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  {
   "cell_type": "markdown",
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   "source": [
    "# Edelman: sudden change in water level in a confined aquifer\n",
    "\n",
    "Example from Analyical Groundwater Modeling, ch. 5, p. 72."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5d696fd9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import timflow.transient as tft\n",
    "\n",
    "from bruggeman.edelman import h_edelman"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "06691fe9",
   "metadata": {},
   "outputs": [],
   "source": [
    "h_edelman"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c2b4e30e",
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 10.0  # m/d, hydraulic conductivity\n",
    "D = 10.0  # m, thickness of aquifer\n",
    "S = 0.2  # -, storage coeffecient\n",
    "Δh = 2.0  # m, rise in water level\n",
    "t0 = 0.0  # time at which Δh is measured"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "63b3fbda",
   "metadata": {},
   "outputs": [],
   "source": [
    "mlconf = tft.ModelMaq(kaq=k, z=[0, -D], Saq=S, tmin=1, tmax=1e2, topboundary=\"phreatic\")\n",
    "hls = tft.River1D(mlconf, tsandh=[(0, Δh)], layers=[0])\n",
    "mlconf.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f881371c",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(0, 200, 101)\n",
    "y = np.zeros_like(x)\n",
    "t = np.logspace(0, 2, 3)\n",
    "\n",
    "plt.figure(figsize=(10, 3))\n",
    "for i in range(len(t)):\n",
    "    h = mlconf.headalongline(x, y, t[i])\n",
    "    plt.plot(x, h.squeeze(), label=f\"t={t[i]:.0f} d\")\n",
    "    ha = h_edelman(x, t[i], k * D, S, Δh, t0)\n",
    "    plt.plot(x, ha, \"k:\")\n",
    "\n",
    "plt.plot([], [], c=\"k\", ls=\"dotted\", label=\"Edelman\")\n",
    "plt.legend(loc=(0, 1), frameon=False, ncol=6, fontsize=\"small\")\n",
    "plt.xlabel(\"x [m]\")\n",
    "plt.ylabel(\"head [m]\")\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6934cad2",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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