{"id":92333,"date":"2026-04-16T13:00:16","date_gmt":"2026-04-16T13:00:16","guid":{"rendered":"https:\/\/gaeatech.com\/knowledge-center\/?p=92333"},"modified":"2026-04-16T02:00:19","modified_gmt":"2026-04-16T02:00:19","slug":"migratev10-example-12-time-dependent-source-landfills","status":"publish","type":"post","link":"https:\/\/gaeatech.com\/knowledge-center\/migratev10-example-12-time-dependent-source-landfills\/","title":{"rendered":"MIGRATEv10 Example 12: Modeling Time-Dependent Source Histories for Multiple Landfill Cells"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\" id=\"h-introduction\">Introduction<\/h2>\n\n\n\n<p>MIGRATEv10 Example 12 builds on Example 11 by introducing a critical real-world factor:<\/p>\n\n\n\n<p>\ud83d\udc49 <strong>Different source histories for multiple landfill cells<\/strong><\/p>\n\n\n\n<p>Rather than assuming constant or identical source conditions, this example models how <strong>staggered construction, filling, and closure timelines<\/strong> affect contaminant migration.<\/p>\n\n\n\n<p>This is a major step toward realistic modeling, where <strong>timing is just as important as geometry and hydrogeology<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-conceptual-model-overview\">Conceptual Model Overview<\/h2>\n\n\n\n<p>The system includes:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Two adjacent landfill cells<\/strong> (same as Example 11)<\/li>\n\n\n\n<li>Identical hydrogeologic conditions<\/li>\n\n\n\n<li><strong>Different operational timelines and source concentrations<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-key-modeling-objective\">Key Modeling Objective<\/h2>\n\n\n\n<p>This example aims to:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Evaluate how <strong>time-varying source concentrations<\/strong> affect plume development<\/li>\n\n\n\n<li>Understand <strong>delayed impacts<\/strong> from secondary sources<\/li>\n\n\n\n<li>Assess concentration at a <strong>down-gradient receptor over time<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-source-history-landfill-cell-1-smaller-earlier\">Source History: Landfill Cell 1 (Smaller, Earlier)<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-filling-phase\">Filling Phase<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Duration: <strong>0 to 10 years<\/strong><\/li>\n\n\n\n<li>Concentration increases <strong>linearly<\/strong> as waste accumulates<\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udc49 In the model, this linear increase is approximated using <strong>two step increases<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-peak-concentration\">Peak Concentration<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Occurs at: <strong>10 years<\/strong><\/li>\n\n\n\n<li>Peak value determined by source assumptions<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-post-closure-behavior\">Post-Closure Behavior<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>After 10 years:\n<ul class=\"wp-block-list\">\n<li>Landfill is closed<\/li>\n\n\n\n<li>Concentration <strong>decreases over time<\/strong><\/li>\n\n\n\n<li>Represents <strong>mass depletion<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-source-history-landfill-cell-2-larger-delayed\">Source History: Landfill Cell 2 (Larger, Delayed)<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-delayed-construction\">Delayed Construction<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Begins: <strong>20 years after closure of Landfill Cell 1<\/strong><\/li>\n\n\n\n<li>Filling occurs between:\n<ul class=\"wp-block-list\">\n<li><strong>30 to 50 years<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-filling-phase-0\">Filling Phase<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Duration: <strong>20 years<\/strong><\/li>\n\n\n\n<li>Concentration increases <strong>linearly<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-peak-concentration-0\">Peak Concentration<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Reached at: <strong>50 years<\/strong><\/li>\n\n\n\n<li>Peak value: <strong>2500 mg\/L<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-post-closure-behavior-0\">Post-Closure Behavior<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>After 50 years:\n<ul class=\"wp-block-list\">\n<li>Landfill is closed<\/li>\n\n\n\n<li>Concentration begins to <strong>decline<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-key-difference-from-example-11\">Key Difference from Example 11<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><th>Feature<\/th><th>Example 11<\/th><th>Example 12<\/th><\/tr><tr><td>Source Type<\/td><td>Constant \/ simultaneous<\/td><td>Time-dependent<\/td><\/tr><tr><td>Landfill Timing<\/td><td>Same<\/td><td>Staggered<\/td><\/tr><tr><td>Concentration Behavior<\/td><td>Static<\/td><td>Dynamic<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\ud83d\udc49 Example 12 introduces <strong>temporal complexity<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-modeling-approach-in-migratev10\">Modeling Approach in MIGRATEv10<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-step-1-use-geometry-from-example-11\">Step 1: Use Geometry from Example 11<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Same landfill cell dimensions<\/li>\n\n\n\n<li>Same hydrogeologic layers<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-step-2-define-time-dependent-sources\">Step 2: Define Time-Dependent Sources<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h-landfill-cell-1\">Landfill Cell 1:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Stepwise increase (0\u201310 years)<\/li>\n\n\n\n<li>Decline after closure<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h-landfill-cell-2\">Landfill Cell 2:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>No contribution until ~30 years<\/li>\n\n\n\n<li>Stepwise increase (30\u201350 years)<\/li>\n\n\n\n<li>Decline after closure<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-step-3-assign-concentration-functions\">Step 3: Assign Concentration Functions<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Approximate linear trends using <strong>step inputs<\/strong><\/li>\n\n\n\n<li>Ensure continuity between phases<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-step-4-run-simulation\">Step 4: Run Simulation<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Track concentration at:\n<ul class=\"wp-block-list\">\n<li>Down-gradient receptor<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Evaluate over full time range<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-graphical-output-depth-vs-distance\">Graphical