class: center, middle, inverse, title-slide .title[ # Amanzi-ATS Transport ] .subtitle[ ## Hands-on tutorial ] .author[ ### Phong Le, Ethan Coon (ORNL) <br> Daniil Svyatsky (LANL) <br> <br> ] .date[ ### November 14, 2024 ] --- # Goals <br> - Understand the basics of the .content-box-purple[`transport PK`] - Build simple to advanced transport models with .content-box-yellow[`Amanzi-ATS`] - .content-box-red[Visualize and analyze] `Amanzi-ATS` model outputs --- # Website <br> **Github <svg aria-hidden="true" role="img" viewBox="0 0 496 512" style="height:1em;width:0.97em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>:** [`https://github.com/amanzi/ats-hands-on-transport`](https://github.com/amanzi/ats-hands-on-transport) <br> **Slides for tutorial:** [`https://amanzi.github.io/ats-hands-on-transport/slides.html`](https://amanzi.github.io/ats-hands-on-transport/slides.html) <br> .font70[ **Other `Amanzi-ATS` resources:** - Documentation: [`https://amanzi.github.io/ats/stable/`](https://amanzi.github.io/ats/stable/) - Short course: [`https://github.com/amanzi/ats-short-course`](https://github.com/amanzi/ats-short-course) - Regression tests: [`https://github.com/amanzi/ats-regression-tests`](https://github.com/amanzi/ats-regression-tests) - Demos: [`https://github.com/amanzi/ats-demos`](https://github.com/amanzi/ats-demos) ] --- # Setting up environment <br> - Pull the `docker` <svg aria-hidden="true" role="img" viewBox="0 0 640 512" style="height:1em;width:1.25em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M349.9 236.3h-66.1v-59.4h66.1v59.4zm0-204.3h-66.1v60.7h66.1V32zm78.2 144.8H362v59.4h66.1v-59.4zm-156.3-72.1h-66.1v60.1h66.1v-60.1zm78.1 0h-66.1v60.1h66.1v-60.1zm276.8 100c-14.4-9.7-47.6-13.2-73.1-8.4-3.3-24-16.7-44.9-41.1-63.7l-14-9.3-9.3 14c-18.4 27.8-23.4 73.6-3.7 103.8-8.7 4.7-25.8 11.1-48.4 10.7H2.4c-8.7 50.8 5.8 116.8 44 162.1 37.1 43.9 92.7 66.2 165.4 66.2 157.4 0 273.9-72.5 328.4-204.2 21.4.4 67.6.1 91.3-45.2 1.5-2.5 6.6-13.2 8.5-17.1l-13.3-8.9zm-511.1-27.9h-66v59.4h66.1v-59.4zm78.1 0h-66.1v59.4h66.1v-59.4zm78.1 0h-66.1v59.4h66.1v-59.4zm-78.1-72.1h-66.1v60.1h66.1v-60.1z"/></svg> image ```bash docker pull --platform linux/amd64 metsi/ideas-watersheds-all-hands-2024:latest ``` <br> - Run the `docker` container to start the `JupyterLab` server ```bash docker run -p 8888:8888 metsi/ideas-watersheds-all-hands-2024:latest ``` --- # VSCode and Dev Containers <br> ### If you prefer VSCode/Cursor editors, use the extensions: - .content-box-green[`Dev Containers`] to connect to the container and edit files (e.g., `XML`). - .font90[Convenient for data transfer between `host` and `container`] <br> - .content-box-purple[`jupyter`] to edit/run notebooks inside the container with VSCode. --- # Clone the repository <br /> - In the `JupyterLab` server, open a terminal and run: <svg aria-hidden="true" role="img" viewBox="0 0 496 512" style="height:1em;width:0.97em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg> ```bash