Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A Hetero-functional Graph State Estimator for Watershed Systems: Application to the Chesapeake Bay

Megan S. Harris, John C. Little, Amro M. Farid

Abstract

Regional watersheds are complex systems of systems encompassing hydrology, land-use decision-making, estuarine ecological feedbacks, and overlapping governance jurisdictions. Their effective management underlies many modern societal challenges and therefore requires models that capture interdependencies between natural and institutional systems. Regional-specific models such as the Chesapeake Assessment Scenario Tool, used in this paper's case study, provide valuable nutrient estimates but rely on structurally opaque watershed routing that limits integration into broader systems-level analyses. This paper introduces a modeling framework for watershed systems. First, a region-independent reference architecture is developed. Second, the Weighted Least Squares Error Hetero-functional Graph State Estimator, an extension of Hetero-functional Graph Theory (HFGT), is adapted to estimate nutrient flows from uncertain data. The framework is demonstrated through instantiation in the Chesapeake Bay Watershed. By establishing a shared ontology grounded in Systems Modeling Language and HFGT, the approach enables integration of economic and governance systems to support sustainable watershed management.

A Hetero-functional Graph State Estimator for Watershed Systems: Application to the Chesapeake Bay

Abstract

Regional watersheds are complex systems of systems encompassing hydrology, land-use decision-making, estuarine ecological feedbacks, and overlapping governance jurisdictions. Their effective management underlies many modern societal challenges and therefore requires models that capture interdependencies between natural and institutional systems. Regional-specific models such as the Chesapeake Assessment Scenario Tool, used in this paper's case study, provide valuable nutrient estimates but rely on structurally opaque watershed routing that limits integration into broader systems-level analyses. This paper introduces a modeling framework for watershed systems. First, a region-independent reference architecture is developed. Second, the Weighted Least Squares Error Hetero-functional Graph State Estimator, an extension of Hetero-functional Graph Theory (HFGT), is adapted to estimate nutrient flows from uncertain data. The framework is demonstrated through instantiation in the Chesapeake Bay Watershed. By establishing a shared ontology grounded in Systems Modeling Language and HFGT, the approach enables integration of economic and governance systems to support sustainable watershed management.
Paper Structure (28 sections, 12 equations, 9 figures, 2 tables)

This paper contains 28 sections, 12 equations, 9 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Original Contribution
  3. Paper Outline
  4. Methodological Background
  5. The Chesapeake Bay Modeling Suite and the Chesapeake Assessment Scenario Tool (CAST)
  6. Hetero-functional Graph Theory (HFGT) Meta-Architecture & Definitions
  7. Weighted Least Squares Error Hetero-functional Graph State Estimation (WLSEHFGSE)
  8. Objective Function
  9. Equality Constraints
  10. Inequality Constraints
  11. Device Model Constraints
  12. Applying the HFGT Meta-Architecture and Definitions to Watershed Systems
  13. Block Definition Diagram for a Generic Watershed System
  14. Activity Diagram of Watershed Systems
  15. HFGT Definitions
  16. ...and 13 more sections

Figures (9)

  • Figure 1: A SysML Block Definition Diagram of the System Form of the Engineering System Meta-Architecture. Adapted from Schoonenberg:2019:00.
  • Figure 2: A SysML Activity Diagram of the System Function of the Engineering System Meta-Architecture. Adapted from Schoonenberg:2019:00.
  • Figure 3: Schematic representation of nutrient flow across land segments, defined as the intersection of watershed and county boundaries. Nutrient loads are distributed from county totals across all nested land segments, aggregated at the watershed level, and routed downstream toward the estuary. The Liberty Dam Watershed is shown as an example, with Carroll County (A) and Baltimore County (B) highlighted chesapeake-bay-program:2024:00.
  • Figure 4: Block Definition Diagram of Watershed Systems
  • Figure 5: Activity Diagram of a Generic Watershed System
  • ...and 4 more figures

Theorems & Definitions (15)

  • Definition 1: System of Systems
  • Definition 2: Engineering System weck:2011:00
  • Definition 3: System Operand Walden:2015:00
  • Definition 4: System Process Hoyle:1998:00Walden:2015:00
  • Definition 5: System Resource Walden:2015:00
  • Definition 6: Buffer Schoonenberg:2019:00Farid:2022:00
  • Definition 7: Capability Schoonenberg:2019:00Farid:2022:00Farid:2016:ISC-BC06
  • Definition 8: The Negative 3$^{rd}$ Order Hetero-functional Incidence Tensor (HFIT) $\widetilde{\cal M}_\rho^-$Farid:2022:00
  • Definition 9: The Positive 3$^{rd}$ Order Hetero-functional Incidence Tensor (HFIT)$\widetilde{\cal M}_\rho^+$Farid:2022:00
  • Definition 10: Engineering System Net Schoonenberg:2022:ISC-J48
  • ...and 5 more