From b1ba94ffa6715a0aeff0b042fbea39be09556b59 Mon Sep 17 00:00:00 2001 From: Alan Edelman Date: Fri, 1 Nov 2024 17:25:53 -0400 Subject: [PATCH] test --- notebooks/14_ferrari_Lecture2a.jl | 3176 +++++++++++++++++++++++++++++ 1 file changed, 3176 insertions(+) create mode 100644 notebooks/14_ferrari_Lecture2a.jl diff --git a/notebooks/14_ferrari_Lecture2a.jl b/notebooks/14_ferrari_Lecture2a.jl new file mode 100644 index 0000000..ced4f7b --- /dev/null +++ b/notebooks/14_ferrari_Lecture2a.jl @@ -0,0 +1,3176 @@ +### A Pluto.jl notebook ### +# v0.20.0 + +using Markdown +using InteractiveUtils + +# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error). +macro bind(def, element) + quote + local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end + local el = $(esc(element)) + global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el) + el + end +end + +# ╔═╡ 3e60b013-98cf-4057-9c96-b627662c85a4 +begin + using DifferentialEquations, Plots, PlutoUI, LinearAlgebra, CSV, DataFrames, Images +end + +# ╔═╡ 42085492-ac8c-11eb-0620-adcb307077f1 +html""" +
+ +
+

Section 2.1

+

+ Climate models: greenhouse effect +

+ +""" + +# ╔═╡ 14195fc4-40e1-4576-973a-69d649fddc02 +TableOfContents(title="📚 Table of Contents", indent=true, depth=4, aside=true) + +# ╔═╡ 92883ed9-5572-41fd-96c7-190279f90804 +md""" +In this lecture we will build a simple climate model that prewdicts the averaged temperature of earth's atmosphere and how it changes in different climates. If you are interested to learn more, you may want to check the "Introduction to Climate Modeling" lecture by former student Henri Drake. [Henri's video](https://computationalthinking.mit.edu/Fall20/lecture20/), +[Henri's original notebook](https://github.com/mitmath/18S191/blob/Fall20/lecture_notebooks/week11/01_energy_balance_model.jl) where he describes the Energy Balance Model. +""" + +# ╔═╡ 2ab34e6f-9059-4f33-8abd-df15b0c00b6b +md""" +## Surface temperature and atmospheric $CO_2$ +""" + +# ╔═╡ 8d2fd4f0-f2f6-4bc8-b753-f34f2abfcc7e +html""" + +""" + +# ╔═╡ 041caa91-5449-4de1-8786-56ae3db74bfe +html"""""" + +# ╔═╡ 21b71237-bfdf-47d1-beb3-eac924c52f6a +md""" +--- +--- +""" + +# ╔═╡ b6c511c8-918d-432c-9756-9641176ff652 +md""" +## Model to predict Earth's surface temperature +""" + +# ╔═╡ e8a5cf48-f647-4fb3-8c0a-4eae97d03e02 +md""" + +The goal is to predict the evolution of the average surface temperature of the Earth as a function of external forcing, like the atmospheric concentration of $CO_2$. Let us start by introducing some notation: + +``T=T(t)`` is the Earth's average surface temperature as a function of time $t$ + +Inititally $t=0$, $T(0)=T_0$ + +We write ``T'`` for ``dT/dt`` and look for an equation of the form: + +``T' = f(t)`` + +where ``f(t)`` represents the external forcing which acts to change the Earth's temperature ``T(t)`` +""" + +# ╔═╡ 8516277a-2c98-4390-90bb-3a2276ef54e4 +md""" +--- + +#### Solving an ODEs of the form ``T'=f(T,p,t)`` in Julia + +0. Define f(T,p,t) +1. ODEProblem( f, f(0), time_span, parameters) +2. solve +3. plot etc +""" + +# ╔═╡ a28f7886-3237-49d0-9c41-84f52aaff2ea +md""" +--- + +### Earth energy budget +""" + +# ╔═╡ 739e914a-9760-4a84-a860-7acadddfc21f +md""" + +The energy (heat) budget of a planet without atmsophere is given by the simple equation: + +$\begin{align} +\text{\color{brown}{change in temperature}} = & + \text{\color{red}{heating from the Sun's rays}} \newline +& - \text{\color{red}{reflected solar radiation}}\newline +& - \text{\color{blue}{outgoing thermal radiation}} +\end{align}$ + +where each of these is interpreted as an average over the entire globe. + + +""" + +# ╔═╡ 3a66b385-737e-49e4-b30d-56b055b7bf44 +html"""""" + +# ╔═╡ 4b074c56-dc58-4c9c-ae64-7b9ba8d92c20 +md""" +--- +#### Start with solar heating only + +""" + +# ╔═╡ ebfeb0b0-d29e-4244-a0e3-a7185f3c8124 +md""" + +``T' = a `` +$(html"