git clone https://github.com/amanzi/ats-hands-on-transport.git ``` --- # Outlines <br> #### .blockquote[Integrated hydrology:] - Understand and run the model (2-D & 3-D) - Visualize and interpret the outputs #### .blockquote[Transport Modeling:] - **Catchment scale:** 2-D & 3-D transport across the entire domain - **River network scale:** 1-D transport within the river corridor - .content-box-green[Develop and couple] transport models with integrated hydrology - Visualize and interpret results --- class: phong-dark # .brand-orange[Integrated hydrology model] --- # Integrated hydrology model **Water mass conservation equations:** .pull-left-21[ - Surface $$ \frac{\partial \Theta_s}{\partial t} + \nabla \cdot \vec{\mathbf{q}_s} = Q_s + Q_e$$ - Subsurface $$ \frac{\partial \Theta_g}{\partial t} + \nabla \cdot \vec{\mathbf{q}_g} = Q_g$$ .font80[**where:**] ] .pull-right-12[ <img src="imgs/hydro_domain.png" height="300px"/> ] .content-box-yellow[ .pull-left[.font70[ - `\(\Theta_s = \eta \times h\)`: .brand-blue[mass of water per unit surface area (mol/m^2)] - `\(q_s\)`: .brand-blue[surface water flux (mol/m/s)] - `\(\eta\)`: .brand-blue[molar density of liquid water (mol/m^3)] - `\(h\)`: .brand-blue[ponded depth (m)] ]] .pull-right[.font70[ - `\(\Theta_g = \eta \times S_w \times \phi\)`: .brand-blue[subsurface water content (mol/m^3)] - `\(q_g\)`: .brand-blue[flux of water in the subsurface (mol/m^2/s)] - `\(S_w\)`: .brand-blue[water saturation (m^3/m^3)] - `\(\phi\)`: .brand-blue[medium porosity (m^3/m^3)] ]] ] .footnote[```Molins et al. (2022)```] --- # Steps to Construct a Model .pull-left-64[ .font90[ - **.brand-blue[Simulation domains]** <svg aria-hidden="true" role="img" viewBox="0 0 576 512" style="height:1em;width:1.12em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M565.6 36.2C572.1 40.7 576 48.1 576 56V392c0 10-6.2 18.9-15.5 22.4l-168 64c-5.2 2-10.9 2.1-16.1 .3L192.5 417.5l-160 61c-7.4 2.8-15.7 1.8-22.2-2.7S0 463.9 0 456V120c0-10 6.1-18.9 15.5-22.4l168-64c5.2-2 10.9-2.1 16.1-.3L383.5 94.5l160-61c7.4-2.8 15.7-1.8 22.2 2.7zM48 136.5V421.2l120-45.7V90.8L48 136.5zM360 422.7V137.3l-144-48V374.7l144 48zm48-1.5l120-45.7V90.8L408 136.5V421.2z"/></svg> - Where the processes happen - .content-box-green[**.brand-blue[Dependency graph]** <svg aria-hidden="true" role="img" viewBox="0 0 576 512" style="height:1em;width:1.12em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M208 80c0-26.5 21.5-48 48-48h64c26.5 0 48 21.5 48 48v64c0 26.5-21.5 48-48 48h-8v40H464c30.9 0 56 25.1 56 56v32h8c26.5 0 48 21.5 48 48v64c0 26.5-21.5 48-48 48H464c-26.5 0-48-21.5-48-48V368c0-26.5 21.5-48 48-48h8V288c0-4.4-3.6-8-8-8H312v40h8c26.5 0 48 21.5 48 48v64c0 26.5-21.5 48-48 48H256c-26.5 0-48-21.5-48-48V368c0-26.5 21.5-48 48-48h8V280H112c-4.4 0-8 3.6-8 8v32h8c26.5 0 48 21.5 48 48v64c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V368c0-26.5 21.5-48 48-48h8V288c0-30.9 25.1-56 56-56H264V192h-8c-26.5 