{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Module 3 : Concentration de CO$_{\\textbf{2}}$ dans l'atmosphère depuis 1958"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import os\n",
    "from urllib.request import urlretrieve\n",
    "import datetime\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importation et formatage des données"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les données sont disponibles sur le [site Web de l'institut Scripps](https://scrippsco2.ucsd.edu/data/atmospheric_co2/primary_mlo_co2_record.html). Nous les récupérons sous forme d'un fichier en format CSV dont chaque ligne correspond à une semaine de la période demandée (29/03/1958 à aujourd'hui 09/12/2024). Nous téléchargeons à ce jour dans le dossier local à [cette URL](https://scrippsco2.ucsd.edu/assets/data/atmospheric/stations/in_situ_co2/weekly/weekly_in_situ_co2_mlo.csv) à l'aide de la bibliothèque `urllib.request`. Si le fichier est déjà téléchargé, nous l'importons depuis le dossier local."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "File data_keeling.csv found at /home/jovyan/work/module3/exo3/data_keeling.csv\n"
     ]
    }
   ],
   "source": [
    "data_url = \"https://scrippsco2.ucsd.edu/assets/data/atmospheric/stations/in_situ_co2/weekly/weekly_in_situ_co2_mlo.csv\"\n",
    "data_file = \"data_keeling.csv\"\n",
    "\n",
    "if not os.path.exists(data_file):\n",
    "    urlretrieve(data_url, data_file)\n",
    "    print(f\"File downloaded and saved as {data_file}\")\n",
    "else:\n",
    "    print(f\"File {data_file} found at {os.path.abspath(data_file)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le fichier contient 44 lignes de commentaires (ignorées en précisant `skiprows=44`) expliquant le fichier et les méthodes de mesure. Il contient ensuite deux colonnes:\n",
    "- Date (premier jour de la période d'une semaine)\n",
    "- Concentration en CO$_2$ (ppm)\n",
    "\n",
    "Aucune ligne ne définit le nom des colonnes. Il faut donc préciser `header=None`, puis préciser le nom des colonnes par la suite."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>Concentration en CO2 (ppm)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1958-03-29</td>\n",
       "      <td>316.19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1958-04-05</td>\n",
       "      <td>317.31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1958-04-12</td>\n",
       "      <td>317.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1958-04-19</td>\n",
       "      <td>317.58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1958-04-26</td>\n",
       "      <td>316.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1958-05-03</td>\n",
       "      <td>316.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1958-05-17</td>\n",
       "      <td>317.56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1958-05-24</td>\n",
       "      <td>317.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1958-07-05</td>\n",
       "      <td>315.85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1958-07-12</td>\n",
       "      <td>315.85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1958-07-19</td>\n",
       "      <td>315.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1958-07-26</td>\n",
       "      <td>315.59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1958-08-02</td>\n",
       "      <td>315.64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1958-08-09</td>\n",
       "      <td>315.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1958-08-16</td>\n",
       "      <td>315.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1958-08-30</td>\n",
       "      <td>314.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1958-09-06</td>\n",
       "      <td>313.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1958-11-08</td>\n",
       "      <td>313.05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1958-11-15</td>\n",
       "      <td>313.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1958-11-22</td>\n",
       "      <td>313.57</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1958-11-29</td>\n",
       "      <td>314.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1958-12-06</td>\n",
       "      <td>314.56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1958-12-13</td>\n",
       "      <td>314.41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1958-12-20</td>\n",
       "      <td>314.77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1958-12-27</td>\n",
       "      <td>315.21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1959-01-03</td>\n",
