The impact of reach averaging Manning’s equation for an in-situ dataset of water surface elevation, width, and slope

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.

Section: Methodsmentioning

confidence: 99%

Section: Geobam and Amhg Physicsmentioning

confidence: 99%

Constraining Remote River Discharge Estimation Using Reach‐Scale Geomorphology

Brinkerhoff

Gleason

Feng

et al. 2020

“…Similarly to BAM, the Metropolis-Manning (MetroMan) algorithm (Durand et al, 2014) uses a Bayesian inference framework to estimate the unobservable flow law parameters needed by the Manning-Strickler equation to estimate discharge. However, unlike BAM, the version of MetroMan used in the present work allows n to vary in both time and space, in an attempt to account for the additional energy dissipation caused by spatial variability of hydraulic properties within a reach (Durand et al, 2016;Rodríguez et al, 2020;Tuozzolo, Langhorst, et al, 2019). Given the parameterization of friction, the assumption that width is much larger than depth, and that the friction slope can be approximated by the water surface slope (low Froude approximation), the Manning-Strickler equation used by MetroMan becomes:…”

Section: Metroman: Metropolis-manning Algorithmmentioning

confidence: 99%

Exploring the Factors Controlling the Error Characteristics of the Surface Water and Ocean Topography Mission Discharge Estimates

Frasson

Durand

Gleason

et al. 2021

Self Cite

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.

“…The averaging scales are set by the capabilities of the sensor and often cannot be selected to guarantee that the hydraulic parameters will be constant over these scales. Since the hydraulic equations are not linear, and parameters may show significant within‐reach variability, it is not the case that spatial averages can be substituted for point measurements, as we will see below, and has been demonstrated using field data (Tuozzolo et al, 2019). Even if the measurement is collected with a spatial resolution sufficient to mimic a point measurement, the level of noise in the remote sensing measurement may be too large to ingest as a point measurement, and spatial averaging needs to be applied so the remote sensing measurements can be utilized meaningfully.…”

Section: Introductionmentioning

confidence: 99%

Observing Rivers With Varying Spatial Scales

Rodríguez

Durand

Frasson

2020

Self Cite

The National Aeronautics and Space Administration/Centre national d'études spatiales Surface Water and Ocean Topography (SWOT) mission will estimate global river discharge using remote sensing. Synoptic remote sensing data extend in situ point measurements but, at any given point, are generally less accurate. We address two questions: (1)What are the scales at which river dynamics can be observed, given spatial sampling and measurement noise characteristics? (2) Is there an equation whose variables are the averaged hydraulic quantities obtained by remote sensing and which describes the dynamics of spatially averaged rivers? We use calibrated hydraulic models to examine the power spectra of the different terms in the momentum equation and conclude that the measurement of river slope sets the scale at which rivers can be observed. We introduce the reach-averaged Saint Venant equations that involve only observable hydraulic variations and which parametrize within-reach variability with a variability index that multiplies the friction coefficient and leads to an increased "effective" friction coefficient. An exact expression is derived for the increase in the effective friction coefficient, and we propose an approximation that requires only estimates of the hydraulic parameter variances. We validate the results using a large set of hydraulic models and find that the approximated variability index is most faithful when the river parameters obey lognormal statistics. The effective friction coefficient, which can vary from a few percent to more than 50% of the point friction coefficient, is proportional to the riverbed elevation variance and inversely proportional to the depth. This has significant implications for estimating discharge from SWOT data. Plain Language Summary Information about the amount of fresh water in rivers is decreasing globally due to a loss of maintained gauges. Remote sensors, such as the National Aeronautics and Space Administration/Centre national d'études spatiales Surface Water and Ocean Topography (SWOT) mission, offer the possibility of extending the decaying gauge network by providing global open access data for rivers. However, the SWOT data are unlike the data that hydrologists know. Due to instrument noise, the river width, elevation, and slope will need to be averaged over distances as long as 10 km. Here, we show that these average parameters can be treated using the equations for point measurements, provided the equations replace the friction from the riverbed by a larger effective friction. This increase accounts for the river scales that are unobserved due to averaging. We relate the increase in effective friction to river width, area, and slope variability that may be available through statistical studies or data from complimentary sensors. We find that the effective friction is dependent on the depth of the river, increasing as the river discharge decreases. The predictions from this paper can be incorporated to improve river discharge retrievals from the SWOT mission that will i...