•Study about discharge inversion in the context of remotly sensed observations of rivers.•The concept of an effective bathymetry-friction pair is introduced.•Several inverse formulations are proposed ...from the zero inertia shallow water equations, with an inversion algorithm.•Inversions of topography and friction pairs, and discharge are performed and analyzed on a set of synthetic and real river flows.
The future SWOT mission (Surface Water and Ocean Topography) will provide cartographic measurements of inland water surfaces (elevation, widths and slope) at an unprecedented spatial and temporal resolution. Given synthetic SWOT like data, forward flow models of hierarchical-complexity are revisited and few inverse formulations are derived and assessed for retrieving the river low flow bathymetry, roughness and discharge (A0,K,Q). The concept of an effective low flow bathymetry A0 (the real one being never observed) and roughness K, hence an effective river dynamics description, is introduced. The few inverse models elaborated for inferring (A0,K,Q) are analyzed in two contexts: (1) only remotely sensed observations of the water surface (surface elevation, width and slope) are available; (2) one additional water depth measurement (or estimate) is available. The inverse models elaborated are independent of data acquisition dynamics; they are assessed on 91 synthetic test cases sampling a wide range of steady-state river flows (the Froude number varying between 0.05 and 0.5 for 1km reaches) and in the case of a flood on the Garonne River (France) characterized by large spatio-temporal variabilities. It is demonstrated that the most complete shallow-water like model allowing to separate the roughness and bathymetry terms is the so-called low Froude model. In Case (1), the resulting RMSE on infered discharges are on the order of 15% for first guess errors larger than 50%. An important feature of the present inverse methods is the fairly good accuracy of the discharge Q obtained, while the identified roughness coefficient K includes the measurement errors and the misfit of physics between the real flow and the hypothesis on which the inverse models rely; the later neglecting the unobserved temporal variations of the flow and the inertia effects. A compensation phenomena between the indentifiedvalues of K and the unobserved bathymetry A0 is highlighted, while the present inverse models lead to an effective river dynamics model that is accurate in the range of the discharge variability observed. In Case (2), the effective bathymetry profile for 80km of the Garonne River is retrieved with 1% relative error only. Next, accurate effective topography-friction pairs and also discharge can be inferred. Finally, defining river reaches from the observation grid tends to average the river properties in each reach, hence tends to smooth the hydraulic variability.
In this study, rating curves (RCs) were determined by applying satellite altimetry to a poorly gauged basin. This study demonstrates the synergistic application of remote sensing and watershed ...modeling to capture the dynamics and quantity of flow in the Amazon River Basin, respectively. Three major advancements for estimating basin‐scale patterns in river discharge are described. The first advancement is the preservation of the hydrological meanings of the parameters expressed by Manning's equation to obtain a data set containing the elevations of the river beds throughout the basin. The second advancement is the provision of parameter uncertainties and, therefore, the uncertainties in the rated discharge. The third advancement concerns estimating the discharge while considering backwater effects. We analyzed the Amazon Basin using nearly one thousand series that were obtained from ENVISAT and Jason‐2 altimetry for more than 100 tributaries. Discharge values and related uncertainties were obtained from the rain‐discharge MGB‐IPH model. We used a global optimization algorithm based on the Monte Carlo Markov Chain and Bayesian framework to determine the rating curves. The data were randomly allocated into 80% calibration and 20% validation subsets. A comparison with the validation samples produced a Nash‐Sutcliffe efficiency (
Ens) of 0.68. When the MGB discharge uncertainties were less than 5%, the
Ens value increased to 0.81 (mean). A comparison with the in situ discharge resulted in an
Ens value of 0.71 for the validation samples (and 0.77 for calibration). The
Ens values at the mouths of the rivers that experienced backwater effects significantly improved when the mean monthly slope was included in the RC. Our RCs were not mission‐dependent, and the
Ens value was preserved when applying ENVISAT rating curves to Jason‐2 altimetry at crossovers. The cease‐to‐flow parameter of our RCs provided a good proxy for determining river bed elevation. This proxy was validated against Acoustic Doppler current profiler (ADCP) cross sections with an accuracy of more than 90%. Altimetry measurements are routinely delivered within a few days, and this RC data set provides a simple and cost‐effective tool for predicting discharge throughout the basin in nearly real time.
