147m¶
dep=28
fig = plot_ellipse_params(dep, 'K1', datastruc, maj_lim = [0,.1], min_lim = [-.05,.05])
M2 98m¶
Strong baroclinic velocities observed in the East node at about 100m. How does that look here?
dep=26
fig = plot_ellipse_params(dep, 'M2', datastruc, maj_lim = [0,.2], min_lim = [-.1,.1], isobaths=[5,20,90, 110])
In Muriel's analysis, the East velocities at 100 m were quite a lot bigger than Mark's analysis of the ADCP data. For example, the model M2 major axis at 100m is about 34 cm/s and the observations were about 26 cm/s.
Why does the model have such a strong peak at 100m? Where does Rich's boundary current show up in the ADCP tidal analysis? There are strong fluctuations at the M2 frequency in the observed East temperature and salinity (~170m) depth so should't we see some baroclinic structure in the observed tidal currents?
K1 98m¶
dep=26
fig = plot_ellipse_params(dep, 'K1', datastruc, maj_lim = [0,.2], min_lim = [-.1,.1],isobaths=[5,20,90, 110])
Both the M2/K1 major axis are elevated in the same place. Why?
It looks like there is a small sill there, as seen in the 110m is bath. That could explain the elevated currents here.