exploratory_analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b66e44f0-c27a-477b-9c2e-20478f49671d",
   "metadata": {},
   "source": [
    "# MPE CDT Summer School on Forecast and Verification\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98ca76a8-d95a-405f-9132-b58e5e11f882",
   "metadata": {},
   "source": [
    "Project 4: Verification of 2 metre temperature (2mt) ensemble seasonal forecasts\n",
    "\n",
    "Introduction: DEMETER (Development of a European Multimodel Ensemble system for seasonal to\n",
    "inTERannual prediction) is an EU initiative to develop a well-validated European multi-model\n",
    "ensemble forecast system for reliable seasonal to inter-annual prediction. It ran from 2000-2003.\n",
    "(SEE Palmer et al, BAMS, 85, 853-872 for further details of the project, and also on the ECMWF.int\n",
    "website). This project offers the opportunity to compare the quality of three 9-member ensembles\n",
    "for three-month average temperature forecasts.\n",
    "\n",
    "Data files: t2m-ecmwf-JJA-1959-2001.txt, t2m-mf-JJA-1959-2001.txt and\n",
    "t2m-ukmo-JJA-1959-2001.txt. These files contain 1-month lead 2 metre temperature (2mt) forecasts\n",
    "produced in May and valid for JJA for the period 1959-2001 (i.e. 43-years of forecasts) for a grid\n",
    "point in central Pacific (latitude 0 o, longitude 140oW) for three coupled seasonal forecast models\n",
    "which were included in the DEMETER project (ECMWF, Meteo-France, and UK Met Office).\n",
    "\n",
    "\n",
    "Goal: To compare and contrast the forecasts from the three models.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "id": "bee098b1-a77b-45e9-8601-d7950514ce20",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import glob\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "path = '/home/julia/Dropbox/Cursos_Materias/MPE_forecast_verification/MPECDT-ForecastVerification/Project4/'\n",
    "\n",
    "def open_data(filepath):\n",
    "    with open(filepath) as f:\n",
    "        table = pd.read_table(f, sep=' ', index_col=0, header=None,   lineterminator='\\n')\n",
    "        \n",
    "    return table\n",
    "\n",
    "def ensemble_mean(data,name):\n",
    "    mean = np.zeros(len(data[1]))\n",
    "    for i in range(9):\n",
    "        mean += data[i+2]\n",
    "    \n",
    "    new_data = data\n",
    "    new_data['ens_mean'] = mean/9\n",
    "    new_data.columns = ['obs', name+'_1', name+'_2', name+'_3',name+'_4', name+'_5', name+'_6',name+'_7', name+'_8', name+'_9','ens_mean']\n",
    "    return new_data\n",
    "\n",
    "def great_ensemble(data_list,name_list):\n",
    "    df = pd.DataFrame({'obs':data_list[0][1]})\n",
    "    df.index = data_list[0].index\n",
    "    for data,name in zip(data_list,name_list):\n",
    "        new_data = data.copy()\n",
    "        new_data.columns = ['obs', name+'_1', name+'_2', name+'_3',name+'_4', name+'_5', name+'_6',name+'_7', name+'_8', name+'_9']\n",
    "        df = df.merge(new_data)\n",
    "        \n",
    "    mean = np.zeros(len(df['obs']))\n",
    "    for i in range(27):\n",
    "        mean += df.iloc[:,i+1]\n",
    "\n",
    "    df['ens_mean'] = mean / 27\n",
    "    return df\n",
    "\n",
    "def obs_vs_ensmean(data,name):\n",
    "    fig = plt.figure()\n",
    "    plt.plot(data['obs'],data['obs'],'--k')\n",
    "    plt.scatter(data['obs'],data['ens_mean'],marker='o',color='r')\n",
    "    plt.title(name)\n",
    "    plt.xlabel('Observations'); plt.ylabel('Forecast')\n",
    "    return fig\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "id": "32a944e6-6ebc-40cd-89a5-b459dba6c5bd",
   "metadata": {},
   "outputs": [],
   "source": [
    "t2m_ecmwf = open_data(path+'data/raw/Proj4_t2m-ecmwf-JJA-1959-2001.txt')\n",
    "t2m_mf = open_data(path+'data/raw/Proj4_t2m-mf-JJA-1959-2001.txt')\n",
    "t2m_uk = open_data(path+'data/raw/Proj4_t2m-ukmo-JJA-1959-2001.txt')\n",
    "\n",