Key Points:
Discharge can be obtained in near‐real‐time from altimetry and rating curve
Including slope in rating curve allows adequate estimate of discharge in backwater conditions
Rating curve parameters provide meaningful information on rivers characteristics
Classical calibration methods in hydrology typically rely on a single cost function computed on long-term streamflow series. Even when hydrological models achieve acceptable scores in NSE and KGE, ...imbalances can still arise between overall model performance and its ability to simulate flood events, particularly flash floods. Multi-scale signatures, which refer to hydrological signatures computed at different temporal and/or spatial scales, and distributed flood modeling, which accounts for spatial variability in input variables and model parameters, are important concepts in hydrological modeling. In this study, the potential of using multi-scale signatures is explored to enhance multi-criteria calibration methods for spatially distributed flood modeling, which remains considerable challenges. We present a novel signatures and sensitivity-based calibration approach implemented into a variational data assimilation algorithm capable to deal with high dimensional spatially distributed hydrological optimization problems. It is tested on 141 flash flood pronecatchments mostly located in the French Mediterranean region. Our approach involves computing several signatures, including flood event signatures, using an automated flood segmentation algorithm. We select suitable signatures for constraining the model based on their global sensitivity with the input parameters through global signature-based sensitivity analysis (GSSA). We then perform two multi-criteria calibration strategies using the selected signatures, including a single-objective optimization approach, which transforms the multi-criteria problem into a single-objective function, and a multi-objective optimization approach, which uses a simple additive weighting method to select an optimal solution from the Pareto set. Our results show significant improvements in both calibration and temporal validation metrics, especially for flood signatures, demonstrating the robustness and delicacy of our signatures-based calibration framework for enhancing flash flood forecasting systems.
•Balancing model performance for flood forecasting by integrating long- and short-term signatures.•Automated flood segmentation algorithm incorporating rainfall characteristics and baseflow separation.•Signatures variance-based sensitivity analysis.•Global calibration with multi-objective functions based on hydrological signatures.•Spatially distributed calibration with signatures-based multi-criteria variational data assimilation.
•Jason-2 altimetry observed water surface height and slope dynamics Yukon River Alaska.•The USGS Dynamic Surface Water Extent applied to Landsat estimated the mean width.•The remote observations were ...used to estimate the river depth, velocity, and discharge.•The remotely sensed discharge was estimated within 5% of measured USGS discharge.•Historical time series of discharge could be developed from archived information.
A methodology based on general hydraulic relations for rivers has been developed to estimate the discharge (flow rate) of rivers using satellite remote sensing observations. The estimates of discharge, flow depth, and flow velocity are derived from remotely observed water surface area, water surface slope, and water surface height, and demonstrated for two reaches of the Yukon River in Alaska, at Eagle (reach length 34.7 km) and near Stevens Village (reach length 38.3 km). The method is based on fundamental equations of hydraulic flow resistance in rivers, including the Manning equation and the Prandtl-von Karman universal velocity distribution equation. The method employs some new hydraulic relations to help define flow resistance and height of the zero flow boundary in the channel. Estimates are made both with and without calibration. The water surface area of the river reach is measured by using a provisional version of the U.S. Geological Survey (USGS) Landsat based product named Dynamic Surface Water Extent (DSWE). The water surface height and slope measurements require a self-consistent datum, and are derived from observations from the Jason-2 satellite altimeter mission. At both reach locations, the Jason-2 radar altimeter non-winter heights consistently tracked the stage recorded at USGS streamgages with a standard deviation of differences (error) during the non-winter periods of less than 7%. Part of the error may be due to differences in the gage and altimeter crossing locations with respect to the range of stage change and the response to changes in discharge at the upstream and downstream locations. For the non-winter periods, the radar derived slope estimates (mean = 0.0003) were constant over the mission lifetime, and in agreement with previously measured USGS water surface slopes and slopes determined from USGS topographic maps. The accuracy of the mean of the uncalibrated daily estimates of discharge varied between reaches, ranging from 13% near Stevens Village (N = 90) to −21% at Eagle (N = 246) based on the absolute error, and 5% to −6% based on the error of the log of the estimates. Calibrating to the mean of USGS daily discharge estimates from the streamflow rating for the same period of record at each streamgage resulted in mean absolute errors ranging from 1% to 2%, and log errors ranging from 1% or less. The error pattern of the estimates shows that without calibration, even though the mean is well simulated, the high and low end values over the range of estimates may have significant bias.
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 among the methods can be important. Finally, we found that at least two methods can work well with the expected amount of measurement error and frequency.