       "      <td>315.24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>1959-01-10</td>\n",
       "      <td>315.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>1959-01-17</td>\n",
       "      <td>315.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>1959-01-24</td>\n",
       "      <td>315.86</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>1959-01-31</td>\n",
       "      <td>315.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3373</th>\n",
       "      <td>2024-04-20</td>\n",
       "      <td>426.91</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3374</th>\n",
       "      <td>2024-04-27</td>\n",
       "      <td>427.13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3375</th>\n",
       "      <td>2024-05-04</td>\n",
       "      <td>426.51</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3376</th>\n",
       "      <td>2024-05-11</td>\n",
       "      <td>427.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3377</th>\n",
       "      <td>2024-05-18</td>\n",
       "      <td>426.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3378</th>\n",
       "      <td>2024-05-25</td>\n",
       "      <td>426.68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3379</th>\n",
       "      <td>2024-06-01</td>\n",
       "      <td>426.78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3380</th>\n",
       "      <td>2024-06-08</td>\n",
       "      <td>427.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3381</th>\n",
       "      <td>2024-06-15</td>\n",
       "      <td>427.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3382</th>\n",
       "      <td>2024-06-22</td>\n",
       "      <td>426.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3383</th>\n",
       "      <td>2024-06-29</td>\n",
       "      <td>425.41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3384</th>\n",
       "      <td>2024-07-06</td>\n",
       "      <td>425.73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3385</th>\n",
       "      <td>2024-07-13</td>\n",
       "      <td>426.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3386</th>\n",
       "      <td>2024-07-20</td>\n",
       "      <td>424.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3387</th>\n",
       "      <td>2024-07-27</td>\n",
       "      <td>424.72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3388</th>\n",
       "      <td>2024-08-03</td>\n",
       "      <td>424.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3389</th>\n",
       "      <td>2024-08-10</td>\n",
       "      <td>422.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3390</th>\n",
       "      <td>2024-08-17</td>\n",
       "      <td>422.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3391</th>\n",
       "      <td>2024-08-24</td>\n",
       "      <td>421.45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3392</th>\n",
       "      <td>2024-08-31</td>\n",
       "      <td>421.57</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3393</th>\n",
       "      <td>2024-09-07</td>\n",
       "      <td>421.81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3394</th>\n",
       "      <td>2024-09-14</td>\n",
       "      <td>421.39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3395</th>\n",
       "      <td>2024-09-21</td>\n",
       "      <td>421.77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3396</th>\n",
       "      <td>2024-09-28</td>\n",
       "      <td>421.51</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3397</th>\n",
       "      <td>2024-10-05</td>\n",
       "      <td>421.86</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3398</th>\n",
       "      <td>2024-10-12</td>\n",
       "      <td>422.13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3399</th>\n",
       "      <td>2024-10-19</td>\n",
       "      <td>422.16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3400</th>\n",
       "      <td>2024-10-26</td>\n",
       "      <td>422.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3401</th>\n",
       "      <td>2024-11-02</td>\n",
       "      <td>423.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3402</th>\n",
       "      <td>2024-11-09</td>\n",
       "      <td>423.18</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3403 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Date  Concentration en CO2 (ppm)\n",
       "0     1958-03-29                      316.19\n",
       "1     1958-04-05                      317.31\n",
       "2     1958-04-12                      317.69\n",
