{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # only need to import the function you want to use\n",
    "#     # secondary functions, that are called within the imported one, don't need to be importex explicitly\n",
    "# from volume_change import V_von_h\n",
    "\n",
    "# V_von_h(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create in and outflux vectors\n",
    "import numpy as np\n",
    "from numpy import cos,sin\n",
    "from volume_change import V_h,h_V\n",
    "\n",
    "t_max = 2600\n",
    "timestep = 10**-2\n",
    "time = np.arange(0,t_max,timestep)\n",
    "\n",
    "#scaling factor in_out\n",
    "# sf_in_out = 1000\n",
    "# influx = sf_in_out*cos(time)*np.exp(-0.01*time)+0.01*time\n",
    "# outflux = sf_in_out*sin(0.5*time)*np.exp(-0.01*time)\n",
    "# scaling factor in_out\n",
    "influx = 75*np.ones_like(time)\n",
    "outflux = 0.001*time**1.75\n",
    "outflux[outflux > 90] = 90\n",
    "\n",
    "\n",
    "h_0 = 0\n",
    "\n",
    "V_t = np.empty_like(time)\n",
    "h_t = np.empty_like(time)\n",
    "delta_Q = np.empty_like(time)\n",
    "delta_V = np.empty_like(time)\n",
    "\n",
    "for i in range(len(time)):\n",
    "    delta_Q[i] = influx[i]-outflux[i]\n",
    "    delta_V[i] = delta_Q[i]*timestep\n",
    "    if i == 0:\n",
    "        V_t[0] = V_h(h_0)\n",
    "    else:\n",
    "        V_t[i] = V_t[i-1]+delta_V[i]\n",
    "    \n",
    "    h_t[i] = h_V(V_t[i])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
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          1982,
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          1983,
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          2016.95,
          2016.96,
          2016.97,
          2016.98,
          2016.99,
          2017,
          2017.01,
          2017.02,
          2017.03,
          2017.04,
          2017.05,
          2017.06,
          2017.07,
          2017.0800000000002,
          2017.0900000000001,
          2017.1000000000001,
          2017.1100000000001,
          2017.1200000000001,
          2017.13,
          2017.14,
          2017.15,
          2017.16,
          2017.17,
          2017.18,
          2017.19,
          2017.2,
          2017.21,
          2017.22,
          2017.23,
          2017.24,
          2017.25,
          2017.26,
          2017.27,
          2017.28,
          2017.29,
          2017.3,
          2017.31,
          2017.32,
          2017.3300000000002,
          2017.3400000000001,
          2017.3500000000001,
          2017.3600000000001,
          2017.3700000000001,
          2017.38,
          2017.39,
          2017.4,
          2017.41,
          2017.42,
          2017.43,
          2017.44,
          2017.45,
          2017.46,
          2017.47,
          2017.48,
          2017.49,
          2017.5,
          2017.51,
          2017.52,
          2017.53,
          2017.54,
          2017.55,
          2017.56,
          2017.57,
          2017.5800000000002,
          2017.5900000000001,
          2017.6000000000001,
          2017.6100000000001,
          2017.6200000000001,
          2017.63,
          2017.64,
          2017.65,
          2017.66,
          2017.67,
          2017.68,
          2017.69,
          2017.7,
          2017.71,
          2017.72,
          2017.73,
          2017.74,
          2017.75,
          2017.76,
          2017.77,
          2017.78,
          2017.79,
          2017.8,
          2017.81,
          2017.82,
          2017.8300000000002,
          2017.8400000000001,
          2017.8500000000001,
          2017.8600000000001,
          2017.8700000000001,
          2017.88,
          2017.89,
          2017.9,
          2017.91,
          2017.92,
          2017.93,
          2017.94,
          2017.95,
          2017.96,
          2017.97,
          2017.98,
          2017.99,
          2018,
          2018.01,
          2018.02,
          2018.03,
          2018.04,
          2018.05,
          2018.06,
          2018.07,
          2018.0800000000002,
          2018.0900000000001,
          2018.1000000000001,
          2018.1100000000001,
          2018.1200000000001,
          2018.13,
          2018.14,
          2018.15,
          2018.16,
          2018.17,
          2018.18,
          2018.19,
          2018.2,
          2018.21,
          2018.22,
          2018.23,
          2018.24,
          2018.25,
          2018.26,
          2018.27,
          2018.28,
          2018.29,
          2018.3,
          2018.31,
          2018.32,
          2018.3300000000002,
          2018.3400000000001,
          2018.3500000000001,
          2018.3600000000001,
          2018.3700000000001,
          2018.38,
          2018.39,
          2018.4,
          2018.41,
          2018.42,
          2018.43,
          2018.44,
          2018.45,
          2018.46,
          2018.47,
          2018.48,
          2018.49,
          2018.5,
          2018.51,
          2018.52,
          2018.53,
          2018.54,
          2018.55,
          2018.56,
          2018.57,
          2018.5800000000002,
          2018.5900000000001,
          2018.6000000000001,
          2018.6100000000001,
          2018.6200000000001,
          2018.63,
          2018.64,
          2018.65,
          2018.66,
          2018.67,
          2018.68,
          2018.69,
          2018.7,
          2018.71,
          2018.72,
          2018.73,
          2018.74,
          2018.75,
          2018.76,
          2018.77,
          2018.78,
          2018.79,
          2018.8,
          2018.81,
          2018.82,
          2018.8300000000002,
          2018.8400000000001,
          2018.8500000000001,
          2018.8600000000001,
          2018.8700000000001,
          2018.88,
          2018.89,
          2018.9,
          2018.91,
          2018.92,
          2018.93,
          2018.94,
          2018.95,
          2018.96,
          2018.97,
