{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lecture 4, Snowball Earth, the ice-albedo feedback, and multiple equilibria" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Thanks a lot to [Henri Drake](https://github.com/hdrake) for providing the lecture.\n", "\n", "The original lecture is part of the MIT class [Introduction to Computational Thinking](https://computationalthinking.mit.edu/Fall20/lecture20/).\n", "\n", "This class uses the [Julia programming language](http://www.julialang.org/). The orignal code can be found under https://github.com/hdrake/simplEarth/blob/master/2_ebm_multiple_equilibria.jl" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Snowball Earth, the ice-albedo feedback, and multiple equilibria" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](https://static01.nyt.com/images/2019/12/17/science/02TB-SNOWBALLEARTH1/02TB-SNOWBALLEARTH1-superJumbo-v2.jpg?quality=90&auto=webp)\n", "[Source (New York Times)](https://static01.nyt.com/images/2019/12/17/science/02TB-SNOWBALLEARTH1/02TB-SNOWBALLEARTH1-superJumbo-v2.jpg?quality=90&auto=webp)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Review of Lecture 2\n", "\n", "Recall from the last Lecture that the zero-dimensional energy balance equation is\n", "\n", "\\begin{gather}\n", "\\color{brown}{C \\frac{dT}{dt}}\n", "\\; \\color{black}{=} \\; \\color{orange}{\\frac{(1 - α)S}{4}}\n", "\\; \\color{black}{-} \\; \\color{blue}{(A - BT)}\n", "\\; \\color{black}{+} \\; \\color{grey}{a \\ln \\left( \\frac{[\\text{CO}₂]}{[\\text{CO}₂]_{\\text{PI}}} \\right)},\n", "\\end{gather}\n", "\n", "![](https://raw.githubusercontent.com/hdrake/hdrake.github.io/master/figures/planetary_energy_balance.png)\n", "\n", "Today, we will ignore changes in CO$_2$, so that\n", "\n", "$\\ln \\left( \\frac{ [\\text{CO}₂]_{\\text{PI}} }{[\\text{CO}₂]_{\\text{PI}}} \\right) = \\ln(1) = 0$\n", "\n", "and the model simplifies to\n", "\n", "\\begin{gather}\n", "\\color{brown}{C \\frac{dT}{dt}}\n", "\\; \\color{black}{=} \\; \\color{orange}{\\frac{(1 - α)S}{4}}\n", "\\; \\color{black}{-} \\; \\color{blue}{(A - BT)}.\n", "\\end{gather}\n", "\n", "\n", "The dynamics of this **Ordinary Differential Equation (ODE)** are quite simple because it is *linear*: we can rewrite it in the form\n", "\n", "$$\\dot{T} = f(T(t))$$\n", "\n", "where \n", "\n", "$$f(x) = \\alpha x + \\beta$$\n", "\n", "is a *linear* function of x. A linear ODE permits only one stable solution, $\\dot{T} = 0$, which in Lecture 1 we found was Earth's pre-industrial temperature $T_{0} = 14$°C. \n", "\n", "In this lecture, we show how a small modification that makes one term in our simple climate model non-linear completely changes its dynamics, allowing us to explain the existence of both \"Snowball Earth\" and the relatively warm pre-industrial climate that allowed humans to thrive." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import xarray as xr\n", "import matplotlib.pyplot as plt\n", "\n", "from ipywidgets import interact, interactive, fixed, interact_manual\n", "import ipywidgets as widgets\n", "\n", "from IPython.display import HTML\n", "from IPython.display import display" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1) Background: Snowball Earth\n", "Geological evidence shows that the Neoproterozoic Era (550 to 1000 million years ago) is marked by two global glaciation events, in which Earth's surface was covered in ice and snow from the Equator to the poles (see review by [Pierrehumbert et al. 2011](https://www.annualreviews.org/doi/full/10.1146/annurev-earth-040809-152447)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](https://news.cnrs.fr/sites/default/files/styles/asset_image_full/public/assets/images/frise_earths_glaciations_72dpi.jpg?itok=MgKrHlIV)\n", "\n", "### 1.1) The ice-albedo feedback\n", "\n", "In Lecture 1, we used a **constant** value $α = 0.3$ for Earth's planetary albedo, which is a reasonable thing to do for small climate variations relative to the present (such as the difference between the present-day and preindustrial climates). In the case of large variations, however, this approximation is not very reliable.