Spheroid/Spectral Components Analysis [GEBCO 2019].ipynb

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   "source": [
    "import xarray as xr\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
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   "execution_count": 2,
   "metadata": {},
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     "text": [
      " * postgresql://localhost:5432/grav_29_1\n",
      "Done.\n",
      " * postgresql://localhost:5432/grav_29_1\n"
     ]
    }
   ],
   "source": [
    "%load_ext sql\n",
    "%sql postgresql://localhost:5432/grav_29_1\n",
    "%sql create extension if not exists postgis\n",
    "%sql"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plotting modules\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def raster_filter_range(raster0, g1, g2):\n",
    "    raster = raster0.copy()\n",
    "    raster.values = raster.values.astype(np.float32)\n",
    "    raster.values = gaussian_filter(raster.values,g1,mode='constant', cval=0) \\\n",
    "            - gaussian_filter(raster.values,g2,mode='constant', cval=0)\n",
    "    return raster\n",
    "\n",
    "def spectrum(raster, gammas, dgamma = 1.0):\n",
    "    rasters = []\n",
    "    for g in gammas:\n",
    "        print (g,\". \", end = '')\n",
    "        _raster = raster_filter_range(raster, g-dgamma/2, g+dgamma/2)\n",
    "        rasters.append(_raster)\n",
    "    return rasters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  25.,   75.,  125.,  175.,  225.,  275.,  325.,  375.,  425.,\n",
       "        475.,  525.,  575.,  625.,  675.,  725.,  775.,  825.,  875.,\n",
       "        925.,  975., 1025., 1075., 1125., 1175., 1225., 1275., 1325.,\n",
       "       1375., 1425.])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Gaussian filter sigma, km\n",
    "sigmaskm = np.linspace(25,1425,29)\n",
    "sigmaskm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Raster from file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;elevation&#x27; (lat: 720, lon: 1440)&gt;\n",
       "[1036800 values with dtype=float32]\n",
       "Coordinates:\n",
       "  * lat      (lat) float64 -89.88 -89.62 -89.38 -89.12 ... 89.38 89.62 89.88\n",
       "  * lon      (lon) float64 -179.9 -179.6 -179.4 -179.1 ... 179.4 179.6 179.9\n",
       "Attributes:\n",
       "    long_name:           Elevation relative to sea level\n",
       "    sdn_parameter_name:  Sea floor height (above mean sea level) {bathymetric...\n",
       "    sdn_parameter_urn:   SDN:P01::ALATZZ01\n",
       "    sdn_uom_name:        Metres\n",
       "    sdn_uom_urn:         SDN:P06::ULAA\n",
       "    standard_name:       height_above_reference_ellipsoid\n",
       "    units:               m</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'elevation'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>lat</span>: 720</li><li><span class='xr-has-index'>lon</span>: 1440</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-60e7be65-3f61-4f4e-8e01-97c9756ea8df' class='xr-array-in' type='checkbox' checked><label for='section-60e7be65-3f61-4f4e-8e01-97c9756ea8df' 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>[1036800 values with dtype=float32]</pre></div></div></li><li class='xr-section-item'><input id='section-6444a52c-ae75-40d6-9ec3-7cd46381b662' class='xr-section-summary-in' type='checkbox'  checked><label for='section-6444a52c-ae75-40d6-9ec3-7cd46381b662' class='xr-section-summary' >Coordinates: <span>(2)</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'>lat</span></div><div class='xr-var-dims'>(lat)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-89.88 -89.62 ... 89.62 89.88</div><input id='attrs-ab3cfb17-ec4b-4440-a7d3-97dbe79b9cc3' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-ab3cfb17-ec4b-4440-a7d3-97dbe79b9cc3' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-0cf85c2c-2c48-4af7-8f46-f3e7b7422b12' class='xr-var-data-in' type='checkbox'><label for='data-0cf85c2c-2c48-4af7-8f46-f3e7b7422b12' 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>latitude</dd><dt><span>long_name :</span></dt><dd>latitude</dd><dt><span>units :</span></dt><dd>degrees_north</dd></dl></div><div class='xr-var-data'><pre>array([-89.875, -89.625, -89.375, ...,  89.375,  89.625,  89.875])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>lon</span></div><div class='xr-var-dims'>(lon)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-179.9 -179.6 ... 179.6 179.9</div><input id='attrs-d6c942ea-d8cc-4bc4-aa3c-218e7d899ec9' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-d6c942ea-d8cc-4bc4-aa3c-218e7d899ec9' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-47a58653-f000-4a2d-80fb-6a8b50fb7f2b' class='xr-var-data-in' type='checkbox'><label for='data-47a58653-f000-4a2d-80fb-6a8b50fb7f2b' 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>longitude</dd><dt><span>long_name :</span></dt><dd>longitude</dd><dt><span>units :</span></dt><dd>degrees_east</dd></dl></div><div class='xr-var-data'><pre>array([-179.875, -179.625, -179.375, ...,  179.375,  179.625,  179.875])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-53f08ec8-453d-43cf-ace0-49c0708f8223' class='xr-section-summary-in' type='checkbox'  checked><label for='section-53f08ec8-453d-43cf-ace0-49c0708f8223' class='xr-section-summary' >Attributes: <span>(7)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>long_name :</span></dt><dd>Elevation relative to sea level</dd><dt><span>sdn_parameter_name :</span></dt><dd>Sea floor height (above mean sea level) {bathymetric height}</dd><dt><span>sdn_parameter_urn :</span></dt><dd>SDN:P01::ALATZZ01</dd><dt><span>sdn_uom_name :</span></dt><dd>Metres</dd><dt><span>sdn_uom_urn :</span></dt><dd>SDN:P06::ULAA</dd><dt><span>standard_name :</span></dt><dd>height_above_reference_ellipsoid</dd><dt><span>units :</span></dt><dd>m</dd></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray 'elevation' (lat: 720, lon: 1440)>\n",
