{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8ef12ff3",
   "metadata": {},
   "source": [
    "# Sensitivity analysis\n",
    "\n",
    "### Sensitivity analysis of critical head difference\n",
    "\n",
    "In this example, we demonstrate how to perform a sensitivity analysis. The purpose of a sensitivity analysis is to determine how the model output responds to variations in the input parameters.\n",
    "\n",
    "We use the critical head difference model according to Sellmeijer. This model applies to the piping failure mechanism, which describes backward internal erosion beneath dikes with predominantly horizontal seepage paths.\n",
    "\n",
    "### Define model\n",
    "\n",
    "First, let's import the necessary packages:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "4989b056",
   "metadata": {},
   "outputs": [],
   "source": [
    "from probabilistic_library import SensitivityProject, DistributionType, SensitivityMethod"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76d8a8db",
   "metadata": {},
   "source": [
    "The critical head difference, $H_c$, according to the Sellmeijer's model is described by the following equations:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b6d5845",
   "metadata": {},
   "source": [
    "$F_{resistance}=\\eta\\cdot \\frac{\\gamma_{sub,particles}}{\\gamma_{water}}\\cdot \\tan \\theta_{sellmeijer,rev}$\n",
    "\n",
    "\n",
    "$F_{scale}=\\frac{d_{70.m}}{\\sqrt[3]{\\kappa\\cdot L}}\\cdot\\left(\\frac{d_{70}}{d_{70.m}}\\right)^{0.4}$ and $\\kappa = \\frac{\\nu_{water}}{g}\\cdot k$\n",
    "\n",
    "\n",
    "$F_{geometry}=0.91\\cdot \\left(\\frac{D}{L}\\right)^{\\frac{0.28}{\\left(\\frac{D}{L}\\right)^{2.8}-1}+0.04}$\n",
    "\n",
    "$H_c = F_{resistance} \\cdot F_{scale} \\cdot F_{geometry} \\cdot L$\n",
    "\n",
    "where: <br>\n",
    "$L$ - seepage length (m) <br>\n",
    "$D$ - thickness of upper sand layer (m) <br>\n",
    "$\\theta$ - bedding angle ($\\circ$) <br>\n",
    "$d_{70}$ - particle diameter (m) <br>\n",
    "$k$ - permeability of the upper sand layer (m/s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "abd29107",
   "metadata": {},
   "outputs": [],
   "source": [
    "from utils.models import model_sellmeijer"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c7d0666",
   "metadata": {},
   "source": [
    "### Sensitivity analysis\n",
    "\n",
