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2 changes: 1 addition & 1 deletion dev/.documenter-siteinfo.json
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{"documenter":{"julia_version":"1.10.0","generation_timestamp":"2024-01-23T10:18:10","documenter_version":"1.2.1"}}
{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2024-01-23T10:23:27","documenter_version":"1.2.1"}}
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println(kfi)
end
Colorbar(fig[1, 4], height = Relative(0.6); opts...)
fig</code></pre><img src="146e9a31.png" alt="Example block output"/><p>The displayed fields are displacement anomalies w.r.t. to the last interglacial, defined as the reference for the ice thickness anomalies. In (Swierczek-Jereczek et al. in prep.), these computations are performed on a finer grid, with an interactive sea level, and show great agreement with a 3D GIA model that runs between 10,000-100,000 slower (however at with advantage of obtaining a global and richer output).</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../tutorial/">« Tutorial</a><a class="docs-footer-nextpage" href="../inversion/">Parameter inversion »</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="Tuesday 23 January 2024 10:18">Tuesday 23 January 2024</span>. Using Julia version 1.10.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
fig</code></pre><img src="146e9a31.png" alt="Example block output"/><p>The displayed fields are displacement anomalies w.r.t. to the last interglacial, defined as the reference for the ice thickness anomalies. In (Swierczek-Jereczek et al. in prep.), these computations are performed on a finer grid, with an interactive sea level, and show great agreement with a 3D GIA model that runs between 10,000-100,000 slower (however at with advantage of obtaining a global and richer output).</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../tutorial/">« Tutorial</a><a class="docs-footer-nextpage" href="../inversion/">Parameter inversion »</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="Tuesday 23 January 2024 10:23">Tuesday 23 January 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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return fig
end
fig1 = plot_viscfields(paraminv)</code></pre><img src="2b851373.png" alt="Example block output"/><p>By performing a Kalman inversion, we can achieve a close match between ground truth and estimated viscosity field:</p><pre><code class="language-julia hljs">solve!(paraminv)
fig2 = plot_viscfields(paraminv)</code></pre><img src="5acd2d4a.png" alt="Example block output"/><p>This remains an academic example, where we try to recover a known parameter field from data generated by the model itself. Nonetheless, the user should get a proof-of-concept and a scheme of how to implement such a procedure themself.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../glacialcycle/">« Glacial cycle</a><a class="docs-footer-nextpage" href="../../APIref/">API reference »</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="Tuesday 23 January 2024 10:18">Tuesday 23 January 2024</span>. Using Julia version 1.10.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
fig2 = plot_viscfields(paraminv)</code></pre><img src="e4352d14.png" alt="Example block output"/><p>This remains an academic example, where we try to recover a known parameter field from data generated by the model itself. Nonetheless, the user should get a proof-of-concept and a scheme of how to implement such a procedure themself.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../glacialcycle/">« Glacial cycle</a><a class="docs-footer-nextpage" href="../../APIref/">API reference »</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="Tuesday 23 January 2024 10:23">Tuesday 23 January 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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hidedecorations!(ax)
hidespines!(ax)
end
fig</code></pre><img src="2e4a9dee.png" alt="Example block output"/><p>The distortion factor <code>Omega.K</code> is not only accessible but also accounted for in all the computations. The projection allows to treat the radially-layered, onion-like structure of the solid Earth as a superposition of horizontal layers. Furthermore, FastIsostasy reduces this 3D problem into a 2D problem by collapsing the depth dimension, mainly through the computation of an effective viscosity field that accounts for the superposition of layers with different viscosities. The user is required to provide the 3D information, which will then be used under the hood to compute the effective viscosity. This tutorial shows such an example.</p><p>We want to render a situation similar to the one depicted below:</p><p><img src="../../assets/sketch_nlayer_model.png" alt="Schematic representation of the three-layer set-up."/></p><p>Initializing a <a href="../../APIref/#FastIsostasy.LayeredEarth"><code>LayeredEarth</code></a> with parameters corresponding to this situation automatically computes the conversion from a 3D to a 2D problem. Since we will compare our solution to an analytical one of a flat Earth, we exceptionally switch off the distortion correction. This can be simply executed by running:</p><pre><code class="language-julia hljs">Omega = ComputationDomain(W, n, correct_distortion = false)