       "[1036800 values with dtype=float32]\n",
       "Coordinates:\n",
       "  * lat      (lat) float64 -89.88 -89.62 -89.38 -89.12 ... 89.38 89.62 89.88\n",
       "  * lon      (lon) float64 -179.9 -179.6 -179.4 -179.1 ... 179.4 179.6 179.9\n",
       "Attributes:\n",
       "    long_name:           Elevation relative to sea level\n",
       "    sdn_parameter_name:  Sea floor height (above mean sea level) {bathymetric...\n",
       "    sdn_parameter_urn:   SDN:P01::ALATZZ01\n",
       "    sdn_uom_name:        Metres\n",
       "    sdn_uom_urn:         SDN:P06::ULAA\n",
       "    standard_name:       height_above_reference_ellipsoid\n",
       "    units:               m"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# GEBCO_2019.15min.nc is reduced GEBCO_2019.nc dataset\n",
    "da = xr.open_dataarray('GEBCO_2019.15min.nc').squeeze(drop=True)\n",
    "da"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Raster to Database"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 3.02 s, sys: 177 ms, total: 3.2 s\n",
      "Wall time: 3.62 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "da.to_dataframe(name='z').to_csv('data.csv', header=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "fname = !pwd\n",
    "fname = fname[0] + '/data.csv'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " * postgresql://localhost:5432/grav_29_1\n",
      "Done.\n",
      "Done.\n",
      "Done.\n",
      "1036800 rows affected.\n",
      "1036800 rows affected.\n",
      "Done.\n",
      "Done.\n",
      "CPU times: user 21.6 ms, sys: 8.42 ms, total: 30.1 ms\n",
      "Wall time: 19.4 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
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   ],
   "source": [
    "%%time\n",
    "%%sql\n",
    "\n",
    "create extension if not exists postgis;\n",
    "drop table if exists data;\n",
    "create table data (lat float, lon float, z float, the_geom geography(Point, 4326));\n",
    "COPY data (lat, lon, z) FROM :fname WITH DELIMITER ',';\n",
    "UPDATE data SET the_geom = ST_SetSRID(ST_MakePoint(lon, lat), 4326);\n",
    "CREATE INDEX data_the_geom_idx ON data USING GIST (the_geom);\n",
    "ANALYZE data;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Grid to Database"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50\n"
     ]
    },
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       ".xr-icon-database,\n",
       ".xr-icon-file-text2 {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;elevation&#x27; (lat: 5, lon: 10)&gt;\n",
       "array([[ 2805.0588  ,  2797.1538  ,  2788.7703  ,  2783.9937  ,  2789.0195  ,\n",
       "         2803.2104  ,  2818.7153  ,  2824.908   ,  2822.3848  ,  2811.987   ],\n",
       "       [-5086.245   , -3070.7808  , -4268.0107  ,   -83.09523 , -2583.5671  ,\n",
       "        -3655.863   , -3167.796   , -4288.536   , -3869.2168  , -4229.5996  ],\n",
       "       [-2500.3286  , -2744.067   , -3929.7122  ,   351.40244 , -5161.817   ,\n",
       "        -4976.954   , -3243.7595  , -4918.477   , -1740.4358  , -2974.047   ],\n",
       "       [-5365.9053  , -5340.63    ,  1261.5225  , -5577.9136  , -5515.9976  ,\n",
       "          893.67267 ,   797.7157  ,   406.9157  ,  -193.5919  , -5435.113   ],\n",
       "       [-2168.0571  ,   367.64948 ,   428.83673 ,  -110.66021 , -1463.6254  ,\n",
       "         1248.1346  ,   168.99744 ,    87.563675,   274.6312  ,  -183.86981 ]],\n",
       "      dtype=float32)\n",
       "Coordinates:\n",
       "  * lat      (lat) float64 -89.88 -52.38 -14.88 22.62 60.12\n",
       "  * lon      (lon) float64 -179.9 -142.4 -104.9 -67.38 ... 82.62 120.1 157.6\n",
       "Attributes:\n",
       "    long_name:           Elevation relative to sea level\n",
       "    sdn_parameter_name:  Sea floor height (above mean sea level) {bathymetric...\n",
       "    sdn_parameter_urn:   SDN:P01::ALATZZ01\n",
       "    sdn_uom_name:        Metres\n",
       "    sdn_uom_urn:         SDN:P06::ULAA\n",
       "    standard_name:       height_above_reference_ellipsoid\n",
       "    units:               m</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'elevation'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>lat</span>: 5</li><li><span class='xr-has-index'>lon</span>: 10</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-411d2ff7-c3ac-4207-a209-5044c504be4c' class='xr-array-in' type='checkbox' checked><label for='section-411d2ff7-c3ac-4207-a209-5044c504be4c' 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>2.805e+03 2.797e+03 2.789e+03 2.784e+03 ... 169.0 87.56 274.6 -183.9</span></div><div class='xr-array-data'><pre>array([[ 2805.0588  ,  2797.1538  ,  2788.7703  ,  2783.9937  ,  2789.0195  ,\n",
       "         2803.2104  ,  2818.7153  ,  2824.908   ,  2822.3848  ,  2811.987   ],\n",
       "       [-5086.245   , -3070.7808  , -4268.0107  ,   -83.09523 , -2583.5671  ,\n",
