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{"documenter":{"julia_version":"1.10.0","generation_timestamp":"2024-01-31T19:14:39","documenter_version":"1.2.1"}}

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<!DOCTYPE html>
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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Box Model · CloudMicrophysics.jl</title><meta name="title" content="Box Model · CloudMicrophysics.jl"/><meta property="og:title" content="Box Model · CloudMicrophysics.jl"/><meta property="twitter:title" content="Box Model · CloudMicrophysics.jl"/><meta name="description" content="Documentation for CloudMicrophysics.jl."/><meta property="og:description" content="Documentation for CloudMicrophysics.jl."/><meta property="twitter:description" content="Documentation for CloudMicrophysics.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script data-outdated-warner src="../assets/warner.js"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"><a class="docs-logo" href="../"><img src="../assets/logo.svg" alt="CloudMicrophysics.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../">CloudMicrophysics.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="../Microphysics0M/">0-moment precipitation microphysics</a></li><li><a class="tocitem" href="../Microphysics1M/">1-moment precipitation microphysics</a></li><li><a class="tocitem" href="../Microphysics2M/">2-moment precipitation microphysics</a></li><li><a class="tocitem" href="../P3Scheme/">P3 Scheme</a></li><li><a class="tocitem" href="../MicrophysicsNonEq/">Non-equilibrium cloud formation</a></li><li><a class="tocitem" href="../ThresholdsTransition/">Smooth transition at thresholds</a></li><li><a class="tocitem" href="../AerosolActivation/">Aerosol activation</a></li><li><a class="tocitem" href="../WaterActivity/">Water Activity</a></li><li><a class="tocitem" href="../IceNucleation/">Ice Nucleation</a></li><li><a class="tocitem" href="../AerosolNucleation/">Aerosol Nucleation</a></li><li><a class="tocitem" href="../IceNucleationParcel0D/">Adiabatic parcel model</a></li><li class="is-active"><a class="tocitem" href>Box Model</a></li><li><a class="tocitem" href="../PrecipitationSusceptibility/">Precipitation Susceptibility</a></li><li><a class="tocitem" href="../API/">API</a></li><li><a class="tocitem" href="../References/">References</a></li><li><a class="tocitem" href="../DevelopersGuide/">Developer&#39;s Guide</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>Box Model</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Box Model</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/CliMA/CloudMicrophysics.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/CloudMicrophysics.jl/blob/main/docs/src/IceNucleationBox0D.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="0-dimensional-Box-Model"><a class="docs-heading-anchor" href="#0-dimensional-Box-Model">0-dimensional Box Model</a><a id="0-dimensional-Box-Model-1"></a><a class="docs-heading-anchor-permalink" href="#0-dimensional-Box-Model" title="Permalink"></a></h1><p>This model solves for number concentration of ice crystals produced via water-activity based immersion freezing in a 0-dimensional setup with a prescribed constant cooling rate. It is used to validate the immersion freezing parameterization and is based on Figure 4 from [<a href="../References/#Alpert2016">50</a>].</p><p>Note that because the cooling rate is prescribed, the temperature change does not depend on the freezing rate and the associated latent heat release. The production rate of ice is given by</p><p class="math-container">\[\begin{equation}
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\frac{dN_{i}}{dt} = J \; N_{l} \; A_{d}
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\end{equation}\]</p><p>where</p><ul><li><span>$J$</span> - is the immersion freezing rate coefficient,</li><li><span>$N_{l}$</span> - is number of liquid droplets,</li><li><span>$A_{d}$</span> - is the surface area available for freezing for a single droplet.</li></ul><p><span>$A_{d}$</span> is currently assumed to be either constant among all droplets or sampled from a lognormal distribution with user defined mean and width.</p><p>In the plots below, we first reproduce Fig. 4 from [<a href="../References/#Alpert2016">50</a>] by computing the apparent and actual nucleation rates based on the paper defined frozen fraction. As as second step we run the box model for constant and variable <span>$A_d$</span> and compare the results. Note that the variable <span>$A_d$</span> scenario is closer to what is observed, while constant <span>$A_d$</span> is closer to what we can currently implement in our bulk microphysics scheme for ESM.</p><pre><code class="language-julia hljs">include(&quot;../../box/Alpert_Knopf_2016_backward.jl&quot;)
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include(&quot;../../box/Alpert_Knopf_2016_forward.jl&quot;)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">CairoMakie.Screen{SVG}
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</code></pre><p><img src="../Alpert_Knopf_2016_backward.svg" alt/> <img src="../Alpert_Knopf_2016_forward.svg" alt/></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../IceNucleationParcel0D/">« Adiabatic parcel model</a><a class="docs-footer-nextpage" href="../PrecipitationSusceptibility/">Precipitation Susceptibility »</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 31 January 2024 19:14">Wednesday 31 January 2024</span>. Using Julia version 1.10.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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