    "data_list = [t2m_ecmwf,t2m_mf,t2m_uk]\n",
    "name_list = ['ecmwf','mf','uk']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "id": "946c17f7-9c9b-4c31-b539-2703c9bb2d60",
   "metadata": {},
   "outputs": [],
   "source": [
    "df =  great_ensemble(data_list, name_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "id": "f934a991-4465-4e7b-886a-f7053febb326",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(df['obs'],df['obs'],'--k')\n",
    "plt.scatter(df['obs'],df['ens_mean'])\n",
    "plt.xlabel('Observations')\n",
    "plt.ylabel('Forecast')\n",
    "plt.title('Full ensemble')\n",
    "plt.savefig(path+'figures/ensamble_bias.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "id": "a8095f7d-891b-4811-8b9b-8953d6d70696",
   "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": [
    "t2m_ecmwf_mean = ensemble_mean(t2m_ecmwf,'ecmwf')\n",
    "fig = obs_vs_ensmean(t2m_ecmwf_mean,'ecmfw')\n",
    "fig.savefig(path+'/figures/ecmwf_bias.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "id": "ba3aa2dd-131b-48e8-8606-2da1f215d370",
   "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": [
    "t2m_mf_mean = ensemble_mean(t2m_mf,'mf')\n",
    "fig = obs_vs_ensmean(t2m_mf_mean,'MF')\n",
    "fig.savefig(path+'/figures/mf_bias.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "id": "409d36fb-13b3-4fe5-a137-caccaa188c6b",
   "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": [
    "t2m_uk_mean = ensemble_mean(t2m_uk,'ecmwf')\n",
    "fig = obs_vs_ensmean(t2m_uk_mean,'UK')\n",
    "fig.savefig(path+'/figures/uk_bias.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b897bac3-1397-49cb-9d9b-026bf57d1608",
   "metadata": {},
   "source": [
    "## Terciles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "840d6bc2-85f0-4d90-90af-1bf4da74319a",
   "metadata": {},
   "outputs": [],
   "source": [
    "terciles = df['obs'].quantile([0.33,0.66]).values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "37e35193-9000-4a6a-a025-30257fd5a33f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3488372093023256"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(np.where(df['obs'] >= terciles[1],1,0))/len(df['obs'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "78e66559-40eb-4fce-9058-fa35a9389e6c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 2.,  2., 12., 17.,  7.,  3.]),\n",
       " array([23.39402852, 24.18343201, 24.97283551, 25.76223901, 26.55164251,\n",
       "        27.341046  , 28.1304495 ]),\n",
       " <BarContainer object of 6 artists>)"
      ]
     },
     "execution_count": 87,
     "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": [
    "plt.hist(df['obs'],bins = 6)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26649597-6d76-430a-a0da-9d5036095c82",
   "metadata": {},
   "source": [
    "## Classification of events - contingency table\n",
    "\n",
    "Below normal, Normal, Above normal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "id": "8dc19be2-c021-496b-9d37-923ac930250d",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 27 #Ensemble members\n",
    "def categorization_terciles(df,N):\n",
    "    terciles = df['obs'].quantile([0.33,0.66]).values\n",
    "    categories = np.where(df['obs'] <= terciles[0],1,0)*(-1) + np.where(df['obs'] >= terciles[1],1,0)\n",
    "    df['obs_cat'] = categories\n",
    "    for i in range(N): \n",
    "        categories = np.where(df.iloc[:,i+2] <= terciles[0],1,0)*(-1) + np.where(df.iloc[:,i+2] >= terciles[1],1,0)\n",
    "        df[df.columns[i+2]+'_cat'] = categories\n",
    "        \n",
    "    return df\n",
    "    \n",
    "def cont_table(obs,sim):\n",
    "    \"\"\"Returns a contingency table\n",
    "    \n",
    "    \n",
    "    input: obs, sim must be arrays where -1 indicates below normal (BN), \n",
    "                                          1 indicates above normal (AN) and\n",
    "                                          0 indicates normal (N)\n",