       "        -3655.863   , -3167.796   , -4288.536   , -3869.2168  , -4229.5996  ],\n",
       "       [-2500.3286  , -2744.067   , -3929.7122  ,   351.40244 , -5161.817   ,\n",
       "        -4976.954   , -3243.7595  , -4918.477   , -1740.4358  , -2974.047   ],\n",
       "       [-5365.9053  , -5340.63    ,  1261.5225  , -5577.9136  , -5515.9976  ,\n",
       "          893.67267 ,   797.7157  ,   406.9157  ,  -193.5919  , -5435.113   ],\n",
       "       [-2168.0571  ,   367.64948 ,   428.83673 ,  -110.66021 , -1463.6254  ,\n",
       "         1248.1346  ,   168.99744 ,    87.563675,   274.6312  ,  -183.86981 ]],\n",
       "      dtype=float32)</pre></div></div></li><li class='xr-section-item'><input id='section-376cae1d-9524-4356-8923-9b9ed06ae73a' class='xr-section-summary-in' type='checkbox'  checked><label for='section-376cae1d-9524-4356-8923-9b9ed06ae73a' class='xr-section-summary' >Coordinates: <span>(2)</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'>lat</span></div><div class='xr-var-dims'>(lat)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-89.88 -52.38 -14.88 22.62 60.12</div><input id='attrs-03cdc30c-54c5-4fab-88e9-2cb8450b8ad9' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-03cdc30c-54c5-4fab-88e9-2cb8450b8ad9' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-2bf1bbc2-790a-4042-a56e-a57109bfb346' class='xr-var-data-in' type='checkbox'><label for='data-2bf1bbc2-790a-4042-a56e-a57109bfb346' 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>latitude</dd><dt><span>long_name :</span></dt><dd>latitude</dd><dt><span>units :</span></dt><dd>degrees_north</dd></dl></div><div class='xr-var-data'><pre>array([-89.875, -52.375, -14.875,  22.625,  60.125])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>lon</span></div><div class='xr-var-dims'>(lon)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-179.9 -142.4 ... 120.1 157.6</div><input id='attrs-3293fabd-183c-44d2-a67b-b8902941b33a' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-3293fabd-183c-44d2-a67b-b8902941b33a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-6213d35b-8a69-49ac-9264-4fec9810b88b' class='xr-var-data-in' type='checkbox'><label for='data-6213d35b-8a69-49ac-9264-4fec9810b88b' 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>longitude</dd><dt><span>long_name :</span></dt><dd>longitude</dd><dt><span>units :</span></dt><dd>degrees_east</dd></dl></div><div class='xr-var-data'><pre>array([-179.875, -142.375, -104.875,  -67.375,  -29.875,    7.625,   45.125,\n",
       "         82.625,  120.125,  157.625])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-6484804c-d413-48bf-83b3-77f66e60dbd6' class='xr-section-summary-in' type='checkbox'  checked><label for='section-6484804c-d413-48bf-83b3-77f66e60dbd6' class='xr-section-summary' >Attributes: <span>(7)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>long_name :</span></dt><dd>Elevation relative to sea level</dd><dt><span>sdn_parameter_name :</span></dt><dd>Sea floor height (above mean sea level) {bathymetric height}</dd><dt><span>sdn_parameter_urn :</span></dt><dd>SDN:P01::ALATZZ01</dd><dt><span>sdn_uom_name :</span></dt><dd>Metres</dd><dt><span>sdn_uom_urn :</span></dt><dd>SDN:P06::ULAA</dd><dt><span>standard_name :</span></dt><dd>height_above_reference_ellipsoid</dd><dt><span>units :</span></dt><dd>m</dd></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray 'elevation' (lat: 5, lon: 10)>\n",
       "array([[ 2805.0588  ,  2797.1538  ,  2788.7703  ,  2783.9937  ,  2789.0195  ,\n",
       "         2803.2104  ,  2818.7153  ,  2824.908   ,  2822.3848  ,  2811.987   ],\n",
       "       [-5086.245   , -3070.7808  , -4268.0107  ,   -83.09523 , -2583.5671  ,\n",
       "        -3655.863   , -3167.796   , -4288.536   , -3869.2168  , -4229.5996  ],\n",
       "       [-2500.3286  , -2744.067   , -3929.7122  ,   351.40244 , -5161.817   ,\n",
       "        -4976.954   , -3243.7595  , -4918.477   , -1740.4358  , -2974.047   ],\n",
       "       [-5365.9053  , -5340.63    ,  1261.5225  , -5577.9136  , -5515.9976  ,\n",
       "          893.67267 ,   797.7157  ,   406.9157  ,  -193.5919  , -5435.113   ],\n",
       "       [-2168.0571  ,   367.64948 ,   428.83673 ,  -110.66021 , -1463.6254  ,\n",
       "         1248.1346  ,   168.99744 ,    87.563675,   274.6312  ,  -183.86981 ]],\n",
       "      dtype=float32)\n",
       "Coordinates:\n",
       "  * lat      (lat) float64 -89.88 -52.38 -14.88 22.62 60.12\n",
       "  * lon      (lon) float64 -179.9 -142.4 -104.9 -67.38 ... 82.62 120.1 157.6\n",
       "Attributes:\n",
       "    long_name:           Elevation relative to sea level\n",
       "    sdn_parameter_name:  Sea floor height (above mean sea level) {bathymetric...\n",
       "    sdn_parameter_urn:   SDN:P01::ALATZZ01\n",
       "    sdn_uom_name:        Metres\n",
       "    sdn_uom_urn:         SDN:P06::ULAA\n",
       "    standard_name:       height_above_reference_ellipsoid\n",
       "    units:               m"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid = da[::150,::150]\n",
    "print (grid.shape[0]*grid.shape[1])\n",
    "grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "grid.to_dataframe(name='z0').to_csv('grid.csv', header=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "fname = !pwd\n",
    "fname = fname[0] + '/grid.csv'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " * postgresql://localhost:5432/grav_29_1\n",
      "Done.\n",
      "Done.\n",