fig</code></pre><img src="28193df2.png" alt="Example block output"/><p>The distortion factor <code>Omega.K</code> is not only accessible but also accounted for in all the computations. The projection allows to treat the radially-layered, onion-like structure of the solid Earth as a superposition of horizontal layers. Furthermore, FastIsostasy reduces this 3D problem into a 2D problem by collapsing the depth dimension, mainly through the computation of an effective viscosity field that accounts for the superposition of layers with different viscosities. The user is required to provide the 3D information, which will then be used under the hood to compute the effective viscosity. This tutorial shows such an example.</p><p>We want to render a situation similar to the one depicted below:</p><p><img src="../../assets/sketch_nlayer_model.png" alt="Schematic representation of the three-layer set-up."/></p><p>Initializing a <a href="../../APIref/#FastIsostasy.LayeredEarth"><code>LayeredEarth</code></a> with parameters corresponding to this situation automatically computes the conversion from a 3D to a 2D problem. Since we will compare our solution to an analytical one of a flat Earth, we exceptionally switch off the distortion correction. This can be simply executed by running:</p><pre><code class="language-julia hljs">Omega = ComputationDomain(W, n, correct_distortion = false)
c = PhysicalConstants(rho_litho = 0.0)
lv = [1e19, 1e21] # viscosity layers (Pa s)
lb = [88e3, 400e3] # depth of layer boundaries (m)
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end
return fig
end
fig = plot3D(fip, [lastindex(t_out) ÷ 2, lastindex(t_out)])</code></pre><img src="d9153b37.png" alt="Example block output"/><p>... and here goes the total displacement at <span>$t = 50 \, \mathrm{kyr}$</span>. You can now access the elastic and viscous displacement at time <code>t_out[k]</code> by respectively calling <code>fip.out.ue[k]</code> and <code>fip.out.u[k]</code>. For the present case, the latter can be compared to an analytic solution that is known for this particular case. Let&#39;s look at the accuracy of our numerical scheme over time by running following plotting commands:</p><pre><code class="language-julia hljs">fig = Figure()
fig = plot3D(fip, [lastindex(t_out) ÷ 2, lastindex(t_out)])</code></pre><img src="0e19298d.png" alt="Example block output"/><p>... and here goes the total displacement at <span>$t = 50 \, \mathrm{kyr}$</span>. You can now access the elastic and viscous displacement at time <code>t_out[k]</code> by respectively calling <code>fip.out.ue[k]</code> and <code>fip.out.u[k]</code>. For the present case, the latter can be compared to an analytic solution that is known for this particular case. Let&#39;s look at the accuracy of our numerical scheme over time by running following plotting commands:</p><pre><code class="language-julia hljs">fig = Figure()
ax = Axis(fig[1, 1])
cmap = cgrad(:jet, length(t_out), categorical = true)
ii, jj = Omega.Mx:Omega.Nx, Omega.My
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step!(fip, ode, (fip.out.t[k-1], fip.out.t[k]))
write_out!(fip, k)
end
fig = plot3D(fip, [lastindex(t_out) ÷ 2, lastindex(t_out)])</code></pre><img src="c0d6e9bc.png" alt="Example block output"/><div class="admonition is-info"><header class="admonition-header">Coupling to julia Ice-Sheet model</header><div class="admonition-body"><p>In case your Ice-Sheet model is programmed in julia, we highly recommend performing the coupling within the function updating the derivatives and let <code>OrdinaryDiffEq.jl</code> handle the rest.</p></div></div><div class="admonition is-warning"><header class="admonition-header">GPU not supported</header><div class="admonition-body"><p><a href="../../APIref/#FastIsostasy.step!"><code>step!</code></a> does not support GPU computation so far. Make sure your model is initialized on CPU.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../introGIA/">« Quick intro to GIA</a><a class="docs-footer-nextpage" href="../glacialcycle/">Glacial cycle »</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="Tuesday 23 January 2024 10:18">Tuesday 23 January 2024</span>. Using Julia version 1.10.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
fig = plot3D(fip, [lastindex(t_out) ÷ 2, lastindex(t_out)])</code></pre><img src="37919fd8.png" alt="Example block output"/><div class="admonition is-info"><header class="admonition-header">Coupling to julia Ice-Sheet model</header><div class="admonition-body"><p>In case your Ice-Sheet model is programmed in julia, we highly recommend performing the coupling within the function updating the derivatives and let <code>OrdinaryDiffEq.jl</code> handle the rest.</p></div></div><div class="admonition is-warning"><header class="admonition-header">GPU not supported</header><div class="admonition-body"><p><a href="../../APIref/#FastIsostasy.step!"><code>step!</code></a> does not support GPU computation so far. Make sure your model is initialized on CPU.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../introGIA/">« Quick intro to GIA</a><a class="docs-footer-nextpage" href="../glacialcycle/">Glacial cycle »</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="Tuesday 23 January 2024 10:23">Tuesday 23 January 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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