Significance Stream/river carbon dioxide (CO 2 ) emission has significant spatial and seasonal variations critical for understanding its macroecosystem controls and plumbing of the terrestrial carbon budget. We relied on direct fluvial CO 2 partial pressure measurements and seasonally varying gas transfer velocity and river network surface area estimates to resolve reach-level seasonal variations of the flux at the global scale. The percentage of terrestrial primary production (GPP) shunted into rivers that ultimately contributes to CO 2 evasion increases with discharge across regions, due to a stronger response in fluvial CO 2 evasion to discharge than GPP. This highlights the importance of hydrology, in particular water throughput, in terrestrial–fluvial carbon transfers and the need to account for this effect in plumbing the terrestrial carbon budget.

The Surface Water and Ocean Topography (SWOT) satellite mission will measure river width, water surface elevation, and slope for rivers wider than 50-100 m. SWOT observations will enable estimation of river discharge by using simple flow laws such as the Manning-Strickler equation, complementing in situ streamgages. Several discharge inversion algorithms designed to compute unobserved flow law parameters (e.g., friction coefficient and bathymetry) have been proposed, but to date, a systematic assessment of factors controlling algorithm performance has not been conducted. Here, we assess the performance of the five algorithms that are expected to be used in the construction of the SWOT product. To perform this assessment, we used synthetic SWOT observations created with hydraulic model output corrupted with SWOT-like error. Prior information provided to the algorithms was purposefully limited to an estimate of mean annual flow (MAF), designed to produce a "worst case" benchmark. Prior MAF error was an important control on algorithm performance, but discharge estimates produced by the algorithms are less biased than the MAF; thus, the discharge algorithms improve on the prior. We show for the first time that accuracy and frequency of remote sensing observations are less important than prior bias, hydraulic variability among reaches, and flow law accuracy in governing discharge algorithm performance. The discharge errors and error sensitivities reported herein are a bounding benchmark, representing worst possible expected errors and error sensitivities. This study lays the groundwork to develop predictive power of algorithm performance, and thus map the global distribution of worst-case SWOT discharge accuracy.Plain Language Summary Measurements of river flow are essential for the allocation of water resources, flood and drought forecast and mitigation efforts, and others. Access to local measurements is not ubiquitous and is particularly difficult for rivers flowing in remote locations or across country borders. Measurements taken by satellites such as the upcoming Surface Water and Ocean Topography (SWOT) mission will offer freely available global data and methods to estimate discharge using such data have been in development. We conducted a comprehensive assessment of the accuracy and precision of five SWOT discharge inversion algorithms under three conditions: (a) ideal, that is if the measurements were available once a day and contained no error; (b) with no measurement error but changing how frequently the measurements were taken, and (c) under different levels of measurement error. We found that the methods consistently improved over the initial estimates of discharge and we identified river hydraulic properties that increase the chances of successful parameter estimation. We also found that despite the use of very similar discharge equations, the subtle differences in equations FRASSON ET AL.

At‐many‐stations hydraulic geometry (AMHG), while useful for estimating river discharge from satellite data, remains empirical and has yet to be reconciled with the at‐a‐station hydraulic geometry (AHG) from which it was originally derived. Here we present evidence, using United States Geological Survey field measurements of channel hydraulics for 155 rivers, that AMHG can be hydraulically and geomorphically reconciled with AHG. Our results indicate that AMHG is rightly understood as an expression of a river‐wide model of hydraulics driven by changes in slope imposed upon AHG physics. The explanatory power of AHG and this river‐wide model combine to determine whether AMHG exists: if both AHG and the river‐wide model adequately describe hydraulics, then we show that AMHG is a necessary mathematical consequence of these two phenomena. We also orient these findings in the context of river discharge estimation and other applications.

Recent advances in remote sensing and the upcoming launch of the joint NASA/CNES/CSA/ UKSA Surface Water and Ocean Topography (SWOT) satellite point toward improved river discharge estimates in ungauged basins. Existing discharge methods rely on "prior river knowledge" to infer parameters not directly measured from space. Here, we show that discharge estimation is improved by classifying and parameterizing rivers based on their unique geomorphology and hydraulics. Using over 370,000 in situ hydraulic observations as training data, we test unsupervised learning and an "expert" method to assign these hydraulics and geomorphology to rivers via remote sensing. This intervention, along with updates to model physics, constitutes a new method we term "geoBAM," an update of the Bayesian At-many-stations hydraulic geometry-Manning's (BAM) algorithm. We tested geoBAM on Landsat imagery over more than 7,500 rivers (108 are gauged) in Canada's Mackenzie River basin and on simulated hydraulic data for 19 rivers that mimic SWOT observations without measurement error. geoBAM yielded considerable improvement over BAM, improving the median Nash-Sutcliffe efficiency (NSE) for the Mackenzie River from −0.05 to 0.26 and from 0.16 to 0.46 for the SWOT rivers. Further, NSE improved by at least 0.10 in 78/108 gauged Mackenzie rivers and 8/19 SWOT rivers. We attribute geoBAM improvement to parameterizing rivers by type rather than globally, but prediction accuracy worsens if parameters are misassigned. This method is easily mapped to rivers at the global scale and paves the way for improving future discharge estimates, especially when coupled with hydrologic models.

