examples/Notebooks/flopy3_SpatialReference_demo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# FloPy \n",
    "\n",
    "### `SpatialReference` demo\n",
    "\n",
    "A short demonstration of functionality in the `SpatialReference` class for locating the model in a \"real world\" coordinate reference system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "flopy is installed in /Users/jdhughes/Documents/Development/flopy_git/flopy_fork/flopy\n",
      "3.7.3 | packaged by conda-forge | (default, Jul  1 2019, 14:38:56) \n",
      "[Clang 4.0.1 (tags/RELEASE_401/final)]\n",
      "numpy version: 1.17.3\n",
      "matplotlib version: 3.1.1\n",
      "flopy version: 3.3.1\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "import os\n",
    "import shutil\n",
    "import numpy as np\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# run installed version of flopy or add local path\n",
    "try:\n",
    "    import flopy\n",
    "except:\n",
    "    fpth = os.path.abspath(os.path.join('..', '..'))\n",
    "    sys.path.append(fpth)\n",
    "    import flopy\n",
    "    \n",
    "from flopy.utils.reference import SpatialReference\n",
    "import flopy.utils.binaryfile as bf\n",
    "\n",
    "print(sys.version)\n",
    "print('numpy version: {}'.format(np.__version__))\n",
    "print('matplotlib version: {}'.format(mpl.__version__))\n",
    "print('flopy version: {}'.format(flopy.__version__))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "outpath = 'data'\n",
    "if os.path.isdir(outpath):\n",
    "    shutil.rmtree(outpath)\n",
    "os.mkdir(outpath)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Description\n",
    "\n",
    "`SpatialReference` is a stand-alone option that describes the location of the model grid in a real-world coordinate reference system. It can be created with some basic information about the model's location."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "nrow, ncol = 10, 10\n",
    "xll, yll = 617822.3, 5114820.7 # origin of the model (lower left corner)\n",
    "dxdy = 250 # grid spacing (in model units)\n",
    "rot = 29 # rotation (positive counterclockwise)\n",
    "\n",
    "# epsg code specifying coordinate reference system\n",
    "# (https://www.epsg-registry.org/)\n",
    "# in this case, UTM zone 16 N, NAD83\n",
    "# https://spatialreference.org/ref/epsg/nad83-utm-zone-16n/\n",
    "model_epsg = 26915\n",
    "\n",
    "# alternatively, a proj4 string can be supplied\n",
    "model_proj4 = 'https://spatialreference.org/ref/epsg/nad83-utm-zone-16n/proj4/'\n",
    "\n",
    "# row and column spacings\n",
    "# (note that delc is column spacings along a row; delr the row spacings along a column)\n",
    "delc = np.ones(nrow, dtype=float) * dxdy\n",
    "delr = np.ones(ncol, dtype=float) * dxdy\n",
    "\n",
    "sr = SpatialReference(delr=delr, delc=delc, xll=xll, yll=yll, rotation=rot, epsg=model_epsg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `SpatialReference` makes many calculations internally, so you don't have to\n",
    "\n",
    "calling the sr object prints the important parameters. Note that the upper right corner of the model, which is often used to specify the origin, has been calculated. A proj4 string has also been fetched from <spatialreference.org> using the supplied epsg code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "xul:616610.2759; yul:5117007.249; rotation:29; proj4_str:+proj=utm +zone=15 +ellps=GRS80 +datum=NAD83 +units=m +no_defs ; units:meters; lenuni:2; length_multiplier:1.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Note the length parameters\n",
    "**units**: Length units for real world coordinate system (typically meters; feet are also supported). This attribute is inferred from the epsg code or proj4 string, but can also be supplied.  \n",
    "**lenuni**: MODFLOW length unit ([see documentation](<https://water.usgs.gov/ogw/modflow/MODFLOW-2005-Guide/>)) (default is 2, meters).  \n",
