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Abstract. Lateral carbon flux through river networks is an important and poorly understood component of the global carbon budget. This work investigates how temperature and hydrology control the production and export of dissolved organic carbon (DOC) in the Susquehanna Shale Hills Critical Zone Observatory in Pennsylvania, USA. Using field measurements of daily stream discharge, evapotranspiration, and stream DOC concentration, we calibrated the catchment-scale biogeochemical reactive transport model BioRT-Flux-PIHM (Biogeochemical Reactive Transport–Flux–Penn State Integrated Hydrologic Model, BFP), which met the satisfactory standard of a Nash–Sutcliffe efficiency (NSE) value greater than 0.5. We used the calibrated model to estimate and compare the daily DOC production rates (Rp; the sum of the local DOC production rates in individual grid cells) and export rate (Re; the product of the concentration and discharge at the stream outlet, or load). Results showed that daily Rp varied by less than an order of magnitude, primarily depending on seasonal temperature. In contrast, daily Re varied by more than 3 orders of magnitude and was strongly associated with variation in discharge and hydrological connectivity. In summer, high temperature and evapotranspiration dried and disconnected hillslopes from the stream, driving Rp to its maximum but Re to its minimum. During this period, the stream only exported DOC from the organic-poor groundwater and from organic-rich soil water in the swales bordering the stream. The DOC produced accumulated in hillslopes and was later flushed out during the wet and cold period (winter and spring) when Re peaked as the stream reconnected with uphill and Rp reached its minimum. The model reproduced the observed concentration–discharge (C–Q) relationship characterized by an unusual flushing–dilution pattern with maximum concentrations at intermediate discharge, indicating three end-members of source waters. A sensitivity analysis indicated that this nonlinearity was caused by shifts in the relative contribution of different source waters to the stream under different flow conditions. At low discharge, stream water reflected the chemistry of organic-poor groundwater; at intermediate discharge, stream water was dominated by the organic-rich soil water from swales; at high discharge, the stream reflected uphill soil water with an intermediate DOC concentration. This pattern persisted regardless of the DOC production rate as long as the contribution of deeper groundwater flow remained low (<18 % of the streamflow). When groundwater flow increased above 18 %, comparable amounts of groundwater and swale soil water mixed in the stream and masked the high DOC concentration from swales. In that case, the C–Q patterns switched to a flushing-only pattern with increasing DOC concentration at high discharge. These results depict a conceptual model that the catchment serves as a producer and storage reservoir for DOC under hot and dry conditions and transitions into a DOC exporter under wet and cold conditions. This study also illustrates how different controls on DOC production and export – temperature and hydrological flow paths, respectively – can create temporal asynchrony at the catchment scale. Future warming and increasing hydrological extremes could accentuate this asynchrony, with DOC production occurring primarily during dry periods and lateral export of DOC dominating in major storm events.

Headwater catchments are the fundamental units that connect the land to the ocean. Hydrological flow and biogeochemical processes are intricately coupled, yet their respective sciences have progressed without much integration. Reaction kinetic theories that prescribe rate dependence on environmental variables (e.g., temperature and water content) have advanced substantially, mostly in well‐mixed reactors, columns, and warming experiments without considering the characteristics of hydrological flow at the catchment scale. These theories have shown significant divergence from observations in natural systems. On the other hand, hydrological theories, including transit time theory, have progressed substantially yet have not been incorporated into understanding reactions at the catchment scale. Here we advocate for the development of integrated hydro‐biogeochemical theories across gradients of climate, vegetation, and geology conditions. The lack of such theories presents barriers for understanding mechanisms and forecasting the future of the Critical Zone under human‐ and climate‐induced perturbations. Although integration has started and co‐located measurements are well under way, tremendous challenges remain. In particular, even in this era of “big data,” we are still limited by data and will need to (1) intensify measurements beyond river channels and characterize the vertical connectivity and broadly the shallow and deep subsurface; (2) expand to older water dating beyond the time scales reflected in stable water isotopes; (3) combine the use of reactive solutes, nonreactive tracers, and isotopes; and (4) augment measurements in environments that are undergoing rapid changes. To develop integrated theories, it is essential to (1) engage models at all stages to develop model‐informed data collection strategies and to maximize data usage; (2) adopt a “simple but not simplistic,” or fit‐for‐purpose approach to include essential processes in process‐based models; (3) blend the use of process‐based and data‐driven models in the framework of “theory‐guided data science.” Within the framework of hypothesis testing, model‐data fusion can advance integrated theories that mechanistically link catchments' internal structures and external drivers to their functioning. It can not only advance the field of hydro‐biogeochemistry, but also enable hind‐ and fore‐casting and serve the society at large. Broadly, future education will need to cultivate thinkers at the intersections of traditional disciplines with hollistic approaches for understanding interacting processes in complex earth systems. This article is categorized under: Engineering Water > Methods

The shallow and deep hypothesis suggests that stream concentration‐discharge (CQ) relationships are shaped by distinct source waters from different depths. Under this hypothesis, baseflows are typically dominated by groundwater and mostly reflect groundwater chemistry, whereas high flows are typically dominated by shallow soil water and mostly reflect soil water chemistry. Aspects of this hypothesis draw on applications like end member mixing analyses and hydrograph separation, yet direct data support for the hypothesis remains scarce. This work tests the shallow and deep hypothesis using co‐located measurements of soil water, groundwater, and streamwater chemistry at two intensively monitored sites, the W‐9 catchment at Sleepers River (Vermont, United States) and the Hafren catchment at Plynlimon (Wales). At both sites, depth profiles of subsurface water chemistry and stream CQ relationships for the 10 solutes analyzed are broadly consistent with the hypothesis. Solutes that are more abundant at depth (e.g., calcium) exhibit dilution patterns (concentration decreases with increasing discharge). Conversely, solutes enriched in shallow soils (e.g., nitrate) generally exhibit flushing patterns (concentration increases with increasing discharge). The hypothesis may hold broadly true for catchments that share such biogeochemical stratifications in the subsurface. Soil water and groundwater chemistries were estimated from high‐ and low‐flow stream chemistries with average relative errors ranging from 24% to 82%. This indicates that streams mirror subsurface waters: stream chemistry can be used to infer scarcely measured subsurface water chemistry, especially where there are distinct shallow and deep end members.

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