Sampling variance of flood quantiles from the generalised logistic distribution estimated using the method of L-moments

International audienceThe method of L-moments is the recommended method for fitting the three parameters (location, scale and shape) of a Generalised Logistic (GLO) distribution when conducting flood frequency analyses in the UK. This paper examines the sampling uncertainty of quantile estimates obtained using the GLO distribution for single site analysis using the median to estimate the location parameter. Analytical expressions for the mean and variance of the quantile estimates were derived, based on asymptotic theory. This has involved deriving expressions for the covariance between the sampling median (location parameter) and the quantiles of the estimated unit-median GLO distribution (growth curve). The accuracy of the asymptotic approximations for many of these intermediate results and for the quantile estimates was investigated by comparing the approximations to the outcome of a series of Monte Carlo experiments. The approximations were found to be adequate for GLO shape parameter values between ?0.35 and 0.25, which is an interval that includes the shape parameter estimates for most British catchments. An investigation into the contribution of different components to the total uncertainty showed that for large returns periods, the variance of the growth curve is larger than the contribution of the median. Therefore, statistical methods using regional information to estimate the growth curve should be considered when estimating design events at large return periods. Keywords: flood frequency analysis, Flood Estimation Handbook, single site, annual maximum series, Generalised Logistic Distribution, uncertaint

Improving the FEH statistical procedures for flood frequency estimation

This report recommends changes to the procedures contained in the Flood Estimation Handbook (FEH), which have been adopted as standard practice by the principal bodies engaged in flood frequency estimation in the UK and, in particular, by the Environment Agency. These procedures provide estimates of the flows that will occur in rivers on moderately rare occasions: flow values that have an exceedance probability in any given year of 50 per cent (a 2-year return period) to 1 per cent (a 100-year return period), or even more rare. In the majority of cases where such estimates are required, the locations affected will be ungauged and too far from established river gauging stations to provide data records that can be immediately transferred. The changes recommended arise, in part, because the HiFlows-UK project has led to the creation of a much-improved database of systematically recorded flood data. Not only are the data records now much longer than those used previously but the HiFlows-UK project put substantial effort into the quality control and assessment of the whole data-set. This means that the data available for analysis have been dramatically improved. Another influence on the renewed procedures has been feedback from users of the FEH, both informal and formal. Without substantially changing the overall framework of the methodology, most technical details of the method have been updated to improve the performance of the procedure. The updates include significant improvements to the theoretical statistical framework underlying the method. In addition, it has been possible to consider some new descriptors of catchment topography and local climate that have been proposed since the FEH study. In particular, a new descriptor that measures floodplain extent has been devised and is now included in the improved procedures. This report is largely a technical description of the studies that have led to the new recommendations. The folllowing are the key improvements. • A new regression model for estimating the median annual maximum flood (QMED) at ungauged catchments (Chapter 4). • An improved procedure for the use of donor catchments for estimation of QMED at ungauged catchments (Chapter 5). • An improved procedure for formation of pooling groups and estimation of pooled growth curves (Chapter 6). Flood estimates produced by the new procedures can be substantially different from those produced using the original FEH procedures. On taking the catchments whose data have been analysed as typical examples, and treating them as if they were ungauged, the ratios of the new estimates to the FEH estimates indicate the following changes. • The changes in QMED range from 0.55 to 2.01, with half being greater than 1.15 (25 per cent of the ratios are less than 1.00, and 25 per cent are greater than 1.24). • For floods with an annual probability of exceedance of 1 per cent (the 1 per cent flood), the changes range from 0.48 to 2.24, with half being greater than 1.14 (25 per cent of the ratios are less than 0.97 and 25 per cent are greater than 1.32). For both QMED and the 1 per cent flood, the new procedure produced lower estimates than the FEH in the East of England, whereas increases in both quantities were generally observed in West England, Wales and Scotland

The amplitude of solar oscillations using stellar techniques

The amplitudes of solar-like oscillations depend on the excitation and damping, both of which are controlled by convection. Comparing observations with theory should therefore improve our understanding of the underlying physics. However, theoretical models invariably compute oscillation amplitudes relative to the Sun, and it is therefore vital to have a good calibration of the solar amplitude using stellar techniques. We have used daytime spectra of the Sun, obtained with HARPS and UCLES, to measure the solar oscillations and made a detailed comparison with observations using the BiSON helioseismology instrument. We find that the mean solar amplitude measured using stellar techniques, averaged over one full solar cycle, is 18.7 +/- 0.7 cm/s for the strongest radial modes (l=0) and 25.2 +/- 0.9 cm/s for l=1. In addition, we use simulations to establish an equation that estimates the uncertainty of amplitude measurements that are made of other stars, given that the mode lifetime is known. Finally, we also give amplitudes of solar-like oscillations for three stars that we measured from a series of short observations with HARPS (gamma Ser, beta Aql and alpha For), together with revised amplitudes for five other stars for which we have previously published results (alpha Cen A, alpha Cen B, beta Hyi, nu Ind and delta Pav).Comment: 8 pages, accepted by ApJ. Minor wording changes and added a referenc