       "3     1958-04-19                      317.58\n",
       "4     1958-04-26                      316.48\n",
       "5     1958-05-03                      316.95\n",
       "6     1958-05-17                      317.56\n",
       "7     1958-05-24                      317.99\n",
       "8     1958-07-05                      315.85\n",
       "9     1958-07-12                      315.85\n",
       "10    1958-07-19                      315.46\n",
       "11    1958-07-26                      315.59\n",
       "12    1958-08-02                      315.64\n",
       "13    1958-08-09                      315.10\n",
       "14    1958-08-16                      315.09\n",
       "15    1958-08-30                      314.14\n",
       "16    1958-09-06                      313.54\n",
       "17    1958-11-08                      313.05\n",
       "18    1958-11-15                      313.26\n",
       "19    1958-11-22                      313.57\n",
       "20    1958-11-29                      314.01\n",
       "21    1958-12-06                      314.56\n",
       "22    1958-12-13                      314.41\n",
       "23    1958-12-20                      314.77\n",
       "24    1958-12-27                      315.21\n",
       "25    1959-01-03                      315.24\n",
       "26    1959-01-10                      315.50\n",
       "27    1959-01-17                      315.69\n",
       "28    1959-01-24                      315.86\n",
       "29    1959-01-31                      315.42\n",
       "...          ...                         ...\n",
       "3373  2024-04-20                      426.91\n",
       "3374  2024-04-27                      427.13\n",
       "3375  2024-05-04                      426.51\n",
       "3376  2024-05-11                      427.20\n",
       "3377  2024-05-18                      426.26\n",
       "3378  2024-05-25                      426.68\n",
       "3379  2024-06-01                      426.78\n",
       "3380  2024-06-08                      427.01\n",
       "3381  2024-06-15                      427.10\n",
       "3382  2024-06-22                      426.54\n",
       "3383  2024-06-29                      425.41\n",
       "3384  2024-07-06                      425.73\n",
       "3385  2024-07-13                      426.10\n",
       "3386  2024-07-20                      424.36\n",
       "3387  2024-07-27                      424.72\n",
       "3388  2024-08-03                      424.42\n",
       "3389  2024-08-10                      422.50\n",
       "3390  2024-08-17                      422.80\n",
       "3391  2024-08-24                      421.45\n",
       "3392  2024-08-31                      421.57\n",
       "3393  2024-09-07                      421.81\n",
       "3394  2024-09-14                      421.39\n",
       "3395  2024-09-21                      421.77\n",
       "3396  2024-09-28                      421.51\n",
       "3397  2024-10-05                      421.86\n",
       "3398  2024-10-12                      422.13\n",
       "3399  2024-10-19                      422.16\n",
       "3400  2024-10-26                      422.36\n",
       "3401  2024-11-02                      423.15\n",
       "3402  2024-11-09                      423.18\n",
       "\n",
       "[3403 rows x 2 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "raw_data = pd.read_csv(data_file, skiprows=44, header=None)\n",
    "raw_data.columns = [\"Date\", \"Concentration en CO2 (ppm)\"]\n",
    "raw_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vérifions si le jeu de données contient des lignes vides."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>Concentration en CO2 (ppm)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Empty DataFrame\n",
       "Columns: [Date, Concentration en CO2 (ppm)]\n",
       "Index: []"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "raw_data[raw_data.isnull().any(axis=1)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aucune ligne n'est vide. Traduisons maintenant la colonne \"Date\" en format date utilisé par pandas, puis passons-là en indice du tableau."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Date\n",
       "1958-03-29    316.19\n",
       "1958-04-05    317.31\n",
       "1958-04-12    317.69\n",
       "1958-04-19    317.58\n",
       "1958-04-26    316.48\n",
       "1958-05-03    316.95\n",
       "1958-05-17    317.56\n",
       "1958-05-24    317.99\n",
       "1958-07-05    315.85\n",
       "1958-07-12    315.85\n",
       "1958-07-19    315.46\n",
