hero_calc_delayed.ipynb

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   "source": [
    "# From\n",
    "https://gist.github.com/TomNicholas/ee5c673f8772beeecd3f58f9b040943f#file-hero_calc_delayed-ipynb"
   ]
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   "id": "2f2852bc-f700-4bcd-b13e-672f10564811",
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    "tags": []
   },
   "source": [
    "### Install packages"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18d3999d-8305-4dea-88c7-e2702a2ce92f",
   "metadata": {},
   "source": [
    "## Define Regions"
   ]
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   "cell_type": "code",
   "execution_count": 1,
   "id": "085ca0d7-93a2-4316-9bee-96ad797b22e2",
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;Depth&#x27; (face: 13, j: 4320, i: 4320)&gt;\n",
       "[242611200 values with dtype=float32]\n",
       "Coordinates:\n",
       "  * face     (face) int64 0 1 2 3 4 5 6 7 8 9 10 11 12\n",
       "  * i        (i) int64 0 1 2 3 4 5 6 7 ... 4313 4314 4315 4316 4317 4318 4319\n",
       "  * j        (j) int64 0 1 2 3 4 5 6 7 ... 4313 4314 4315 4316 4317 4318 4319\n",
       "Attributes:\n",
       "    coordinate:     XC YC\n",
       "    long_name:      ocean depth\n",
       "    standard_name:  ocean_depth\n",
       "    units:          m</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'Depth'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>face</span>: 13</li><li><span class='xr-has-index'>j</span>: 4320</li><li><span class='xr-has-index'>i</span>: 4320</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-4ceb74df-1cb7-4a60-a5aa-72539a011e9c' class='xr-array-in' type='checkbox' checked><label for='section-4ceb74df-1cb7-4a60-a5aa-72539a011e9c' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>...</span></div><div class='xr-array-data'><pre>[242611200 values with dtype=float32]</pre></div></div></li><li class='xr-section-item'><input id='section-cd9d4a61-498a-4c3f-a97c-5f499afb51ca' class='xr-section-summary-in' type='checkbox'  checked><label for='section-cd9d4a61-498a-4c3f-a97c-5f499afb51ca' class='xr-section-summary' >Coordinates: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>face</span></div><div class='xr-var-dims'>(face)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 6 7 8 9 10 11 12</div><input id='attrs-dc9c42d1-3e97-4151-a04d-6c61c608d8f9' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-dc9c42d1-3e97-4151-a04d-6c61c608d8f9' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-2402cd1b-536a-41f2-b046-63e68aa4420d' class='xr-var-data-in' type='checkbox'><label for='data-2402cd1b-536a-41f2-b046-63e68aa4420d' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'><dt><span>standard_name :</span></dt><dd>face_index</dd></dl></div><div class='xr-var-data'><pre>array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>i</span></div><div class='xr-var-dims'>(i)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 ... 4316 4317 4318 4319</div><input id='attrs-6079545d-af76-49b6-894a-d11ad7725dc0' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-6079545d-af76-49b6-894a-d11ad7725dc0' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-8dfacda1-670d-4cfd-8775-bed989de3bb2' class='xr-var-data-in' type='checkbox'><label for='data-8dfacda1-670d-4cfd-8775-bed989de3bb2' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'><dt><span>axis :</span></dt><dd>X</dd><dt><span>long_name :</span></dt><dd>x-dimension of the t grid</dd><dt><span>standard_name :</span></dt><dd>x_grid_index</dd><dt><span>swap_dim :</span></dt><dd>XC</dd></dl></div><div class='xr-var-data'><pre>array([   0,    1,    2, ..., 4317, 4318, 4319])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>j</span></div><div class='xr-var-dims'>(j)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 ... 4316 4317 4318 4319</div><input id='attrs-f735ab26-a75d-48ed-826d-bdab84a89904' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-f735ab26-a75d-48ed-826d-bdab84a89904' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-c612c20c-690a-4027-a713-de7292832dce' class='xr-var-data-in' type='checkbox'><label for='data-c612c20c-690a-4027-a713-de7292832dce' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'><dt><span>axis :</span></dt><dd>Y</dd><dt><span>long_name :</span></dt><dd>y-dimension of the t grid</dd><dt><span>standard_name :</span></dt><dd>y_grid_index</dd><dt><span>swap_dim :</span></dt><dd>YC</dd></dl></div><div class='xr-var-data'><pre>array([   0,    1,    2, ..., 4317, 4318, 4319])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-20e2ae0e-a6c0-448e-9944-4ca4c8333f83' class='xr-section-summary-in' type='checkbox'  checked><label for='section-20e2ae0e-a6c0-448e-9944-4ca4c8333f83' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>coordinate :</span></dt><dd>XC YC</dd><dt><span>long_name :</span></dt><dd>ocean depth</dd><dt><span>standard_name :</span></dt><dd>ocean_depth</dd><dt><span>units :</span></dt><dd>m</dd></dl></div></li></ul></div></div>"
      ],
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       "<xarray.DataArray 'Depth' (face: 13, j: 4320, i: 4320)>\n",
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       "  * j        (j) int64 0 1 2 3 4 5 6 7 ... 4313 4314 4315 4316 4317 4318 4319\n",
       "Attributes:\n",
       "    coordinate:     XC YC\n",
       "    long_name:      ocean depth\n",
       "    standard_name:  ocean_depth\n",
       "    units:          m"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import xarray as xr\n",
    "import numpy as np\n",
    "\n",
    "ds_grid = xr.open_dataset(\n",
    "    \"gs://pangeo-ecco-llc4320/grid\", \n",
    "    engine=\"zarr\", \n",
    "    storage_options={'requester_pays': True},\n",
    ")\n",
    "lat = ds_grid['YC'].reset_coords(drop=True).rename('lat')\n",
    "lon = ds_grid['XC'].reset_coords(drop=True).rename('lon')\n",
    "depth = ds_grid['Depth'].reset_coords(drop=True)\n",
    "depth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "337209a2-f245-42d6-9b82-d2054073b086",
   "metadata": {},
   "outputs": [
    {
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
       "Dimensions:        (face: 13, j: 8, i: 8)\n",
       "Coordinates:\n",
       "  * face           (face) int64 0 1 2 3 4 5 6 7 8 9 10 11 12\n",
       "Dimensions without coordinates: j, i\n",
       "Data variables:\n",
       "    lat_max        (face, j, i) float32 -86.8 -87.05 -86.08 ... -83.3 -85.71\n",
       "    lat_min        (face, j, i) float32 -89.75 -90.0 -88.67 ... -86.79 -88.17\n",
       "    lon_max        (face, j, i) float32 -30.56 64.91 64.96 ... -45.51 -61.2\n",
       "    lon_min        (face, j, i) float32 -114.9 -114.5 2.951 ... -79.91 -115.0\n",
       "    area_fraction  (face, j, i) float64 0.0 0.0 0.0 0.0 ... 0.3923 0.0 0.0 0.0\n",
       "    f_coriolis     (face, j, i) float32 -0.0001458 -0.0001458 ... -0.0001456\n",
       "    i_min          (i) int16 0 540 1080 1620 2160 2700 3240 3780\n",
       "    i_max          (i) int16 540 1080 1620 2160 2700 3240 3780 4320\n",
       "    j_min          (j) int16 0 540 1080 1620 2160 2700 3240 3780\n",
       "    j_max          (j) int16 540 1080 1620 2160 2700 3240 3780 4320\n",
       "Attributes:\n",
       "    coordinate:     YC XC\n",
       "    long_name:      latitude\n",
       "    standard_name:  latitude\n",
       "    units:          degrees_north</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-cbef233a-0cb7-41ce-a3a9-95d3c2889b28' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-cbef233a-0cb7-41ce-a3a9-95d3c2889b28' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>face</span>: 13</li><li><span>j</span>: 8</li><li><span>i</span>: 8</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-edd31f26-2faa-422d-b038-98f379164b57' class='xr-section-summary-in' type='checkbox'  checked><label for='section-edd31f26-2faa-422d-b038-98f379164b57' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>face</span></div><div class='xr-var-dims'>(face)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 6 7 8 9 10 11 12</div><input id='attrs-c7cb84fd-d30e-404c-9f4c-bc44821ce78f' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-c7cb84fd-d30e-404c-9f4c-bc44821ce78f' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-fb59d7af-1835-4883-9e07-1fe651624570' class='xr-var-data-in' type='checkbox'><label for='data-fb59d7af-1835-4883-9e07-1fe651624570' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'><dt><span>standard_name :</span></dt><dd>face_index</dd></dl></div><div class='xr-var-data'><pre>array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-7f446697-bda7-4268-800e-7f7c1f5fe581' class='xr-section-summary-in' type='checkbox'  checked><label for='section-7f446697-bda7-4268-800e-7f7c1f5fe581' class='xr-section-summary' >Data variables: <span>(10)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>lat_max</span></div><div class='xr-var-dims'>(face, j, i)</div><div class='xr-var-dtype'>float32</div><div class='xr-var-preview xr-preview'>-86.8 -87.05 ... -83.3 -85.71</div><input id='attrs-44e71151-5fab-4652-bc38-e35220661479' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-44e71151-5fab-4652-bc38-e35220661479' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-e9069552-d4dc-47a7-978b-b53e129852b9' class='xr-var-data-in' type='checkbox'><label for='data-e9069552-d4dc-47a7-978b-b53e129852b9' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'><dt><span>coordinate :</span></dt><dd>YC XC</dd><dt><span>long_name :</span></dt><dd>latitude</dd><dt><span>standard_name :</span></dt><dd>latitude</dd><dt><span>units :</span></dt><dd>degrees_north</dd></dl></div><div class='xr-var-data'><pre>array([[[-86.79975  , -87.05127  , -86.08039  , -84.81813  ,\n",
       "         -83.4634   , -82.13406  , -80.951866 , -80.077896 ],\n",
       "        [-83.92985  , -84.057304 , -83.52606  , -82.703186 ,\n",
       "         -81.703384 , -80.64416  , -79.65887  , -78.912285 ],\n",
       "        [-80.36082  , -80.43661  , -80.11475  , -79.58819  ,\n",
       "         -78.91048  , -78.15715  , -77.43191  , -76.87062  ],\n",
       "        [-76.242615 , -76.28589  , -76.1013   , -75.79484  ,\n",
       "         -75.3935   , -74.94019  , -74.49858  , -74.154434 ],\n",
       "        [-71.63809  , -71.65012  , -71.59884  , -71.51385  ,\n",
       "         -71.402916 , -71.27828  , -71.157684 , -71.06434  ],\n",
       "        [-67.25439  , -67.25439  , -67.25439  , -67.25439  ,\n",
       "         -67.25439  , -67.25439  , -67.25439  , -67.25439  ],\n",
       "        [-62.56236  , -62.56236  , -62.56236  , -62.56236  ,\n",
       "         -62.56236  , -62.56236  , -62.56236  , -62.56236  ],\n",
       "        [-57.012096 , -57.012096 , -57.012096 , -57.012096 ,\n",
       "         -57.012096 , -57.012096 , -57.012096 , -57.012096 ]],\n",
       "\n",
       "       [[-50.690105 , -50.690105 , -50.690105 , -50.690105 ,\n",
       "         -50.690105 , -50.690105 , -50.690105 , -50.690105 ],\n",
       "        [-43.533653 , -43.533653 , -43.533653 , -43.533653 ,\n",
       "...\n",
       "        [ 13.728166 ,   3.4684877,  -6.9436836, -17.074287 ,\n",
       "         -26.658613 , -35.512856 , -43.533653 , -50.690105 ]],\n",
       "\n",
       "       [[-57.012096 , -62.56236  , -67.25439  , -71.02229  ,\n",
       "         -73.99867  , -76.61734  , -78.5788   , -79.6919   ],\n",
       "        [-57.012096 , -62.56236  , -67.25439  , -71.02148  ,\n",
       "         -73.99564  , -76.61243  , -78.57234  , -79.68445  ],\n",
       "        [-57.012096 , -62.56236  , -67.25439  , -71.0448   ,\n",
       "         -74.08211  , -76.75297  , -78.75713  , -79.89803  ],\n",
       "        [-57.012096 , -62.56236  , -67.25439  , -71.12453  ,\n",
       "         -74.3766   , -77.23266  , -79.3925   , -80.6383   ],\n",
       "        [-57.012096 , -62.56236  , -67.25439  , -71.239334 ,\n",
       "         -74.79793  , -77.922745 , -80.322655 , -81.743835 ],\n",
       "        [-57.012096 , -62.56236  , -67.25439  , -71.3649   ,\n",
       "         -75.255516 , -78.67999  , -81.37447  , -83.04198  ],\n",
       "        [-57.012096 , -62.56236  , -67.25439  , -71.481636 ,\n",
       "         -75.67849  , -79.39047  , -82.40569  , -84.40048  ],\n",
       "        [-57.012096 , -62.56236  , -67.25439  , -71.57572  ,\n",
       "         -76.01802  , -79.970764 , -83.296005 , -85.70665  ]]],\n",
       "      dtype=float32)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>lat_min</span></div><div class='xr-var-dims'>(face, j, i)</div><div class='xr-var-dtype'>float32</div><div class='xr-var-preview xr-preview'>-89.75 -90.0 ... -86.79 -88.17</div><input id='attrs-72407cdd-f855-4faa-b929-0566e4672d46' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-72407cdd-f855-4faa-b929-0566e4672d46' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-de2ac3e5-7140-47df-98b3-cd20cbc41945' class='xr-var-data-in' type='checkbox'><label for='data-de2ac3e5-7140-47df-98b3-cd20cbc41945' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'><dt><span>coordinate :</span></dt><dd>YC XC</dd><dt><span>long_name :</span></dt><dd>latitude</dd><dt><span>standard_name :</span></dt><dd>latitude</dd><dt><span>units :</span></dt><dd>degrees_north</dd></dl></div><div class='xr-var-data'><pre>array([[[-89.752815 , -89.99737  , -88.66502  , -87.08984  ,\n",
       "         -85.528854 , -84.00613  , -82.572464 , -81.32298  ],\n",
       "        [-87.352005 , -87.363556 , -87.04516  , -86.07464  ,\n",
       "         -84.81296  , -83.458755 , -82.129944 , -80.94842  ],\n",
       "        [-84.19536  , -84.20057  , -84.05048  , -83.51912  ,\n",
       "         -82.696495 , -81.69712  , -80.638466 , -79.65391  ],\n",
       "        [-80.51404  , -80.517075 , -80.429016 , -80.10704  ,\n",
       "         -79.58058  , -78.9032   , -78.15037  , -77.425804 ],\n",
       "        [-76.32588  , -76.32761  , -76.27752  , -76.092926 ,\n",
       "         -75.786644 , -75.38567  , -74.932884 , -74.49193  ],\n",
       "        [-71.65445  , -71.65492  , -71.64105  , -71.58997  ,\n",
       "         -71.50537  , -71.395    , -71.27102  , -71.15109  ],\n",
       "        [-67.24637  , -67.24637  , -67.24637  , -67.24637  ,\n",
       "         -67.24637  , -67.24637  , -67.24637  , -67.24637  ],\n",
       "        [-62.55294  , -62.55294  , -62.55294  , -62.55294  ,\n",
       "         -62.55294  , -62.55294  , -62.55294  , -62.55294  ]],\n",
       "\n",
       "       [[-57.001026 , -57.001026 , -57.001026 , -57.001026 ,\n",
       "         -57.001026 , -57.001026 , -57.001026 , -57.001026 ],\n",
       "        [-50.677643 , -50.677643 , -50.677643 , -50.677643 ,\n",
       "...\n",
       "        [  3.4877594,  -6.924565 , -17.055962 , -26.641497 ,\n",
       "         -35.497208 , -43.5196   , -50.677643 , -57.001026 ]],\n",
       "\n",
       "       [[-62.55294  , -67.24637  , -71.05833  , -74.14847  ,\n",
       "         -76.86533  , -78.90823  , -80.075356 , -80.40884  ],\n",
