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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., Key Points Thirty‐five‐year global reconstruction of river flows at unprecedented 2.94 million reaches extracted from 90‐m high‐accuracy DEMNovel bias correction (“sparse CDF matching”) is conducted grid‐by‐grid against machine learning‐derived global runoff characteristics mapsEvaluation against >14,000 gauges shows data robustness for hydrologic applications and utility in spaceborne discharge estimation efforts

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 dataset of acoustic Doppler current profiler (ADCP) measurements at USGS stream gauges. A dataset 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.

The upcoming Surface Water and Ocean Topography (SWOT) mission will measure water surface heights and widths for rivers wider than 100 m. At its native resolution, SWOT height errors are expected to be on the order of meters, which prevent the calculation of water surface slopes and the use of slope‐dependent discharge equations. To mitigate height and width errors, the high‐resolution measurements will be grouped into reaches (∼5 to 15 km), where slope and discharge are estimated. We describe three automated river segmentation strategies for defining optimum reaches for discharge estimation: (1) arbitrary lengths, (2) identification of hydraulic controls, and (3) sinuosity. We test our methodologies on 9 and 14 simulated SWOT overpasses over the Sacramento and the Po Rivers, respectively, which we compare against hydraulic models of each river. Our results show that generally, height, width, and slope errors decrease with increasing reach length. However, the hydraulic controls and the sinuosity methods led to better slopes and often height errors that were either smaller or comparable to those of arbitrary reaches of compatible sizes. Estimated discharge errors caused by the propagation of height, width, and slope errors through the discharge equation were often smaller for sinuosity (on average 8.5% for the Sacramento and 6.9% for the Po) and hydraulic control (Sacramento: 7.3% and Po: 5.9%) reaches than for arbitrary reaches of comparable lengths (Sacramento: 8.6% and Po: 7.8%). This analysis suggests that reach definition methods that preserve the hydraulic properties of the river network may lead to better discharge estimates.

This paper demonstrates improved retrieval of snow water equivalent (SWE) from spaceborne passive microwave measurements for the sparsely-forested Upper Kern watershed (511 km2) in the southern Sierra Nevada (USA). This is accomplished by assimilating AMSR-E 36.5 GHz measurements into model predictions of SWE at 90-m spatial resolution using the Ensemble Batch Smoother (EnBS) data assimilation framework. For each water year (WY) from 2003 to 2008, SWE was estimated for the accumulation season (October 1st to April 1st) with the assimilation of the measurements in the dry snow season (December 1st to February 28th). The EnBS SWE estimation was validated against snow courses and snow pillows. On average, the EnBS accumulation season SWE RMSE was 77.4 mm (13.1%, relative to peak accumulation), despite deep snow (average peak SWE of 545 mm). The prior model estimate without assimilation had an accumulation season average RMSE of 119.7 mm. After assimilation, the overall bias of the accumulation season SWE estimates was reduced by 84.2%, and the RMSE reduced by 35.4%. The assimilation also reduced the bias and the RMSE of the April 1st SWE estimates by 80.9% and 45.4%, respectively. The EnBS is expected to work well above treeline and for dry snow. This article is protected by copyright. All rights reserved.

The objective of this study is to compare the effectiveness of three algorithms that estimate discharge from remotely sensed observables (river width, water surface height, and water surface slope) in anticipation of the forthcoming NASA/CNES Surface Water and Ocean Topography (SWOT) mission. SWOT promises to provide these measurements simultaneously, and the river discharge algorithms included here are designed to work with these data. Two algorithms were built around Manning's equation, the Metropolis Manning (MetroMan) method, and the Mean Flow and Geomorphology (MFG) method, and one approach uses hydraulic geometry to estimate discharge, the at-many-stations hydraulic geometry (AMHG) method. A well-calibrated and ground-truthed hydrodynamic model of the Ganges river system (HEC-RAS) was used as reference for three rivers from the Ganges River Delta: the main stem of Ganges, the Arial-Khan, and the Mohananda Rivers. The high seasonal variability of these rivers due to the Monsoon presented a unique opportunity to thoroughly assess the discharge algorithms in light of typical monsoon regime rivers. It was found that the MFG method provides the most accurate discharge estimations in most cases, with an average relative root-mean-squared error (RRMSE) across all three reaches of 35.5%. It is followed closely by the Metropolis Manning algorithm, with an average RRMSE of 51.5%. However, the MFG method's reliance on knowledge of prior river discharge limits its application on ungauged rivers. In terms of input data requirement at ungauged regions with no prior records, the Metropolis Manning algorithm provides a more practical alternative over a region that is lacking in historical observations as the algorithm requires less ancillary data. The AMHG algorithm, while requiring the least prior river data, provided the least accurate discharge measurements with an average wet and dry season RRMSE of 79.8% and 119.1%, respectively, across all rivers studied. This poor performance is directly traced to poor estimation of AMHG via a remotely sensed proxy, and results improve commensurate with MFG and MetroMan when prior AMHG information is given to the method. Therefore, we cannot recommend use of AMHG without inclusion of this prior information, at least for the studied rivers. The dry season discharge (within-bank flow) was captured well by all methods, while the wet season (floodplain flow) appeared more challenging. The picture that emerges from this study is that a multialgorithm approach may be appropriate during flood inundation periods in Ganges Delta.