      "50 rows affected.\n",
      "50 rows affected.\n",
      "Done.\n",
      "Done.\n",
      "CPU times: user 13.7 ms, sys: 5.79 ms, total: 19.5 ms\n",
      "Wall time: 70.4 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "%%sql\n",
    "\n",
    "drop table if exists grid;\n",
    "create table grid (lat float, lon float, z0 float, the_geom geography(Point, 4326));\n",
    "COPY grid (lat, lon, z0) FROM :fname WITH DELIMITER ',';\n",
    "UPDATE grid SET the_geom = ST_SetSRID(ST_MakePoint(lon, lat), 4326);\n",
    "CREATE INDEX grid_the_geom_idx ON grid USING GIST (the_geom);\n",
    "ANALYZE grid;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gaussian Filtering in Database"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " * postgresql://localhost:5432/grav_29_1\n",
      "Done.\n",
      "Done.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%sql\n",
    "\n",
    "DROP FUNCTION IF EXISTS gaussian_transform(sigma float, geom geography);\n",
    "CREATE OR REPLACE FUNCTION gaussian_transform(sigma float, geom geography)\n",
    "    RETURNS TABLE (z float, count bigint)\n",
    "    AS '\n",
    "with weights as (\n",
    "    select\n",
    "        z,\n",
    "        exp(-(pow(ST_Distance($2,the_geom,false),2))/(2*pow($1,2))) as weight\n",
    "    from data\n",
    "    where ST_Buffer($2,4.*$1) && the_geom and ST_DWithin($2, the_geom, 4.*$1)\n",
    ")\n",
    "select\n",
    "    sum(z*weight)/sum(weight) as z,\n",
    "    count(1) as count\n",
    "from weights\n",
    "'\n",
    "LANGUAGE SQL STABLE;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " * postgresql://localhost:5432/grav_29_1\n",
      "Done.\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "Done.\n",
      "sigmakm 25.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 75.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 125.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 175.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 225.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 275.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 325.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 375.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 425.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 475.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 525.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 575.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 625.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 675.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 725.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 775.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 825.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 875.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 925.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 975.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 1025.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 1075.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 1125.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 1175.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 1225.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 1275.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 1325.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 1375.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "sigmakm 1425.0\n",
      " * postgresql://localhost:5432/grav_29_1\n",
      "50 rows affected.\n",
      "CPU times: user 119 ms, sys: 22 ms, total: 141 ms\n",
      "Wall time: 7min 29s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "%sql drop table if exists gaussian_transform;\n",
    "%sql create table gaussian_transform (sigmakm int, lat float, lon float, z0 float, z float, count bigint);\n",
    "\n",
    "for sigmakm in sigmaskm:\n",
    "    print (\"sigmakm\", sigmakm)\n",
    "    %sql insert into gaussian_transform \\\n",
    "         select :sigmakm, lat, lon, z0, t.* from grid, gaussian_transform(:sigmakm*1000, the_geom) as t;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Show Gaussian Transform map"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " * postgresql://localhost:5432/grav_29_1\n",
      "1450 rows affected.\n",
      "Returning data to local variable gaussian\n"
     ]
    }
   ],
   "source": [
    "%sql gaussian << select * from gaussian_transform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "gaussian = gaussian.DataFrame()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
       "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
       "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
       "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
       "  --xr-background-color: var(--jp-layout-color0, white);\n",
       "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
       "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
       "}\n",
       "\n",
       "html[theme=dark],\n",
       "body.vscode-dark {\n",
       "  --xr-font-color0: rgba(255, 255, 255, 1);\n",
       "  --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
       "  --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
       "  --xr-border-color: #1F1F1F;\n",
       "  --xr-disabled-color: #515151;\n",
       "  --xr-background-color: #111111;\n",
       "  --xr-background-color-row-even: #111111;\n",
       "  --xr-background-color-row-odd: #313131;\n",
       "}\n",
       "\n",
       ".xr-wrap {\n",
