Notebook to Generate Bathymetry and Current Data for snells_law_verfication.ipynb
=================================================================================

This notebook generates current and bathymetry arrays that are used to
run ``snells_law_verification.ipynb``. Files are saved in netcdf3
classic format to the forcing subdirectory.

General Setup
-------------

.. code:: ipython3

    import numpy as np
    import xarray as xr
    import matplotlib.pyplot as plt

.. code:: ipython3

    NX = 300
    NY = 150
    dl = 50
    xs = np.arange(0, NX*dl, dl, dtype=np.float64)
    ys = np.arange(0, NY*dl, dl, dtype=np.float64)
    base_array = np.ones((NY, NX), dtype=np.float64)

Step Bathymetry
---------------

.. code:: ipython3

    n_shelfs = 10
    depth_max = 100
    d_depth = 10
    
    # Create descending order 1D array of depths for each x coordinate
    depths_x = depth_max - np.floor(np.linspace(0, n_shelfs, NX, endpoint=False))*d_depth
    
    step_bathymetry_array = depths_x * base_array
    step_bathymetry_ds = xr.Dataset(data_vars={'depth': (('y', 'x'), step_bathymetry_array)},
                               coords={'x': ('x', xs), 'y': ('y', ys)})
    # Plot bathymetry to double check
    step_bathymetry_ds.depth.plot(cmap='viridis_r')




.. parsed-literal::

    <matplotlib.collections.QuadMesh at 0x19fec58e1e0>




.. image:: ./data_generation_5_1.png


.. code:: ipython3

    # Save step bathymetry array to file
    step_bathymetry_ds.to_netcdf('forcing/step_bathymetry.nc', format='NETCDF3_CLASSIC')

Null Current Field
------------------

.. code:: ipython3

    u_array = base_array*0
    v_array = base_array*0
    
    null_current_ds = xr.Dataset(data_vars={'u': (('y', 'x'), u_array), 'v': (('y', 'x'), v_array)},
                                 coords={'x': ('x', xs), 'y': ('y', ys)})
    
    # Plot currents to double check
    null_current_ds.u.plot()
    plt.show()
    null_current_ds.v.plot()
    plt.show()



.. image:: ./data_generation_8_0.png



.. image:: ./data_generation_8_1.png


.. code:: ipython3

    # Save null current dataset to file
    null_current_ds.to_netcdf('forcing/null_current.nc', format='NETCDF3_CLASSIC')

Flat Deep Water Bathymetry
--------------------------

.. code:: ipython3

    flat_depth = 10_000 # Sufficiently Deep no wave should feel the bottom
    flat_bathymetry_array = flat_depth * base_array
    flat_bathymetry_ds = xr.Dataset(data_vars={'depth': (('y', 'x'), flat_bathymetry_array)},
                               coords={'x': ('x', xs), 'y': ('y', ys)})
    
    # Plot Bathymetry to double check
    flat_bathymetry_ds.depth.plot()




.. parsed-literal::

    <matplotlib.collections.QuadMesh at 0x19fec9dd040>




.. image:: ./data_generation_11_1.png


.. code:: ipython3

    # Save flat deep-water bathymetry dataset to file
    flat_bathymetry_ds.to_netcdf('forcing/deep_water_flat_bathymetry.nc', format='NETCDF3_CLASSIC')

Shear Currents
--------------

.. code:: ipython3

    U = 0
    V = 2
    
    u_array = base_array*U
    v_array = base_array*0
    v_array[:, NX//2:] = V
    
    shear_current_ds = xr.Dataset(data_vars={'u': (('y', 'x'), u_array), 'v': (('y', 'x'), v_array)},
                               coords={'x': ('x', xs), 'y': ('y', ys)})
    
    # Plot currents to double check
    shear_current_ds.u.plot()
    plt.show()
    spaced_shear_current_ds = shear_current_ds.sel(x=slice(None,None,20), y=slice(None,None,20))
    fig, ax = plt.subplots()
    shear_current_ds.v.plot(ax=ax)
    ax.quiver(spaced_shear_current_ds.x, spaced_shear_current_ds.y, spaced_shear_current_ds.u, spaced_shear_current_ds.v)



.. image:: ./data_generation_14_0.png




.. parsed-literal::

    <matplotlib.quiver.Quiver at 0x19feda5c140>




.. image:: ./data_generation_14_2.png


.. code:: ipython3

    # Save shear current dataset to file
    shear_current_ds.to_netcdf('forcing/shear_current_2v.nc', format='NETCDF3_CLASSIC')