       "        [-62.55294  , -67.24637  , -71.038925 , -74.076355 ,\n",
       "         -76.74795  , -78.7534   , -79.89581  , -80.22155  ],\n",
       "        [-62.55294  , -67.24637  , -71.11813  , -74.37016  ,\n",
       "         -77.22679  , -79.3878   , -80.6351   , -80.99422  ],\n",
       "        [-62.55294  , -67.24637  , -71.232285 , -74.79082  ,\n",
       "         -77.91616  , -80.31717  , -81.739914 , -82.15803  ],\n",
       "        [-62.55294  , -67.24637  , -71.35718  , -75.24783  ,\n",
       "         -78.672844 , -81.36838  , -83.03749  , -83.54715  ],\n",
       "        [-62.55294  , -67.24637  , -71.47333  , -75.670395 ,\n",
       "         -79.38295  , -82.39912  , -84.39547  , -85.04932  ],\n",
       "        [-62.55294  , -67.24637  , -71.566956 , -76.00968  ,\n",
       "         -79.96306  , -83.28911  , -85.70108  , -86.60192  ],\n",
       "        [-62.55294  , -67.24637  , -71.62907  , -76.23423  ,\n",
       "         -80.35316  , -83.92294  , -86.79368  , -88.174225 ]]],\n",
       "      dtype=float32)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>lon_max</span></div><div class='xr-var-dims'>(face, j, i)</div><div class='xr-var-dtype'>float32</div><div class='xr-var-preview xr-preview'>-30.56 64.91 64.96 ... -45.51 -61.2</div><input id='attrs-34bd9b38-de01-4f19-a6ea-6937a70101f3' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-34bd9b38-de01-4f19-a6ea-6937a70101f3' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-5f997482-05fc-4cfe-931c-1f39e1588560' class='xr-var-data-in' type='checkbox'><label for='data-5f997482-05fc-4cfe-931c-1f39e1588560' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'><dt><span>coordinate :</span></dt><dd>YC XC</dd><dt><span>long_name :</span></dt><dd>longitude</dd><dt><span>standard_name :</span></dt><dd>longitude</dd><dt><span>units :</span></dt><dd>degrees_east</dd></dl></div><div class='xr-var-data'><pre>array([[[ -30.559948 ,   64.90655  ,   64.95875  ,   64.97499  ,\n",
       "           64.98339  ,   64.98885  ,   64.99296  ,   64.99639  ],\n",
       "        [ -27.848696 ,    2.8529806,   25.12474  ,   38.140602 ,\n",
       "           46.407528 ,   52.280216 ,   56.886284 ,   60.819626 ],\n",
       "        [ -27.108912 ,   -9.868414 ,    6.4901924,   20.298056 ,\n",
       "           31.680925 ,   41.198067 ,   49.43258  ,   56.871426 ],\n",
       "        [ -26.84586  ,  -13.679045 ,   -0.6050568,   11.799965 ,\n",
       "           23.398312 ,   34.21401  ,   44.378822 ,   54.080547 ],\n",
       "        [ -26.764791 ,  -15.059965 ,   -3.3474274,    8.219004 ,\n",
       "           19.592861 ,   30.760115 ,   41.73835  ,   52.57126  ],\n",
       "        [ -26.760416 ,  -15.487511 ,   -4.213777 ,    7.052837 ,\n",
       "           18.309807 ,   29.556084 ,   40.792248 ,   52.020412 ],\n",
       "        [ -26.760416 ,  -15.510417 ,   -4.2604165,    6.9895835,\n",
       "           18.239584 ,   29.489584 ,   40.739582 ,   51.989582 ],\n",
       "        [ -26.760416 ,  -15.510417 ,   -4.2604165,    6.9895835,\n",
       "           18.239584 ,   29.489584 ,   40.739582 ,   51.989582 ]],\n",
       "\n",
       "       [[ -26.760416 ,  -15.510417 ,   -4.2604165,    6.9895835,\n",
       "           18.239584 ,   29.489584 ,   40.739582 ,   51.989582 ],\n",
       "        [ -26.760416 ,  -15.510417 ,   -4.2604165,    6.9895835,\n",
       "...\n",
       "        [ -38.010418 ,  -38.010418 ,  -38.010418 ,  -38.010418 ,\n",
       "          -38.010418 ,  -38.010418 ,  -38.010418 ,  -38.010418 ]],\n",
       "\n",
       "       [[-116.760414 , -116.760414 , -116.7561   , -116.67918  ,\n",
       "         -116.469986 , -116.08842  , -115.55703  , -115.00048  ],\n",
       "        [-105.510414 , -105.510414 , -105.510414 , -105.53353  ,\n",
       "         -105.942505 , -107.057686 , -109.105385 , -111.97896  ],\n",
       "        [ -94.260414 ,  -94.260414 ,  -94.260414 ,  -94.3075   ,\n",
       "          -95.14437  ,  -97.46127  , -101.83621  , -108.18244  ],\n",
       "        [ -83.010414 ,  -83.010414 ,  -83.010414 ,  -83.074326 ,\n",
       "          -84.21837  ,  -87.46571  ,  -93.90342  , -103.84386  ],\n",
       "        [ -71.760414 ,  -71.760414 ,  -71.760414 ,  -71.831436 ,\n",
       "          -73.11401  ,  -76.872986 ,  -84.851006 ,  -98.46381  ],\n",
       "        [ -60.510418 ,  -60.510418 ,  -60.510418 ,  -60.577732 ,\n",
       "          -61.804718 ,  -65.52858  ,  -74.12083  ,  -91.13222  ],\n",
       "        [ -49.260418 ,  -49.260418 ,  -49.260418 ,  -49.313774 ,\n",
       "          -50.29424  ,  -53.368095 ,  -61.117085 ,  -79.9867   ],\n",
       "        [ -38.010418 ,  -38.010418 ,  -38.010418 ,  -38.041668 ,\n",
       "          -38.61929  ,  -40.474148 ,  -45.51033  ,  -61.197704 ]]],\n",
       "      dtype=float32)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>lon_min</span></div><div class='xr-var-dims'>(face, j, i)</div><div class='xr-var-dtype'>float32</div><div class='xr-var-preview xr-preview'>-114.9 -114.5 ... -79.91 -115.0</div><input id='attrs-3af77896-4d16-4765-8fae-44cb8d1c3fa6' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-3af77896-4d16-4765-8fae-44cb8d1c3fa6' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-034d98af-df67-4fa1-871b-78bd14aee68a' class='xr-var-data-in' type='checkbox'><label for='data-034d98af-df67-4fa1-871b-78bd14aee68a' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'><dt><span>coordinate :</span></dt><dd>YC XC</dd><dt><span>long_name :</span></dt><dd>longitude</dd><dt><span>standard_name :</span></dt><dd>longitude</dd><dt><span>units :</span></dt><dd>degrees_east</dd></dl></div><div class='xr-var-data'><pre>array([[[-114.93228   , -114.485664  ,    2.9509041 ,   25.209188  ,\n",
       "           38.20309   ,   46.452972  ,   52.31301   ,   56.909225  ],\n",
       "        [ -61.100605  ,  -30.484154  ,   -9.824568  ,    6.5386205 ,\n",
       "           20.34413   ,   31.721094  ,   41.23123   ,   49.458782  ],\n",
       "        [ -45.464153  ,  -27.812773  ,  -13.650324  ,   -0.57347125,\n",
       "           11.832302  ,   23.429485  ,   34.24263   ,   44.404087  ],\n",
       "        [ -40.44432   ,  -27.083197  ,  -15.036728  ,   -3.3229249 ,\n",
       "            8.244166  ,   19.617998  ,   30.784578  ,   41.761623  ],\n",
       "        [ -38.5956    ,  -26.823744  ,  -15.466365  ,   -4.192369  ,\n",
       "            7.0744195 ,   18.33145   ,   29.577663  ,   40.813652  ],\n",
       "        [ -38.020435  ,  -26.743858  ,  -15.489583  ,   -4.2395835 ,\n",
       "            7.0104165 ,   18.260416  ,   29.510416  ,   40.760418  ],\n",
       "        [ -37.989582  ,  -26.739584  ,  -15.489583  ,   -4.2395835 ,\n",
       "            7.0104165 ,   18.260416  ,   29.510416  ,   40.760418  ],\n",
       "        [ -37.989582  ,  -26.739584  ,  -15.489583  ,   -4.2395835 ,\n",
       "            7.0104165 ,   18.260416  ,   29.510416  ,   40.760418  ]],\n",
       "\n",
       "       [[ -37.989582  ,  -26.739584  ,  -15.489583  ,   -4.2395835 ,\n",
       "            7.0104165 ,   18.260416  ,   29.510416  ,   40.760418  ],\n",
       "        [ -37.989582  ,  -26.739584  ,  -15.489583  ,   -4.2395835 ,\n",
       "...\n",
       "        [ -49.239582  ,  -49.239582  ,  -49.239582  ,  -49.239582  ,\n",
       "          -49.239582  ,  -49.239582  ,  -49.239582  ,  -49.239582  ]],\n",
       "\n",
       "       [[-127.989586  , -127.989586  , -127.989586  , -127.95845   ,\n",
       "         -127.40699   , -125.89788   , -123.10888   , -119.16558   ],\n",
       "        [-116.739586  , -116.739586  , -116.739586  , -116.73527   ,\n",
       "         -116.65906   , -116.45206   , -116.07467   , -115.54939   ],\n",
       "        [-105.489586  , -105.489586  , -105.51248   , -105.92126   ,\n",
       "         -107.03726   , -109.0876    , -111.96648   , -114.99738   ],\n",
       "        [ -94.239586  ,  -94.239586  ,  -94.28618   ,  -95.121544  ,\n",
       "          -97.43714   , -101.812096  , -108.16218   , -114.99408   ],\n",
       "        [ -82.989586  ,  -82.989586  ,  -83.05279   ,  -84.19422   ,\n",
       "          -87.43807   ,  -93.87246   , -103.81437   , -114.990234  ],\n",
       "        [ -71.739586  ,  -71.739586  ,  -71.8098    ,  -73.08903   ,\n",
       "          -76.84248   ,  -84.81297   ,  -98.42269   , -114.9853    ],\n",
       "        [ -60.489582  ,  -60.489582  ,  -60.556118  ,  -61.779488  ,\n",
       "          -65.49642   ,  -74.07635   ,  -91.07561   , -114.97809   ],\n",
       "        [ -49.239582  ,  -49.239582  ,  -49.292297  ,  -50.26946   ,\n",
       "          -53.33605   ,  -61.0688    ,  -79.909386  , -114.96531   ]]],\n",
       "      dtype=float32)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>area_fraction</span></div><div class='xr-var-dims'>(face, j, i)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0</div><input id='attrs-4585d125-ee17-4433-b120-669799bdd99e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-4585d125-ee17-4433-b120-669799bdd99e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-b55e8d92-49c3-4c24-839b-b3974f4f793e' class='xr-var-data-in' type='checkbox'><label for='data-b55e8d92-49c3-4c24-839b-b3974f4f793e' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[[0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n",
       "         0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],\n",
       "        [0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n",
       "         0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],\n",
       "        [0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n",
       "         0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],\n",
       "        [2.29636488e-01, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n",
       "         0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],\n",
       "        [9.95065158e-01, 4.13556241e-01, 2.90809328e-02, 0.00000000e+00,\n",
       "         0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],\n",
       "        [1.00000000e+00, 1.00000000e+00, 9.28408779e-01, 7.60428669e-01,\n",
       "         6.60860768e-01, 7.43792867e-01, 5.05648148e-01, 9.35905350e-02],\n",
       "        [1.00000000e+00, 1.00000000e+00, 1.00000000e+00, 1.00000000e+00,\n",
       "         1.00000000e+00, 1.00000000e+00, 1.00000000e+00, 9.48034979e-01],\n",
       "        [9.99825103e-01, 9.99152949e-01, 1.00000000e+00, 1.00000000e+00,\n",
       "         1.00000000e+00, 1.00000000e+00, 1.00000000e+00, 1.00000000e+00]],\n",
       "\n",
       "       [[9.83480796e-01, 1.00000000e+00, 1.00000000e+00, 9.99780521e-01,\n",
       "         1.00000000e+00, 1.00000000e+00, 1.00000000e+00, 9.99485597e-01],\n",
       "        [1.00000000e+00, 1.00000000e+00, 1.00000000e+00, 9.99996571e-01,\n",
       "...\n",
       "         9.80384088e-02, 6.56862140e-01, 1.00000000e+00, 9.19344993e-01],\n",
       "        [9.99948560e-01, 3.81032236e-01, 2.54972565e-02, 3.26388889e-01,\n",
       "         9.67225652e-01, 1.00000000e+00, 1.00000000e+00, 9.92692044e-01]],\n",
       "\n",
       "       [[1.00000000e+00, 1.00000000e+00, 1.00000000e+00, 8.44753086e-01,\n",
       "         0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],\n",
       "        [1.00000000e+00, 1.00000000e+00, 1.00000000e+00, 9.71546639e-01,\n",
       "         3.95576132e-02, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],\n",
       "        [1.00000000e+00, 1.00000000e+00, 1.00000000e+00, 3.24756516e-01,\n",
       "         0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],\n",
       "        [1.00000000e+00, 1.00000000e+00, 9.98590535e-01, 3.86165981e-01,\n",
       "         0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],\n",
       "        [1.00000000e+00, 1.00000000e+00, 8.19499314e-01, 1.55089163e-01,\n",
       "         0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],\n",
       "        [9.98326475e-01, 6.82153635e-01, 1.72966392e-01, 1.38545953e-03,\n",
       "         0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],\n",
       "        [9.80579561e-01, 9.00490398e-01, 9.88641975e-01, 8.93936900e-01,\n",
       "         4.77263374e-02, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],\n",
       "        [9.94303841e-01, 1.00000000e+00, 1.00000000e+00, 1.00000000e+00,\n",
       "         3.92283951e-01, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00]]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>f_coriolis</span></div><div class='xr-var-dims'>(face, j, i)</div><div class='xr-var-dtype'>float32</div><div class='xr-var-preview xr-preview'>-0.0001458 ... -0.0001456</div><input id='attrs-ceec15e1-dd27-4e4d-ad6c-95b6e3d6a844' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-ceec15e1-dd27-4e4d-ad6c-95b6e3d6a844' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-c091335f-d2b0-47bc-a4ba-215e4fea83f4' class='xr-var-data-in' type='checkbox'><label for='data-c091335f-d2b0-47bc-a4ba-215e4fea83f4' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[[-1.4576480e-04, -1.4578199e-04, -1.4568868e-04, -1.4548631e-04,\n",
       "         -1.4518082e-04, -1.4478849e-04, -1.4434720e-04, -1.4393109e-04],\n",
       "        [-1.4540895e-04, -1.4542612e-04, -1.4533322e-04, -1.4513225e-04,\n",
       "         -1.4482945e-04, -1.4444163e-04, -1.4400706e-04, -1.4359868e-04],\n",
       "        [-1.4451018e-04, -1.4452684e-04, -1.4443658e-04, -1.4424167e-04,\n",
       "         -1.4394986e-04, -1.4357870e-04, -1.4316656e-04, -1.4278259e-04],\n",
       "        [-1.4284125e-04, -1.4285612e-04, -1.4277551e-04, -1.4260254e-04,\n",
       "         -1.4234598e-04, -1.4202423e-04, -1.4167205e-04, -1.4134945e-04],\n",
       "        [-1.4016188e-04, -1.4017159e-04, -1.4011975e-04, -1.4000927e-04,\n",
       "         -1.3984791e-04, -1.3964948e-04, -1.3943725e-04, -1.3924691e-04],\n",
       "        [-1.3646185e-04, -1.3646270e-04, -1.3645814e-04, -1.3644857e-04,\n",
       "         -1.3643476e-04, -1.3641809e-04, -1.3640063e-04, -1.3638531e-04],\n",
       "        [-1.3210521e-04, -1.3210521e-04, -1.3210521e-04, -1.3210521e-04,\n",
       "         -1.3210521e-04, -1.3210521e-04, -1.3210521e-04, -1.3210521e-04],\n",
       "        [-1.2607624e-04, -1.2607624e-04, -1.2607624e-04, -1.2607624e-04,\n",
       "         -1.2607624e-04, -1.2607624e-04, -1.2607624e-04, -1.2607624e-04]],\n",
       "\n",
       "       [[-1.1779487e-04, -1.1779487e-04, -1.1779487e-04, -1.1779487e-04,\n",
       "         -1.1779487e-04, -1.1779487e-04, -1.1779487e-04, -1.1779487e-04],\n",
       "        [-1.0689933e-04, -1.0689933e-04, -1.0689933e-04, -1.0689933e-04,\n",
       "...\n",
       "        [ 2.1870324e-05, -4.4124886e-06, -3.0370986e-05, -5.4362528e-05,\n",
       "         -7.5353179e-05, -9.2863098e-05, -1.0689965e-04, -1.1779563e-04]],\n",
       "\n",
       "       [[-1.2607590e-04, -1.3210571e-04, -1.3637617e-04, -1.3912356e-04,\n",
