{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/140813"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/140813","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Hetero-functional Graph Theory for Convergent Systems of Systems: Model-Based Applications in Watershed and Economic Systems","abstract":"Modern societal challenges defined by the Sustainable Development Goals of the United Nations are deeply interconnected. Addressing issues such as water scarcity, ecosystem degradation, or food security requires understanding the coupled systems that shape them, including hydrology, infrastructure, ecology, economics, and governance. While modelers within each discipline develop increasingly accurate representations of individual systems, real-world problems arise from the feedbacks between them. Actions intended to improve one domain can unintentionally disrupt another; for instance, reducing fertilizer to prevent eutrophication may also affect agricultural productivity. To address such interdependencies, this dissertation develops a unified, ontology-based modeling framework that integrates Model-Based Systems Engineering (MBSE) with Hetero-functional Graph Theory (HFGT). The dissertation progresses from domain-specific modeling studies toward a general convergence paradigm, illustrating how environmental and economic systems can be represented within a consistent system of systems architecture. The framework is first demonstrated in the context of simplified hydrological systems, where lakes, rivers, land segments, and outlet points are modeled using resistance-based transport laws and continuity equations adapted into the Hetero-functional Network Minimum Cost Flow (HFNMCF) optimization problem. This initial study establishes that environmental processes can be represented as a class of engineering systems within the HFGT meta-architecture when defined by an MBSE-based reference architecture. The approach is then extended to larger watershed systems and instantiated for the Chesapeake Bay Watershed. The approach classifies watershed systems under the HFGT meta-architecture then develops a watershed-specific Weighted Least Squares Error HFGT State Estimator to infer nitrogen and phosphorus flows across land–river–estuary networks under data sparsity and structural uncertainty. The paper then simulates the Chesapeake Bay Watershed using spatially and temporally resolved data from the Chesapeake Assessment Scenario Tool (CAST). This chapter demonstrates the scalability of the MBSE–HFGT framework and highlights its capacity for transparent, extensible environmental modeling at regional watershed scales. Having established the methodology through hydrologic and watershed applications, the dissertation then introduces a broader convergence paradigm. This chapter presents the meta-cognition map, which explains how scientific knowledge is generated across observation, abstraction, visualization, mathematics, and computation. The convergence paradigm draws directly on insights from the hydrology and watershed work as well as other domain applications to articulate the characteristics required for modeling complex Anthropocene systems of systems, including ontology, transparency, extensibility, and cross-domain alignment. The final chapters extend the MBSE–HFGT framework beyond environmental systems as preliminary steps to advance the cross-domain convergence paradigm. An economic input–output model is likewise classified as an engineering system under the HFGT meta-architecture and simulated as an HFNMCF optimization problem. Similarly, a system dynamics representation of the Mono Lake system is then translated into the MBSE–HFGT formalism, allowing a structural comparison between traditional causal-loop modeling and the capability-based, ontology-driven approach developed in this dissertation. Together, these studies establish a coherent, extensible methodology for representing and estimating complex systems across environmental and economic domains. By integrating system structure and function through a common ontology and demonstrating this integration across multiple domains, this dissertation provides a pathway toward convergent modeling of coupled human–natural systems in the Anthropocene.","abstract_html":"Modern societal challenges defined by the Sustainable Development Goals of the United Nations are deeply interconnected. Addressing issues such as water scarcity, ecosystem degradation, or food security requires understanding the coupled systems that shape them, including hydrology, infrastructure, ecology, economics, and governance. While modelers within each discipline develop increasingly accurate representations of individual systems, real-world problems arise from the feedbacks between them. Actions intended to improve one domain can unintentionally disrupt another; for instance, reducing fertilizer to prevent eutrophication may also affect agricultural productivity. To address such interdependencies, this dissertation develops a unified, ontology-based modeling framework that integrates Model-Based Systems Engineering (MBSE) with Hetero-functional Graph Theory (HFGT). The dissertation progresses from domain-specific modeling studies toward a general convergence paradigm, illustrating how environmental and economic systems can be represented within a consistent system of systems architecture. The framework is first demonstrated in the context of simplified hydrological systems, where lakes, rivers, land segments, and outlet points are modeled using resistance-based transport laws and continuity equations adapted into the Hetero-functional Network Minimum Cost Flow (HFNMCF) optimization problem. This initial study establishes that environmental processes can be represented as a class of engineering systems within the HFGT meta-architecture when defined by an MBSE-based reference architecture. The approach is then extended to larger watershed systems and instantiated for the Chesapeake Bay Watershed. The approach classifies watershed systems under the HFGT meta-architecture then develops a watershed-specific Weighted Least Squares Error HFGT State Estimator to infer nitrogen and phosphorus flows across land–river–estuary networks under data sparsity and structural uncertainty. The paper then simulates the