TCRE.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1220,
   "id": "surrounded-embassy",
   "metadata": {},
   "outputs": [],
   "source": [
    "using ClimateMARGO\n",
    "using Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1221,
   "id": "elegant-hormone",
   "metadata": {},
   "outputs": [],
   "source": [
    "using ClimateMARGO.Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1222,
   "id": "mobile-general",
   "metadata": {},
   "outputs": [],
   "source": [
    "using ClimateMARGO.Diagnostics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1223,
   "id": "latest-correlation",
   "metadata": {},
   "outputs": [],
   "source": [
    "using ClimateMARGO.Utils"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1224,
   "id": "motivated-vermont",
   "metadata": {},
   "outputs": [],
   "source": [
    "using Random\n",
    "using Distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1225,
   "id": "united-accreditation",
   "metadata": {},
   "outputs": [],
   "source": [
    "using Interpolations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1226,
   "id": "accepting-gossip",
   "metadata": {},
   "outputs": [],
   "source": [
    "using CSV, DataFrames"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1344,
   "id": "apparent-guest",
   "metadata": {},
   "outputs": [],
   "source": [
    "include(\"ebm.jl\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1345,
   "id": "reported-breast",
   "metadata": {},
   "outputs": [],
   "source": [
    "data_path = \"GCB2020v18_MtCO2_flat/GCB2020v18_MtCO2_flat.csv\"\n",
    "data = DataFrame(CSV.File(data_path));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1346,
   "id": "unlimited-trinity",
   "metadata": {},
   "outputs": [],
   "source": [
    "year = data[data[!, \"Country\"] .== \"Global\", 3];\n",
    "q_hist = data[data[!, \"Country\"] .== \"Global\", 4]*1e-3;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1347,
   "id": "external-shade",
   "metadata": {},
   "outputs": [],
   "source": [
    "interp = extrapolate(interpolate((year,), q_hist, Gridded(Linear())), 0);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1348,
   "id": "latest-cherry",
   "metadata": {},
   "outputs": [],
   "source": [
    "λ_mean = -1.3\n",
    "λ_var = 0.44\n",
    "N = 50000\n",
    "\n",
    "λ_dist = Normal(λ_mean, λ_var);\n",
    "λ_samples = rand(λ_dist, N);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1349,
   "id": "warming-malta",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.6088307246376714"
      ]
     },
     "execution_count": 1349,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "λ = quantile(λ_samples, 2/3)\n",
    "FCO2_double = 4.00\n",
    "ECS = -FCO2_double/λ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1350,
   "id": "authentic-national",
   "metadata": {},
   "outputs": [
    {
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      ]
     },
     "execution_count": 1350,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1 = histogram(λ_samples, bins=range(-3.5, stop = 0, length = 40), label=\"Climate feedback parameter\", alpha=0.3, ylims=(0, 5000))\n",
    "vline!(p1, [λ], label=\"66% quantile\", lw=2)\n",
    "p2 = histogram(-FCO2_double ./ λ_samples, xlims=(0, 10), bins=range(0, stop = 10, length = 40), label=\"Equilibrium Climate Sensitivity\", alpha=0.3, ylims=(0, 8000))\n",
    "vline!(p2, [ECS], label=\"66% quantile\", lw=2)\n",
    "p = plot(p1, p2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1351,
   "id": "perceived-destination",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "IRF (generic function with 1 method)"
      ]
     },
