{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# En enkel drivhusmodell\n",
    "Seminar 3 i FYS1035, høsten 2022. Anja Røyne, UiO"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Start med å kjøre cella under for å importere pakkene vi trenger.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import *\n",
    "from pylab import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nå skal vi ta med jordas atmosfære. Vi skal bruke noe som likner på modellen fra video nummer 2, men som vi husker, gav den alt for høy temperatur. For å gjøre modellen mer realistisk skal vi ta hensyn til at ikke all utstrålingen blir fanget opp av atmosfæren. Det kan vi gjøre ved å innføre en emissivitet $\\epsilon$ for atmosfæren, slik at utstrålingen fra atmosfæren blir \n",
    "\n",
    "$Q_{ut,a} = \\sigma \\epsilon T_a^4$\n",
    "\n",
    "I tillegg skal vi, for enkelhets skyld, anta at en andel $1-\\epsilon$ av varmestrålingen fra jorda passerer  gjennom atmosfæren og rett ut i verdensrommet. Varmen som absorberes av atmosfæren blir da\n",
    "\n",
    "$Q_{inn,a} = \\epsilon Q_{ut,j}$\n",
    "\n",
    "Til slutt kan vi ta med at jorda har en albedo $a$, slik at $Q_{inn} = (1-a)S$. \n",
    "\n",
    "Energibalanse for atmosfæren:\n",
    "\n",
    "$T_a^4 = \\frac{1}{2}T_j^4$\n",
    "\n",
    "Energibalanse for bakken:\n",
    "\n",
    "$(1-a)S+\\epsilon\\sigma T_a^4 = \\sigma T_j^4$\n",
    "\n",
    "Setter inn for atmosfæretemperaturen:\n",
    "\n",
    "$(1-a)S+\\frac{1}{2}\\epsilon\\sigma T_j^4 = \\sigma T_j^4$\n",
    "\n",
    "$(1-\\frac{1}{2}\\epsilon)T_j^4 = \\frac{(1-a)S}{\\sigma}$\n",
    "\n",
    "$T_j = \\left(\\frac{(1-a)S}{\\sigma(1-1/2\\epsilon)}\\right)^{\\frac{1}{4}}$\n",
    "\n",
    "Som et utgangspunkt kan vi sette $a = 0.3$. \n",
    "\n",
    "**Hva må $\\epsilon$ være for at vi skal få en realistisk overflatetemperatur (nær 15$^{\\circ}$C)?** Det kan vi finne ut ved å plotte $T_j$ som funksjon av $\\epsilon$:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'likevektstemperatur (grader celcius)')"
      ]
     },
     "execution_count": 7,
     "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": [