    "    returns: contingency table with [# (obs AN & forecast AN), # (obs AN & forecast non-AN), #obs AN\n",
    "                                    # (obs non-AN & forecast AN), # (non-obs AN & forecast non-AN), #obs non-AN]\"\"\"\n",
    "    cont_table = [[np.sum(np.where((obs > 0) & (sim > 0),1,0)),\n",
    "              np.sum(np.where((obs > 0) & (sim <=0),1,0)),\n",
    "              np.sum(np.where(obs > 0,1,0))],\n",
    "              [np.sum(np.where((obs <= 0) & (sim > 0),1,0)),\n",
    "              np.sum(np.where((obs <= 0) & (sim <= 0),1,0)),\n",
    "              np.sum(np.where(obs <= 0,1,0))]]\n",
    "    return np.array(cont_table)\n",
    "\n",
    "df_cat = categorization_terciles(df,27)\n",
    "df_uk_cat = categorization_terciles(t2m_uk_mean,9)\n",
    "df_ecmwf_cat = categorization_terciles(t2m_ecmwf_mean,9)\n",
    "df_mf_cat = categorization_terciles(t2m_mf_mean,9)\n",
    "cont_table_ensmean = cont_table(df_cat['obs_cat'],df_cat['ens_mean_cat'])\n",
    "cont_table_ensmean_mf = cont_table(df_mf_cat['obs_cat'],df_mf_cat['ens_mean_cat'])\n",
    "cont_table_ensmean_ecmwf = cont_table(df_ecmwf_cat['obs_cat'],df_ecmwf_cat['ens_mean_cat'])\n",
    "cont_table_ensmean_uk = cont_table(df_uk_cat['obs_cat'],df_uk_cat['ens_mean_cat'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "id": "927c832e-c258-4bc2-bed7-571d50c661db",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "contingency table:  [[ 6  9 15]\n",
      " [ 3 25 28]]\n",
      "hit rate above normal:  0.4\n",
      "false alarm rate above normal:  0.6\n"
     ]
    }
   ],
   "source": [
    "print('contingency table: ',cont_table_ensmean)\n",
    "print('hit rate above normal: ' , cont_table_ensmean[0,0]/cont_table_ensmean[0,2])\n",
    "print('false alarm rate above normal: ' , cont_table_ensmean[0,1]/cont_table_ensmean[0,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "id": "6498a010-aa24-4e8b-b781-fc83ecd06dd8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "contingency table:  [[14  1 15]\n",
      " [12 16 28]]\n",
      "hit rate above normal:  0.9333333333333333\n",
      "false alarm rate above normal:  0.06666666666666667\n"
     ]
    }
   ],
   "source": [
    "print('contingency table: ',cont_table_ensmean_mf)\n",
    "print('hit rate above normal: ' , cont_table_ensmean_mf[0,0]/cont_table_ensmean_mf[0,2])\n",
    "print('false alarm rate above normal: ' , cont_table_ensmean_mf[0,1]/cont_table_ensmean_mf[0,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "id": "8973465a-fe14-4547-b2ea-51be1766b400",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "contingency table:  [[ 5 10 15]\n",
      " [ 2 26 28]]\n",
      "hit rate above normal:  0.3333333333333333\n",
      "false alarm rate above normal:  0.6666666666666666\n"
     ]
    }
   ],
   "source": [
    "print('contingency table: ',cont_table_ensmean_uk)\n",
    "print('hit rate above normal: ' , cont_table_ensmean_uk[0,0]/cont_table_ensmean_uk[0,2])\n",
    "print('false alarm rate above normal: ' , cont_table_ensmean_uk[0,1]/cont_table_ensmean_uk[0,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "id": "d6ca6894-ebd5-4900-8074-0245b93a8565",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "contingency table:  [[ 0 15 15]\n",
      " [ 0 28 28]]\n",
      "hit rate above normal:  0.0\n",
      "false alarm rate above normal:  1.0\n"
     ]
    }
   ],
   "source": [
    "print('contingency table: ',cont_table_ensmean_ecmwf)\n",
    "print('hit rate above normal: ' , cont_table_ensmean_ecmwf[0,0]/cont_table_ensmean_ecmwf[0,2])\n",
    "print('false alarm rate above normal: ' , cont_table_ensmean_ecmwf[0,1]/cont_table_ensmean_ecmwf[0,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "id": "2380abfc-9877-423f-8531-df0e700ce59d",
   "metadata": {},
   "outputs": [],
   "source": [
    "cont_table = [[np.sum(np.where((df_cat['obs_cat'] > 0) & (df_cat['mf_1_cat'] > 0),1,0)),\n",
