groundwater_dupuit_percolator_example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# This notebook illustrates the usage of the GroundwaterDupuitPercolator Landlab component\n",
    "\n",
    "The GroundwaterDupuitPercolator is a simple Landlab component that simulates a shallow, unconfined aquifer using the Dupuit approximation, also known as the shallow-aquifer approximation. This approximation treats the horizontal hydraulic gradient as identical to the slope of the water table, and is appropriate for aquifers that are much wider than they are thick.\n",
    "\n",
    "## Governing equations\n",
    "\n",
    "Imagine an unconfined aquifer in which the height of the water table, $W$, varies both in space and time. The porosity of the aquifer is $\\phi$. The aquifer sits on top of an impermeable geologic unit, and the elevation of the that unit is $b$ (for \"base\"). The base elevation can also vary with position. The thickness of the aquifer, $H$, at any given point is therefore the difference between the water table height and the aquifer's base:\n",
    "\n",
    "$H = W - b$.\n",
    "\n",
    "The aquifer receives water through recharge (infiltration of rain and snow melt), at a rate of $R$ (depth per time). It could also lose water through surface seepage, where the water table intersects the ground surface (this is a feature to be added to a future version). It might also lose water through pumping, which we'll describe below.\n",
    "\n",
    "The horizontal groundwater velocity is $\\mathbf{u}$. It's also useful to think in terms of the discharge per unit width, $\\mathbf{q}$, which is the product of velocity and thickness. Mass balance dictates that:\n",
    "\n",
    "$\\phi \\frac{\\partial H}{\\partial t} = R - \\left( \\frac{\\partial q_x}{\\partial x} + \\frac{\\partial q_y}{\\partial y} \\right)$,\n",
    "\n",
    "where $q_x$ and $q_y$ are the components of discharge in the $x$ and $y$ directions, respectively (so, for example, $q_x$ might represent eastward flow and $q_y$ northward flow; a negative value would indicate that flow is to the west or south).\n",
    "\n",
    "The discharge is described by Darcy's law, again using the approximation that the hydraulic gradient is equal to the water-table slope:\n",
    "\n",
    "$q_x = -K H \\frac{\\partial W}{\\partial x}$, and\n",
    "\n",
    "$q_y = -K H \\frac{\\partial W}{\\partial y}$.\n",
    "\n",
    "Note here that we are assuming isotropic conductivity.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numerical solution\n",
    "\n",
    "We divide the domain up into a grid of cells. As with many other Landlab components, the grid maybe a regular \"raster\" with square cells, or hexagonal, or even irregular. In this description, we'll assume the cells are square and $\\Delta x$ wide, but the principles apply generally.\n",
    "\n",
    "As with most Landlab grids, the grid is composed of a set of *nodes*. Each of the interior nodes (the ones not along the grid perimeters) lives inside a *cell*. Each adjacent pair of nodes is connected by a *link*, which has a direction: one node is the tail node, and one is the head node. Cells have *faces*, which in a regular raster with uniform spacing are also $\\Delta x$ wide.\n",
    "\n",
    "The water-table gradient at each link $i$ is calculated using:\n",
    "\n",
    "$G_j = (W_{jh} - W_{jt}) / L_j$,\n",
    "\n",
    "where $W_{jh}$ is the water-table elevation of the head node of link $j$, $W_{jt}$ is the tail node, and $L_j$ is the length of link $j$ (equal to $\\Delta x$ in a uniform raster grid).\n",
    "\n",
    "The groundwater velocity at each link $j$ is:\n",
    "\n",
    "$u_j = -K_j G_j$,\n",
    "\n",
    "where $K_j$ is the conductivity at link $j$ (note that the user can choose whether to make conductivity uniform or spatially varying; if uniform, then of course all the $K_j$ values are the same).\n",
    "\n",
    "The groundwater discharge at each link $j$ is:\n",
    "\n",
    "$q_j = u_j H_j$,\n",
    "\n",
    "where the aquifer depth at the link, $H_j$, is the average of the depth at the two bounding nodes:\n",
    "\n",
    "$H_j = (H_{jh} + H_{jt} ) / 2$.\n",
    "\n",
    "Once discharge has been calculated, the water-table thicknesses are updated using the following, which is an explicit forward-in-time method:\n",