     "execution_count": 1351,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = [0.2173, 0.2240, 0.2824, 0.2763]\n",
    "τ = [394.4, 36.54, 4.304]\n",
    "\n",
    "heavyfunc(f, t) = f .* (t.>=0.)\n",
    "\n",
    "function IRF(t, a, τ)\n",
    "    return a[1] .+ sum([aa .* exp.(-t/ττ) for (aa, ττ) in zip(a[2:end], τ)])\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1352,
   "id": "artificial-appendix",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "CO2 (generic function with 1 method)"
      ]
     },
     "execution_count": 1352,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CO2up(t) = CO2up_land(t) + CO2up_ocean(t)\n",
    "CO2pulse(t, t0) = heavyfunc(1. .- CO2up(t .- t0), t .- t0)\n",
    "CO2(t, dt, q, c0) = c0 .+ sum([q[n]*CO2pulse(t, t[n])*dt for n = 1:length(t)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1353,
   "id": "recognized-russell",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{String,Float64} with 5 entries:\n",
       "  \"B\"  => 1.10839\n",
       "  \"Cu\" => 7.3\n",
       "  \"κ\"  => 0.73\n",
       "  \"Cd\" => 106.0\n",
       "  \"Δt\" => 1.0"
      ]
     },
     "execution_count": 1353,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params = deepcopy(ClimateMARGO.IO.included_configurations[\"default\"])\n",
    "m = ClimateModel(params);\n",
    "\n",
    "phys = m.physics\n",
    "T0 = phys.T0\n",
    "c0 = phys.c0\n",
    "Cd = phys.Cd\n",
    "κ = phys.κ\n",
    "\n",
    "a = FCO2_double/log(2.)\n",
    "\n",
    "Finf = 0.\n",
    "G = zeros(length(t_arr));\n",
    "\n",
    "physics = Dict(\"Δt\" => Δt, \"Cu\" => 7.3, \"Cd\" => Cd, \"κ\" => κ, \"B\" => -λ)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1354,
   "id": "creative-snowboard",
   "metadata": {},
   "outputs": [],
   "source": [
    "Δt = 1.\n",
    "initial_year = 1800\n",
    "final_year = 2300.\n",
    "t_arr = collect(initial_year:Δt:final_year)\n",
    "\n",
    "peak_emission_year = 2020.\n",
    "E_ = interp(t_arr)\n",
    "E_max = maximum(E_)\n",
    "E_[t_arr .>= peak_emission_year] = E_max ./ (1 .+ exp.((t_arr .- peak_emission_year .- 40.) ./ 7.5))[t_arr .>= peak_emission_year]\n",
    "E_[E_ .< 0.] .= 0.;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1355,
   "id": "protective-omega",
   "metadata": {},
   "outputs": [],
   "source": [
    "c_ = CO2(t_arr, Δt, GtCO2_to_ppm(E_), c0)\n",
    "F_ = F(a, c0, Finf, c_, G)\n",
    "T_ = DICE_EBM(t_arr, Δt, F_, physics=physics);\n",
    "Ecum_ = cumsum(E_);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1356,
   "id": "prostate-cradle",
   "metadata": {},
   "outputs": [],
   "source": [
    "interp_TCRE = extrapolate(interpolate((Ecum_[1:nmax],), T_[1:nmax], Gridded(Linear())), 0);\n",
    "x = 0:10:maximum(Ecum_[1:nmax]);\n",
    "y = interp_TCRE(x);\n",
    "βhat = inv(transpose(x)*x) * transpose(x) * y;\n",
    "yhat = x*βhat\n",
    "\n",
    "xplot = 0:10:5000;\n",
    "yhatplot = xplot*βhat\n",
    "plot!(xplot, yhatplot, lw=1.5, color=:black, label=\"\")\n",
    "\n",
    "tn_present = findmin(abs.(t_arr .- 2020))[2]\n",
    "n_present = findmin(abs.(x .- Ecum_[tn_present]))[2]\n",
    "RCB = sum(x[n:end])\n",
    "\n",
    "T_limit = 1.5\n",
    "n_limit = findmin(abs.(yhat .- T_limit))[2]\n",
    "\n",
    "plot!([x[n_present]], [yhat[n_present]], marker=:star, markersize=8, color=:red, linewidth=0., label=\"2020\", ylim=(0., 2.3), xlim=(0, 3500))\n",
    "plot!([x[n_limit]], [yhat[n_limit]], marker=:circle, markersize=8, color=:red, linewidth=0., label=\"2020\", ylim=(0., 2.3), xlim=(0, 3500))\n",
    "\n",
    "RCB = x[n_limit] - x[n_present]\n",
    "\n",
    "years_to_net_zero = 2*RCB/qmax\n",
    "\n",
    "net_zero_year = peak_emission_year + years_to_net_zero\n",
