Thermally incised meltwater channels that flow each summer across melt-prone surfaces of the Greenland ice sheet have received little direct study. We use high-resolution WorldView-1/2 satellite mapping and in situ measurements to characterize supraglacial water storage, drainage pattern, and discharge across 6,812 km 2 of southwest Greenland in July 2012, after a record melt event. Efficient surface drainage was routed through 523 high-order stream/river channel networks, all of which terminated in moulins before reaching the ice edge. Low surface water storage (3.6 ± 0.9 cm), negligible impoundment by supraglacial lakes or topographic depressions, and high discharge to moulins (2.54-2.81 cm·d) indicate that the surface drainage system conveyed its own storage volume every <2 d to the bed. Moulin discharges mapped inside ∼52% of the source ice watershed for Isortoq, a major proglacial river, totaled ∼41-98% of observed proglacial discharge, highlighting the importance of supraglacial river drainage to true outflow from the ice edge. However, Isortoq discharges tended lower than runoff simulations from the Modèle Atmosphérique Régional (MAR) regional climate model (0.056-0.112 km ), and when integrated over the melt season, totaled just 37-75% of MAR, suggesting nontrivial subglacial water storage even in this melt-prone region of the ice sheet. We conclude that (i) the interior surface of the ice sheet can be efficiently drained under optimal conditions, (ii) that digital elevation models alone cannot fully describe supraglacial drainage and its connection to subglacial systems, and (iii) that predicting outflow from climate models alone, without recognition of subglacial processes, may overestimate true meltwater export from the ice sheet to the ocean.Greenland ice sheet | supraglacial hydrology | meltwater runoff | mass balance | remote sensing M eltwater runoff from the Greenland ice sheet (GrIS) accounts for half or more of its total mass loss to the global ocean (1, 2) but remains one of the least-studied hydrologic processes on Earth. Each summer, a complex system of supraglacial meltwater ponds, lakes, streams, rivers, and moulins develops across large areas of the southwestern GrIS surface, especially below ∼1,300 m elevation (3-7), with supraglacial erosion driven by thermal and radiative processes (5). Digital elevation models (DEMs) suggest a poorly drained surface resulting from abundant topographic depressions, which computational flow routing models must artificially "fill" to allow hydrological flow paths extending from the ice sheet interior to its edge (8-11). The realism of such modeled flow paths remains largely untested by real-world observations. To date, most observational studies of GrIS supraglacial hydrology have focused on large lakes (∼1 km 2

Rivers provide critical water supply for many human societies and ecosystems, yet global knowledge of their flow rates is poor. We show that useful estimates of absolute river discharge (in cubic meters per second) may be derived solely from satellite images, with no ground-based or a priori information whatsoever. The approach works owing to discovery of a characteristic scaling law uniquely fundamental to natural rivers, here termed a river's at-many-stations hydraulic geometry. A first demonstration using Landsat Thematic Mapper images over three rivers in the United States, Canada, and China yields absolute discharges agreeing to within 20-30% of traditional in situ gauging station measurements and good tracking of flow changes over time. Within such accuracies, the door appears open for quantifying river resources globally with repeat imaging, both retroactively and henceforth into the future, with strong implications for water resource management, food security, ecosystem studies, flood forecasting, and geopolitics. S ome 80% of the world's population and 65% of its river ecosystems are threatened by insecure water supply, yet global knowledge of the river discharges upon which these depend is surprisingly poor (1, 2). For much of the world, river gauge measurements are rare, nonexistent, or proprietary. Even wellmonitored countries have sparsely distributed networks, thus limiting current understanding of water losses along river courses, habitat changes, and flood risk (3, 4). Satellites, in contrast, provide spatially dense coverage globally, attracting calls for a global river discharge mapping capacity from space (5-10). However, previous efforts to estimate river discharge from remotely sensed observations have all required inclusion of some form of ancillary ground-based information, such as gauge measurements, bathymetric surveys, and/or calibrated hydrology models that are simply unavailable for most of the planet (11-18). To remove this dependence on ground-based information, we show that useful estimates of absolute river discharge (i.e., in units of cubic meters per second) may be derived solely from multiple satellite images of a river, with no ground-based or a priori information whatsoever, through use of a characteristic scaling law, here termed a river's atmany-stations hydraulic geometry (AMHG). As will be shown in this paper, AMHG effectively halves the number of parameters required by traditional hydraulic geometry, thus paving the way for remote estimation of a single remaining parameter-and thus river discharge-through repeated satellite image observations along a river course. The presence of AMHG is verified in 12 of 12 rivers examined, using 88 in situ gauging stations, three fieldcalibrated hydrodynamic models incorporating 772 field-surveyed bathymetric cross-sections, and 42 Landsat Thematic Mapper (TM) satellite images (SI Text, section S1, Materials and Methods and Tables S1 and S2). Following a description of width AMHG, an innovative satellite discharge estimation approach i...