    "\n",
    "$H_i^{t+1} = H_i^t + R\\Delta t + \\Delta t \\Sigma_{j=1}^{N_i} q_j \\lambda_j \\delta_{ij}$.\n",
    "\n",
    "The last term on the right represents adding up all in the ground inflows and outflows at the $N_i$ faces of the cell that contains node $i$. If the grid is a uniform rectilinear one (e.g., a Landlab RasterModelGrid), then $N_i = 4$ (except when there are closed boundaries on one or more sides of the cell, in which case $N_i$ would be less than 4). Here $\\lambda_j$ is the width of the cell face crossed by link $j$, and $\\delta_{ij}$ is either 1 or -1: it is 1 if the link points *into* the cell, and -1 if it points *out* of the cell. The time step size is $\\Delta t$. The subscript represents time step number: $H^t$ is thickness at the end of the previous time step, and $H^{t+1}$ is thickness at the end of the new time step."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1: simple steady, sloping aquifer\n",
    "\n",
    "In this example, we have an idealized 1 km2 area divided into 20 x 20 m cells. The water table on the left (west) is 10 m higher than on the east, which sets up a west-to-east flow. We can experiment with introducing a collection of pumping locations. Pumping is simulated by modifying a matrix of recharge values: we'll set recharge to zero (for simplicity) everywhere but at a few select locations, representing wells, where water is pumped at a given rate.\n",
    "\n",
    "Start by importing some packages:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from landlab import RasterModelGrid\n",
    "from landlab import imshow_grid\n",
    "import matplotlib.pyplot as plt\n",
    "from dupuit_percolator import GroundwaterDupuitPercolator\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a Landlab grid, with north and south boundaries closed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xd1f019b00>]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "boundaries = {'top': 'closed', 'bottom': 'closed'}\n",
    "grid = RasterModelGrid((51, 51), spacing=20.0, bc=boundaries)\n",
    "plt.plot(grid.x_of_node, grid.y_of_node, 'k.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create some fields. These will include elevation (which doesn't do anything in the current version of the model, but we can use it assess the depth to the water table), the water table height, and the water table base. We'll set the elevation to a uniform 100 m. The water table will slope down from west to east by 10 m over 1 km. The water table height will be fixed at 90 m at the left (west) boundary, and at 80 m at the right (east). The base will likewise slope downward from 40 m at left to 30 m at right, so when the flow is steady, the aquifer has uniform thickness.\n",
    "\n",
    "We give each field the name required by the GroundwaterDupuitPercolator component (otherwise, it won't recognize these as the proper fields)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "elev = grid.add_zeros('node', 'topographic__elevation')\n",
    "elev += 100\n",
    "base = grid.add_zeros('node', 'aquifer_base__elevation')\n",
    "base[:] = 40.0 - 0.01 * grid.x_of_node\n",
    "wtable = grid.add_zeros('node', 'water_table__elevation')\n",
    "wtable[:] = 90.0 - 0.01 * grid.x_of_node"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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": [
    "imshow_grid(grid, 'topographic__elevation')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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": [
    "imshow_grid(grid, 'aquifer_base__elevation')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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": [