    "The goal is to estimate the effect of the input parameters $k$, $L$, $d_{70}$, and $D$ on the critical head difference.\n",
    "To achieve this, we perform a sensitivity analysis. We begin by creating a sensitivity project and defining the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "fa1879e9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model model_sellmeijer:\n",
      "Input parameters:\n",
      "  k\n",
      "  L\n",
      "  d70\n",
      "  D\n",
      "Output parameters:\n",
      "  delta_h_c\n"
     ]
    }
   ],
   "source": [
    "project = SensitivityProject()\n",
    "project.model = model_sellmeijer\n",
    "\n",
    "project.model.print()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cde91cc9",
   "metadata": {},
   "source": [
    "We define all the input parameters of the model as random variables:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "ad1ee1db",
   "metadata": {},
   "outputs": [],
   "source": [
    "def project_variables(project):\n",
    "\n",
    "    project.variables[\"k\"].distribution = DistributionType.log_normal\n",
    "    project.variables[\"k\"].mean = 0.000245598\n",
    "    project.variables[\"k\"].variation = 0.25\n",
    "\n",
    "    project.variables[\"L\"].distribution = DistributionType.log_normal\n",
    "    project.variables[\"L\"].mean = 40.0\n",
    "    project.variables[\"L\"].variation = 0.25\n",
    "\n",
    "    project.variables[\"d70\"].distribution = DistributionType.log_normal\n",
    "    project.variables[\"d70\"].mean = 0.00019\n",
    "    project.variables[\"d70\"].variation = 0.25\n",
    "\n",
    "    project.variables[\"D\"].distribution = DistributionType.log_normal\n",
    "    project.variables[\"D\"].mean = 30.0\n",
    "    project.variables[\"D\"].variation = 0.25\n",
    "\n",
    "    return project"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bdb052d7",
   "metadata": {},
   "source": [
    "The sensitivity analysis can be performed using one of two methods: `single_variation` or `sobol`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d508761",
   "metadata": {},
   "source": [
    "### Single variation\n",
    "\n",
    "This method evaluates the effect of varying a single input variable on the model output while keeping all other variables fixed at their median values. It is a straightforward approach, typically used as an initial step before applying more advanced sensitivity analysis techniques.\n",
    "\n",
