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": [
      "3.6.5 | packaged by conda-forge | (default, Apr  6 2018, 13:44:09) \n",
      "[GCC 4.2.1 Compatible Apple LLVM 6.1.0 (clang-602.0.53)]\n",
      "numpy version: 1.14.5\n",
      "matplotlib version: 2.2.2\n",
      "flopy version: 3.2.10\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "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",
    "# http://spatialreference.org/ref/epsg/nad83-utm-zone-16n/\n",
    "model_epsg = 26915\n",
    "\n",
    "# alternatively, a proj4 string can be supplied\n",
    "model_proj4 = 'http://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",
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       "        [617578.55431287, 617645.20033456, 617711.84635624,\n",
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       "        [617615.49680593, 617682.14282762, 617748.7888493 ,\n",
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       "         618252.25349415],\n",
       "        [617689.38179206, 617756.02781374, 617822.67383543,\n",
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       "        [617800.20927125, 617866.85529293, 617933.50131462,\n",
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       "         618237.02789441, 618303.6739161 , 618370.31993778,\n",
       "         618436.96595947]]),\n",
       " array([[5115472.30845253, 5115509.25094559, 5115546.19343866,\n",
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       "         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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       "  [617956.3397142234, 5115679.111646595]],\n",
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       "  [617593.406077182, 5115390.810666534]],\n",
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       "  [617859.9901639182, 5115538.580638786],\n",
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       "  [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_rc(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": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x10cd2ecc0>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "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": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}