    "# fysiske verdier:\n",
    "S = 342 # W/m2, innstråling\n",
    "sigma = 5.67e-8 # J/m2K, Stefan-Boltzmann-konstanten\n",
    "a = 0.3 # albedo\n",
    "# liste over verdier for epsilon:\n",
    "n = 90 # antall verdier\n",
    "epsilon = linspace(0,1,n) # gir listen med (startverdi, stoppverdi, antall)\n",
    "\n",
    "# regner ut likevektstemperaturene\n",
    "Tj = # SETT INN RIKTIG LIKNING\n",
    "# gjør om til celcius\n",
    "Tj_c = Tj - 273.15\n",
    "\n",
    "# plotter resultatene\n",
    "plot(epsilon,Tj_c)\n",
    "xlabel(\"emissiviteten til atmosfæren\")\n",
    "ylabel(\"likevektstemperatur (grader celcius)\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Jordas gjennomsnittstemperatur er omtrent 15$^o$C. Hva er en rimelig verdi for emissiviteten?**\n",
    "\n",
    "Nå kan vi lage en modell for hvordan jorda med drivhuseffekt vil utvikle seg over tid. Vi kan anta at varmekapasiteten til atmosfæren er $c_a=1.02\\cdot10^7$ J/m$^2$K ([tatt herfra](https://atmos.washington.edu/~dennis/321/321_Lecture_12.pdf)). Da blir modellen slik:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Etter 25.00 år er temperaturen blitt -11.42 grader celcius.\n"
     ]
    },
    {
     "data": {
      "image/png": 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+vbDzHKurp1ezbFMDs1duCzuKiEi3uiwOZhY1sx+lKkw2u3TyYEoL87hn9uqwo4iIdKu7meBagWmJ6ULlGBQVRLli6lD+uWAD23Y3hR1HRKRLyVxWeh14yMw+ambva1uCDpaNrp5eTVNrjPvnvNP9i0VEQpRMcagEtnJgsp+2CX/kCI0bUErN8Aruna0b0yKS3rrqBAeAu38iFUFyxdXTq/nqfW/w8vKtnD6mKuw4IiKH1W1xMLPfc0jvZAB3vzaQRFnu4hMG8Z1H3+Kul1epOIhI2uq2OACPtnteCFyOpgk9aoX5Ua46pZrbnlvOO9saGVZZHHYkEZEOkukh/dd2yx+JD9M9Kfho2etjpw3HzLjrpVVhRxEROayj6QQ3Fkjfke4ywKA+RVx8wiD+/No7NOxrCTuOiEgH3RYHM6s3s11tC/AI8I3go2W3a88YQf2+Fu6vVbNWEUk/yVxWKnX3snbLOHf/ayrCZbMp1RVMqS7n9y+tIhZTs1YRSS/JnDk8ncw2OXLXnjGSuq2N/EsTAYlImulqJrhCM6sEqsyswswqE8sIYHCqAmazCycNZFCfQm5/YUXYUUREDtLVmcOngTnAhMRj2/IQ8Kvgo2W//GiET545itkrtzGnTqO1ikj66LQ4uPvP3X0k8DV3H+XuIxPLie7+yxRmzGpXnTKMiuJ8bnlmedhRRET2S2b4jJvNbBJwPPFOcG3b/xBksFxRXJDHx08fyU+fWsKi9bs4blBZ2JFERJK6IX0DcHNiOQe4Cbgs4Fw55ZrTh9O7IMqtz+rsQUTSQzKd4N4PvAvYkBiE70SgV6