       "         -1.4113661e-04, -1.4252645e-04, -1.4332446e-04, -1.4365077e-04],\n",
       "        [-1.2607590e-04, -1.3210571e-04, -1.3637420e-04, -1.3910558e-04,\n",
       "         -1.4110537e-04, -1.4248866e-04, -1.4328367e-04, -1.4360900e-04],\n",
       "        [-1.2607590e-04, -1.3210571e-04, -1.3638147e-04, -1.3919923e-04,\n",
       "         -1.4126737e-04, -1.4268419e-04, -1.4349348e-04, -1.4382359e-04],\n",
       "        [-1.2607590e-04, -1.3210571e-04, -1.3639574e-04, -1.3937370e-04,\n",
       "         -1.4156509e-04, -1.4303984e-04, -1.4387269e-04, -1.4421041e-04],\n",
       "        [-1.2607590e-04, -1.3210571e-04, -1.3641219e-04, -1.3958354e-04,\n",
       "         -1.4191559e-04, -1.4345236e-04, -1.4430884e-04, -1.4465378e-04],\n",
       "        [-1.2607590e-04, -1.3210571e-04, -1.3642990e-04, -1.3978928e-04,\n",
       "         -1.4225162e-04, -1.4384158e-04, -1.4471664e-04, -1.4506688e-04],\n",
       "        [-1.2607590e-04, -1.3210571e-04, -1.3644464e-04, -1.3996403e-04,\n",
       "         -1.4253112e-04, -1.4416073e-04, -1.4504846e-04, -1.4540185e-04],\n",
       "        [-1.2607590e-04, -1.3210571e-04, -1.3645587e-04, -1.4009124e-04,\n",
       "         -1.4273135e-04, -1.4438693e-04, -1.4528215e-04, -1.4563723e-04]]],\n",
       "      dtype=float32)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>i_min</span></div><div class='xr-var-dims'>(i)</div><div class='xr-var-dtype'>int16</div><div class='xr-var-preview xr-preview'>0 540 1080 1620 2160 2700 3240 3780</div><input id='attrs-9d8c3034-ad27-4096-aa51-b27a2d564daf' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-9d8c3034-ad27-4096-aa51-b27a2d564daf' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-736333b3-6009-4f7c-938c-d34d7e497f60' class='xr-var-data-in' type='checkbox'><label for='data-736333b3-6009-4f7c-938c-d34d7e497f60' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'><dt><span>axis :</span></dt><dd>X</dd><dt><span>long_name :</span></dt><dd>x-dimension of the t grid</dd><dt><span>standard_name :</span></dt><dd>x_grid_index</dd><dt><span>swap_dim :</span></dt><dd>XC</dd></dl></div><div class='xr-var-data'><pre>array([   0,  540, 1080, 1620, 2160, 2700, 3240, 3780], dtype=int16)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>i_max</span></div><div class='xr-var-dims'>(i)</div><div class='xr-var-dtype'>int16</div><div class='xr-var-preview xr-preview'>540 1080 1620 ... 3240 3780 4320</div><input id='attrs-0a950824-4d98-4d81-9755-d3b42b307e27' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-0a950824-4d98-4d81-9755-d3b42b307e27' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-409a6542-2eaa-47d6-9470-fc81e2d26e36' class='xr-var-data-in' type='checkbox'><label for='data-409a6542-2eaa-47d6-9470-fc81e2d26e36' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([ 540, 1080, 1620, 2160, 2700, 3240, 3780, 4320], dtype=int16)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>j_min</span></div><div class='xr-var-dims'>(j)</div><div class='xr-var-dtype'>int16</div><div class='xr-var-preview xr-preview'>0 540 1080 1620 2160 2700 3240 3780</div><input id='attrs-cc5b8665-6fc2-4a08-be27-bc02c7352593' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-cc5b8665-6fc2-4a08-be27-bc02c7352593' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-35498d30-28b7-4197-81f4-212dd293a638' class='xr-var-data-in' type='checkbox'><label for='data-35498d30-28b7-4197-81f4-212dd293a638' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'><dt><span>axis :</span></dt><dd>Y</dd><dt><span>long_name :</span></dt><dd>y-dimension of the t grid</dd><dt><span>standard_name :</span></dt><dd>y_grid_index</dd><dt><span>swap_dim :</span></dt><dd>YC</dd></dl></div><div class='xr-var-data'><pre>array([   0,  540, 1080, 1620, 2160, 2700, 3240, 3780], dtype=int16)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>j_max</span></div><div class='xr-var-dims'>(j)</div><div class='xr-var-dtype'>int16</div><div class='xr-var-preview xr-preview'>540 1080 1620 ... 3240 3780 4320</div><input id='attrs-df1d1d2a-ad21-47a5-b19b-8d79cbf11aff' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-df1d1d2a-ad21-47a5-b19b-8d79cbf11aff' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-92382458-5710-4122-bcc1-cc1eaccc23ce' class='xr-var-data-in' type='checkbox'><label for='data-92382458-5710-4122-bcc1-cc1eaccc23ce' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([ 540, 1080, 1620, 2160, 2700, 3240, 3780, 4320], dtype=int16)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-4f89792f-d5cb-40b0-8786-32f607eaca49' class='xr-section-summary-in' type='checkbox'  checked><label for='section-4f89792f-d5cb-40b0-8786-32f607eaca49' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>coordinate :</span></dt><dd>YC XC</dd><dt><span>long_name :</span></dt><dd>latitude</dd><dt><span>standard_name :</span></dt><dd>latitude</dd><dt><span>units :</span></dt><dd>degrees_north</dd></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.Dataset>\n",
       "Dimensions:        (face: 13, j: 8, i: 8)\n",
       "Coordinates:\n",
       "  * face           (face) int64 0 1 2 3 4 5 6 7 8 9 10 11 12\n",
       "Dimensions without coordinates: j, i\n",
       "Data variables:\n",
       "    lat_max        (face, j, i) float32 -86.8 -87.05 -86.08 ... -83.3 -85.71\n",
       "    lat_min        (face, j, i) float32 -89.75 -90.0 -88.67 ... -86.79 -88.17\n",
       "    lon_max        (face, j, i) float32 -30.56 64.91 64.96 ... -45.51 -61.2\n",
       "    lon_min        (face, j, i) float32 -114.9 -114.5 2.951 ... -79.91 -115.0\n",
       "    area_fraction  (face, j, i) float64 0.0 0.0 0.0 0.0 ... 0.3923 0.0 0.0 0.0\n",
       "    f_coriolis     (face, j, i) float32 -0.0001458 -0.0001458 ... -0.0001456\n",
       "    i_min          (i) int16 0 540 1080 1620 2160 2700 3240 3780\n",
       "    i_max          (i) int16 540 1080 1620 2160 2700 3240 3780 4320\n",
       "    j_min          (j) int16 0 540 1080 1620 2160 2700 3240 3780\n",
       "    j_max          (j) int16 540 1080 1620 2160 2700 3240 3780 4320\n",
       "Attributes:\n",
       "    coordinate:     YC XC\n",
       "    long_name:      latitude\n",
       "    standard_name:  latitude\n",
       "    units:          degrees_north"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "region_shape = (540, 540)\n",
    "\n",
    "i_max = (depth.i.coarsen(i=region_shape[1]).max() + 1).rename('i_max').drop('i').astype('i2')\n",
    "i_min = depth.i.coarsen(i=region_shape[1]).min().rename('i_min').drop('i').astype('i2')\n",
    "j_max = (depth.j.coarsen(j=region_shape[0]).max() + 1).rename('j_max').drop('j').astype('i2')\n",
    "j_min = (depth.j.coarsen(j=region_shape[0]).min()).rename('j_min').drop('j').astype('i2')\n",
    "\n",
    "lat_max = lat.coarsen(j=region_shape[0], i=region_shape[1]).max().rename('lat_max').drop(['i', 'j'])\n",
    "lat_min = lat.coarsen(j=region_shape[0], i=region_shape[1]).min().rename('lat_min').drop(['i', 'j'])\n",
    "lon_max = lon.coarsen(j=region_shape[0], i=region_shape[1]).max().rename('lon_max').drop(['i', 'j'])\n",
    "lon_min = lon.coarsen(j=region_shape[0], i=region_shape[1]).min().rename('lon_min').drop(['i', 'j'])\n",
    "\n",
    "rotation_rate = 7.2921e-5  # rad/s\n",
    "f_coriolis = (\n",
    "    2 * rotation_rate * np.sin(lat*np.pi/180)\n",
    ").coarsen(j=region_shape[0], i=region_shape[1]).mean().rename('f_coriolis').drop(['i', 'j'])\n",
    "f_coriolis\n",
    "\n",
    "mask = (depth > 100).rename('mask').drop(['i', 'j'])\n",
    "fraction = mask.coarsen(j=region_shape[0], i=region_shape[1]).mean().rename('area_fraction')\n",
    "\n",
    "regions = xr.merge([lat_max, lat_min, lon_max, lon_min, fraction, f_coriolis, i_min, i_max, j_min, j_max])\n",
    "regions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fd435135-0d6b-4908-b67f-511edcb72c4a",
   "metadata": {},
   "outputs": [],
   "source": [
    "del depth, lat, lon # try to free some memory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "03b28dc6-e1df-4bf5-a6d9-7ccb30d8a2a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>face</th>\n",
       "      <th>j</th>\n",
       "      <th>i</th>\n",
       "      <th>lat_max</th>\n",
       "      <th>lat_min</th>\n",
       "      <th>lon_max</th>\n",
       "      <th>lon_min</th>\n",
       "      <th>area_fraction</th>\n",
       "      <th>f_coriolis</th>\n",
       "      <th>i_min</th>\n",
       "      <th>i_max</th>\n",
       "      <th>j_min</th>\n",
       "      <th>j_max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-86.799751</td>\n",
       "      <td>-89.752815</td>\n",
       "      <td>-30.559948</td>\n",
       "      <td>-114.932281</td>\n",
       "      <td>0.000000</td>\n",
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       "      <td>540</td>\n",
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       "      <td>540</td>\n",
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       "      <th>1</th>\n",
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       "      <td>1</td>\n",
       "      <td>-87.051270</td>\n",
       "      <td>-89.997368</td>\n",
       "      <td>64.906548</td>\n",
       "      <td>-114.485664</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.000146</td>\n",
       "      <td>540</td>\n",
       "      <td>1080</td>\n",
       "      <td>0</td>\n",
       "      <td>540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>-86.080391</td>\n",
       "      <td>-88.665024</td>\n",
       "      <td>64.958748</td>\n",
       "      <td>2.950904</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.000146</td>\n",
       "      <td>1080</td>\n",
       "      <td>1620</td>\n",
       "      <td>0</td>\n",
       "      <td>540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>-84.818130</td>\n",
       "      <td>-87.089844</td>\n",
       "      <td>64.974991</td>\n",
       "      <td>25.209188</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.000145</td>\n",
       "      <td>1620</td>\n",
       "      <td>2160</td>\n",
       "      <td>0</td>\n",
       "      <td>540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>-83.463402</td>\n",
       "      <td>-85.528854</td>\n",
       "      <td>64.983391</td>\n",
       "      <td>38.203091</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.000145</td>\n",
       "      <td>2160</td>\n",
       "      <td>2700</td>\n",
       "      <td>0</td>\n",
       "      <td>540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>827</th>\n",
       "      <td>12</td>\n",
       "      <td>7</td>\n",
       "      <td>3</td>\n",
       "      <td>-71.575722</td>\n",
       "      <td>-76.234230</td>\n",
       "      <td>-38.041668</td>\n",
       "      <td>-50.269459</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.000140</td>\n",
       "      <td>1620</td>\n",
       "      <td>2160</td>\n",
       "      <td>3780</td>\n",
       "      <td>4320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>828</th>\n",
       "      <td>12</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>-76.018021</td>\n",
       "      <td>-80.353157</td>\n",
       "      <td>-38.619289</td>\n",
       "      <td>-53.336048</td>\n",
       "      <td>0.392284</td>\n",
       "      <td>-0.000143</td>\n",
       "      <td>2160</td>\n",
       "      <td>2700</td>\n",
       "      <td>3780</td>\n",
       "      <td>4320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>829</th>\n",
       "      <td>12</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>-79.970764</td>\n",
       "      <td>-83.922943</td>\n",
       "      <td>-40.474148</td>\n",
       "      <td>-61.068802</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.000144</td>\n",
       "      <td>2700</td>\n",
       "      <td>3240</td>\n",
       "      <td>3780</td>\n",
       "      <td>4320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>830</th>\n",
       "      <td>12</td>\n",
       "      <td>7</td>\n",
       "      <td>6</td>\n",
       "      <td>-83.296005</td>\n",
       "      <td>-86.793678</td>\n",
       "      <td>-45.510330</td>\n",
       "      <td>-79.909386</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.000145</td>\n",
       "      <td>3240</td>\n",
       "      <td>3780</td>\n",
       "      <td>3780</td>\n",
       "      <td>4320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>831</th>\n",
       "      <td>12</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>-85.706650</td>\n",
       "      <td>-88.174225</td>\n",
       "      <td>-61.197704</td>\n",
       "      <td>-114.965309</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.000146</td>\n",
       "      <td>3780</td>\n",
       "      <td>4320</td>\n",
       "      <td>3780</td>\n",
       "      <td>4320</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>832 rows × 13 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     face  j  i    lat_max    lat_min    lon_max     lon_min  area_fraction  \\\n",
       "0       0  0  0 -86.799751 -89.752815 -30.559948 -114.932281       0.000000   \n",
       "1       0  0  1 -87.051270 -89.997368  64.906548 -114.485664       0.000000   \n",
       "2       0  0  2 -86.080391 -88.665024  64.958748    2.950904       0.000000   \n",
       "3       0  0  3 -84.818130 -87.089844  64.974991   25.209188       0.000000   \n",
       "4       0  0  4 -83.463402 -85.528854  64.983391   38.203091       0.000000   \n",
       "..    ... .. ..        ...        ...        ...         ...            ...   \n",
       "827    12  7  3 -71.575722 -76.234230 -38.041668  -50.269459       1.000000   \n",
       "828    12  7  4 -76.018021 -80.353157 -38.619289  -53.336048       0.392284   \n",
       "829    12  7  5 -79.970764 -83.922943 -40.474148  -61.068802       0.000000   \n",
       "830    12  7  6 -83.296005 -86.793678 -45.510330  -79.909386       0.000000   \n",
       "831    12  7  7 -85.706650 -88.174225 -61.197704 -114.965309       0.000000   \n",
       "\n",
       "     f_coriolis  i_min  i_max  j_min  j_max  \n",
       "0     -0.000146      0    540      0    540  \n",
       "1     -0.000146    540   1080      0    540  \n",
       "2     -0.000146   1080   1620      0    540  \n",
       "3     -0.000145   1620   2160      0    540  \n",
       "4     -0.000145   2160   2700      0    540  \n",
       "..          ...    ...    ...    ...    ...  \n",
       "827   -0.000140   1620   2160   3780   4320  \n",
       "828   -0.000143   2160   2700   3780   4320  \n",
       "829   -0.000144   2700   3240   3780   4320  \n",
       "830   -0.000145   3240   3780   3780   4320  \n",
       "831   -0.000146   3780   4320   3780   4320  \n",
       "\n",
       "[832 rows x 13 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "region_df = regions.to_dataframe().reset_index()\n",
    "region_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e6a3a3b6-7418-4701-a858-2dffe9b0a84d",
   "metadata": {},
   "outputs": [
    {