       "  display: block;\n",
       "  min-width: 300px;\n",
       "  max-width: 700px;\n",
       "}\n",
       "\n",
       ".xr-text-repr-fallback {\n",
       "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-header {\n",
       "  padding-top: 6px;\n",
       "  padding-bottom: 6px;\n",
       "  margin-bottom: 4px;\n",
       "  border-bottom: solid 1px var(--xr-border-color);\n",
       "}\n",
       "\n",
       ".xr-header > div,\n",
       ".xr-header > ul {\n",
       "  display: inline;\n",
       "  margin-top: 0;\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-obj-type,\n",
       ".xr-array-name {\n",
       "  margin-left: 2px;\n",
       "  margin-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-obj-type {\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-sections {\n",
       "  padding-left: 0 !important;\n",
       "  display: grid;\n",
       "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
       "}\n",
       "\n",
       ".xr-section-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-section-item input {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-section-item input + label {\n",
       "  color: var(--xr-disabled-color);\n",
       "}\n",
       "\n",
       ".xr-section-item input:enabled + label {\n",
       "  cursor: pointer;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-section-item input:enabled + label:hover {\n",
       "  color: var(--xr-font-color0);\n",
       "}\n",
       "\n",
       ".xr-section-summary {\n",
       "  grid-column: 1;\n",
       "  color: var(--xr-font-color2);\n",
       "  font-weight: 500;\n",
       "}\n",
       "\n",
       ".xr-section-summary > span {\n",
       "  display: inline-block;\n",
       "  padding-left: 0.5em;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:disabled + label {\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-section-summary-in + label:before {\n",
       "  display: inline-block;\n",
       "  content: '►';\n",
       "  font-size: 11px;\n",
       "  width: 15px;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:disabled + label:before {\n",
       "  color: var(--xr-disabled-color);\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label:before {\n",
       "  content: '▼';\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label > span {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-section-summary,\n",
       ".xr-section-inline-details {\n",
       "  padding-top: 4px;\n",
       "  padding-bottom: 4px;\n",
       "}\n",
       "\n",
       ".xr-section-inline-details {\n",
       "  grid-column: 2 / -1;\n",
       "}\n",
       "\n",
       ".xr-section-details {\n",
       "  display: none;\n",
       "  grid-column: 1 / -1;\n",
       "  margin-bottom: 5px;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked ~ .xr-section-details {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-array-wrap {\n",
       "  grid-column: 1 / -1;\n",
       "  display: grid;\n",
       "  grid-template-columns: 20px auto;\n",
       "}\n",
       "\n",
       ".xr-array-wrap > label {\n",
       "  grid-column: 1;\n",
       "  vertical-align: top;\n",
       "}\n",
       "\n",
       ".xr-preview {\n",
       "  color: var(--xr-font-color3);\n",
       "}\n",
       "\n",
       ".xr-array-preview,\n",
       ".xr-array-data {\n",
       "  padding: 0 5px !important;\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-array-data,\n",
       ".xr-array-in:checked ~ .xr-array-preview {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-array-in:checked ~ .xr-array-data,\n",
       ".xr-array-preview {\n",
       "  display: inline-block;\n",
       "}\n",
       "\n",
       ".xr-dim-list {\n",
       "  display: inline-block !important;\n",
       "  list-style: none;\n",
       "  padding: 0 !important;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list li {\n",
       "  display: inline-block;\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list:before {\n",
       "  content: '(';\n",
       "}\n",
       "\n",
       ".xr-dim-list:after {\n",
       "  content: ')';\n",
       "}\n",
       "\n",
       ".xr-dim-list li:not(:last-child):after {\n",
       "  content: ',';\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-has-index {\n",
       "  font-weight: bold;\n",
       "}\n",
       "\n",
       ".xr-var-list,\n",
       ".xr-var-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-var-item > div,\n",
       ".xr-var-item label,\n",
       ".xr-var-item > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-even);\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-var-item > .xr-var-name:hover span {\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-var-list > li:nth-child(odd) > div,\n",
       ".xr-var-list > li:nth-child(odd) > label,\n",
       ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-odd);\n",
       "}\n",
       "\n",
       ".xr-var-name {\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-var-dims {\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-var-dtype {\n",
       "  grid-column: 3;\n",
       "  text-align: right;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-preview {\n",
       "  grid-column: 4;\n",
       "}\n",
       "\n",
       ".xr-var-name,\n",
       ".xr-var-dims,\n",
       ".xr-var-dtype,\n",
       ".xr-preview,\n",
       ".xr-attrs dt {\n",
       "  white-space: nowrap;\n",
       "  overflow: hidden;\n",
