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Abstract Nitrogen (N) wet deposition chemistry impacts watershed biogeochemical cycling. The timescale and magnitude of (a)synchrony between wet deposition N inputs and watershed N outputs remains unresolved. We quantify deposition‐river N (a)synchrony with transfer entropy (TE), an information theory metric enabling quantification of lag‐dependent feedbacks in a hydrologic system by calculating directional information flow between variables. Synchrony is defined as a significant amount of TE‐calculated reduction in uncertainty of river N from wet deposition N after conditioning for antecedent river N conditions. Using long‐term timeseries of wet deposition and river DON, NO₃⁻, and NH₄⁺concentrations from the Lamprey River watershed, New Hampshire (USA), we constrain the role of wet deposition N to watershed biogeochemistry. Wet deposition N contributed information to river N at timescales greater than quick‐flow runoff generation, indicating that river N losses are a lagged non‐linear function of hydro‐biogeochemical forcings. River DON received the most information from all three wet deposition N solutes while wet deposition DON and NH₄⁺contributed the most information to all three river N solutes. Information theoretic algorithms facilitated data‐driven inferences on the hydro‐biogeochemical processes influencing the fate of N wet deposition. For example, signals of mineralization and assimilation at a timescale of 12 to 21‐weeks lag display greater synchrony than nitrification, and we find that N assimilation is a positive lagged function of increasing N wet deposition. Although wet deposition N is not the main driver of river N, it contributes a significant amount of information resolvable at time scales of transport and transformations. 

Evaluating whether hydrological models are right for the right reasons demands reproducible model benchmarking and diagnostics that evaluate not just statistical predictive model performance but also internal processes. Such model benchmarking and diagnostic efforts will benefit from standardized methods and ready-to-use toolkits. Using the Jupyter platform, this work presents HydroBench, a model-agnostic benchmarking tool consisting of three sets of metrics: 1) common statistical predictive measures, 2) hydrological signature-based process metrics, including a new time-linked flow duration curve and 3) information-theoretic diagnostics that measure the flow of information among model variables. As a test case, HydroBench was applied to compare two model products (calibrated and uncalibrated) of the National Hydrologic Model - Precipitation Runoff Modeling System (NHM-PRMS) at the Cedar River watershed, WA, United States. Although the uncalibrated model has the highest predictive performance, particularly for high flows, the signature-based diagnostics showed that the model overestimates low flows and poorly represents the recession processes. Elucidating why low flows may have been overestimated, the information-theoretic diagnostics indicated a higher flow of information from precipitation to snowmelt to streamflow in the uncalibrated model compared to the calibrated model, where information flowed more directly from precipitation to streamflow. This test case demonstrated the capability of HydroBench in process diagnostics and model predictive and functional performance evaluations, along with their tradeoffs. Having such a model benchmarking tool not only provides modelers with a comprehensive model evaluation system but also provides an open-source tool that can further be developed by the hydrological community. 

Abstract How precipitation (P) is translated into streamflow (Q) and over what timescales (i.e., “memory”) is difficult to predict without calibration of site‐specific models or using geochemical approaches, posing barriers to prediction in ungauged basins or advancement of general theories. Here, we used a data‐driven approach to identify regional patterns and exogenous controls on P–Q interactions. We applied an information flow analysis, which quantifies uncertainty reduction, to a daily time series of P and Q from 671 watersheds across the conterminous United States. We first demonstrated that information transfer from P to Q primarily reflects the quickflow component of water‐budgets, based on a watershed model. Readily quantifiable information flows show a functional relationship with model parameters, suggesting utility for model calibration. Second, applied to real watersheds, P–Q information flows exhibit seasonally varying behavior within regions in a manner consistent with dominant runoff generation mechanisms. However, the timing and the magnitude of information flows also reflect considerable subregional heterogeneity, likely attributable to differences in watershed size, baseflow contributions, and variation in aerial coverage of preferential flow paths. A regression analysis showed that a combination of climate and watershed characteristics are predictive of P–Q information flows. Though information flows cannot, in most cases, uniquely determine dominant runoff mechanisms, they provide a means to quantify the heterogeneous outcomes of those mechanisms within regions, thereby serving as a benchmarking tool for models developed at the regional scale. Last, information flows characterize regionally specific ways in which catchment connectivity changes from the wet to dry season.