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       "      <td>-4.239583</td>\n",
       "      <td>0.760429</td>\n",
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       "      <td>0</td>\n",
       "      <td>540</td>\n",
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       "      <th>825</th>\n",
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       "      <td>1.000000</td>\n",
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       "      <td>2160</td>\n",
       "      <td>3780</td>\n",
       "      <td>4320</td>\n",
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      ],
      "text/plain": [
       "     face  j  i    lat_max    lat_min    lon_max    lon_min  area_fraction  \\\n",
       "32      0  4  0 -71.638092 -76.325882 -26.764791 -38.595600       0.995065   \n",
       "40      0  5  0 -67.254387 -71.654449 -26.760416 -38.020435       1.000000   \n",
       "41      0  5  1 -67.254387 -71.654922 -15.487511 -26.743858       1.000000   \n",
       "42      0  5  2 -67.254387 -71.641052  -4.213777 -15.489583       0.928409   \n",
       "43      0  5  3 -67.254387 -71.589973   7.052837  -4.239583       0.760429   \n",
       "..    ... .. ..        ...        ...        ...        ...            ...   \n",
       "819    12  6  3 -71.481636 -76.009682 -49.313774 -61.779488       0.893937   \n",
       "824    12  7  0 -57.012096 -62.552940 -38.010418 -49.239582       0.994304   \n",
       "825    12  7  1 -62.562359 -67.246368 -38.010418 -49.239582       1.000000   \n",
       "826    12  7  2 -67.254387 -71.629066 -38.010418 -49.292297       1.000000   \n",
       "827    12  7  3 -71.575722 -76.234230 -38.041668 -50.269459       1.000000   \n",
       "\n",
       "     f_coriolis  i_min  i_max  j_min  j_max  \n",
       "32    -0.000140      0    540   2160   2700  \n",
       "40    -0.000136      0    540   2700   3240  \n",
       "41    -0.000136    540   1080   2700   3240  \n",
       "42    -0.000136   1080   1620   2700   3240  \n",
       "43    -0.000136   1620   2160   2700   3240  \n",
       "..          ...    ...    ...    ...    ...  \n",
       "819   -0.000140   1620   2160   3240   3780  \n",
       "824   -0.000126      0    540   3780   4320  \n",
       "825   -0.000132    540   1080   3780   4320  \n",
       "826   -0.000136   1080   1620   3780   4320  \n",
       "827   -0.000140   1620   2160   3780   4320  \n",
       "\n",
       "[437 rows x 13 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "regions_keep = region_df[region_df.area_fraction > 0.6]\n",
    "regions_keep"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ccd8cd05-62fe-4f67-93c0-768ccab71983",
   "metadata": {},
   "outputs": [],
   "source": [
    "def iter_regions():\n",
    "    for idx in regions_keep.index:\n",
    "        face, i_min, i_max, j_min, j_max = regions_keep[['face', 'i_min', 'i_max', 'j_min', 'j_max']].loc[idx]\n",
    "        f = regions_keep.f_coriolis.loc[idx]\n",
    "        j_slice = slice(j_min, j_max)\n",
    "        i_slice = slice(i_min, i_max)\n",
    "        region_selector = dict(face=2, j=j_slice, j_g=j_slice, i=i_slice, i_g=i_slice)\n",
    "        yield idx, region_selector, f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c26b25a8-b7b1-4729-9b57-3522986c09ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(32,\n",
       " {'face': 2,\n",
       "  'j': slice(2160, 2700, None),\n",
       "  'j_g': slice(2160, 2700, None),\n",
       "  'i': slice(0, 540, None),\n",
       "  'i_g': slice(0, 540, None)},\n",
       " -0.00014016188)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for r, selector, f in iter_regions():\n",
    "    break\n",
    "r, selector, f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "12b321b6-da8e-43ab-9945-5cfc714f70a0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def iter_time(time_blocks=240, time_subset=24, ntot=9030):\n",
    "    for nstart in range(0, ntot, time_blocks):\n",
    "        if nstart + time_blocks <= ntot:\n",
    "            yield slice(nstart, nstart+time_blocks, time_subset)\n",
    "\n",
    "for time_slice in iter_time():\n",
    "    pass\n",
    "\n",
    "time_coarse = ds_grid.time.coarsen(time=240, boundary='trim').mean()\n",
    "assert len(time_coarse) == len(list(iter_time()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "053fe600-9879-41ea-99db-dc0bbd2e4461",
   "metadata": {},
   "source": [
    "## Initialize Target Dataset\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a8df1387-6cb5-4a0b-af87-1ee9a0253a58",
   "metadata": {},
   "outputs": [],
   "source": [
    "ntime = len(time_coarse)\n",
    "nregions = len(regions_keep)\n",
    "n_strain_bins = 100\n",
    "n_vort_bins = 200"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "20d93d13-e815-4362-a809-ebbbe27f4cd2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def vort_strain_bins(n_strain_bins, n_vort_bins, f=1, vort_max=7, strain_max=7):\n",
    "    f_abs = abs(f)\n",
    "    vort_bins = np.linspace(-vort_max * f_abs, vort_max * f_abs, n_vort_bins)\n",
    "    strain_bins = np.linspace(0.0, strain_max * f_abs, n_strain_bins)\n",
    "    return vort_bins, strain_bins\n",
    "    \n",
    "def center_bin(bounds):\n",
    "    return 0.5 * (bounds[:-1] + bounds[1:])\n",
    "    \n",
    "vort_bins, strain_bins = vort_strain_bins(n_strain_bins, n_vort_bins)\n",
    "vort_bins = center_bin(vort_bins)\n",
    "strain_bins = center_bin(strain_bins)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8a848afa-0daf-4b34-9920-da4948368043",
   "metadata": {},
   "outputs": [
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
       "Dimensions:                (time_coarse: 37, region: 437, vort: 199, strain: 99)\n",
       "Coordinates: (12/14)\n",
       "  * time_coarse            (time_coarse) datetime64[ns] 2011-09-17T23:30:00 ....\n",
       "  * region                 (region) int64 32 40 41 42 43 ... 819 824 825 826 827\n",
       "  * vort                   (vort) float64 -6.965 -6.894 -6.824 ... 6.894 6.965\n",
       "  * strain                 (strain) float64 0.03535 0.1061 ... 6.894 6.965\n",
       "    lat_max                (region) float32 -71.64 -67.25 ... -67.25 -71.58\n",
       "    lat_min                (region) float32 -76.33 -71.65 ... -71.63 -76.23\n",
       "    ...                     ...\n",
       "    area_fraction          (region) float64 0.9951 1.0 1.0 ... 1.0 1.0 1.0\n",
       "    f_coriolis             (region) float32 -0.0001402 -0.0001365 ... -0.0001401\n",
       "    i_min                  (region) int16 0 0 540 1080 1620 ... 0 540 1080 1620\n",
       "    i_max                  (region) int16 540 540 1080 1620 ... 1080 1620 2160\n",
       "    j_min                  (region) int16 2160 2700 2700 2700 ... 3780 3780 3780\n",
       "    j_max                  (region) int16 2700 3240 3240 3240 ... 4320 4320 4320\n",
       "Data variables:\n",
       "    vort_strain_histogram  (time_coarse, region, strain, vort) float64 dask.array&lt;chunksize=(1, 1, 99, 199), meta=np.ndarray&gt;</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-03e965b0-667e-4fc4-b7be-53a29b3687be' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-03e965b0-667e-4fc4-b7be-53a29b3687be' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>time_coarse</span>: 37</li><li><span class='xr-has-index'>region</span>: 437</li><li><span class='xr-has-index'>vort</span>: 199</li><li><span class='xr-has-index'>strain</span>: 99</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-f8800230-b8f5-4afe-acc1-c911611a2fba' class='xr-section-summary-in' type='checkbox'  checked><label for='section-f8800230-b8f5-4afe-acc1-c911611a2fba' class='xr-section-summary' >Coordinates: <span>(14)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>time_coarse</span></div><div class='xr-var-dims'>(time_coarse)</div><div class='xr-var-dtype'>datetime64[ns]</div><div class='xr-var-preview xr-preview'>2011-09-17T23:30:00 ... 2012-09-...</div><input id='attrs-dac07d80-d6f6-4b0f-a49d-ae1e3510c5ba' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-dac07d80-d6f6-4b0f-a49d-ae1e3510c5ba' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-bc230030-ae1c-4058-b05b-47e9fa098d9e' class='xr-var-data-in' type='checkbox'><label for='data-bc230030-ae1c-4058-b05b-47e9fa098d9e' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;2011-09-17T23:30:00.000000000&#x27;, &#x27;2011-09-27T23:30:00.000000000&#x27;,\n",
       "       &#x27;2011-10-07T23:30:00.000000000&#x27;, &#x27;2011-10-17T23:30:00.000000000&#x27;,\n",
       "       &#x27;2011-10-27T23:30:00.000000000&#x27;, &#x27;2011-11-06T23:30:00.000000000&#x27;,\n",
       "       &#x27;2011-11-16T23:30:00.000000000&#x27;, &#x27;2011-11-26T23:30:00.000000000&#x27;,\n",
       "       &#x27;2011-12-06T23:30:00.000000000&#x27;, &#x27;2011-12-16T23:30:00.000000000&#x27;,\n",
       "       &#x27;2011-12-26T23:30:00.000000000&#x27;, &#x27;2012-01-05T23:30:00.000000000&#x27;,\n",
       "       &#x27;2012-01-15T23:30:00.000000000&#x27;, &#x27;2012-01-25T23:30:00.000000000&#x27;,\n",
       "       &#x27;2012-02-04T23:30:00.000000000&#x27;, &#x27;2012-02-14T23:30:00.000000000&#x27;,\n",
       "       &#x27;2012-02-24T23:30:00.000000000&#x27;, &#x27;2012-03-05T23:30:00.000000000&#x27;,\n",
       "       &#x27;2012-03-15T23:30:00.000000000&#x27;, &#x27;2012-03-25T23:30:00.000000000&#x27;,\n",
       "       &#x27;2012-04-04T23:30:00.000000000&#x27;, &#x27;2012-04-14T23:30:00.000000000&#x27;,\n",
       "       &#x27;2012-04-24T23:30:00.000000000&#x27;, &#x27;2012-05-04T23:30:00.000000000&#x27;,\n",
       "       &#x27;2012-05-14T23:30:00.000000000&#x27;, &#x27;2012-05-24T23:30:00.000000000&#x27;,\n",
       "       &#x27;2012-06-03T23:30:00.000000000&#x27;, &#x27;2012-06-13T23:30:00.000000000&#x27;,\n",
       "       &#x27;2012-06-23T23:30:00.000000000&#x27;, &#x27;2012-07-03T23:30:00.000000000&#x27;,\n",
       "       &#x27;2012-07-13T23:30:00.000000000&#x27;, &#x27;2012-07-23T23:30:00.000000000&#x27;,\n",
       "       &#x27;2012-08-02T23:30:00.000000000&#x27;, &#x27;2012-08-12T23:30:00.000000000&#x27;,\n",
       "       &#x27;2012-08-22T23:30:00.000000000&#x27;, &#x27;2012-09-01T23:30:00.000000000&#x27;,\n",
       "       &#x27;2012-09-11T23:30:00.000000000&#x27;], dtype=&#x27;datetime64[ns]&#x27;)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>region</span></div><div class='xr-var-dims'>(region)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>32 40 41 42 43 ... 824 825 826 827</div><input id='attrs-ad8adb56-9f86-4e9f-8834-42fa47cf81c4' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-ad8adb56-9f86-4e9f-8834-42fa47cf81c4' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-91d983c9-974f-4164-b0a2-19eb05da12c4' class='xr-var-data-in' type='checkbox'><label for='data-91d983c9-974f-4164-b0a2-19eb05da12c4' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([ 32,  40,  41, ..., 825, 826, 827])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>vort</span></div><div class='xr-var-dims'>(vort)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-6.965 -6.894 ... 6.894 6.965</div><input id='attrs-57b6481e-9339-491c-9e9f-0089d83cacb3' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-57b6481e-9339-491c-9e9f-0089d83cacb3' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-93f0caad-cd7d-492e-b1fc-2e70250021ce' class='xr-var-data-in' type='checkbox'><label for='data-93f0caad-cd7d-492e-b1fc-2e70250021ce' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([-6.964824, -6.894472, -6.824121, -6.753769, -6.683417, -6.613065,\n",
       "       -6.542714, -6.472362, -6.40201 , -6.331658, -6.261307, -6.190955,\n",
       "       -6.120603, -6.050251, -5.979899, -5.909548, -5.839196, -5.768844,\n",
       "       -5.698492, -5.628141, -5.557789, -5.487437, -5.417085, -5.346734,\n",
       "       -5.276382, -5.20603 , -5.135678, -5.065327, -4.994975, -4.924623,\n",
       "       -4.854271, -4.78392 , -4.713568, -4.643216, -4.572864, -4.502513,\n",
       "       -4.432161, -4.361809, -4.291457, -4.221106, -4.150754, -4.080402,\n",
       "       -4.01005 , -3.939698, -3.869347, -3.798995, -3.728643, -3.658291,\n",
       "       -3.58794 , -3.517588, -3.447236, -3.376884, -3.306533, -3.236181,\n",
       "       -3.165829, -3.095477, -3.025126, -2.954774, -2.884422, -2.81407 ,\n",
       "       -2.743719, -2.673367, -2.603015, -2.532663, -2.462312, -2.39196 ,\n",
       "       -2.321608, -2.251256, -2.180905, -2.110553, -2.040201, -1.969849,\n",
       "       -1.899497, -1.829146, -1.758794, -1.688442, -1.61809 , -1.547739,\n",
       "       -1.477387, -1.407035, -1.336683, -1.266332, -1.19598 , -1.125628,\n",
       "       -1.055276, -0.984925, -0.914573, -0.844221, -0.773869, -0.703518,\n",
       "       -0.633166, -0.562814, -0.492462, -0.422111, -0.351759, -0.281407,\n",
       "       -0.211055, -0.140704, -0.070352,  0.      ,  0.070352,  0.140704,\n",
       "        0.211055,  0.281407,  0.351759,  0.422111,  0.492462,  0.562814,\n",
       "        0.633166,  0.703518,  0.773869,  0.844221,  0.914573,  0.984925,\n",
       "        1.055276,  1.125628,  1.19598 ,  1.266332,  1.336683,  1.407035,\n",
       "        1.477387,  1.547739,  1.61809 ,  1.688442,  1.758794,  1.829146,\n",
       "        1.899497,  1.969849,  2.040201,  2.110553,  2.180905,  2.251256,\n",
       "        2.321608,  2.39196 ,  2.462312,  2.532663,  2.603015,  2.673367,\n",
       "        2.743719,  2.81407 ,  2.884422,  2.954774,  3.025126,  3.095477,\n",
       "        3.165829,  3.236181,  3.306533,  3.376884,  3.447236,  3.517588,\n",
       "        3.58794 ,  3.658291,  3.728643,  3.798995,  3.869347,  3.939698,\n",
       "        4.01005 ,  4.080402,  4.150754,  4.221106,  4.291457,  4.361809,\n",
       "        4.432161,  4.502513,  4.572864,  4.643216,  4.713568,  4.78392 ,\n",
       "        4.854271,  4.924623,  4.994975,  5.065327,  5.135678,  5.20603 ,\n",
       "        5.276382,  5.346734,  5.417085,  5.487437,  5.557789,  5.628141,\n",
       "        5.698492,  5.768844,  5.839196,  5.909548,  5.979899,  6.050251,\n",
       "        6.120603,  6.190955,  6.261307,  6.331658,  6.40201 ,  6.472362,\n",
       "        6.542714,  6.613065,  6.683417,  6.753769,  6.824121,  6.894472,\n",
       "        6.964824])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>strain</span></div><div class='xr-var-dims'>(strain)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.03535 0.1061 ... 6.894 6.965</div><input id='attrs-cf6b4485-5671-438c-b408-edbe56c111c7' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-cf6b4485-5671-438c-b408-edbe56c111c7' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-c4bae7c3-fc3f-45cc-9c2e-70db537055f4' class='xr-var-data-in' type='checkbox'><label for='data-c4bae7c3-fc3f-45cc-9c2e-70db537055f4' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0.035354, 0.106061, 0.176768, 0.247475, 0.318182, 0.388889, 0.459596,\n",
       "       0.530303, 0.60101 , 0.671717, 0.742424, 0.813131, 0.883838, 0.954545,\n",
