Satellite-supported flood forecasting in river networks: a real case study

Satellite-based (e.g., Synthetic Aperture Radar [SAR]) water level observations (WLOs) of the floodplain can be sequentially assimilated into a hydrodynamic model to decrease forecast uncertainty. This has the potential to keep the forecast on track, so providing an Earth Observation (EO) based flood forecast system. However, the operational applicability of such a system for floods developed over river networks requires further testing. One of the promising techniques for assimilation in this field is the family of ensemble Kalman (EnKF) filters. These filters use a limited-size ensemble representation of the forecast error covariance matrix. This representation tends to develop spurious correlations as the forecast-assimilation cycle proceeds, which is a further complication for dealing with floods in either urban areas or river junctions in rural environments. Here we evaluate the assimilation of WLOs obtained from a sequence of real SAR overpasses (the X-band COSMO-Skymed constellation) in a case study. We show that a direct application of a global Ensemble Transform Kalman Filter (ETKF) suffers from filter divergence caused by spurious correlations. However, a spatially-based filter localization provides a substantial moderation in the development of the forecast error covariance matrix, directly improving the forecast and also making it possible to further benefit from a simultaneous online inflow error estimation and correction. Additionally, we propose and evaluate a novel along-network metric for filter localization, which is physically-meaningful for the flood over a network problem. Using this metric, we further evaluate the simultaneous estimation of channel friction and spatially-variable channel bathymetry, for which the filter seems able to converge simultaneously to sensible values. Results also indicate that friction is a second order effect in flood inundation models applied to gradually varied flow in large rivers. The study is not conclusive regarding whether in an operational situation the simultaneous estimation of friction and bathymetry helps the current forecast. Overall, the results indicate the feasibility of stand-alone EO-based operational flood forecasting.

The reception of T. S. Bayer’s 'Historia Regni Graecorum Bactriani' (1738)

Theophilus (Gottlieb) Siegfried Bayer (1694-1738) is usually credited as the first person in modern times to address the history of the Greeks in Bactria in a serious way. Bayer’s Historia Regni Graecorum Bactriani, brings together numismatic and historical research. He describes two Graeco-Bactrian coins which he was able to examine first hand, and collects and comments upon the Classical historical sources on the Greek kingdoms of Bactria and India. It was published in St. Petersburg in 1738, where Bayer, a German, held an academic position. In this short article, I am interested in two questions surrounding the Historia Regni Graecorum Bactriani. First (and relatively briefly), how Bayer conducted his research without first hand access to source material and without himself travelling in Bactria – or indeed further east than St. Petersburg. Secondly, the way in which Bayer’s scholarship was received by some of his contemporaries and by later writers, outside the field of Bactrian studies.

Recent lake-level and outflow variations at Lake Viljandi, Estonia: validation of a coupled lake-catchment modelling scheme for climate change studies

Changes in the depth of Lake Viljandi between 1940 and 1990 were simulated using a lake water and energy-balance model driven by standard monthly weather data. Catchment runoff was simulated using a one-dimensional hydrological model, with a two-layer soil, a single-layer snowpack, a simple representation of vegetation cover and similarly modest input requirements. Outflow was modelled as a function of lake level. The simulated record of lake level and outflow matched observations of lake-level variations (r = 0.78) and streamflow (r = 0.87) well. The ability of the model to capture both intra- and inter-annual variations in the behaviour of a specific lake, despite the relatively simple input requirements, makes it extremely suitable for investigations of the impacts of climate change on lake water balance.

Simulation of long-term thermal characteristics of three Estonian lakes

A one-dimensional surface energy-balance lake model, coupled to a thermodynamic model of lake ice, is used to simulate variations in the temperature of and evaporation from three Estonian lakes: Karujärv, Viljandi and Kirjaku. The model is driven by daily climate data, derived by cubic-spline interpolation from monthly mean data, and was run for periods of 8 years (Kirjaku) up to 30 years (Viljandi). Simulated surface water temperature is in good agreement with observations: mean differences between simulated and observed temperatures are from −0.8°C to +0.1°C. The simulated duration of snow and ice cover is comparable with observed. However, the model generally underpredicts ice thickness and overpredicts snow depth. Sensitivity analyses suggest that the model results are robust across a wide range (0.1–2.0 m−1) of lake extinction coefficient: surface temperature differs by less than 0.5°C between extreme values of the extinction coefficient. The model results are more sensitive to snow and ice albedos. However, changing the snow (0.2–0.9) and ice (0.15–0.55) albedos within realistic ranges does not improve the simulations of snow depth and ice thickness. The underestimation of ice thickness is correlated with the overestimation of snow cover, since a thick snow layer insulates the ice and limits ice formation. The overestimation of snow cover results from the assumption that all the simulated winter precipitation occurs as snow, a direct consequence of using daily climate data derived by interpolation from mean monthly data.

