Estimating discharge from inundation imagery

Remote sensing from space-borne platforms is often seen as an appealing method of monitoring components of the hydrological cycle, including river discharge, due to its spatial coverage. However, data from these platforms is often less than ideal because the geophysical properties of interest are rarely measured directly and the measurements that are taken can be subject to significant errors. This study assimilated water levels derived from a TerraSAR-X synthetic aperture radar image and digital aerial photography with simulations from a two dimensional hydraulic model to estimate discharge, inundation extent, depths and velocities at the confluence of the rivers Severn and Avon, UK. An ensemble Kalman filter was used to assimilate spot heights water levels derived by intersecting shorelines from the imagery with a digital elevation model. Discharge was estimated from the ensemble of simulations using state augmentation and then compared with gauge data. Assimilating the real data reduced the error between analyzed mean water levels and levels from three gauging stations to less than 0.3 m, which is less than typically found in post event water marks data from the field at these scales. Measurement bias was evident, but the method still provided a means of improving estimates of discharge for high flows where gauge data are unavailable or of poor quality. Posterior estimates of discharge had standard deviations between 63.3 m3s-1 and 52.7 m3s-1, which were below 15% of the gauged flows along the reach. Therefore, assuming a roughness uncertainty of 0.03-0.05 and no model structural errors discharge could be estimated by the EnKF with accuracy similar to that arguably expected from gauging stations during flood events. Quality control prior to assimilation, where measurements were rejected for being in areas of high topographic slope or close to tall vegetation and trees, was found to be essential. The study demonstrates the potential, but also the significant limitations of currently available imagery to reduce discharge uncertainty in un-gauged or poorly gauged basins when combined with model simulations in a data assimilation framework.

Statistical downscaling of river flows

An extensive statistical ‘downscaling’ study is done to relate large-scale climate information from a general circulation model (GCM) to local-scale river flows in SW France for 51 gauging stations ranging from nival (snow-dominated) to pluvial (rainfall-dominated) river-systems. This study helps to select the appropriate statistical method at a given spatial and temporal scale to downscale hydrology for future climate change impact assessment of hydrological resources. The four proposed statistical downscaling models use large-scale predictors (derived from climate model outputs or reanalysis data) that characterize precipitation and evaporation processes in the hydrological cycle to estimate summary flow statistics. The four statistical models used are generalized linear (GLM) and additive (GAM) models, aggregated boosted trees (ABT) and multi-layer perceptron neural networks (ANN). These four models were each applied at two different spatial scales, namely at that of a single flow-gauging station (local downscaling) and that of a group of flow-gauging stations having the same hydrological behaviour (regional downscaling). For each statistical model and each spatial resolution, three temporal resolutions were considered, namely the daily mean flows, the summary statistics of fortnightly flows and a daily ‘integrated approach’. The results show that flow sensitivity to atmospheric factors is significantly different between nival and pluvial hydrological systems which are mainly influenced, respectively, by shortwave solar radiations and atmospheric temperature. The non-linear models (i.e. GAM, ABT and ANN) performed better than the linear GLM when simulating fortnightly flow percentiles. The aggregated boosted trees method showed higher and less variable R2 values to downscale the hydrological variability in both nival and pluvial regimes. Based on GCM cnrm-cm3 and scenarios A2 and A1B, future relative changes of fortnightly median flows were projected based on the regional downscaling approach. The results suggest a global decrease of flow in both pluvial and nival regimes, especially in spring, summer and autumn, whatever the considered scenario. The discussion considers the performance of each statistical method for downscaling flow at different spatial and temporal scales as well as the relationship between atmospheric processes and flow variability.

Efficient shock capturing for isentropic flows using arithmetic averaging

A shock capturing scheme is presented for the equations of isentropic flow based on upwind differencing applied to a locally linearized set of Riemann problems. This includes the two-dimensional shallow water equations using the familiar gas dynamics analogy. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency, leading to arithmetic averaging. This is in contrast to usual ‘square root’ averages found in this type of Riemann solver where the computational expense can be prohibitive. The scheme is applied to a two-dimensional dam-break problem and the approximate solution compares well with those given by other authors.