       "  text-overflow: ellipsis;\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
       "  overflow: visible;\n",
       "  width: auto;\n",
       "  z-index: 1;\n",
       "}\n",
       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
       "}\n",
       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2 {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
       "Dimensions:  (lat: 5, lon: 10, sigmakm: 29)\n",
       "Coordinates:\n",
       "  * sigmakm  (sigmakm) int64 25 75 125 175 225 275 ... 1225 1275 1325 1375 1425\n",
       "  * lat      (lat) float64 -89.88 -52.38 -14.88 22.62 60.12\n",
       "  * lon      (lon) float64 -179.9 -142.4 -104.9 -67.38 ... 82.62 120.1 157.6\n",
       "Data variables:\n",
       "    z0       (sigmakm, lat, lon) float64 2.805e+03 2.797e+03 ... 274.6 -183.9\n",
       "    z        (sigmakm, lat, lon) float64 2.821e+03 2.814e+03 ... -1.238e+03\n",
       "    count    (sigmakm, lat, lon) int64 5083 5083 5083 ... 269196 269643 269424</pre><div class='xr-wrap' hidden><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-750b38d5-1d4d-406c-bde2-8e703b2d18e5' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-750b38d5-1d4d-406c-bde2-8e703b2d18e5' 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'>lat</span>: 5</li><li><span class='xr-has-index'>lon</span>: 10</li><li><span class='xr-has-index'>sigmakm</span>: 29</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-e50fcb3d-6edf-4ab8-8ffb-b031fcbe9c55' class='xr-section-summary-in' type='checkbox'  checked><label for='section-e50fcb3d-6edf-4ab8-8ffb-b031fcbe9c55' 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'>sigmakm</span></div><div class='xr-var-dims'>(sigmakm)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>25 75 125 175 ... 1325 1375 1425</div><input id='attrs-3e38d92b-5f28-4edd-9b88-cd4396d1dda4' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-3e38d92b-5f28-4edd-9b88-cd4396d1dda4' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-0ae0c863-4991-4bd8-961a-326788cd42cc' class='xr-var-data-in' type='checkbox'><label for='data-0ae0c863-4991-4bd8-961a-326788cd42cc' 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([  25,   75,  125,  175,  225,  275,  325,  375,  425,  475,  525,  575,\n",
       "        625,  675,  725,  775,  825,  875,  925,  975, 1025, 1075, 1125, 1175,\n",
       "       1225, 1275, 1325, 1375, 1425])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>lat</span></div><div class='xr-var-dims'>(lat)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-89.88 -52.38 -14.88 22.62 60.12</div><input id='attrs-78297f44-0eb7-4e3f-9a14-89be20dff79e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-78297f44-0eb7-4e3f-9a14-89be20dff79e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-cd76822d-98b4-4e95-8e74-5a87ea5d8998' class='xr-var-data-in' type='checkbox'><label for='data-cd76822d-98b4-4e95-8e74-5a87ea5d8998' 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([-89.875, -52.375, -14.875,  22.625,  60.125])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>lon</span></div><div class='xr-var-dims'>(lon)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-179.9 -142.4 ... 120.1 157.6</div><input id='attrs-ab74687f-af02-451b-ae2f-d2d9ef4e380b' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-ab74687f-af02-451b-ae2f-d2d9ef4e380b' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-431380fa-17f0-44f0-a1fb-f400f43ec640' class='xr-var-data-in' type='checkbox'><label for='data-431380fa-17f0-44f0-a1fb-f400f43ec640' 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([-179.875, -142.375, -104.875,  -67.375,  -29.875,    7.625,   45.125,\n",
       "         82.625,  120.125,  157.625])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-f47ddc07-2a4a-44f2-9db1-18c75a68172d' class='xr-section-summary-in' type='checkbox'  checked><label for='section-f47ddc07-2a4a-44f2-9db1-18c75a68172d' class='xr-section-summary' >Data variables: <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>z0</span></div><div class='xr-var-dims'>(sigmakm, lat, lon)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>2.805e+03 2.797e+03 ... -183.9</div><input id='attrs-a4ca6ee8-8339-4ed8-85c7-20269fe621cf' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-a4ca6ee8-8339-4ed8-85c7-20269fe621cf' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-497ffa1b-082b-4607-9fa4-b13f49263e60' class='xr-var-data-in' type='checkbox'><label for='data-497ffa1b-082b-4607-9fa4-b13f49263e60' 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([[[ 2805.0588  ,  2797.1538  ,  2788.7703  , ...,  2824.908   ,\n",
       "          2822.3848  ,  2811.987   ],\n",
       "        [-5086.245   , -3070.7808  , -4268.0107  , ..., -4288.536   ,\n",
       "         -3869.2168  , -4229.5996  ],\n",
       "        [-2500.3286  , -2744.067   , -3929.7122  , ..., -4918.477   ,\n",
       "         -1740.4358  , -2974.047   ],\n",
       "        [-5365.9053  , -5340.63    ,  1261.5225  , ...,   406.9157  ,\n",
       "          -193.5919  , -5435.113   ],\n",
       "        [-2168.0571  ,   367.64948 ,   428.83673 , ...,    87.563675,\n",
       "           274.6312  ,  -183.86981 ]],\n",
       "\n",
       "       [[ 2805.0588  ,  2797.1538  ,  2788.7703  , ...,  2824.908   ,\n",
       "          2822.3848  ,  2811.987   ],\n",
       "        [-5086.245   , -3070.7808  , -4268.0107  , ..., -4288.536   ,\n",
       "         -3869.2168  , -4229.5996  ],\n",