       "       1.025253, 1.09596 , 1.166667, 1.237374, 1.308081, 1.378788, 1.449495,\n",
       "       1.520202, 1.590909, 1.661616, 1.732323, 1.80303 , 1.873737, 1.944444,\n",
       "       2.015152, 2.085859, 2.156566, 2.227273, 2.29798 , 2.368687, 2.439394,\n",
       "       2.510101, 2.580808, 2.651515, 2.722222, 2.792929, 2.863636, 2.934343,\n",
       "       3.005051, 3.075758, 3.146465, 3.217172, 3.287879, 3.358586, 3.429293,\n",
       "       3.5     , 3.570707, 3.641414, 3.712121, 3.782828, 3.853535, 3.924242,\n",
       "       3.994949, 4.065657, 4.136364, 4.207071, 4.277778, 4.348485, 4.419192,\n",
       "       4.489899, 4.560606, 4.631313, 4.70202 , 4.772727, 4.843434, 4.914141,\n",
       "       4.984848, 5.055556, 5.126263, 5.19697 , 5.267677, 5.338384, 5.409091,\n",
       "       5.479798, 5.550505, 5.621212, 5.691919, 5.762626, 5.833333, 5.90404 ,\n",
       "       5.974747, 6.045455, 6.116162, 6.186869, 6.257576, 6.328283, 6.39899 ,\n",
       "       6.469697, 6.540404, 6.611111, 6.681818, 6.752525, 6.823232, 6.893939,\n",
       "       6.964646])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>lat_max</span></div><div class='xr-var-dims'>(region)</div><div class='xr-var-dtype'>float32</div><div class='xr-var-preview xr-preview'>-71.64 -67.25 ... -67.25 -71.58</div><input id='attrs-b2981858-219c-4539-890a-e95535fb092d' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b2981858-219c-4539-890a-e95535fb092d' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-3537c76b-0454-43cf-a4c8-9fe302683867' class='xr-var-data-in' type='checkbox'><label for='data-3537c76b-0454-43cf-a4c8-9fe302683867' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([-71.63809  , -67.25439  , -67.25439  , -67.25439  , -67.25439  ,\n",
       "       -67.25439  , -67.25439  , -62.56236  , -62.56236  , -62.56236  ,\n",
       "       -62.56236  , -62.56236  , -62.56236  , -62.56236  , -62.56236  ,\n",
       "       -57.012096 , -57.012096 , -57.012096 , -57.012096 , -57.012096 ,\n",
       "       -57.012096 , -57.012096 , -57.012096 , -50.690105 , -50.690105 ,\n",
       "       -50.690105 , -50.690105 , -50.690105 , -50.690105 , -50.690105 ,\n",
       "       -50.690105 , -43.533653 , -43.533653 , -43.533653 , -43.533653 ,\n",
       "       -43.533653 , -43.533653 , -43.533653 , -43.533653 , -35.512856 ,\n",
       "       -35.512856 , -35.512856 , -35.512856 , -35.512856 , -35.512856 ,\n",
       "       -35.512856 , -35.512856 , -26.658613 , -26.658613 , -26.658613 ,\n",
       "       -26.658613 , -26.658613 , -26.658613 , -26.658613 , -17.074287 ,\n",
       "       -17.074287 , -17.074287 , -17.074287 , -17.074287 ,  -6.9436836,\n",
       "        -6.9436836,  -6.9436836,  -6.9436836,  -6.9436836,   3.4684877,\n",
       "         3.4684877,   3.4684877,   3.4684877,   3.4684877,  13.728166 ,\n",
       "        13.728166 ,  23.51997  ,  23.51997  ,  32.634415 ,  32.634415 ,\n",
       "        40.941288 ,  40.941288 ,  40.941288 ,  40.941288 ,  40.941288 ,\n",
       "        48.387123 ,  48.387123 ,  48.387123 ,  54.97932  ,  54.97932  ,\n",
       "        54.97932  ,  60.577198 ,  60.886032 ,  61.133186 ,  65.28349  ,\n",
       "        66.123726 ,  66.75619  ,  66.982475 ,  70.53659  ,  71.647964 ,\n",
       "        72.03908  ,  72.03908  , -62.56236  , -62.56236  , -62.56236  ,\n",
       "...\n",
       "       -67.25439  , -71.06434  ,  32.634415 ,  23.51997  ,  23.51997  ,\n",
       "        32.634415 ,  23.51997  ,  71.647964 ,  40.941288 ,  32.634415 ,\n",
       "        23.51997  ,  66.123726 ,  60.886032 ,  54.97932  ,  48.387123 ,\n",
       "        40.941288 ,  32.634415 ,  23.51997  ,  60.577198 ,  54.97932  ,\n",
       "        48.387123 ,  40.941288 ,  32.634415 ,  23.51997  ,  13.728166 ,\n",
       "         3.4684877,  -6.9436836, -17.074287 , -26.658613 , -35.512856 ,\n",
       "       -43.533653 , -50.690105 ,  13.728166 ,   3.4684877,  -6.9436836,\n",
       "       -17.074287 , -26.658613 , -35.512856 , -43.533653 , -50.690105 ,\n",
       "        13.728166 ,   3.4684877,  -6.9436836, -17.074287 , -26.658613 ,\n",
       "       -35.512856 , -43.533653 , -50.690105 ,  13.728166 ,   3.4684877,\n",
       "        -6.9436836, -17.074287 , -26.658613 , -35.512856 , -43.533653 ,\n",
       "       -50.690105 , -17.074287 , -26.658613 , -35.512856 , -43.533653 ,\n",
       "       -50.690105 ,  13.728166 , -35.512856 , -43.533653 , -50.690105 ,\n",
       "        13.728166 , -26.658613 , -35.512856 , -43.533653 , -50.690105 ,\n",
       "       -57.012096 , -62.56236  , -67.25439  , -71.02229  , -57.012096 ,\n",
       "       -62.56236  , -67.25439  , -71.02148  , -57.012096 , -62.56236  ,\n",
       "       -67.25439  , -57.012096 , -62.56236  , -67.25439  , -57.012096 ,\n",
       "       -62.56236  , -67.25439  , -57.012096 , -62.56236  , -57.012096 ,\n",
       "       -62.56236  , -67.25439  , -71.481636 , -57.012096 , -62.56236  ,\n",
       "       -67.25439  , -71.57572  ], dtype=float32)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>lat_min</span></div><div class='xr-var-dims'>(region)</div><div class='xr-var-dtype'>float32</div><div class='xr-var-preview xr-preview'>-76.33 -71.65 ... -71.63 -76.23</div><input id='attrs-d1a5caa6-7244-4c86-8af3-add3ec609e1a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-d1a5caa6-7244-4c86-8af3-add3ec609e1a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-197c2c96-8a65-4303-b4d6-a6b179cb69ed' class='xr-var-data-in' type='checkbox'><label for='data-197c2c96-8a65-4303-b4d6-a6b179cb69ed' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([-76.32588  , -71.65445  , -71.65492  , -71.64105  , -71.58997  ,\n",
       "       -71.50537  , -71.395    , -67.24637  , -67.24637  , -67.24637  ,\n",
       "       -67.24637  , -67.24637  , -67.24637  , -67.24637  , -67.24637  ,\n",
       "       -62.55294  , -62.55294  , -62.55294  , -62.55294  , -62.55294  ,\n",
       "       -62.55294  , -62.55294  , -62.55294  , -57.001026 , -57.001026 ,\n",
       "       -57.001026 , -57.001026 , -57.001026 , -57.001026 , -57.001026 ,\n",
       "       -57.001026 , -50.677643 , -50.677643 , -50.677643 , -50.677643 ,\n",
       "       -50.677643 , -50.677643 , -50.677643 , -50.677643 , -43.5196   ,\n",
       "       -43.5196   , -43.5196   , -43.5196   , -43.5196   , -43.5196   ,\n",
       "       -43.5196   , -43.5196   , -35.497208 , -35.497208 , -35.497208 ,\n",
       "       -35.497208 , -35.497208 , -35.497208 , -35.497208 , -26.641497 ,\n",
       "       -26.641497 , -26.641497 , -26.641497 , -26.641497 , -17.055962 ,\n",
       "       -17.055962 , -17.055962 , -17.055962 , -17.055962 ,  -6.924565 ,\n",
       "        -6.924565 ,  -6.924565 ,  -6.924565 ,  -6.924565 ,   3.4877594,\n",
       "         3.4877594,  13.746807 ,  13.746807 ,  23.537529 ,  23.537529 ,\n",
       "        32.650574 ,  32.650574 ,  32.650574 ,  32.650574 ,  32.650574 ,\n",
       "        40.95588  ,  40.95588  ,  40.95588  ,  48.400112 ,  48.400112 ,\n",
       "        48.400112 ,  54.99076  ,  54.99076  ,  54.99076  ,  60.42966  ,\n",
       "        60.587257 ,  60.896996 ,  61.14459  ,  65.29275  ,  66.13415  ,\n",
       "        66.766754 ,  66.766754 , -67.24637  , -67.24637  , -67.24637  ,\n",
       "...\n",
       "       -71.15109  , -74.49193  ,  23.537529 ,  13.746807 ,  13.746807 ,\n",
       "        23.537529 ,  13.746807 ,  66.13415  ,  32.650574 ,  23.537529 ,\n",
       "        13.746807 ,  60.587257 ,  54.99076  ,  48.400112 ,  40.95588  ,\n",
       "        32.650574 ,  23.537529 ,  13.746807 ,  54.99076  ,  48.400112 ,\n",
       "        40.95588  ,  32.650574 ,  23.537529 ,  13.746807 ,   3.4877594,\n",
       "        -6.924565 , -17.055962 , -26.641497 , -35.497208 , -43.5196   ,\n",
       "       -50.677643 , -57.001026 ,   3.4877594,  -6.924565 , -17.055962 ,\n",
       "       -26.641497 , -35.497208 , -43.5196   , -50.677643 , -57.001026 ,\n",
       "         3.4877594,  -6.924565 , -17.055962 , -26.641497 , -35.497208 ,\n",
       "       -43.5196   , -50.677643 , -57.001026 ,   3.4877594,  -6.924565 ,\n",
       "       -17.055962 , -26.641497 , -35.497208 , -43.5196   , -50.677643 ,\n",
       "       -57.001026 , -26.641497 , -35.497208 , -43.5196   , -50.677643 ,\n",
       "       -57.001026 ,   3.4877594, -43.5196   , -50.677643 , -57.001026 ,\n",
       "         3.4877594, -35.497208 , -43.5196   , -50.677643 , -57.001026 ,\n",
       "       -62.55294  , -67.24637  , -71.05833  , -74.14847  , -62.55294  ,\n",
       "       -67.24637  , -71.038925 , -74.076355 , -62.55294  , -67.24637  ,\n",
       "       -71.11813  , -62.55294  , -67.24637  , -71.232285 , -62.55294  ,\n",
       "       -67.24637  , -71.35718  , -62.55294  , -67.24637  , -62.55294  ,\n",
       "       -67.24637  , -71.566956 , -76.00968  , -62.55294  , -67.24637  ,\n",
       "       -71.62907  , -76.23423  ], dtype=float32)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>lon_max</span></div><div class='xr-var-dims'>(region)</div><div class='xr-var-dtype'>float32</div><div class='xr-var-preview xr-preview'>-26.76 -26.76 ... -38.01 -38.04</div><input id='attrs-f6447c48-5797-4f9e-86fa-838c0b8d6bcd' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-f6447c48-5797-4f9e-86fa-838c0b8d6bcd' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-8542c8d8-99e7-46c7-b362-cbaab8b04913' class='xr-var-data-in' type='checkbox'><label for='data-8542c8d8-99e7-46c7-b362-cbaab8b04913' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([ -26.764791 ,  -26.760416 ,  -15.487511 ,   -4.213777 ,\n",
       "          7.052837 ,   18.309807 ,   29.556084 ,  -26.760416 ,\n",
       "        -15.510417 ,   -4.2604165,    6.9895835,   18.239584 ,\n",
       "         29.489584 ,   40.739582 ,   51.989582 ,  -26.760416 ,\n",
       "        -15.510417 ,   -4.2604165,    6.9895835,   18.239584 ,\n",
       "         29.489584 ,   40.739582 ,   51.989582 ,  -26.760416 ,\n",
       "        -15.510417 ,   -4.2604165,    6.9895835,   18.239584 ,\n",
       "         29.489584 ,   40.739582 ,   51.989582 ,  -26.760416 ,\n",
       "        -15.510417 ,   -4.2604165,    6.9895835,   18.239584 ,\n",
       "         29.489584 ,   40.739582 ,   51.989582 ,  -26.760416 ,\n",
       "        -15.510417 ,   -4.2604165,    6.9895835,   18.239584 ,\n",
       "         29.489584 ,   40.739582 ,   51.989582 ,  -26.760416 ,\n",
       "        -15.510417 ,   -4.2604165,    6.9895835,   18.239584 ,\n",
       "         40.739582 ,   51.989582 ,  -26.760416 ,  -15.510417 ,\n",
       "         -4.2604165,    6.9895835,   51.989582 ,  -26.760416 ,\n",
       "        -15.510417 ,   -4.2604165,    6.9895835,   51.989582 ,\n",
       "        -26.760416 ,  -15.510417 ,   -4.2604165,    6.9895835,\n",
       "         51.989582 ,  -26.760416 ,  -15.510417 ,  -26.760416 ,\n",
       "        -15.510417 ,  -26.760416 ,  -15.510417 ,  -26.760416 ,\n",
       "        -15.510417 ,   -4.2604165,   18.239584 ,   29.489584 ,\n",
       "...\n",
       "        -38.010418 ,  -38.010418 ,  -38.010418 ,  -38.010418 ,\n",
       "       -116.760414 , -116.760414 , -116.760414 , -116.760414 ,\n",
       "       -116.760414 , -116.760414 , -116.760414 , -116.760414 ,\n",
       "       -105.510414 , -105.510414 , -105.510414 , -105.510414 ,\n",
       "       -105.510414 , -105.510414 , -105.510414 , -105.510414 ,\n",
       "        -94.260414 ,  -94.260414 ,  -94.260414 ,  -94.260414 ,\n",
       "        -94.260414 ,  -94.260414 ,  -94.260414 ,  -94.260414 ,\n",
       "        -83.010414 ,  -83.010414 ,  -83.010414 ,  -83.010414 ,\n",
       "        -83.010414 ,  -83.010414 ,  -83.010414 ,  -83.010414 ,\n",
       "        -71.760414 ,  -71.760414 ,  -71.760414 ,  -71.760414 ,\n",
       "        -71.760414 ,  -49.260418 ,  -49.260418 ,  -49.260418 ,\n",
       "        -49.260418 ,  -38.010418 ,  -38.010418 ,  -38.010418 ,\n",
       "        -38.010418 ,  -38.010418 , -116.760414 , -116.760414 ,\n",
       "       -116.7561   , -116.67918  , -105.510414 , -105.510414 ,\n",
       "       -105.510414 , -105.53353  ,  -94.260414 ,  -94.260414 ,\n",
       "        -94.260414 ,  -83.010414 ,  -83.010414 ,  -83.010414 ,\n",
       "        -71.760414 ,  -71.760414 ,  -71.760414 ,  -60.510418 ,\n",
       "        -60.510418 ,  -49.260418 ,  -49.260418 ,  -49.260418 ,\n",
       "        -49.313774 ,  -38.010418 ,  -38.010418 ,  -38.010418 ,\n",
       "        -38.041668 ], dtype=float32)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>lon_min</span></div><div class='xr-var-dims'>(region)</div><div class='xr-var-dtype'>float32</div><div class='xr-var-preview xr-preview'>-38.6 -38.02 ... -49.29 -50.27</div><input id='attrs-611709bf-ad25-470d-ab12-913a4496d880' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-611709bf-ad25-470d-ab12-913a4496d880' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-f91db873-6af3-4fe8-8bbd-26d128323c39' class='xr-var-data-in' type='checkbox'><label for='data-f91db873-6af3-4fe8-8bbd-26d128323c39' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([ -38.5956   ,  -38.020435 ,  -26.743858 ,  -15.489583 ,\n",
       "         -4.2395835,    7.0104165,   18.260416 ,  -37.989582 ,\n",
       "        -26.739584 ,  -15.489583 ,   -4.2395835,    7.0104165,\n",
       "         18.260416 ,   29.510416 ,   40.760418 ,  -37.989582 ,\n",
       "        -26.739584 ,  -15.489583 ,   -4.2395835,    7.0104165,\n",
       "         18.260416 ,   29.510416 ,   40.760418 ,  -37.989582 ,\n",
       "        -26.739584 ,  -15.489583 ,   -4.2395835,    7.0104165,\n",
       "         18.260416 ,   29.510416 ,   40.760418 ,  -37.989582 ,\n",
       "        -26.739584 ,  -15.489583 ,   -4.2395835,    7.0104165,\n",
       "         18.260416 ,   29.510416 ,   40.760418 ,  -37.989582 ,\n",
       "        -26.739584 ,  -15.489583 ,   -4.2395835,    7.0104165,\n",
       "         18.260416 ,   29.510416 ,   40.760418 ,  -37.989582 ,\n",
       "        -26.739584 ,  -15.489583 ,   -4.2395835,    7.0104165,\n",
       "         29.510416 ,   40.760418 ,  -37.989582 ,  -26.739584 ,\n",
       "        -15.489583 ,   -4.2395835,   40.760418 ,  -37.989582 ,\n",
       "        -26.739584 ,  -15.489583 ,   -4.2395835,   40.760418 ,\n",
       "        -37.989582 ,  -26.739584 ,  -15.489583 ,   -4.2395835,\n",
       "         40.760418 ,  -37.989582 ,  -26.739584 ,  -37.989582 ,\n",
       "        -26.739584 ,  -37.989582 ,  -26.739584 ,  -37.989582 ,\n",
       "        -26.739584 ,  -15.489583 ,    7.0104165,   18.260416 ,\n",
       "...\n",
       "        -49.239582 ,  -49.239582 ,  -49.239582 ,  -49.239582 ,\n",
       "       -127.989586 , -127.989586 , -127.989586 , -127.989586 ,\n",
       "       -127.989586 , -127.989586 , -127.989586 , -127.989586 ,\n",
       "       -116.739586 , -116.739586 , -116.739586 , -116.739586 ,\n",
       "       -116.739586 , -116.739586 , -116.739586 , -116.739586 ,\n",