       "1958-07-26    315.59\n",
       "1958-08-02    315.64\n",
       "1958-08-09    315.10\n",
       "1958-08-16    315.09\n",
       "1958-08-30    314.14\n",
       "1958-09-06    313.54\n",
       "1958-11-08    313.05\n",
       "1958-11-15    313.26\n",
       "1958-11-22    313.57\n",
       "1958-11-29    314.01\n",
       "1958-12-06    314.56\n",
       "1958-12-13    314.41\n",
       "1958-12-20    314.77\n",
       "1958-12-27    315.21\n",
       "1959-01-03    315.24\n",
       "1959-01-10    315.50\n",
       "1959-01-17    315.69\n",
       "1959-01-24    315.86\n",
       "1959-01-31    315.42\n",
       "               ...  \n",
       "2024-04-20    426.91\n",
       "2024-04-27    427.13\n",
       "2024-05-04    426.51\n",
       "2024-05-11    427.20\n",
       "2024-05-18    426.26\n",
       "2024-05-25    426.68\n",
       "2024-06-01    426.78\n",
       "2024-06-08    427.01\n",
       "2024-06-15    427.10\n",
       "2024-06-22    426.54\n",
       "2024-06-29    425.41\n",
       "2024-07-06    425.73\n",
       "2024-07-13    426.10\n",
       "2024-07-20    424.36\n",
       "2024-07-27    424.72\n",
       "2024-08-03    424.42\n",
       "2024-08-10    422.50\n",
       "2024-08-17    422.80\n",
       "2024-08-24    421.45\n",
       "2024-08-31    421.57\n",
       "2024-09-07    421.81\n",
       "2024-09-14    421.39\n",
       "2024-09-21    421.77\n",
       "2024-09-28    421.51\n",
       "2024-10-05    421.86\n",
       "2024-10-12    422.13\n",
       "2024-10-19    422.16\n",
       "2024-10-26    422.36\n",
       "2024-11-02    423.15\n",
       "2024-11-09    423.18\n",
       "Length: 3403, dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "raw_data[\"Date\"] = pd.to_datetime(raw_data[\"Date\"])\n",
    "data = pd.Series(data = raw_data[\"Concentration en CO2 (ppm)\"].tolist(), index = raw_data[\"Date\"])\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vérifions si des données sont manquantes, _i.e._ si deux dates ont plus d'une semaine d'écart."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1958-05-03 00:00:00 1958-05-17 00:00:00\n",
      "1958-05-24 00:00:00 1958-07-05 00:00:00\n",
      "1958-08-16 00:00:00 1958-08-30 00:00:00\n",
      "1958-09-06 00:00:00 1958-11-08 00:00:00\n",
      "1959-01-31 00:00:00 1959-02-14 00:00:00\n",
      "1959-03-07 00:00:00 1959-03-21 00:00:00\n",
      "1959-05-23 00:00:00 1959-06-06 00:00:00\n",
      "1959-08-08 00:00:00 1959-08-22 00:00:00\n",
      "1962-08-18 00:00:00 1962-09-15 00:00:00\n",
      "1962-12-22 00:00:00 1963-01-05 00:00:00\n",
      "1963-02-09 00:00:00 1963-02-23 00:00:00\n",
      "1963-04-27 00:00:00 1963-05-11 00:00:00\n",
      "1963-11-16 00:00:00 1963-11-30 00:00:00\n",
      "1964-01-18 00:00:00 1964-05-30 00:00:00\n",
      "1964-06-06 00:00:00 1964-06-27 00:00:00\n",
      "1964-08-01 00:00:00 1964-08-15 00:00:00\n",
      "1966-07-09 00:00:00 1966-08-06 00:00:00\n",
      "1966-10-29 00:00:00 1966-11-12 00:00:00\n",
      "1967-01-14 00:00:00 1967-02-04 00:00:00\n",
      "1976-06-19 00:00:00 1976-07-03 00:00:00\n",
      "1984-03-24 00:00:00 1984-04-28 00:00:00\n",
      "1985-07-27 00:00:00 1985-08-10 00:00:00\n",
      "2003-06-07 00:00:00 2003-06-21 00:00:00\n",
      "2003-10-04 00:00:00 2003-10-25 00:00:00\n",
      "2005-02-19 00:00:00 2005-03-26 00:00:00\n",
      "2006-02-04 00:00:00 2006-02-25 00:00:00\n",
      "2007-01-20 00:00:00 2007-02-03 00:00:00\n",
      "2012-09-29 00:00:00 2012-10-20 00:00:00\n",
      "2020-01-11 00:00:00 2020-01-25 00:00:00\n",
      "2022-11-26 00:00:00 2022-12-17 00:00:00\n"
     ]
    }
   ],
   "source": [
    "dates = data.index\n",
    "for d1, d2 in zip(dates[:-1], dates[1:]):\n",
    "    delta = d2 - d1\n",
    "    if delta - pd.Timedelta(1,'W') > pd.Timedelta('1s'):\n",
    "        print(d1, d2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quelques données sont manquantes, mais leur nombre est largement inférieur au nombre de données, et sont éparses après les années 1960. Nous pouvons donc considérer l'erreur induite par le manque de données négligeable.\n",
    "\n",
    "Néanmoins, nous pouvons combler ces données en utilisant des moyennes glissantes pour aider à la visualisation, tout en gardant en mémoire les dates avec des données interpolées, afin de les exclure de l'analyse quantitative. Cela est effectué à l'aide du tableau `interpolated_marks` :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1958-03-29    0\n",
       "1958-04-05    0\n",
       "1958-04-12    0\n",
       "1958-04-19    0\n",
       "1958-04-26    0\n",