0-48-21.5-48-48V80z"/></svg>] - Which `PKs` to use and how they are coupled - **.brand-blue[Model parameters]** <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M0 416c0 17.7 14.3 32 32 32l54.7 0c12.3 28.3 40.5 48 73.3 48s61-19.7 73.3-48L480 448c17.7 0 32-14.3 32-32s-14.3-32-32-32l-246.7 0c-12.3-28.3-40.5-48-73.3-48s-61 19.7-73.3 48L32 384c-17.7 0-32 14.3-32 32zm128 0a32 32 0 1 1 64 0 32 32 0 1 1 -64 0zM320 256a32 32 0 1 1 64 0 32 32 0 1 1 -64 0zm32-80c-32.8 0-61 19.7-73.3 48L32 224c-17.7 0-32 14.3-32 32s14.3 32 32 32l246.7 0c12.3 28.3 40.5 48 73.3 48s61-19.7 73.3-48l54.7 0c17.7 0 32-14.3 32-32s-14.3-32-32-32l-54.7 0c-12.3-28.3-40.5-48-73.3-48zM192 128a32 32 0 1 1 0-64 32 32 0 1 1 0 64zm73.3-64C253 35.7 224.8 16 192 16s-61 19.7-73.3 48L32 64C14.3 64 0 78.3 0 96s14.3 32 32 32l86.7 0c12.3 28.3 40.5 48 73.3 48s61-19.7 73.3-48L480 128c17.7 0 32-14.3 32-32s-14.3-32-32-32L265.3 64z"/></svg> - Physical and numerical properties - **.brand-blue[Initial and boundary conditions]** <svg aria-hidden="true" role="img" viewBox="0 0 640 512" style="height:1em;width:1.25em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M308.5 135.3c7.1-6.3 9.9-16.2 6.2-25c-2.3-5.3-4.8-10.5-7.6-15.5L304 89.4c-3-5-6.3-9.9-9.8-14.6c-5.7-7.6-15.7-10.1-24.7-7.1l-28.2 9.3c-10.7-8.8-23-16-36.2-20.9L199 27.1c-1.9-9.3-9.1-16.7-18.5-17.8C173.9 8.4 167.2 8 160.4 8h-.7c-6.8 0-13.5 .4-20.1 1.2c-9.4 1.1-16.6 8.6-18.5 17.8L115 56.1c-13.3 5-25.5 12.1-36.2 20.9L50.5 67.8c-9-3-19-.5-24.7 7.1c-3.5 4.7-6.8 9.6-9.9 14.6l-3 5.3c-2.8 5-5.3 10.2-7.6 15.6c-3.7 8.7-.9 18.6 6.2 25l22.2 19.8C32.6 161.9 32 168.9 32 176s.6 14.1 1.7 20.9L11.5 216.7c-7.1 6.3-9.9 16.2-6.2 25c2.3 5.3 4.8 10.5 7.6 15.6l3 5.2c3 5.1 6.3 9.9 9.9 14.6c5.7 7.6 15.7 10.1 24.7 7.1l28.2-9.3c10.7 8.8 23 16 36.2 20.9l6.1 29.1c1.9 9.3 9.1 16.7 18.5 17.8c6.7 .8 13.5 1.2 20.4 1.2s13.7-.4 20.4-1.2c9.4-1.1 16.6-8.6 18.5-17.8l6.1-29.1c13.3-5 25.5-12.1 36.2-20.9l28.2 9.3c9 3 19 .5 24.7-7.1c3.5-4.7 6.8-9.5 9.8-14.6l3.1-5.4c2.8-5 5.3-10.2 7.6-15.5c3.7-8.7 .9-18.6-6.2-25l-22.2-19.8c1.1-6.8 1.7-13.8 1.7-20.9s-.6-14.1-1.7-20.9l22.2-19.8zM112 176a48 48 0 1 1 96 0 48 48 0 1 1 -96 0zM504.7 500.5c6.3 7.1 16.2 9.9 25 6.2c5.3-2.3 10.5-4.8 15.5-7.6l5.4-3.1c5-3 9.9-6.3 14.6-9.8c7.6-5.7 10.1-15.7 7.1-24.7l-9.3-28.2c8.8-10.7 16-23 20.9-36.2l29.1-6.1c9.3-1.9 16.7-9.1 17.8-18.5c.8-6.7 1.2-13.5 1.2-20.4s-.4-13.7-1.2-20.4c-1.1-9.4-8.6-16.6-17.8-18.5L583.9 307c-5-13.3-12.1-25.5-20.9-36.2l9.3-28.2c3-9 .5-19-7.1-24.7c-4.7-3.5-9.6-6.8-14.6-9.9l-5.3-3c-5-2.8-10.2-5.3-15.6-7.6c-8.7-3.7-18.6-.9-25 6.2l-19.8 22.2c-6.8-1.1-13.8-1.7-20.9-1.7s-14.1 .6-20.9 1.7l-19.8-22.2c-6.3-7.1-16.2-9.9-25-6.2c-5.3 2.3-10.5 4.8-15.6 7.6l-5.2 3c-5.1 3-9.9 6.3-14.6 9.9c-7.6 5.7-10.1 15.7-7.1 24.7l9.3 28.2c-8.8 10.7-16 23-20.9 36.2L315.1 313c-9.3 1.9-16.7 9.1-17.8 18.5c-.8 6.7-1.2 13.5-1.2 20.4s.4 13.7 1.2 20.4c1.1 9.4 8.6 16.6 17.8 18.5l29.1 6.1c5 13.3 12.1 25.5 20.9 36.2l-9.3 28.2c-3 9-.5 19 7.1 24.7c4.7 3.5 9.5 6.8 14.6 9.8l5.4 3.1c5 