    "**length_multiplier**: multiplier for scaling grid from MODFLOW units to real world crs units. This parameter is inferred from the above units, or can be supplied directly.  \n",
    "\n",
    "#### `SpatialReference` parameters can be updated dynamically"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# switch the MODFLOW units to feet\n",
    "sr.lenuni = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "xul:617452.8751; yul:5115487.16; rotation:29; proj4_str:+proj=utm +zone=15 +ellps=GRS80 +datum=NAD83 +units=m +no_defs ; units:meters; lenuni:1; length_multiplier:0.3048"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Note that the length multiplier and xul, yul changed\n",
    "the lower left corner was maintained because it was specified. If xul, yul had been specified instead, that would have been preserved."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(617822.3, 5114820.7)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sr.xll, sr.yll"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### information about the grid coordinates\n",
    "\n",
    "#### cell centroids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[617504.66932675, 617571.31534843, 617637.96137011,\n",
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       "         618104.4835219 ],\n",
       "        [617541.61181981, 617608.25784149, 617674.90386318,\n",
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       "         617941.48794991, 618008.1339716 , 618074.77999328,\n",
       "         618141.42601496],\n",
       "        [617578.55431287, 617645.20033456, 617711.84635624,\n",
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       "         617978.43044298, 618045.07646466, 618111.72248634,\n",
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       "        [617615.49680593, 617682.14282762, 617748.7888493 ,\n",
       "         617815.43487099, 617882.08089267, 617948.72691435,\n",
       "         618015.37293604, 618082.01895772, 618148.66497941,\n",
       "         618215.31100109],\n",
       "        [617652.439299  , 617719.08532068, 617785.73134237,\n",
       "         617852.37736405, 617919.02338573, 617985.66940742,\n",
       "         618052.3154291 , 618118.96145079, 618185.60747247,\n",
       "         618252.25349415],\n",
       "        [617689.38179206, 617756.02781374, 617822.67383543,\n",
       "         617889.31985711, 617955.9658788 , 618022.61190048,\n",
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       "         618289.19598722],\n",
       "        [617726.32428512, 617792.97030681, 617859.61632849,\n",
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       "        [617763.26677819, 617829.91279987, 617896.55882155,\n",
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       "        [617800.20927125, 617866.85529293, 617933.50131462,\n",
       "         618000.1473363 , 618066.79335798, 618133.43937967,\n",
       "         618200.08540135, 618266.73142304, 618333.37744472,\n",
       "         618400.0234664 ],\n",
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       "         618037.08982936, 618103.73585105, 618170.38187273,\n",
       "         618237.02789441, 618303.6739161 , 618370.31993778,\n",
       "         618436.96595947]]),\n",
       " array([[5115472.30845253, 5115509.25094559, 5115546.19343866,\n",
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       "        [5115405.66243085, 5115442.60492391, 5115479.54741697,\n",
       "         5115516.48991003, 5115553.4324031 , 5115590.37489616,\n",
       "         5115627.31738922, 5115664.25988229, 5115701.20237535,\n",
       "         5115738.14486841],\n",
       "        [5115339.01640916, 5115375.95890222, 5115412.90139529,\n",
       "         5115449.84388835, 5115486.78638141, 5115523.72887448,\n",
       "         5115560.67136754, 5115597.6138606 , 5115634.55635366,\n",
