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River networks regulate carbon and nutrient exchange between continents, atmosphere, and oceans. However, contributions of riverine processing are poorly constrained at continental scales. Scaling relationships of cumulative biogeochemical function with watershed size (allometric scaling) provide an approach for quantifying the contributions of fluvial networks in the Earth system. Here we show that allometric scaling of cumulative riverine function with watershed area ranges from linear to superlinear, with scaling exponents constrained by network shape, hydrological conditions, and biogeochemical process rates. Allometric scaling is superlinear for processes that are largely independent of substrate concentration (e.g., gross primary production) due to superlinear scaling of river network surface area with watershed area. Allometric scaling for typically substrate-limited processes (e.g., denitrification) is linear in river networks with high biogeochemical activity or low river discharge but becomes increasingly superlinear under lower biogeochemical activity or high discharge, conditions that are widely prevalent in river networks. The frequent occurrence of superlinear scaling indicates that biogeochemical activity in large rivers contributes disproportionately to the function of river networks in the Earth system.

Abstract. Repeated sampling of spatially distributed riverchemistry can be used to assess the location, scale, and persistence ofcarbon and nutrient contributions to watershed exports. Here, we provide acomprehensive set of water chemistry measurements and ecohydrologicalmetrics describing the biogeochemical conditions of permafrost-affectedArctic watersheds. These data were collected in watershed-wide synopticcampaigns in six stream networks across northern Alaska. Three watershedsare associated with the Arctic Long-Term Ecological Research site at ToolikField Station (TFS), which were sampled seasonally each June and August from2016 to 2018. Three watersheds were associated with the National ParkService (NPS) of Alaska and the U.S. Geological Survey (USGS) and weresampled annually from 2015 to 2019. Extensive water chemistrycharacterization included carbon species, dissolved nutrients, and majorions. The objective of the sampling designs and data acquisition was tocharacterize terrestrial–aquatic linkages and processing of material instream networks. The data allow estimation of novel ecohydrological metricsthat describe the dominant location, scale, and overall persistence ofecosystem processes in continuous permafrost. These metrics are (1)subcatchment leverage, (2) variance collapse, and (3) spatial persistence.Raw data are available at the National Park Service Integrated Resource Management Applications portal (O'Donnell et al., 2021, https://doi.org/10.5066/P9SBK2DZ) and within the Environmental Data Initiative (Abbott, 2021, https://doi.org/10.6073/pasta/258a44fb9055163dd4dd4371b9dce945).

Riverine fluxes of carbon and inorganic nutrients are increasing in virtually all large permafrost-affected rivers, indicating major shifts in Arctic landscapes. However, it is currently difficult to identify what is causing these changes in nutrient processing and flux because most long-term records of Arctic river chemistry are from small, headwater catchments draining <200 km²or from large rivers draining >100,000 km². The interactions of nutrient sources and sinks across these scales are what ultimately control solute flux to the Arctic Ocean. In this context, we performed spatially-distributed sampling of 120 subcatchments nested within three Arctic watersheds spanning alpine, tundra, and glacial-lake landscapes in Alaska. We found that the dominant spatial scales controlling organic carbon and major nutrient concentrations was 3–30 km², indicating a continuum of diffuse and discrete sourcing and processing dynamics. These patterns were consistent seasonally, suggesting that relatively fine-scale landscape patches drive solute generation in this region of the Arctic. These network-scale empirical frameworks could guide and benchmark future Earth system models seeking to represent lateral and longitudinal solute transport in rapidly changing Arctic landscapes.