    "tn_net_zero = findmin(abs.(t_arr .- net_zero_year))[2]\n",
    "\n",
    "E_net_zero = interp(t_arr)\n",
    "E_net_zero[(t_arr .>= peak_emission_year) .& (t_arr .< net_zero_year)] .= E_max\n",
    "E_net_zero[t_arr .>= peak_emission_year] = (E_max * (1 .- (t_arr .- peak_emission_year)/(net_zero_year - peak_emission_year)))[t_arr .>= peak_emission_year]\n",
    "E_net_zero[E_net_zero .< 0.] .= 0.;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1357,
   "id": "unnecessary-oriental",
   "metadata": {},
   "outputs": [],
   "source": [
    "c_net_zero = CO2(t_arr, Δt, GtCO2_to_ppm(E_net_zero), c0)\n",
    "F_net_zero = F(a, c0, Finf, c_net_zero, G)\n",
    "T_net_zero = DICE_EBM(t_arr, Δt, F_net_zero, physics=physics);\n",
    "Ecum_net_zero = cumsum(E_net_zero);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1358,
   "id": "ancient-november",
   "metadata": {},
   "outputs": [],
   "source": [
    "c_stab = deepcopy(c_net_zero)\n",
    "cmax, n_cmax = findmax(c_stab)\n",
    "c_stab[n_cmax:end] .= cmax\n",
    "F_stab = F(a, c0, Finf, c_stab, G)\n",
    "T_stab = DICE_EBM(t_arr, Δt, F_stab, physics=physics);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1512,
   "id": "proper-principal",
   "metadata": {},
   "outputs": [],
   "source": [
    "E_smooth = interp(t_arr)\n",
    "E_smooth[t_arr .>= peak_emission_year] = E_max ./ (1 .+ exp.((t_arr .- peak_emission_year .- years_to_net_zero/2) ./ 3.5))[t_arr .>= peak_emission_year]\n",
    "E_smooth[E_smooth .< 0.] .= 0.;\n",
    "\n",
    "c_smooth = CO2(t_arr, Δt, GtCO2_to_ppm(E_smooth), c0)\n",
    "F_smooth = F(a, c0, Finf, c_smooth, G)\n",
    "T_smooth = DICE_EBM(t_arr, Δt, F_smooth, physics=physics);\n",
    "Ecum_smooth = cumsum(E_smooth);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1515,
   "id": "eleven-improvement",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Warning: Multiple series with different color share a colorbar. Colorbar may not reflect all series correctly.\n",
      "└ @ Plots /Users/hdrake/.julia/packages/Plots/g9iOb/src/backends/gr.jl:498\n"
     ]
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       "  1727.84,1898.53 1730.12,1898.49 1732.4,1898.44 1734.67,1898.39 1736.95,1898.33 1739.23,1898.27 1741.51,1898.21 1743.78,1898.14 1746.06,1898.07 1748.34,1898 \n",
       "  1750.62,1897.93 1752.89,1897.85 1755.17,1897.76 1757.45,1897.68 1759.73,1897.58 1762,1897.49 1764.28,1897.38 1766.56,1897.27 1768.84,1897.16 1771.12,1897.04 \n",
       "  1773.39,1896.91 1775.67,1896.78 1777.95,1896.64 1780.23,1896.49 1782.5,1896.33 1784.78,1896.17 1787.06,1896 1789.34,1895.83 1791.61,1895.65 1793.89,1895.47 \n",
       "  1796.17,1895.28 1798.45,1895.09 1800.72,1894.87 1803,1894.65 1805.28,1894.41 1807.56,1894.17 1809.83,1893.91 1812.11,1893.65 1814.39,1893.39 1816.67,1893.1 \n",
       "  1818.94,1892.81 1821.22,1892.5 1823.5,1892.17 1825.78,1891.84 1828.05,1891.49 1830.33,1891.14 1832.61,1890.78 1834.89,1890.41 1837.17,1890.02 1839.44,1889.61 \n",
       "  1841.72,1889.18 1844,1888.72 1846.28,1888.23 1848.55,1887.73 1850.83,1887.2 1853.11,1886.64 1855.39,1886.06 1857.66,1885.45 1859.94,1884.78 1862.22,1884.1 \n",
       "  1864.5,1883.39 1866.77,1882.65 1869.05,1881.89 1871.33,1881.11 1873.61,1880.28 1875.88,1879.46 1878.16,1878.65 1880.44,1877.82 1882.72,1876.97 1884.99,1876.12 \n",
       "  1887.27,1875.3 1889.55,1874.47 1891.83,1873.67 1894.1,1872.88 1896.38,1872.05 1898.66,1871.21 1900.94,1870.34 1903.22,1869.47 1905.49,1868.57 1907.77,1867.65 \n",
       "  1910.05,1866.69 1912.33,1865.74 1914.6,1864.83 1916.88,1863.99 1919.16,1863.19 1921.44,1862.37 1923.71,1861.54 1925.99,1860.66 1928.27,1859.72 1930.55,1858.77 \n",