Cpckx5cQEfPnU4j85fR93W3WHHERFJqjjscfcY0GJmZcAmYFSwsXLPv88YSV4kwq+f09mDiIQvmeJQa2blwG+It1aaC8wONFUOGlBWyAdPHsZfatewemtj2HFEJMd1N4e0Ad939x3u/mvgPOAazfEQjM+fM4ZIxPjFv5aGHUVEclx3c0g78GC79VXuPj/wVDlqYJ9CPnrqcB6Yu4YVmxvCjiMiOSyZy0qvmNnJgScRAD579mh65UX52VM6exCR8CRTHM4hXiCWm9l8M1tgZjp7CEhVSS+uOX0Ej8xfx+IN9WHHEZEclUxxuIh466RzgUuBSxKPEpBPnzWK3gV5/M+Ti8OOIiI5Kpkhu+uAYcC5ieeNybxPjl5F7wJmnjWKx9/cyGurNOaSiKResj2kvwFcl9iUD9wdZCiBT545kgFlvfju3xcRbxcgIpI6yZwBXE58uIzdAO6+DigNMpTEx1z6v+eP5413dvDo/PVhxxGRHJNMcWhKNGl1ADPrHWwkaXPF1KEcN6iMHz72NvtaWsOOIyI5JJnicJ+Z3QaUm9mngKeI95aWgEUjxvUXH8ea7Xv4w0t1YccRkRySzA3pHwP3A38FxgHfdvebgw4mcTPGVnH2+H784umlbKrfG3YcEckRybY6WgC8ADyfeC4pdMOlE9nXEuMH/3g77CgikiOSaa30SeID7b2P+PDdr5jZtUEHkwNGVvXmU2eN5IHX1zJ7pZq2ikjwkjlz+Dowxd0/7u7XANOIN22VFPr8OWMYUl7Etx9aSEtrLOw4IpLlkikOa4D24zjUA+8EE0c6U1yQx7cuOZ63N9Rz18u6OS0iwUqmOKwFXjWzGxMd4l4BlpnZV83sq8HGk/YumDiAfxvXj/95YjFrd+wJO46IZLFkisNy4sN2t3XTfQhYT7wjnDrDpZCZ8d33TsKB6/+2QD2nRSQwed29wN3/OxVB2pjZjcCngM2JTf/l7v9IZYZ0NqyymK9fMJ7/fuQtHpy3lsunDA07kohkoWRaK9WY2d/MbG5iyO75KRiy+6fuflJiUWE4xMdOG8HU6nL++5G32NKwL+w4IpKFkrms9Efg98AVxIfqblskJNGI8cMrJtO4r5UbHnoz7DgikoWSKQ6b3f1hd1/p7nVtS8C5vpA4Q7nDzCoC/q6MNHZAKV961xj+vmA9D81bG3YcEcky1t1NTTN7F3AV8DSw/xqGuz9w1F9q9hQw8DC7rifeGmoL8Rvg/w8Y5O4dOt2Z2UxgJkB1dfW0urrca97Z0hrjytteZummBh778lkMKS8KO5KIZBAzm+PuNYfdl0RxuBuYALwJtPW+8sP9we5pZjYCeNTdJ3X1upqaGq+trQ06Tlqq27qbi3/+AicM7cM9nzyVSMTCjiQiGaKr4tBtayXgRHc/oYczdcrMBrl72wQGlwMLU/XdmWh4397ccNlE/vP++fx21gpmnjU67EgikgWSuefwipkdH3iSA24yswWJFlHnAF9J4XdnpA9MG8qFEwfyo8cX8/rq7WHHEZEskMxlpUXAaGAl8XsORvyy0uTg4yUnly8rtdnZ2My7b34Bd3j0izOo6F0QdiQRSXNdXVZK5szhQmAscD7xJqyXoKasaadPcT63fHgqm+v38ZX75hGLqfe0iBy9ZCb7qQOGAecmnjcm8z5JvclDy/nWpcfz7OLN3Prc8rDjiEgGS6aH9A3Eh+i+LrEpH7g7yFBy9D4yvZrLThzMT55YzEvLtoQdR0QyVDJnAJcDlwG7Adx9HRpwL22ZGd9/3wmM6lfC5+6ZS93W3WFHEpEMlExxaPL4XWsHMLPewUaSY9W7Vx6//Vj8HtO1d77Grr3NIScSkUyTTHG4z8xuA8rN7FPAU8Bvg40lx2pEVW9+/ZFp1G1t5Av3vK7Z40TkiCRzQ/rHwP3AX4HxwLfd/RdBB5Njd+qovnzv8kk8v2Qz3/37orDjiEgG6baHtJn90N2/ATx5mG2S5j54cjVLNzbw21krGVpRxCfPHBV2JBHJAMlcVjrvMNsu6ukgEpzrLj6Oi08YyHf/vogH5q4JO46IZIBOzxzM7LPA54BRh0zuUwq8GHQw6TnRiPHTD57EjsbX+Pr98ykvzufcCQPCjiUiaayrM4d7iPeEfpiDJ/mZ5u4fSUE26UG98qLc/rEajh9Uxuf+OJfaVdvCjiQiaazT4uDuO919lbtfxcE9pCNmNjJlCaXHlPTK485PnMzgPkV84s7XmPfOjrAjiUiaOpoe0gWoh3TG6lvSi7s/OZ2K4gI++ttXNYqriByWekjnoMHlRfxp5qlUlhTwsd/NZq4KhIgcQj2kc9ShBWJOne5BiMgB6iGdwwb1iReIqpICPvzbV3lm8aawI4lImlAP6Rw3qE8Rf/nM6YzuV8Kn7qpVPwgRAZK7IX2Ruz/p7l9396+5+5Nm9plUhJPU6Ffaiz/NPJVTRlby1fve4DfPrwg7koiELJnLSt8ys3PbVszsG8B7goskYSgtzOf3nziZi08YyPf+sYhvPbiQZg3WJ5Kzuh1biXhLpUfN7OvEpwydkNgmWaZXXpSbr5rKsIq3ue35FazY0sAtV0+jT3F+2NFEJMWSueewhXgx+BUwGHi/u2uCgCwVjRjXXXwcP3r/ZGav3MZ7b3mR5Zsbwo4lIinWaXEws3oz22Vm9cAyYBzwAWCXme1KVUAJxwdqhnHvp05l155m3vvLF3ls4fqwI4lICnU1fEapu5e1eyx09xJ3LwX6pDCjhKRmRCUPfeEMRvUv4TN3z+U7j7xFU4vuQ4jkgmRaK33nkPUIGj4jZwytKOYvnz6Nj58+gjteXMmHbn+ZtTv2hB1LRAKWTGulajO7DsDMegEPAksDTSVppSAvwo2XTeRXV09lycYGLvzp8zwwdw3xjvMiko2SKQ6fAE5IFIhHgGfc/cZAU0laevfkQfzjS2cyYVApX73vDT5791y2NuwLO5aIBKCrG9JTzWwqMAX4OfBB4mcMzyW2Sw6q7lvMn2aexnUXTeBfb2/igp+9wJNvbQw7loj0MOvs0oCZPdPF+9zdz+1if0rV1NR4bW1t2DFyzqL1u/jKn+fx9oZ6Lpw4kBsuO55BfYrCjiUiSTKzOe5ec9h92XDdWMUhPE0tMX7zwgp+8fRS8iLG/z1/PNecPoJoxMKOJiLdOObiYGbvBiYChW3b3P07nb8jtVQcwrd6ayPfemghzy3ZzKQhZXz7komcMrIy7Fgi0oWuikMyTVl/Tfx+wxcBI94RbniPJpSMV923mDs/cTK/vHoKWxuauPK2l/n0/9aycsvusKOJyFHo9szBzOa7++R2jyXAA+5+fmoidk9nDullT1Mrv5u1glueXU5za4yPnjqCL5w7hsreBWFHE5F2junMAWjr8dRoZoOBZmBkT4WT7FNUEOUL547l2a+fzfunDeXOl1Zy5g//xU2Pvc323U1hxxORJCRTHB41s3LgR8BcYBVwb5ChJDv0Ly3k+++bzONfPotzJvTn1ueWc+ZNz/CTJxazo1FFQiSdHVFrpUQP6UJ33xlcpCOny0qZYfGGen7+9BL+sWADxQVRrqwZxr/PGMmwyuKwo4nkpGNqrWRmhcDngBmAA7OAW919b08HPVoqDpnl7Q27uP35FTw8bx0xdy6aNIhPnTWKk4aVhx1NJKcca3G4D6jnwGB7VwEV7v6BHk15DFQcMtP6nXu486VV3PPKaur3tXDSsHKunl7NpZMHU1QQDTueSNY71uLwhruf2N22MKk4ZLb6vc38pXYNf3y1juWbd1NamMf7pgzh6unDGT+wNOx4IlnrWFsrvW5mp7b7sOnAi8cY6ANm9qaZxcys5pB915nZMjNbbGYXHMv3SGYoLczn2hkjeeqr/8afZ57KuRP6c+/sd7jgZ89z6c2z+O0LK9i0K22uYorkhK7GVlpA/B5DPjAeWJ1YHw685e6TjvpLzY4DYsBtwNfcvTax/XjiLaFOIT4l6VPAOHdv7erzdOaQfbbtbuJvr6/lwdfXsmDtTiIGp4+u4j0nDebCSQMpLdS81iLH6qguK5lZl72g3b2uB4I9y8HF4brEZ38/sf44cKO7v9zV56g4ZLdlmxp4aN5aHpq3jtXbGimIRjhtdF/OnziA844bQP+ywu4/REQ6SNuB9w5THH4JvOLudyfWfwf8093vP8x7ZwIzAaqrq6fV1R1zrZI05+7MXb2Dxxau5/E3N7J6WyMAU6rLOe/4AZw9rj/HDSrFTIP+iSSjq+KQF+CXPgUMPMyu6939oc7edphth61e7n47cDvEzxyOKqRkFDNj2vAKpg2