2.8 10.2 5.3 15.5 7.6c8.7 3.7 18.6 .9 25-6.2l19.8-22.2c6.8 1.1 13.8 1.7 20.9 1.7s14.1-.6 20.9-1.7l19.8 22.2zM464 304a48 48 0 1 1 0 96 48 48 0 1 1 0-96z"/></svg> <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M464 256A208 208 0 1 1 48 256a208 208 0 1 1 416 0zM0 256a256 256 0 1 0 512 0A256 256 0 1 0 0 256zM232 120V256c0 8 4 15.5 10.7 20l96 64c11 7.4 25.9 4.4 33.3-6.7s4.4-25.9-6.7-33.3L280 243.2V120c0-13.3-10.7-24-24-24s-24 10.7-24 24z"/></svg> - State of the system at `\(t=t_0\)` - How system behaves at the boundaries at `\(t \ge t_0\)` - **.brand-blue[Forcing, sources and sinks]** <svg aria-hidden="true" role="img" viewBox="0 0 640 512" style="height:1em;width:1.25em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M294.2 1.2c5.1 2.1 8.7 6.7 9.6 12.1l10.4 62.4c-23.3 10.8-42.9 28.4-56 50.3c-14.6-9-31.8-14.1-50.2-14.1c-53 0-96 43-96 96c0 35.5 19.3 66.6 48 83.2c.8 31.8 13.2 60.7 33.1 82.7l-56 39.2c-4.5 3.1-10.3 3.8-15.4 1.6s-8.7-6.7-9.6-12.1L98.1 317.9 13.4 303.8c-5.4-.9-10-4.5-12.1-9.6s-1.5-10.9 1.6-15.4L52.5 208 2.9 137.2c-3.2-4.5-3.8-10.3-1.6-15.4s6.7-8.7 12.1-9.6L98.1 98.1l14.1-84.7c.9-5.4 4.5-10 9.6-12.1s10.9-1.5 15.4 1.6L208 52.5 278.8 2.9c4.5-3.2 10.3-3.8 15.4-1.6zM208 144c13.8 0 26.7 4.4 37.1 11.9c-1.2 4.1-2.2 8.3-3 12.6c-37.9 14.6-67.2 46.6-77.8 86.4C151.8 243.1 144 226.5 144 208c0-35.3 28.7-64 64-64zm69.4 276c11 7.4 14 22.3 6.7 33.3l-32 48c-7.4 11-22.3 14-33.3 6.7s-14-22.3-6.7-33.3l32-48c7.4-11 22.3-14 33.3-6.7zm96 0c11 7.4 14 22.3 6.7 33.3l-32 48c-7.4 11-22.3 14-33.3 6.7s-14-22.3-6.7-33.3l32-48c7.4-11 22.3-14 33.3-6.7zm96 0c11 7.4 14 22.3 6.7 33.3l-32 48c-7.4 11-22.3 14-33.3 6.7s-14-22.3-6.7-33.3l32-48c7.4-11 22.3-14 33.3-6.7zm96 0c11 7.4 14 22.3 6.7 33.3l-32 48c-7.4 11-22.3 14-33.3 6.7s-14-22.3-6.7-33.3l32-48c7.4-11 22.3-14 33.3-6.7zm74.5-116.1c0 44.2-35.8 80-80 80H288c-53 0-96-43-96-96c0-47.6 34.6-87 80-94.6l0-1.3c0-53 43-96 96-96c34.9 0 65.4 18.6 82.2 46.4c13-9.1 28.8-14.4 45.8-14.4c44.2 0 80 35.8 80 80c0 5.9-.6 11.7-1.9 17.2c37.4 6.7 65.8 39.4 65.8 78.7z"/></svg> - External forces that drive changes in the system - Material or energy added/removed to/from the system ]] -- <br> .pull-right-46[ **ATS `xml` top level list:** ```r Main - mesh: ["mesh-typed-spec-list"] - regions: ["region-typedinline-spec-list"] - cycle driver: ["coordinator-spec"] - PKs: ["pk-typedinline-spec-list"] - state: ["state-spec"] *- visualization: ["visualization-spec-list"] *- checkpoint: ["checkpoint-spec"] *- observations: ["observation-spec-list"] ``` ] .footnote[[ATS Documentation](https://amanzi.github.io/ats/stable/input_spec/main.html)] --- # Domain of simulation .pull-left-31[ <iframe width="800" height="550" src="imgs/domain.html", frameborder="0"></iframe> ] .pull-right-13[ <br> <br> .font60[ .content-box-purple[ .center[.brand-blue[**Entire Catchment**]] **Dimensions:** 400 x 500 m **\# of surface cells:** 1521 **\# of river corridor cells:** 62 **\# of soil layers:** 7 **\# of subsurface cells:** 