{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# ENV/ATM 415: Climate Laboratory\n", "\n", "[Brian E. J. Rose](http://www.atmos.albany.edu/facstaff/brose/index.html), University at Albany\n", "\n", "# Lecture 16: The one-dimensional Energy Balance Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Contents\n", "\n", "1. [Heat transport and the energy budget for each latitude band](#section1)\n", "2. [Parameterizing the radiation terms](#section2)\n", "3. [Tuning the longwave parameters with reanalysis data](#section3)\n", "4. [The one-dimensional diffusive energy balance model](#section4)\n", "5. [The annual-mean EBM](#section5)\n", "6. [Tuning the diffusivity](#section6)\n", "7. [Summary: parameter values in the diffusive EBM](#section7)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "____________\n", "\n", "\n", "## 1. Heat transport and the energy budget for each latitude band\n", "____________" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Way back at the beginning of the semester we wrote down a **global average energy budget** that looked like\n", "\n", "$$ C \\frac{dT}{dt} = \\text{ASR} - \\text{OLR} $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Last time we talked about the additional **local heating** of each latitude band associated with atmospheric and oceanic motions:\n", "\n", "$$ h = - \\frac{1}{2 \\pi a^2 \\cos⁡\\phi } \\frac{\\partial \\mathcal{H}}{\\partial \\phi} $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using this, we can write down a **local energy budget** expressing how the temperature of each latitude band should change:\n", "\n", "$$ C \\frac{\\partial T}{\\partial t} = \\text{ASR} - \\text{OLR} - \\frac{1}{2 \\pi a^2 \\cos⁡\\phi } \\frac{\\partial \\mathcal{H}}{\\partial \\phi}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now the temperature $T$ is a function of latitude $\\phi$ as well as time $t$ (so we write it as a partial derivative) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also introduced the **diffusive heat transport parameterization**\n", "\n", "$$ \\mathcal{H}(\\phi) = -2 \\pi ~a^2 \\cos\\phi D \\frac{\\partial T}{\\partial \\phi} $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Putting this parameterization into the budget above gives\n", "\n", "$$ C \\frac{\\partial T}{\\partial t} = \\text{ASR} - \\text{OLR} + \\frac{D}{\\cos⁡\\phi } \\frac{\\partial}{\\partial \\phi} \\left( \\cos\\phi \\frac{\\partial T}{\\partial \\phi} \\right)$$\n", "\n", "(where we pulled the parameter $D$ out of the derivative because we are assuming it is a constant)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "____________\n", "\n", "\n", "## 2. Parameterizing the radiation terms\n", "____________" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To turn our **budget** into a **model**, we need specific parameterizations that link the radiation ASR and OLR to surface temperature $T$ (the state variable for our model)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Fixed albedo assumption" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, as usual, we can write the solar term as\n", "\n", "$$ \\text{ASR} = (1-\\alpha) ~ Q $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For now, we will **assume that the planetary albedo is fixed (does not depend on temperature)**. Therefore the entire shortwave term $(1-\\alpha) Q$ is a fixed source term in our budget. It varies in space and time but does not depend on $T$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the solar term is (at least in annual average) larger at equator than poles… and transport term acts to flatten out the temperatures." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Parameterizing the longwave radiation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we almost have a model we can solve for $T$! Just need a function OLR$(T)$ expressing the temperature dependence of the emission to space.\n", "\n", "So… what’s the link between OLR and temperature????\n", "\n", "[ discuss ]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We spent a good chunk of the course looking at this question, and developed a model of a vertical column of air.\n", "\n", "We are trying now to build a model of the equator-to-pole (or pole-to-pole) temperature structure." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We COULD use an array of column models, representing temperature as a function of height and latitude (and time).\n", "\n", "But instead, we will keep things simple, one spatial dimension at a time." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Introduce the following **simple parameterization**:\n", "\n", "$$ \\text{OLR} = A + B T $$\n", "\n", "With:\n", "\n", "- $T$ the zonal average surface temperature in ºC\n", "- $A$ is a constant in W m$^{-2}$\n", "- $B$ is a constant in W m$^{-2}$ ºC$^{-1}$.