v4L8uPo4lGxt44s0NPPHWRm56bDE3PbaYqpJezBjTlzPH9mPG2CoG6KxC5KgEVhzc/f8cxdvWAMParQ8F1vVMIskmZsb4gaWMH1jKF981lg079/LC0s3MWraFWcu28OC8+L824waUcOqovtSMqOSUEZUM7KNiIZKMdLusNBG4hwM3pJ8GxuqGtByJWMxZtGEXs5bGC8Wcuu00NsX/FRpaUcTJIyqpGVHBScPKGTeglPxoMo32RLJP2t1zMLPLgZuBfsAOYJ67X5DYdz1wLdACfNnd/9nd56k4SFdaWmMsWl/Pa6u2UVu3jdkrt7MlMfd1QV6E4waVMXlIH04Y2ocThvRhbP8S8lQwJAekXXHoaSoOciTcndXbGnljzU4WrNnBgrU7Wbh2Fw37WgDolRdh7IASxvUvZdzAUsYPKGXsgBKGlBfpZrdkFRUHkW7EYs7KrbtZuHYnC9bsZPHGepZubGBDu853Jb3yGDughFFVJYysKmZ4396MrOrN8L7F6nchGUnFQeQo7WxsZsmmepZsrGfJhnqWbGxgxZYGNu7ad9DrqkoKGN43XiiGVRQzuLyQweVF8aVPkcaKkrQUSlNWkWzQpzifk0dUcvKIg+fDbmxqYfW2RlZt2c2qrW2Pu3lp2VY21q/l0P/nquxdwKA+8YIxpLyIAWWFVJUU0K+01/6lb+9eRCO6bCXpQcVB5CgUF+QxYWAZEwaWddjX1BJj4669rNuxh3U797BuR+L5jj2s3trIK8u3Up+4v9FexOJFpKrkQMGoLC6gvDif8uICKvY/z9//vCg/qvsgEggVB5EeVpAXYVhlcZeTGDU2tbClvonNDXvZXL/vwNKwj831TWxu2MeKzbvZtruJPc2dt+QuyItQkSgWpYV5lPTKo6Qwn5JeeQfWe+VRUphHaeIxvi/+mqKCKEX5UfKjpiIjB1FxEAlBcUEe1X3zqO7b/Sx4e5tb2bmnmR2NzWxvbGJHY1PieXO750007Gth6+4m6rY2smtvC3tB7J0AAAcdSURBVA37mtnbHEsqTzRiFOVHKcyPUlQQoSg/un+9uCBKUUFiX9tSEKUgGqEgr92SWO+VWM+PRg56Ta+8CAXR6EHvyY8aBdGIClMaUnEQSXOFiT/SRzMUSHNrjN37Wqjf20LDvsSyt4Vde5tp2NfC3uYYe5pa2NPcyp6mGHuaW9nb3Mqeptb4tuZWtu5uYs/2xHq77T3ZliUaMaIRI6/dY140ctB6/DFCXvTg9WjE2m1LvCdq5EeMSMSImBE1IxKJ96yPGETNEs8T6xHbvy9ibe9j//62zzmw7cB2a/v8xD7b/3lgJB7NMDh4G4nt7Z+3veag93T93qqSAsb07/l5T1QcRLJYfjRCeXEB5cUFPfq57k5zq9PcGqOpJUZT4nFfy8HrTS0xmlsT29tta2pp3b/e3Oq0xpyWmNMai9ESc1paD15v3b8t1u61B7btbTmw3hpzmtte1+q4OzGH2EGPTizmuENr27rHj6s1Fn+eKS6ZPIhfXj21xz9XxUFEjpiZUZBnFORF6N0r7DTBaCsq8WIRLyQxd1rd8diBItPabl/M431m2hcbT3yWO4nn4CTWE+/j0O3tvh8Oee/+z4w/71sSzA+g4iAichjxy0XkbPNiDSAjIiIdqDiIiEgHKg4iItKBioOIiHSg4iAiIh2oOIiISAcqDiIi0kFWzOdgZpuBuqN8exWwpQfjZAIdc27QMeeGYznm4e7e73A7sqI4HAszq+1ssotspWPODTrm3BDUMeuykoiIdKDiICIiHag4wO1hBwiBjjk36JhzQyDHnPP3HEREpCOdOYiISAcqDiIi0kHOFgczu9DMFpvZMjP7Zth5UsXMVpnZAjObZ2a1YecJgpndYWabzGxhu22VZvakmS1NPFaEmbGndXLMN5rZ2sRvPc/MLg4zY08ys2Fm9oyZLTKzN83sPxLbs/Z37uKYA/mdc/Keg5lFgSXAecAa4DXgKnd/K9RgKWBmq4Aad8/ajkJmdhbQAPzB3Scltt0EbHP3HyT+Z6DC3b8RZs6e1Mkx3wg0uPuPw8wWBDMbBAxy97lmVgrMAd4LfJws/Z27OOYrCeB3ztUzh1OAZe6+wt2bgD8B7wk5k/QQd38e2HbI5vcAdyWe30X