    "imshow_grid(grid, 'water_table__elevation')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll make an array for recharge rate, in meters per second. Initially, it will be all zeros; later, we'll add negative values to certain nodes to represent pumping. We'll make it a field so that if we later decide to write output to a file, it will be included."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "recharge = grid.add_zeros('node', 'recharge_rate')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, make a component:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "gdp = GroundwaterDupuitPercolator(grid, recharge_rate='recharge_rate', hydraulic_conductivity=0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now run the component. If we've set everything up right, we should have a velocity from left to right of 0.0001 m/s. This comes from Darcy's law: we have a conductivity of 0.01 m/s (pretty conductive), and a gradient of -0.01; so minus conductivity times gradient gives 0.0001 m/s. Let's test it out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00010000000000000143"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gdp.run_one_step(1.0)\n",
    "np.amax(gdp.vel)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The velocity should be 0.0001 at \"horizontal\" (east-west) links, and zero elsewhere. We can test this by inspecting just horizontal links (some will still have zero values; these are boundary links). We'll do the same for discharge too. It should be 0.0001 m/s times 50 m = 0.005 m2/s."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.00000000e+00,   0.00000000e+00,   0.00000000e+00, ...,\n",
       "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00],\n",
       "       [  1.00000000e-04,   1.00000000e-04,   1.00000000e-04, ...,\n",
       "          1.00000000e-04,   1.00000000e-04,   1.00000000e-04],\n",
       "       [  1.00000000e-04,   1.00000000e-04,   1.00000000e-04, ...,\n",
       "          1.00000000e-04,   1.00000000e-04,   1.00000000e-04],\n",
       "       ..., \n",
       "       [  1.00000000e-04,   1.00000000e-04,   1.00000000e-04, ...,\n",
       "          1.00000000e-04,   1.00000000e-04,   1.00000000e-04],\n",
       "       [  1.00000000e-04,   1.00000000e-04,   1.00000000e-04, ...,\n",
       "          1.00000000e-04,   1.00000000e-04,   1.00000000e-04],\n",
       "       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00, ...,\n",
       "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gdp.vel[grid.horizontal_links]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.   ,  0.   ,  0.   , ...,  0.   ,  0.   ,  0.   ],\n",
       "       [ 0.005,  0.005,  0.005, ...,  0.005,  0.005,  0.005],\n",
       "       [ 0.005,  0.005,  0.005, ...,  0.005,  0.005,  0.005],\n",
       "       ..., \n",
       "       [ 0.005,  0.005,  0.005, ...,  0.005,  0.005,  0.005],\n",
       "       [ 0.005,  0.005,  0.005, ...,  0.005,  0.005,  0.005],\n",
       "       [ 0.   ,  0.   ,  0.   , ...,  0.   ,  0.   ,  0.   ]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gdp.q[grid.horizontal_links]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 2: pumping\n",
    "\n",
    "For the next example, we will put a pump in the middle of the domain, and withdraw 0.02 m3/s (about 1700 m3/day). We expect to see a cone of depression around the pump location."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "80.0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gdp.recharge[1301] = -0.020\n",
    "np.amin(gdp.wtable)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now run the model for some period of time and look at the result:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "dt = 100.0  # time step in seconds (rough guess at stability)\n",
    "for i in range(10000):  # about 12 days\n",
    "    gdp.run_one_step(dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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": [
    "imshow_grid(grid, 'water_table__elevation')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "68.888289270433461"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.amin(grid.at_node['water_table__elevation'])  # how low has water in the well gone?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now turn off the pump and let the system recover:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "gdp.recharge[1301] = 0.0\n",
    "for i in range(100):\n",
    "    gdp.run_one_step(dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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": [
    "imshow_grid(grid, 'water_table__elevation')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, we have used a high conductivity, so it responds quite quickly. Using a lower conductivity would produce a slower response, and would also allow larger time steps."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 3: steady convex water table with recharge\n",