\n", "\n", "Think of $A$ as an inverse measure of the greenhouse gas amount (Why?).\n", "\n", "The parameter $B$ is closely related to the **climate feedback parameter** $\\lambda$ that we defined a while back. The only difference is that in the EBM we are going to explicitly separate the **albedo feedback** from all other radiative feedbacks." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "____________\n", "\n", "\n", "## 3. Tuning the longwave parameters with reanalysis data\n", "____________" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### OLR versus surface temperature in NCEP Reanalysis data\n", "\n", "Let's look at the data to find reasonable values for $A$ and $B$." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import xarray as xr\n", "import climlab" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Dimensions: (lat: 94, lon: 192, nbnds: 2, time: 12)\n", "Coordinates:\n", " * lon (lon) float32 0.0 1.875 3.75 5.625 7.5 9.375 11.25 ...\n", " * time (time) float64 -6.571e+05 -6.57e+05 -6.57e+05 ...\n", " * lat (lat) float32 88.542 86.6531 84.7532 82.8508 80.9473 ...\n", "Dimensions without coordinates: nbnds\n", "Data variables:\n", " climatology_bounds (time, nbnds) float64 ...\n", " skt (time, lat, lon) float64 ...\n", " valid_yr_count (time, lat, lon) float64 ...\n", "Attributes:\n", " title: 4x daily NMC reanalysis\n", " description: Data is from NMC initialized reanalysis\\n...\n", " platform: Model\n", " Conventions: COARDS\n", " not_missing_threshold_percent: minimum 3% values input to have non-missi...\n", " history: Created 2011/07/12 by doMonthLTM\\nConvert...\n", " References: http://www.esrl.noaa.gov/psd/data/gridded...\n", " dataset_title: NCEP-NCAR Reanalysis 1\n" ] } ], "source": [ "ncep_url = \"http://www.esrl.noaa.gov/psd/thredds/dodsC/Datasets/ncep.reanalysis.derived/\"\n", "ncep_air = xr.open_dataset( ncep_url + \"pressure/air.mon.1981-2010.ltm.nc\", decode_times=False)\n", "ncep_Ts = xr.open_dataset( ncep_url + \"surface_gauss/skt.sfc.mon.1981-2010.ltm.nc\", decode_times=False)\n", "lat_ncep = ncep_Ts.lat; lon_ncep = ncep_Ts.lon\n", "print( ncep_Ts)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "Ts_ncep_annual = ncep_Ts.skt.mean(dim=('lon','time'))" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "ncep_ulwrf = xr.open_dataset( ncep_url + \"other_gauss/ulwrf.ntat.mon.1981-2010.ltm.nc\", decode_times=False)\n", "ncep_dswrf = xr.open_dataset( ncep_url + \"other_gauss/dswrf.ntat.mon.1981-2010.ltm.nc\", decode_times=False)\n", "ncep_uswrf = xr.open_dataset( ncep_url + \"other_gauss/uswrf.ntat.mon.1981-2010.ltm.nc\", decode_times=False)\n", "OLR_ncep_annual = ncep_ulwrf.ulwrf.mean(dim=('lon','time'))\n", "ASR_ncep_annual = (ncep_dswrf.dswrf - ncep_uswrf.uswrf).mean(dim=('lon','time'))" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Best fit is A = 214 W/m2 and B = 1.6 W/m2/degC\n" ] } ], "source": [ "from scipy.stats import linregress\n", "slope, intercept, r_value, p_value, std_err = linregress(Ts_ncep_annual, OLR_ncep_annual)\n", "\n", "print( 'Best fit is A = %0.0f W/m2 and B = %0.1f W/m2/degC' %(intercept, slope))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We're going to plot the data and the best fit line, but also another line using these values:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# More standard values\n", "A = 210.\n", "B = 2." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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VDrdqicHz1hNdNpKDx1Kzpc+PkTCrR0cRtX0rb85/ljr/JLCw/hXcd/NQStas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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax1 = plt.subplots(figsize=(8,6))\n", "ax1.plot( Ts_ncep_annual, OLR_ncep_annual, 'o' , label='data')\n", "ax1.plot( Ts_ncep_annual, intercept + slope * Ts_ncep_annual, 'k--', label='best fit')\n", "ax1.plot( Ts_ncep_annual, A + B * Ts_ncep_annual, 'r--', label='B=2')\n", "ax1.set_xlabel('Surface temperature (C)', fontsize=16)\n", "ax1.set_ylabel('OLR (W m$^{-2}$)', fontsize=16)\n", "ax1.set_title('OLR versus surface temperature from NCEP reanalysis', fontsize=18)\n", "ax1.legend(loc='upper left')\n", "ax1.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Discuss these curves...\n", "\n", "Suggestion of at least 3 different regimes with different slopes (cold, medium, warm).\n", "\n", "Unbiased \"best fit\" is actually a poor fit over all the intermediate temperatures.\n", "\n", "The astute reader will note that... by taking the zonal average of the data before the regression, we are biasing this estimate toward cold temperatures. [WHY?]