8P6qs0ckxZy13X+/ucxPP64FFwBCy+Hfu4pgDkavFYQjwTrv1NQT4DznNOPCEmc0xs5lhh0mhAe6+HuL/kQH9Q86TKl8ws/mJy05Zc4mlPTMbAUwBXiVHfudDjhkC+J1ztTgcblLYXLm+doa7TwUuAj6fuBwh2elWYDRwErAe+Em4cXqemZUAfwW+7O67ws6TCoc55kB+51wtDmuAYe3WhwLrQsqSUu6+LvG4Cfgb8UtsuWBj4ppt27XbTSHnCZy7b3T3VnePAb8hy35rM8sn/kfyj+7+QGJzVv/OhzvmoH7nXC0OrwFjzWykmRUAHwIeDjlT4Mysd+JGFmbWGzgfWNj1u7LGw8A1iefXAA+FmCUl2v5IJlxOFv3WZmbA74BF7v4/7XZl7e/c2TEH9TvnZGslgERzr58BUeAOd/9eyJECZ2ajiJ8tAOQB92TjcZvZvcDZxIcy3gjcADwI3AdUA6uBD7h71tzA7eSYzyZ+qcGBVcCn267HZzozmwG8ACwAYonN/0X8GnxW/s5dHPNVBPA752xxEBGRzuXqZSUREemCioOIiHSg4iAiIh2oOIiISAcqDiIhMLPfm9lDiXbrImlHxUEkxcxsEvHhWx4h3tdEJO2oOIh0wczKzexz7dYHm9n9nbz2WTOr6WTf/Yl+JhAfvsXo5r8/M/uxmZ17lNFFjomKg0jXyoH9xcHd17n7+4/kA8xsIhB19xWJz1hAvJPWpcCTnbwnCtwM5MxcI5JeVBxEuvYDYHRiEpUfmdmItgl1zKzIzP6UGA3zz0BRJ5/xYdoN42BmtwITgVHA9e22rzKzb5vZLOI9e+uAvmY2MKBjE+lUXtgBRNLcN4FJ7n4S7B8quc1ngUZ3n2xmk4G5nXzGGcC97davd/dtibODp81ssrvPT+zb6+4z2r12buL9fz32QxFJns4cRI7eWcDdAIk/7vM7ed0gYHO79SvNbC7wOvEziOPb7fvzIe/dBAzukbQiR0BnDiLHJpnByfYAhQBmNhL4GnCyu283szvb9iXsPuS9hYn3i6SUzhxEulYPlHay73ni9xPamqdO7uR1i4AxiedlxAvATjMbQHzSpa6MI4uG2pbMoeIg0gV33wq8aGYLzexHh+y+FSgxs/nAfwKzO/mYvxMfPht3f4P45aQ3gTuAFzv77kQHuTFA7bEcg8jR0JDdIgEzsyLgGeJTtLYewfsuB6a6+7cCCyfSCZ05iATM3fcQn3xnyBG+NY8snPdZMoPOHEREpAOdOYiISAcqDiIi0oGKg4iIdKDiICIiHag4iIhIByoOIiLSwf8H5WZKi4eZnvsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fysiske verdier:\n",
    "S = 342 # W/m2, innstråling\n",
    "sigma = 5.67e-8 # J/m2K, Stefan-Boltzmann-konstanten\n",
    "epsilon = # SETT INN VERDI\n",
    "a = 0.3 # albedo\n",
    "c_j = 4.0e8 # J/m2K, varmekapasitet for jorda\n",
    "c_a = 1.02e7 # J/m2K, varmekapasitet for atmosfæren\n",
    "T0j_c = 10 #grader celcius, starttemperatur for jordoverflaten\n",
    "T0a_c = 2 #grader celcius, starttemperatur for atmosfæren\n",
    "\n",
    "# regner om starttemperaturene til kelvin:\n",
    "T0j = T0j_c + 273.15\n",
    "T0a = T0a_c + 273.15\n",
    "# numeriske verdier:\n",
    "N = 500 # antall tidssteg\n",
    "dt = 0.05*365*24*3600 # antall sekunder per tidssteg (antall år * dager pr år * timer pr dag * sekunder pr time)\n",
    "\n",
