Estimate River Discharge Research Articles

River Discharge and Bathymetry Estimation from Inversion of Surface Currents and Water Surface Elevation Observations

AbstractWe developed an approach for estimating river discharge and water depth from measurements of surface velocity and water surface elevation, based on analytical velocity–depth and velocity–slope relationships derived from the steady gravity–friction momentum balance and mass conservation. A key component in this approach is specifying the influence of bottom friction on the modeled depth-averaged flow. Accordingly, we considered two commonly used bottom friction parameterizations—a depth-independent Darcy friction coefficient and a depth-dependent friction coefficient based on the Manning’s roughness parameter. Assuming that the bottom friction coefficient is known, the unknown discharge was determined by minimizing the difference between the measured total head profile and the one determined from the velocity–slope relationship. The model performance and its sensitivity to key assumptions were evaluated using existing bathymetry data, and surface velocity and elevation observations obtained during field experiments on the Kootenai River near Bonners Ferry, Idaho, and the Hanford reach of the Columbia River. We found that the Manning’s friction parameterization provided superior depth and discharge estimates, compared to the Darcy friction law. For both steady and moderately unsteady flow, inversions based on the Manning’s friction provided discharge and thalweg depth estimates with relative errors not exceeding 5% and 12%, respectively.

Daily River Discharge Estimates by Merging Satellite Optical Sensors and Radar Altimetry Through Artificial Neural Network

Thanks to the large number of satellites, the multimission approach is becoming a viable method to integrate measurements and intensify the number of samples in space and time for monitoring the earth system. In this paper, we merged data from different satellite missions, optical sensors, and altimetry, for estimating daily river discharge through the application of the artificial neural network (ANN) technique. ANN was selected among other retrieval techniques because it offers an easy but effective way of combining input data from different sources into the same retrieval algorithm. The network is trained in a calibration period and validated in an independent period against in situ observations of river discharge for two gauging sites: Lokoja along the Niger River and Pontelagoscuro along the Po River. For optical sensors, we found that the temporal resolution is more important than the spatial resolution for obtaining accurate discharge estimates. Our results show that Landsat fails in the estimation of extreme events by missing most of the peak values due to its long revisit time (14–16 days). Better performances are obtained from Moderate Resolution Imaging Spectroradiometer (MODIS) and Medium Resolution Imaging Spectrometer. Radar altimetry provides results in between MODIS-TERRA and MODIS-AQUA at Lokoja, whereas it outperforms all single optical sensors at Pontelagoscuro. The multimission approach, involving optical sensors and altimetry, is found the most reliable tool to estimate river discharge with a relative root-mean-square error of 0.12% and 0.27% and Nash–Sutcliffe coefficient of 0.98 and 0.83 for the Niger and Po rivers, respectively.

Ensemble learning regression for estimating river discharges using satellite altimetry data: Central Congo River as a Test-bed

Hydraulic variables obtained from remotely sensed data have been successfully used to estimate river discharge (Q). However, most studies have used a rating curve based on a single hydraulic variable or the Manning equation (multiplicative method). In this study, we developed a mathematically different approach to estimating Q by applying the ensemble learning regression method (here termed ELQ), which is one of the machine learning techniques that linearly combine several functions to reduce errors, over the Congo mainstem as a test-bed. Using the training dataset (November 2002 – November 2006) of water levels (H) derived from different Envisat altimetry observations, the ELQ-estimated Q at the Brazzaville in-situ station showed reduced root-mean-square error (RMSE) of 823 m3 s−1 (relative RMSE (RMSE normalized by the average in-situ Q, RRMSE) of 2.08%) compared to the Q obtained using a single rating curve. ELQ also showed improved performance for the validation dataset (December 2006 – September 2010). Based on the error analysis, we found the correlation coefficients between input variables affect the performance of ELQ. Thus, we introduced an index, termed the Degree of compensation (IDoC), which describes how ELQ performs compared to the classic hydraulic relation (e.g., H-Q rating curve). The performance of ELQ improves when IDoC increases because the additional information could be added in the ELQ process. Since ELQ can combine several variables obtained over different locations, it would be advantageous, particularly if there exist few virtual stations along a river reach. It is expected that ELQ can be also applied to the products of the Surface Water Ocean Topography (SWOT) mission, which will provide direct measurements of surface water slope (S), effective river width (We), and H, to be launched in 2021.