          2018.98,
          2018.99,
          2019,
          2019.01,
          2019.02,
          2019.03,
          2019.04,
          2019.05,
          2019.06,
          2019.07,
          2019.0800000000002,
          2019.0900000000001,
          2019.1000000000001,
          2019.1100000000001,
          2019.1200000000001,
          2019.13,
          2019.14,
          2019.15,
          2019.16,
          2019.17,
          2019.18,
          2019.19,
          2019.2,
          2019.21,
          2019.22,
          2019.23,
          2019.24,
          2019.25,
          2019.26,
          2019.27,
          2019.28,
          2019.29,
          2019.3,
          2019.31,
          2019.32,
          2019.3300000000002,
          2019.3400000000001,
          2019.3500000000001,
          2019.3600000000001,
          2019.3700000000001,
          2019.38,
          2019.39,
          2019.4,
          2019.41,
          2019.42,
          2019.43,
          2019.44,
          2019.45,
          2019.46,
          2019.47,
          2019.48,
          2019.49,
          2019.5,
          2019.51,
          2019.52,
          2019.53,
          2019.54,
          2019.55,
          2019.56,
          2019.57,
          2019.5800000000002,
          2019.5900000000001,
          2019.6000000000001,
          2019.6100000000001,
          2019.6200000000001,
          2019.63,
          2019.64,
          2019.65,
          2019.66,
          2019.67,
          2019.68,
          2019.69,
          2019.7,
          2019.71,
          2019.72,
          2019.73,
          2019.74,
          2019.75,
          2019.76,
          2019.77,
          2019.78,
          2019.79,
          2019.8,
          2019.81,
          2019.82,
          2019.8300000000002,
          2019.8400000000001,
          2019.8500000000001,
          2019.8600000000001,
          2019.8700000000001,
          2019.88,
          2019.89,
          2019.9,
          2019.91,
          2019.92,
          2019.93,
          2019.94,
          2019.95,
          2019.96,
          2019.97,
          2019.98,
          2019.99,
          2020,
          2020.01,
          2020.02,
          2020.03,
          2020.04,
          2020.05,
          2020.06,
          2020.07,
          2020.0800000000002,
          2020.0900000000001,
          2020.1000000000001,
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          2020.1200000000001,
          2020.13,
          2020.14,
          2020.15,
          2020.16,
          2020.17,
          2020.18,
          2020.19,
          2020.2,
          2020.21,
          2020.22,
          2020.23,
          2020.24,
          2020.25,
          2020.26,
          2020.27,
          2020.28,
          2020.29,
          2020.3,
          2020.31,
          2020.32,
          2020.3300000000002,
          2020.3400000000001,
          2020.3500000000001,
          2020.3600000000001,
          2020.3700000000001,
          2020.38,
          2020.39,
          2020.4,
          2020.41,
          2020.42,
          2020.43,
          2020.44,
          2020.45,
          2020.46,
          2020.47,
          2020.48,
          2020.49,
          2020.5,
          2020.51,
          2020.52,
          2020.53,
          2020.54,
          2020.55,
          2020.56,
          2020.57,
          2020.5800000000002,
          2020.5900000000001,
          2020.6000000000001,
          2020.6100000000001,
          2020.6200000000001,
          2020.63,
          2020.64,
          2020.65,
          2020.66,
          2020.67,
          2020.68,
          2020.69,
          2020.7,
          2020.71,
          2020.72,
          2020.73,
          2020.74,
          2020.75,
          2020.76,
          2020.77,
          2020.78,
          2020.79,
          2020.8,
          2020.81,
          2020.82,
          2020.8300000000002,
          2020.8400000000001,
          2020.8500000000001,
          2020.8600000000001,
          2020.8700000000001,
          2020.88,
          2020.89,
          2020.9,
          2020.91,
          2020.92,
          2020.93,
          2020.94,
          2020.95,
          2020.96,
          2020.97,
          2020.98,
          2020.99,
          2021,
          2021.01,
          2021.02,
          2021.03,
          2021.04,
          2021.05,
          2021.06,
          2021.07,
          2021.0800000000002,
          2021.0900000000001,
          2021.1000000000001,
          2021.1100000000001,
          2021.1200000000001,
          2021.13,
          2021.14,
          2021.15,
          2021.16,
          2021.17,
          2021.18,
          2021.19,
          2021.2,
          2021.21,
          2021.22,
          2021.23,
          2021.24,
          2021.25,
          2021.26,
          2021.27,
          2021.28,
          2021.29,
          2021.3,
          2021.31,
          2021.32,
          2021.3300000000002,
          2021.3400000000001,
          2021.3500000000001,
          2021.3600000000001,
          2021.3700000000001,
          2021.38,
          2021.39,
          2021.4,
          2021.41,
          2021.42,
          2021.43,
          2021.44,
          2021.45,
          2021.46,
          2021.47,
          2021.48,
          2021.49,
          2021.5,
          2021.51,
          2021.52,
          2021.53,
          2021.54,
          2021.55,
          2021.56,
          2021.57,
          2021.5800000000002,
          2021.5900000000001,
          2021.6000000000001,
          2021.6100000000001,
          2021.6200000000001,
          2021.63,
          2021.64,
          2021.65,
          2021.66,
          2021.67,
          2021.68,
          2021.69,
          2021.7,
          2021.71,
          2021.72,
          2021.73,
          2021.74,
          2021.75,
          2021.76,
          2021.77,
          2021.78,
          2021.79,