    "# lager en liste over alle tidspunktene: \n",
    "t = arange(1,N+1,1) \n",
    "# lager en tom liste der jeg skal lagre temperaturene for hvert år:\n",
    "Tj = zeros(N)\n",
    "Ta = zeros(N)\n",
    "\n",
    "# tidsløkka:\n",
    "for i in t: # dette skal gjøres for hver verdi av \"t\" etter tur, til lista er tom\n",
    "    # alt som hører inne i løkka skal være flyttet ett hakk inn til høyre.\n",
    "    if i == 1: # to likhetstegn brukes for å sjekke om i er akkurat lik 1\n",
    "        Tj[i-1] = T0j \n",
    "        Ta[i-1] = T0a \n",
    "        # Python teller plassene i lister fra 0. Her sier jeg at i år 1 skal jeg legge startverdien på plass 0 i temperatur-lista\n",
    "    else: # hvis vi ikke er i første år\n",
    "        # atmosfærens utstråling\n",
    "        Q_ut_a = # SETT INN RIKTIG LIKNING\n",
    "        # innstråling på jorda\n",
    "        Q_inn_j = # SETT INN RIKTIG LIKNING\n",
    "        # utstråling fra jorda\n",
    "        Q_ut_j = # SETT INN RIKTIG LIKNING\n",
    "        # temperatur, jorda\n",
    "        Tj[i-1] = Tj[i-2]+ 1/c_j*(Q_inn_j-Q_ut_j)*dt # oppdaterer temperaturen basert på energibalansen\n",
    "        # temperatur, atmosfæren\n",
    "        Q_inn_a = # SETT INN RIKTIG LIKNING\n",
    "        Ta[i-1] = Ta[i-2]+ 1/c_a*(Q_inn_a-Q_ut_a)*dt # oppdaterer temperaturen basert på energibalansen\n",
    "                \n",
    "# tilbake til celcius\n",
    "Tj_c = Tj-273.15\n",
    "        \n",
    "# plotte resultatet:\n",
    "plot(t*dt/(365*24*3600),Tj_c)\n",
    "xlabel(\"tid (år)\")\n",
    "ylabel(\"bakketemperatur (grader celcius)\")\n",
    "\n",
    "# hva blir sluttresultatet\n",
    "print(\"Etter\",format(t[-1]*dt/(365*24*3600),\".2f\"),\"år er temperaturen blitt\",format(Tj_c[-1],\".2f\"),\"grader celcius.\") "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**I modellen over: hvilken parameter gir det mest mening å endre på dersom du vil se på effekten av en kraftigere drivhuseffekt? Prøv og se hva utslaget blir. Var det som forventet?**"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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