Chesapeake Bay Watershed using spatially and temporally resolved data from the Chesapeake Assessment Scenario Tool (CAST). This chapter demonstrates the scalability of the MBSE–HFGT framework and highlights its capacity for transparent, extensible environmental modeling at regional watershed scales. Having established the methodology through hydrologic and watershed applications, the dissertation then introduces a broader convergence paradigm. This chapter presents the meta-cognition map, which explains how scientific knowledge is generated across observation, abstraction, visualization, mathematics, and computation. The convergence paradigm draws directly on insights from the hydrology and watershed work as well as other domain applications to articulate the characteristics required for modeling complex Anthropocene systems of systems, including ontology, transparency, extensibility, and cross-domain alignment. The final chapters extend the MBSE–HFGT framework beyond environmental systems as preliminary steps to advance the cross-domain convergence paradigm. An economic input–output model is likewise classified as an engineering system under the HFGT meta-architecture and simulated as an HFNMCF optimization problem. Similarly, a system dynamics representation of the Mono Lake system is then translated into the MBSE–HFGT formalism, allowing a structural comparison between traditional causal-loop modeling and the capability-based, ontology-driven approach developed in this dissertation. Together, these studies establish a coherent, extensible methodology for representing and estimating complex systems across environmental and economic domains. By integrating system structure and function through a common ontology and demonstrating this integration across multiple domains, this dissertation provides a pathway toward convergent modeling of coupled human–natural systems in the Anthropocene.","abstract_has_math":false,"creators":["Harris, Megan Stephanie"],"institution":"Virginia Tech","degree_name":"Doctor of Philosophy","degree_level":"doctoral","degree_discipline":"Civil Engineering","degree_department":"Civil and Environmental Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":["Little, John C."],"committee_members":["Morales, Carlos Andres Lopez","Saksena, Siddharth","Farid, Amro","Rippy, Megan A."],"year":2026,"date_issued":"2026-01-14","date_published":"2026-01-14","updated_at":"2026-07-22T22:20:12Z","subjects":["model-based systems engineering","hetero-functional graph theory","watershed modeling","economic modeling","system dynamics"],"languages":["en"],"rights":["Creative Commons Attribution 4.0 International"],"rights_urls":["http://creativecommons.org/licenses/by/4.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:45521"],"render_values":[{"text":"vt_gsexam:45521","href":null,"code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10919/140813","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Little, John C."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Morales, Carlos Andres Lopez","Saksena, Siddharth","Farid, Amro","Rippy, Megan A."]},{"key":"dc:contributor.department","label":"Department","values":["Civil and Environmental Engineering"]},{"key":"dc:creator","label":"Author","values":["Harris, Megan Stephanie"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2026-01-15T09:00:57Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2026-01-15T09:00:57Z"]},{"key":"dc:date.issued","label":"Date","values":["2026-01-14"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Civil Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["model-based systems engineering","hetero-functional graph theory","watershed modeling","economic modeling","system dynamics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Creative Commons Attribution 4.0 International"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://creativecommons.org/licenses/by/4.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:45521"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10919/140813"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Modern societal challenges defined by the Sustainable Development Goals of the United Nations are deeply interconnected. Addressing issues such as water scarcity, ecosystem degradation, or food security requires understanding the coupled systems that shape them, including hydrology, infrastructure, ecology, economics, and governance. While modelers within each discipline develop increasingly accurate representations of individual systems, real-world problems arise from the feedbacks between them. Actions intended to improve one domain can unintentionally disrupt another; for instance, reducing fertilizer to prevent eutrophication may also affect agricultural productivity. To address such interdependencies, this dissertation develops a unified, ontology-based modeling framework that integrates Model-Based Systems Engineering (MBSE) with Hetero-functional Graph Theory (HFGT). The dissertation progresses from domain-specific modeling studies toward a general convergence paradigm, illustrating how environmental and economic systems can be represented within a consistent system of systems architecture. The framework is first demonstrated in the context of simplified hydrological systems, where lakes, rivers, land segments, and outlet points are modeled using resistance-based transport laws and continuity equations adapted into the Hetero-functional Network Minimum Cost Flow (HFNMCF) optimization problem. This initial study establishes that environmental processes can be represented as a class of engineering systems within the HFGT meta-architecture when defined by an MBSE-based reference architecture. The approach is then extended to larger watershed systems and instantiated for the Chesapeake Bay Watershed. The approach classifies watershed systems under the HFGT meta-architecture then develops a watershed-specific Weighted Least Squares Error HFGT State Estimator to infer nitrogen and phosphorus flows across land–river–estuary networks under data sparsity and structural uncertainty. The paper then simulates the Chesapeake Bay Watershed using spatially and temporally resolved data from the Chesapeake Assessment Scenario Tool (CAST). This chapter demonstrates the scalability of the MBSE–HFGT framework and