          2021.8,
          2021.81,
          2021.82,
          2021.8300000000002,
          2021.8400000000001,
          2021.8500000000001,
          2021.8600000000001,
          2021.8700000000001,
          2021.88,
          2021.89,
          2021.9,
          2021.91,
          2021.92,
          2021.93,
          2021.94,
          2021.95,
          2021.96,
          2021.97,
          2021.98,
          2021.99,
          2022,
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          2022.06,
          2022.07,
          2022.0800000000002,
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          2022.15,
          2022.16,
          2022.17,
          2022.18,
          2022.19,
          2022.2,
          2022.21,
          2022.22,
          2022.23,
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          2022.27,
          2022.28,
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          2022.3,
          2022.31,
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          2022.3300000000002,
          2022.3400000000001,
          2022.3500000000001,
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          2022.3700000000001,
          2022.38,
          2022.39,
          2022.4,
          2022.41,
          2022.42,
          2022.43,
          2022.44,
          2022.45,
          2022.46,
          2022.47,
          2022.48,
          2022.49,
          2022.5,
          2022.51,
          2022.52,
          2022.53,
          2022.54,
          2022.55,
          2022.56,
          2022.57,
          2022.5800000000002,
          2022.5900000000001,
          2022.6000000000001,
          2022.6100000000001,
          2022.6200000000001,
          2022.63,
          2022.64,
          2022.65,
          2022.66,
          2022.67,
          2022.68,
          2022.69,
          2022.7,
          2022.71,
          2022.72,
          2022.73,
          2022.74,
          2022.75,
          2022.76,
          2022.77,
          2022.78,
          2022.79,
          2022.8,
          2022.81,
          2022.82,
          2022.8300000000002,
          2022.8400000000001,
          2022.8500000000001,
          2022.8600000000001,
          2022.8700000000001,
          2022.88,
          2022.89,
          2022.9,
          2022.91,
          2022.92,
          2022.93,
          2022.94,
          2022.95,
          2022.96,
          2022.97,
          2022.98,
          2022.99,
          2023,
          2023.01,
          2023.02,
          2023.03,
          2023.04,
          2023.05,
          2023.06,
          2023.07,
          2023.0800000000002,
          2023.0900000000001,
          2023.1000000000001,
          2023.1100000000001,
          2023.1200000000001,
          2023.13,
          2023.14,
          2023.15,
          2023.16,
          2023.17,
          2023.18,
          2023.19,
          2023.2,
          2023.21,
          2023.22,
          2023.23,
          2023.24,
          2023.25,
          2023.26,
          2023.27,
          2023.28,
          2023.29,
          2023.3,
          2023.31,
          2023.32,
          2023.3300000000002,
          2023.3400000000001,
          2023.3500000000001,
          2023.3600000000001,
          2023.3700000000001,
          2023.38,
          2023.39,
          2023.4,
          2023.41,
          2023.42,
          2023.43,
          2023.44,
          2023.45,
          2023.46,
          2023.47,
          2023.48,
          2023.49,
          2023.5,
          2023.51,
          2023.52,
          2023.53,
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          2023.55,
          2023.56,
          2023.57,
          2023.5800000000002,
          2023.5900000000001,
          2023.6000000000001,
          2023.6100000000001,
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          2023.63,
          2023.64,
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          2023.7,
          2023.71,
          2023.72,
          2023.73,
          2023.74,
          2023.75,
          2023.76,
          2023.77,
          2023.78,
          2023.79,
          2023.8,
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          2023.8400000000001,
          2023.8500000000001,
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          2023.8700000000001,
          2023.88,
          2023.89,
          2023.9,
          2023.91,
          2023.92,
          2023.93,
          2023.94,
          2023.95,
          2023.96,
          2023.97,
          2023.98,
          2023.99,
          2024,
          2024.01,
          2024.02,
          2024.03,
          2024.04,
          2024.05,
          2024.06,
          2024.07,
          2024.0800000000002,
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          2024.13,
          2024.14,
          2024.15,
          2024.16,
          2024.17,
          2024.18,
          2024.19,
          2024.2,
          2024.21,
          2024.22,
          2024.23,
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          2024.25,
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          2024.27,
          2024.28,
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          2024.3,
          2024.31,
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          2024.3300000000002,
          2024.3400000000001,
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          2024.3700000000001,
          2024.38,
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          2024.4,
          2024.41,
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          2024.47,
          2024.48,
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          2024.5,
          2024.51,
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          2024.55,
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          2025,