       "  1932.82,1857.78 1935.1,1856.74 1937.38,1855.65 1939.66,1854.53 1941.93,1853.38 1944.21,1852.21 1946.49,1851.11 1948.77,1850.02 1951.04,1848.9 1953.32,1847.73 \n",
       "  1955.6,1846.55 1957.88,1845.29 1960.16,1843.93 1962.43,1842.52 1964.71,1841.04 1966.99,1839.52 1969.27,1837.91 1971.54,1836.19 1973.82,1834.39 1976.1,1832.51 \n",
       "  1978.38,1830.55 1980.65,1828.48 1982.93,1826.36 1985.21,1824.17 1987.49,1821.89 1989.76,1819.52 1992.04,1817.03 1994.32,1814.44 1996.6,1811.75 1998.87,1808.93 \n",
       "  2001.15,1805.97 2003.43,1802.82 2005.71,1799.49 2007.98,1796 2010.26,1792.33 2012.54,1788.57 2014.82,1784.75 2017.09,1780.84 2019.37,1776.84 2021.65,1772.74 \n",
       "  2023.93,1768.53 2026.21,1764.29 2028.48,1760.08 2030.76,1755.92 2033.04,1751.8 2035.32,1747.66 2037.59,1743.48 2039.87,1739.26 2042.15,1734.96 2044.43,1730.56 \n",
       "  2046.7,1726.08 2048.98,1721.52 2051.26,1716.88 2053.54,1712.26 2055.81,1707.65 2058.09,1703.05 2060.37,1698.43 2062.65,1693.75 2064.92,1689.05 2067.2,1684.34 \n",
       "  2069.48,1679.61 2071.76,1674.84 2074.03,1670.03 2076.31,1665.17 2078.59,1660.19 2080.87,1655.05 2083.14,1649.74 2085.42,1644.26 2087.7,1638.62 2089.98,1632.83 \n",
       "  2092.26,1627.01 2094.53,1621.07 2096.81,1614.98 2099.09,1608.78 2101.37,1602.51 2103.64,1596.2 2105.92,1589.89 2108.2,1583.6 2110.48,1577.32 2112.75,1571.02 \n",
       "  2115.03,1564.71 2117.31,1558.45 2119.59,1552.23 2121.86,1546.07 2124.14,1539.96 2126.42,1533.92 2128.7,1527.94 2130.97,1522.01 2133.25,1516.15 2135.53,1510.36 \n",
       "  2137.81,1504.62 2140.08,1498.94 2142.36,1493.32 2144.64,1487.76 2146.92,1482.27 2149.19,1476.83 2151.47,1471.45 2153.75,1466.14 2156.03,1460.89 2158.31,1455.71 \n",
       "  2160.58,1450.6 2162.86,1445.57 2165.14,1440.61 2167.42,1435.73 2169.69,1430.93 2171.97,1426.23 2174.25,1421.62 2176.53,1417.12 2178.8,1412.72 2181.08,1408.45 \n",
       "  2183.36,1404.29 2185.64,1400.27 2187.91,1396.39 2190.19,1392.66 2192.47,1389.09 2194.75,1385.68 2197.02,1382.44 2199.3,1379.38 2201.58,1376.51 2203.86,1373.83 \n",
       "  2206.13,1371.34 2208.41,1369.04 2210.69,1366.94 2212.97,1365.04 2215.24,1363.33 2217.52,1361.81 2219.8,1360.47 2222.08,1359.31 2224.36,1358.31 2226.63,1357.47 \n",
       "  2228.91,1356.78 2231.19,1356.22 2233.47,1355.79 2235.74,1355.47 2238.02,1355.26 2240.3,1355.14 2242.58,1355.1 2244.85,1355.14 2247.13,1355.24 2249.41,1355.39 \n",
       "  2251.69,1355.59 2253.96,1355.83 2256.24,1356.1 2258.52,1356.4 2260.8,1356.72 2263.07,1357.06 2265.35,1357.41 2267.63,1357.77 2269.91,1358.14 2272.18,1358.51 \n",
       "  2274.46,1358.88 2276.74,1359.26 2279.02,1359.62 2281.3,1359.99 2283.57,1360.35 2285.85,1360.7 2288.13,1361.05 2290.41,1361.39 2292.68,1361.72 2294.96,1362.05 \n",
       "  2297.24,1362.36 2299.52,1362.67 2301.79,1362.97 2304.07,1363.26 2306.35,1363.54 2308.63,1363.81 2310.9,1364.07 2313.18,1364.32 2315.46,1364.56 2317.74,1364.8 \n",
       "  2320.01,1365.03 2322.29,1365.24 2324.57,1365.45 2326.85,1365.66 2329.12,1365.85 2331.4,1366.03 2333.68,1366.21 2335.96,1366.38 2338.23,1366.54 2340.51,1366.7 \n",
       "  2342.79,1366.85 2345.07,1366.99 2347.35,1367.12 2349.62,1367.25 2351.9,1367.37 2354.18,1367.49 2356.46,1367.6 2358.73,1367.7 2361.01,1367.8 2363.29,1367.89 \n",
       "  2365.57,1367.97 2367.84,1368.05 2370.12,1368.13 2372.4,1368.2 2374.68,1368.26 2376.95,1368.32 2379.23,1368.38 2381.51,1368.43 2383.79,1368.47 2386.06,1368.51 \n",
       "  2388.34,1368.55 2390.62,1368.58 2392.9,1368.61 2395.17,1368.64 2397.45,1368.66 2399.73,1368.68 2402.01,1368.69 2404.28,1368.7 2406.56,1368.71 2408.84,1368.71 \n",
       "  2411.12,1368.72 2413.4,1368.71 2415.67,1368.71 2417.95,1368.7 2420.23,1368.69 2422.51,1368.68 2424.78,1368.66 2427.06,1368.64 2429.34,1368.62 2431.62,1368.6 \n",