highlights its capacity for transparent, extensible environmental modeling at regional watershed scales. Having established the methodology through hydrologic and watershed applications, the dissertation then introduces a broader convergence paradigm. This chapter presents the meta-cognition map, which explains how scientific knowledge is generated across observation, abstraction, visualization, mathematics, and computation. The convergence paradigm draws directly on insights from the hydrology and watershed work as well as other domain applications to articulate the characteristics required for modeling complex Anthropocene systems of systems, including ontology, transparency, extensibility, and cross-domain alignment. The final chapters extend the MBSE–HFGT framework beyond environmental systems as preliminary steps to advance the cross-domain convergence paradigm. An economic input–output model is likewise classified as an engineering system under the HFGT meta-architecture and simulated as an HFNMCF optimization problem. Similarly, a system dynamics representation of the Mono Lake system is then translated into the MBSE–HFGT formalism, allowing a structural comparison between traditional causal-loop modeling and the capability-based, ontology-driven approach developed in this dissertation. Together, these studies establish a coherent, extensible methodology for representing and estimating complex systems across environmental and economic domains. By integrating system structure and function through a common ontology and demonstrating this integration across multiple domains, this dissertation provides a pathway toward convergent modeling of coupled human–natural systems in the Anthropocene."]},{"key":"dc:description.abstractgeneral","label":"General Abstract","values":["The United Nations' 17 Sustainable Development Goals identify the planet's most urgent challenges, including clean water, sustainable agriculture, and resilient ecosystems. These goals are deeply interconnected: progress toward one often depends on understanding how others behave. For example, improving water quality requires insight not only into hydrology but also land use, agriculture, economics, and the ways these systems influence one another. Scientists and engineers build models to study these systems, but most tools focus on a single domain. Hydrologists model how rainfall and land management shape water quality, while economists model fertilizer use, production decisions, and trade. However, natural and human systems do not operate in isolation. Actions in one domain, such as changing fertilizer practices, can ripple across others, affecting rivers, farms, and regional economies. Without a way to represent these connections, important feedbacks can be overlooked. This dissertation develops a framework for linking these separate models into a unified system of systems. The approach combines Model-Based Systems Engineering and Hetero-functional Graph Theory to represent relationships among natural, engineered, and social systems using a shared, consistent language. This allows models from different disciplines to be described, compared, and connected more easily. The framework is first demonstrated using simplified examples of water and nutrient movement among lakes, rivers, and land segments, showing how environmental processes can be represented within a common structure. It is then applied to the Chesapeake Bay Watershed, where diverse hydrological and land-use data are used to estimate nitrogen and phosphorus flows across thousands of interconnected segments. This produces a more transparent and flexible representation of watershed behavior. As a first step toward integrating economic and environmental decision-making, the framework is extended to represent basic economic input–output systems, showing how production technologies and resource flows can be modeled using the same structural concepts. Finally, it is applied to a system previously modeled with system dynamics--a widely used tool for environmental decision support--to compare how the two methods represent structure and system behavior including feedbacks. By linking scientific knowledge across disciplines, this research provides a foundation for understanding the broader consequences of environmental and policy decisions. The framework supports more transparent and extensible strategies for sustainability, helping decision-makers navigate the complexity of interconnected human–natural systems."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Doctor of Philosophy"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["Hetero-functional Graph Theory for Convergent Systems of Systems: Model-Based Applications in Watershed and Economic Systems"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Little, John C."],"dc:contributor.committeemember":["Morales, Carlos Andres Lopez","Saksena, Siddharth","Farid, Amro","Rippy, Megan A."],"dc:contributor.department":["Civil and Environmental Engineering"],"dc:creator":["Harris, Megan Stephanie"],"dc:date.accessioned":["2026-01-15T09:00:57Z"],"dc:date.available":["2026-01-15T09:00:57Z"],"dc:date.issued":["2026-01-14"],"dc:description.abstract":["Modern societal challenges defined by the Sustainable Development Goals of the United Nations are deeply interconnected. Addressing issues such as water scarcity, ecosystem degradation, or food security requires understanding the coupled systems that shape them, including hydrology, infrastructure, ecology, economics, and governance. While modelers within each discipline develop increasingly accurate representations of individual systems, real-world problems arise from the feedbacks between them. Actions intended to improve one domain can unintentionally disrupt another; for instance, reducing fertilizer to prevent eutrophication may also affect agricultural productivity. To address such interdependencies, this dissertation develops a unified, ontology-based modeling framework that integrates Model-Based Systems Engineering (MBSE) with Hetero-functional Graph Theory (HFGT). The dissertation progresses from domain-specific modeling studies toward a general convergence paradigm, illustrating how environmental and economic systems can be represented within a consistent system of systems architecture. The