    "The method produces `low`, `medium`, and `high` quantiles of the model output for each input parameter. The low and high quantiles can be specified by the user in the project settings as `low_value` and `high_value`, respectively. By default, these parameters are set to $0.05$ and $0.95$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "ca737fb9",
   "metadata": {},
   "outputs": [],
   "source": [
    "project_variables(project)\n",
    "project.settings.sensitivity_method = SensitivityMethod.single_variation\n",
    "project.settings.low_value = 0.01\n",
    "project.settings.high_value = 0.99\n",
    "\n",
    "project.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88959dc4",
   "metadata": {},
   "source": [
    "The results of the method are stored in `project.results[0].values`. The results can be printed and plotted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "d8099ee4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter: delta_h_c\n",
      "Values:\n",
      "  k: low = 2.796, medium = 2.31, high = 1.908\n",
      "  L: low = 1.489, medium = 2.31, high = 3.726\n",
      "  d70: low = 1.848, medium = 2.31, high = 2.888\n",
      "  D: low = 2.543, medium = 2.31, high = 2.181\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sens = project.results[0]\n",
    "sens.print()\n",
    "sens.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b821ad38",
   "metadata": {},
   "source": [
    "Let's decrease the variation of the input parameter $L$ and perform the sensitivity analysis again:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "de85ab43",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter: delta_h_c\n",
      "Values:\n",
      "  k: low = 2.854, medium = 2.358, high = 1.948\n",
      "  L: low = 1.962, medium = 2.358, high = 2.852\n",
      "  d70: low = 1.886, medium = 2.358, high = 2.948\n",
      "  D: low = 2.599, medium = 2.358, high = 2.222\n"
     ]
    },
    {
     "data": {
      "image/png": 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3l9TUVGnZsqWfSw8AAAKR481SxV1X48UXXzQbAABAQA8FBwAA8AXCDQAAsArhBgAAWIVwAwAArEK4AQAAViHcAAAAqxBuAACAVQg3AADAKoQbAABgFcKNLXQVOCc2+Af3137cY7txf/2KcAMAAKxCuAEAAFYh3AAAAKsQbgAAgFUINwAAwCqEGwAAYBXCDQAAsArhBgAAWIVwAwAArEK4AQAAViHcAAAAqxBuAACAVQg3AADAKoQbAABgFcINAACwSoTTBQAAAKUj7MkwR97XNcklTqLmBgAAWIVwAwAArEK4AQAAViHcAAAAqxBuAACAVQg3AADAKoQbAABgFcINAACwCuEGAABYhXADAACsQrgBAABWIdwAAACrEG4AAIBVCDcAAMAqhBsAAGAVwg0AALAK4QYAAFiFcAMAAKxCuAEAAFYh3AAAAKsQbgAAgFUINwAAwCqOhpvk5GTp2LGjVK5cWWrVqiWDBg2SnTt3Xva8hQsXSvPmzSUyMlJatWolS5Ys8Ut5AQBA4HM03KxatUrGjh0rX3/9tSxfvlzOnTsnN998s5w6darAc1JTU2Xo0KEyatQo2bRpkwlEum3bts2vZQcAAIEpzOVyuSRAHD161NTgaOi54YYb8j1myJAhJvx8/PHHnn1dunSRNm3ayKxZsy77HtnZ2RITEyNZWVkSHR0tvhYWJo5wiVNvHDB/fOzm0B+ssMmOvK24JoXgnyvusV+E2r/RYRbd3+J8fwdUnxstsKpWrVqBx6xbt0769Onjta9v375mf35ycnLMLyT3BgAA7BUw4ebixYuSmJgo3bp1k+uuu67A4w4dOiS1a9f22qfPdX9B/Xo06bm32NhYn5cdAAAEjoAJN9r3RvvNvPPOOz69blJSkqkRcm+ZmZk+vT4AAAgsERIAxo0bZ/rQrF69Who0aFDosXXq1JHDhw977dPnuj8/5cuXNxsAAAgNjtbcaF9mDTYffvihfPHFF9KoUaPLntO1a1dZsWKF1z4daaX7AQAAIpxuilqwYIEsXrzYzHXj7jejfWMqVKhgHickJEj9+vVN3xn14IMPSo8ePSQlJUX69+9vmrHS0tJk9uzZTn4UhAjnRloAAIKi5mbmzJmmH0zPnj2lbt26nu3dd9/1HJORkSEHDx70PI+PjzeBSMNMXFycvPfee7Jo0aJCOyEDAIDQ4WjNTVGm2Fm5cmWefYMHDzYbnBf2pDNVGSE5DwoAILhGSwEAAPgC4QYAAFiFcAMAAKxCuAEAAFYh3AAAAKsQbgAAgFUINwAAwCoBsbYUAITyDNSKmZsA36HmBgAAWIVwAwAArEK4AQAAViHcAAAAqxBuAACAVQg3AADAKoQbAABgFcINAACwCuEGAABYhXADAACsUqJw8/vf/17++te/5tk/ffp0SUxM9EW5AAAA/Bdu3n//fenWrVue/fHx8fLee++VrCQAAABOhZuffvpJYmJi8uyPjo6WH3/80RflAgAA8F+4adKkiSxdujTP/k8//VQaN25cspIAAAD4QERJTho/fryMGzdOjh49Kr169TL7VqxYISkpKTJt2jRflAsAAMB/4ebee++VnJwcefbZZ+Xpp582+xo2bCgzZ86UhISEkpUEAADAyaHgv/vd72T//v1y+PBhyc7Oln/+8595gs3atWtNCAIAAAiaeW5q1qwplSpVyve1fv36yYEDB670LQAAAAJjEj+Xy1WalwcAAMiDGYoBAIBVCDcAAMAqhBsAAGCVUg03YWFhpXl5AACAPOhQDAAArFKiSfyK6sSJE6V5eQAAAN/U3OjEfb/97W+lXr16EhERIeHh4V4bAABAUNXcjBgxQjIyMuSJJ56QunXr0rcGAAAEd7hZs2aNfPXVV9KmTRvflwgAAMDfzVKxsbF0FgYAAPaEm2nTpsljjz0m+/bt832JAAAA/NEsVbVqVa++NadOnZJrrrlGoqKipGzZsl7H/vzzz1dSJgAAgNIPN1pbAwAAYE24GT58eLEv/vzzz8v9998vVapUKfa5AAAAATdD8XPPPUcTFQAA8CuWXwAAAFZhVXAAAGAVwg0AALAK4QYAAFiFcAMAAKxSquGme/fuUqFChdJ8CwAAgCtfODO3M2fOyNmzZ732RUdHm59Lliy50ssDAACUfs3N6dOnZdy4cVKrVi2pWLGiWZoh91ZUq1evlgEDBki9evXM0g6LFi0q9PiVK1ea4y7dDh06VJKPAQAALFSicDNhwgT54osvZObMmVK+fHl5/fXX5cknnzQh5a233irydXR9qri4OJkxY0ax3n/nzp1y8OBBz6YhCwAAoMTNUh999JEJMT179pSRI0eavjVNmjSRq6++WubPny/33HNPka7Tr18/sxWXhhmWdAAAAD6rudElFRo3buzpX+NeYuH66683TU2lrU2bNlK3bl256aabZO3atYUem5OTI9nZ2V4bAACwV4nCjQabvXv3msfNmzeXv//9754andKsUdFAM2vWLHn//ffNFhsba2qP0tPTCzwnOTlZYmJiPJueAwAA7FWiZiltitqyZYv06NFDHnvsMdMpePr06XLu3DmZOnWqlJZmzZqZzS0+Pl727NkjL774ovzv//5vvuckJSXJ+PHjPc+15oaAAwCAvUoUbh566CHP4z59+sj3338vGzduNP1uWrdu7cvyXVanTp1kzZo1Bb6uHZ51AwAAoaFEzVLamVj7srhpR+Lbb7/dNFEVZ7SUL2zevNk0VwEAAJQ43GizVFZWVp79J06cMK8V1cmTJ0040U1pPx59nJGR4WlSSkhI8Bw/bdo0Wbx4sezevVu2bdsmiYmJZkj62LFjuZsAAKDkzVIul8tMnnep/fv