\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's take these reference values:\n", "\n", "$$ A = 210 ~ \\text{W m}^{-2}, ~~~ B = 2 ~ \\text{W m}^{-2}~^\\circ\\text{C}^{-1} $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that in the **global average**, recall $\\overline{T_s} = 288 \\text{ K} = 15^\\circ\\text{C}$\n", "\n", "And so this parameterization gives \n", "\n", "$$ \\overline{\\text{OLR}} = 210 + 15 \\times 2 = 240 ~\\text{W m}^{-2} $$\n", "\n", "And the observed global mean is $\\overline{\\text{OLR}} = 239 ~\\text{W m}^{-2} $\n", "So this is consistent.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Relationship between $B$ and feedback parameters" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recall that when we looked at climate forcing and feedback, we said that overall response to a forcing $\\Delta R$ in W m$^{-2}$ is\n", "\n", "$$ \\Delta T = \\frac{\\Delta R}{\\lambda} $$\n", "\n", "and where $\\lambda$ is the overall **climate feedback parameter**:\n", "\n", "$$\\lambda = \\lambda_0 - \\sum_{i=1}^{N} \\lambda_i $$\n", "\n", "and\n", "\n", "- $\\lambda_0 = 3.3$ W m$^{-2}$ K$^{-1}$ is the no-feedback climate response\n", "- $\\sum_{i=1}^{N} \\lambda_i$ is the sum of all radiative feedbacks, defined to be **positive** for **amplifying processes**." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "More positive feedbacks thus mean that $\\lambda$ is a smaller number, which means the response to a given forcing is larger!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here in the EBM the parameter $B$ plays the same role as $\\lambda$ -- a smaller number means a more sensitive model." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our estimate $B = 2 ~ \\text{W m}^{-2}~^\\circ\\text{C}^{-1}$ thus implies that the sum of all LW feedback processes (including water vapor, lapse rates and clouds) is\n", "\n", "$$ \\sum_{i=1}^{N} \\lambda_i = 3.3 ~\\text{W m}^{-2}~^\\circ\\text{C}^{-1} - 2 ~\\text{W m}^{-2}~^\\circ\\text{C}^{-1} = 1.3 ~\\text{W m}^{-2}~^\\circ\\text{C}^{-1} $$ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looking back at the chart of feedback parameter values from GCMs, does this seem plausible?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "____________\n", "\n", "\n", "## 4. The one-dimensional diffusive energy balance model\n", "____________\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Putting the above OLR parameterization into our budget equation gives\n", "\n", "$$ C \\frac{\\partial T}{\\partial t} = (1-\\alpha) ~ Q - \\left( A + B~T \\right) + \\frac{D}{\\cos⁡\\phi } \\frac{\\partial }{\\partial \\phi} \\left( \\cos⁡\\phi ~ \\frac{\\partial T}{\\partial \\phi} \\right) $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is the equation for a very important and useful simple model of the climate system. It is typically referred to as the (one-dimensional) Energy Balance Model.\n", "\n", "(although as we have seen over and over, EVERY climate model is actually an “energy balance model” of some kind)\n", "\n", "Also for historical reasons this is often called the **Budyko-Sellers model**, after Budyko and Sellers who both (independently of each other) published influential papers on this subject in 1969." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recap: parameters in this model are\n", "\n", "- C: heat capacity in J m$^{-2}$ ºC$^{-1}$\n", "- A: longwave emission at 0ºC in W m$^{-2}$\n", "- B: increase in emission per degree, in W m$^{-2}$ ºC$^{-1}$\n", "- D: horizontal (north-south) diffusivity of the climate system in W m$^{-2}$ ºC$^{-1}$\n", "\n", "We also need to specify the albedo." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Tune albedo formula to match observations\n", "\n", "Let's go back to the NCEP Reanalysis data to see how planetary albedo actually varies as a function of latitude." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "days = np.linspace(1.,50.)/50 * climlab.constants.days_per_year\n", "Qann_ncep = np.mean( climlab.solar.insolation.daily_insolation(lat_ncep, days ),axis=1)\n", "albedo_ncep = 1 - ASR_ncep_annual / Qann_ncep\n", "\n", "albedo_ncep_global = np.average(albedo_ncep, weights=np.cos(np.deg2rad(lat_ncep)))" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The annual, global mean planetary albedo is 0.354\n" ] }, { "data": { "text/plain": [ "Text(0,0.5,'Albedo')" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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hqjuAHN/rmSbQISaSV24axYTBXXhm6Q4ufGQJ5//1I15ZscuKhmnxsrYcYOqz\nK0iKj+KNH55J76Q4tyOFBCfvON4d2OM3nQuM8l9BREYAKar6roj8tM62y+tsayN5NaHYqAhmXXs6\nh0oqWLBuL3PX5PGLt9dzUa82jBundqLPtCj5R8p4L3sv72Tnk51bxMCu7fjnjSNJjLMrtAPlZLGo\n79vmy5+tIhIG/BWYdqLb+r3GdGA6QHJyMllZWSeT03ElJSVBmw0gBbhjoPISESzYUcWNj/+HKQMi\nCQvyghHs+9WfZXVGY1k9qszLqeKdbVUo0KtdGFf3j2RcSjXrVy1rtpwQWvu1Pk4Wi1y830O1egD5\nftPxwGAgy/crtgswX0QmBrAtAKr6FPAUQGZmpo4bN64J4zedrKwsgjWbv/HjlB89tYj3d1TRITGZ\nh783lIggHkQtVPYrWFanNJS1uLyKn8xey3+3HeDy07tzx9nppCXGNm9AP6G0X+vjZLFYCaSLSC8g\nD+8J62trF6pqEZBYOy0iWcBPVXWViJQBr4rIX4BuQDrwqYNZDd7hQa7q14aBfXvx50VfUFxWxaPX\nnE7bSDv5Z0JLzoESpv9zFbsLS3lw0iCmjE61ptVT5NjPRlWtBm4DFgKbgDmqukFEHvAdPTS07QZg\nDrAR+Ddwq6rasKnNQES4/Zx0HrxsMP/d7D0RWFRa5XYsYwK2dGsB333sY4rLq3j15tFMHZNmhaIJ\nOHlkgaouABbUmXfvcdYdV2f6t8BvHQtnGjR1dCoJsZH8ePZarnpyGS/84AwbhdMEvdc+3c0v560n\nvXMcz9yQSY+OdqFdUwneBmnjuouGdOWF759B3pEyLpv1MetybdRaE5w8HuWh9zcx8611fKtvIm/M\nGGOFoolZsTANOrNvInN/eCYRYWFc9eQy/r3ervo2waWqxsNP3/ycJ/+3nSmje/LsDZnER7dxO1aL\nY8XCNKp/l3jm3XoW/bvE88NXVvPKil1uRzIGgMoaZcZLq3lrTR53ndePBycNDuoefKHM9qoJSFJ8\nFLOnj+Y7/ZL49fyNbN5X7HYk08qVVlbzp1XlfLjlAA9eNpg7zkm3E9kOsmJhAhbdJpw/XzmMdm0j\n+Mnrn1NZbTdSMu6o8Sh3vLaWrYc9/H3yCKaOTnU7UotnxcKckIS4KB66fCib9hbz9/9udTuOaaUe\nWrCJDzbt57oBkVw6rJvbcVoFKxbmhJ03MJkrM3rwWFaO3UjJNLuXl+/imaU7mHZmGuem2ons5mLF\nwpyUey8dSNf2bfm/OZ9zrKLa7TimlfhkWwH3zd/A2ad15leXfOOOB8ZBVizMSYmPbsOfrxrGzkPH\n+PU7G9yOY1qBI6WV3PX656TbMpovAAAVrklEQVQlxPD3a0YQHmYns5uTFQtz0kb3TuDWcX2ZsyqX\nd7O/Mc6jMU1GVfnFvPUUlFTwyOQRxEU5OviEqYcVC3NK7jw3nRE9OzDzrXXsKSx1O45poeatzeO9\n7L385Lx+DO7e3u04rZIVC3NK2oSH8ffJI0Dhx6+vpbrGutOappV7uJR7520gM7UjM77Tx+04rZYV\nC3PKUjrF8JvvDmb1rsM89P5mt+OYFkRVmfnWOjyq/PXq4XaewkVWLEyTmDS8O9POTOPZpTt4a02u\n23FMC7Fo436WbC3gpxf0J6WTDQzoJisWpsn84uIBjOmdwD1vrSM794jbcUyIq6iu4TfvbSK9cxxT\n7Apt11mxME2mTXgY/7h2BElxUdzy0moOHq1wO5IJYc8u3cHuwlLuvXQgbWxwQNfZfwHTpBLionjq\n+gwKj1Vy/3y7/sKcnP3F5fzjwxzOG5jMt9OT3I5jcLhYiMgEEdkiIjkick89y2eIyDoRWSsiS0Vk\noG9+moiU+eavFZEnnMxpmtagbu354bg+vLduL8u2HXI7jglBf3h/M9U1yi8vHuB2FOPjWLEQkXBg\nFnAhMBC4prYY+HlVVYeo6nDgYeAvfsu2qepw32OGUzmNM24Z24fuHdry63c2WHdac0I+2Liftz7L\n46Zv9yI1IdbtOMbHySOLkUCOqm5X1UpgNjDJfwVV9b8pQiygDuYxzahtZDi/uHgAm/cd5bWVe9yO\nY0LEgeJyfjY3mwFd23HnueluxzF+nCwW3QH/b4lc37yvEZFbRWQb3iOLO/wW9RKRz0TkfyLybQdz\nGodcOLgLo3t34s//2cKR0kq345gg5/Eo//fG55RWVvPoNcOJigh3O5LxI6rO/JgXkSuBC1T1Jt/0\nVGCkqt5+nPWv9a1/g4hEAXGqekhEMoB5wKA6RyKIyHRgOkBycnLG7NmzHflbTlVJSQlxcXFuxwhI\nU2fdc9TDvR+XcXbPCKYOjGqy14XWvV+d5FbWf++oYvaWSq4fGMnZPQMbetz266kbP378alXNbHRF\nVXXkAYwBFvpNzwRmNrB+GFB0nGVZQGZD75eRkaHBavHixW5HCJgTWe+dt07T7nlX1+wqbNLXbe37\n1SluZF2zq1DTf75Ab3pxpXo8noC3s/166oBVGsB3upPNUCuBdBHpJSKRwGRgvv8KIuLfKHkxsNU3\nP8l3ghwR6Q2kA9sdzGoc9NML+pMcH83Mt9ZRZSe7TR17Cku5+Z+rSG4fxR++N9Tuox2kHCsWqloN\n3AYsBDYBc1R1g4g8ICITfavdJiIbRGQtcBdwg2/+WCBbRD4H3gRmqGqhU1mNs+Kj2/DgZYPZvO8o\nT31kNd98pbi8ihtfXElFtYfnp51Bp9hItyOZ43B0UHhVXQAsqDPvXr/ndx5nu7nAXCezmeZ13sBk\nLhrShUf+u5WLhnSlV6J1iWztqmo83PrKGrYfPMY/fzCSvp3j3Y5kGmBXcJtmc/+lg4iKCGPmW9l4\nPNZLujWrrPZw15zPWbK1gN99dwhn9k10O5JphBUL02w6t4vmVxcPZPn2QmYtznE7jnHJsYpqbnxx\nJe98ns/MC0/jqjNS3I5kAmD3JjTN6srMHnyyrYC/fPAFw3t2sHF/WpnDxyr5/gsryc49wsPfG2qF\nIoTYkYVpViLC7y4fQnrnOO6cvZb8I2VuRzLNpKrGww3Pf8rGvcU8MSXDCkWIsWJhml1MZASPT8mg\noqqGW19dQ2W1dadtDR79MIfs3CIeuXo45w/q4nYcc4KsWBhX9EmK4+ErhvHZ7iP86JXVlFfVuB3J\nOOjzPUeYtTiHy0d058IhXd2OY06CnbMwrrl4aFcKSwfzq3nrufmfq3hqaiZtI1vfeEAlFdWs2XWY\nHQXH2FFwjDAR7jq/H3FRLeN/z/KqGu6as5bO8VHcN3GQ23HMSWoZn0YTsqaOTiU6Ioy752Zzw/Of\n8ty0M1rMl2Qgdh06xnXPrCD3sPfcTWxkOOXVHlbvPsyL3z+DDjGhf5HanxZuYdvBY7x040jatw1s\nzCcTfKwZyrjuyswU/jZ5BKt3Hea6Z1ZQVFrldqRmsWXfUa58YhklFdU8fX0mn/78HNb/+gIev+50\nNuUXM/mp5SF/a9pXV+zmmaU7mDo61Xq+hTgrFiYoTBzW7asvyaeXU1AS2l+SjVm75whXP7UMgDm3\njOG8gcl0bheNiHD+oC48Oy2TXYdKuerJZRw4Wu5y2pPz6ord/PztdZx9Wmd+eYnd8S7UWbEwQaP2\nS3JHQQlXPbmMvUUts1vt+rwipjyzgvjoCN6ccSb9kr85zMW305N46caR7C0q4+43s2tHXw4Zr336\nVaF4fMrpdm+KFsCKhQkq3i/JURwsruDKJ5axp7DU7UhNak9hKdOeX0m76Ahenz6Gngkxx103M60T\nP7vgNBZvOcgbq3ObMeWJq67x8OmOQv6y6Asuf+xjZr61jvH9k6xQtCBWLEzQOSOtE6/cPIqj5dVc\n/eQydhYccztSkzhUUsH1z31KVY2Hf944km4d2ja6zbQz0xjVqxMPvrMxaC9g/CSngAmPLOGqJ5fx\njw+34lH4ybn9eHxKhhWKFsSKhQlKQ3t04NWbR1Fe7eHqp5aRc6DE7UinpLRK+cELK9lbVMZz0zID\nHmE1LEz44xXDqFHl7rnB1Ry1v7ic21/7jGufWUFFdQ2PTB7OZ/eez7xbz+LOc9OJbmOFoiVpPX0U\nTcgZ1K09r908muueWcHkp5bz5owxpLk8tHlRWRX/Xr+XlTsP0y66DQlxkSTFRzGmdwIpnepvUso5\ncJQHlpVRUF7GE1MyyEjtdELv2TMhhpkXDeBX89bz2qd7uHZUz6b4U06ax6PMXrmHhxZsoqLGw53n\npPPDcX2sOLRwVixMUOvfJZ7Z00dz5ROfcMPznzL3h2eSGNe09/IOxCc5Bby4bCeLNx+kssZDQmwk\n5VU1HKv86srzId3bc9GQrozu3YkeHWNIjIvkPxv3c9frawlHefXmMYzsdWKFotaUUT15Lzufhxdu\n5qIhXVy7/mLXoWPcPTeb5dsLGdM7gYcuH+J6ATfNw4qFCXp9O8fx7LQzuPbp5dz4wkpemz6amMjm\n+ehuP1jC7xZs4oNNB0iMi+K60T25bHh3hvZoj4hQVllDflEZ/920n/fW7eMP/9785bbRbcIor/Iw\nLKUDN/SpOOlCAd4BGO+7dBAX/30Jf/tgK/c385XQVTUenl26g7998AVtwsJ46PIhTD4jxW6B2opY\nsTAh4fSeHXn0mtO55aVV3PrKGp6+PtPR9ztSWskj/93KS8t2Ed0mnJ9N6M8Pzur1jaaWtpHh9EmK\no09SHNPH9iHvSBmb9xazp7CU3MNlxEe34Zbv9Gb5x0tOOdOAru24ZmRPXlq+i+tG9SS9ni63Tli7\n5wj3zM1m876jnDcwmQcmDaJr+8ZPzpuWxdFiISITgEeAcOAZVf19neUzgFuBGqAEmK6qG33LZgI3\n+pbdoaoLncxqgt95A5N58LLB/OLt9fy/N7O5tHPTn+ytqvHw6ord/PWDLyguq+LqM1K467z+JMUH\n1vTVvUNbugfQy+lk3XVeP975PJ8H3t3IP38w0vFf9k9/tJ3fvb+J5PhonpiSwYTBNlpsa+VYsRCR\ncGAWcB6QC6wUkfm1xcDnVVV9wrf+ROAvwAQRGQhMBgYB3YAPRKSfqtrQpK3cdaNSOVJaxR8XbuFQ\njwjGfUcJC2uaL8yPcwq4b/4Gcg6UMKZ3Ar+6ZCADu7VrktduKglxUdx5bj8efHcjH24+wDkDkh17\nr0f/u5U/L/qCi4Z04Q/fG0p8tI3r1Jo52XV2JJCjqttVtRKYDUzyX0FVi/0mY4Han4qTgNmqWqGq\nO4Ac3+sZw63j+3LH2X35KLea++ZvOOXupPlHyrj1lTVc98wKKqs9PDU1g1dvHhV0haLW9WNS6ZMU\nyy/eXs+G/KImf31V5U8Lt/DnRV9w+Yju/H3yCCsUBnGq37aIXAFMUNWbfNNTgVGqelud9W4F7gIi\ngbNVdauI/ANYrqov+9Z5FnhfVd+ss+10YDpAcnJyxuzZsx35W05VSUkJcXFxbscISKhkVVVeWX+M\nD/KEcT0imDIwkogTPMKo8Sj/2VXN2zmVqMIlvdtwYa82RIY3fdNOU+/XXcU1/G11BceqlZuGRDGy\nS9M0EpRVKy+vP8bH+4SxPSKYNiiSsCA+iR0qn1cI3qzjx49fraqNngR08pxFfZ+wb1QmVZ0FzBKR\na4FfAjecwLZPAU8BZGZm6rhx404lr2OysrII1mx1hVJWWEx6elcez9pGcVgcj12XQZf20QFtuT6v\niHveymZ9XinnDujMfZcOOu51Ek3Bif164fhyfvjyGh5bexgd14MfjutDu1M4Ali8+QC/mbee/CPC\nLWN7c/eE05qsic8pofR5DaWs9XGyWOQC/jfZ7QHkN7D+bODxk9zWtEIiwt0TTmNQt3b87M1sLnl0\nCX+9ejjf6pt43BO/xeVV/P2DrTz/yU46xUby2HWnc+HgLiHZBbRzfDSv3jyK+/61gceztvH8xzu4\naHBXrsjswbAeHYj1uy9IaWU12w8eY8u+o6zLK2J9XhHbDpYQGxVBQmwkEeFhrN51mL6d4/j5qGhu\nvshGiTVf52SxWAmki0gvIA/vCetr/VcQkXRV3eqbvBiofT4feFVE/oL3BHc68KmDWU0Iu2RoN/on\nxzPj5dVMffZTXxfTFCYN7/7lzXZqPMobq/bwx4VbKCytZPIZKdwzYQDtY0K7LT4qIpzff28o14zs\nyZxVe5i/Np+3PssDIC4qguR2UZRXecjzG1eqbZtwBnVrx4TBXSmvquHQsUqKSiv5ybn9mDGuN8uW\nnno3X9PyOFYsVLVaRG4DFuLtOvucqm4QkQeAVao6H7hNRM4FqoDDeJug8K03B9gIVAO3Wk8o05D0\n5Hjm3/Yt3lqTy2uf7uHef23g1+9sJDYynLaR4XgUDh6tIDO1Iy9cOpIhPdq7HblJDUvpwLCUDvzq\nkoFkbTnAzkOl7CsqZ19ROVFtwpiclEKfznGkd46jd1Ic4UHevGSCj6PXWajqAmBBnXn3+j2/s4Ft\nfwv81rl0pqWJjYpg6pg0po5JY11uEYs27qO4vJrSymoqqj2cfVpnJg7rFpJNToGKbhPOhMFd3Y5h\nWiC7gtu0SEN6tG9xRw/GuMmGKDfGGNMoKxbGGGMaZcXCGGNMo6xYGGOMaZQVC2OMMY2yYmGMMaZR\nViyMMcY0yoqFMcaYRjk2RHlzE5GDwC63cxxHIlDgdogAWVZnWFZnWNZTl6qqSY2t1GKKRTATkVWB\njBcfDCyrMyyrMyxr87FmKGOMMY2yYmGMMaZRViyax1NuBzgBltUZltUZlrWZ2DkLY4wxjbIjC2OM\nMY2yYuEQEXldRNb6HjtFZK1vfpqIlPkte8LtrAAicr+I5Pnlushv2UwRyRGRLSJygcs5/ygim0Uk\nW0TeFpEOvvnBul8n+PZbjojc43YefyKSIiKLRWSTiGwQkTt984/7WXCT7/+jdb5Mq3zzOonIIhHZ\n6vu3YxDk7O+379aKSLGI/DhY92ugrBmqGYjIn4EiVX1ARNKAd1V1sLupvk5E7gdKVPVPdeYPBF4D\nRuK9H/oHQD+3bnMrIucDH/pu2/sHAFW9Oxj3q4iEA18A5wG5eO9Lf42qbnQ1mI+IdAW6quoaEYkH\nVgOXAVdRz2fBbSKyE8hU1QK/eQ8Dhar6e18x7qiqd7uVsS7fZyAPGAV8nyDcr4GyIwuHifcenlfh\n/cINRZOA2apaoao7gBy8hcMVqvofVa32TS4HeriVJQAjgRxV3a6qlcBsvPszKKjqXlVd43t+FNgE\ndHc31QmbBLzoe/4i3mIXTM4BtqlqsF4wHDArFs77NrBfVbf6zeslIp+JyP9E5NtuBavHbb7mnef8\nDue7A3v81skleL5QfgC87zcdbPs1mPfd1/iOzEYAK3yz6vssuE2B/4jIahGZ7puXrKp7wVv8gM6u\npavfZL7+QzEY92tArFicAhH5QETW1/Pw//V4DV//sOwFeqrqCOAu4FURaRcEeR8H+gDDfRn/XLtZ\nPS/laNtlIPtVRH4BVAOv+Ga5tl8b0Oz77mSISBwwF/ixqhZz/M+C285S1dOBC4FbRWSs24EaIiKR\nwETgDd+sYN2vAYlwO0AoU9VzG1ouIhHA5UCG3zYVQIXv+WoR2Qb0A1Y5GLX2vRvMW0tEngbe9U3m\nAil+i3sA+U0c7WsC2K83AJcA56jvpJub+7UBzb7vTpSItMFbKF5R1bcAVHW/33L/z4KrVDXf9+8B\nEXkbbzPffhHpqqp7fedgDrga8usuBNbU7s9g3a+BsiMLZ50LbFbV3NoZIpLkO+mFiPQG0oHtLuX7\nku9/tFrfBdb7ns8HJotIlIj0wpv30+bOV0tEJgB3AxNVtdRvfjDu15VAuoj08v3KnIx3fwYF3/m0\nZ4FNqvoXv/nH+yy4RkRifSfhEZFY4Hy8ueYDN/hWuwH4lzsJ6/W1VoVg3K8nwo4snFW3vRJgLPCA\niFQDNcAMVS1s9mTf9LCIDMfbTLITuAVAVTeIyBxgI95mn1vd6gnl8w8gCljk/a5juarOIAj3q6/H\n1m3AQiAceE5VN7iZqY6zgKnAOvF17QZ+DlxT32fBZcnA277/5hHAq6r6bxFZCcwRkRuB3cCVLmb8\nkojE4O0F57/v6v1/LFRY11ljjDGNsmYoY4wxjbJiYYwxplFWLIwxxjTKioUxxphGWbEwxhjTKCsW\nxtRDREpOYN1xInKm3/QMEbne93yaiHQ7ifffKSKJJ7qdMU6x6yyMOXXjgBLgEwBV9R8efRrei6+C\n6sptY06UFQtjAiQilwK/BCKBQ8B1QFtgBlAjIlOA2/GONFqC98KrTOAVESkDxuAd2TVTVQtEJBP4\nk6qOE5EEvBdwJuG9Ql783ncKcIfvfVcAP3L5wkjTClkzlDGBWwqM9g1WOBv4maruBJ4A/qqqw1V1\nSe3Kqvom3rGprvMtK2vgte8Dlvpeez7QE0BEBgBX4x1Ebzjeq9Ova/o/zZiG2ZGFMYHrAbzuG+Mn\nEtjRhK89Fu+gk6jqeyJy2Df/HLwDUa70DXXRluAaLM+0ElYsjAnco8BfVHW+iIwD7j+J16jmqyP6\n6DrL6ht7R4AXVXXmSbyXMU3GmqGMCVx7vLfIhK9GOgU4CsQfZ5u6y3by1ZD13/Ob/xG+5iURuRCo\nvTHOf4ErRKSzb1knEUk9yfzGnDQrFsbUL0ZEcv0ed+E9knhDRJYABX7rvgN8V0TW1nOHvheAJ3zL\n2gK/Bh7xvYb/SepfA2NFZA3e4bd3A/ju1/1LvHeIywYWAf5DXRvTLGzUWWOMMY2yIwtjjDGNsmJh\njDGmUVYsjDHGNMqKhTHGmEZZsTDGGNMoKxbGGGMaZcXCGGNMo6xYGGOMadT/B0EqB0XGCbXaAAAA\nAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "print( 'The annual, global mean planetary albedo is %0.3f' %albedo_ncep_global)\n", "fig,ax = plt.subplots()\n", "ax.plot(lat_ncep, albedo_ncep)\n", "ax.grid();\n", "ax.set_xlabel('Latitude')\n", "ax.set_ylabel('Albedo')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**The albedo increases markedly toward the poles.**\n", "\n", "There are several reasons for this:\n", "\n", "- surface snow and ice increase toward the poles\n", "- Cloudiness is an important (but complicated) factor.