       "        [-2500.3286  , -2744.067   , -3929.7122  , ..., -4918.477   ,\n",
       "         -1740.4358  , -2974.047   ],\n",
       "        [-5365.9053  , -5340.63    ,  1261.5225  , ...,   406.9157  ,\n",
       "          -193.5919  , -5435.113   ],\n",
       "        [-2168.0571  ,   367.64948 ,   428.83673 , ...,    87.563675,\n",
       "...\n",
       "          2822.3848  ,  2811.987   ],\n",
       "        [-5086.245   , -3070.7808  , -4268.0107  , ..., -4288.536   ,\n",
       "         -3869.2168  , -4229.5996  ],\n",
       "        [-2500.3286  , -2744.067   , -3929.7122  , ..., -4918.477   ,\n",
       "         -1740.4358  , -2974.047   ],\n",
       "        [-5365.9053  , -5340.63    ,  1261.5225  , ...,   406.9157  ,\n",
       "          -193.5919  , -5435.113   ],\n",
       "        [-2168.0571  ,   367.64948 ,   428.83673 , ...,    87.563675,\n",
       "           274.6312  ,  -183.86981 ]],\n",
       "\n",
       "       [[ 2805.0588  ,  2797.1538  ,  2788.7703  , ...,  2824.908   ,\n",
       "          2822.3848  ,  2811.987   ],\n",
       "        [-5086.245   , -3070.7808  , -4268.0107  , ..., -4288.536   ,\n",
       "         -3869.2168  , -4229.5996  ],\n",
       "        [-2500.3286  , -2744.067   , -3929.7122  , ..., -4918.477   ,\n",
       "         -1740.4358  , -2974.047   ],\n",
       "        [-5365.9053  , -5340.63    ,  1261.5225  , ...,   406.9157  ,\n",
       "          -193.5919  , -5435.113   ],\n",
       "        [-2168.0571  ,   367.64948 ,   428.83673 , ...,    87.563675,\n",
       "           274.6312  ,  -183.86981 ]]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>z</span></div><div class='xr-var-dims'>(sigmakm, lat, lon)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>2.821e+03 2.814e+03 ... -1.238e+03</div><input id='attrs-f54734d2-a79f-4b31-bcb2-85fd60f0c6b6' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-f54734d2-a79f-4b31-bcb2-85fd60f0c6b6' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-ef8dc197-dd04-48f7-b1bb-33a23b9013b2' class='xr-var-data-in' type='checkbox'><label for='data-ef8dc197-dd04-48f7-b1bb-33a23b9013b2' 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([[[ 2821.25165725,  2813.70813415,  2806.31078353, ...,\n",
       "          2823.14615883,  2826.09777463,  2824.44448362],\n",
       "        [-5069.8636046 , -3174.03991817, -4226.76808687, ...,\n",
       "         -4158.90492562, -3956.7888836 , -4174.02842787],\n",
       "        [-2502.80360344, -3469.85171739, -3882.73067838, ...,\n",
       "         -4926.82411056, -1960.55893703, -3223.97915356],\n",
       "        [-5290.35514453, -5400.93359098,  1315.60656108, ...,\n",
       "           450.25784329,  -284.84779613, -5322.06204803],\n",
       "        [-1946.51620171,   514.91094885,   430.81323222, ...,\n",
       "           102.594088  ,   312.98969057,  -167.70508292]],\n",
       "\n",
       "       [[ 2852.83221623,  2846.30534268,  2839.04385432, ...,\n",
       "          2852.06678693,  2855.89324418,  2855.2869648 ],\n",
       "        [-5054.21367784, -3576.9349907 , -4174.32274181, ...,\n",
       "         -3969.32247733, -3998.12880681, -4199.24196491],\n",
       "        [-2243.49773129, -3380.55166985, -3908.14844626, ...,\n",
       "         -4859.96089052, -2122.18710059, -3273.26983071],\n",
       "        [-5250.21646684, -5366.30116959,  1189.8650787 , ...,\n",
       "           462.15105144,  -530.36700306, -5099.41191283],\n",
       "        [-1759.97542914,   333.88508044,   412.34785394, ...,\n",
       "...\n",
       "          1449.9487966 ,  1448.20643138,  1444.60193751],\n",
       "        [-3192.97460775, -3790.04286555, -3449.43276078, ...,\n",
       "         -2596.54307228, -2622.47933542, -2712.578508  ],\n",
       "        [-3922.50711576, -4342.04735079, -3625.82051094, ...,\n",
       "         -4120.08881134, -1855.75365291, -2451.28624936],\n",
       "        [-5015.22144118, -4692.9578082 , -1579.86486576, ...,\n",
       "           112.26757357, -1389.92112142, -4733.88786402],\n",
       "        [-1654.11506661, -1276.91476189,  -294.60354267, ...,\n",
       "            14.20377419,  -154.76791196, -1196.4816789 ]],\n",
       "\n",
       "       [[ 1359.2877442 ,  1356.07299805,  1354.7864153 , ...,\n",
       "          1366.64160237,  1365.01639611,  1361.61020746],\n",
       "        [-3126.20802273, -3715.19038392, -3370.32679877, ...,\n",
       "         -2522.13140408, -2523.004949  , -2641.23405423],\n",
       "        [-3924.767723  , -4350.53360773, -3613.05283862, ...,\n",
       "         -4075.73001337, -1895.4201697 , -2474.01721915],\n",
       "        [-5000.79044905, -4647.91763556, -1613.60828205, ...,\n",
       "            76.18977074, -1377.57237175, -4678.99931058],\n",
       "        [-1678.46499983, -1308.56731028,  -352.47743632, ...,\n",
       "           -21.87344881,  -213.52254654, -1238.11903275]]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>count</span></div><div class='xr-var-dims'>(sigmakm, lat, lon)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>5083 5083 5083 ... 269643 269424</div><input id='attrs-a942462c-5ffc-44d2-9e80-6bf6cdc2a028' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-a942462c-5ffc-44d2-9e80-6bf6cdc2a028' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-bf7db960-038a-4a56-8fbc-ac63ed3db521' class='xr-var-data-in' type='checkbox'><label for='data-bf7db960-038a-4a56-8fbc-ac63ed3db521' 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([[[  5083,   5083,   5083, ...,   5083,   5083,   5083],\n",