10647 `\(\Delta\)`z = [0.1, 0.1, 0.1, 0.2, 0.2, 0.4, 0.4] ** Soil thickness:** 1.5 (m) ]] .font60[ .content-box-yellow[ .center[.brand-red[<svg aria-hidden="true" role="img" viewBox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M384 80c8.8 0 16 7.2 16 16V416c0 8.8-7.2 16-16 16H64c-8.8 0-16-7.2-16-16V96c0-8.8 7.2-16 16-16H384zM64 32C28.7 32 0 60.7 0 96V416c0 35.3 28.7 64 64 64H384c35.3 0 64-28.7 64-64V96c0-35.3-28.7-64-64-64H64z"/></svg> **Square City**]] **Dimensions:** 50 x 50 m **\# of surface cells:** 92 ]] ] .font60[.footnote[<a href="imgs/domain.html" target="_blank">```domain of simulation```</a>]] --- # Dependency Graph - Integrated Hydrology .pull-left-64[ <iframe src="imgs/dependency_hydro.html" width="600" height="500" frameborder="0"></iframe> ] .font70[ - **PK:** [`Process kernels`](https://amanzi.github.io/ats/stable/input_spec/process_kernels/index.html) - **MPC:** [`Multi-process-couplers`](https://amanzi.github.io/ats/stable/input_spec/process_kernels/mpcs/index.html) ] -- .pull-right-46[ .font70[ ```xml <ParameterList name="Main"> <ParameterList name="cycle driver"> <ParameterList name="PK tree"> <ParameterList name="flow coupler"> <Parameter name="PK type" type="string" value="coupled water" /> <ParameterList name="flow"> <Parameter name="PK type" type="string" value="richards flow" /> </ParameterList> <ParameterList name="overland flow"> <Parameter name="PK type" type="string" value="overland flow, pressure basis" /> </ParameterList> </ParameterList> </ParameterList> </ParameterList> * OTHER LISTS... <ParameterList name="PKs"> <ParameterList name="flow coupler"> <Parameter name="PK type" type="string" value="coupled water" /> <Parameter name="PKs order" type="Array(string)" value="{flow, overland flow}" /> </ParameterList> * OTHER PKS (i.e., flow, overland flow) </ParameterList> </ParameterList> ``` ]] --- # Hydrology Model Parameters .small[ .pull-left-64[ - Surface $$ \frac{\partial \eta h}{\partial t} + \nabla \cdot \mathbf{q}_s = Q_s + Q_e$$ - Subsurface $$ \frac{\partial \eta S_w \phi}{\partial t} + \nabla \cdot \mathbf{q}_g = Q_g$$ ]] -- .footnotesize[.pull-right-46[ <br> `$$\mathbf{q}_s = -\eta h \frac{h^{4/3}} {n_{mann} \sqrt{|\nabla z|} } \nabla (\eta + z)$$` <br> `$$\mathbf{q}_g = -\frac{\eta}{\mu} k_r K (\nabla p + \rho g\mathbf{z})$$` .content-box-green[ - `\(n_{mann}\)`: Manning's coefficient - `\(\mu\)`: liquid viscosity - `\(k_r\)`: relative permeability - `\(K\)`: absolute permeability - ... ]] ] -- .pull-left[ .font50[ ```xml <ParameterList name="state"> <ParameterList name="evaluators"> * OTHER EVALUATORS ... <ParameterList name="viscosity_liquid"> <Parameter name="evaluator type" type="string" value="independent variable constant" /> <Parameter name="value" type="double" value="0.00059" /> </ParameterList> <ParameterList name="surface-manning_coefficient"> <Parameter name="evaluator type" type="string" value="independent variable constant" /> <Parameter