\n", "- Albedo increases with solar zenith angle (the angle at which the direct solar beam strikes a surface)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Approximating the observed albedo\n", "\n", "The albedo curve can be approximated by a smooth function that increases with latitude:\n", "\n", "$$ \\alpha(\\phi) \\approx \\alpha_0 + \\alpha_2 P_2(\\sin\\phi) $$\n", "\n", "where $P_2$ is a function called the 2nd Legendre polynomial. Don't worry about exactly what this means. This is what it looks like:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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/aFRUFcKaTm+FA79Ap5egTFWrHvpyUipjZ20nKTWDn8e3oZyvx903Ksbuup7C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\nhEUppfhgSCPK+3kw/c8oTsS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"text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Add a new curve to the previous figure\n", "a0 = albedo_ncep_global\n", "a2 = 0.25\n", "ax.plot(lat_ncep, a0 + a2 * climlab.utils.legendre.P2(np.sin(np.deg2rad(lat_ncep))))\n", "fig" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of course we are not fitting all the details of the observed albedo curve. But we do get the correct global mean a reasonable representation of the equator-to-pole gradient in albedo." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "____________\n", "\n", "\n", "## 5. The annual-mean EBM\n", "____________" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For now, we will be focusing on the **annual mean** model. \n", "\n", "For the insolation, we set $Q(\\phi,t) = \\bar{Q}(\\phi)$, the annual mean value (large at equator, small at pole)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Animating the adjustment of annual mean EBM to equilibrium" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before looking at the details of how to set up an EBM in `climlab`, let's look at an animation of the adjustment of the model (its temperature and energy budget) from an isothermal initial condition.\n", "\n", "For reference, all the code necessary to generate the animation is here in the notebook." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "# Some imports needed to make and display animations\n", "from IPython.display import HTML\n", "from matplotlib import animation\n", "\n", "def setup_figure():\n", " templimits = -20,32\n", " radlimits = -340, 340\n", " htlimits = -6,6\n", " latlimits = -90,90\n", " lat_ticks = np.arange(-90,90,30)\n", "\n", " fig, axes = plt.subplots(3,1,figsize=(8,10))\n", " axes[0].set_ylabel('Temperature (deg C)')\n", " axes[0].set_ylim(templimits)\n", " axes[1].set_ylabel('Energy budget (W m$^{-2}$)')\n", " axes[1].set_ylim(radlimits)\n", " axes[2].set_ylabel('Heat transport (PW)')\n", " axes[2].set_ylim(htlimits)\n", " axes[2].set_xlabel('Latitude')\n", " for ax in axes: ax.set_xlim(latlimits); ax.set_xticks(lat_ticks); ax.grid()\n", " fig.suptitle('Diffusive energy balance model with annual-mean insolation', fontsize=14)\n", " return fig, axes\n", "\n", "def initial_figure(model):\n", " # Make figure and axes\n", " fig, axes = setup_figure()\n", " # plot initial data\n", " lines = []\n", " lines.append(axes[0].plot(model.lat, model.Ts)[0])\n", " lines.append(axes[1].plot(model.lat, model.ASR, 'k--', label='SW')[0])\n", " lines.append(axes[1].plot(model.lat, -model.OLR, 'r--', label='LW')[0])\n", " lines.append(axes[1].plot(model.lat, model.net_radiation, 'c-', label='net rad')[0])\n", " lines.append(axes[1].plot(model.lat, model.heat_transport_convergence(), 'g--', label='dyn')[0])\n", " lines.append(axes[1].plot(model.lat, \n", " np.squeeze(model.net_radiation)+model.heat_transport_convergence(), 'b-', label='total')[0])\n", " axes[1].legend(loc='upper right')\n", " lines.append(axes[2].plot(model.lat_bounds, model.diffusive_heat_transport())[0])\n", " lines.append(axes[0].text(60, 25, 'Day 0'))\n", " return fig, axes, lines\n", "\n", "def animate(day, model, lines):\n", " model.step_forward()\n", " # The rest of this is just updating the plot\n", " lines[0].set_ydata(model.Ts)\n", " lines[1].set_ydata(model.ASR)\n", " lines[2].set_ydata(-model.OLR)\n", " lines[3].set_ydata(model.net_radiation)\n", " lines[4].set_ydata(model.heat_transport_convergence())\n", " lines[5].set_ydata(np.squeeze(model.net_radiation)+model.heat_transport_convergence())\n", " lines[6].set_ydata(model.diffusive_heat_transport())\n", " lines[-1].set_text('Day {}'.format(int(model.time['days_elapsed'])))\n", " return lines " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "# A model starting from isothermal initial conditions\n", "e = climlab.EBM_annual()\n", "e.Ts[:] = 15. # in degrees Celsius\n", "e.compute_diagnostics()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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gv8BAgmsL/DUF9YiIiEjEIu0xCA8bPO3uVwHDoyxbREREUi/SHgN33wUcY2aH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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot initial data\n", "fig, axes, lines = initial_figure(e)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "ani = animation.FuncAnimation(fig, animate, frames=np.arange(1, 100), fargs=(e, lines))" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HTML(ani.to_html5_video())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "____________\n", "\n", "\n", "## 6. Tuning the diffusivity\n", "____________" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We want to choose a value of $D$ that gives a reasonable approximation to observations:\n", "\n", "- $\\Delta T \\approx 45$ ºC between equator and pole\n", "- $\\mathcal{H}_{max} \\approx 5.5$ PW (peak heat transport)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "climlab Process of type . \n", "State variables and domain shapes: \n", " Ts: (40, 1) \n", "The subprocess tree: \n", "Untitled: \n", " LW: \n", " insolation: \n", " albedo: \n", " diffusion: \n", "\n" ] } ], "source": [ "ebm = climlab.EBM_annual(num_lat=40, A=210, B=2, a0=0.354, a2=0.25, D=1.)