Water quality monitoring networks in large river basins typically develop incrementally across multiple independent agencies, generating spatial redundancy, uneven parameter coverage, and inefficient allocation of monitoring resources. This study develops and applies a Mixed-Integer Linear Programming (MILP) framework, grounded in the process integration (PI) philosophy of resource conservation targeting, to rationalize the multi-agency water quality monitoring network of the Paraíba do Sul River Basin, Brazil. A novel composite Information Score (IS) metric is introduced, integrating four dimensions of monitoring quality — parameter coverage, Shannon entropy of measurement distributions, temporal extent, and record density — analogous to the quality constraints used in industrial water allocation network synthesis. The MILP model minimizes the number of active stations while guaranteeing coverage of all monitored river segments under CONAMA Resolution 357/2005 Class II. Applied to the Instituto Estadual do Ambiente (INEA) network of 450 stations and 202,625 records (2012–2023), the optimal solution retains 155 stations — a 65.6% reduction — while achieving full river-segment coverage and an 18.9% improvement in mean IS. An <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varepsilon\)</EquationSource> </InlineEquation>-constraint Pareto frontier delineates three operating zones in the cost-versus-information trade-off space. Cross-agency comparison with the 48-year CETESB network (13 stations, São Paulo — SP; mean IS <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\varvec{=\,0.817}\)</EquationSource> </InlineEquation>; 93,968 records, 1978–2026) reveals that longer-operating, parameter-rich stations achieve substantially superior IS values, validating the IS as a robust indicator of monitoring maturity. CONAMA Class II exceedance reveals pervasive impairment in the Rio de Janeiro (RJ) reach (total phosphorus: 56.0%; BOD<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(_{\varvec{5}}\)</EquationSource> </InlineEquation>: 39.3%) versus substantially lower rates in the São Paulo (SP) reach monitored by CETESB (TP: 23.8%; BOD<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(_{\varvec{5}}\)</EquationSource> </InlineEquation>: 2.0%), confirming the utility of harmonized network optimization for inter-agency spatial comparison. The proposed framework is generalizable to any multi-station river basin network, advancing the application of PI tools in environmental resource management.

A Mixed-Integer Linear Programming Framework for Water Quality Monitoring Network Rationalization: A Process Integration Approach Applied to the Paraíba do Sul River Basin, Brazil

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2026年6月30日

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Hugo Pimentel Tavares,
Nilo Antônio de Souza Sampaio

摘要

Water quality monitoring networks in large river basins typically develop incrementally across multiple independent agencies, generating spatial redundancy, uneven parameter coverage, and inefficient allocation of monitoring resources. This study develops and applies a Mixed-Integer Linear Programming (MILP) framework, grounded in the process integration (PI) philosophy of resource conservation targeting, to rationalize the multi-agency water quality monitoring network of the Paraíba do Sul River Basin, Brazil. A novel composite Information Score (IS) metric is introduced, integrating four dimensions of monitoring quality — parameter coverage, Shannon entropy of measurement distributions, temporal extent, and record density — analogous to the quality constraints used in industrial water allocation network synthesis. The MILP model minimizes the number of active stations while guaranteeing coverage of all monitored river segments under CONAMA Resolution 357/2005 Class II. Applied to the Instituto Estadual do Ambiente (INEA) network of 450 stations and 202,625 records (2012–2023), the optimal solution retains 155 stations — a 65.6% reduction — while achieving full river-segment coverage and an 18.9% improvement in mean IS. An \(\varepsilon\) -constraint Pareto frontier delineates three operating zones in the cost-versus-information trade-off space. Cross-agency comparison with the 48-year CETESB network (13 stations, São Paulo — SP; mean IS \(\varvec{=\,0.817}\) ; 93,968 records, 1978–2026) reveals that longer-operating, parameter-rich stations achieve substantially superior IS values, validating the IS as a robust indicator of monitoring maturity. CONAMA Class II exceedance reveals pervasive impairment in the Rio de Janeiro (RJ) reach (total phosphorus: 56.0%; BOD \(_{\varvec{5}}\) : 39.3%) versus substantially lower rates in the São Paulo (SP) reach monitored by CETESB (TP: 23.8%; BOD \(_{\varvec{5}}\) : 2.0%), confirming the utility of harmonized network optimization for inter-agency spatial comparison. The proposed framework is generalizable to any multi-station river basin network, advancing the application of PI tools in environmental resource management.