Using modelled discharge to develop satellite-based river gauging: a case study for the Amazon Basin

Abstract. River discharge measurements have proven invaluable to monitor the global water cycle, assess flood risk, and guide water resource management. However, there is a delay, and ongoing decline, in the availability of gauging data and stations are highly unevenly distributed globally. While not a substitute for river discharge measurement, remote sensing is a cost-effective technology to acquire information on river dynamics in situations where ground-based measurements are unavailable. The general approach has been to relate satellite observation to discharge measured in situ, which prevents its use for ungauged rivers. Alternatively, hydrological models are now available that can be used to estimate river discharge globally. While subject to greater errors and biases than measurements, model estimates of river discharge do expand the options for applying satellite-based discharge monitoring in ungauged rivers. Our aim was to test whether satellite gauging reaches (SGRs), similar to virtual stations in satellite altimetry, can be constructed based on Moderate Resolution Imaging Spectroradiometer (MODIS) optical or Global Flood Detection System (GFDS) passive microwave-derived surface water extent fraction and simulated discharge from the World-Wide Water (W3) model version 2. We designed and tested two methods to develop SGRs across the Amazon Basin and found that the optimal grid cell selection method performed best for relating MODIS and GFDS water extent to simulated discharge. The number of potential river reaches to develop SGRs increases from upstream to downstream reaches as rivers widen. MODIS SGRs are feasible for more river reaches than GFDS SGRs due to its higher spatial resolution. However, where they could be constructed, GFDS SGRs predicted discharge more accurately as observations were less affected by cloud and vegetation. We conclude that SGRs are suitable for automated large-scale application and offer a possibility to predict river discharge variations from satellite observations alone, for both gauged and ungauged rivers.

Estimation of River Discharge Solely from Remote-Sensing Derived Data: An Initial Study Over the Yangtze River

A novel approach has been developed to estimating river discharge solely using satellite-derived parameters. The temporal river width observations from Moderate Resolution Imaging Spectroradiometer (MODIS), made at two stream segments a distance apart, are plotted to identify the time lag. The river velocity estimate is then computed using the time lag and distance between the width measurement locations, producing a resultant velocity of 0.96 m/s. The estimated velocity is comparable to that computed from in situ gauge-observed data. An empirical relationship is then utilized to estimate river depth. In addition, the channel condition values published in tables are used to estimate the roughness coefficient. The channel slope is derived from the digital elevation model averaged over a river section approximately 516 km long. Finally, the temporal depth changes is captured by adjusting the estimated depth to the Envisat satellite altimetry -derived water level changes, and river width changes from Landsat ETM+. The newly developed procedure was applied to two river sites for validation. In both cases, the river discharges were estimated with reasonable accuracy (with Nash–Sutcliffe values >0.50). The performance evaluation of discharge estimation using satellite-derived parameters was also analyzed. Since the methodology for estimating discharge is solely dependent on global satellite datasets, it represents a promising technique for use on rivers worldwide.