       "1958-05-03    0\n",
       "1958-05-10    1\n",
       "1958-05-17    0\n",
       "1958-05-24    0\n",
       "1958-05-31    1\n",
       "1958-06-07    1\n",
       "1958-06-14    1\n",
       "1958-06-21    1\n",
       "1958-06-28    1\n",
       "1958-07-05    0\n",
       "1958-07-12    0\n",
       "1958-07-19    0\n",
       "1958-07-26    0\n",
       "1958-08-02    0\n",
       "1958-08-09    0\n",
       "1958-08-16    0\n",
       "1958-08-23    1\n",
       "1958-08-30    0\n",
       "1958-09-06    0\n",
       "1958-09-13    1\n",
       "1958-09-20    1\n",
       "1958-09-27    1\n",
       "1958-10-04    1\n",
       "1958-10-11    1\n",
       "1958-10-18    1\n",
       "             ..\n",
       "2024-04-20    0\n",
       "2024-04-27    0\n",
       "2024-05-04    0\n",
       "2024-05-11    0\n",
       "2024-05-18    0\n",
       "2024-05-25    0\n",
       "2024-06-01    0\n",
       "2024-06-08    0\n",
       "2024-06-15    0\n",
       "2024-06-22    0\n",
       "2024-06-29    0\n",
       "2024-07-06    0\n",
       "2024-07-13    0\n",
       "2024-07-20    0\n",
       "2024-07-27    0\n",
       "2024-08-03    0\n",
       "2024-08-10    0\n",
       "2024-08-17    0\n",
       "2024-08-24    0\n",
       "2024-08-31    0\n",
       "2024-09-07    0\n",
       "2024-09-14    0\n",
       "2024-09-21    0\n",
       "2024-09-28    0\n",
       "2024-10-05    0\n",
       "2024-10-12    0\n",
       "2024-10-19    0\n",
       "2024-10-26    0\n",
       "2024-11-02    0\n",
       "2024-11-09    0\n",
       "Freq: 7D, Length: 3477, dtype: int64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "full_index = pd.date_range(start=data.index[0], end=data.index[-1], freq='7D')\n",
    "full_data = data.reindex(full_index)\n",
    "while full_data.isna().any():\n",
    "    rolling_mean = full_data.rolling(window=5, min_periods=3).mean()\n",
    "    full_data[full_data.isna()] = rolling_mean[full_data.isna()]\n",
    "interpolated_marks = pd.Series(data=np.where(data.reindex(full_index).isna(), 1, 0), index=full_index)\n",
    "interpolated_marks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interprétation des données"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Commençons par représenter l'évolution de la concentration en CO$_2$ depuis 1958."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f1109cb3358>"
      ]
     },
     "execution_count": 8,
     "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": [
    "full_data.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On observe une oscillation rapide autour d'une évolution plus lente. Nous pouvons donc modéliser l'évolution temporelle comme :\n",
    "\n",
    "$$C(t)=f(t)+A\\cos\\Big(\\frac{2\\pi}{T}(t-t_0)\\Big)\\ ,$$\n",
    "\n",
    "où $C(t)$ est la concentration en CO$_2$, $t$ est le temps, $f(t)$ est une fonction monotone qui croît lentement et $A$ est l'amplitude des oscillations autour de $f$, $T$ est leur fréquence et $t_0$ est leur origine temporelle."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Caractérisation des oscillations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Regardons les dernières années afin de mieux caractériser les oscillations rapides."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f10d3431748>"
      ]
     },
     "execution_count": 9,
     "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": [
    "data[-200:].plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les oscillations semblent avoir une période d'un an (variations annuelles). Le pic de concentration a lieu au début de l'été, soit vers juin. Afin d'affiner l'analyse, nous pouvons considérer que sur un an, l'évolution de $f$ peut s'apparenter à une droite (sa tangente au milieu de l'an donné).\n",
    "\n",
    "Concentrons-nous sur la dernière année : entre automne 2023 et automne 2024. Nous cherchons à isoler les données entre début septembre 2023 et fin septembre 2024, afin d'être certains d'englober toute la variation annuelle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "period1 = pd.Period(pd.Timestamp(2023, 9, 1), 'W')\n",
    "period2 = pd.Period(pd.Timestamp(2024, 9, 30), 'W')\n",
    "data_last_year = full_data[full_data[((full_data.index >= period1.start_time) & (full_data.index <= period1.end_time))].index[0]:\n",
    "     full_data[((full_data.index >= period2.start_time) & (full_data.index <= period2.end_time))].index[0]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vérifions si nous comprenons bien toute l'année voulue :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f10d33b47b8>"
