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.

The state estimation of flow demands in gas networks from sparse pressure telemetry

This paper presents novel observer-based techniques for the estimation of flow demands in gas networks, from sparse pressure telemetry. A completely observable model is explored, constructed by incorporating difference equations that assume the flow demands are steady. Since the flow demands usually vary slowly with time, this is a reasonable approximation. Two techniques for constructing robust observers are employed: robust eigenstructure assignment and singular value assignment. These techniques help to reduce the effects of the system approximation. Modelling error may be further reduced by making use of known profiles for the flow demands. The theory is extended to deal successfully with the problem of measurement bias. The pressure measurements available are subject to constant biases which degrade the flow demand estimates, and such biases need to be estimated. This is achieved by constructing a further model variation that incorporates the biases into an augmented state vector, but now includes information about the flow demand profiles in a new form.

The effects of environmental perturbation and measurement error on estimates of the shape parameter in the theta-logistic model of population regulation

The theta-logistic is a widely used generalisation of the logistic model of regulated biological processes which is used in particular to model population regulation. Then the parameter theta gives the shape of the relationship between per-capita population growth rate and population size. Estimation of theta from population counts is however subject to bias, particularly when there are measurement errors. Here we identify factors disposing towards accurate estimation of theta by simulation of populations regulated according to the theta-logistic model. Factors investigated were measurement error, environmental perturbation and length of time series. Large measurement errors bias estimates of theta towards zero. Where estimated theta is close to zero, the estimated annual return rate may help resolve whether this is due to bias. Environmental perturbations help yield unbiased estimates of theta. Where environmental perturbations are large, estimates of theta are likely to be reliable even when measurement errors are also large. By contrast where the environment is relatively constant, unbiased estimates of theta can only be obtained if populations are counted precisely Our results have practical conclusions for the design of long-term population surveys. Estimation of the precision of population counts would be valuable, and could be achieved in practice by repeating counts in at least some years. Increasing the length of time series beyond ten or 20 years yields only small benefits. if populations are measured with appropriate accuracy, given the level of environmental perturbation, unbiased estimates can be obtained from relatively short censuses. These conclusions are optimistic for estimation of theta. (C) 2008 Elsevier B.V All rights reserved.

Cloud droplet size and liquid water path retrievals from zenith radiance measurements: examples from the Atmospheric Radiation Measurement Program and the Aerosol Robotic Network

The ground-based Atmospheric Radiation Measurement Program (ARM) and NASA Aerosol Robotic Net- work (AERONET) routinely monitor clouds using zenith ra- diances at visible and near-infrared wavelengths. Using the transmittance calculated from such measurements, we have developed a new retrieval method for cloud effective droplet size and conducted extensive tests for non-precipitating liquid water clouds. The underlying principle is to combine a liquid-water-absorbing wavelength (i.e., 1640 nm) with a non-water-absorbing wavelength for acquiring information on cloud droplet size and optical depth. For simulated stratocumulus clouds with liquid water path less than 300 g m−2 and horizontal resolution of 201 m, the retrieval method underestimates the mean effective radius by 0.8μm, with a root-mean-squared error of 1.7 μm and a relative deviation of 13%. For actual observations with a liquid water path less than 450 g m−2 at the ARM Oklahoma site during 2007– 2008, our 1.5-min-averaged retrievals are generally larger by around 1 μm than those from combined ground-based cloud radar and microwave radiometer at a 5-min temporal resolution. We also compared our retrievals to those from combined shortwave flux and microwave observations for relatively homogeneous clouds, showing that the bias between these two retrieval sets is negligible, but the error of 2.6 μm and the relative deviation of 22 % are larger than those found in our simulation case. Finally, the transmittance-based cloud effective droplet radii agree to better than 11 % with satellite observations and have a negative bias of 1 μm. Overall, the retrieval method provides reasonable cloud effective radius estimates, which can enhance the cloud products of both ARM and AERONET.