    "\n",
    "In this example, we use a long, narrow domain, and set only the east boundary open. Steady, uniform recharge is applied. The expected analytical solution for the steady case is as follows. With a groundwater divide at the left boundary, the flow is to the right (increasing $x$). The input from recharge at a given position $x$ is:\n",
    "\n",
    "$q_{in} = Rx$.\n",
    "\n",
    "The output is given by Darcy's law:\n",
    "\n",
    "$q_{out} = -K H \\frac{dH}{dx} = -\\frac{K}{2}\\frac{dH^2}{dx}$.\n",
    "\n",
    "Setting the two equal,\n",
    "\n",
    "$\\frac{dH^2}{dx} = -\\frac{2R}{K} x$.\n",
    "\n",
    "As a boundary condition, we'll say that the water table height at the right side, a distance $L$ from the groundwater divide, is $H_L$. We can then integrate:\n",
    "\n",
    "$\\int_0^y x$\n",
    "\n",
    "$\\int_H^{H_L} dH^2 = -\\frac{2R}{K} \\int_x^L x dx$\n",
    "\n",
    "$H_L^2 - H^2 = -\\frac{R}{K} (L^2 - x^2)$\n",
    "\n",
    "$H^2 = H_L^2 + \\frac{R}{K} (L^2 - x^2)$\n",
    "\n",
    "$H = \\sqrt{H_L^2 + \\frac{R}{K} (L^2 - x^2)}$.\n",
    "\n",
    "For $H_L=0$, the expected height at the divide is $\\sqrt{RL^2/K}$, and the equation can be nondimensionalized as:\n",
    "\n",
    "$H' = \\frac{H}{\\sqrt{RL^2/K}} = \\sqrt{(1 - x'^2)}$, for $0 \\le x \\le 1$.\n",
    "\n",
    "We can visualize the solution:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, \"H'\")"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xprime = np.arange(0, 1, 0.01)\n",
    "hprime = np.sqrt(1.0 - xprime * xprime)\n",
    "plt.plot(xprime, hprime)\n",
    "plt.xlabel(\"x'\")\n",
    "plt.ylabel(\"H'\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The curve looks this way because as you go left to right, the system needs to carry more water, yet it is thinner, so it has to increase the water-table slope to compensate.\n",
    "\n",
    "We'll configure a dimensional version of this with the GroundwaterDupuitPercolator component."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted water table height at divide, meters: 33.166247903553995\n"
     ]
    }
   ],
   "source": [
    "R = 1.0e-7  # steady, uniform recharge rate, in m/s\n",
    "K = 0.0001  # uniform hydraulic conductivity, in m/s\n",
    "L = 1000.0  # domain length, m\n",
    "HL = 10.0   # aquifer thickness at right boundary, m\n",
    "\n",
    "H0 = (HL * HL + (R / K) * (L * L)) ** 0.5\n",
    "print('Predicted water table height at divide, meters: ' + str(H0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "boundaries = {'top': 'closed', 'left': 'closed', 'bottom': 'closed'}\n",
    "grid2 = RasterModelGrid((5, 41), spacing=25.0, bc=boundaries)\n",
    "elev2 = grid2.add_zeros('node', 'topographic__elevation')\n",
    "elev2[:] = 35.0\n",
    "base2 = grid2.add_zeros('node', 'aquifer_base__elevation')\n",
    "wt2 = grid2.add_zeros('node', 'water_table__elevation')\n",
    "wt2[:] = HL\n",
    "gdp2 = GroundwaterDupuitPercolator(grid2, hydraulic_conductivity=K, recharge_rate=R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Water table height (m)')"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "middle_row = np.where(grid2.y_of_node == 75.0)[0][1:]\n",
    "plt.plot(grid2.x_of_node[middle_row], wt2[middle_row])\n",
    "plt.xlabel('Distance (m)')\n",
    "plt.ylabel('Water table height (m)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xd1f512710>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dt = 8.0e4\n",
    "for i in range(10000):\n",
    "    gdp2.run_one_step(dt)\n",
    "plt.plot(grid2.x_of_node[middle_row], wt2[middle_row], 'k.-')\n",
    "plt.xlabel('Distance (m)')\n",
    "plt.ylabel('Water table height (m)')\n",
    "plt.ylim([0.0, 35.0])\n",
    "x = grid2.x_of_node[middle_row]\n",
    "y = (HL * HL + (R/K)*(L*L - x*x))**0.5\n",
    "plt.plot(x, y, 'r')\n",
    "plt.legend(['Numerical solution', 'Analytical solution'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "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": [
    "imshow_grid(grid2, wt2)"
   ]
  }
 ],
 "metadata": {
  "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": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}