Output: Depth vs Distance<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"804\" height=\"881\" src=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-43.jpg\" alt=\"\" class=\"wp-image-92334\" srcset=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-43.jpg 804w, https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-43-274x300.jpg 274w, https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-43-768x842.jpg 768w\" sizes=\"auto, (max-width: 804px) 100vw, 804px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-pdf-report\">PDF Report<\/h2>\n\n\n<div class=\"ead-preview\"><div class=\"ead-document\" style=\"position: relative;padding-top: 90%\"><div class=\"ead-iframe-wrapper\"><iframe src=\"\/\/docs.google.com\/viewer?url=https%3A%2F%2Fgaeatech.com%2Fknowledge-center%2Fwp-content%2Fuploads%2F2026%2F04%2Fmigrate-example12.pdf&amp;embedded=true&amp;hl=en\" title=\"Embedded Document\" class=\"ead-iframe\" style=\"width: 100%;height: 100%;border: 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long?<\/span>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<p>\n\t\t\t\t\t\t\t<div class=\"ead-document-btn ead-reload-btn\" role=\"button\">\n\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/plugins\/embed-any-document\/images\/reload.svg\" alt=\"Reload\" width=\"12\" height=\"12\"\/> Reload document\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<span>|<\/span>\n\t\t\t\t\t\t\t<a href=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/migrate-example12.pdf\" class=\"ead-document-btn\" target=\"_blank\">\n\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/plugins\/embed-any-document\/images\/open.svg\" alt=\"Open\" width=\"12\" height=\"12\"\/> Open in new tab\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div><\/div>\n\n\n<p><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-interpretation-of-results\">Interpretation of Results<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-1-early-time-behavior-0-20-years\">1. Early-Time Behavior (0\u201320 years)<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Dominated by <strong>Landfill Cell 1<\/strong><\/li>\n\n\n\n<li>Rising then declining concentrations<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-2-mid-time-behavior-20-50-years\">2. Mid-Time Behavior (20\u201350 years)<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Transition period<\/li>\n\n\n\n<li>Landfill Cell 1 impact decreases<\/li>\n\n\n\n<li>Landfill Cell 2 begins contributing<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-3-late-time-behavior-50-years\">3. Late-Time Behavior (50+ years)<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Dominated by <strong>Landfill Cell 2<\/strong><\/li>\n\n\n\n<li>Higher peak concentrations due to:\n<ul class=\"wp-block-list\">\n<li>Larger size<\/li>\n\n\n\n<li>Higher peak value (2500 mg\/L)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-key-insights\">Key Insights<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-1-timing-controls-impact\">1. Timing Controls Impact<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Even a large landfill cell may have <strong>delayed influence<\/strong><\/li>\n\n\n\n<li>Early impacts may come from smaller sources<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-2-overlapping-plumes\">2. Overlapping Plumes<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Plumes may:\n<ul class=\"wp-block-list\">\n<li>Overlap<\/li>\n\n\n\n<li>Reinforce each other<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Resulting in <strong>complex concentration patterns<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-3-long-term-risk\">3. Long-Term Risk<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Delayed sources can extend contamination over <strong>long timeframes<\/strong><\/li>\n\n\n\n<li>Important for:\n<ul class=\"wp-block-list\">\n<li>Monitoring<\/li>\n\n\n\n<li>Risk assessment<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-practical-applications\">Practical Applications<\/h2>\n\n\n\n<p>This type of modeling is critical for:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Phased landfill development<\/strong><\/li>\n\n\n\n<li>Long-term environmental planning<\/li>\n\n\n\n<li>Regulatory compliance over decades<\/li>\n\n\n\n<li>Forecasting <strong>future contamination scenarios<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-key-takeaways\">Key Takeaways<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Source history significantly affects contaminant transport<\/li>\n\n\n\n<li>Time-dependent modeling is essential for realism<\/li>\n\n\n\n<li>Delayed sources can dominate long-term impacts<\/li>\n\n\n\n<li>MIGRATEv10 can simulate <strong>complex temporal behavior effectively<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-final-thoughts\">Final Thoughts<\/h2>\n\n\n\n<p>MIGRATEv10 Example 12 highlights that contaminant transport is not just a function of space\u2014but also <strong>time<\/strong>. By incorporating realistic source histories, this example provides a more accurate representation of how landfills impact groundwater over decades.<\/p>\n\n\n\n<p>This example is especially important for:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Long-term environmental assessments<\/li>\n\n\n\n<li>Multi-phase landfill operations<\/li>\n\n\n\n<li>Predictive modeling for future site conditions<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introduction MIGRATEv10 Example 12 builds on Example 11 by introducing a critical real-world factor: \ud83d\udc49 Different source histories for multiple landfill cells Rather than assuming constant or identical source conditions, this example models how staggered construction, filling, and closure timelines affect contaminant migration. This is a major step toward realistic modeling, where timing is just [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":92336,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[858,1690],"tags":[501,24,469,675,1689,1710],"class_list":["post-92333","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-contaminant-transport-modeling","category-migrateexamples","tag-contaminant-transport","tag-environmental-engineering","tag-groundwater-modeling","tag-landfill-modeling","tag-migratev10","tag-time-dependent-sources"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.4 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>MIGRATEv10 Example 12 Time-Dependent Sources Explained - Knowledge Center<\/title>\n<meta name=\"description\" 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