") Solution: ``T(t) = a t + T_0`` + +""" + +# ╔═╡ de443120-f6e1-4fa4-a915-2a316e7fab9d +S_0 = 1366/4; # solar insolation [W/m^2] (energy per unit time per unit area) + +# ╔═╡ 81630f00-2bde-48f2-b8a6-472c732ff8da +C = 355.; # atmosphere and upper-ocean heat capacity [Wyr/m^2/°K] + +# ╔═╡ 2251e66d-0188-477c-acf2-14ed3c51e85f +a = S_0/C; + +# ╔═╡ b38f98a0-fee8-4746-a136-247e78230f34 +begin + temp₀ = 0; #absolute zero [K] + timespan = 1000.; +end + +# ╔═╡ a1683297-6ad5-4143-bb3a-ff0b6b52ace4 +m1 = ODEProblem( (temp, p, t)-> a, temp₀, (0, timespan) ) + +# ╔═╡ 3785b312-4228-44e5-992b-90cd23f2bac2 +begin + model1=solve(m1) + model1.u.-=273.15 + plot(model1, legend = false, + background_color_inside = :black, + xlabel = "years", + ylabel = "Temperature °C", + ylim = (-273.15,400), + c = :red, + lw = :3) + hline!( [temp₀,temp₀] ,c=:white,ls=:dash) + annotate!( 700, 35+temp₀-273.15, text("Initial Temperature = $(temp₀) K",color=:white)) + title!("Earth's heat budget absorbing solar radiation only") +end + +# ╔═╡ 4bf60f27-8db5-42c1-83d8-750bec2060e5 +md""" +--- + +#### Adding reflection of solar radiation +\ +``T' = (1 - \alpha)a ``$(html"
") Solution: ``T(t) = (1 -\alpha) a t + T_0`` + +where $\alpha$ is called ablbedo and equal to 30\%. + +""" + +# ╔═╡ 67153542-28cb-4d8a-ae86-b13be5f84557 +alpha = 0.3; # albedo, or planetary reflectivity [unitless] + +# ╔═╡ ad973c4b-0162-48fb-b5e0-342d772af800 +m2 = ODEProblem( (temp, p, t)-> a * (1-alpha), temp₀, (0, timespan) ) + +# ╔═╡ 54801ddc-c1a6-4e82-8264-08c2205d18ed +begin + model2=solve(m2) + model2.u.-=273.15 + plot(model2, legend = false, + background_color_inside = :black, + xlabel = "years", + ylabel = "Temperature °C", + ylim = (-273.15,400), + c = :red, + lw = :3) + hline!( [temp₀,temp₀] ,c=:white,ls=:dash) + annotate!( 700, 35+temp₀-273.15, text("Initial Temperature = $(temp₀) K",color=:white)) + title!("Earth's heat budget absorbing and reflecting solar radiation") +end + +# ╔═╡ e2799d05-36a7-4547-8663-90708ce01ce8 +md""" +--- + +#### Adding radiative cooling +\ +``T' = (1-\alpha) a - b T^4 ``$(html"
") + +Comment: At long times, the temperatures reaches a stable value: +``T(t) = \left(\frac{(1-\alpha)a }{b}\right)^{1/4}`` + +""" + +# ╔═╡ 3ba79372-aa57-49a8-9d50-146ef8f7d0b3 +sigma = 5.670374419*10^(−8); # [W/m^2/K^4] + +# ╔═╡ 17800b4d-a879-4270-b39d-c44901f46391 +b = sigma/C; + +# ╔═╡ 578a80ad-fcf1-4d5c-81e5-205113bbf78d +m3 = ODEProblem( (temp, p, t)-> a * (1-alpha) - b*temp^4, temp₀, (0, timespan) ) + +# ╔═╡ 7af3719c-bf0c-4502-a098-66f797f1b6ea +begin + model3=solve(m3) + model3.u.-=273.15 + plot(model3, legend = false, + background_color_inside = :black, + xlabel = "years", + ylabel = "Temperature °C", + ylim = (-273.15,400), + c = :red, + lw = :3) + hline!( [temp₀,temp₀] ,c=:white,ls=:dash) + annotate!( 700, 35+temp₀-273.15, text("Initial Temperature = $(temp₀) K",color=:white)) + title!("Earth's heat budget including outgoing radiation") +end + +# ╔═╡ 9fca410f-87bd-405d-8336-3ae109ee60f9 +md""" +--- + +#### Adding an atmosphere +\ +``T' = (1-\alpha) a - (1-\epsilon/2)b T^4 ``$(html"