name="value" type="double" value="0.15" /> </ParameterList> <ParameterList name="permeability"> <Parameter name="evaluator type" type="string" value="independent variable constant" /> <Parameter name="value" type="double" value="5e-13" /> </ParameterList> <ParameterList name="relative_permeability"> <Parameter name="evaluator type" type="string" value="relative permeability, water retention model" /> <Parameter name="model parameters" type="string" value="WRM parameters" /> </ParameterList> * OTHER EVALUATORS ... </ParameterList> </ParameterList> ``` ]] --- # Forcings & sources/sinks <br /> .pull-left[ <img src="slides_files/figure-html/unnamed-chunk-4-1.png" width="864" style="display: block; margin: auto;" /> .content-box-purple[.small[`No source/sink in this example`]] ] .pull-right[ .font80[ ```xml <ParameterList name="state"> <ParameterList name="evaluators"> <ParameterList name="surface-water_source"> <Parameter name="evaluator type" type="string" value="independent variable" /> <ParameterList name="function"> <ParameterList name="domain rain"> <Parameter name="region" type="string" value="surface domain" /> <Parameter name="component" type="string" value="cell" /> * <ParameterList name="function"> * <ParameterList name="function-tabular"> * <Parameter name="x values" type="Array(double)" value="{0, 57600}" /> * <Parameter name="y values" type="Array(double)" value="{5e-06, 0}" /> * <Parameter name="forms" type="Array(string)" value="{constant}" /> * </ParameterList> * </ParameterList> </ParameterList> </ParameterList> </ParameterList> </ParameterList> ``` ]] --- # Initial and boundary conditions .pull-left[ #### .blockquote[Initial conditions .gray[(true)]] .small[ - located inside each PK in the `xml` file - can be: - created from functions - loaded from files (e.g. checkpoints) ] #### .blockquote[Boundary conditions] .small[ - located inside each PK in the `xml` file - if not specified, no-flow BCs are applied ]] .pull-right[ .font80[ ```xml <ParameterList name="flow"> * <ParameterList name="initial condition"> <Parameter name="hydrostatic head [m]" type="double" value="-1.1" /> <Parameter name="hydrostatic water density [kg m^-3]" type="double" value="1000" /> </ParameterList> * <ParameterList name="boundary conditions"> </ParameterList> </ParameterList> ... <ParameterList name="overland flow"> * <ParameterList name="initial condition"> <Parameter name="initialize surface head from subsurface" type="bool" value="true" /> </ParameterList> * <ParameterList name="boundary conditions"> <ParameterList name="zero gradient"> <ParameterList name="outlet"> <Parameter name="regions" type="Array(string)" value="{surface outlet face}" /> </ParameterList> </ParameterList> </ParameterList> </ParameterList> ``` ]] .footnote[`See the documentation for details about ICs and BCs:` [`https://amanzi.github.io/ats/stable/input_spec/common.html`](https://amanzi.github.io/ats/stable/input_spec/common.html)] --- class: phong-dark # .brand-orange[Transport hands-on] --- # Transport <br> .pull-left[ **Advection-Dispersion Equation (ADE):** $$ \frac{\partial (\Theta C)}{\partial t} + \nabla \cdot(\mathbf{u} C) - \nabla \cdot (D \Theta \nabla C) + S = 0 $$ ] .pull-right[ .font80[ .content-box-purple[ - `\(C\)`: .brand-blue[the concentration of the solute (molC/molH2O)], - `\(S\)`: .brand-blue[any source term], - `\(D\)`: .brand-blue[diffusion coefficient (m^2/s)], - `\(\mathbf{u}\)`: .brand-blue[the flow velocity field (m/s)]. ]]] -- <br> <br> .green[ **For transport in a subsurface domain** (`\(\Omega \in \mathbb{R}^3\)`): `\(\Theta = \eta \phi S_w\)`, `\(\mathbf{u}=q_g\)`, `\(D=D_g\)`. ] -- <br> .orange[ **For transport in a surface domain** (`\(\Omega \in \mathbb{R}^n\)`; `\(n=1,2\)`): `\(\Theta = \eta h\)`, `\(\mathbf{u}=q_s\)`, `\(D=D_s\)`. ] --- # Dependency Graph - Transport Let's construct the **dependency graph** (or `PK tree`) for the integrated transport model. <iframe src="imgs/dependency.html" width="1200" height="600" frameborder="0"></iframe> .footnote[ <a href="imgs/dependency_transport.html" target="_blank">```graph: transport```</a> <a href="imgs/dependency_transport_reactive.html" target="_blank">```graph: reactive transport```</a> <a href="imgs/dependency_transport_reactive_ecohydrology.html" target="_blank">```graph: reactive transport & ecohydrology```</a> ] --- # Transport Model Parameters **Advection-Dispersion Equation (ADE):** $$ \frac{\partial (\Theta C)}{\partial t} + \nabla \cdot(\mathbf{u} C) - \nabla \cdot (D \Theta \nabla C) + S = 0 $$ -- .pull-left[ .small[ - `\(C\)`: .brand-red[unknown concentration] <svg aria-hidden="true" role="img" viewBox="0 0 320 512" style="height:1em;width:0.62em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M278.6 233.4c12.5 12.5 12.5 32.8 0 45.3l-160 160c-12.5 12.5-32.8 12.5-45.3 0s-12.5-32.8 0-45.3L210.7 256 73.4 118.6c-12.5-12.5-12.5-32.8 0-45.3s32.8-12.5 45.3 0l160 160z"/></svg> `we want it` - `\(S\)`: .brand-red[source term] <svg aria-hidden="true" role="img" viewBox="0 0 320 512" style="height:1em;width:0.62em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M278.6 233.4c12.5 12.5 12.5 32.8 0 45.3l-160 160c-12.5 12.5-32.8 12.5-45.3 0s-12.5-32.8 0-45.3L210.7 256 73.4 118.6c-12.5-12.5-12.5-32.8 0-45.3s32.8-12.5 45.3 0l160 160z"/></svg> `we specify it` - `\(D\)`: .brand-red[dispersion coefficient] <svg aria-hidden="true" role="img" viewBox="0 0 320 512" style="height:1em;width:0.62em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M278.6 233.4c12.5 12.5 12.5 32.8 0 45.3l-160 160c-12.5 12.5-32.8 12.5-45.3 0s-12.5-32.8 0-45.3L210.7 256 73.4 118.6c-12.5-12.5-12.5-32.8 0-45.3s32.8-12.5 45.3 0l160 160z"/></svg> `we specify it` - `\(\mathbf{u}, \Theta\)`: <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M9.4 233.4c-12.5 12.5-12.5 32.8 0 45.3l128 128c12.5 12.5 32.8 12.5 45.3 0s12.5-32.8 0-45.3L109.3 288 480 288c17.7 0 32-14.3 32-32s-14.3-32-32-32l-370.7 