       "         5115671.49884673],\n",
       "        [5115272.37038748, 5115309.31288054, 5115346.2553736 ,\n",
       "         5115383.19786667, 5115420.14035973, 5115457.08285279,\n",
       "         5115494.02534585, 5115530.96783892, 5115567.91033198,\n",
       "         5115604.85282504],\n",
       "        [5115205.72436579, 5115242.66685886, 5115279.60935192,\n",
       "         5115316.55184498, 5115353.49433804, 5115390.43683111,\n",
       "         5115427.37932417, 5115464.32181723, 5115501.2643103 ,\n",
       "         5115538.20680336],\n",
       "        [5115139.07834411, 5115176.02083717, 5115212.96333024,\n",
       "         5115249.9058233 , 5115286.84831636, 5115323.79080942,\n",
       "         5115360.73330249, 5115397.67579555, 5115434.61828861,\n",
       "         5115471.56078167],\n",
       "        [5115072.43232243, 5115109.37481549, 5115146.31730855,\n",
       "         5115183.25980161, 5115220.20229468, 5115257.14478774,\n",
       "         5115294.0872808 , 5115331.02977386, 5115367.97226693,\n",
       "         5115404.91475999],\n",
       "        [5115005.78630074, 5115042.7287938 , 5115079.67128687,\n",
       "         5115116.61377993, 5115153.55627299, 5115190.49876606,\n",
       "         5115227.44125912, 5115264.38375218, 5115301.32624524,\n",
       "         5115338.26873831],\n",
       "        [5114939.14027906, 5114976.08277212, 5115013.02526518,\n",
       "         5115049.96775825, 5115086.91025131, 5115123.85274437,\n",
       "         5115160.79523743, 5115197.7377305 , 5115234.68022356,\n",
       "         5115271.62271662],\n",
       "        [5114872.49425737, 5114909.43675044, 5114946.3792435 ,\n",
       "         5114983.32173656, 5115020.26422962, 5115057.20672269,\n",
       "         5115094.14921575, 5115131.09170881, 5115168.03420188,\n",
       "         5115204.97669494]]))"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sr.xcentergrid, sr.ycentergrid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### cell vertices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       " [[617623.1096058033, 5115494.399181282],\n",
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       " [[617756.4016491713, 5115568.284167407],\n",
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       "  [617823.0476708553, 5115605.2266604705]],\n",
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       "  [617956.3397142234, 5115679.111646595],\n",
       "  [617889.6936925392, 5115642.169153533]],\n",
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       "  [618022.9857359073, 5115716.054139659],\n",
       "  [617956.3397142234, 5115679.111646595]],\n",
       " [[618022.9857359073, 5115716.054139659],\n",
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       "  [617593.406077182, 5115390.810666534],\n",
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       "  [617660.0520988662, 5115427.7531595975],\n",
       "  [617593.406077182, 5115390.810666534]],\n",
       " [[617660.0520988662, 5115427.7531595975],\n",
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       "  [617763.6406136125, 5115398.049630977],\n",
       "  [617726.6981205501, 5115464.69565266],\n",
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       " [[617726.6981205501, 5115464.69565266],\n",
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       "  [617793.3441422342, 5115501.638145722],\n",
       "  [617726.6981205501, 5115464.69565266]],\n",
       " [[617793.3441422342, 5115501.638145722],\n",
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       "  [617896.9326569806, 5115471.934617103],\n",
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       "  [618318.5256804094, 5115182.885966187],\n",
       "  [618385.1717020934, 5115219.82845925],\n",
       "  [618348.2292090305, 5115286.4744809335],\n",
       "  [618281.5831873465, 5115249.531987871]],\n",
       " [[618348.2292090305, 5115286.4744809335],\n",