       "        [    65,     65,     65, ...,     65,     65,     65],\n",
       "        [    45,     45,     45, ...,     45,     45,     45],\n",
       "        [    45,     45,     45, ...,     45,     45,     45],\n",
       "        [    79,     79,     79, ...,     79,     79,     79]],\n",
       "\n",
       "       [[ 15343,  15343,  15343, ...,  15343,  15343,  15343],\n",
       "        [   595,    595,    595, ...,    595,    595,    594],\n",
       "        [   379,    379,    379, ...,    379,    379,    379],\n",
       "        [   391,    391,    391, ...,    391,    391,    391],\n",
       "        [   727,    727,    727, ...,    727,    727,    727]],\n",
       "\n",
       "       [[ 25631,  25631,  25631, ...,  25631,  25631,  25631],\n",
       "        [  1655,   1655,   1653, ...,   1654,   1655,   1654],\n",
       "        [  1057,   1057,   1057, ...,   1057,   1057,   1057],\n",
       "        [  1107,   1106,   1107, ...,   1107,   1105,   1107],\n",
       "        [  2030,   2031,   2030, ...,   2029,   2030,   2031]],\n",
       "\n",
       "       ...,\n",
       "\n",
       "       [[274013, 274013, 274013, ..., 274013, 274013, 274013],\n",
       "        [229740, 229788, 229805, ..., 229847, 229807, 229825],\n",
       "        [119877, 118369, 118866, ..., 119626, 118393, 118323],\n",
       "        [127197, 126017, 126755, ..., 127096, 126141, 126243],\n",
       "        [246504, 247094, 246691, ..., 246647, 246843, 246775]],\n",
       "\n",
       "       [[284299, 284299, 284299, ..., 284299, 284299, 284299],\n",
       "        [242540, 242668, 242620, ..., 242643, 242618, 242615],\n",
       "        [129284, 127603, 128173, ..., 129023, 127539, 127566],\n",
       "        [137427, 136024, 136919, ..., 137324, 136185, 136304],\n",
       "        [257844, 258619, 258102, ..., 258021, 258318, 258182]],\n",
       "\n",
       "       [[294567, 294567, 294567, ..., 294567, 294567, 294567],\n",
       "        [254977, 255233, 255091, ..., 255067, 255072, 255066],\n",
       "        [139108, 137226, 137890, ..., 138812, 137066, 137211],\n",
       "        [148157, 153006, 147592, ..., 148054, 146747, 146850],\n",
       "        [269048, 269961, 269335, ..., 269196, 269643, 269424]]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-a8eb7c7e-9766-418d-9ba2-924dcc55e168' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-a8eb7c7e-9766-418d-9ba2-924dcc55e168' 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:  (lat: 5, lon: 10, sigmakm: 29)\n",
       "Coordinates:\n",
       "  * sigmakm  (sigmakm) int64 25 75 125 175 225 275 ... 1225 1275 1325 1375 1425\n",
       "  * lat      (lat) float64 -89.88 -52.38 -14.88 22.62 60.12\n",
       "  * lon      (lon) float64 -179.9 -142.4 -104.9 -67.38 ... 82.62 120.1 157.6\n",
       "Data variables:\n",
       "    z0       (sigmakm, lat, lon) float64 2.805e+03 2.797e+03 ... 274.6 -183.9\n",
       "    z        (sigmakm, lat, lon) float64 2.821e+03 2.814e+03 ... -1.238e+03\n",
       "    count    (sigmakm, lat, lon) int64 5083 5083 5083 ... 269196 269643 269424"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gaussian = gaussian.set_index(['sigmakm','lat','lon']).to_xarray()\n",
    "gaussian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 3.58 ms, sys: 2.46 ms, total: 6.04 ms\n",
      "Wall time: 6.31 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# discrete power spectrum\n",
    "power_spectrum = gaussian.std(['lat','lon'])['z'].rename('spectrum')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,6))\n",
    "\n",
    "ax = fig.add_subplot(1, 3, 1)\n",
    "ax.plot(power_spectrum.sigmakm.values, power_spectrum.values, c='blue')\n",
    "ax.set_yscale('log')\n",
    "ax.set_title(f'Power Spectrum (Log)\\n', fontsize=22)\n",
    "ax.set_ylabel('Log (Spectral density)',fontsize=18)\n",
    "ax.set_xlabel('Wavelength, km', fontsize=18)\n",
    "ax.set_yticks([])\n",
    "ax.set_yticks([], minor=True)\n",
    "\n",
    "ax = fig.add_subplot(1, 3, 2)\n",
    "ax.plot(power_spectrum.sigmakm.values, power_spectrum.values, c='blue')\n",
    "ax.set_xscale('log')\n",
    "ax.set_yscale('log')\n",
    "ax.set_title(f'Power Spectrum (LogLog)\\n', fontsize=22)\n",
    "ax.set_ylabel('Log (Spectral density)',fontsize=18)\n",
    "ax.set_xlabel('Log (Wavelength), km', fontsize=18)\n",
    "ax.set_yticks([])\n",
    "ax.set_yticks([], minor=True)\n",
    "\n",
    "ax = fig.add_subplot(1, 3, 3)\n",
    "# calculate fractality index\n",
    "slope = np.diff(np.log10(power_spectrum))/np.diff(np.log10(power_spectrum.sigmakm))\n",
    "depths = (power_spectrum.sigmakm.values[1:]+power_spectrum.sigmakm.values[:-1])/2/np.sqrt(2)\n",
    "fractal = (3 - (slope/2))\n",
    "ax.plot(depths, 1000*fractal, c='blue')\n",
    "ax.set_title(f'Density\\n', fontsize=22)\n",
    "ax.set_ylabel('ρ, kg/m³',fontsize=18)\n",
    "ax.set_xlabel('Depth, km', fontsize=18)\n",
    "\n",
    "plt.suptitle('GEBCO 2019 Bathymetry Power Spectrum and Fractality Density', fontsize=28)\n",
    "fig.tight_layout(rect=[0.03, 0.0, 1, 0.9])\n",
    "plt.savefig('Spectral Components Analysis [GEBCO 2019].jpg', dpi=150, quality=95)\n",
    "plt.show()"
   ]
  }
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