       "  2433.89,1368.57 2436.17,1368.54 2438.45,1368.52 2440.73,1368.48 2443,1368.45 2445.28,1368.41 2447.56,1368.38 2449.84,1368.34 2452.11,1368.3 2454.39,1368.26 \n",
       "  2456.67,1368.21 2458.95,1368.17 2461.22,1368.12 2463.5,1368.08 2465.78,1368.03 2468.06,1367.98 2470.33,1367.93 2472.61,1367.87 2474.89,1367.82 2477.17,1367.77 \n",
       "  2479.45,1367.71 2481.72,1367.66 2484,1367.6 2486.28,1367.54 2488.56,1367.49 2490.83,1367.43 2493.11,1367.37 2495.39,1367.31 2497.67,1367.25 2499.94,1367.19 \n",
       "  2502.22,1367.13 2504.5,1367.07 2506.78,1367.01 2509.05,1366.95 2511.33,1366.89 2513.61,1366.83 2515.89,1366.77 2518.16,1366.7 2520.44,1366.64 2522.72,1366.58 \n",
       "  2525,1366.52 2527.27,1366.46 2529.55,1366.4 2531.83,1366.33 2534.11,1366.27 2536.38,1366.21 2538.66,1366.15 2540.94,1366.09 2543.22,1366.03 2545.5,1365.97 \n",
       "  2547.77,1365.91 2550.05,1365.85 2552.33,1365.8 2554.61,1365.74 2556.88,1365.68 2559.16,1365.62 2561.44,1365.57 2563.72,1365.51 2565.99,1365.45 2568.27,1365.4 \n",
       "  2570.55,1365.34 2572.83,1365.29 2575.1,1365.24 2577.38,1365.18 2579.66,1365.13 2581.94,1365.08 2584.21,1365.03 2586.49,1364.98 2588.77,1364.93 2591.05,1364.88 \n",
       "  2593.32,1364.84 2595.6,1364.79 2597.88,1364.74 2600.16,1364.7 2602.44,1364.65 2604.71,1364.61 2606.99,1364.57 2609.27,1364.53 2611.55,1364.49 2613.82,1364.45 \n",
       "  2616.1,1364.41 2618.38,1364.37 2620.66,1364.33 2622.93,1364.3 2625.21,1364.26 2627.49,1364.23 2629.77,1364.19 2632.04,1364.16 2634.32,1364.13 2636.6,1364.1 \n",
       "  2638.88,1364.07 2641.15,1364.04 2643.43,1364.01 2645.71,1363.99 2647.99,1363.96 2650.26,1363.94 2652.54,1363.91 2654.82,1363.89 2657.1,1363.87 2659.37,1363.85 \n",
       "  2661.65,1363.83 2663.93,1363.81 2666.21,1363.8 2668.49,1363.78 2670.76,1363.76 2673.04,1363.75 2675.32,1363.74 2677.6,1363.73 2679.87,1363.72 2682.15,1363.71 \n",
       "  2684.43,1363.7 2686.71,1363.69 2688.98,1363.68 2691.26,1363.68 2693.54,1363.67 2695.82,1363.67 2698.09,1363.67 2700.37,1363.67 2702.65,1363.67 2704.93,1363.67 \n",
       "  2707.2,1363.67 2709.48,1363.68 2711.76,1363.68 2714.04,1363.69 2716.31,1363.69 2718.59,1363.7 2720.87,1363.71 2723.15,1363.72 2725.42,1363.73 2727.7,1363.75 \n",
       "  2729.98,1363.76 2732.26,1363.77 2734.54,1363.79 2736.81,1363.81 2739.09,1363.82 2741.37,1363.84 2743.65,1363.86 2745.92,1363.88 2748.2,1363.91 2750.48,1363.93 \n",
       "  2752.76,1363.95 \n",
       "  \"/>\n",
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       "  1613.96,1899.47 1616.24,1899.47 1618.52,1899.47 1620.79,1899.46 1623.07,1899.45 1625.35,1899.44 1627.63,1899.43 1629.9,1899.42 1632.18,1899.41 1634.46,1899.4 \n",
       "  1636.74,1899.39 1639.01,1899.38 1641.29,1899.37 1643.57,1899.36 1645.85,1899.35 1648.13,1899.34 1650.4,1899.33 1652.68,1899.32 1654.96,1899.3 1657.24,1899.29 \n",
       "  1659.51,1899.28 1661.79,1899.26 1664.07,1899.25 1666.35,1899.24 1668.62,1899.22 1670.9,1899.21 1673.18,1899.19 1675.46,1899.18 1677.73,1899.16 1680.01,1899.15 \n",
       "  1682.29,1899.13 1684.57,1899.11 1686.84,1899.09 1689.12,1899.07 1691.4,1899.05 1693.68,1899.02 1695.95,1899 1698.23,1898.98 1700.51,1898.95 1702.79,1898.92 \n",
       "  1705.07,1898.9 1707.34,1898.87 1709.62,1898.84 1711.9,1898.81 1714.18,1898.77 1716.45,1898.74 1718.73,1898.7 1721.01,1898.66 1723.29,1898.62 1725.56,1898.58 \n",
       "  1727.84,1898.53 1730.12,1898.49 1732.4,1898.44 1734.67,1898.39 1736.95,1898.33 1739.23,1898.27 1741.51,1898.21 1743.78,1898.14 1746.06,1898.07 1748.34,1898 \n",