\n", "\n", "While oceans are dark and absorbant, $α_{ocean} \\approx 0.05$, ice and snow are bright and reflective: $\\alpha_{ice,\\,snow} \\approx 0.5$ to $0.9$. Thus, if much of the ocean's surface freezes over, we expect Earth's albedo to rise dramatically, causing more sunlight to be reflected to space, which in turn causes even more cooling and more of the ocean to freeze, etc. This *non-linear positive feedback effect* is referred to as the **ice-albedo feedback** (see illustration below).\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](https://upload.wikimedia.org/wikipedia/commons/d/df/Ice_albedo_feedback.jpg)\n", "\n", "We can represent the ice-albedo feedback crudely in our energy balance model by allowing the albedo to depend on temperature:\n", "\n", "$$\\alpha(T) = \\begin{cases}\n", "\\alpha_{i} & \\mbox{if }\\;\\; T \\leq -10\\text{°C} &\\text{(completely frozen)}\\\\\n", "\\alpha_{i} + (\\alpha_{0}-\\alpha_{i})\\frac{T + 10}{20} & \\mbox{if }\\;\\; -10\\text{°C} \\leq T \\leq 10\\text{°C} &\\text{(partially frozen)}\\\\\n", "\\alpha_{0} &\\mbox{if }\\;\\; T \\geq 10\\text{°C} &\\text{(no ice)}\n", "\\end{cases}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.2) Adding the ice-albedo feedback to our simple climate model\n", "First, we program albedo as a function of temperature." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def calc_alpha(T, alpha0, alphai = 0.5, deltaT=10.):\n", " if T < - deltaT:\n", " return alphai\n", " elif -deltaT <= T < deltaT:\n", " return alphai + (alpha0 - alphai)*(T + deltaT) / (2*deltaT)\n", " elif T >= deltaT: \n", " return alpha0" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(13, 0.252, 'no ice')" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "calc_alpha_vec = np.vectorize(calc_alpha) # boolean evaluations need to be vectorized\n", "T_example = np.arange(-20, 20)\n", "plt.plot(T_example, calc_alpha_vec(T_example[:], 0.3), color = \"black\")\n", "plt.ylim(0.2,0.6)\n", "plt.plot([-20, -10], [0.2, 0.2])\n", "plt.fill_between([-20, -10], y1=0.2, y2=0.6, color = \"lightblue\", alpha = 0.2)\n", "plt.fill_between([10, 20], y1=0.2, y2=0.6, color = \"red\", alpha = 0.12)\n", "plt.ylabel(\"albedo $α$\\n(planetary reflectivity)\")\n", "plt.xlabel(\"Temperature [°C]\")\n", "plt.text(-18.5, 0.252, s=\"completely\\nfrozen\", size=10, color=\"darkblue\")\n", "plt.text(-3, 0.252, s=\"partiall frozen\", size=10, color=\"darkgrey\")\n", "plt.text(13, 0.252, s=\"no ice\", size=10, color=\"darkred\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To add this function into our energy balance model from Lecture 1 (which we've copied into the cell below), all we have to do is overwrite the definition of the timestep! method to specify that the temperature-dependent albedo should be updated based on the current state:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "class ebm():\n", " \"\"\"\n", " Zero order energy balance model\n", " \"\"\"\n", "\n", " def __init__(self, T, t, deltat, CO2):\n", " self.T = np.array(T)\n", " self.t = t\n", " \n", " self.deltat = deltat\n", " self.C = 51.\n", " self.a = 5.\n", " self.B = -1.3\n", " self.co2_pi = 280.\n", " self.alpha = 0.3\n", " self.S = 1368.\n", " self.co2 = CO2\n", " self.CO2_PI = 280.\n", " self.A = 221.2\n", "\n", " def absorbed_solar_radiation(self):\n", " return (self.S*(1-self.alpha2)/4.) # [W/m^2]\n", " def outgoing_thermal_radiation(self):\n", " if self.T.size == 1:\n", " return self.A - self.B*self.T\n", " else:\n", " return self.A - self.B*self.T[-1]\n", " def greenhouse_effect(self):\n", " if self.T.size == 1:\n", " return self.a*np.log(self.co2(self.t)/self.CO2_PI)\n", " else:\n", " return self.a*np.log(self.co2(self.t[-1])/self.CO2_PI)\n", " \n", " def tendency(self):\n", " if self.T.size == 1:\n", " return 1. / self.C * (\n", " + self.absorbed_solar_radiation()\n", " - self.outgoing_thermal_radiation()\n", " + self.greenhouse_effect()\n", " )\n", " else:\n", " return 1. / self.C * (\n", " + self.absorbed_solar_radiation()\n", " - self.outgoing_thermal_radiation()\n", " + self.greenhouse_effect()\n", " ) \n", " \n", " def run(self, end_year):\n", " for year in range(end_year):\n", " self.timestep()\n", " \n", " def timestep(self):\n", " if self.T.size == 1:\n", " self.alpha2 = calc_alpha(self.T, alpha0=self.alpha) # Added the function call here\n", " self.T = np.append(self.T, self.T + self.deltat * self.tendency())\n", " self.t = np.append(self.t, self.t + self.deltat)\n", " else:\n", " self.alpha2 = calc_alpha(self.T[-1], alpha0=self.alpha) # Added the function call here\n", " self.T = np.append(self.T, self.T[-1] + self.deltat * self.tendency())\n", " self.t = np.append(self.t, self.t[-1] + self.deltat)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2) Multiple Equilibria\n", "OR: the existence of \"alternate Earths\"\n", "\n", "Human civilization flourished over the last several thousand years in part because Earth's global climate has been remarkably stable and forgiving. The preindustrial combination of natural greenhouse effect and incoming solar radiation yielded temperatures between the freezing and boiling points of water across most of the planet, allowing ecoystems based on liquid water to thrive.\n", "\n", "The climate system, however, is rife with non-linear effects like the ice-albedo effect, which reveal just how fragile our habitable planet is and just how unique our stable pre-industrial climate was.\n", "\n", "We learned in the last lecture that in response to temperature fluctuations, net-negative feedbacks act to restore Earth's temperature back towards a single equilibrium state in which absorbed solar radiation is balanced by outgoing thermal radiation. Here, we explore how non-linear positive feedbacks can temporarily result in a net-positive feedback and modify Earth's state space." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def CO2_const(t): # define CO2 scenario\n", " return 280" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f, (ax) = plt.subplots(1, figsize = (8,8))\n", "\n", "for count, T0_sample in enumerate(range(-60, 30, 5)):\n", " EBM = ebm(T0_sample, 0, 1., CO2_const)\n", " EBM.run(200)\n", " ax.plot(EBM.t, EBM.T)\n", "\n", "ax.set_xlabel(\"year\")\n", "ax.set_ylabel(\"Temperature [°C]\")\n", "ax.set_ylim(-60,30)\n", "ax.text(120,-25, s=\"Completly frozen\", size = 10, color = \"darkblue\")\n", "ax.fill_between([0, 200], y1=-60, y2=-10, color = \"lightblue\", alpha = 0.2)\n", "ax.fill_between([0, 200], y1=10, y2=30, alpha=0.09, color=\"red\")\n", "ax.text(120,20, s=\"no ice\", size = 10, color = \"darkred\")\n", "\n", "T_un = 7.5472\n", "deltaTs = 1e-2*np.array([-2, -1., 0., 1., 2.])\n", "for deltaT in deltaTs:\n", " ebm_un = ebm(T_un+deltaT, 0., 1, CO2_const)\n", " ebm_un.run(200)\n", " ax.plot(ebm_un.t, ebm_un.T, ls = \"--\")\n", " \n", "ax.grid()\n", "\n", "ax.plot(200, 14, marker=\"o\", label=\"Our pre-industrial climate (stable ''warm'' branch)\", color=\"orange\", markersize=8)\n", "ax.plot(200, -38.3, marker=\"o\", label=\"Alternate universe pre-industrial climate (stable ''cold'' branch)\", color=\"aqua\", markersize=8)\n", "ax.plot(200, T_un, marker=\"o\", label=\"Impossible alternate climate (unstable branch\", color=\"lightgrey\", markersize=8)\n", "ax.legend(loc=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that for T₀ ⪆ 7.55 °C, all of the curves seem to converge on the T = 14°C equilibrium (or fixed point) that we saw in Lecture 20. Curves that start below this value warm up and while curves that start above this value will cool down. For T₀ ⪅ 7.55 °C, however, the temperatures converge on a much colder equilibrium around T = -40°C. This is the Snowball Earth equilibrium. These two states are referred to as stable equilibria because even if the state gets temporarily pushed slightly away from its equilibrium, it will eventually converge right back to its equilibrium.