       "       -105.489586 , -105.489586 , -105.489586 , -105.489586 ,\n",
       "       -105.489586 , -105.489586 , -105.489586 , -105.489586 ,\n",
       "        -94.239586 ,  -94.239586 ,  -94.239586 ,  -94.239586 ,\n",
       "        -94.239586 ,  -94.239586 ,  -94.239586 ,  -94.239586 ,\n",
       "        -82.989586 ,  -82.989586 ,  -82.989586 ,  -82.989586 ,\n",
       "        -82.989586 ,  -60.489582 ,  -60.489582 ,  -60.489582 ,\n",
       "        -60.489582 ,  -49.239582 ,  -49.239582 ,  -49.239582 ,\n",
       "        -49.239582 ,  -49.239582 , -127.989586 , -127.989586 ,\n",
       "       -127.989586 , -127.95845  , -116.739586 , -116.739586 ,\n",
       "       -116.739586 , -116.73527  , -105.489586 , -105.489586 ,\n",
       "       -105.51248  ,  -94.239586 ,  -94.239586 ,  -94.28618  ,\n",
       "        -82.989586 ,  -82.989586 ,  -83.05279  ,  -71.739586 ,\n",
       "        -71.739586 ,  -60.489582 ,  -60.489582 ,  -60.556118 ,\n",
       "        -61.779488 ,  -49.239582 ,  -49.239582 ,  -49.292297 ,\n",
       "        -50.26946  ], dtype=float32)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>area_fraction</span></div><div class='xr-var-dims'>(region)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.9951 1.0 1.0 ... 1.0 1.0 1.0</div><input id='attrs-e49d3d72-b144-4c4c-8633-f0535cbf4f53' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-e49d3d72-b144-4c4c-8633-f0535cbf4f53' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-87d3675c-0928-488f-9a5a-df579716c0c3' class='xr-var-data-in' type='checkbox'><label for='data-87d3675c-0928-488f-9a5a-df579716c0c3' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0.99506516, 1.        , 1.        , 0.92840878, 0.76042867,\n",
       "       0.66086077, 0.74379287, 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        , 0.94803498,\n",
       "       0.9998251 , 0.99915295, 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 0.9834808 , 1.        ,\n",
       "       1.        , 0.99978052, 1.        , 1.        , 1.        ,\n",
       "       0.9994856 , 1.        , 1.        , 1.        , 0.99999657,\n",
       "       1.        , 1.        , 0.99920096, 0.99717764, 1.        ,\n",
       "       1.        , 0.99972222, 0.99960905, 1.        , 0.99999314,\n",
       "       1.        , 1.        , 1.        , 1.        , 0.99997257,\n",
       "       1.        , 0.90623457, 0.89062757, 0.99995199, 0.99505487,\n",
       "       1.        , 1.        , 1.        , 0.61056584, 0.89089506,\n",
       "       1.        , 0.9997668 , 0.99998628, 0.83075446, 0.93757888,\n",
       "       1.        , 1.        , 0.99912551, 0.84729424, 1.        ,\n",
       "       0.94006859, 1.        , 0.85918038, 1.        , 0.97893347,\n",
       "       0.99662551, 0.99716392, 0.66421811, 0.61971879, 0.66055898,\n",
       "       1.        , 1.        , 0.8336214 , 1.        , 1.        ,\n",
       "       0.60821674, 1.        , 1.        , 0.78292181, 1.        ,\n",
       "       0.69730796, 0.88197188, 0.94665638, 0.7641118 , 0.98415981,\n",
       "       1.        , 0.75385117, 0.85815501, 0.99818587, 0.97239026,\n",
       "...\n",
       "       1.        , 0.98992112, 0.99686214, 1.        , 0.97625514,\n",
       "       0.69040809, 0.76503772, 0.67210562, 0.96623457, 0.99962277,\n",
       "       0.92959534, 0.75233882, 0.97776063, 0.60229424, 0.66328532,\n",
       "       1.        , 1.        , 1.        , 0.95354252, 1.        ,\n",
       "       0.98033951, 1.        , 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        , 0.99998285,\n",
       "       1.        , 1.        , 0.99999314, 1.        , 1.        ,\n",
       "       1.        , 0.99980796, 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 0.99993141, 1.        ,\n",
       "       0.99977023, 1.        , 1.        , 0.83404321, 0.99159465,\n",
       "       1.        , 0.99974966, 1.        , 1.        , 0.99997942,\n",
       "       1.        , 0.99965706, 0.99068587, 0.82405007, 0.68582647,\n",
       "       0.83228395, 0.64829218, 0.65686214, 1.        , 0.91934499,\n",
       "       0.99994856, 0.96722565, 1.        , 1.        , 0.99269204,\n",
       "       1.        , 1.        , 1.        , 0.84475309, 1.        ,\n",
       "       1.        , 1.        , 0.97154664, 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 0.99859053, 1.        ,\n",
       "       1.        , 0.81949931, 0.99832647, 0.68215364, 0.98057956,\n",
       "       0.9004904 , 0.98864198, 0.8939369 , 0.99430384, 1.        ,\n",
       "       1.        , 1.        ])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>f_coriolis</span></div><div class='xr-var-dims'>(region)</div><div class='xr-var-dtype'>float32</div><div class='xr-var-preview xr-preview'>-0.0001402 ... -0.0001401</div><input id='attrs-ae22cdeb-a8df-4efe-bf9f-3664f86ec502' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-ae22cdeb-a8df-4efe-bf9f-3664f86ec502' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-78e41ffc-3e37-4b10-8431-4168a5e98216' class='xr-var-data-in' type='checkbox'><label for='data-78e41ffc-3e37-4b10-8431-4168a5e98216' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([-1.4016188e-04, -1.3646185e-04, -1.3646270e-04, -1.3645814e-04,\n",
       "       -1.3644857e-04, -1.3643476e-04, -1.3641809e-04, -1.3210521e-04,\n",
       "       -1.3210521e-04, -1.3210521e-04, -1.3210521e-04, -1.3210521e-04,\n",
       "       -1.3210521e-04, -1.3210521e-04, -1.3210521e-04, -1.2607624e-04,\n",
       "       -1.2607624e-04, -1.2607624e-04, -1.2607624e-04, -1.2607624e-04,\n",
       "       -1.2607624e-04, -1.2607624e-04, -1.2607624e-04, -1.1779487e-04,\n",
       "       -1.1779487e-04, -1.1779487e-04, -1.1779487e-04, -1.1779487e-04,\n",
       "       -1.1779487e-04, -1.1779487e-04, -1.1779487e-04, -1.0689933e-04,\n",
       "       -1.0689933e-04, -1.0689933e-04, -1.0689933e-04, -1.0689933e-04,\n",
       "       -1.0689933e-04, -1.0689933e-04, -1.0689933e-04, -9.2862865e-05,\n",
       "       -9.2862865e-05, -9.2862865e-05, -9.2862865e-05, -9.2862865e-05,\n",
       "       -9.2862865e-05, -9.2862865e-05, -9.2862865e-05, -7.5352888e-05,\n",
       "       -7.5352888e-05, -7.5352888e-05, -7.5352888e-05, -7.5352888e-05,\n",
       "       -7.5352888e-05, -7.5352888e-05, -5.4362139e-05, -5.4362139e-05,\n",
       "       -5.4362139e-05, -5.4362139e-05, -5.4362139e-05, -3.0370917e-05,\n",
       "       -3.0370917e-05, -3.0370917e-05, -3.0370917e-05, -3.0370917e-05,\n",
       "       -4.4124590e-06, -4.4124590e-06, -4.4124590e-06, -4.4124590e-06,\n",
       "       -4.4124590e-06,  2.1870484e-05,  2.1870484e-05,  4.6658643e-05,\n",
       "        4.6658643e-05,  6.8730245e-05,  6.8730245e-05,  8.7420958e-05,\n",
       "        8.7420958e-05,  8.7420958e-05,  8.7420958e-05,  8.7420958e-05,\n",
       "...\n",
       "        1.0259064e-04,  8.7420420e-05,  6.8730333e-05,  4.6658890e-05,\n",
       "        2.1870324e-05, -4.4124886e-06, -3.0370986e-05, -5.4362528e-05,\n",
       "       -7.5353179e-05, -9.2863098e-05, -1.0689965e-04, -1.1779563e-04,\n",
       "        2.1870324e-05, -4.4124886e-06, -3.0370986e-05, -5.4362528e-05,\n",
       "       -7.5353179e-05, -9.2863098e-05, -1.0689965e-04, -1.1779563e-04,\n",
       "        2.1870324e-05, -4.4124886e-06, -3.0370986e-05, -5.4362528e-05,\n",
       "       -7.5353179e-05, -9.2863098e-05, -1.0689965e-04, -1.1779563e-04,\n",
       "        2.1870324e-05, -4.4124886e-06, -3.0370986e-05, -5.4362528e-05,\n",
       "       -7.5353179e-05, -9.2863098e-05, -1.0689965e-04, -1.1779563e-04,\n",
       "       -5.4362528e-05, -7.5353179e-05, -9.2863098e-05, -1.0689965e-04,\n",
       "       -1.1779563e-04,  2.1870324e-05, -9.2863098e-05, -1.0689965e-04,\n",
       "       -1.1779563e-04,  2.1870324e-05, -7.5353179e-05, -9.2863098e-05,\n",
       "       -1.0689965e-04, -1.1779563e-04, -1.2607590e-04, -1.3210571e-04,\n",
       "       -1.3637617e-04, -1.3912356e-04, -1.2607590e-04, -1.3210571e-04,\n",
       "       -1.3637420e-04, -1.3910558e-04, -1.2607590e-04, -1.3210571e-04,\n",
       "       -1.3638147e-04, -1.2607590e-04, -1.3210571e-04, -1.3639574e-04,\n",
       "       -1.2607590e-04, -1.3210571e-04, -1.3641219e-04, -1.2607590e-04,\n",
       "       -1.3210571e-04, -1.2607590e-04, -1.3210571e-04, -1.3644464e-04,\n",
       "       -1.3996403e-04, -1.2607590e-04, -1.3210571e-04, -1.3645587e-04,\n",
       "       -1.4009124e-04], dtype=float32)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>i_min</span></div><div class='xr-var-dims'>(region)</div><div class='xr-var-dtype'>int16</div><div class='xr-var-preview xr-preview'>0 0 540 1080 ... 0 540 1080 1620</div><input id='attrs-9f38ff07-e9c7-4d7a-8923-c6f7152ce7ce' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-9f38ff07-e9c7-4d7a-8923-c6f7152ce7ce' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-6aaf0d5a-c912-4e61-89f8-c521c7e56c0f' class='xr-var-data-in' type='checkbox'><label for='data-6aaf0d5a-c912-4e61-89f8-c521c7e56c0f' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([   0,    0,  540, 1080, 1620, 2160, 2700,    0,  540, 1080, 1620,\n",
       "       2160, 2700, 3240, 3780,    0,  540, 1080, 1620, 2160, 2700, 3240,\n",
       "       3780,    0,  540, 1080, 1620, 2160, 2700, 3240, 3780,    0,  540,\n",
       "       1080, 1620, 2160, 2700, 3240, 3780,    0,  540, 1080, 1620, 2160,\n",
       "       2700, 3240, 3780,    0,  540, 1080, 1620, 2160, 3240, 3780,    0,\n",
       "        540, 1080, 1620, 3780,    0,  540, 1080, 1620, 3780,    0,  540,\n",
       "       1080, 1620, 3780,    0,  540,    0,  540,    0,  540,    0,  540,\n",
       "       1080, 2160, 2700,    0,  540, 1080,    0,  540, 1080,    0,  540,\n",
       "       1080,    0,  540, 1080, 1620,  540, 1080, 1620, 2160,    0,  540,\n",
       "       1080, 1620, 2160, 2700, 3240, 3780,    0,  540, 1080, 1620, 2160,\n",
       "       2700, 3240, 3780,    0,  540, 1080, 1620, 2160, 2700, 3240, 3780,\n",
       "          0,  540, 1080, 1620, 2160, 2700, 3240, 3780,    0,  540, 1080,\n",
       "       1620, 2160, 2700, 3240, 3780,    0,  540, 1080, 1620, 2160,    0,\n",
       "        540, 1080, 1620, 2160, 2700,    0,  540, 1080, 1620, 2160, 2700,\n",
       "          0,  540, 1080, 1620, 3240,    0,  540, 1080, 1620, 2700, 3240,\n",
       "       3780,    0,  540, 2700, 3240, 3780, 3780, 3780,    0,  540, 1080,\n",
       "       2160,    0,  540, 1080, 1620, 2160, 2700,    0, 1080, 1620, 2160,\n",
       "       2700, 3240,    0,  540, 1080, 1620, 2160, 2700, 3240, 3780,    0,\n",
       "       1620, 2160, 2700, 3240, 3780, 2700, 3240, 3780, 1080, 1620, 1080,\n",
       "       1620, 2160, 2700, 3240, 3780, 1620, 2160, 2700, 3240, 3780, 1080,\n",
       "       1620, 2160, 2700, 3240, 3780, 1080, 1620, 2160, 2700, 3240, 3780,\n",
       "       1620, 2160, 2700, 3240, 3780, 1620, 2160, 2700, 3240, 3780, 1080,\n",
       "       1620, 2160, 2700, 3240, 3780, 1620, 2160, 2700, 3240, 3780,    0,\n",
       "        540, 1080, 3240, 3780,    0,  540, 1080, 1620, 2160, 2700, 3240,\n",
       "       3780,    0,  540, 1080, 1620, 2160, 2700, 3240, 3780,    0,  540,\n",
       "       1080, 1620, 2160, 2700, 3240, 3780,    0,  540, 1080, 1620, 2160,\n",
       "       2700, 3240, 3780,    0,  540, 1080, 1620, 2160, 2700, 3240, 3780,\n",
       "          0,  540, 1080, 1620, 2160, 2700, 3240, 3780,    0,  540, 1080,\n",
       "       1620, 2160, 2700, 3240, 3780,    0,  540,    0,  540,    0,  540,\n",
       "       1080, 1620,    0,  540, 1080, 1620,    0,  540, 1080, 1620, 2160,\n",
       "          0,  540, 1080, 1620,    0,  540, 1080, 1620,    0,  540, 1080,\n",
       "       1620, 3240, 3780, 3780, 3240, 3780,    0, 2700, 3240, 3780,  540,\n",
       "       1080, 1620, 2160, 2700, 3240, 3780, 1080, 1620, 2160, 2700, 3240,\n",
       "       3780,    0,  540, 1080, 1620, 2160, 2700, 3240, 3780,    0,  540,\n",
       "       1080, 1620, 2160, 2700, 3240, 3780,    0,  540, 1080, 1620, 2160,\n",
       "       2700, 3240, 3780,    0,  540, 1080, 1620, 2160, 2700, 3240, 3780,\n",
       "       1620, 2160, 2700, 3240, 3780,    0, 2700, 3240, 3780,    0, 2160,\n",
       "       2700, 3240, 3780,    0,  540, 1080, 1620,    0,  540, 1080, 1620,\n",
       "          0,  540, 1080,    0,  540, 1080,    0,  540, 1080,    0,  540,\n",
       "          0,  540, 1080, 1620,    0,  540, 1080, 1620], dtype=int16)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>i_max</span></div><div class='xr-var-dims'>(region)</div><div class='xr-var-dtype'>int16</div><div class='xr-var-preview xr-preview'>540 540 1080 ... 1080 1620 2160</div><input id='attrs-349461cf-2fc2-4ab8-bc68-86f711b561cd' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-349461cf-2fc2-4ab8-bc68-86f711b561cd' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-5d04c54a-4e25-4008-b975-6c72d484344e' class='xr-var-data-in' type='checkbox'><label for='data-5d04c54a-4e25-4008-b975-6c72d484344e' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([ 540,  540, 1080, 1620, 2160, 2700, 3240,  540, 1080, 1620, 2160,\n",
       "       2700, 3240, 3780, 4320,  540, 1080, 1620, 2160, 2700, 3240, 3780,\n",
       "       4320,  540, 1080, 1620, 2160, 2700, 3240, 3780, 4320,  540, 1080,\n",
       "       1620, 2160, 2700, 3240, 3780, 4320,  540, 1080, 1620, 2160, 2700,\n",
       "       3240, 3780, 4320,  540, 1080, 1620, 2160, 2700, 3780, 4320,  540,\n",
       "       1080, 1620, 2160, 4320,  540, 1080, 1620, 2160, 4320,  540, 1080,\n",
       "       1620, 2160, 4320,  540, 1080,  540, 1080,  540, 1080,  540, 1080,\n",
       "       1620, 2700, 3240,  540, 1080, 1620,  540, 1080, 1620,  540, 1080,\n",
       "       1620,  540, 1080, 1620, 2160, 1080, 1620, 2160, 2700,  540, 1080,\n",
       "       1620, 2160, 2700, 3240, 3780, 4320,  540, 1080, 1620, 2160, 2700,\n",
       "       3240, 3780, 4320,  540, 1080, 1620, 2160, 2700, 3240, 3780, 4320,\n",
       "        540, 1080, 1620, 2160, 2700, 3240, 3780, 4320,  540, 1080, 1620,\n",
       "       2160, 2700, 3240, 3780, 4320,  540, 1080, 1620, 2160, 2700,  540,\n",
       "       1080, 1620, 2160, 2700, 3240,  540, 1080, 1620, 2160, 2700, 3240,\n",
       "        540, 1080, 1620, 2160, 3780,  540, 1080, 1620, 2160, 3240, 3780,\n",
       "       4320,  540, 1080, 3240, 3780, 4320, 4320, 4320,  540, 1080, 1620,\n",
       "       2700,  540, 1080, 1620, 2160, 2700, 3240,  540, 1620, 2160, 2700,\n",
       "       3240, 3780,  540, 1080, 1620, 2160, 2700, 3240, 3780, 4320,  540,\n",
       "       2160, 2700, 3240, 3780, 4320, 3240, 3780, 4320, 1620, 2160, 1620,\n",
       "       2160, 2700, 3240, 3780, 4320, 2160, 2700, 3240, 3780, 4320, 1620,\n",
       "       2160, 2700, 3240, 3780, 4320, 1620, 2160, 2700, 3240, 3780, 4320,\n",
       "       2160, 2700, 3240, 3780, 4320, 2160, 2700, 3240, 3780, 4320, 1620,\n",
       "       2160, 2700, 3240, 3780, 4320, 2160, 2700, 3240, 3780, 4320,  540,\n",