3m067RZWWliY33nij57m7b8zw4cNl7ty5Zg4bd9BROhPyww8/LAcOHJCoqCjTBPb55597XQMAAIS2YoWbtm3bemYF7t27t0RE/Of0CxcumJqXW265pcjX05FOGpQKogEnt0ceecRsAAAAPgk3gwYNMj+16ahv375SqVIlz2vlypWThg0byh133FGcSwIAADgXbiZNmmR+aogZMmSIREZG+rY0AAAATvS50T4xAAAAQR1udLXv/DoR58e9HAMAAEDAhhsdhg0AAGBNuKEpCgAAWDuJn9I1nR5//HEZOnSoHDlyxOz79NNPZfv27b4sHwAAQOmHm1WrVkmrVq1k/fr18sEHH5iZhpUupukeUQUAABA04UZXAn/mmWdk+fLlZn4bt169esnXX3/ty/IBAACUfrjZunWr/PrXv86zv1atWvLjjz+W5JIAAADOhZsqVaqYdZ8utWnTJqlfv74vygUAAOC/cHP33XfLo48+KocOHTJz31y8eFHWrl0rf/jDH7xW8QYAAAiKcPPcc89J8+bNJTY21nQmbtmypXTv3l3i4+PNCCoAAICgWn5BOxG/9tprMnHiRNP/RgOOrhjetGlT35cQAACgNMLN+PHjC3099yipqVOnFqcMAAAA/g832lk4t/T0dDl//rw0a9bMPN+1a5eEh4dL+/btfVc6AACA0go3X375pVfNTOXKlWXevHlmQU117NgxGTlypOl7AwAAEFQdilNSUiQ5OdkTbJQ+1on99DUAAICgCjfZ2dly9OjRPPt134kTJ3xRLgAAAP+FG52dWJugdF2p/fv3m+3999+XUaNGye23316ykgAAADg1FHzWrFlmwr5hw4bJuXPn/n2hiAgTbqZMmeKLcgEAAPgv3ERFRckrr7xigsyePXvMvmuuuUYqVqxYslIAAAA4GW7cNMy0bt3aV2UBAABwps8NAABAoCLcAAAAqxBuAACAVQg3AADAKoQbAABgFcINAACwCuEGAABYhXADAACsQrgBAABWIdwAAACrEG4AAIBVCDcAAMAqhBsAAGAVwg0AALAK4QYAAFiFcAMAAKxCuAEAAFYh3AAAAKsQbgAAgFUINwAAwCqEGwAAYBXCDQAAsArhBgAAWIVwAwAArEK4AQAAViHcAAAAqzgablavXi0DBgyQevXqSVhYmCxatOiy56xcuVLatWsn5cuXlyZNmsjcuXP9UlYAABAcHA03p06dkri4OJkxY0aRjt+7d6/0799fbrzxRtm8ebMkJibK6NGjZdmyZaVeVgAAEBwinHzzfv36ma2oZs2aJY0aNZKUlBTzvEWLFrJmzRp58cUXpW/fvvmek5OTYza37OxsH5QcAAAEqqDqc7Nu3Trp06eP1z4NNbq/IMnJyRITE+PZYmNj/VBSAADglKAKN4cOHZLatWt77dPnWhvzyy+/5HtOUlKSZGVlebbMzEw/lRYAAIRcs5Q/aMdj3QAAQGgIqpqbOnXqyOHDh7326fPo6GipUKGCY+UCAACBI6jCTdeuXWXFihVe+5YvX272AwAAOB5uTp48aYZ06+Ye6q2PMzIyPP1lEhISPMfff//98s9//lMeeeQR+f777+WVV16Rv//97/LQQw859hkAAEBgcTTcpKWlSdu2bc2mxo8fbx5PnDjRPD948KAn6CgdBv7JJ5+Y2hqdH0eHhL/++usFDgMHAAChx9EOxT179hSXy1Xg6/nNPqznbNq0qZRLBgAAglVQ9bkBAAC4HMINAACwCuEGAABYhXADAACsQrgBAABWIdwAAACrEG4AAIBVCDcAAMAqhBsAAGAVwg0AALAK4QYAAFiFcAMAAKxCuAEAAFYh3AAAAKsQbgAAgFUINwAAwCqEGwAAYBXCDQAAsArhBgAAWIVwAwAArEK4AQAAViHcAAAAqxBuAACAVQg3AADAKoQbAABgFcINAACwCuEGAABYhXADAACsQrgBAABWIdwAAACrEG4AAIBVCDcAAMAqhBsAAGAVwg0AALAK4QYAAFiFcAMAAKxCuAEAAFYh3AAAAKsQbgAAgFUINwAAwCqEGwAAYBXCDQAAsArhBgAAWIVwAwAArEK4AQAAViHcAAAAqxBuAACAVQg3AADAKgERbmbMmCENGzaUyMhI6dy5s3zzzTcFHjt37lwJCwvz2vQ8AACAgAg37777rowfP14mTZok6enpEhcXJ3379pUjR44UeE50dLQcPHjQs/3www9+LTMAAAhcjoebqVOnypgxY2TkyJHSsmVLmTVrlkRFRcmcOXMKPEdra+rUqePZateu7dcyAwCAwOVouDl79qxs3LhR+vTp858ClSljnq9bt67A806ePClXX321xMbGysCBA2X79u0FHpuTkyPZ2dleGwAAsJej4ebHH3+UCxcu5Kl50eeHDh3K95xmzZqZWp3FixfL22+/LRcvXpT4+HjZv39/vscnJydLTEyMZ9NABAAA7OV4s1Rxde3aVRISEqRNmzbSo0cP+eCDD6RmzZry6quv5nt8UlKSZGVlebbMzEy/lxkAAPhPhDioRo0aEh4eLocPH/bar8+1L01RlC1bVtq2bSu7d+/O9/Xy5cubDQAAhAZHa27KlSsn7du3lxUrVnj2aTOTPtcamqLQZq2tW7dK3bp1S7GkAAAgWDhac6N0GPjw4cOlQ4cO0qlTJ5k2bZqcOnXKjJ5S2gRVv35903dGPfXUU9KlSxdp0qSJHD9+XKZMmWKGgo8ePdrhTwIAAAKB4+FmyJAhcvToUZk4caLpRKx9aZYuXerpZJyRkWFGULkdO3bMDB3XY6tWrWpqflJTU80wcgAAgDCXy+WSEKJDwXXUlHYu1skAfS0sTBzhEmfeOGyyI28rrknO/LHl/vpHqN1fxT32D/4OB+/9Lc73d9CNlgIAACgM4QYAAFiFcAMAAKxCuAEAAFYh3AAAAKsQbgAAgFUINwAAwCqEGwAAYBXCDQAAsArhBgAAWIVwAwAArEK4AQAAViHcAAAAqxBuAACAVQg3AADAKoQbAABgFcINAACwCuEGAABYhXADAACsQrgBAABWIdwAAACrEG4AAIBVCDcAAMAqhBsAAGAVwg0AALAK4QYAAFiFcAMAAKxCuAEAAFYh3AAAAKsQbgAAgFUINwAAwCqEGwAAYBXCDQAAsArhBgAAWIVwAwAArEK4AQAAViHcAAAAqxBuAACAVQg3AADAKoQbAABgFcINAACwCuEGAABYhXADAACsQrgBAABWIdwAAACrEG4AAIBVCDcAAMAqhBsAAGAVwg0AALBKQISbGTNmSMOGDSUyMlI6d+4s33zzTaHHL1y4UJo3b26Ob9WqlSxZssRvZQUAAIHN8XDz7rvvyvjx42XSpEmSnp4ucXFx0rdvXzly5Ei+x6empsrQoUNl1KhRsmnTJhk0aJDZtm3b5veyAwCAwON4uJk6daqMGTNGRo4cKS1btpRZs2ZJVFSUzJkzJ9/jX3rpJbnllltkwoQJ0qJFC3n66aelXbt2Mn36dL+XHQAABJ4IJ9/87NmzsnHjRklKSvLsK1OmjPTp00fWrVuX7zm6X2t6ctOankWLFuV7fE5OjtncsrKyzM/s7GyxiWOf5owzb2vb/bsc7q/9uMd24/767poul+vyB7scdODAAS2hKzU11Wv/hAkTXJ06dcr3nLJly7oWLFjgtW/GjBmuWrVq5Xv8pEmTzHuwsbGxsbGxSdBvmZmZl80Xjtbc+IPWCuWu6bl48aL8/PPPUr16dQkLC5NQp0k4NjZWMjMzJTo62uniwMe4v/bjHtuN+/sfWmNz4sQJqVevnlyOo+GmRo0aEh4eLocPH/bar8/r1KmT7zm6vzjHly9f3my5ValS5YrLbhv9SxPqf3Fsxv21H/fYbtzff4uJiZGA71Bcrlw5ad++vaxYscKrZkWfd+3aNd9zdH/u49Xy5csLPB4AAIQWx5ultMlo+PDh0qFDB+nUqZNMmzZNTp06ZUZPqYSEBKlfv74kJyeb5w8++KD06NFDUlJSpH///vLOO+9IWlqazJ492+FPAgAAAoHj4WbIkCFy9OhRmThxohw6dEjatGkjS5culdq1a5vXMzIyzAgqt/j4eFmwYIE8/vjj8sc//lGaNm1qRkpdd911Dn6K4KVNdjrH0KVNd7AD99d+3GO7cX9LJkx7FZfwXAAAgIDj+CR+AAAAvkS4AQAAViHcAAAAqxBuQlTPnj0lMTHR6WIAKCL+zgJFR7gBLDVixAgZNGiQ08VAKdDZ1fPbpkyZ4jlGZ2K/5557zMRvOnHpqFGj5OTJk46WG0X/u+u+p2XLljWjh2+66SazoLTOBYfLI9wAQJA5ePCg16ZfevpFeMcdd3iO0WCzfft2M8npxx9/LKtXr5b77rvP0XKj6G655RZzb/ft2yeffvqp3HjjjWaet9tuu03Onz/vdPECHuEGxieffGKmtZ4/f77TRQFCnk5kqhOYVqpUSerWrWsmLc1Nl5vJvS1evNh8+TVu3Ni8vmPHDjNf2Ouvvy6dO3eW66+/Xl5++WUz6em//vUvhz4VikPntdF7q5PYtmvXzszrpvdZg87cuXOdLl7AI9zATIo4dOhQE2z0f3sAnDVhwgRZtWqV+TL77LPPZOXKlZKenp7vsbq2nv7nRJud3NatW2eaonTmd7c+ffqYCVHXr1/vl88A3+vVq5fExcXJBx984HRRAp7jMxTDWTNmzJA//elP8tFHH5llLQA4S/vFvPHGG/L2229L7969zb558+ZJgwYN8j1eX6tcubLcfvvtnn0623utWrW8jouIiJBq1aqZ1xC8mjdvLt9++63TxQh4hJsQ9t5778mRI0dk7dq10rFjR6eLA0BE9uzZI2fPnjXNSW4aSpo1a5bv8drfRmtcIyMj/VhKOEUXFdD+VSgczVIhrG3btlKzZk3zjyOrcADB56uvvpKdO3fK6NGjvfZrXw39j0tu2glVR1Dpawhe2p+qUaNGThcj4BFuQtg111wjX375pWnXf+CBB5wuDoD///dSh//m7htz7Ngx2bVrV55jtfmqffv2ph9Gbl27dpXjx4/Lxo0bPfu++OILM4w4d40Qgovew61bt3qNikP+aJYKcb/61a9MwNEJwrRNftq0aU4XCT6UlZUlmzdv9tpXvXp1iY2NdaxMKJyOkNLOwdqpWO+V9p3RfnHaGTi37OxsWbhwYZ6RVKpFixZmKPGYMWNk1qxZcu7cORk3bpzcfffdUq9ePT9+GpRUTk6O6R914cIF02lcR78lJyeboeA6kg6FI9zAtOXr/wg04ISHh+f7jyWCk46y0ebH3PSLU4cII3DpZHzasXjAgAGms/DDDz9sgmpuOqxbm5N1pGN+dPSjBhrtlKzBSP+3/9e//tVPnwBXSsOMTgOg/+msWrWqqZ3T+zd8+PA8QRd5hbnobAEAACxC/AMAAFYh3AAAAKsQbgAAgFUINwAAwCqEGwAAYBXCDQAAsArhBgAAWIVwAwAArEK4ARA09u3bZ1ZEvnRJicKMGDFCBg0aVOgxOjt3YmKiD0oIIBCw/AKAoKFrYh08eFBq1KjhdFEABDDCDYCgcPbsWSlXrpzUqVPH6aIACHA0SwHwudmzZ5vVpy9evOi1f+DAgXLvvffKnj17zOPatWubVbA7duwon3/+udexDRs2lKefftqsgBwdHS333XdfnmYpXTFZFwJt1KiRVKhQwSwC+9JLL+VbpieffFJq1qxprnX//febsFTYisx/+MMfpH79+lKxYkXp3LmzWYTU7YcffjCLWuqChvr6tddeK0uWLLnC3xoAX6HmBoDPDR48WB544AH58ssvzarU6ueffzYrHWsI0BWvb731Vnn22WelfPny8tZbb5mwsHPnTrnqqqs81/nLX/4iEydOlEmTJuX7PhqeGjRoIAsXLpTq1atLamqqCUG6mvJdd93lOW7FihUSGRlpAooGpJEjR5rj9f3zo6tpf/fdd2blbQ1pH374odxyyy2ydetWadq0qYwdO9aEo9WrV5two8dqSAMQIHRVcADwtYEDB7ruvfdez/NXX33VVa9ePdeFCxfyPf7aa691vfzyy57nV199tWvQoEFex+zdu9el/2xt2rSpwPcdO3as64477vA8Hz58uKtatWquU6dOefbNnDnTValSJU9ZevTo4XrwwQfN4x9++MEVHh7uOnDggNd1e/fu7UpKSjKPW7Vq5Zo8eXKRfxcA/ItmKQCl4p577pH333/fNPGo+fPny9133y1lypQxNTfa7NOiRQupUqWKqfXYsWOHZGRkeF2jQ4cOl32fGTNmSPv27U2Tk15Hm8QuvU5cXJxERUV5nnft2tWUITMzM8/1tHZGm7t+9atfmeu5t1WrVpnmNPX73/9ennnmGenWrZupVfr2229L/HsC4Hs0SwEoFdrM5HK55JNPPjF9ar766it58cUXzWsabJYvX26anZo0aWL6y9x55515+sFok09htNlIr5WSkmICS+XKlWXKlCmyfv36EpdbQ094eLhs3LjR/MzN3fQ0evRo6du3r/lsn332mSQnJ5syaFMcAOcRbgCUCu3jcvvtt5sam927d5vOvu3atTOvrV271sw/8+tf/9oTKLQvTHHpdeLj4+V//ud/PPvctSu5bdmyRX755RcTotTXX39tgooOLb9U27ZtTc3NkSNHpHv37gW+t56rHZN1S0pKktdee41wAwQImqUAlGrTlNZuzJkzxzx20065H3zwgRn1pMFj2LBheUZWFYVeJy0tTZYtWya7du2SJ554QjZs2JDnOK0R0lFV2vFXOzRrU5J2GtYmsktpc5SWVUdpaRn37t0r33zzjamd0c+idMI/fU99LT093XSc1iY2AIGBcAOg1PTq1UuqVatmRkFpgHGbOnWqGUattS7afKVNPO5aneL47//+b1M7NGTIEDNc+6effvKqxXHTEVsahG644QZz7H/913/J5MmTC7zum2++acLNww8/bGqcdIZjDU3ukVxas6MjpjTQ6CgqDUSvvPJKscsPoHSEaa/iUro2AACA31FzAwAArEK4AQAAViHcAAAAqxBuAACAVQg3AADAKoQbAABgFcINAACwCuEGAABYhXADAACsQrgBAABWIdwAAACxyf8DvZ+T9cqgoEIAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "project.variables[\"L\"].variation = 0.1\n",
    "\n",
    "project.run()\n",
    "sens = project.results[0]\n",
    "sens.print()\n",