Effects of Input Data Content on the Uncertainty of Simulating Water Resources

The widely used, partly-deterministic Soil and Water Assessment Tool (SWAT) requires a large amount of spatial input data, such as a digital elevation model (DEM), land use, and soil maps. Modelers make an effort to apply the most specific data possible for the study area to reflect the heterogeneous characteristics of landscapes. Regional data, especially with fine resolution, is often preferred. However, such data is not always available and can be computationally demanding. Despite being coarser, global data are usually free and available to the public. Previous studies revealed the importance for single investigations of different input maps. However, it remains unknown whether higher-resolution data can lead to reliable results. This study investigates how global and regional input datasets affect parameter uncertainty when estimating river discharges. We analyze eight different setups for the SWAT model for a catchment in Luxembourg, combining different land-use, elevation, and soil input data. The Metropolis–Hasting Markov Chain Monte Carlo (MCMC) algorithm is used to infer posterior model parameter uncertainty. We conclude that our higher resolved DEM improves the general model performance in reproducing low flows by 10%. The less detailed soil-map improved the fit of low flows by 25%. In addition, more detailed land-use maps reduce the bias of the model discharge simulations by 50%. Also, despite presenting similar parameter uncertainty (P-factor ranging from 0.34 to 0.41 and R-factor from 0.41 to 0.45) for all setups, the results show a disparate parameter posterior distribution. This indicates that no assessment of all sources of uncertainty simultaneously is compensated by the fitted parameter values. We conclude that our result can give some guidance for future SWAT applications in the selection of the degree of detail for input data.

River discharge estimation under uncertainty from synthetic SWOT-type observations using variational data assimilation

Variational data assimilation is used for discharge estimation for the Garonne River downstream reach, using the 1D full Saint-Venant hydraulic model SIC². Based on water surface elevation observations with the level of noise expected for the forthcoming Surface Water and Ocean Topography (SWOT) mission, discharge estimation problem under uncertainty in the bathymetry and the friction has been considered. Two observation sampling periods has been tested, with the purpose of investigating the influence of the temporal frequency of observations. We emphasize that the temporal sampling frequency should be consistent with the characteristic (travel) time of the dynamical system, in which case the discharge is successfully estimated (rRMSE = 4.6%). Larger temporal sampling intervals require complementary information given by a-priori information on discharge or combined in-situ and remote sensing data assimilation. Simultaneous estimation of discharge and the spatially distributed functions may lead to the equifinality issue. In this case, the estimates of the bathymetry and the friction only help to achieve a better estimation quality of discharge, but may not be usable for subsequent experiments.

Discharge Estimation in Ungauged Basins Through Variational Data Assimilation: The Potential of the SWOT Mission

AbstractSpace‐borne instruments can measure river water surface elevation, slope, and width. Remote sensing of river discharge in ungauged basins is far more challenging, however. This work investigates the estimation of river discharge from simulated observations of the forthcoming Surface Water and Ocean Topography (SWOT) satellite mission using a variant of the classical variational data assimilation method “4D‐Var.” The variational assimilation scheme simultaneously estimates discharge, river bathymetry, and bed roughness in the context of a 1.5 D full Saint‐Venant hydraulic model. Algorithms and procedures are developed to apply the method to fully ungauged basins. The method was tested on the Po and Sacramento Rivers. The SWOT hydrology simulator was used to produce synthetic SWOT observations at each overpass time by simulating the interaction of SWOT radar measurements with the river water surface and nearby land surface topography at a scale of approximately 1 m, thus accounting for layover, thermal noise, and other effects. SWOT data products were synthesized by vectorizing the simulated radar returns, leading to height and width estimates at 200 m increments along the river centerlines. The ingestion of simulated SWOT data generally led to local improvements on prior bathymetry and roughness estimates which allowed the prediction of river discharge at the overpass times with relative root mean squared errors of 12.1% and 11.2% for the Po and Sacramento Rivers, respectively. Nevertheless, equifinality issues that arise from the simultaneous estimation of bed elevation and roughness may prevent their use for different applications, other than discharge estimation through the presented framework.

River discharge estimation from synthetic SWOT-type observations using variational data assimilation and the full Saint-Venant hydraulic model