       "       1080, 1620, 3780, 4320,  540, 1080, 1620, 2160, 2700, 3240, 3780,\n",
       "       4320,  540, 1080, 1620, 2160, 2700, 3240, 3780, 4320,  540, 1080,\n",
       "       1620, 2160, 2700, 3240, 3780, 4320,  540, 1080, 1620, 2160, 2700,\n",
       "       3240, 3780, 4320,  540, 1080, 1620, 2160, 2700, 3240, 3780, 4320,\n",
       "        540, 1080, 1620, 2160, 2700, 3240, 3780, 4320,  540, 1080, 1620,\n",
       "       2160, 2700, 3240, 3780, 4320,  540, 1080,  540, 1080,  540, 1080,\n",
       "       1620, 2160,  540, 1080, 1620, 2160,  540, 1080, 1620, 2160, 2700,\n",
       "        540, 1080, 1620, 2160,  540, 1080, 1620, 2160,  540, 1080, 1620,\n",
       "       2160, 3780, 4320, 4320, 3780, 4320,  540, 3240, 3780, 4320, 1080,\n",
       "       1620, 2160, 2700, 3240, 3780, 4320, 1620, 2160, 2700, 3240, 3780,\n",
       "       4320,  540, 1080, 1620, 2160, 2700, 3240, 3780, 4320,  540, 1080,\n",
       "       1620, 2160, 2700, 3240, 3780, 4320,  540, 1080, 1620, 2160, 2700,\n",
       "       3240, 3780, 4320,  540, 1080, 1620, 2160, 2700, 3240, 3780, 4320,\n",
       "       2160, 2700, 3240, 3780, 4320,  540, 3240, 3780, 4320,  540, 2700,\n",
       "       3240, 3780, 4320,  540, 1080, 1620, 2160,  540, 1080, 1620, 2160,\n",
       "        540, 1080, 1620,  540, 1080, 1620,  540, 1080, 1620,  540, 1080,\n",
       "        540, 1080, 1620, 2160,  540, 1080, 1620, 2160], dtype=int16)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>j_min</span></div><div class='xr-var-dims'>(region)</div><div class='xr-var-dtype'>int16</div><div class='xr-var-preview xr-preview'>2160 2700 2700 ... 3780 3780 3780</div><input id='attrs-89352f9d-8ab6-4014-affe-035986903d76' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-89352f9d-8ab6-4014-affe-035986903d76' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-2b803b84-5526-4dcc-a64c-2591b3033385' class='xr-var-data-in' type='checkbox'><label for='data-2b803b84-5526-4dcc-a64c-2591b3033385' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([2160, 2700, 2700, 2700, 2700, 2700, 2700, 3240, 3240, 3240, 3240,\n",
       "       3240, 3240, 3240, 3240, 3780, 3780, 3780, 3780, 3780, 3780, 3780,\n",
       "       3780,    0,    0,    0,    0,    0,    0,    0,    0,  540,  540,\n",
       "        540,  540,  540,  540,  540,  540, 1080, 1080, 1080, 1080, 1080,\n",
       "       1080, 1080, 1080, 1620, 1620, 1620, 1620, 1620, 1620, 1620, 2160,\n",
       "       2160, 2160, 2160, 2160, 2700, 2700, 2700, 2700, 2700, 3240, 3240,\n",
       "       3240, 3240, 3240, 3780, 3780,    0,    0,  540,  540, 1080, 1080,\n",
       "       1080, 1080, 1080, 1620, 1620, 1620, 2160, 2160, 2160, 2700, 2700,\n",
       "       2700, 3240, 3240, 3240, 3240, 3780, 3780, 3780, 3780, 3240, 3240,\n",
       "       3240, 3240, 3240, 3240, 3240, 3240, 3780, 3780, 3780, 3780, 3780,\n",
       "       3780, 3780, 3780,    0,    0,    0,    0,    0,    0,    0,    0,\n",
       "        540,  540,  540,  540,  540,  540,  540,  540, 1080, 1080, 1080,\n",
       "       1080, 1080, 1080, 1080, 1080, 1620, 1620, 1620, 1620, 1620, 2160,\n",
       "       2160, 2160, 2160, 2160, 2160, 2700, 2700, 2700, 2700, 2700, 2700,\n",
       "       3240, 3240, 3240, 3240, 3240, 3780, 3780, 3780, 3780, 3780, 3780,\n",
       "       3780,    0,    0,    0,    0,    0,  540, 1080,  540,  540,  540,\n",
       "        540, 1080, 1080, 1080, 1080, 1080, 1080, 1620, 1620, 1620, 1620,\n",
       "       1620, 1620, 2160, 2160, 2160, 2160, 2160, 2160, 2160, 2160, 2700,\n",
       "       2700, 2700, 2700, 2700, 2700, 3240, 3240, 3240, 3780, 3780,    0,\n",
       "          0,    0,    0,    0,    0,  540,  540,  540,  540,  540, 1080,\n",
       "       1080, 1080, 1080, 1080, 1080, 1620, 1620, 1620, 1620, 1620, 1620,\n",
       "       2160, 2160, 2160, 2160, 2160, 2700, 2700, 2700, 2700, 2700, 3240,\n",
       "       3240, 3240, 3240, 3240, 3240, 3780, 3780, 3780, 3780, 3780,    0,\n",
       "          0,    0,    0,    0,  540,  540,  540,  540,  540,  540,  540,\n",
       "        540, 1080, 1080, 1080, 1080, 1080, 1080, 1080, 1080, 1620, 1620,\n",
       "       1620, 1620, 1620, 1620, 1620, 1620, 2160, 2160, 2160, 2160, 2160,\n",
       "       2160, 2160, 2160, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700,\n",
       "       3240, 3240, 3240, 3240, 3240, 3240, 3240, 3240, 3780, 3780, 3780,\n",
       "       3780, 3780, 3780, 3780, 3780,    0,    0,  540,  540, 1080, 1080,\n",
       "       1080, 1080, 1620, 1620, 1620, 1620, 2160, 2160, 2160, 2160, 2160,\n",
       "       2700, 2700, 2700, 2700, 3240, 3240, 3240, 3240, 3780, 3780, 3780,\n",
       "       3780,    0,    0,  540, 2160, 2160, 2700, 2700, 2700, 2700, 3240,\n",
       "       3240, 3240, 3240, 3240, 3240, 3240, 3780, 3780, 3780, 3780, 3780,\n",
       "       3780,    0,    0,    0,    0,    0,    0,    0,    0,  540,  540,\n",
       "        540,  540,  540,  540,  540,  540, 1080, 1080, 1080, 1080, 1080,\n",
       "       1080, 1080, 1080, 1620, 1620, 1620, 1620, 1620, 1620, 1620, 1620,\n",
       "       2160, 2160, 2160, 2160, 2160, 3240, 3240, 3240, 3240, 3780, 3780,\n",
       "       3780, 3780, 3780,    0,    0,    0,    0,  540,  540,  540,  540,\n",
       "       1080, 1080, 1080, 1620, 1620, 1620, 2160, 2160, 2160, 2700, 2700,\n",
       "       3240, 3240, 3240, 3240, 3780, 3780, 3780, 3780], dtype=int16)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>j_max</span></div><div class='xr-var-dims'>(region)</div><div class='xr-var-dtype'>int16</div><div class='xr-var-preview xr-preview'>2700 3240 3240 ... 4320 4320 4320</div><input id='attrs-278f95cf-61ef-4a44-8cf8-5f2901fdc58d' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-278f95cf-61ef-4a44-8cf8-5f2901fdc58d' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-c8d13fbf-f30c-44aa-8fff-999221f9f0bc' class='xr-var-data-in' type='checkbox'><label for='data-c8d13fbf-f30c-44aa-8fff-999221f9f0bc' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([2700, 3240, 3240, 3240, 3240, 3240, 3240, 3780, 3780, 3780, 3780,\n",
       "       3780, 3780, 3780, 3780, 4320, 4320, 4320, 4320, 4320, 4320, 4320,\n",
       "       4320,  540,  540,  540,  540,  540,  540,  540,  540, 1080, 1080,\n",
       "       1080, 1080, 1080, 1080, 1080, 1080, 1620, 1620, 1620, 1620, 1620,\n",
       "       1620, 1620, 1620, 2160, 2160, 2160, 2160, 2160, 2160, 2160, 2700,\n",
       "       2700, 2700, 2700, 2700, 3240, 3240, 3240, 3240, 3240, 3780, 3780,\n",
       "       3780, 3780, 3780, 4320, 4320,  540,  540, 1080, 1080, 1620, 1620,\n",
       "       1620, 1620, 1620, 2160, 2160, 2160, 2700, 2700, 2700, 3240, 3240,\n",
       "       3240, 3780, 3780, 3780, 3780, 4320, 4320, 4320, 4320, 3780, 3780,\n",
       "       3780, 3780, 3780, 3780, 3780, 3780, 4320, 4320, 4320, 4320, 4320,\n",
       "       4320, 4320, 4320,  540,  540,  540,  540,  540,  540,  540,  540,\n",
       "       1080, 1080, 1080, 1080, 1080, 1080, 1080, 1080, 1620, 1620, 1620,\n",
       "       1620, 1620, 1620, 1620, 1620, 2160, 2160, 2160, 2160, 2160, 2700,\n",
       "       2700, 2700, 2700, 2700, 2700, 3240, 3240, 3240, 3240, 3240, 3240,\n",
       "       3780, 3780, 3780, 3780, 3780, 4320, 4320, 4320, 4320, 4320, 4320,\n",
       "       4320,  540,  540,  540,  540,  540, 1080, 1620, 1080, 1080, 1080,\n",
       "       1080, 1620, 1620, 1620, 1620, 1620, 1620, 2160, 2160, 2160, 2160,\n",
       "       2160, 2160, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 3240,\n",
       "       3240, 3240, 3240, 3240, 3240, 3780, 3780, 3780, 4320, 4320,  540,\n",
       "        540,  540,  540,  540,  540, 1080, 1080, 1080, 1080, 1080, 1620,\n",
       "       1620, 1620, 1620, 1620, 1620, 2160, 2160, 2160, 2160, 2160, 2160,\n",
       "       2700, 2700, 2700, 2700, 2700, 3240, 3240, 3240, 3240, 3240, 3780,\n",
       "       3780, 3780, 3780, 3780, 3780, 4320, 4320, 4320, 4320, 4320,  540,\n",
       "        540,  540,  540,  540, 1080, 1080, 1080, 1080, 1080, 1080, 1080,\n",
       "       1080, 1620, 1620, 1620, 1620, 1620, 1620, 1620, 1620, 2160, 2160,\n",
       "       2160, 2160, 2160, 2160, 2160, 2160, 2700, 2700, 2700, 2700, 2700,\n",
       "       2700, 2700, 2700, 3240, 3240, 3240, 3240, 3240, 3240, 3240, 3240,\n",
       "       3780, 3780, 3780, 3780, 3780, 3780, 3780, 3780, 4320, 4320, 4320,\n",
       "       4320, 4320, 4320, 4320, 4320,  540,  540, 1080, 1080, 1620, 1620,\n",
       "       1620, 1620, 2160, 2160, 2160, 2160, 2700, 2700, 2700, 2700, 2700,\n",
       "       3240, 3240, 3240, 3240, 3780, 3780, 3780, 3780, 4320, 4320, 4320,\n",
       "       4320,  540,  540, 1080, 2700, 2700, 3240, 3240, 3240, 3240, 3780,\n",
       "       3780, 3780, 3780, 3780, 3780, 3780, 4320, 4320, 4320, 4320, 4320,\n",
       "       4320,  540,  540,  540,  540,  540,  540,  540,  540, 1080, 1080,\n",
       "       1080, 1080, 1080, 1080, 1080, 1080, 1620, 1620, 1620, 1620, 1620,\n",
       "       1620, 1620, 1620, 2160, 2160, 2160, 2160, 2160, 2160, 2160, 2160,\n",
       "       2700, 2700, 2700, 2700, 2700, 3780, 3780, 3780, 3780, 4320, 4320,\n",
       "       4320, 4320, 4320,  540,  540,  540,  540, 1080, 1080, 1080, 1080,\n",
       "       1620, 1620, 1620, 2160, 2160, 2160, 2700, 2700, 2700, 3240, 3240,\n",
       "       3780, 3780, 3780, 3780, 4320, 4320, 4320, 4320], dtype=int16)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-acf029f5-b076-4def-8b57-18817a1c2a7c' class='xr-section-summary-in' type='checkbox'  checked><label for='section-acf029f5-b076-4def-8b57-18817a1c2a7c' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>vort_strain_histogram</span></div><div class='xr-var-dims'>(time_coarse, region, strain, vort)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>dask.array&lt;chunksize=(1, 1, 99, 199), meta=np.ndarray&gt;</div><input id='attrs-0272381c-6840-40db-8cdd-22bdc3ccf36a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-0272381c-6840-40db-8cdd-22bdc3ccf36a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-baaa3c0e-9bfb-4e2c-976c-480a7dbd1152' class='xr-var-data-in' type='checkbox'><label for='data-baaa3c0e-9bfb-4e2c-976c-480a7dbd1152' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><table>\n",
       "    <tr>\n",
       "        <td>\n",
       "            <table>\n",
       "                <thead>\n",
       "                    <tr>\n",
       "                        <td> </td>\n",
       "                        <th> Array </th>\n",
       "                        <th> Chunk </th>\n",
       "                    </tr>\n",
       "                </thead>\n",
       "                <tbody>\n",
       "                    \n",
       "                    <tr>\n",
       "                        <th> Bytes </th>\n",
       "                        <td> 2.37 GiB </td>\n",
       "                        <td> 153.91 kiB </td>\n",
       "                    </tr>\n",
       "                    \n",
       "                    <tr>\n",
       "                        <th> Shape </th>\n",
       "                        <td> (37, 437, 99, 199) </td>\n",
       "                        <td> (1, 1, 99, 199) </td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                        <th> Count </th>\n",
       "                        <td> 16169 Tasks </td>\n",
       "                        <td> 16169 Chunks </td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                    <th> Type </th>\n",
       "                    <td> float64 </td>\n",
       "                    <td> numpy.ndarray </td>\n",
       "                    </tr>\n",
       "                </tbody>\n",
       "            </table>\n",
       "        </td>\n",
       "        <td>\n",
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       "</table></div></li></ul></div></li><li class='xr-section-item'><input id='section-6d7569f8-d857-4356-96b5-b1c6f82f2954' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-6d7569f8-d857-4356-96b5-b1c6f82f2954' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.Dataset>\n",
       "Dimensions:                (time_coarse: 37, region: 437, vort: 199, strain: 99)\n",
       "Coordinates: (12/14)\n",
       "  * time_coarse            (time_coarse) datetime64[ns] 2011-09-17T23:30:00 ....\n",
       "  * region                 (region) int64 32 40 41 42 43 ... 819 824 825 826 827\n",
       "  * vort                   (vort) float64 -6.965 -6.894 -6.824 ... 6.894 6.965\n",
       "  * strain                 (strain) float64 0.03535 0.1061 ... 6.894 6.965\n",
       "    lat_max                (region) float32 -71.64 -67.25 ... -67.25 -71.58\n",
       "    lat_min                (region) float32 -76.33 -71.65 ... -71.63 -76.23\n",
       "    ...                     ...\n",
       "    area_fraction          (region) float64 0.9951 1.0 1.0 ... 1.0 1.0 1.0\n",
       "    f_coriolis             (region) float32 -0.0001402 -0.0001365 ... -0.0001401\n",
       "    i_min                  (region) int16 0 0 540 1080 1620 ... 0 540 1080 1620\n",
       "    i_max                  (region) int16 540 540 1080 1620 ... 1080 1620 2160\n",
       "    j_min                  (region) int16 2160 2700 2700 2700 ... 3780 3780 3780\n",
       "    j_max                  (region) int16 2700 3240 3240 3240 ... 4320 4320 4320\n",
       "Data variables:\n",
       "    vort_strain_histogram  (time_coarse, region, strain, vort) float64 dask.array<chunksize=(1, 1, 99, 199), meta=np.ndarray>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import dask.array as dsa\n",
    "ds_target = xr.DataArray(\n",
    "    dsa.empty(\n",
    "        shape=(ntime, nregions, n_strain_bins-1, n_vort_bins-1),\n",
    "        chunks=(1, 1, n_strain_bins-1, n_vort_bins-1),\n",
    "        dtype=\"f8\"\n",
    "    ),\n",
    "    name=\"vort_strain_histogram\",\n",
    "    dims=['time_coarse', 'region', 'strain', 'vort'],\n",
    "    coords={\n",
    "        \"time_coarse\": time_coarse.values,\n",
    "        \"region\": regions_keep.index.values,\n",
    "        'vort': vort_bins,\n",
    "        'strain': strain_bins\n",
    "    }\n",
    ").to_dataset()\n",
    "\n",
    "ds_region = xr.Dataset(regions_keep.drop(columns=['i', 'j', 'face'])).rename({'dim_0': 'region'})\n",
    "ds_target = ds_target.assign_coords(coords=ds_region)\n",
    "ds_target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "cfb71dfa-563c-4ade-96db-7d4e77b14b72",
   "metadata": {},
   "outputs": [],
   "source": [
    "for c in ds_target.coords:\n",
    "    ds_target[c].encoding['chunks'] = ds_target[c].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a9ce9ecc-ad0c-4d7c-9d57-4cbc3940dfff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'gcs://pangeo-integration-te-3eea-prod-scratch-bucket/yangleir/llc4320/vort_strain_histogram.zarr'"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import os\n",
    "target_url = os.environ['SCRATCH_BUCKET'] + '/llc4320/vort_strain_histogram.zarr'\n",