\n", "print(ebm)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Integrating for 1800 steps, 7304.844000000001 days, or 20.0 years.\n", "Total elapsed time is 19.99999999999943 years.\n" ] } ], "source": [ "ebm.integrate_years(20.)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Field([[-12.26380533],\n", " [-11.90335191],\n", " [-11.18600118],\n", " [-10.11933409],\n", " [ -8.71602774],\n", " [ -6.99587506],\n", " [ -4.99120883],\n", " [ -2.7496105 ],\n", " [ -0.32575346],\n", " [ 2.22075802],\n", " [ 4.82660239],\n", " [ 7.4259771 ],\n", " [ 9.95205275],\n", " [ 12.33865448],\n", " [ 14.52211192],\n", " [ 16.44318978],\n", " [ 18.04899789],\n", " [ 19.29477742],\n", " [ 20.14546523],\n", " [ 20.57694989],\n", " [ 20.57694989],\n", " [ 20.14546524],\n", " [ 19.29477743],\n", " [ 18.04899791],\n", " [ 16.44318981],\n", " [ 14.52211196],\n", " [ 12.33865452],\n", " [ 9.9520528 ],\n", " [ 7.42597714],\n", " [ 4.82660244],\n", " [ 2.22075807],\n", " [ -0.3257534 ],\n", " [ -2.74961044],\n", " [ -4.99120876],\n", " [ -6.995875 ],\n", " [ -8.71602768],\n", " [-10.11933402],\n", " [-11.18600112],\n", " [-11.90335184],\n", " [-12.26380526]])" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ebm.Ts" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "32.84075522594018\n" ] } ], "source": [ "deltaT = np.max(ebm.Ts) - np.min(ebm.Ts)\n", "print(deltaT)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ -0.00000000e+00, -9.18904284e-02, -3.64621108e-01,\n", " -8.09080950e-01, -1.40900546e+00, -2.13887046e+00,\n", " -2.95710444e+00, -3.80557880e+00, -4.62917406e+00,\n", " -5.37363147e+00, -5.98702816e+00, -6.42232424e+00,\n", " -6.64021012e+00, -6.61185866e+00, -6.32125688e+00,\n", " -5.76684312e+00, -4.96224035e+00, -3.93595867e+00,\n", " -2.73003339e+00, -1.39766258e+00, -1.04149739e-08,\n", " 1.39766256e+00, 2.73003337e+00, 3.93595865e+00,\n", " 4.96224033e+00, 5.76684310e+00, 6.32125687e+00,\n", " 6.61185864e+00, 6.64021011e+00, 6.42232423e+00,\n", " 5.98702816e+00, 5.37363146e+00, 4.62917406e+00,\n", " 3.80557879e+00, 2.95710444e+00, 2.13887046e+00,\n", " 1.40900546e+00, 8.09080950e-01, 3.64621108e-01,\n", " 9.18904284e-02, -0.00000000e+00])" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#. The heat transport in PW\n", "ebm.heat_transport()" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "6.6402101078967064" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# what's the peak value?\n", "np.max(ebm.heat_transport())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Class exercise\n", "\n", "Repeat these calculations with some different values of $D$. We'll crowd-source the optimal value that best matches our observational targets." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Results\n", "\n", "12 students calculated $\\Delta T$ and $\\mathcal{H}_{max}$ for different values of the diffusivity parameter $D$. \n", "\n", "We collected the data on the whiteboard during class:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![column sketch](http://www.atmos.albany.edu/facstaff/brose/classes/ENV415_Spring2018/images/classdata.jpg)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are the same data entered into a [Pandas data frame](http://pandas.pydata.org/pandas-docs/stable/10min.html)." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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$D$$\\Delta T$$\\mathcal{H}_{max}$
01.00033.0006.600
10.50052.0005.300
20.63845.0075.800
30.55049.4605.500
40.58047.8505.600
50.60046.8005.700
60.57048.3705.590
70.63045.8505.760
812.0003.5608.600
90.42357.6864.960
100.45055.7165.095
110.000126.1240.000
120.63048.3705.760
\n", "