0 73.4-73.4c12.5-12.5 12.5-32.8 0-45.3s-32.8-12.5-45.3 0l-128 128z"/></svg> .content-box-green[`from the hydrology model`] - `\(\Theta_g = \eta \times \phi \times S_w\)`, `\(\mathbf{u}=q_g\)` - `\(\Theta_s = \eta \times h\)`, `\(\mathbf{u}=q_s\)` ]] -- .pull-right[ .footnotesize[ ```xml <ParameterList name="TRANPORT_PK"> * <ParameterList name="source terms"> <ParameterList name="component mass source"> <ParameterList name="SOURCE_NAME"> <Parameter name="component names" type="Array(string)" value="{TRACER_NAME}"/> <Parameter name="regions" type="Array(string)" value="{REGION}"/> <Parameter name="spatial distribution method" type="string" value="METHOD"/> <ParameterList name="source function"> <<<<< FUNCTION DEFINITION >>>>> </ParameterList> </ParameterList> </ParameterList> </ParameterList> <ParameterList name="material properties"> <ParameterList name="domain"> <Parameter name="regions" type="Array(string)" value="{REGION_DOMAIN}" /> <<<<< OTHERS PARAMETERS >>>>> <ParameterList name="parameters for scalar"> * <Parameter name="dispersion coefficient [m^2 s^-1]" type="double" value="####" /> </ParameterList> </ParameterList> </ParameterList> </ParameterList> ``` ]] --- # Initial and boundary conditions <br /> **Initial conditions** - We set concentration to zero everywhere at the beginning ```xml <ParameterList name="TRANPORT_PK"> <ParameterList name="initial condition" type="ParameterList"> <Parameter name="constant" type="double" value="0" /> </ParameterList> </ParameterList> ``` **Boundary conditions** - We use no-flux BCs at the boundaries <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M502.6 278.6c12.5-12.5 12.5-32.8 0-45.3l-128-128c-12.5-12.5-32.8-12.5-45.3 0s-12.5 32.8 0 45.3L402.7 224 32 224c-17.7 0-32 14.3-32 32s14.3 32 32 32l370.7 0-73.4 73.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l128-128z"/></svg> `do not need to specify` --- # Sources and sinks - We inject tracer at a constant rate at the city for a short period of time .small[ ```xml <ParameterList name="TRANPORT_PK"> * <ParameterList name="source terms"> <ParameterList name="component mass source"> <ParameterList name="Tracer injection"> <Parameter name="component names" type="Array(string)" value="{Tracer1}" /> <Parameter name="regions" type="Array(string)" value="{tracer_injection}" /> <Parameter name="spatial distribution method" type="string" value="volume" /> <ParameterList name="source function"> <ParameterList name="function-tabular" type="ParameterList"> <Parameter name="x values" type="Array(double)" value="{ 0,14400,18000}" /> <Parameter name="y values" type="Array(double)" value="{ 0, 1000, 0}" /> <Parameter name="forms" type="Array(string)" value="{constant, constant}" /> </ParameterList> </ParameterList> </ParameterList> </ParameterList> </ParameterList> </ParameterList> ``` .content-box-purple[`volume`]: source is considered as extensive quantity (molC/s) and is evenly distributed across the region. ]