The upcoming Surface Water and Ocean Topography satellite mission, to be launched in 2021, will measure river water surface elevation, slope and width, with an unprecedented level of accuracy for a remote sensing tool. This work investigates the river discharge estimation from synthetic SWOT observations, in the presence of strong uncertainties in the model inputs, i.e. the river bathymetry and bed roughness. The estimation problem is solved by a novel variant of the standard variational data assimilation, the ‘4D-Var’ method, involving the full Saint-Venant 1.5D-network hydraulic model SIC2. The assimilation scheme simultaneously estimates the discharge, bed elevation and bed roughness coefficient and is designed to assimilate both satellite and in situ measurements. The method is tested on a 50 km-long reach of the Garonne River during a five-month period of the year 2010, characterized by multiple flooding events. First, the impact of the sampling frequency on discharge estimation is investigated. Secondly, discharge as well as the spatially distributed bed elevation and bed roughness coefficient are determined simultaneously. Results demonstrate feasibility and efficiency of the chosen combination of the estimation method and of the hydraulic model. Assimilation of the SWOT data results into an accurate estimation of the discharge at observation times, and a local improvement in the bed level and bed roughness coefficient. However, the latter estimates are not generally usable for different independent experiments.

Measuring Mountain River Discharge Using Seismographs Emplaced Within the Hyporheic Zone

AbstractFlow and sediment transport dynamics in fluvial systems play critical roles in shaping river morphology, in the design and use of riverine infrastructure, and in the broader management of watersheds. However, these properties are often difficult to measure comprehensively. Previous work has suggested the use of proximal seismic signals resulting from flow and bed load transport to construct more complete records of these fluvial processes. We investigate a small (184 km2; < 20 m3/s), snowmelt‐fed mountain river in the Northern Colorado Rocky Mountains during May–August 2015 to capture peak runoff with colocated measurements of discharge and seismic noise. Three‐component seismometers were placed in close proximity to the channel bank (~1 m) within the hyporheic zone (at times submerged beneath the water table). We recorded a broad spectrum of seismic signals excited by discharge, including novel, low‐frequency (0.1–2 Hz) signals observed predominantly on the horizontal components. The characteristics of these low‐frequency signals are not consistent with an elastically propagating seismic wave. We instead infer that they likely arise from the sensor tilting in response to viscoelastic deformation occurring near the channel and propose large‐scale turbulent eddies as a forcing mechanism. Calibrating horizontal seismic power with hydrograph flow rates over the course of a rainstorm for individual sensors, we demonstrate that these unique signals can be used to accurately estimate river discharge with simple regressions. This technique shows promise for augmenting seismic monitoring of rivers by enabling discharge rates to be estimated from outside the channel using easily deployed and noninvasive seismic instrumentation.

The Potential Applications of Satellite Altimetry with SARAL/AltiKa for Indian Inland Waters

The satellite radar altimetry datasets are now extensively used for continental water monitoring although it was primarily designed for oceanic surface and ice cap studies. Water level estimated from satellite altimetry can help to assess many hydrological parameters like river discharge and reservoir volume. These parameters can be employed for calibration and validation purposes of hydrological and hydrodynamic models, rating curve (stage-discharge relationship) generation, near real-time flood forecasting, reservoir operations and transboundary water related issues. Satellite with Argos and AltiKa (SARAL/AltiKa), a joint venture of Indian Space Research Organisation and Centre National d’Etudes Spatiales, is one of the pioneer missions in the history of satellite radar altimetry. It is first high-frequency (Ka-band, 35.75 GHz) mission with the highest sampling rate (40 Hz). The applications of radar altimetry to inland hydrology have been significantly increased in recent years in India. Major studies have been carried out in Ganga, Brahmaputra, Tapi and Godavari river basins with AltiKa data. AltiKa datasets have been successfully used for retrieving water level in reservoir and river, estimating river discharge and calculating reservoir sedimentation. Considering the stress on India’s fresh water resources and the importance of SARAL/AltiKa mission, this work was carried out. The present review paper may be helpful to understand the working principle of altimetry, altimetry waveform, waveform retracking methods, water stage, river discharge and changes in reservoir’s water storage calculation, and the status of altimetry applications to inland hydrology, specifically solicitation of SARAL/AltiKa in the Indian context.