       "  1750.62,1897.93 1752.89,1897.85 1755.17,1897.76 1757.45,1897.68 1759.73,1897.58 1762,1897.49 1764.28,1897.38 1766.56,1897.27 1768.84,1897.16 1771.12,1897.04 \n",
       "  1773.39,1896.91 1775.67,1896.78 1777.95,1896.64 1780.23,1896.49 1782.5,1896.33 1784.78,1896.17 1787.06,1896 1789.34,1895.83 1791.61,1895.65 1793.89,1895.47 \n",
       "  1796.17,1895.28 1798.45,1895.09 1800.72,1894.87 1803,1894.65 1805.28,1894.41 1807.56,1894.17 1809.83,1893.91 1812.11,1893.65 1814.39,1893.39 1816.67,1893.1 \n",
       "  1818.94,1892.81 1821.22,1892.5 1823.5,1892.17 1825.78,1891.84 1828.05,1891.49 1830.33,1891.14 1832.61,1890.78 1834.89,1890.41 1837.17,1890.02 1839.44,1889.61 \n",
       "  1841.72,1889.18 1844,1888.72 1846.28,1888.23 1848.55,1887.73 1850.83,1887.2 1853.11,1886.64 1855.39,1886.06 1857.66,1885.45 1859.94,1884.78 1862.22,1884.1 \n",
       "  1864.5,1883.39 1866.77,1882.65 1869.05,1881.89 1871.33,1881.11 1873.61,1880.28 1875.88,1879.46 1878.16,1878.65 1880.44,1877.82 1882.72,1876.97 1884.99,1876.12 \n",
       "  1887.27,1875.3 1889.55,1874.47 1891.83,1873.67 1894.1,1872.88 1896.38,1872.05 1898.66,1871.21 1900.94,1870.34 1903.22,1869.47 1905.49,1868.57 1907.77,1867.65 \n",
       "  1910.05,1866.69 1912.33,1865.74 1914.6,1864.83 1916.88,1863.99 1919.16,1863.19 1921.44,1862.37 1923.71,1861.54 1925.99,1860.66 1928.27,1859.72 1930.55,1858.77 \n",
       "  1932.82,1857.78 1935.1,1856.74 1937.38,1855.65 1939.66,1854.53 1941.93,1853.38 1944.21,1852.21 1946.49,1851.11 1948.77,1850.02 1951.04,1848.9 1953.32,1847.73 \n",
       "  1955.6,1846.55 1957.88,1845.29 1960.16,1843.93 1962.43,1842.52 1964.71,1841.04 1966.99,1839.52 1969.27,1837.91 1971.54,1836.19 1973.82,1834.39 1976.1,1832.51 \n",
       "  1978.38,1830.55 1980.65,1828.48 1982.93,1826.36 1985.21,1824.17 1987.49,1821.89 1989.76,1819.52 1992.04,1817.03 1994.32,1814.44 1996.6,1811.75 1998.87,1808.93 \n",
       "  2001.15,1805.97 2003.43,1802.82 2005.71,1799.49 2007.98,1796 2010.26,1792.33 2012.54,1788.57 2014.82,1784.75 2017.09,1780.84 2019.37,1776.84 2021.65,1772.74 \n",
       "  2023.93,1768.53 2026.21,1764.29 2028.48,1760.08 2030.76,1755.92 2033.04,1751.8 2035.32,1747.66 2037.59,1743.48 2039.87,1739.26 2042.15,1734.96 2044.43,1730.56 \n",
       "  2046.7,1726.08 2048.98,1721.52 2051.26,1716.88 2053.54,1712.26 2055.81,1707.65 2058.09,1703.05 2060.37,1698.43 2062.65,1693.75 2064.92,1689.05 2067.2,1684.34 \n",
       "  2069.48,1679.61 2071.76,1674.84 2074.03,1670.03 2076.31,1665.17 2078.59,1660.19 2080.87,1655.05 2083.14,1649.74 2085.42,1644.26 2087.7,1638.62 2089.98,1632.83 \n",
       "  2092.26,1627.01 2094.53,1621.07 2096.81,1614.98 2099.09,1608.78 2101.37,1602.51 2103.64,1596.2 2105.92,1589.89 2108.2,1583.6 2110.48,1577.32 2112.75,1571.02 \n",
       "  2115.03,1564.71 2117.31,1558.44 2119.59,1552.29 2121.86,1546.33 2124.14,1540.61 2126.42,1535.15 2128.7,1529.98 2130.97,1525.09 2133.25,1520.49 2135.53,1516.18 \n",
       "  2137.81,1512.15 2140.08,1508.4 2142.36,1504.92 2144.64,1501.72 2146.92,1498.77 2149.19,1496.08 2151.47,1493.65 2153.75,1491.46 2156.03,1489.51 2158.31,1487.81 \n",
       "  2160.58,1486.34 2162.86,1485.11 2165.14,1484.1 2167.42,1483.33 2169.69,1482.78 2171.97,1482.46 2174.25,1482.36 2176.53,1482.49 2178.8,1482.84 2181.08,1483.41 \n",
       "  2183.36,1484.11 2185.64,1484.89 2187.91,1485.71 2190.19,1486.53 2192.47,1487.35 2194.75,1488.14 2197.02,1488.91 2199.3,1489.64 2201.58,1490.35 2203.86,1491.02 \n",
       "  2206.13,1491.66 2208.41,1492.27 2210.69,1492.85 2212.97,1493.41 2215.24,1493.94 2217.52,1494.45 2219.8,1494.94 2222.08,1495.4 2224.36,1495.85 2226.63,1496.28 \n",
       "  2228.91,1496.7 2231.19,1497.1 2233.47,1497.49 2235.74,1497.86 2238.02,1498.22 2240.3,1498.56 2242.58,1498.9 2244.85,1499.22 2247.13,1499.54 2249.41,1499.84 \n",