The Surface Water Ocean Topography (SWOT) satellite mission expected to launch in 2021 will offer a unique opportunity to map river discharge at an unprecedented spatial resolution globally from observations of water surface elevation, width, and slope. Because river discharge will not be directly observed from SWOT, a number of algorithms of varying complexity have been developed to estimate discharge from SWOT observables. Outstanding issues include the lack of accurate prior information and parameter equifinality. We developed a new data assimilation discharge algorithm that aimed to overcome these limitations by integrating a data-driven approach to estimate priors with a model informed by hydraulic geometry relations. A comprehensive simulated dataset of 18 rivers was used to evaluate the algorithm and four different configurations (rectangular channel, generic channel, and geomorphologically classified channel with and without regularization) to assess the impact of progressively adding hydraulic geometry constraints to the estimation problem. The algorithm with the full set of constraints outperformed the other configurations with median Nash-Sutcliffe coefficients of 0.77, compared with −0.46, 0.31 and 0.66, while other error metrics showed similar improvement. Results from this study show the promise of this hybrid data-driven approach to estimating river discharge from SWOT observations, although a number of enhancements need to be tested to improve the operational applicability of the algorithm.

Dissolved organic matter (DOM) is one of the largest fluxes of carbon in inland water ecosystems and a central component of riverine metabolism. DOM, which is approximately 50% dissolved organic carbon (DOC) by mass (Dittmar & Stubbins, 2014;Krogh, 1934), is a nutrient and energy source, capable of transporting metals and pollutants, and a driver of light availability in water bodies (Kaplan & Cory, 2016;Schlesinger & Melack, 1981). Large amounts of riverine DOC enter the ocean annually, where it is an important source of reduced carbon (Raymond & Spencer, 2015). Although the amount of DOC entering the ocean is relatively well known, its representative chemical composition, reactivity, and the seasonality of its input are not as

The relative capacity for watersheds to eliminate or export reactive constituents has important implications on aquatic ecosystem ecology and biogeochemistry. Removal efficiency depends on factors that affect either the reactivity or advection of a constituent within river networks. Here, we characterized Damköhler number (Da) for dissolved organic carbon (DOC) uptake in global river networks. Da equals the advection to reaction timescale ratio and thus provides a unitless indicator for DOC reaction intensity during transport within river networks. We aim to demonstrate the spatial and temporal patterns and interplays among factors that determine DOC uptake across global river networks. We show that watershed size imposes a primary control on river network DOC uptake due to a three orders of magnitude difference in water residence time (WRT) between the smallest and largest river networks. DOC uptake capacity in tropical river networks is 2–6 times that in temperate and the Arctic river networks, coinciding with larger DOC removals in warm than in cold watersheds. River damming has a profound impact on DOC uptake due to significantly extended WRTs, particularly in temperate watersheds where most constructed dams are situated. Global warming is projected to increase river network DOC uptake by ca. 19% until year 2100 under the RCP4.5 scenario.

Inland waters play an important role in the global carbon cycle, contributing significant greenhouse gas (GHG) emissions to the atmosphere (Bastviken et al., 2011; Cole et al., 2007; Raymond et al., 2013). River networks are generally conceptualized as active biogeochemical reactors that mix, store, and evade GHGs and constituents transported from upstream together with those generated from in-stream production (Cole et al., 2007; see also; Raymond et al., 2016; Zarnetske et al., 2018). Ultimately, inland waters store, evade, and transport over half of the carbon that they receive from the terrestrial ecosystem before reaching the oceans (Hotchkiss et al., 2015), thereby playing a fundamental role in global carbon processes. Running inland waters (hereafter termed 'rivers') are generally supersaturated with GHGs and exhibit a net evasive flux of these gases from water to air (Cole & Caraco, 2001; Jones et al., 2003). This flux [M/L 2 T] is relatively easy to calculate with in situ knowledge of the gas concentration gradient between the water [gas] water and the air [gas] air [M/L 3 ] and the gas transfer velocity k [L/T] (Equation 1).