    "target_url"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "1291b076-38c2-46b3-8851-f8b755b992ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Delayed('_finalize_store-a8150dbc-355c-4096-a994-4fa90af2b005')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ds_target.to_zarr(target_url, compute=False, mode='w')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "e7459462-1370-44d2-88bd-573fba891863",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7874c60b43794fcaa121172b01174d75",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Tree(nodes=(Node(disabled=True, name='/', nodes=(Node(disabled=True, icon='table', name='area_fraction (437,) …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import zarr\n",
    "zgroup = zarr.open_group(target_url)\n",
    "zgroup.tree()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "089896e6-b054-4673-a619-099757517413",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting git+https://github.com/xgcm/xgcm.git\n",
      "  Cloning https://github.com/xgcm/xgcm.git to /tmp/pip-req-build-t8zcg4no\n",
      "  Running command git clone --filter=blob:none --quiet https://github.com/xgcm/xgcm.git /tmp/pip-req-build-t8zcg4no\n",
      "  Resolved https://github.com/xgcm/xgcm.git to commit c66861d8ef3ad86acd1eaabff7c33033fbc53378\n",
      "  Running command git submodule update --init --recursive -q\n",
      "  Preparing metadata (setup.py) ... \u001b[?25ldone\n",
      "\u001b[?25hRequirement already satisfied: xarray>=0.20.0 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from xgcm==0.8.1.dev34+gc66861d) (2022.6.0)\n",
      "Requirement already satisfied: dask in /srv/conda/envs/notebook/lib/python3.9/site-packages (from xgcm==0.8.1.dev34+gc66861d) (2022.5.1)\n",
      "Requirement already satisfied: numpy in /srv/conda/envs/notebook/lib/python3.9/site-packages (from xgcm==0.8.1.dev34+gc66861d) (1.22.4)\n",
      "Requirement already satisfied: future in /srv/conda/envs/notebook/lib/python3.9/site-packages (from xgcm==0.8.1.dev34+gc66861d) (0.18.2)\n",
      "Requirement already satisfied: packaging>=20.0 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from xarray>=0.20.0->xgcm==0.8.1.dev34+gc66861d) (21.3)\n",
      "Requirement already satisfied: pandas>=1.2 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from xarray>=0.20.0->xgcm==0.8.1.dev34+gc66861d) (1.4.2)\n",
      "Requirement already satisfied: fsspec>=0.6.0 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from dask->xgcm==0.8.1.dev34+gc66861d) (2022.5.0)\n",
      "Requirement already satisfied: partd>=0.3.10 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from dask->xgcm==0.8.1.dev34+gc66861d) (1.2.0)\n",
      "Requirement already satisfied: toolz>=0.8.2 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from dask->xgcm==0.8.1.dev34+gc66861d) (0.11.2)\n",
      "Requirement already satisfied: cloudpickle>=1.1.1 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from dask->xgcm==0.8.1.dev34+gc66861d) (2.1.0)\n",
      "Requirement already satisfied: pyyaml>=5.3.1 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from dask->xgcm==0.8.1.dev34+gc66861d) (5.4.1)\n",
      "Requirement already satisfied: pyparsing!=3.0.5,>=2.0.2 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from packaging>=20.0->xarray>=0.20.0->xgcm==0.8.1.dev34+gc66861d) (3.0.9)\n",
      "Requirement already satisfied: python-dateutil>=2.8.1 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from pandas>=1.2->xarray>=0.20.0->xgcm==0.8.1.dev34+gc66861d) (2.8.2)\n",
      "Requirement already satisfied: pytz>=2020.1 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from pandas>=1.2->xarray>=0.20.0->xgcm==0.8.1.dev34+gc66861d) (2022.1)\n",
      "Requirement already satisfied: locket in /srv/conda/envs/notebook/lib/python3.9/site-packages (from partd>=0.3.10->dask->xgcm==0.8.1.dev34+gc66861d) (1.0.0)\n",
      "Requirement already satisfied: six>=1.5 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from python-dateutil>=2.8.1->pandas>=1.2->xarray>=0.20.0->xgcm==0.8.1.dev34+gc66861d) (1.16.0)\n",
      "Building wheels for collected packages: xgcm\n",
      "  Building wheel for xgcm (setup.py) ... \u001b[?25ldone\n",
      "\u001b[?25h  Created wheel for xgcm: filename=xgcm-0.8.1.dev34+gc66861d-py3-none-any.whl size=94925 sha256=7321a5518693915bdc6e89f87a95debeff0f07d9ef5991c15295e54906524fbc\n",
      "  Stored in directory: /tmp/pip-ephem-wheel-cache-slw0s4nq/wheels/26/7a/09/292d90418050fbb90e9ea92a07bb96aec29bfe790cbdd2c396\n",
      "Successfully built xgcm\n",
      "Installing collected packages: xgcm\n",
      "  Attempting uninstall: xgcm\n",
      "    Found existing installation: xgcm 0.6.1\n",
      "    Uninstalling xgcm-0.6.1:\n",
      "      Successfully uninstalled xgcm-0.6.1\n",
      "\u001b[31mERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.\n",
      "xmip 0.6.1rc0 requires xgcm<0.7.0, but you have xgcm 0.8.1.dev34+gc66861d which is incompatible.\u001b[0m\u001b[31m\n",
      "\u001b[0mSuccessfully installed xgcm-0.8.1.dev34+gc66861d\n"
     ]
    }
   ],
   "source": [
    "# We need xgcm >0.7.0 to get grid ufuncs\n",
    "!pip install git+https://github.com/xgcm/xgcm.git"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d0b45d6-e89c-444d-9b98-33581dc71ec2",
   "metadata": {},
   "source": [
    "### Define calculation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1895574d-f404-49f8-a4d1-203efb1fda2f",
   "metadata": {},
   "source": [
    "We want to calculate the integral formula for [relative vorticity](https://mitgcm.readthedocs.io/en/latest/algorithm/algorithm.html?highlight=vorticity#relative-vorticity) in terms of circulation around a grid cell:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc1974cc-2da2-4ffe-a7de-9a4709815285",
   "metadata": {},
   "source": [
    "$$\n",
    "  \\zeta_3 = \\frac{\\Gamma}{A_\\zeta} = \\frac{1}{{\\cal A}_\\zeta} ( \\delta_i \\Delta y_c v - \\delta_j \\Delta x_c u )\n",
    "$$\n",
    "\n",
    "where $u$ and $v$ are horizontal and vertical components of surface velocity respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "d934c608-d786-454c-8ceb-10a28ebedd43",
   "metadata": {},
   "outputs": [],
   "source": [
    "import xgcm\n",
    "\n",
    "def vort_ufunc(u, dxc, v, dyc, raz):\n",
    "    u_trans = u * dxc\n",
    "    v_trans = v * dyc\n",
    "    v_diff_x = v_trans[..., 1:, 1:] - v_trans[..., 1:, :-1]\n",
    "    u_diff_y = u_trans[..., 1:, 1:] - u_trans[..., :-1, 1:]\n",
    "    return (v_diff_x - u_diff_y) / raz[..., 1:, 1:]\n",
    "\n",
    "\n",
    "def vort(ds, grid):\n",
    "    \"\"\"Dimensionally-consistent relative vorticity\"\"\"\n",
    "\n",
    "    u = ds.U\n",
    "    v = ds.V\n",
    "    dxC = grid._ds.dxC\n",
    "    dyC = grid._ds.dyC\n",
    "    rAz = grid._ds.rAz\n",
    "       \n",
    "    zeta = grid.apply_as_grid_ufunc(\n",
    "        vort_ufunc,\n",
    "        u, dxC, v, dyC, rAz,\n",
    "        axis= 5 * [(\"Y\", \"X\")],\n",
    "        signature=\"(Y:center,X:left),(Y:center,X:left),(Y:left,X:center),(Y:left,X:center),(Y:left,X:left)->(Y:left,X:left)\",\n",
    "        boundary_width={\"X\": (1, 0), \"Y\": (1, 0)},\n",
    "        boundary=\"fill\",\n",
    "        fill_value=np.nan,\n",
    "        dask=\"forbidden\",   # data should have been loaded in already\n",
    "    )\n",
    "    \n",
    "    return zeta"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b85e2606-39a9-40b4-ad0e-23856feffd26",
   "metadata": {},
   "source": [
    "We also want the **strain magnitude**, given by the vector magnitude of the two strain components, normal strain ($\\sigma_n$) and shear strain ($\\sigma_s$)\n",
    "\n",
    "$$\n",
    "\\sigma = \\sqrt{\\sigma_n^2 + \\sigma_s^2}\n",
    "$$\n",
    "\n",
    "where the components are given in terms of surface velocity components $u$ and $v$ as\n",
    "\n",
    "$$\n",
    "\\sigma_n = \\frac{\\partial u}{\\partial x} - \\frac{\\partial v}{\\partial y}\n",
    "$$\n",
    "$$\n",
    "\\sigma_s = \\frac{\\partial v}{\\partial x} - \\frac{\\partial u}{\\partial y}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "ddc9d3e8-8581-45ef-a98d-fcfa6931b865",
   "metadata": {},
   "outputs": [],
   "source": [
    "def strain_ufunc(u, dxc, v, dyc):\n",
    "    \n",
    "    # TODO are these derivatives actually correct??\n",
    "    u_diff_x = (u[..., 1:] - u[..., :-1]) / dxc[..., 1:]\n",
    "    v_diff_x = (v[..., 1:] - v[..., :-1]) / dxc[..., 1:]\n",
    "    u_diff_y = (u[..., 1:, :] - u[..., :-1, :]) / dyc[..., 1:, :]\n",
    "    v_diff_y = (v[..., 1:, :] - v[..., :-1, :]) / dyc[..., 1:, :]\n",
    "    \n",
    "    u_diff_x_trimmed = u_diff_x[..., 1:, :]\n",
    "    v_diff_x_trimmed = v_diff_x[..., 1:, :]\n",
    "    u_diff_y_trimmed = u_diff_y[..., 1:]\n",
    "    v_diff_y_trimmed = v_diff_y[..., 1:]\n",
    "    \n",
    "    strain_normal = u_diff_x_trimmed - v_diff_y_trimmed\n",
    "    strain_shear = v_diff_x_trimmed + u_diff_y_trimmed\n",
    "    \n",
    "    strain_mag = np.sqrt(strain_normal ** 2 +  strain_shear ** 2)\n",
    "    \n",
    "    return strain_mag\n",
    "    \n",
    "\n",
    "def strain(ds, grid):\n",
    "    \"\"\"Strain magnitude\"\"\"\n",
    "    \n",
    "    u = ds.U\n",
    "    v = ds.V\n",
    "    dxC = grid._ds.dxC\n",
    "    dyC = grid._ds.dyC\n",
    "    \n",
    "    sigma = grid.apply_as_grid_ufunc(\n",
    "        strain_ufunc,\n",
    "        u, dxC, v, dyC,\n",
    "        axis= 4 * [(\"Y\", \"X\")],\n",
    "        signature=\"(Y:center,X:left),(Y:center,X:left),(Y:left,X:center),(Y:left,X:center)->(Y:left,X:left)\",\n",
    "        boundary_width={\"X\": (1, 0), \"Y\": (1, 0)},\n",
    "        boundary=\"fill\",\n",
    "        fill_value=np.nan,\n",
    "        dask=\"forbidden\",   # data should have been loaded in already\n",
    "    )\n",
    "    \n",
    "    return sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "4d474071-5a3b-4946-bf8f-c38ba7e7a104",
   "metadata": {},
   "outputs": [],
   "source": [
    "from xhistogram.xarray import histogram\n",
    "\n",
    "def hist(omega, sigma, f, n_strain_bins, n_vort_bins):\n",
    "\n",
    "    vort_bins, strain_bins = vort_strain_bins(n_strain_bins, n_vort_bins)\n",
    "        \n",
    "    vort = omega.rename('vort') / f\n",
    "    strain = sigma.rename('strain') / abs(f)\n",
    "    return histogram(\n",
    "        vort,\n",
    "        strain, \n",
    "        dim=['i_g', 'j_g'], \n",
    "        bins=[vort_bins, strain_bins],\n",
    "        block_size=None,  # avoids a divide-by-zero bug in xhistogram's code for automatically determining block_size\n",
    "        density=True,  # we don't care about number of grid points, so plot probability density\n",
    "        keep_coords=True,\n",
    "    )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85a8a28f-2a4d-46d1-b5a4-5adeb1ecf8d0",
   "metadata": {},
   "source": [
    "## Compute Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "839f98fa-c630-4a47-98f6-72b3d94448d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def open_llc4320_velocity_data(chunks=None):\n",
    "    \n",
    "    ds_SSU = xr.open_dataset(\n",
    "        \"gs://pangeo-ecco-llc4320/ssu\", \n",
    "        engine=\"zarr\", \n",
    "        storage_options={'requester_pays': True}, \n",
    "        chunks=chunks, \n",
    "        consolidated=True, \n",
    "    )\n",
    "    \n",
    "    ds_SSV = xr.open_dataset(\n",
    "        \"gs://pangeo-ecco-llc4320/ssv\", \n",
    "        engine=\"zarr\", \n",
    "        storage_options={'requester_pays': True}, \n",
    "        chunks=chunks, \n",
    "        consolidated=True, \n",
    "    )\n",
    "    \n",
    "    # Open grid data\n",
    "    ds_grid = xr.open_dataset(\n",
    "        \"gs://pangeo-ecco-llc4320/grid\", \n",
    "        engine=\"zarr\", \n",
    "        storage_options={'requester_pays': True}, \n",
    "        chunks=chunks, \n",
    "        consolidated=True, \n",
    "    )\n",
    "    \n",
    "    coords_to_keep = ['dxC', 'dyC', 'rAz']\n",
    "    ds_grid = ds_grid.reset_coords()[coords_to_keep]\n",
    "    \n",
    "    ds = xr.merge([ds_SSU, ds_SSV, ds_grid])\n",
    "    return ds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "ee34c0b9-45a4-4500-8560-66623ead315f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def store_hist(h, ntime, nregion, target_url):\n",
    "    h_mean = h.mean('time').rename(\"vort_strain_histogram\").to_dataset()\n",
    "    h_mean = h_mean.expand_dims(['region', 'time_coarse'])\n",
    "    h_mean = h_mean.rename({\"strain_bin\": \"strain\", \"vort_bin\": \"vort\"}).drop(\"face\")\n",
    "    h_mean = h_mean.transpose('time_coarse', 'region', 'strain', 'vort')\n",
    "    h_mean.to_zarr(\n",
    "        target_url,\n",
    "        region={\n",
    "            \"time_coarse\": slice(ntime, ntime+1),\n",
    "            \"region\": slice(nregion, nregion+1),\n",
    "            \"vort\": slice(None, None),\n",
    "            \"strain\": slice(None, None)\n",
    "        }\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "bc959cf9-ecb0-4985-a4bb-df4d0b2c6d09",
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_and_store_histogram(ntime, time_slice, nregion, region_slice, f, n_strain_bins, n_vort_bins, target_url):\n",
    "    ds = open_llc4320_velocity_data()\n",
    "    ds_reg = ds.isel(time=time_slice).isel(**region_slice)\n",
    "    ds_reg.load()\n",
    "    grid = xgcm.Grid(ds_reg, periodic=False)\n",
    "    omega = vort(ds_reg, grid)\n",
    "    sigma = strain(ds_reg, grid)    \n",
    "    h = hist(omega, sigma, f, n_strain_bins, n_vort_bins)\n",
    "    store_hist(h, ntime, nregion, target_url)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "6fb5ea98-346e-4668-b753-747e99de4e07",
   "metadata": {},
   "outputs": [],
   "source": [
    "import dask\n",
    "@dask.delayed\n",
    "def calc_and_store_histogram_delayed(ntime, time_slice, nregion, region_slice, f, n_strain_bins, n_vort_bins, target_url):\n",
    "    calc_and_store_histogram(ntime, time_slice, nregion, region_slice, f, n_strain_bins, n_vort_bins, target_url)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "60af24f7-3d98-422f-9059-1c833b6bbc8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16169"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_calcs = []\n",
    "for ntime, time_slice in enumerate(iter_time()):\n",
    "    for nregion, (region, region_slice, f) in enumerate(iter_regions()):\n",
    "        all_calcs.append(\n",
    "            calc_and_store_histogram_delayed(ntime, time_slice, nregion, region_slice, f, n_strain_bins, n_vort_bins, target_url)\n",
    "        )\n",
    "len(all_calcs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e6be36c3-f692-4325-8866-ea031f8d7994",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "549c4d44-9450-4eaf-b39d-87430772de50",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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