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The reflection on the long persistence of unsatisfactory results, has led us to upset the most common idea of fraction: fraction-of-something. To this, we have: (a) corrected the “primitive intuition” of fraction by constructing an “intuitive representation”, (b) set the familiarization of children with fractions as a goal, and (c) practiced the idea of fraction as megaconcept. In our enquiring we have focused on the Pythagorean statement: the comparison is a logos. This latter is like a modern act of mathematisation of the comparison and it is the starting point of our didactic practice. It has the following features: (a) it is imposed, (b) it is a leap, (c) it is elementary, (d) it is an axios, (e) it has the characteristic of resence/absence along the path towards the megaconcept.

The current work addresses one of the key building blocks towards an improved understanding of flood processes and associated changes in flood characteristics and regimes in Europe: the development of a comprehensive, extensive European flood database. The presented work results from ongoing cross-border research collaborations initiated with data collection and joint interpretation in mind. A detailed account of the current state, characteristics and spatial and temporal coverage of the European Flood Database, is presented. At this stage, the hydrological data collection is still growing and consists at this time of annual maximum and daily mean discharge series, from over 7000 hydrometric stations of various data series lengths. Moreover, the database currently comprises data from over 50 different data sources. The time series have been obtained from different national and regional data sources in a collaborative effort of a joint European flood research agreement based on the exchange of data, models and expertise, and from existing international data collections and open source websites. These ongoing efforts are contributing to advancing the understanding of regional flood processes beyond individual country boundaries and to a more coherent flood research in Europe.

Monthly duration curves have been constructed from climate data across Europe to help address the relative frequency of ecologically critical low flow stages in temporary rivers, when flow persists only in disconnected pools in the river bed. The hydrological model is based on a partitioning of precipitation to estimate water available for evapotranspiration and plant growth and for residual runoff. The duration curve for monthly flows has then been analysed to give an estimate of bankfull flow based on recurrence interval. The corresponding frequency for pools is then based on the ratio of bank full discharge to pool flow, arguing from observed ratios of cross-sectional areas at flood and low flows to estimate pool flow as 0.1% of bankfull flow, and so estimate the frequency of the pool conditions that constrain survival of river-dwelling arthropods and fish. The methodology has been applied across Europe at 15 km resolution, and can equally be applied under future climatic scenarios. © 2011 Author(s).

The paper uses a simple water balance model that partitions the precipitation between actual evapotranspiration, quick flow and delayed flow, and has sufficient complexity to capture the essence of climate and vegetation controls on this partitioning. Using this model, monthly flow duration curves have been constructed from climate data across Europe to address the relative frequency of ecologically critical low flow stages in semi-arid rivers, when flow commonly persists only in disconnected pools in the river bed. The hydrological model is based on a dynamic partitioning of precipitation to estimate water available for evapotranspiration and plant growth and for residual runoff. The duration curve for monthly flows has then been analysed to give an estimate of bankfull flow based on recurrence interval. Arguing from observed ratios of cross-sectional areas at flood and low flows, hydraulic geometry suggests that disconnected flow under >pool> conditions is approximately 0.1% of bankfull flow. Flow duration curves define a measure of bankfull discharge on the basis of frequency. The corresponding frequency for pools is then read from the duration curve, using this (0.1%) ratio to estimate pool discharge from bank full discharge. The flow duration curve then provides an estimate of the frequency of poorly connected pool conditions, corresponding to this discharge, that constrain survival of river-dwelling arthropods and fish. The methodology has here been applied across Europe at 15 km resolution, and the potential is demonstrated for applying the methodology under alternative climatic scenarios.