" ], "text/plain": [ " $D$ $\\Delta T$ $\\mathcal{H}_{max}$\n", "0 1.000 33.000 6.600\n", "1 0.500 52.000 5.300\n", "2 0.638 45.007 5.800\n", "3 0.550 49.460 5.500\n", "4 0.580 47.850 5.600\n", "5 0.600 46.800 5.700\n", "6 0.570 48.370 5.590\n", "7 0.630 45.850 5.760\n", "8 12.000 3.560 8.600\n", "9 0.423 57.686 4.960\n", "10 0.450 55.716 5.095\n", "11 0.000 126.124 0.000\n", "12 0.630 48.370 5.760" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "classdata = pd.DataFrame({'$D$': [1., 0.5, 0.638, 0.55, 0.58, 0.6, 0.57, 0.63, 12.0, 0.423, 0.45, 0., 0.63], \n", " '$\\Delta T$': [33., 52., 45.007, 49.46, 47.85, 46.8, 48.37, 45.85, 3.56, 57.686, 55.716, 126.124, 48.37],\n", " '$\\mathcal{H}_{max}$': [6.6, 5.3, 5.8, 5.5, 5.6, 5.7, 5.59, 5.76, 8.60, 4.96, 5.095, 0., 5.76],\n", " })\n", "classdata" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can do fun things like make a scatterplot of the data:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(2,1)\n", "classdata.plot.scatter(x='$D$', y='$\\Delta T$', ax=axes[0])\n", "classdata.plot.scatter(x='$D$', y='$\\mathcal{H}_{max}$', ax=axes[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Evidently the temperature gradient $\\Delta T$ decreases with $D$, while the heat transport increases with $D$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A more systematic search" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "Darray = np.arange(0., 2.05, 0.05)\n", "\n", "model_list = []\n", "Tmean_list = []\n", "deltaT_list = []\n", "Hmax_list = []\n", "\n", "for D in Darray:\n", " ebm = climlab.EBM_annual(A=210, B=2, a0=0.354, a2=0.25, D=D)\n", " ebm.integrate_years(20., verbose=False)\n", " Tmean = ebm.global_mean_temperature()\n", " deltaT = np.max(ebm.Ts) - np.min(ebm.Ts)\n", " energy_in = np.squeeze(ebm.ASR - ebm.OLR)\n", " Htrans = ebm.heat_transport()\n", " Hmax = np.max(Htrans)\n", " model_list.append(ebm)\n", " Tmean_list.append(Tmean)\n", " deltaT_list.append(deltaT)\n", " Hmax_list.append(Hmax)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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gPz8/qWJOtn0MirkyJFu8UEzMBQVUX76czIULqbFoEZmLFpG5eLE9X7yYzMWL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\nLwBdzaxNaiOJiBw9FWkiEnWnAqucc+X17DsQuz2YwjwiIk1CRZqIRN2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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "color1 = 'b'\n", "color2 = 'r'\n", "\n", "fig, ax1 = plt.subplots(figsize=(8,6))\n", "ax1.plot(Darray, deltaT_list, color=color1)\n", "ax1.plot(Darray, Tmean_list, 'b--')\n", "ax1.set_xlabel('D (W m$^{-2}$ K$^{-1}$)', fontsize=14)\n", "ax1.set_xticks(np.arange(Darray[0], Darray[-1], 0.2))\n", "ax1.set_ylabel('$\\Delta T$ (equator to pole)', fontsize=14, color=color1)\n", "for tl in ax1.get_yticklabels():\n", " tl.set_color(color1)\n", "ax2 = ax1.twinx()\n", "ax2.plot(Darray, Hmax_list, color=color2)\n", "ax2.set_ylabel('Maximum poleward heat transport (PW)', fontsize=14, color=color2)\n", "for tl in ax2.get_yticklabels():\n", " tl.set_color(color2)\n", "ax1.set_title('Effect of diffusivity on temperature gradient and heat transport in the EBM', fontsize=16)\n", "# Add our crowd-sourced data to the figure\n", "classdata.plot.scatter(x='$D$', y='$\\Delta T$', ax=ax1)\n", "classdata.plot.scatter(x='$D$', y='$\\mathcal{H}_{max}$', ax=ax2)\n", "for ax in [ax1, ax2]:\n", " ax.set_xlim(0,2)\n", "ax1.plot([0.6, 0.6], [0, 140], 'k-')\n", "ax1.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When $D=0$, every latitude is in radiative equilibrium and the heat transport is zero. As we have already seen, this gives an equator-to-pole temperature gradient much too high.\n", "\n", "When $D$ is **large**, the model is very efficient at moving heat poleward. The heat transport is large and the temperture gradient is weak.\n", "\n", "The real climate seems to lie in a sweet spot in between these limits.\n", "\n", "It looks like our fitting criteria are met reasonably well with $D=0.6$ W m$^{-2}$ K$^{-1}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Also, note that the **global mean temperature** (plotted in dashed blue) is completely insensitive to $D$. Why do you think this is so?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "____________\n", "\n", "\n", "## 7. Summary: parameter values in the diffusive EBM\n", "____________" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our model is defined by the following equation\n", "\n", "$$ C \\frac{\\partial T}{\\partial t} = (1-\\alpha) ~ Q - \\left( A + B~T \\right) + \\frac{D}{\\cos⁡\\phi } \\frac{\\partial }{\\partial \\phi} \\left( \\cos⁡\\phi ~ \\frac{\\partial T}{\\partial \\phi} \\right) $$\n", "\n", "with the albedo given by\n", "\n", "$$ \\alpha(\\phi) = \\alpha_0 + \\alpha_2 P_2(\\sin\\phi) $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have chosen the following parameter values, which seems to give a reasonable fit to the observed **annual mean temperature and energy budget**:\n", "\n", "- $ A = 210 ~ \\text{W m}^{-2}$\n", "- $ B = 2 ~ \\text{W m}^{-2}~^\\circ\\text{C}^{-1} $\n", "- $ a_0 = 0.354$\n", "- $ a_2 = 0.25$\n", "- $ D = 0.6 ~ \\text{W m}^{-2}~^\\circ\\text{C}^{-1} $" ] }, { "cell_type": "code", "execution_count": null, "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": "3.6.2" } }, "nbformat": 4, "nbformat_minor": 2 }