Impact of forest maintenance on water shortages: Hydrologic modeling and effects of climate change

The importance of water quantity for domestic and industrial water supply, agriculture, and the economy more broadly has led to the development of many water quantity assessment methods. In this study, surface flow and soil water in the forested upper reaches of the Yoshino River are compared using a distributed hydrological model with Forest Maintenance Module under two scenarios; before and after forest maintenance. We also examine the impact of forest maintenance on these variables during extreme droughts. Results show that surface flow and soil water increased after forest maintenance. In addition, projections of future water resources were estimated using a hydrological model and the output from a 20km mesh Global Climate Model (GCM20). River discharge for the near-future (2015–2039) is similar to that of the present (1979–2003). Estimated river discharge for the future (2075–2099) was found to be substantially more extreme than in the current period, with 12m3/s higher peak discharge in August and 7m3/s lower in July compared to the discharges of the present period. Soil water for the future is estimated to be lower than for the present and near future in May. The methods discussed in this study can be applied in other regions and the results help elucidate the impact of forests and climate change on water resources.

Estimating River Depth from SWOT-Type Observables Obtained by Satellite Altimetry and Imagery

The proposed Surface Water and Ocean Topography (SWOT) mission aims to improve spaceborne estimates of river discharge through its measurements of water surface elevation, river width and slope. SWOT, however, will not observe baseflow depth, which limits its value in estimating river discharge especially for those rivers with heterogeneous channel geometry. In this study, we aim to obtain river depths from spaceborne observations together with in situ data of river discharge. We first obtain SWOT-like observables from current satellite techniques. We obtain river water level and slope time series from multi-mission altimetry and effective river width from satellite imagery (MODIS). We then employ a Gauss–Helmert adjustment model to estimate average river depth for 16 defined reaches along the Po River in Italy, for which we use our spaceborne observations in two recognized models for discharge estimation. The average river depth estimates along the Po River are validated against surveyed cross-section information, which shows a generally good agreement in the range of ∼10% relative root mean squared error. Furthermore, we analyzed the sensitivity of error in the estimated river depth to errors of individual parameters. We show that the estimated river depth is less influenced by errors of river width and river discharge, while it is strongly influenced by errors in water level. This result gives a perspective to the SWOT mission to infer river depth by coarse estimates of river width and discharge.

A Muskingum-based methodology for river discharge estimation and rating curve development under significant lateral inflow conditions

Quite often the discharge at a site is estimated using the rating curve developed for that site and its development requires river flow measurements, which are costly, tedious and dangerous during severe floods. To circumvent the conventional rating curve development approach, Perumal et al. in 2007 and 2010 applied the Variable Parameter Muskingum Stage-hydrograph (VPMS) routing method for developing stage-discharge relationships especially at those ungauged river sites where stage measurements and details of section geometry are available, but discharge measurements are not made. The VPMS method enables to estimate rating curves at ungauged river sites with acceptable accuracy. But the application of the method is subjected to the limitation of negligible presence of lateral flow within the routing reach. To overcome this limitation, this study proposes an extension of the VPMS method, henceforth, known herein as the VPMS-Lin method, for enabling the streamflow assessment even when significant lateral inflow occurs along the river reach considered for routing. The lateral inflow is estimated through the continuity equation expressed in the characteristic form asadvocated by Barbetta et al. in 2012.The VPMS-Lin, is tested on two rivers characterized by different geometric and hydraulic properties: 1) a 50km reach of the Tiber River in (central Italy) and 2) a 73km reach of the Godavari River in the peninsular India. The study demonstrates that both the upstream and downstream discharge hydrographs are well reproduced, with a root mean square error equal on average to about 35 and 1700m3s−1 for the Tiber River and the Godavari River case studies, respectively. Moreover, simulation studies carried out on a river stretch of the Tiber River using the one-dimensional hydraulic model MIKE11 and the VPMS-Lin models demonstrate the accuracy of the VMPS-Lin model, which besides enabling the estimation of streamflow, also enables the estimation of reach averaged optimal roughness coefficients for the considered routing events.