    "              np.sum(np.where((df_cat['obs_cat'] > 0) & (df_cat['mf_1_cat'] <=0),1,0)),\n",
    "              np.sum(np.where(df_cat['obs_cat'] > 0,1,0))],\n",
    "              [np.sum(np.where((df_cat['obs_cat'] <= 0) & (df_cat['mf_1_cat'] > 0),1,0)),\n",
    "              np.sum(np.where((df_cat['obs_cat'] <= 0) & (df_cat['mf_1_cat'] <= 0),1,0)),\n",
    "              np.sum(np.where(df_cat['obs_cat'] <= 0,1,0))]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "e3288cec-8550-4777-bf2b-578093ca3db5",
   "metadata": {},
   "outputs": [],
   "source": [
    "cont_table = np.array(cont_table)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "7aff6c07-47dc-44aa-8f63-3996598543f6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hit rate above normal:  0.9333333333333333\n",
      "false alarm rate above normal:  0.06666666666666667\n"
     ]
    }
   ],
   "source": [
    "print('hit rate above normal: ' , cont_table[0,0]/cont_table[0,2])\n",
    "print('false alarm rate above normal: ' , cont_table[0,1]/cont_table[0,2])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d4880cb-9e85-43e7-ba32-9776be46865c",
   "metadata": {},
   "source": [
    "## Probabilities of events - ROC curve\n",
    "\n",
    "For example for the French forecast. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 456,
   "id": "f718289c-0ea9-4e05-aea8-d89781075473",
   "metadata": {},
   "outputs": [],
   "source": [
    "#The event is still defined as above or below normal considering the terciles, but now it is FORCASTED if it exceeds a threshold\n",
    "def above_below_normal(data,obs = df_cat['obs'],N=9):\n",
    "    #Probability of being Temp Above Normal\n",
    "    AN = np.sum(np.where(data.iloc[:,11:20] > 0,1,0) , axis=1)/N\n",
    "    #Probability of being Temp Below Normal\n",
    "    BN = np.sum(np.where(data.iloc[:,11:20] < 0,1,0) , axis=1)/N\n",
    "    #Probability of being Temp Normal\n",
    "    Normal = np.sum(np.where(data.iloc[:,11:20] == 0,1,0) , axis=1)/N\n",
    "    data_prob = pd.DataFrame({'AN':AN,'N':Normal,'BN':BN})\n",
    "    data_prob['obs'] = obs.values\n",
    "    return data_prob\n",
    "\n",
    "N = 9 #Ensemble members\n",
    "def categorization_threshold(df,N,thresh):\n",
    "    terciles = df['obs'].quantile([0.33,0.66]).values\n",
    "    categories = np.where(df['obs'] <= terciles[0],1,0)*(-1) + np.where(df['obs'] >= terciles[1],1,0)\n",
    "    df['obs_cat'] = categories\n",
    "    for i in range(N): \n",
    "        categories = np.where(df['AN'] < thresh,1,0)*(-1) + np.where(df['AN'] >= thresh,1,0)\n",
    "        df[str(thresh)] = categories\n",
    "        \n",
    "    return df\n",
    "    \n",
    "def cont_table(obs,sim):\n",
    "    \"\"\"Returns a contingency table\n",
    "    \n",
    "    \n",
    "    input: obs, sim must be arrays where -1 indicates below normal (BN), \n",
    "                                          1 indicates above normal (AN) and\n",
    "                                          0 indicates normal (N)\n",
    "    returns: contingency table with [# (obs AN & forecast AN), # (obs AN & forecast non-AN), #obs AN\n",
    "                                    # (obs non-AN & forecast AN), # (non-obs AN & forecast non-AN), #obs non-AN]\"\"\"\n",
    "    cont_table = [[np.sum(np.where((obs > 0) & (sim > 0),1,0)),\n",
    "              np.sum(np.where((obs > 0) & (sim <=0),1,0)),\n",
    "              np.sum(np.where(obs > 0,1,0))],\n",
    "              [np.sum(np.where((obs <= 0) & (sim > 0),1,0)),\n",
    "              np.sum(np.where((obs <= 0) & (sim <= 0),1,0)),\n",
    "              np.sum(np.where(obs <= 0,1,0))]]\n",
    "    return np.array(cont_table)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 447,
   "id": "9dc83916-1673-4a99-a2e3-d81fa58a8325",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "704182d1-0933-4c64-a3ad-b170d0f58f8f",
   "metadata": {},
   "source": [
    "## MF forecast"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 457,