Key Points
The ability of algorithms to produce improved discharge estimates is related to measurable hydraulic properties of the domain
Sampling frequency had little impact on algorithm performance. Algorithms based on unsteady continuity equation experienced bigger impacts
The algorithms were robust to Surface Water and Ocean Topography measurement errors. Best performance found among algorithms using the low Froude approximation
The Surface Water and Ocean Topography (SWOT) mission will vastly expand measurements of global rivers, providing critical new data sets for both gaged and ungaged basins. SWOT discharge products ...(available approximately 1 year after launch) will provide discharge for all river that reaches wider than 100 m. In this paper, we describe how SWOT discharge produced and archived by the US and French space agencies will be computed from measurements of river water surface elevation, width, and slope and ancillary data, along with expected discharge accuracy. We present for the first time a complete estimate of the SWOT discharge uncertainty budget, with separate terms for random (standard error) and systematic (bias) uncertainty components in river discharge time series. We expect that discharge uncertainty will be less than 30% for two-thirds of global reaches and will be dominated by bias. Separate river discharge estimates will combine both SWOT and in situ data; these “gage-constrained” discharge estimates can be expected to have lower systematic uncertainty. Temporal variations in river discharge time series will be dominated by random error and are expected to be estimated within 15% for nearly all reaches, allowing accurate inference of event flow dynamics globally, including in ungaged basins. We believe this level of accuracy lays the groundwork for SWOT to enable breakthroughs in global hydrologic science.
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.
Key Points
Choice of river segmentation strategies affect the quality of reach‐averaged products produced by remote sensing
Reach definition methods based on hydraulic properties of rivers appear to lead to better discharge than reaches of arbitrary lengths
Method for the detection of unlisted hydraulic structures compatible with future SWOT data are proposed and tested
This contribution presents a novel multi-dimensional (multi-D) hydraulic–hydrological
numerical model with variational data assimilation capabilities. It
allows multi-scale modeling over large ...domains, combining in situ
observations with high-resolution hydrometeorology and satellite
data. The multi-D hydraulic model relies on the 2D shallow-water equations
solved with a 1D–2D adapted single finite-volume solver. One-dimensional-like reaches
are built through meshing methods that cause the 2D solver to degenerate
into 1D. They are connected to 2D portions that act as local zooms,
for modeling complex flow zones such as floodplains and confluences,
via 1D-like–2D interfaces. An existing parsimonious hydrological model,
GR4H, is implemented and coupled to the hydraulic model. The forward-inverse
multi-D computational model is successfully validated on virtual
and real cases of increasing complexity, including using the second-order scheme version. Assimilating multiple observations of flow signatures
leads to accurate inferences of multi-variate and spatially distributed
parameters among bathymetry friction, upstream and lateral hydrographs and hydrological model parameters. This notably demonstrates the possibility
for information feedback towards upstream hydrological catchments, that is, backward hydrology. A 1D-like model of part of the Garonne
River is built and accurately reproduces flow lines and propagations
of a 2D reference model. A multi-D model of the complex Adour basin
network, with inflow from the semi-distributed hydrological model, is built.
High-resolution flow simulations are obtained on a large domain, including fine zooms on floodplains, with a relatively low computational cost since the network contains mostly 1D-like reaches. The current work constitutes an upgrade of the DassFlow computational platform. The adjoint of the whole tool chain is obtained by automatic code differentiation.
•Sensitivity of the hydrological response to the spatial characteristic of the forcing.•Test the forecasting capabilities of the FFG using a distributed hydrological model.•New forecasting method ...based on FFG but integrating the spatial forcing variability.
Just as with the storms that cause them, flash floods are highly variable and non-linear phenomena in both time and space; hence understanding and anticipating the genesis of flash floods is far from straightforward. There is therefore a huge requirement for tools with the potential to provide advance warning of situations likely to lead to flash floods, and thus provide additional time for the flood forecasting services. The Flash Flood Guidance (FFG) method is used on US catchments to estimate the average number of inches of rainfall for given durations required to produce flash flooding. This rainfall amount is used afterwards as a flood warning threshold. In Europe, flash floods often occur on small catchments (approximately 100km2) and it has already been shown that the spatial variability of rainfall has a great impact on the catchment response (Le Lay and Saulnier, 2007). Therefore, in this study, an improved FFG method which accounts for rainfall spatial variability is proposed. The objectives of this paper are (i) to assess the FFG method applicability on French Mediterranean catchments with a distributed process-oriented hydrological model and (ii) to assess the effect of the rainfall spatial variability on this method. The results confirm the influence of the spatial variability of rainfall events in relation with its interaction with soil properties.
PDF