framework is first demonstrated in the context of simplified hydrological systems, where lakes, rivers, land segments, and outlet points are modeled using resistance-based transport laws and continuity equations adapted into the Hetero-functional Network Minimum Cost Flow (HFNMCF) optimization problem. This initial study establishes that environmental processes can be represented as a class of engineering systems within the HFGT meta-architecture when defined by an MBSE-based reference architecture. The approach is then extended to larger watershed systems and instantiated for the Chesapeake Bay Watershed. The approach classifies watershed systems under the HFGT meta-architecture then develops a watershed-specific Weighted Least Squares Error HFGT State Estimator to infer nitrogen and phosphorus flows across land–river–estuary networks under data sparsity and structural uncertainty. The paper then simulates the Chesapeake Bay Watershed using spatially and temporally resolved data from the Chesapeake Assessment Scenario Tool (CAST). This chapter demonstrates the scalability of the MBSE–HFGT framework and highlights its capacity for transparent, extensible environmental modeling at regional watershed scales. Having established the methodology through hydrologic and watershed applications, the dissertation then introduces a broader convergence paradigm. This chapter presents the meta-cognition map, which explains how scientific knowledge is generated across observation, abstraction, visualization, mathematics, and computation. The convergence paradigm draws directly on insights from the hydrology and watershed work as well as other domain applications to articulate the characteristics required for modeling complex Anthropocene systems of systems, including ontology, transparency, extensibility, and cross-domain alignment. The final chapters extend the MBSE–HFGT framework beyond environmental systems as preliminary steps to advance the cross-domain convergence paradigm. An economic input–output model is likewise classified as an engineering system under the HFGT meta-architecture and simulated as an HFNMCF optimization problem. Similarly, a system dynamics representation of the Mono Lake system is then translated into the MBSE–HFGT formalism, allowing a structural comparison between traditional causal-loop modeling and the capability-based, ontology-driven approach developed in this dissertation. Together, these studies establish a coherent, extensible methodology for representing and estimating complex systems across environmental and economic domains. By integrating system structure and function through a common ontology and demonstrating this integration across multiple domains, this dissertation provides a pathway toward convergent modeling of coupled human–natural systems in the Anthropocene."],"dc:description.abstractgeneral":["The United Nations' 17 Sustainable Development Goals identify the planet's most urgent challenges, including clean water, sustainable agriculture, and resilient ecosystems. These goals are deeply interconnected: progress toward one often depends on understanding how others behave. For example, improving water quality requires insight not only into hydrology but also land use, agriculture, economics, and the ways these systems influence one another. Scientists and engineers build models to study these systems, but most tools focus on a single domain. Hydrologists model how rainfall and land management shape water quality, while economists model fertilizer use, production decisions, and trade. However, natural and human systems do not operate in isolation. Actions in one domain, such as changing fertilizer practices, can ripple across others, affecting rivers, farms, and regional economies. Without a way to represent these connections, important feedbacks can be overlooked. This dissertation develops a framework for linking these separate models into a unified system of systems. The approach combines Model-Based Systems Engineering and Hetero-functional Graph Theory to represent relationships among natural, engineered, and social systems using a shared, consistent language. This allows models from different disciplines to be described, compared, and connected more easily. The framework is first demonstrated using simplified examples of water and nutrient movement among lakes, rivers, and land segments, showing how environmental processes can be represented within a common structure. It is then applied to the Chesapeake Bay Watershed, where diverse hydrological and land-use data are used to estimate nitrogen and phosphorus flows across thousands of interconnected segments. This produces a more transparent and flexible representation of watershed behavior. As a first step toward integrating economic and environmental decision-making, the framework is extended to represent basic economic input–output systems, showing how production technologies and resource flows can be modeled using the same structural concepts. Finally, it is applied to a system previously modeled with system dynamics--a widely used tool for environmental decision support--to compare how the two methods represent structure and system behavior including feedbacks. By linking scientific knowledge across disciplines, this research provides a foundation for understanding the broader consequences of environmental and policy decisions. The framework supports more transparent and extensible strategies for sustainability, helping decision-makers navigate the complexity of interconnected human–natural systems."],"dc:description.degree":["Doctor of Philosophy"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:45521"],"dc:identifier.uri":["https://hdl.handle.net/10919/140813"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["Creative Commons Attribution 4.0 International"],"dc:rights.uri":["http://creativecommons.org/licenses/by/4.0/"],"dc:subject":["model-based systems engineering","hetero-functional graph theory","watershed modeling","economic modeling","system dynamics"],"dc:title":["Hetero-functional Graph Theory for Convergent Systems of Systems: Model-Based Applications in Watershed and Economic Systems"],"dc:type":["Dissertation"],"thesis:degree_discipline":["Civil Engineering"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:20:12Z"}