International audienceThe Surface Water and Ocean Topography (SWOT) satellite mission planned for launch in 2020 will map river elevations and inundated area globally for rivers >100 m wide. In advance of this launch, we here evaluated the possibility of estimating discharge in ungauged rivers using synthetic, daily ‘‘remote sensing’’ measurements derived from hydraulic models corrupted with minimal observational errors. Five discharge algorithms were evaluated, as well as the median of the five, for 19 rivers spanning a range of hydraulic and geomorphic conditions. Reliance upon a priori information, and thus applicability to truly ungauged reaches, varied among algorithms: one algorithm employed only global limits on velocity and depth, while the other algorithms relied on globally available prior estimates of discharge. We found at least one algorithm able to estimate instantaneous discharge to within 35% relative root-mean-squared error (RRMSE) on 14/16 nonbraided rivers despite out-of-bank flows, multichannel planforms, and backwater effects. Moreover, we found RRMSE was often dominated by bias; the median standard deviation of relativeresiduals across the 16 nonbraided rivers was only 12.5%. SWOT discharge algorithm progress is therefore encouraging, yet future efforts should consider incorporating ancillary data or multialgorithm synergy to improve results

SignificanceMeltwater runoff is an important hydrological process operating on the Greenland ice sheet surface that is rarely studied directly. By combining satellite and drone remote sensing with continuous field measurements of discharge in a large supraglacial river, we obtained 72 h of runoff observations suitable for comparison with climate model predictions. The field observations quantify how a large, fluvial supraglacial catchment attenuates the magnitude and timing of runoff delivered to its terminal moulin and hence the bed. The data are used to calibrate classical fluvial hydrology equations to improve meltwater runoff models and to demonstrate that broad-scale surface water drainage patterns that form on the ice surface powerfully alter the timing, magnitude, and locations of meltwater penetrating into the ice sheet.

Spatiotemporally continuous global river discharge estimates across the full spectrum of stream orders are vital to a range of hydrologic applications, yet they remain poorly constrained. Here we present a carefully designed modeling effort (Variable Infiltration Capacity land surface model and Routing Application for Parallel computatIon of Discharge river routing model) to estimate global river discharge at very high resolutions. The precipitation forcing is from a recently published 0.1° global product that optimally merged gauge‐, reanalysis‐, and satellite‐based data. To constrain runoff simulations, we use a set of machine learning‐derived, global runoff characteristics maps (i.e., runoff at various exceedance probability percentiles) for grid‐by‐grid model calibration and bias correction. To support spaceborne discharge studies, the river flowlines are defined at their true geometry and location as much as possible—approximately 2.94 million vector flowlines (median length 6.8 km) and unit catchments are derived from a high‐accuracy global digital elevation model at 3‐arcsec resolution (~90 m), which serves as the underlying hydrography for river routing. Our 35‐year daily and monthly model simulations are evaluated against over 14,000 gauges globally. Among them, 35% (64%) have a percentage bias within ±20% (±50%), and 29% (62%) have a monthly Kling‐Gupta Efficiency ≥0.6 (0.2), showing data robustness at the scale the model is assessed. This reconstructed discharge record can be used as a priori information for the Surface Water and Ocean Topography satellite mission's discharge product, thus named “Global Reach‐level A priori Discharge Estimates for Surface Water and Ocean Topography”. It can also be used in other hydrologic applications requiring spatially explicit estimates of global river flows.

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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 forthcoming Surface Water and Ocean Topography (SWOT) NASA satellite mission will measure water surface width, height, and slope of major rivers worldwide. The resulting data could provide an unprecedented account of river discharge at continental scales, but reliable methods need to be identified prior to launch. Here we present a novel algorithm for discharge estimation from only remotely sensed stream width, slope, and height at multiple locations along a mass‐conserved river segment. The algorithm, termed the Bayesian AMHG‐Manning (BAM) algorithm, implements a Bayesian formulation of streamflow uncertainty using a combination of Manning's equation and at‐many‐stations hydraulic geometry (AMHG). Bayesian methods provide a statistically defensible approach to generating discharge estimates in a physically underconstrained system but rely on prior distributions that quantify the a priori uncertainty of unknown quantities including discharge and hydraulic equation parameters. These were obtained from literature‐reported values and from a USGS data set of acoustic Doppler current profiler (ADCP) measurements at USGS stream gauges. A data set of simulated widths, slopes, and heights from 19 rivers was used to evaluate the algorithms using a set of performance metrics. Results across the 19 rivers indicate an improvement in performance of BAM over previously tested methods and highlight a path forward in solving discharge estimation using solely satellite remote sensing.