Assessing the impact of urbanization on storm runoff in a peri-urban catchment using historical change in impervious cover

his paper investigates changes in storm runoff resulting from the transformation of previously rural landscapes into peri-urban areas. Two adjacent catchments (∼5 km2) located within the town of Swindon in the United Kingdom were monitored during 2011 and 2012 providing continuous records of rainfall, runoff and actual evaporation. One catchment is highly urbanized and the other is a recently developed peri-urban area containing two distinct areas of drainage: one with mixed natural and storm drainage pathways, the other entirely storm drainage. Comparison of observed storm hydrographs showed that the degree of area serviced by storm drainage was a stronger determinant of storm runoff response than either impervious area or development type and that little distinction in hydrological response exists between urban and peri-urban developments of similar impervious cover when no significant hydraulic alteration is present. Historical levels of urbanization and impervious cover were mapped from the 1960s to the 2010s based on digitized historical topographic maps and were combined with a hydrological model to enable backcasting of the present day storm runoff response to that of the catchments in their earlier states. Results from the peri-urban catchment showed an increase in impervious cover from 11% in the 1960s to 44% in 2010s, and introduction of a large-scale storm drainage system in the early 2000s, was accompanied by a 50% reduction in the Muskingum routing parameter k, reducing the characteristic flood duration by over 50% while increasing peak flow by over 400%. Comparisons with changes in storm runoff response in the more urban area suggest that the relative increase in peak flows and reduction in flood duration and response time of a catchment is greatest at low levels of urbanization and that the introduction of storm water conveyance systems significantly increases the flashiness of storm runoff above that attributed to impervious area alone. This study demonstrates that careful consideration is required when using impervious cover data within hydrological models and when designing flood mitigation measures, particularly in peri-urban areas where a widespread loss in pervious surfaces and alteration of drainage pathways can significantly alter the storm runoff response. Recommendations include utilizing more refined urban land use typologies that can better represent physical alteration of hydrological pathways

Strong-field ionization of atoms and molecules: The two-term saddle point method

We derive an analytical formula for the ionization rate of neutral atoms and molecules in a strong monochromatic field. Our model is based on the strong-field approximation with transition amplitudes calculated by an extended saddle point method. We show that the present two-term saddle point method reproduces even complicated structures in angular resolved photo electron spectra

Calculating asteroseismic diagrams for solar-like oscillations

With the success of the Kepler and CoRoT missions, the number of stars with detected solar-like oscillations has increased by several orders of magnitude, for the first time we are able to perform large-scale ensemble asteroseismology of these stars. In preparation for this golden age of asteroseismology we have computed expected values of various asteroseismic observables from models of varying mass and metallicity. The relationships between these asteroseismic observables, such as the separations between mode frequencies, are able to significantly constrain estimates of the ages and masses of these stars. We investigate the scaling relation between the large frequency separation, Delta nu, and mean stellar density. Furthermore we present model evolutionary tracks for several asteroseismic diagrams. We have extended the so-called C-D diagram beyond the main sequence to the subgiants and the red-giant branch. We also consider another asteroseismic diagram, the epsilon diagram, which is more sensitive to variations in stellar properties at the subgiant stages and can aid in determining the correct mode identification. The recent discovery of gravity-mode period spacings in red giants forms the basis for a third asteroseismic diagram. We compare the evolutionary model tracks in these asteroseismic diagrams with results from pre-Kepler studies of solar-like oscillations, and early results from Kepler.Comment: 14 pages, 15 figures and 2 tables, accepted for publication in the Astrophysical Journa

Stationary vs non-stationary modelling of flood frequency distribution across northwest England

Extraordinary flood events occurred recently in northwest England, with several severe floods in Cumbria, Lancashire and the Manchester area in 2004, 2009 and 2015. These clustered extraordinary events have raised the question of whether any changes in the magnitude and frequency of river flows in the region can be detected. For this purpose, the annual maximum series of 39 river gauging stations in the study area are analysed. In particular, non-stationary models that include time, annual rainfall and annual temperature as predictors are investigated. Most records demonstrate a marked non-stationary behaviour and an increase of up to 75% in flood quantile estimates during the study period. Annual rainfall explains the largest proportion of variability in the peak flow series relative to other predictors considered in our study, providing practitioners with a useful framework for updating flood quantile estimates based on the dynamics of this highly accessible and informative climate indicator

Solar-like oscillations in the G2 subgiant beta Hydri from dual-site observations

We have observed oscillations in the nearby G2 subgiant star beta Hyi using high-precision velocity observations obtained over more than a week with the HARPS and UCLES spectrographs. The oscillation frequencies show a regular comb structure, as expected for solar-like oscillations, but with several l=1 modes being strongly affected by avoided crossings. The data, combined with those we obtained five years earlier, allow us to identify 28 oscillation modes. By scaling the large frequency separation from the Sun, we measure the mean density of beta Hyi to an accuracy of 0.6%. The amplitudes of the oscillations are about 2.5 times solar and the mode lifetime is 2.3 d. A detailed comparison of the mixed l=1 modes with theoretical models should allow a precise estimate of the age of the star.Comment: 13 pages, 14 figures, accepted by ApJ. Fixed minor typo (ref to Fig 14