    "sens.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75804902",
   "metadata": {},
   "source": [
    "### Sobol indices\n",
    "\n",
    "The Sobol method is a variance-based sensitivity analysis that decomposes the variance of the model output into fractions attributable to individual input parameters. The method produces a `first order index` and a `total index` for each input parameter. \n",
    "\n",
    "The `first order index` measures the effect of varying a single parameter on the output, averaged over variations in all other input parameters. The `total index` quantifies the contribution of a parameter to the output variance, including all variance arising from its interactions with other input variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "71bde011",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter: delta_h_c\n",
      "Values:\n",
      "  k: first order index = 0.1207, total index = 0.1224\n",
      "  L: first order index = 0.6698, total index = 0.6999\n",
      "  d70: first order index = 0.1592, total index = 0.1671\n",
      "  D: first order index = 0.02125, total index = 0.02487\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "project = project_variables(project)\n",
    "project.settings.sensitivity_method = SensitivityMethod.sobol\n",
    "\n",
    "project.run()\n",
    "sens = project.results[0]\n",
    "sens.print()\n",
    "sens.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "886391a2",
   "metadata": {},
   "source": [
    "Let's decrease the variance of the parameter $L$ and recompute the Sobol indices:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "0ee2fde1",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "gallery",
     "uncertainty"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter: delta_h_c\n",
      "Values:\n",
      "  k: first order index = 0.2796, total index = 0.2888\n",
      "  L: first order index = 0.2537, total index = 0.2754\n",
      "  d70: first order index = 0.3816, total index = 0.394\n",
      "  D: first order index = 0.0522, total index = 0.05352\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "project.variables[\"L\"].variation = 0.1\n",
    "\n",
    "project.run()\n",
    "sens = project.results[0]\n",
    "sens.print()\n",
    "sens.plot()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "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": "3.12.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}