       "  [618385.1717020934, 5115219.82845925],\n",
       "  [618451.8177237775, 5115256.770952312],\n",
       "  [618414.8752307146, 5115323.416973996],\n",
       "  [618348.2292090305, 5115286.4744809335]],\n",
       " [[617785.3575069372, 5114887.346021685],\n",
       "  [617822.3, 5114820.7],\n",
       "  [617888.946021684, 5114857.642493063],\n",
       "  [617852.0035286212, 5114924.288514747],\n",
       "  [617785.3575069372, 5114887.346021685]],\n",
       " [[617852.0035286212, 5114924.288514747],\n",
       "  [617888.946021684, 5114857.642493063],\n",
       "  [617955.5920433681, 5114894.584986126],\n",
       "  [617918.6495503053, 5114961.231007811],\n",
       "  [617852.0035286212, 5114924.288514747]],\n",
       " [[617918.6495503053, 5114961.231007811],\n",
       "  [617955.5920433681, 5114894.584986126],\n",
       "  [618022.2380650521, 5114931.5274791885],\n",
       "  [617985.2955719893, 5114998.173500873],\n",
       "  [617918.6495503053, 5114961.231007811]],\n",
       " [[617985.2955719893, 5114998.173500873],\n",
       "  [618022.2380650521, 5114931.5274791885],\n",
       "  [618088.8840867361, 5114968.469972251],\n",
       "  [618051.9415936733, 5115035.115993936],\n",
       "  [617985.2955719893, 5114998.173500873]],\n",
       " [[618051.9415936733, 5115035.115993936],\n",
       "  [618088.8840867361, 5114968.469972251],\n",
       "  [618155.5301084202, 5115005.412465314],\n",
       "  [618118.5876153574, 5115072.058486999],\n",
       "  [618051.9415936733, 5115035.115993936]],\n",
       " [[618118.5876153574, 5115072.058486999],\n",
       "  [618155.5301084202, 5115005.412465314],\n",
       "  [618222.1761301041, 5115042.354958377],\n",
       "  [618185.2336370413, 5115109.0009800615],\n",
       "  [618118.5876153574, 5115072.058486999]],\n",
       " [[618185.2336370413, 5115109.0009800615],\n",
       "  [618222.1761301041, 5115042.354958377],\n",
       "  [618288.8221517883, 5115079.297451439],\n",
       "  [618251.8796587255, 5115145.943473124],\n",
       "  [618185.2336370413, 5115109.0009800615]],\n",
       " [[618251.8796587255, 5115145.943473124],\n",
       "  [618288.8221517883, 5115079.297451439],\n",
       "  [618355.4681734722, 5115116.239944503],\n",
       "  [618318.5256804094, 5115182.885966187],\n",
       "  [618251.8796587255, 5115145.943473124]],\n",
       " [[618318.5256804094, 5115182.885966187],\n",
       "  [618355.4681734722, 5115116.239944503],\n",
       "  [618422.1141951563, 5115153.182437565],\n",
       "  [618385.1717020934, 5115219.82845925],\n",
       "  [618318.5256804094, 5115182.885966187]],\n",
       " [[618385.1717020934, 5115219.82845925],\n",
       "  [618422.1141951563, 5115153.182437565],\n",
       "  [618488.7602168403, 5115190.124930628],\n",
       "  [618451.8177237775, 5115256.770952312],\n",
       "  [618385.1717020934, 5115219.82845925]]]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sr.vertices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transformations\n",
    "\n",
    "#### model coordinates to real-world coordinates\n",
    "e.g., for working with MODPATH output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([617822.3       , 617824.59641594]),\n",
       " array([5114820.7       , 5114822.84415994]))"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sr.transform(np.array([0, 10.]), np.array([0, 2.5]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### real-word coordinates to model coordinates\n",