Spatio-temporal monitoring of suspended sediments in the Solimões River (2000–2014)

The Amazon River sediment discharge has been estimated at between 600 and 1200Mt/year, of which more than 50% comes from the Solimões River. Because of the area's inaccessibility, few studies have examined the sediment discharge spatial and temporal pattern in the upper Solimões region. In this study, we use MODIS satellite images to retrieve and understand the spatial and temporal behaviour of suspended sediments in the Solimões River from Peru to Brazil. Six virtual suspended sediment gauging stations were created along the Solimões River on a 2050-km-long transect. At each station, field-derived river discharge estimates were available and field-sampling trips were conducted for validation of remote-sensing estimates during different periods of the annual hydrological cycle between 2007 and 2014. At two stations, 10-day surface suspended sediment data were available from the SO-HYBAM monitoring program (881 field SSS samples). MODIS-derived sediment discharge closely matched the field observations, showing a relative RMSE value of 27.3% (0.48Mtday) overall. Satellite-retrieved annual sediment discharge at the Tamshiyacu (Peru) and Manacapuru (Brazil) stations is estimated at 521 and 825Mt/year, respectively. While upstream the river presents one main sediment discharge peak during the hydrological cycle, a secondary sediment discharge peak is detected downstream during the declining water levels, which is induced by sediment resuspension from the floodplain, causing a 72% increase on average from June to September.

Estimating discharge in gravel‐bed river using non‐contact ground‐penetrating and surface‐velocity radars

AbstractDischarge measurement is a critical task for gravel‐bed channels. Under high‐flow conditions, the elevation of the riverbed changes significantly by intensive torrential flow. The stage–discharge relations commonly used for stream discharge estimation may no longer be adequate. The contact‐type velocity measuring is also subject to measurement errors and/or instrument failures by the high‐flow velocities, driftwood, stumps, and debris. This study developed a new real‐time method to estimate river discharge in gravel‐bed channels. A systematic measuring technology combining ground‐penetrating radar and surface‐velocity radar was employed. The rating curves representing the relations of water surface velocity to the channel cross‐sectional mean velocity and flow area were established. Stream discharge was then deduced from the resulting mean velocity and flow area. The proposed method was examined in a steep gravel‐bed reach of the Cho‐Shui River in central Taiwan. The estimated stream discharge during three flood events were compared to the prediction by using the stage–discharge relation and the index‐velocity method. The proposed method of this study is capable of computing reasonable values of discharge for an entire flood hydrograph, whereas the other two methods tend to produce large extrapolation errors. Moreover, when the computed discharge is used in 2D flood flow simulation, the proposed method demonstrates better performance than the commonly used stage–discharge and index‐velocity methods.

Estimation of River Discharge at Ungauged Catchment using GIS Map Correlation Method as Applied in Sta. Lucia River in Mauban, Quezon, Philippines

This paper presents use of GIS Map Correlation Method, a novel method of Prediction of Ungauged Basin, which is used to estimate the river flow at an ungauged catchment. The PUB Method used here intends to reduce the time and costs of data gathering procedure since it will just rely on a reference calibrated watershed that has almost the same characteristics in terms of slope, curve number, land cover, climatic condition, and average basin elevation. Furthermore, this utilized a set of modelling software which used digital elevation models (DEM), rainfall and discharge data. The researchers estimated the river flow of Sta. Lucia River in Quezon province, which is the ungauged catchment. The researchers assessed 11 gauged catchments and determined which basin could be correlated to Sta. Lucia. After finding the most correlated basin, the researchers used the data considering adjusted parameters of the gauged catchment. In evaluating the accuracy of the method, the researchers simulated a rainfall event in the said catchment and compared the actual discharge and the generated discharge from HEC-HMS. The researchers found out that method showed a good fit in the compared results, proving GMC Method is effective for use in the calibration of ungauged catchments.