The Flood Estimation Handbook (FEH) was published in 1999 and has effectively become the national standard for flood frequency estimation in the UK. The FEH, which encompasses a suite of methods for statistical frequency analysis of rainfall and floods, was innovative both in its use of digital catchment information and in the way that data from a number of sites can be pooled together to improve the quality of estimates at gauged and ungauged sites. The major benefits of the FEH have been seen in improved risk management and policy implementation, and have had a considerable impact on the UK economy. This paper considers each of the three key components of the FEH, the rainfall frequency model, the statistical approach to flood frequency estimation and the rainfall-runoff method, and describes how recent and ongoing research is leading to methodological improvements. In the case of rainfall frequency, research related to reservoir safety assessment funded by Defra is currently revising the FEH depth-duration-frequency model for return periods of 100 to over 10,000 years. An Environment Agency-funded project to update the FEH statistical flood frequency procedures has built on theoretical developments together with the availability of flood peak data from HiFlows-UK, resulting in substantial improvements to the predictive capability of the method. Finally, the rainfall-runoff method, which was originally developed as part of the 1975 Flood Studies Report, has been replaced by the ReFH model for design hydrograph analysis. Other related aspects of the FEH are also being explored, for example the development of new flood risk maps based on the revised methods together with high resolution digital terrain models. Current research is focusing on comparisons with the results of so-called next generation methods based on a continuous simulation approach. An important aspect of the development of FEH methods is putting the theory into practice and the paper highlights how

This paper investigates a new approach to spatial generalisation of rainfall–runoff model parameters – site-similarity with pooling groups – for use in flood frequency estimation at ungauged sites using continuous simulation. The method is developed for the generalisation of a simple conceptual model, the Probability Distributed Model, with four parameters which require specific estimation. The study is based on a relatively large sample of catchments in Great Britain. Various options are investigated within the approach. In the final version, the pooling group comprises the 10 calibrated catchments closest, in catchment property space, to the target site, where the catchment properties used to define the space differ for each parameter of the model. An analysis that, explicitly, takes account of calibration uncertainty as a source of error enables the uncertainty associated with generalised parameter values to be reduced, justifiably. The approach uses calibration uncertainty estimated through jack-knifing and employs a weighting scheme within pooling groups that uses weights which vary both with distance in the catchment property space and with the calibration uncertainty. Models using generalised values from this approach perform relatively well compared with direct calibration. Although performance appears to be better in some areas of the country than others, there are no obvious relationships between catchment properties and performance.

The depth–duration–frequency (DDF) model developed as part of the Flood Estimation Handbook (FEH) enables estimates of design rainfall to be made at any location in the UK. This study presents a shortcut method for estimating seasonal design rainfall for a summer and winter season, respectively, using a simple seasonal correction factor in combination with the FEH DDF estimate of design rainfall. The seasonal correction factors were derived for the summer and winter season for a range of durations. The observed correction factors were linked to standard average annual rainfall available from the FEH CD-ROM, thereby enabling the use of this method at any location in the UK. The results obtained in this study are shown to correspond well to the summary statistics on seasonal rainfall presented in the Flood Studies Report.

This study investigated whether pituicytes were able to produce and release nitric oxide (NO), and which type of nitric oxide synthase (NOS) would be responsible for this phenomenon. Lipopolysaccharide (LPS) 1 micro g/ml was used as inflammatory mediator. Because pituicytes are known to secrete interleukin (IL)-6 upon stimulation with LPS, this parameter was also investigated. Cultured pituicytes, from 4-week-old male mice, were stimulated with LPS for 6 h or 24 h. At 24 h, there was a significant increase in accumulated nitrite indicating NO formation. In contrast, IL-6 release was already significantly higher 6 h after stimulation and further increased at 24 h. The correlation between accumulated nitrite and secreted IL-6 was 0.84 after 24 h of incubation with LPS. The expression of inducible NOS (iNOS) mRNA in the pituicytes was significantly higher than the control level after 6 h and 24 h of exposure to LPS, with levels at 6 h being significantly higher than those at 24 h. There was no detected expression of endothelial NOS or neuronal NOS mRNA. Cultured pituicytes were also subjected to immunocytochemistry for iNOS protein at 6, 12, and 24 h after stimulation with LPS. Most cells were positive for iNOS, but there were no observable differences with the time points that we used. Collectively, these results show that pituicytes are able to produce NO, and that the inducible form of NOS is responsible for this production. Furthermore, there is a weak correlation between NO and IL-6 released from pituicytes after 24 h of stimulation with LPS.