      ]
     },
     "execution_count": 11,
     "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": [
    "data_last_year.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Parfait. Maintenant, trouvons les deux données minimales (au début et à la fin de l'oscillation respectivement) afin de trouver la pente de $f$. $f$ étant croissante, le premier minimum est le minimum de l'année isolée. Les valeurs de début d'année 2024 étant supérieures au deuxième minimum, nous pouvons le trouver en contraignant `year == 2024`. On vérifie par la suite que les minima trouvés sont bien ceux attendus par l'analyse graphique.\n",
    "\n",
    "Nous pourrons ensuite enlever cette contribution lente pour avoir une oscillation brute, et mesurer son amplitude.\n",
    "\n",
    "__Remarque__ : nous faisons en fait un traitement de signal à la main ; nous aurrions aussi pu utiliser un filtre passe-haut avec une coupure de fréquence choisie soigneusement pour obtenir le même résultat. Ce document étant censé être accessible à tous, il est préférable de ne pas utiliser de méthode trop technique."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2023-09-23    417.77\n",
      "Freq: 7D, dtype: float64\n",
      "2024-09-14    421.39\n",
      "Freq: 7D, dtype: float64\n",
      "3.57980392156864\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f10cf0f0400>"
      ]
     },
     "execution_count": 19,
     "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": [
    "min_2023 = data_last_year.where(data_last_year == min(data_last_year)).dropna()\n",
    "data_last_year_2024 = data_last_year[data_last_year.index.year == 2024]\n",
    "min_2024 = data_last_year_2024.where(data_last_year_2024 == min(data_last_year_2024)).dropna()\n",
    "print(min_2023)\n",
    "print(min_2024)\n",
    "\n",
    "# Pour définir la droite correspondant à l'évolution de f(t), il est plus simple de repasser sur des indices numériques\n",
    "data_last_year_filtered = pd.Series(data=data_last_year.values, index=range(len(data_last_year)))\n",
    "dy = min_2024.values[0] - min_2023.values[0]\n",
    "min_2023_filtered = data_last_year_filtered.where(data_last_year_filtered == min(data_last_year_filtered)).dropna()\n",
    "data_last_year_filtered_2024 = data_last_year_filtered[data_last_year.index.year == 2024]\n",
    "min_2024_filtered = data_last_year_filtered_2024.where(data_last_year_filtered_2024 == min(data_last_year_filtered_2024)).dropna()\n",
    "dx = min_2024_filtered.index[0] - min_2023_filtered.index[0]\n",
    "data_f = min_2023.values[0] + (dy / dx) * (range(len(data_last_year)) - min_2023_filtered.index[0])\n",
    "f = pd.Series(data=data_f, index=data_last_year.index)\n",
    "data_last_year_filtered.index = data_last_year.index\n",
    "\n",
    "data_last_year_filtered -= f\n",
    "data_last_year_filtered.index = data_last_year.index\n",
    "amp = data_last_year_filtered.max() / 2\n",
    "print(amp)\n",
    "data_last_year_filtered.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous obtenons une amplitude de 3.6 ppm, soit un écart entre minimum et maximum annuel d'environ 7.2 ppm. De plus, nous pouvons voir que pour la variation annuelle, la croissance est plus lente que la décroissance, et donc le maximum n'est pas exactement 6 mois après le minimum. Nous négligerons cette déviation par rapport à notre modèle."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Modélisation de l'évolution en arrière-plan"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous pouvons désormais isoler l'évolution lente d'arrière-plan $f(t)$ en moyennant sur un an les valeurs (on recrée artificiellement un filtre passe-bas) :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f10cf200400>"
      ]
     },
     "execution_count": 13,
     "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": [
    "filled_data = full_data.copy()\n",
    "filled_data[interpolated_marks == 1] = np.nan\n",
    "rolling_base = pd.Series(data=filled_data.values, index=range(len(filled_data)))\n",
    "rolling_mean = rolling_base.rolling(window=52, center=True).mean()\n",
    "rolling_mean.index = full_index\n",
    "rolling_mean.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On voit bien que la dérivée de cette courbe est strictement croissante. Une modélisation simple est par exemple un polynôme du second degré en temps : $f(t)=at^2+bt+c$. En utilisant la fonction `numpy.polyfit`, nous pouvons retrouver les paramètres $a$, $b$ et $c$ correspondant à notre jeu de données :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.868211382735772e-16 4.000936624074663e-09 0.002605559356891354\n"