Discharge estimation and forecasting by MODIS and altimetry data in Niger-Benue River

Flooding is one of the most devastating natural hazards in the world and its forecast is essential in flood risk reduction and disaster response decision. The lack of adequate monitoring networks, especially in developing countries prevents near real-time flood prediction that could help to reduce the loss of lives and economic damages. In the last few years, increasing availability of multi-satellite sensors induced to develop new techniques for retrieving river discharge and especially in supporting discharge nowcasting and forecasting activities. Recently, the potential of radar altimetry to estimate water levels and discharge in ungauged river sites with good accuracy has been demonstrated. However, the considerable benefit derived from this technique is attenuated by the low revisit time of the satellite (10 or 35days, depending on the satellite mission) causing delays on the predicting operations. For this reason, sensors with a higher temporal resolution such as the MODerate resolution Imaging Spectroradiometer (MODIS), working in visible/Infra-Red bands, can support flood forecasting.In this study, we performed the forecast of river discharge by using MODIS and we compared it with the radar altimetry and in-situ data along the Niger-Benue River in Nigeria to develop an operational flood forecasting scheme that could help in rapid emergency response and decision making processes. In the first step, four MODIS products (daily and, 8-day from the TERRA and AQUA satellites) at two gauged sites were used for discharge estimation. Secondly, the capability of remote sensing sensors to forecast discharge a few days (~4days) in advance at a downstream section using MODIS is analyzed and also compared with the one obtained by the use of radar altimetry by ENVISAT and Jason-2.The results confirmed the capability of the MODIS data to estimate river discharge with performance indices >0.97 and 0.95 in terms of coefficient of correlation and Nash Sutcliffe efficiency. In particular, RMSE does not exceed 1300m3/s and the fractional RMSE ranges between 0.15 and 0.23. For the forecasting exercise, both altimetry and MODIS provide satisfactory results with positive coefficient of persistence considering 4days of lead time (>0.34). Although altimetry was found to be more accurate in the forecasting of river discharge (RMSE ~350m3/s), the much higher temporal resolution of MODIS guarantees a continuity that is more suitable to address operational activities.

Simple statistical models for relating river discharge with precipitation and air temperature—Case study of River Vouga (Portugal)

Simple statistical models were developed to relate available meteorological data with daily river discharge (RD) for rivers not influenced by melting of ice and snow. In a case study of the Vouga River (Portugal), the RD could be determined by a linear combination of the recent (PR) and non-recent (PNR) atmospheric precipitation history. It was found that a simple linear model including only PR and PNR cannot account for low RD. The model was improved by including non-linear terms of precipitation that accounted for the water loss. Additional improvement of the models was possible by including average monthly air temperature (T). The best model was robust when up to 60% of the original data were randomly removed. The advantage is the simplicity of the models, which take into account only PR, PNR and T. These models can provide a useful tool for RD estimation from current meteorological data.

River discharge estimation at daily resolution from satellite altimetry over an entire river basin

One of the main challenges of hydrological modeling is the poor spatiotemporal coverage of in situ discharge databases which have steadily been declining over the past few decades. It has been demonstrated that water heights over rivers from satellite altimetry can sensibly be used to deal with the growing lack of in situ discharge data. However, the altimetric discharge is often estimated from a single virtual station suffering from coarse temporal resolution, sometimes with data outages, poor modeling and inconsistent sampling. In this study, we propose a method to estimate daily river discharge using altimetric time series of an entire river basin including its tributaries. Here, we implement a linear dynamic model to (1) provide a scheme for data assimilation of multiple altimetric discharge along a river; (2) estimate daily discharge; (3) deal with data outages, and (4) smooth the estimated discharge. The model consists of a stochastic process model that benefits from the cyclostationary behavior of discharge. Our process model comprises the covariance and cross-covariance information of river discharge at different gauges. Combined with altimetric discharge time series, we solve the linear dynamic system using the Kalman filter and smoother providing unbiased discharge with minimum variance. We evaluate our method over the Niger basin, where we generate altimetric discharge using water level time series derived from missions ENVISAT, SARAL/AltiKa, and Jason-2. Validation against in situ discharge shows that our method provides daily river discharge with an average correlation of 0.95, relative RMS error of 12%, relative bias of 10% and NSE coefficient of 0.7. Using a modified NSE-metric, that assesses the non-cyclostationary behavior, we show that our estimated discharge outperforms available legacy mean daily discharge.