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          2026,
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          1980,
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          1981,
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          1976,
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          1977,
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          1978,
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          1979,
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          1979.99,
          1980,
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          1980.27,
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          1981,
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          1981.3300000000002,
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          1981.5,
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          1981.7,
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          1981.73,
          1981.74,
          1981.75,
          1981.76,
          1981.77,
          1981.78,
          1981.79,
          1981.8,
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          1981.88,
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          1981.9,
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          1981.97,
          1981.98,
          1981.99,
          1982,
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          1982.0800000000002,
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          1982.24,
          1982.25,
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          1982.27,
          1982.28,
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          1982.3,
          1982.31,
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          1982.3300000000002,
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          1982.38,
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          1982.47,
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          1982.5,
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          1982.57,
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          1982.63,
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          1982.7,
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          1982.73,
          1982.74,
          1982.75,
          1982.76,
          1982.77,
          1982.78,
          1982.79,
          1982.8,
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          1982.88,
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          1982.98,
          1982.99,
          1983,
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          1983.0800000000002,
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          1983.19,
          1983.2,
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          1983.24,
          1983.25,
          1983.26,
          1983.27,
          1983.28,
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          1983.3,
          1983.31,
          1983.32,
          1983.3300000000002,
          1983.3400000000001,
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          1983.38,
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          1983.47,
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          1983.5,
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          1983.5800000000002,
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          1983.68,
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          1983.7,
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          1983.73,
          1983.74,
          1983.75,
          1983.76,
          1983.77,
          1983.78,
          1983.79,
          1983.8,
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          1983.8300000000002,
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          1983.99,
          1984,
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          1984.0800000000002,
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          1984.2,
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          1984.25,
          1984.26,
          1984.27,
          1984.28,
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          1984.3,
          1984.31,
          1984.32,
          1984.3300000000002,
          1984.3400000000001,
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          1984.38,
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          1984.48,
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          1984.5,
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          1984.73,
          1984.74,
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          1984.76,
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          1984.8,
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          1984.97,
          1984.98,
          1984.99,
          1985,
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          1985.0800000000002,
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          1985.2,
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          1985.25,
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          1985.27,
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          1985.3,
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          1985.3300000000002,
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          1985.38,
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          1985.5,
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          1985.5800000000002,
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          1985.73,
          1985.74,
          1985.75,
          1985.76,
          1985.77,
          1985.78,
          1985.79,
          1985.8,
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          1985.99,
          1986,