       "  2251.69,1500.13 2253.96,1500.41 2256.24,1500.68 2258.52,1500.95 2260.8,1501.2 2263.07,1501.45 2265.35,1501.69 2267.63,1501.92 2269.91,1502.14 2272.18,1502.35 \n",
       "  2274.46,1502.56 2276.74,1502.75 2279.02,1502.95 2281.3,1503.13 2283.57,1503.31 2285.85,1503.48 2288.13,1503.64 2290.41,1503.8 2292.68,1503.95 2294.96,1504.1 \n",
       "  2297.24,1504.24 2299.52,1504.37 2301.79,1504.5 2304.07,1504.62 2306.35,1504.74 2308.63,1504.85 2310.9,1504.96 2313.18,1505.06 2315.46,1505.16 2317.74,1505.25 \n",
       "  2320.01,1505.34 2322.29,1505.42 2324.57,1505.5 2326.85,1505.57 2329.12,1505.64 2331.4,1505.71 2333.68,1505.77 2335.96,1505.83 2338.23,1505.88 2340.51,1505.94 \n",
       "  2342.79,1505.98 2345.07,1506.03 2347.35,1506.07 2349.62,1506.11 2351.9,1506.14 2354.18,1506.17 2356.46,1506.2 2358.73,1506.23 2361.01,1506.25 2363.29,1506.27 \n",
       "  2365.57,1506.29 2367.84,1506.3 2370.12,1506.31 2372.4,1506.32 2374.68,1506.33 2376.95,1506.34 2379.23,1506.34 2381.51,1506.34 2383.79,1506.34 2386.06,1506.34 \n",
       "  2388.34,1506.33 2390.62,1506.33 2392.9,1506.32 2395.17,1506.31 2397.45,1506.3 2399.73,1506.28 2402.01,1506.27 2404.28,1506.25 2406.56,1506.24 2408.84,1506.22 \n",
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      ]
     },
     "execution_count": 1515,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Warning: Multiple series with different color share a colorbar. Colorbar may not reflect all series correctly.\n",
      "└ @ Plots /Users/hdrake/.julia/packages/Plots/g9iOb/src/backends/gr.jl:498\n"
     ]
    }
   ],
   "source": [
    "p1 = plot(t_arr, E_, color=:darkred, linewidth=2.5, label=\"moderate mitigation (~2ºC)\")\n",
    "idx = tn_present:1:tn_net_zero\n",
    "plot!(t_arr[idx], E_net_zero[idx], fillrange=[E_net_zero[idx].*0., E_net_zero[idx]], fillalpha=0.1, c=:blue, lw=0, label=\"Remaining Carbon Budget for <1.5ºC (RCB-1.5)\")\n",
    "#plot!(t_arr, E_smooth, xlim=(1950, 2100), ylim=(-9.5, 60.), color=:blue, linewidth=1.5, alpha=0.3, label=nothing)\n",
    "plot!(t_arr, E_net_zero, xlim=(1950, 2100), ylim=(-9.5, 60.), color=:blue, linewidth=2.5, label=\"mitigation inferred from RCB-1.5\")\n",
    "plot!(legend=:topleft, background_color_legend=RGBA(1., 1., 1., 0.5), foreground_color_legend=RGBA(0., 0., 0., 0.))\n",
    "plot!(t_arr[1:tn_present], E_[1:tn_present], color=:black, linewidth=3, label=nothing)\n",
    "vline!([net_zero_year], color=:black, alpha=0.5, linestyle=:dash, label=nothing, linewidth=1.8)\n",
    "plot!(xlabel=\"year\", ylabel=\"emissions [GtCO₂ₑ]\", title=\"a) stylized emissions scenarios\", titlefont=font(12), titleloc=:left)\n",
    "plot!([peak_emission_year, net_zero_year], [-2.15, -2.15],arrow=arrow(:closed,:both), linestyle=:dash, linewidth=0.9, markersize=1., color=:royalblue1, label=nothing)\n",
    "plot!([peak_emission_year-1.5, peak_emission_year-1.5], [0, Emax],arrow=arrow(:closed,:both), linestyle=:dash, linewidth=0.9, markersize=1., color=:royalblue1, label=nothing)\n",
    "annotate!(peak_emission_year+years_to_net_zero/20, 1.5, text(string(\"RCB =\\n(E₀×Δt)/2\"), :royalblue1, :bottom, :left, 10))\n",
    "annotate!(peak_emission_year+years_to_net_zero/2, -5.5, text(string(\"Δt\"), :royalblue1, :center, 10))\n",
    "annotate!(peak_emission_year-4.25, Emax/2., text(string(\"E₀\"), :royalblue1, :center, 10))\n",
    "\n",
    "p2 = plot(t_arr, c_, color=:darkred, linewidth=2.5, label=nothing)\n",
    "#plot!(t_arr, c_smooth, color=:blue, linewidth=1.5, alpha=0.3, label=nothing)\n",
    "plot!(t_arr, c_net_zero, color=:blue, linewidth=2.5, label=nothing)\n",
