Wasserstein distributional distance and linear programming convergence planning as monitoring network benchmarking tools: cross-continental surface water quality assessment across Brazilian and European river basins.

Evaluating the performance of long-term water quality monitoring networks against international reference systems requires analytical tools capable of comparing entire empirical distributions - not merely summary statistics - yet distributional benchmarking methods have rarely been applied at the cross-continental scale. This study develops and applies a four-method analytical framework - combining Wasserstein-1 distributional distance (earth mover's distance), Shannon-entropy-weighted TOPSIS, linear programming (LP) convergence planning, and principal component analysis with hierarchical cluster analysis (PCA/HCA) - to compare ten São Paulo river basins (Brazil) against 23 European countries monitored under the Water Framework Directive (WFD), using a harmonised dataset of 646,356 CETESB records and 998,410 GRQA v1.4 records covering seven common physicochemical parameters over a shared window of 2016-2022. The Wasserstein-1 analysis reveals that the distributional gap is non-uniform: Afluentes do Paraíba do Sul (composite W 1 = 0.245 ) and the Cantareira system ( W 1 = 0.333 ) are already within the distributional range of lower-ranking European countries, while the Alto Tietê ( W 1 = 2.060 ) and Médio Tietê ( W 1 = 1.392 ) are distributional outliers. Shannon-entropy-weighted TOPSIS ranking of the 20 entities with complete parameter coverage (all ten Brazilian basins and the ten European countries with complete five-parameter medians) places Afluentes-PSB seventh overall (score = 0.901), above Portugal, Poland, Germany, and Belgium, while the Alto Tietê (0.246) and Médio Tietê (0.194) rank last. Mann-Whitney U tests confirm statistically significant distributional differences for six of seven parameters, with large Cliff's δ for temperature ( δ = + 0.858 ), dissolved oxygen ( δ = - 0.768 ), and biochemical oxygen demand ( δ = + 0.571 ); nitrate is the sole parameter with no significant difference ( p = 0.354 ; δ = - 0.010 , negligible). The LP convergence model, constrained by historically observed maximum improvement rates in the CETESB dataset, identifies dissolved oxygen as the binding convergence constraint for seven of ten basins, with critical-path convergence times ranging from 4.4 years (Afluentes-PSB) to 14.8 years (Alto Tietê) under the 90th-percentile feasibility assumption, lengthening to 5.5 and 28.7 years respectively under a more conservative 75th-percentile assumption; total phosphorus carries the highest LP cost weight ( w = 0.669 ) but is the rate-limiting parameter for only one basin (Tietê-Médio). Rankings are robust to the weighting scheme (Kendall's τ ≥ 0.86 against equal-weight and CRITIC alternatives). Applied externally to 33 Polish and 26 Italian sub-basins under a leave-one-country-out design, basin scores correlate negatively with an independent measure of anthropogenic pressure in both countries ( ρ = - 0.44 and - 0.42 ), indicating that the benchmarking and ranking components transfer to monitoring systems on which the framework was not developed. PCA/HCA distinguishes four typological clusters: the Tietê metropolitan arc (Cluster 2), a predominantly European mainstream (Cluster 1), a clean-reference group (Cluster 3) comprising four Brazilian basins together with Portugal, and an intermediate-impaired group (Cluster 4). These findings demonstrate that São Paulo's monitoring network is not uniformly distant from the European reference; the proposed framework provides a replicable, distribution-sensitive KPI for monitoring network performance assessment applicable to any national network linked to an international reference archive.