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          1986.0800000000002,
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          1986.2,
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          1986.25,
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          1986.27,
          1986.28,
          1986.29,
          1986.3,
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          1986.32,
          1986.3300000000002,
          1986.3400000000001,
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          1986.38,
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          1986.44,
          1986.45,
          1986.46,
          1986.47,
          1986.48,
          1986.49,
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          2020,
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          2021,
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          2022,
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          2023,
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          2024,
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          2025,
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          2025.99,
          2026,
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          2026.98,
          2026.99,
          2027,
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          2027.98,
          2027.99,
          2028,
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          2028.98,
          2028.99,
          2029,
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          1975,
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          1976,
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          1977,
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          1978,
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          1979,
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          1980,
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          1981,
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          1981.0800000000002,
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          1981.3300000000002,
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          1981.98,
          1981.99,
          1982,
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          1982.0800000000002,
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          1982.3300000000002,
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          1982.38,
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          1982.5800000000002,
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          1982.63,
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          1982.7,
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          1982.73,
          1982.74,
          1982.75,
          1982.76,
          1982.77,
          1982.78,
          1982.79,
          1982.8,
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          1982.8300000000002,
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          1982.88,
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          1982.9,
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          1982.93,
          1982.94,
          1982.95,
          1982.96,
          1982.97,
          1982.98,
          1982.99,
          1983,
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          2016.74,
          2016.75,
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          2016.78,
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          2016.93,
          2016.94,
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          2016.98,
          2016.99,
          2017,
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          2017.2,
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          2017.23,
          2017.24,
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          2017.26,
          2017.27,
          2017.28,
          2017.29,
          2017.3,
          2017.31,
          2017.32,
          2017.3300000000002,
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          2017.38,
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          2017.93,
          2017.94,
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          2017.96,
          2017.97,
          2017.98,
          2017.99,
          2018,
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          2018.27,
          2018.28,
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          2018.3,
          2018.31,
          2018.32,
          2018.3300000000002,
          2018.3400000000001,
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          2018.38,
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          2019,
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   "source": [
    "import plotly.express as px\n",
    "from plotly.subplots import make_subplots\n",
    "import plotly.graph_objects as go\n",
    "import pandas as pd\n",
    "\n",
    "df = pd.DataFrame(np.transpose([time,influx,outflux,h_t,V_t]),columns=['time','influx','outflux','h_t','V_t'])\n",
    "\n",
    "# print(any(h_t<0))\n",
    "# print(any(h_t>40))\n",
    "\n",
    "fig = make_subplots(3,1)\n",
    "\n",
    "fig.add_trace(go.Scatter(x=df['time'],y=df['h_t']),row=1,col=1)\n",
    "fig.add_trace(go.Scatter(x=df['time'],y=df['V_t']),row=2,col=1)\n",
    "fig.add_trace(go.Scatter(x=df['time'],y=df['influx']),row=3,col=1)\n",
    "fig.add_trace(go.Scatter(x=df['time'],y=df['outflux']),row=3,col=1)\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "h_1:  10\n",
      "h_2:  15\n",
      "h_3:  20\n",
      "x_1:  100\n",
      "x_2:  101\n",
      "x_3:  30\n"
     ]
    }
   ],
   "source": [
    "from volume_change import show_parameters\n",
    "show_parameters()"
   ]
  }
 ],
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