    "plot!(t_arr, c_stab, xlim=(1800, 2300), ylim=(280, 550), color=:blue, linewidth=3., alpha=0.5, linestyle=:dot, label=\"concentration\\nstabilization\")\n",
    "plot!(legend=:topleft, background_color_legend=RGBA(1., 1., 1., 0.5), foreground_color_legend=RGBA(0., 0., 0., 0.))\n",
    "vline!([net_zero_year], color=:black, alpha=0.5, linestyle=:dash, label=\"net-zero year\", linewidth=1.8)\n",
    "plot!(xlabel=\"year\", ylabel=\"CO₂ₑ concentrations [ppm]\", title=\"b) carbon cycle response\", titlefont=font(12), titleloc=:left)\n",
    "\n",
    "p3 = plot(t_arr, T_, color=:darkred, linewidth=2.5, label=nothing)\n",
    "plot!(t_arr, T_net_zero, color=:blue, linewidth=2.5, label=nothing)\n",
    "plot!(t_arr, T_stab, xlim=(1800, 2300), ylim=(0., 2.5), color=:blue, linewidth=3., alpha=0.5, linestyle=:dot, label=nothing)\n",
    "vline!([net_zero_year], color=:black, alpha=0.5, linestyle=:dash, label=nothing, linewidth=1.8)\n",
    "plot!(xlabel=\"year\", ylabel=\"global warming [ºC]\", title=\"c) temperature response\", titlefont=font(12), titleloc=:left)\n",
    "\n",
    "p4 = plot()\n",
    "for n in 1:length(t_arr)\n",
    "    plot!([Ecum_[n]], [maximum(T_[1:n])],  marker=:dot, marker_z=[t_arr[n]], markersize=4., markerstrokewidth=0., color=:reds, alpha=0.3, clim=(1950, 2050), label=nothing)\n",
    "    plot!([Ecum_net_zero[n]], [maximum(T_net_zero[1:n])], marker=:dot, marker_z=[t_arr[n]], markersize=4., markerstrokewidth=0., color=:blues, alpha=0.3, clim=(1950, 2050), label=nothing)\n",
    "end\n",
    "\n",
    "plot!(colorbar_title = \"year\")\n",
    "plot!(x, yhat, linewidth=2., color=:black, alpha=0.5, label=\"TCRE = ΔT/E\")\n",
    "\n",
    "plot!([x[n_present], x[n_present]], [0., yhat[n_present]], color=:blue, linestyle=:dash, label=nothing)\n",
    "plot!([x[n_limit], x[n_limit]], [0., yhat[n_limit]], color=:blue, linestyle=:dash, label=nothing)\n",
    "\n",
    "plot!([x[n_present]], [yhat[n_present]], marker=:star, markersize=7, color=:deepskyblue, linewidth=0., label=\"Present\", ylim=(0., 2.3), xlim=(0, 3250))\n",
    "plot!([x[n_limit]], [yhat[n_limit]], marker=:dtriangle, markersize=6.5, color=:deepskyblue, linewidth=0., label=\"1.5ºC Limit\", ylim=(0., 2.3), xlim=(0, 3250))\n",
    "plot!(legend=:topleft, background_color_legend=RGBA(1., 1., 1., 0.5), foreground_color_legend=RGBA(0., 0., 0., 0.))\n",
    "plot!(xlabel=\"cumulative emissions [GtCO₂ₑ]\", ylabel=\"peak global warming [ºC]\")\n",
    "plot!(title=\"d) Transient Climate Response to cumulative Emissions (TCRE)\", titlefont=font(12), titleloc=:left)\n",
    "\n",
    "plot!([x[n_present], x[n_limit]], [0.125, 0.125],arrow=arrow(:closed,:both), color=:royalblue1, label=nothing)\n",
    "annotate!(x[n_present]+RCB/2., 0.425, text(string(\"RCB =\\n\",Int64(round(RCB)),\" GtCO₂ₑ\"), :royalblue1, :center, 8))\n",
    "\n",
    "l = @layout [a; b c; d]\n",
    "p = plot(p1, p2, p3, p4, layout=l, size=(700, 800))\n",
    "\n",
    "savefig(p, \"TCRE.pdf\");\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1495,
   "id": "signed-reservation",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.6088307246376714"
      ]
     },
     "execution_count": 1495,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "FCO2_double/(-λ)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1518,
   "id": "closed-booking",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "27.990152622502052"
      ]
     },
     "execution_count": 1518,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "years_to_net_zero\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "overall-bulletin",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "file_extension": ".jl",
   "mimetype": "application/julia",
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