Efficient incorporation of channel cross-section geometry uncertainty into regional and global scale flood inundation models

This paper investigates the challenge of representing structural differences in river channel cross-section geometry for regional to global scale river hydraulic models and the effect this can have on simulations of wave dynamics. Classically, channel geometry is defined using data, yet at larger scales the necessary information and model structures do not exist to take this approach. We therefore propose a fundamentally different approach where the structural uncertainty in channel geometry is represented using a simple parameterization, which could then be estimated through calibration or data assimilation. This paper first outlines the development of a computationally efficient numerical scheme to represent generalised channel shapes using a single parameter, which is then validated using a simple straight channel test case and shown to predict wetted perimeter to within 2% for the channels tested. An application to the River Severn, UK is also presented, along with an analysis of model sensitivity to channel shape, depth and friction. The channel shape parameter was shown to improve model simulations of river level, particularly for more physically plausible channel roughness and depth parameter ranges. Calibrating channel Manning’s coefficient in a rectangular channel provided similar water level simulation accuracy in terms of Nash-Sutcliffe efficiency to a model where friction and shape or depth were calibrated. However, the calibrated Manning coefficient in the rectangular channel model was ~2/3 greater than the likely physically realistic value for this reach and this erroneously slowed wave propagation times through the reach by several hours. Therefore, for large scale models applied in data sparse areas, calibrating channel depth and/or shape may be preferable to assuming a rectangular geometry and calibrating friction alone.

Re-creation of heathland on improved pasture using topsoil removal and sulphur amendments: edaphic drivers and impacts on ericoid mycorrhizas

Understanding the factors that drive successful re-creation and restoration of lowland heaths is crucially important for achieving the long-term conservation of this threatened habitat type. In this study we investigated the changes in soil chemistry, plant community and interactions between Calluna vulgaris and symbiotic ericoid mycorrhizas (ERM) that occurred when improved pasture was subjected to one of three treatments (i) acidification with elemental sulphur (ii) acidification with ferrous sulphur (iii) removal of the topsoil. We found that the soil stripping treatment produced the greatest reduction in available phosphate but did not decrease soil pH. Conversely, acidification with elemental sulphur decreased pH but increased availability of phosphate and potentially toxic cations. The elemental sulphur treatment produced plant communities that most closely resembled those on surrounding heaths and acid grasslands. The most important driver was low pH and concomitant increased availability of potentially toxic cations. Plant community development was found to be little related to levels of available soil phosphate, particularly at low pH. The elemental sulphur treatment also produced the best germination and growth of C. vulgaris over 4–5 years. However, this treatment was found to inhibit the development of symbiotic relationships between C. vulgaris and ERM. This may affect the long-term persistence of re-created vegetation and its interactions with other components of heathland communities.

Spectral analysis and the Aharonov-Bohm\~ effect on certain almost-Riemannian manifold

We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl's law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalised Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator.

Accumulation of complex eigenvalues of an indefinite Sturm--Liouville operator with a shifted Coulomb potential

For a particular family of long-range potentials V, we prove that the eigenvalues of the indefinite Sturm–Liouville operator A = sign(x)(−Δ+V(x)) accumulate to zero asymptotically along specific curves in the complex plane. Additionally, we relate the asymptotics of complex eigenvalues to the two-term asymptotics of the eigenvalues of associated self-adjoint operators.

The problem of two fixed centers: bifurcation diagram for positive energies

We give a comprehensive analysis of the Euler-Jacobi problem of motion in the field of two fixed centers with arbitrary relative strength and for positive values of the energy. These systems represent nontrivial examples of integrable dynamics and are analysed from the point of view of the energy-momentum mapping from the phase space to the space of the integration constants. In this setting, we describe the structure of the scattering trajectories in phase space and derive an explicit description of the bifurcation diagram, i.e., the set of critical value of the energy-momentum map.

Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two

We consider the billiard dynamics in a non-compact set of ℝ d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called quenched random Lorentz tube. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.

Recurrence for quenched random Lorentz tubes

We consider the billiard dynamics in a striplike set that is tessellated by countably many translated copies of the same polygon. A random configuration of semidispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global choice of scatterers, is called quenched random Lorentz tube. We prove that under general conditions, almost every system in the ensemble is recurrent.

How do people perceive, understand, and anticipate responding to flash flood risks and warnings? Results from a public survey in Boulder, Colorado, USA

This study investigates flash flood forecast and warning communication, interpretation, and decision making, using data from a survey of 418 members of the public in Boulder, Colorado, USA. Respondents to the public survey varied in their perceptions and understandings of flash flood risks in Boulder, and some had misconceptions about flash flood risks, such as the safety of crossing fast-flowing water. About 6% of respondents indicated consistent reversals of US watch-warning alert terminology. However, more in-depth analysis illustrates the multi-dimensional, situationally dependent meanings of flash flood alerts, as well as the importance of evaluating interpretation and use of warning information along with alert terminology. Some public respondents estimated low likelihoods of flash flooding given a flash flood warning; these were associated with lower anticipated likelihood of taking protective action given a warning. Protective action intentions were also lower among respondents who had less trust in flash flood warnings, those who had not made prior preparations for flash flooding, and those who believed themselves to be safer from flash flooding. Additional analysis, using open-ended survey questions about responses to warnings, elucidates the complex, contextual nature of protective decision making during flash flood threats. These findings suggest that warnings can play an important role not only by notifying people that there is a threat and helping motivate people to take protective action, but also by helping people evaluate what actions to take given their situation.