   "id": "3fd2e79c-8d00-4735-b009-d2aad6803b30",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 9  6 15]\n",
      " [ 0 28 28]]\n",
      "hit rate above normal:  0.6\n",
      "false alarm rate above normal:  0.0\n"
     ]
    }
   ],
   "source": [
    "df_mf_prob = above_below_normal(df_mf_cat,obs = df_cat['obs'],N=9)\n",
    "\n",
    "t = 1\n",
    "n = 9\n",
    "hit_rate = []; fa_rate = []\n",
    "bins = np.array([0,1/10,2/10,3/10,4/10,5/10,6/10,7/10,8/10,9/10,1])\n",
    "for t in bins:\n",
    "    cats_mf_prob = categorization_threshold(df_mf_prob,n,t)\n",
    "    cats_mf_prob_table = cont_table(cats_mf_prob['obs_cat'],cats_mf_prob[str(t)])\n",
    "    hit_rate.append( cats_mf_prob_table[0,0]/(cats_mf_prob_table[0,2]))\n",
    "    fa_rate.append(cats_mf_prob_table[1,0]/(cats_mf_prob_table[1,2]))\n",
    "    \n",
    "print(cats_mf_prob_table)\n",
    "print('hit rate above normal: ' , cats_mf_prob_table[0,0]/(cats_mf_prob_table[0,2]))\n",
    "print('false alarm rate above normal: ' , cats_mf_prob_table[1,0]/(cats_mf_prob_table[1,2]))\n",
    "\n",
    "hit_rate.append(0)\n",
    "fa_rate.append(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d1028d2-5ad1-4160-83c9-3ea3c117512c",
   "metadata": {},
   "source": [
    "### ROC curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 460,
   "id": "0b65b66d-559b-472f-b872-ae1859036fa0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'ROC curve  - MF forecast - AUC: 0.9023809523809524')"
      ]
     },
     "execution_count": 460,
     "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": [
    "plt.plot(np.array(fa_rate),np.array(hit_rate))\n",
    "plt.plot(np.array([0,1]),np.array([0,1]))\n",
    "plt.scatter(np.array(fa_rate),np.array(hit_rate))\n",
    "\n",
    "\n",
    "integral = 0\n",
    "for i in range(len(hit_rate)-1):\n",
    "    suma = (hit_rate[i] + hit_rate[i+1]) * abs(fa_rate[i+1] - fa_rate[i])/2\n",
    "    integral += suma\n",
    "\n",
    "plt.title('ROC curve  - MF forecast - AUC: '+ str(integral))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 451,
   "id": "35b149c7-61d8-4d12-bdca-fa947d590ad1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.0,\n",
       " 1.0,\n",
       " 1.0,\n",
       " 1.0,\n",
       " 1.0,\n",
       " 0.9333333333333333,\n",
       " 0.8,\n",
       " 0.8,\n",
       " 0.7333333333333333,\n",
       " 0.6,\n",
       " 0.6]"
      ]
     },
     "execution_count": 451,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hit_rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 452,
   "id": "59cb9f63-5610-4f1d-9de5-ea1ef305daf0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.0,\n",
       " 0.6785714285714286,\n",
       " 0.6785714285714286,\n",
       " 0.5714285714285714,\n",
       " 0.4642857142857143,\n",
       " 0.42857142857142855,\n",
       " 0.25,\n",
       " 0.25,\n",
       " 0.14285714285714285,\n",
       " 0.0,\n",
       " 0.0]"
      ]
     },
     "execution_count": 452,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fa_rate"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3baf129a-eb1d-43c8-b14e-6ff2f34df5b5",
   "metadata": {},
   "source": [
    "## ECMWF forecast"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 463,
   "id": "0fe73165-69ef-416e-a763-6d3c1eaf7c4f",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0 15 15]\n",
      " [ 0 28 28]]\n",
      "hit rate above normal:  [1.0, 1.0, 0.5333333333333333, 0.3333333333333333, 0.2, 0.06666666666666667, 0.0, 0.0, 0.0, 0.0, 0.0, 0]\n",
      "false alarm rate above normal:  [1.0, 0.17857142857142858, 0.10714285714285714, 0.03571428571428571, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'ROC curve  - ECMWF forecast - AUC: 0.9166666666666666')"
      ]
     },
     "execution_count": 463,
     "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": [
    "df_ecmwf_prob = above_below_normal(df_ecmwf_cat,obs = df_cat['obs'],N=9)\n",