") + +Comment: At long times, the temperatures reaches a stable value: +``T(t) = \left(\frac{(1-\alpha)S }{(1-\epsilon/2)b}\right)^{1/4}`` + +""" + +# ╔═╡ de777b52-8ff7-4fc9-bdbc-17d64abf8926 +T₀=273.15-18; + +# ╔═╡ ae54e5a6-f4ab-4196-845e-612e7c7ebb5c +md""" + +epsilon = $(@bind epsilon Slider(0:.01:1, show_value=true, default=0) ) + +""" + +# ╔═╡ 3aa13ecd-9d4a-4b41-b15f-f85e2b8f8bf6 +m4 = ODEProblem( (temp, p, t)-> a * (1-alpha) - (1-epsilon/2)*b*temp^4, T₀, (0, timespan) ) + +# ╔═╡ 2d3740ae-bbeb-49a5-a51e-0b5079e68592 +begin + model4=solve(m4) + model4.u.-=273.15 + plot(model4, legend = false, + background_color_inside = :black, + xlabel = "years", + ylabel = "Temperature °C", + ylim = (-30,35), + c = :red, + lw = :3) + hline!( [(a*(1-alpha)/b)^(1/4)-273.15,(a*(1-alpha)/b)^(1/4)-273.15] ,c=:white,ls=:dash) + annotate!( 700, -7+T₀-273.15, text("Initial Temperature = $(T₀-273.15) C",color=:white)) + title!("Earth's temperature with an atmosphere") +end + +# ╔═╡ 3c3f7997-ca76-4536-8331-634fff7fbcb7 +md""" +--- + +#### Adding carbon to present day atmosphere +\ +``T' = (1-\alpha) a - (1-\epsilon(CO_2)/2)b T^4 ``$(html"
") + + +""" + +# ╔═╡ 87a384f1-1679-4f1a-aaad-ac85c117b959 +T₁=((1-alpha)*a/((1-0.745/2)*b))^(1/4) + +# ╔═╡ 7a6019d9-41af-4e5c-80e6-25dc52ac1819 +eps(CO₂,T) = 0.745+0.02 * log(CO₂/280)/log(2)+0.01*(T-T₁) + +# ╔═╡ ce1792bc-36d2-49b2-bd92-351e09bb3a4f +md""" + +CO₂ = $(@bind CO₂ Slider(280:1:560, show_value=true, default=280) ) + +""" + +# ╔═╡ a61b1671-ad76-4a34-8d63-3f687fffe836 +m5 = ODEProblem( (temp, p, t)-> a * (1-alpha) - (1-eps(CO₂,T₁)/2)*b*temp^4, T₁, (0, timespan) ) + +# ╔═╡ 819431a7-cdcd-430a-a89a-2db90eb22e7c +begin + model5=solve(m5) + model5.u.-=273.15 + plot(model5, legend = false, + background_color_inside = :black, + xlabel = "years", + ylabel = "Temperature °C", + ylim = (12.4,17), + c = :red, + lw = :3) + hline!( [T₁-273.15,T₁-273.15] ,c=:white,ls=:dash) + annotate!( 700, -.5+T₁-273.15, text("Initial Temperature = $(round(10*(T₁-273.15))/10) C",color=:white)) + title!("Earth's temperature deepndence on CO₂") +end + +# ╔═╡ ee9724f1-5414-4c3d-85b9-e394afea2e72 +md""" +--- + +#### Adding water vapor feedback +\ +``T' = (1-\alpha) a - (1-\epsilon(CO_2,T)/2)b T^4 ``$(html"
") + + +""" + +# ╔═╡ 0b6e8dd2-a060-4ed9-aa03-de48e3c7c3e1 +m6 = ODEProblem( (temp, p, t)-> a * (1-alpha) - (1-eps(CO₂,temp)/2)*b*temp^4, T₁, (0, timespan) ) + +# ╔═╡ 5b153580-78ee-4a73-b936-507b3b39f02c +begin + model6=solve(m6) + model6.u.-=273.15 + plot(model6, legend = false, + background_color_inside = :black, + xlabel = "years", + ylabel = "Temperature °C", + ylim = (12.4,17), + c = :red, + lw = :3) + hline!( [T₁-273.15,T₁-273.15] ,c=:white,ls=:dash) + annotate!( 700, -.5+T₁-273.15, text("Initial Temperature = $(round(10*(T₁-273.15))/10) C",color=:white)) + title!("Earth's temperature with an atmosphere") +end + +# ╔═╡ 00000000-0000-0000-0000-000000000001 +PLUTO_PROJECT_TOML_CONTENTS = """ +[deps] +CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b" +DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0" +DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa" +Images = "916415d5-f1e6-5110-898d-aaa5f9f070e0" +LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" +Plots = 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╠═3aa13ecd-9d4a-4b41-b15f-f85e2b8f8bf6 +# ╟─ae54e5a6-f4ab-4196-845e-612e7c7ebb5c +# ╟─2d3740ae-bbeb-49a5-a51e-0b5079e68592 +# ╟─3c3f7997-ca76-4536-8331-634fff7fbcb7 +# ╠═87a384f1-1679-4f1a-aaad-ac85c117b959 +# ╠═7a6019d9-41af-4e5c-80e6-25dc52ac1819 +# ╠═a61b1671-ad76-4a34-8d63-3f687fffe836 +# ╟─ce1792bc-36d2-49b2-bd92-351e09bb3a4f +# ╟─819431a7-cdcd-430a-a89a-2db90eb22e7c +# ╟─ee9724f1-5414-4c3d-85b9-e394afea2e72 +# ╠═0b6e8dd2-a060-4ed9-aa03-de48e3c7c3e1 +# ╟─5b153580-78ee-4a73-b936-507b3b39f02c +# ╟─00000000-0000-0000-0000-000000000001 +# ╟─00000000-0000-0000-0000-000000000002