    "e.g., for specifying observations for Hydmod"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(9.97497282274192, 2.4982681834038707)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sr.transform(617824.59, 5114822.84, inverse=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### model row, column for real-world coordinate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(9, 9)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sr.get_ij(671900., 618000.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Grid bounds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(617452.8750693724, 5114820.7, 618488.7602168403, 5115856.585147467)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sr.bounds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Shapefile of grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "wrote data/grid.shp\n"
     ]
    }
   ],
   "source": [
    "sr.write_shapefile(os.path.join(outpath, 'grid.shp'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### grid spec file\n",
    "(for PEST)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "sr.write_gridSpec(os.path.join(outpath, 'grid.spc'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading `SpatialReference`\n",
    "\n",
    "`SpatialReference` is included in flopy models at the model level;  \n",
    "with `model.write()` the basic parameters are written to the comment header of the Name file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['# Name file for mf2005; generated by Flopy.\\n', '#xul:619653; yul:3353277; rotation:15; proj4_str:+proj=utm +zone=14 +ellps=WGS84 +datum=WGS84 +units=m +no_defs; start_datetime:1/1/2015\\n']\n"
     ]
    }
   ],
   "source": [
    "# load an existing model\n",
    "model_ws = os.path.join(\"..\", \"data\", \"freyberg_multilayer_transient\")\n",
    "with open(model_ws + '/freyberg.nam') as input:\n",
    "    print(input.readlines()[0:2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### on load\n",
    "`SpatialReference` info is read from  \n",
    "1) **usgs.model.reference**, if it exists (https://water.usgs.gov/ogw/policy/gw-model/modelers-setup.html)  \n",
    "2) otherwise, the Name file  \n",
    "\n",
    "if no spatial reference information is found, a default sr object is created"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "ml = flopy.modflow.Modflow.load(\"freyberg.nam\", model_ws=model_ws, verbose=False,\n",
    "                               check=False, exe_name=\"mfnwt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "xul:619653; yul:3353277; rotation:15; proj4_str:+proj=utm +zone=14 +ellps=WGS84 +datum=WGS84 +units=m +no_defs; units:meters; lenuni:2; length_multiplier:1.0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ml.sr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adding/modifying `SpatialReference` for a model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "xul:150000; yul:30000; rotation:25; proj4_str:+proj=utm +zone=15 +ellps=clrk66 +datum=NAD27 +units=m +no_defs ; units:meters; lenuni:2; length_multiplier:1.0"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ml.sr = SpatialReference(delr=ml.dis.delr, delc=ml.dis.delc, \n",
    "                         xul=150000, yul=30000, rotation=25, epsg=26715)\n",
    "ml.sr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### individual parameters can also be updated"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "xul:150000; yul:30000; rotation:25; proj4_str:+proj=utm +zone=14 +ellps=WGS84 +datum=WGS84 +units=m +no_defs; units:meters; lenuni:2; length_multiplier:1.0"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ml.sr.proj4_str = \"+proj=utm +zone=14 +ellps=WGS84 +datum=WGS84 +units=m +no_defs\"\n",
    "ml.sr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### note that the epsg code was cleared when the proj4 string was updated"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "ml.sr.epsg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### interpolation between cells\n",
    "(e.g. for head values at point locations)\n",
    "\n",
    "#### read in some head results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hdsobj = bf.HeadFile(model_ws + '/freyberg.hds')\n",
    "hds = hdsobj.get_data()\n",
    "hds[hds < -999] = np.nan\n",