    "\n",
    "def roc_curve(df_prob,bins,n):\n",
    "    hit_rate = []; fa_rate = []\n",
    "    for t in bins:\n",
    "        cats_prob = categorization_threshold(df_prob,n,t)\n",
    "        cats_prob_table = cont_table(cats_prob['obs_cat'],cats_prob[str(t)])\n",
    "        hit_rate.append( cats_prob_table[0,0]/(cats_prob_table[0,2]))\n",
    "        fa_rate.append(cats_prob_table[1,0]/(cats_prob_table[1,2]))\n",
    "    \n",
    "    return hit_rate,fa_rate,cats_prob_table\n",
    "\n",
    "n = 9\n",
    "bins = np.array([0,1/10,2/10,3/10,4/10,5/10,6/10,7/10,8/10,9/10,1])\n",
    "hit_rate, fa_rate, cats_prob_table = roc_curve(df_ecmwf_prob,bins,n)\n",
    "hit_rate.append(0)\n",
    "fa_rate.append(0)\n",
    "\n",
    "print(cats_prob_table)\n",
    "print('hit rate above normal: ' , hit_rate)\n",
    "print('false alarm rate above normal: ' , fa_rate)\n",
    "\n",
    "\n",
    "plt.plot(np.array(fa_rate),np.array(hit_rate))\n",
    "plt.plot(np.array([0,1]),np.array([0,1]))\n",
    "plt.scatter(np.array(fa_rate),np.array(hit_rate))\n",
    "\n",
    "\n",
    "integral = 0\n",
    "for i in range(len(hit_rate)-1):\n",
    "    suma = (hit_rate[i] + hit_rate[i+1]) * abs(fa_rate[i+1] - fa_rate[i])/2\n",
    "    integral += suma\n",
    "\n",
    "plt.title('ROC curve  - ECMWF forecast - AUC: '+ str(integral))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29f96b81-5326-4d55-9e3e-bff2070b6e26",
   "metadata": {},
   "source": [
    "## UK Forecast"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 464,
   "id": "9c02be47-32dd-4bd4-b99b-7bd0a556d7f2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2 13 15]\n",
      " [ 0 28 28]]\n",
      "hit rate above normal:  [1.0, 1.0, 0.6666666666666666, 0.4666666666666667, 0.4, 0.26666666666666666, 0.26666666666666666, 0.26666666666666666, 0.26666666666666666, 0.13333333333333333, 0.13333333333333333, 0]\n",
      "false alarm rate above normal:  [1.0, 0.21428571428571427, 0.17857142857142858, 0.07142857142857142, 0.07142857142857142, 0.07142857142857142, 0.03571428571428571, 0.03571428571428571, 0.0, 0.0, 0.0, 0]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'ROC curve  - UK forecast - AUC: 0.8952380952380952')"
      ]
     },
     "execution_count": 464,
     "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": [
    "df_uk_prob = above_below_normal(df_uk_cat,obs = df_cat['obs'],N=9)\n",
    "\n",
    "def roc_curve(df_prob,bins,n):\n",
    "    hit_rate = []; fa_rate = []\n",
    "    for t in bins:\n",
    "        cats_prob = categorization_threshold(df_prob,n,t)\n",
    "        cats_prob_table = cont_table(cats_prob['obs_cat'],cats_prob[str(t)])\n",
    "        hit_rate.append( cats_prob_table[0,0]/(cats_prob_table[0,2]))\n",
    "        fa_rate.append(cats_prob_table[1,0]/(cats_prob_table[1,2]))\n",
    "    \n",
    "    return hit_rate,fa_rate,cats_prob_table\n",
    "\n",
    "n = 9\n",
    "bins = np.array([0,1/10,2/10,3/10,4/10,5/10,6/10,7/10,8/10,9/10,1])\n",
    "hit_rate, fa_rate, cats_prob_table = roc_curve(df_uk_prob,bins,n)\n",
    "hit_rate.append(0)\n",
    "fa_rate.append(0)\n",
    "\n",
    "print(cats_prob_table)\n",
    "print('hit rate above normal: ' , hit_rate)\n",
    "print('false alarm rate above normal: ' , fa_rate)\n",
    "\n",
    "\n",
    "plt.plot(np.array(fa_rate),np.array(hit_rate))\n",
    "plt.plot(np.array([0,1]),np.array([0,1]))\n",
    "plt.scatter(np.array(fa_rate),np.array(hit_rate))\n",
    "\n",
    "\n",
    "integral = 0\n",
    "for i in range(len(hit_rate)-1):\n",
    "    suma = (hit_rate[i] + hit_rate[i+1]) * abs(fa_rate[i+1] - fa_rate[i])/2\n",
    "    integral += suma\n",
    "\n",
    "plt.title('ROC curve  - UK forecast - AUC: '+ str(integral))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b8ef2ba3-4812-474c-8f42-4a6c0a760805",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.9.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}