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| <!DOCTYPE html> | ||
| <html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Milankovitch Cycles · Insolation.jl</title><meta name="title" content="Milankovitch Cycles · Insolation.jl"/><meta property="og:title" content="Milankovitch Cycles · Insolation.jl"/><meta property="twitter:title" content="Milankovitch Cycles · Insolation.jl"/><meta name="description" content="Documentation for Insolation.jl."/><meta property="og:description" content="Documentation for Insolation.jl."/><meta property="twitter:description" content="Documentation for Insolation.jl."/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../search_index.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">Insolation.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li><a class="tocitem" href="../ZenithAngleEquations/">Zenith Angle Equations</a></li><li><a class="tocitem" href="../InsolationExamples/">Insolation Examples</a></li><li class="is-active"><a class="tocitem" href>Milankovitch Cycles</a><ul class="internal"><li><a class="tocitem" href="#Variations-in-orbital-parameters"><span>Variations in orbital parameters</span></a></li><li><a class="tocitem" href="#Variations-in-date-of-vernal-equinox-and-perihelion-on-centennial-timescales"><span>Variations in date of vernal equinox and perihelion on centennial timescales</span></a></li><li><a class="tocitem" href="#Variations-in-date-of-vernal-equinox-on-millenial-timescales"><span>Variations in date of vernal equinox on millenial timescales</span></a></li></ul></li><li><a class="tocitem" href="../library/">APIs</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Milankovitch Cycles</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Milankovitch Cycles</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/CliMA/Insolation.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/CliMA/Insolation.jl/blob/main/docs/src/Milankovitch.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Milankovitch-Cycles"><a class="docs-heading-anchor" href="#Milankovitch-Cycles">Milankovitch Cycles</a><a id="Milankovitch-Cycles-1"></a><a class="docs-heading-anchor-permalink" href="#Milankovitch-Cycles" title="Permalink"></a></h1><h2 id="Variations-in-orbital-parameters"><a class="docs-heading-anchor" href="#Variations-in-orbital-parameters">Variations in orbital parameters</a><a id="Variations-in-orbital-parameters-1"></a><a class="docs-heading-anchor-permalink" href="#Variations-in-orbital-parameters" title="Permalink"></a></h2><pre><code class="language-julia hljs">using Insolation | ||
| using Plots | ||
|
|
||
| od = Insolation.OrbitalData() | ||
| dt = collect(-500e3:100:500e3); # years | ||
| y = hcat(collect.(orbital_params.(Ref(od), dt))...); | ||
| ϖ, γ, e = y[1,:], y[2,:], y[3,:]; | ||
|
|
||
| p1 = plot(dt ./ (1e3), sin.(ϖ), legend=false); | ||
| ylabel!("sin(ϖ)"); | ||
| p2 = plot(dt ./ (1e3), γ, legend=false); | ||
| ylabel!("γ"); | ||
| p3 = plot(dt ./ (1e3), e, legend=false); | ||
| ylabel!("e"); | ||
| xlabel!("Time (kyr)") | ||
| plot(p1, p2, p3, layout = grid(3,1), size=(600,400), dpi=250); | ||
| savefig("orbital_params.png")</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">"/home/runner/work/Insolation.jl/Insolation.jl/docs/build/orbital_params.png"</code></pre><p><img src="../orbital_params.png" alt/></p><h2 id="Variations-in-date-of-vernal-equinox-and-perihelion-on-centennial-timescales"><a class="docs-heading-anchor" href="#Variations-in-date-of-vernal-equinox-and-perihelion-on-centennial-timescales">Variations in date of vernal equinox and perihelion on centennial timescales</a><a id="Variations-in-date-of-vernal-equinox-and-perihelion-on-centennial-timescales-1"></a><a class="docs-heading-anchor-permalink" href="#Variations-in-date-of-vernal-equinox-and-perihelion-on-centennial-timescales" title="Permalink"></a></h2><pre><code class="language-julia hljs">using Roots | ||
| using Optim | ||
| include("find_equinox_perihelion_dates.jl") | ||
|
|
||
| years = 1800:2200; | ||
| days_eq = zeros(length(years)); | ||
| days_per = zeros(length(years)); | ||
| od = Insolation.OrbitalData() | ||
| for (i,year) in enumerate(years) | ||
| f = (x -> zdiff(x, year, od)) | ||
| days_eq[i] = find_zeros(f,-30,60)[1] | ||
|
|
||
| f = (x -> edist(x, year, od)) | ||
| res = optimize(f,-50,50) | ||
| days_per[i] = Optim.minimizer(res)[1] | ||
| end | ||
|
|
||
| plot((years), days_eq, legend=false, dpi=250) | ||
| xlabel!("Year") | ||
| ylabel!("Day in March") | ||
| title!("Date of vernal equinox") | ||
| savefig("equinox_dates.png") | ||
|
|
||
| plot((years), days_per, legend=false, dpi=250) | ||
| xlabel!("Year") | ||
| ylabel!("Day in Jan") | ||
| title!("Date of perihelion") | ||
| savefig("perihelion_dates.png")</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">"/home/runner/work/Insolation.jl/Insolation.jl/docs/build/perihelion_dates.png"</code></pre><p>The Gregorian calendar was introduced (with leap years and leap centuries) precisely to keep the vernal equinox approximately fixed at March 21 on centennial timescales. <img src="../equinox_dates.png" alt/> <img src="../perihelion_dates.png" alt/></p><h2 id="Variations-in-date-of-vernal-equinox-on-millenial-timescales"><a class="docs-heading-anchor" href="#Variations-in-date-of-vernal-equinox-on-millenial-timescales">Variations in date of vernal equinox on millenial timescales</a><a id="Variations-in-date-of-vernal-equinox-on-millenial-timescales-1"></a><a class="docs-heading-anchor-permalink" href="#Variations-in-date-of-vernal-equinox-on-millenial-timescales" title="Permalink"></a></h2><pre><code class="language-julia hljs">using Roots | ||
| include("find_equinox_perihelion_dates.jl") | ||
| od = Insolation.OrbitalData() | ||
| years = -50e3:100:30e3 | ||
| days_eq = zeros(length(years)) | ||
| for (i,year) in enumerate(years) | ||
| f = (x -> zdiff(x, year, od)) | ||
| days_eq[i] = find_zeros(f,-100,100)[1] | ||
| end | ||
|
|
||
| plot((years / 1000), days_eq, legend=false, dpi=250) | ||
| xlabel!("kyr") | ||
| ylabel!("Day in March") | ||
| title!("Date of vernal equinox") | ||
| savefig("equinox_dates_long.png")</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">"/home/runner/work/Insolation.jl/Insolation.jl/docs/build/equinox_dates_long.png"</code></pre><p>As we can see however, the vernal equinox changes appreciably on very long timescales. For studies of paleoclimates, it is often conventional to reference the day of year relative to the vernal equinox rather than relative to January 1 to make meaningful comparisons of "seasons" and the like. <img src="../equinox_dates_long.png" alt/></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../InsolationExamples/">« Insolation Examples</a><a class="docs-footer-nextpage" href="../library/">APIs »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Wednesday 14 February 2024 20:00">Wednesday 14 February 2024</span>. Using Julia version 1.7.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> |
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