     ]
    },
    {
     "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": [
    "t = np.arange(len(rolling_mean))\n",
    "rolling = pd.Series(data=rolling_mean.values, index=t).dropna()\n",
    "p = np.polyfit(rolling.index, rolling.values, 2, cov=True)\n",
    "a = p[0][0]\n",
    "b = p[0][1]\n",
    "c = p[0][2]\n",
    "err = p[1]\n",
    "a_err = err[0, 0]\n",
    "b_err = err[1, 1]\n",
    "c_err = err[2, 2]\n",
    "f = pd.Series(data=a*t**2+b*t+c, index=full_index)\n",
    "f.plot()\n",
    "print(a_err, b_err, c_err)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous retrouvons bien la dynamique de fond, qui plus est avec des incertitudes assez faibles sur les coefficients calculés. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prédiction de la dynamique complète"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous pouvons maintenant recréer la dynamique totale de $C(t) = f(t) + A\\cos\\Big(\\frac{2\\pi}{T}(t-t_0)\\Big)$, avec $t_0$ fixé à la mi-mars 1959 (6 mois après la mi-septembre), soit `t[50]` :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DatetimeIndex(['1958-03-29', '1958-04-05', '1958-04-12', '1958-04-19',\n",
      "               '1958-04-26', '1958-05-03', '1958-05-10', '1958-05-17',\n",
      "               '1958-05-24', '1958-05-31', '1958-06-07', '1958-06-14',\n",
      "               '1958-06-21', '1958-06-28', '1958-07-05', '1958-07-12',\n",
      "               '1958-07-19', '1958-07-26', '1958-08-02', '1958-08-09',\n",
      "               '1958-08-16', '1958-08-23', '1958-08-30', '1958-09-06',\n",
      "               '1958-09-13', '1958-09-20', '1958-09-27', '1958-10-04',\n",
      "               '1958-10-11', '1958-10-18', '1958-10-25', '1958-11-01',\n",
      "               '1958-11-08', '1958-11-15', '1958-11-22', '1958-11-29',\n",
      "               '1958-12-06', '1958-12-13', '1958-12-20', '1958-12-27',\n",
      "               '1959-01-03', '1959-01-10', '1959-01-17', '1959-01-24',\n",
      "               '1959-01-31', '1959-02-07', '1959-02-14', '1959-02-21',\n",
      "               '1959-02-28', '1959-03-07', '1959-03-14', '1959-03-21'],\n",
      "              dtype='datetime64[ns]', freq='7D') 1959-03-14 00:00:00\n"
     ]
    }
   ],
   "source": [
    "print(full_index[:52], full_index[50])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f10cf03aa20>"
      ]
     },
     "execution_count": 16,
     "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": [
    "C = f + pd.Series(data=amp * np.cos(2 * np.pi * (t-50) / 52.1429), index=f.index)\n",
    "C.plot()\n",
    "data.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notre modélisation a l'air de bien fonctionner. Voyons maintenant les prédictions en 2030 (nous sommes déjà presque en 2025...) :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "index_extended = pd.date_range(start=data.index[0], end=pd.Timestamp(2031, 1, 1), freq='7D')\n",
    "t_extended = np.arange(len(index_extended))\n",
    "f_extended = pd.Series(data=a*t_extended**2+b*t_extended+c, index=index_extended)\n",
    "C_extended = f_extended + pd.Series(data=amp * np.cos(2 * np.pi * (t_extended-50) / 52.1429), index=f_extended.index)\n",
    "fig, ax = plt.subplots(1)\n",
    "ax.plot(C_extended[-500:], label='Prédiction complète')\n",
    "ax.plot(f_extended[-500:], label='Prédiction concentration de fond')\n",
    "ax.plot(data[-200:], label='Mesures')\n",
    "ax.set_xlabel(\"Date\")\n",
    "ax.set_ylabel(r\"Concentration en CO$_2$ (ppm)\")\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La valeur de la concentration en CO$_2$ prédite pour 2030 est la moyenne de `C_extended` sur cette année :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "438.5762020682022\n"
     ]
    }
   ],
   "source": [
    "start_date = pd.Timestamp(2030, 1, 1)\n",
    "end_date = pd.Timestamp(2030, 12, 31)\n",
    "C_2030 = C_extended[(index_extended > start_date) & (index_extended < end_date)].mean()\n",
    "print(C_2030)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La valeur prédite est de $438.6~\\mathrm{ppm}$ pour 2030. Néanmoins, notre modèle polynomial n'est peut-être pas le bon. En effet, comme on peut le voir sur le graphique précédent, la hausse semble s'accélérer sur les deux dernières années mesurées. Cela peut notamment être dû aux déséquilibres des échanges de CO$_2$ à cause du réchauffement global, ayant atteint tout juste le seuil des $1.5~°\\mathrm{C}$ en 2024..."
   ]
  }
 ],
 "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}