    "plt.imshow(hds[0])\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(150000.0, 20936.9221296335, 158757.72155259026, 32113.0913087035)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ml.sr.bounds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### get interpolated head at some points\n",
    "uses `scipy.interpolate.gridddata` to interpolate values between cell centers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.2041737, 4.218045 ], dtype=float32)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ml.sr.interpolate(hds[0], ([157000, 160000], [30000, 27000]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "ml.sr.xll = 0\n",
    "ml.sr.yll = 0\n",
    "ml.sr.rotation = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rasterizing features\n",
    "\n",
    "requires the `rasterio` and `fiona` modules, available via **conda-forge** (mac or windows), or the **Unofficial Python Binaries** website (windows)\n",
    "\n",
    "#### create a geoJSON-style geometry\n",
    "(this could be easily read in from a shapefile"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "try:\n",
    "    import fiona\n",
    "except:\n",
    "    fiona = None\n",
    "    print('fiona is not available')\n",
    "try:\n",
    "    from rasterio.features import rasterize\n",
    "    from rasterio import Affine\n",
    "except:\n",
    "    rasterize = None\n",
    "    Affine = None\n",
    "    print('rasterio is not available')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### read in a shapefile"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "if fiona is not None:\n",
    "    shpname = '../data/freyberg/gis/bedrock_outcrop_hole.shp'\n",
    "    with fiona.open(shpname) as src:\n",
    "        records = [r for r in src]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### list the feature geometries and attributes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "if fiona is not None:\n",
    "    geoms = [r['geometry'] for r in records]\n",
    "    attr = [r['properties'] for r in records]\n",
    "    attr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### select an attribute to map onto the model grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "if fiona is not None:\n",
    "    geoms = [(g, attr[i]['OBJECTID']) for i, g in enumerate(geoms)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### make an `rasterio.Affine` object using info from the sr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "if rasterize is not None:\n",
    "    dx = ml.dis.delr.array[0]\n",
    "    dy = ml.dis.delc.array[0]\n",
    "    trans = Affine(dx, ml.sr.rotation, ml.sr.xul, \n",
    "                   ml.sr.rotation, -dy, ml.sr.yul)\n",
    "    trans"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### rasterize the features, applying the attribute values to cells intersecting each one\n",
    "In this case, the cells with zeros are those that don't intersect a feature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANoAAAD8CAYAAAAR6LrwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAY3klEQVR4nO3df7BV5X3v8fcnoKgoCYZIuf5ISMO0wUxtlEG8Zpo43kakJtiZ2MGmkZsxQ68192rv7Q9oZ9K/mEmTO53UsTEyiVdoYyhjtGEy+IPSpGkbUdEYFdF4AlYpXKmaq5g0KOd87h/r2bjOPvvHOuesvdnPOd8Xs2av/axfD8z+sp71rGd9l2wTQuittx3vCoQwHUSghdAHEWgh9EEEWgh9EIEWQh9EoIXQB10DTdJtkg5JerJUdrqk7ZKeTZ9zS8vWSRqS9Iyky0rlF0h6Ii27SZJS+SxJf5vKH5T0nnr/iiGMJelsSd+RtEfSbkk3tFhH6bc6JOlxSeeXli1Pv/EhSWu7HtB2xwn4NeB84MlS2ReAtWl+LfDnaX4x8ENgFrAQ+DEwIy17CLgIEHAPcHkq/z3gK2l+FfC33eoUU0yTnYAFwPlp/jTgR8DipnVWpN+qgGXAg6l8Rvptvxc4Mf3mF3c6Xtczmu3vAa80Fa8ENqb5jcCVpfLNto/Y3gcMAUslLQDm2H7ARU03NW3T2NedwKWNs10IvWL7oO1H0/xhYA9wZtNqK4FNLuwE3pF+y0uBIdt7bb8BbE7rtjVzgvWcb/tgo8KSzkjlZwI7S+vtT2Vvpvnm8sY2L6R9HZX0KvBO4KXmg0paA6wB0IknXnDC/DOaVwkD7I0X9r9k+12T2cdll8z2y68Md13vkceP7AZ+XiraYHtDq3XT5coHgQebFh37bSaN322r8gs71WeigdZOqzORO5R32mZsYfEPtQFg1jln+8w/uHEidQzHyb4b/uBfJ7uPl18Z5qH7zum63owFz/7c9pJu60k6FfgmcKPt15oXt9ik2++5pYn2Or6YTqGkz0OpfD9wdmm9s4ADqfysFuWjtpE0E3g7Y5uqIQDFr3mkwp8qJJ1AEWRft31Xi1U6/Z5blbc10UDbCqxO86uBb5XKV6WexIXAIuCh1Mw8LGlZuv66pmmbxr4+AfxDuo4LYQxj3vRw16mb9Dv8GrDH9l+0WW0rcE3qfVwGvJp+yw8DiyQtlHQiRSfe1k7H69p0lPQN4CPAPEn7gT8DPg9skXQt8DxwFYDt3ZK2AE8BR4Hr7WN/6+uA24GTKXpy7knlXwP+WtIQxZlsVbc6hemt6hmri4uBTwFPSHoslf0JcA6A7a8A2yh6HoeAnwGfTsuOSvoscB9FD+Rttnd3OljXQLN9dZtFl7ZZfz2wvkX5LuADLcp/TgrUELoxZriGBo/tf6b1tVZ5HQPXt1m2jSIQK6m7MySEnhvp3O8wkCLQQlYMDEeghdB7cUYLoccMvJlhp3QEWsiKcTQdQ+g5w3B+cRaBFvJSjAzJTwRayIwY7nz7ayBFoIWsFJ0hEWgh9FRxHy0CLYSeG4kzWgi9FWe0EPrAiOEMk7dFoIXsRNMxhB4z4g3PON7VGLcItJCV4oZ1NB1D6LnoDAmhx2wx7DijhdBzIzWd0STdBlwBHLI9Js2GpD8EPpm+zgTeD7zL9iuSngMOA8PA0W6p7SLQQlaKzpDafra3AzdTZM4eeyz7i8AXASR9DPh92+VUiJfYHpPot5UItJCVOjtDbH9vHC9VuRr4xkSPlV9jN0x7w1bXqU6STgGWUyRbbTBwv6RHUqr6juKMFrIyjpEh8yTtKn1vm3u/go8B/9LUbLzY9oH03ontkp5OL4RpKQItZGekWq/jS1Vy71e0iqZmo+0D6fOQpLsp3jDTNtCi6RiyUgwqflvXqS6S3g58mLdS2CNptqTTGvPAR4EnW++hEGe0kBUj3qxpCFabdPcnwLGU4AC/Cdxv+6elTecDd6fX+M0E7rB9b6djRaCFrNjUdsO6Q7r78jq3U9wGKJftBc4bz7Ei0EJmVNsN636KQAtZMfWd0fopAi1kJx78DKHHjOLBzxB6rUg3l9/PNr8ah2kuEqiG0HOm8siQgRKBFrKT4xltUv81SPp9SbslPSnpG5JOknS6pO2Snk2fc0vrr5M0JOkZSZeVyi+Q9ERadpPSLfcQmtlixG/rOg2aCddI0pnA/wCWpKdTZ1AMvlwL7LC9CNiRviNpcVp+LsUjB1+W1BhLcwuwBliUpuUTrVeY2orOkBldp0Ez2abjTOBkSW8CpwAHgHUU48cANgLfBf4YWAlstn0E2CdpCFiaHgmfY/sBAEmbgCuBeyZZt3Eb+q1bJ72P92353RpqEtrLM2fIhGts+9+A/w08DxwEXrV9PzDf9sG0zkHgjLTJmcALpV3sT2Vnpvnm8jEkrZG0S9Ku4dd/2mqVMMUVnSHqOg2ayTQd51KcpRYC/wmYLel3Om3SoswdyscW2htsL7G9ZMaps8db5TBF9PMxmbpMpun4X4B9tv8dQNJdwH8GXpS0wPZBSQuAQ2n9/cDZpe3Pomhq7k/zzeUhjJHryJDJhP7zwDJJp6RewkuBPcBWYHVaZzVvPTC3FVglaZakhRSdHg+l5uVhScvSfq4pbRPCGCO8res0aCZ8RrP9oKQ7gUeBo8APgA3AqcAWSddSBONVaf3dkrYAT6X1r7c9nHZ3HcUzPydTdIL0vSMk5MGGN0cGL5C6mVSvo+0/o3gqtewIxdmt1frrgfUtyncBYxJY5qhVz2X0RNanaDpOs0AL4XjIcWRIBFrISqN7Pzf5nYPDNFffECxJt0k6JKllBitJH5H0qqTH0vS50rLlaSjhkKS13Y4VZ7SQnRpzhtxOh9z7yT/ZvqJckIYO/hXw6xS3px6WtNX2U+12EoEWslL0OtYzlnGcuffLlgJDKRsWkjZTDN5oG2jRdAxZadywrjAEa15juF6auubHb+MiST+UdI+kc1NZu+GEbcUZLWSnYtOxjpTgjwLvtv26pBXA31EMtKg8bLAhzmghK/0cVGz7Nduvp/ltwAmS5tF+OGFbcUYL2enXDWtJvwC8aNuSllKcmF4G/h+wKA0l/DeK5yx/u9O+ItBCVmxxtKZAq5B7/xPAdZKOAv8BrLJt4KikzwL3UTzwfJvt3Z2OFYEWslNj07Bj7n3bN1N0/7datg3YVvVYEWghK7mODIlAC9mJQAuhx3J98DMCLWQnXtsUQo/ZcHS6PfgZwvEQTccQeiyu0ULoE0eghdB70RkSQo/ZcY0WQh+I4eh1DKH34hothB6LsY4h9IOL67TcRKCF7ESvYwg95ugMCaE/oukYQh/k2OuY3zk4TGt2EWjdpioqpAT/pKTH0/R9SeeVlj0n6YmUKnxXt2PFGS1kp8bu/dvpnBJ8H/Bh2z+RdDnF+/8uLC2/xPZLVQ4UgRayU9c1WreU4La/X/q6k9GvgB6XCLSQFSNGqvU6zmtq0m2wvWESh76W0W+iNXC/JAO3dtt3BFrITsUTWh0pwQGQdAlFoH2oVHyx7QOSzgC2S3ra9vfa7WNSnSGS3iHpTklPS9oj6SJJp0vaLunZ9Dm3tP669D6pZyRdViq/IF1YDkm6Kb00PoSxauwMqULSrwBfBVbafvlYNewD6fMQcDfFG2bammyv418C99r+ZeA8YA+wFthhexGwI31H0mKK1MnnAsuBL6f3TAHcAqyheIHAorQ8hNZcYaqBpHOAu4BP2f5RqXy2pNMa88BHgZY9lw0TbjpKmgP8GvBfAWy/AbwhaSVFmmWAjcB3gT+meH/UZttHgH2ShoClkp4D5th+IO13E3Alo9vDIRxT1xmrQkrwzwHvpDgpABxNzdH5wN2pbCZwh+17Ox1rMtdo7wX+Hfg/6f7CI8ANwHzbB1NlD6Y2LBTvj9pZ2r7xTqk303xz+RjpHVdrAGbMndtqlTDFGRgZ6VtK8M8An2lRvpeiBVfZZJqOM4HzgVtsfxD4KamZ2Ea7d0pVfteU7Q22l9heMuPU2eOtb5gKDFjdpwEzmUDbD+y3/WD6fidF4L0oaQFA+jxUWr/VO6X2M/r+RNd3TYXpze4+DZoJB5rt/wu8IOmXUtGlFO/w3QqsTmWrgW+l+a3AKkmz0nulFgEPpWbmYUnLUm/jNaVtQhirT50hdZrsfbT/Dnxd0onAXuDTFMG7RdK1wPPAVQC2d0vaQhGMR4HrbQ+n/VxHMRzmZIpOkOgICW3U233fL5MKNNuPAa1uCl7aZv31wPoW5buAD0ymLmEaGcAzVjcxMiTkxeCaeh37KQItZCgCLYTei6ZjCH0QgRZCjzVuWGcmAi1kZxBvSHcTgRbyE72OIfSe4owWQo8N6BCrbiLQQmYGc3R+NxFoIT9xRguhD0aOdwXGLwIt5CXT+2iREjxkR+4+VdpP95TgSlnZhlJa8PNLy5anbG5DkjplFgAi0EKO6nvw83Y6Z1y7nLcys62hyNZGyt72V2n5YuDqlOWtrQi0MG2lhKevdFhlJbDJhZ3AO1J6jqXAkO29Kfvb5rRuWxFoITsVm47zJO0qTWsmcKgzgRdK3xsZ2tqVtxWdISEvpuoQrDpSgk86c1tDBFrIT//uo7XL3HZim/K2oukYslNXr2MFW4FrUu/jMuDVlLXtYWCRpIUpMdWqtG5bcUYL+akvt363lODbgBXAEPAziixv2D4q6bPAfcAM4DbbuzsdKwJtgt635XePdxWmr/peRNgtJbiB69ss20YRiJVEoIWs1Nw07JsItJCfePAzhN6LM1oI/RCBlrd2HRxDv3Vrn2sS2oprtBD6JAIthN5Thg9+xsiQEPogzmghP9F0DKHHojNk6orhVgMmAi2EPohAC6G3xDTtdZQ0Q9IPJH07fT9d0nZJz6bPuaV116WsQc9IuqxUfoGkJ9KymyTlN5gt9EeFZ9EG8Rquju79G4A9pe9rgR22FwE70ndSlqBVwLkUmYe+nLIJQZFdaA1vZRzqlJkoTHf1ZcHqm0kFmqSzgN8AvloqXglsTPMbgStL5ZttH7G9j+JhuqUpq9Ac2w+k5382lbYJYazpFmjAl4A/YnSS5vnpcW/S