Recent efforts have sought to estimate river discharge and other surface water-related quantities using spaceborne sensors, with better spatial coverage but worse temporal sampling as compared with in situ measurements. The Surface Water and Ocean Topography (SWOT) mission will provide river discharge estimates globally from space. However, questions on how to optimally use the spatially distributed but asynchronous satellite observations to generate continuous fields still exist. This paper presents a statistical model (River Kriging-RK), for estimating discharge time series in a river network in the context of the SWOT mission. RK uses discharge estimates at different locations and times to produce a continuous field using spatiotemporal kriging. A key component of RK is the space-time river discharge covariance, which was derived analytically from the diffusive wave approximation of Saint Venant's equations. The RK covariance also accounts for the loss of correlation at confluences. The model performed well in a case study on Ganges-Brahmaputra-Meghna (GBM) River system in Bangladesh using synthetic SWOT observations. The correlation model reproduced empirically derived values. RK (R2=0.83) outperformed other kriging-based methods (R2=0.80), as well as a simple time series linear interpolation (R2=0.72). RK was used to combine discharge from SWOT and in situ observations, improving estimates when the latter is included (R2=0.91). The proposed statistical concepts may eventually provide a feasible framework to estimate continuous discharge time series across a river network based on SWOT data, other altimetry missions, and/or in situ data.

This paper used a data assimilation framework to estimate spatially and temporally continuous snow water equivalent (SWE) from a 27 year reanalysis (from water year 1985 to 2011) of the Landsat-5 record for the Kern River watershed in the Sierra Nevada, California. The data assimilation approach explicitly treats sources of uncertainty from model parameters, meteorological inputs, and observations. The method is comprised of two main components: (1) a coupled land surface model (LSM) and snow depletion curve (SDC) model, which is used to generate an ensemble of predictions of SWE and fractional snow cover area (FSCA) for a given set of prior (uncertain) inputs, and (2) a retrospective reanalysis step, which updates estimation variables to be consistent with the observed fractional snow cover time series. The final posterior SWE estimate is generated from the LSM-SDC using the posterior estimation variables consistently with all postulated sources of uncertainty in the model, inputs, and observations. A reasonable agreement was found between the SWE reanalysis and in situ SWE observations and streamflow data. The data set was studied to evaluate factors controlling SWE spatial and temporal variability. Elevation was found to be the primary control on spatial patterns of peak-SWE and day-of-peak. The easting coordinate had additional explanatory power, which is hypothesized to be related to rain shadow effects due to the prevailing storm track directions. The spatial patterns were found to be interannually inconsistent. However, drier years and lower elevations were found more variable than wetter years and higher elevations, respectively. Only a very small percentage of the Kern River watershed had a significant trend in peak-SWE and day-of-peak. Trends deemed to be significant were found to be positive (peak-SWE is increasing and day-of-peak occurs later) at higher elevations, but negative (peak-SWE is decreasing and day-of-peak occurs earlier) at lower elevations. The reanalysis approach proved to be useful in terms of identifying subwatershed variability and trends, and could be extended to larger regions and areas where in situ data are sparse or unavailable.

[1] The Surface Water and Ocean Topography (SWOT) radar interferometer satellite mission will provide unprecedented global measurements of water surface elevation (h) for inland water bodies. However, like most remote sensing technologies SWOT will not observe river channel bathymetry below the lowest observed water surface, thus limiting its value for estimating river depth and/or discharge. This study explores if remotely sensed observations of river inundation width and h alone, when accumulated over time, may be used to estimate this unmeasurable flow depth. To test this possibility, synthetic values of h and either cross-sectional flow width (w) or effective width (We, inundation area divided by reach length) are extracted from 1495 previously surveyed channel cross-sections for the Upper Mississippi, Illinois, Rio Grande, and Ganges-Brahmaputra river systems, and from 62 km of continuously acquired sonar data for the Upper Mississippi. Two proposed methods (called “Linear” and “Slope-Break”) are tested that seek to identify a small subset of geomorphically “optimal” locations where w or We covary strongly with h, such that they may be usefully extrapolated to estimate mean cross-sectional flow depth (d). While the simplest Linear Method is found to have considerable uncertainty, the Slope-Break Method, identifying locations where two distinct hydraulic relationships are identified (one for moderate to high flows and one for low flows), holds promise. Useful slope breaks were discovered in all four river systems, ranging from 6 (0.04%) to 242 (16%) of the 1495 studied cross-sections, assuming channel bathymetric exposures ranging from 20% to 95% of bankfull conditions, respectively. For all four rivers, the derived depth estimates from the Slope-Break Method have root mean squared errors (RMSEs) of