\n", "\n", "So what happens is T₀ ≈ 7.55 °C? For some exact temperature near there, there is indeed an equilibrim state: if you start with that temperature you will stay there forever. However, if the temperature starts off even one one-hundredth of a degree above or below this exact value, we see that temperatures eventually converge to one of the other two equilibria. Thus, we call this intermediate equilibrium an unstable equilibrium, because any infinitesimal push away will cause it to careen away towards another state." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Excourse:\n", "\n", "* Nonlinear dynamics: stability and bifurcations\n", "\n", "https://github.com/mitmath/18S191/blob/master/lecture_notebooks/week11/nonlinear_dynamics_bifurcations.jl" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.2) Radiative stability analysis\n", "We can understand why our model has two stable equilibria and one unstable equilibrium by applying concepts from dynamical systems theory.\n", "\n", "Recall that, with fixed CO₂ concentrations, our energy balance model differential equation can be expressed as:\n", "\n", "$$C\\frac{dT}{dT} = ASR(T) - OTR(T)$$\n", "\n", "where now the Absorbed Solar Radiatio (ASR) is also temperature dependent because the albedeo $\\alpha (T)$ is.\n", "\n", "In particular, by plotting the right-hand-side tendency terms as a function of the state variable $T$, we can plot a stability diagram for our system that tells us whether the plan will warm ($C\\frac{dT}{dt}$ > 0) or cool ($C\\frac{dT}{dt}$ < 0)\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "EBM = ebm(T_un, 0., 1, CO2_const)\n", "temp_range = np.arange(-60, 30)\n", "\n", "OTR, ASR = np.zeros((len(temp_range))), np.zeros((len(temp_range)))\n", "\n", "for count, i in enumerate(temp_range):\n", " EBM.T = np.array(i)\n", " EBM.alpha2 = calc_alpha(EBM.T, EBM.alpha)\n", " \n", " OTR[count] = EBM.outgoing_thermal_radiation()\n", " ASR[count] = EBM.absorbed_solar_radiation()\n", " \n", "imbalance = ASR - OTR" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f, (ax, bx) = plt.subplots(1,2, figsize=(8,4))\n", "ax.plot(temp_range, OTR, label= \"Outgoing Thermal Radiation\")\n", "ax.plot(temp_range, ASR, label = \"Absorbed Solar Radiation\")\n", "ax.set_xlabel(\"temperature [°C]\")\n", "ax.set_ylabel(\"energy flux [W/$m^2$]\")\n", "\n", "bx.fill_between([-60, 30], y1=0, y2=40, alpha=0.2, color=\"red\")\n", "bx.fill_between([-60, 30], y1=-50, y2=0, alpha=0.2, color=\"blue\")\n", "bx.set_xlabel(\"temperature [°C]\")\n", "bx.set_ylabel(\"energy flux [W/$m^2$]\")\n", "bx.set_ylim(-50,40)\n", "\n", "bx.plot(temp_range, imbalance, color = \"black\", label = \"Radiative Imbalance\\n (ASR-OTR)\")\n", "bx.text(-60, 35, \"warming\", color =\"darkred\", size = 12)\n", "bx.text(-60, -40, \"cooling\", color =\"darkblue\", size = 12)\n", "\n", "ax.legend(); bx.legend()\n", "ax.grid(); bx.grid()\n", "f.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3) Transitioning to and from Snowball Earth\n", "### 3.1) Turning up the Sun\n", "\n", "Over the entire history of the Earth, the Sun is thought to have brightened by about 40%.\n", "\n", "![](https://rainbow.ldeo.columbia.edu/courses/s4021/ec98/fys.gif)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the Neoproterozoic (~700 million years ago), the Sun was 93% as bright as it is today, such that the incoming solar radiation was $S$ = 1272 W/m², Earth's average temperature plunged to $T = -50$°C, and Earth's ice-covered surface had a high albedo (reflectivity) of $\\alpha_i = 0.5$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.2) Did the increasing brightness of the Sun melt the Snowball?\n", "If we start out in the Neoproterozoic climate and all we do is increase solar insolation to today's value of $ S = 1368 W/m^2$, can we warm the planet up to the pre-industrial temperature of T = 14°C?" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "smin = 1200\n", "smax = 1800\n", "smax_limited = 1650\n", "svec = np.arange(smin, smax)\n", "svec = np.append(svec, svec[::-1])\n", "tvec = np.zeros(svec.size)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "t_restart = -100\n", "for i, S in enumerate(svec):\n", " EBM = ebm(t_restart, 0., 5., CO2_const);\n", " EBM.S = S\n", " EBM.run(400)\n", " t_restart = EBM.T[-1]\n", " tvec[i] = EBM.T[-1]" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize = (8,6))\n", "plt.plot(svec[0:len(svec)//2], tvec[0:len(svec)//2], color = \"blue\", label = \"cool branch\", alpha = 0.3)\n", "plt.plot(svec[len(svec)//2:], tvec[len(svec)//2:], color = \"red\", label = \"warm branch\", alpha = 0.3)\n", "plt.axvline(1368, color = \"yellow\", lw = 5, alpha = 0.2, label = \"Pre-industiral / present insolation\")\n", "\n", "plt.plot(1368, tvec[svec==1368][1], marker=\"o\", label=\"Our preindustrial climate\", color=\"orange\", markersize=8)\n", "plt.plot(1368, tvec[svec==1368][0], marker=\"o\", label=\"Alternate preindustrial climate\", color=\"lightblue\", markersize=8)\n", "plt.plot(1368*0.93, -48, marker=\"o\", label=\"neoproterozoic (700 Mya)\", color=\"lightgrey\", markersize=8)\n", "\n", "plt.xlabel(\"solar insolation S [W/m$^2$]\")\n", "plt.ylabel(\"Global temperature T [°C]\")\n", "\n", "plt.fill_between([1200, 1800], y1=-60, y2=-10, color = \"lightblue\", alpha = 0.2)\n", "plt.fill_between([1200, 1800], y1=10, y2=70, alpha=0.09, color=\"red\")\n", "\n", "plt.ylim(-60,70)\n", "plt.xlim(1200,1800)\n", "\n", "plt.legend()\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Abrupt climate transitions\n", "\n", "In this model, temperature variations are fairly smooth unless temperatures rise above -10°C or fall below 10°C, in which case the *ice-albedo positive feedback* kicks in and causes an **abrupt climate transition**. While this is just a simple hypothetical model, these kinds of abrupt climate transitions show up all the time in the paleoclimate record and in more realistic climate model simulations.\n", "![](https://www.pnas.org/content/pnas/115/52/13288/F1.large.jpg)\n", "\n", "This simulation teaches us that we should not take the stability of our climate for granted and that pushing our present climate outside of its historical regime of stability could trigger catastrophic abrupt climate transitions.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.3) If not the Sun, how did Snowball Earth melt?\n", "\n", "The leading theory is that a slow but steady outgassing of CO$_2$ from volcanoes eventually caused a strong enough greenhouse gas effect to offset the cooling effect of the frozen surface's high albedo and raise temperatures above the melting point $-10$°C.\n", "\n", "![](https://hartm242.files.wordpress.com/2011/03/snowball-earth.jpg)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In Homework 1, you will extend the above model to include the effect of CO₂ and determine how much CO2 would need to be added to the snowball for it to melt." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Towards realistic climate modelling\n", "In this simple model, the preindustrial climate of °C is so warm that there is no ice anywhere on the planet. Indeed, the only two valid stable climates are one with no ice or one with ice everywhere.\n", "\n", "So how did Earth's preindustrial climate, which was relatively stable for thousands of years, have substantial ice caps at the poles?\n", "\n", "The \"Aquaplanet\", a simple three-dimensional ocean-world climate model\n", "\n", "An \"Aquaplanet\" is a three-dimensional global climate simulation of a hypothetical planet covered entirely by a single global Ocean. While this is of course very different from Earth, where 27% of the planet is covered in land, the \"Aquaplanet\" exhibits many of the same characteristics as Earth and is much more realistic than our zero-dimensional climate model above.\n", "\n", "The video below shows that the Aquaplanet simulation exhibits a third equilibrium state, with a mostly-liquid ocean but ice caps at the poles, in addition to the two we found in our zero-dimensional model.\n", "\n", "In Homework 2, you will build a simple two-dimensional version of the aqua-planet and explore its stability." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[youtube](https://www.youtube-nocookie.com/embed/lYm_IyBHMUs)\n" ] } ], "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": "3.8.2" } }, "nbformat": 4, "nbformat_minor": 4 }