5xmpvFNGof0tyseQtKaR1Wj49Z9OsuohV9Oq6SjpCuCQ7UeqbtKibFwZhWxvsL3E9pIZp86ueNgw5WR4RptMr+PFwMclrQBOAuZI+hvgRUkLbB9MzcJDaf12GYX2p/nm8hDGcn29jpKWA39Jkffjq7Y/37T8D4FPpq8zgfcD77L9iqTngMPAMHC0W2q7CZ/RbK+zfZbt91B0cvyD7d+hyAa0Oq22GvhWmt8KrJI0S9JCik6Ph1Lz8rCkZam38ZrSNiGMVcMZrUpab9tftP2rtn8VWAf8o+1yZuNL0vKu+SN7cR/t88AWSdcCzwNXpUrvlrQFeAo4Clxvezhtcx1FHvSTgXvSFEJLNV2DHUvrDSCpkdb7qTbrXw18Y6IHqyXQbH8X+G6afxm4tM1664H1Lcp3AR+ooy5hGqgWaPMk7Sp932B7Q+l7q865C1vtSNIpFLecPttUi/slGbi1ad9jxMiQkJfqnR3dUoKPJ633x4B/aWo2Xmz7gKQzgO2Snk4vzWgpnkcLWRG1de+365xrZRVNzUbbB9LnIeBuiqZoWxFoITs1BVqltN6S3g58mFIHnaTZkk5rzAMfBVq+zLAhmo4hPzV0hrRL6y3pv6XlX0mr/iZwv+3yCIn5wN1pSO5M4A7b93Y6XgRayE99KcHHpPUuBVjj++0UPeLlsr3AeeM5VgRayMuADrHqJgIt5CcCLYTey/HBzwi0kJ1oOobQawM6Or+bCLSQnwi0EHqrMTIkNxFoITsayS/SItBCXuIaLYT+iKZjCP0QgRZC78UZLYR+iEALocdqzILVTxFoIStxHy2EfnF+kRaBFrITZ7QQei3TG9aRnCdkRyPdp0r7kZand/UNSVrbYvlHJL0q6bE0fa7qts3ijBayU0evYykl+K9TpJ57WNJW282Ziv/J9hUT3PaYOKOFvJiiM6Tb1N2xlOC23wAaKcF7sm0EWshOxbyO8xrv0kvTmqbdtHtfX7OLJP1Q0j2Szh3ntsdE0zHkp38pwR8F3m379fR6sr+jeAvSeNKJA3FGC5npZ0pw26/Zfj3NbwNOkDSvyrbNItBCXmw00n2qoGtKcEm/kN7Zh6SlFPHycpVtm0XTMeSnfynBPwFcJ+ko8B/AKtsGWm7b6XgRaCE7dY0M6ZYS3PbNwM1Vt+0kAi3kxUDkDAmhD/KLs4l3hkg6W9J3JO2RtFvSDan8dEnbJT2bPueWtlmXhqw8I+myUvkFkp5Iy25qXICG0EpNvY59NZlex6PA/7L9fmAZcH16q/1aYIftRcCO9J20bBVwLsX7gL+chrIA3AKsobhHsSgtD6Glmnod+2rCgWb7oO1H0/xhYA/F3fGVwMa02kbgyjS/Eths+4jtfcAQsFTSAmCO7QdSj86m0jYhjOaK04Cp5RpN0nuADwIPAvNtH4QiGNPLtKEIwp2lzRrDVt5M883lrY6zhuLMx0mcwi/euHPU8h9/adkk/yZh0BU3rAcwkrqY9A1rSacC3wRutP1ap1VblLlD+dhCe4PtJbaXnMCs8Vc2TA0jFaYBM6lAk3QCRZB93fZdqfjF1BwkfR5K5e2GrexP883lIbQku+s0aCbT6yjga8Ae239RWrQVWJ3mV/PW2+y3AqskzZK0kKLT46HUzDwsaVna5zWlbUIYbRpeo10MfAp4QtJjqexPgM8DWyRdCzwPXAWQhrdsAZ6i6LG83vZw2u46ihdynwzck6YQWhjMXsVuJhxotv+Z1tdXAJe22WY9sL5F+S7gAxOtS0Nz5whEB8mUNIBNw25iZEjISyRQDaFP4owWQh/kF2cRaCE/Gsmv7RiBFvJiBvKGdDdTPtBa9URC9EbmSgzmDelupnyghSkow0CL5DwhP/UkUK2SEvyTkh5P0/clnVda9lx6hvIxSbu6HSvOaCEvNV2jVUzrvQ/4sO2fSLoc2ABcWFp+ie2XqhwvAi1kp6Zex2NpvQEkNdJ6Hws0298vrb+T0YPfx2XaBloM1+qddh1Q+2rZe/WmYRet0npf2GZdgGsZPQbXwP2SDNxqe0Ong03bQAuZarzkort5TddOG5qCofJzkJIuoQi0D5WKL7Z9ID3YvF3S07a/164yEWghP9Vajt1y71dK6y3pV4CvApfbfrlRbvtA+jwk6W6KpmjbQItex5Cdmh78rJIS/BzgLuBTtn9UKp8t6bTGPPBR4MlOB4szWshPDddoFVOCfw54J0XGNoCj6Sw5H7g7lc0E7rB9b6fjRaCFvNgwXM8YrAopwT8DfKbFdnuB85rLO4lAC/nJcGRIBFrITwRaCD0WL7kIoR8Mzu85mQi0kBdTW2dIP0WglcSza+PT7t+r5+IaLYQ+iEALoddqG1TcVxFoIS8GIjlPCH0QZ7QwVR23jo8x6huC1U8RaCEvBsd9tBD6IEaGhNAHcY0WQo/Z0esYQl/EGS3kZHB6EsfDeHi4+2oDJgIt5CUekwmhTzLs3h+YLFjd8qCHACmt44i7TlVUyL0vSTel5Y9LOr/qts0GItBKedAvBxYDV0tafHxrFQaS04Of3aYuKv7mLgcWpWkNcMs4th1lIAKNUh50228AjTzoIYzh4eGuUwVVfnMrgU0u7ATeIWlBxW1HGZRrtEp50CWtofifBeDI3/vOjkkra3PDnXXsZR5Q6c0j/dIhF36v6vruye7gMD+57+9957wKq57UJSV4ld9cq3XOrLjtKIMSaJXyoKd/qA0AknZ1Sfk8UHKq7yDX1fbymnZV5TfXbp3KefsbBiXQKuVBD6FGVX5z7dY5scK2owzKNVrXPOgh1KzKb24rcE3qfVwGvGr7YMVtRxmIM1q7POhdNuv4PqoBlFN9c6rrhFTMvb8NWAEMAT8DPt1p207HkzMcNxZCbgal6RjClBaBFkIfZBlogzBcS9LZkr4jaY+k3ZJuSOWnS9ou6dn0Obe0zbpU52ckXVYqv0DSE2nZTUov3upBnWdI+oGkbw96Xacc21lNFBefPwbeS9HN+kNg8XGoxwLg/DR/GvAjiuE4XwDWpvK1wJ+n+cWprrOAhenvMCMtewi4iOL+zD0Ur3HtRZ3/J3AH8O30fWDrOtWmHM9oAzFcy/ZB24+m+cPAHooRAyuBjWm1jcCVaX4lsNn2Edv7KHqylqYhPXNsP+Dil7yptE1tJJ0F/AbF+5gbBrKuU1GOgdZuWMxxI+k9wAeBB4H5Lu61kD7PSKt1Gs6zv0V53b4E/BGjX7U+qHWdcnIMtHEPf+klSacC3wRutP1ap1VblE1oOM94SboCOGT7kaqbtCjrS12nqoG4YT1OAzNcS9IJFEH2ddt3peIXJS2wfTA1tQ6l8nb13p/mm8vrdDHwcUkrgJOAOZL+ZkDrOjUd74vE8U4U/znspbhIb3SGnHsc6iGKa5QvNZV/kdEdDF9I8+cyuoNhL291MDwMLOOtDoYVPaz3R3irM2Sg6zqVpuNegQn+WFZQ9PL9GPjT41SHD1E0mx4HHkvTCuCdwA7g2fR5emmbP011foZSbx2wBHgyLbuZNGKnR/UuB9pA13UqTTEEK4Q+yLEzJITsRKCF0AcRaCH0QQRaCH0QgRZCH0SghdAHEWgh9MH/B0JvVARzt8NBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "if rasterize is not None:\n",
    "    r = rasterize(geoms, out_shape=(ml.nrow, ml.ncol), transform=trans)\n",
    "\n",
    "    fig, ax = plt.subplots()\n",
    "    qm = ml.sr.plot_array(r, ax=ax)\n",
    "    ax.set_aspect(1)\n",
    "    plt.colorbar(qm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}