A mass conservative and water storage consistent variable parameter Muskingum-Cunge approach

International audienceThe variable parameter Muskingum-Cunge (MC) flood routing approach, together with several variants proposed in the literature, does not fully preserve the mass balance, particularly when dealing with very mild slopes (?3). This paper revisits the derivation of the MC and demonstrates (i) that the loss of mass balance in MC is caused by the use of time variant parameters which violate the implicit assumption embedded in the original derivation of the Muskingum scheme, which implies constant parameters and at the same time (ii) that the parameters estimated by means of the Cunge approach violate the two basic equations of the Muskingum formulation. The paper also derives the modifications needed to allow the MC to fully preserve the mass balance and, at the same time, to comply with the original Muskingum formulation in terms of water storage. The properties of the proposed algorithm have been assessed by varying the cross section, the slope, the roughness, the space and the time integration steps. The results of all the tests also show that the new algorithm is always mass conservative. Finally, it is also shown that the proposed approach closely approaches the full de Saint Venant equation solution, both in terms of water levels and discharge, when the parabolic approximation holds

Influence of parameter estimation uncertainty in Kriging: Part 1 - Theoretical Development

International audienceThis paper deals with a theoretical approach to assessing the effects of parameter estimation uncertainty both on Kriging estimates and on their estimated error variance. Although a comprehensive treatment of parameter estimation uncertainty is covered by full Bayesian Kriging at the cost of extensive numerical integration, the proposed approach has a wide field of application, given its relative simplicity. The approach is based upon a truncated Taylor expansion approximation and, within the limits of the proposed approximation, the conventional Kriging estimates are shown to be biased for all variograms, the bias depending upon the second order derivatives with respect to the parameters times the variance-covariance matrix of the parameter estimates. A new Maximum Likelihood (ML) estimator for semi-variogram parameters in ordinary Kriging, based upon the assumption of a multi-normal distribution of the Kriging cross-validation errors, is introduced as a mean for the estimation of the parameter variance-covariance matrix. Keywords: Kriging, maximum likelihood, parameter estimation, uncertaint

Coupling meteorological and hydrological models for flood forecasting

International audienceThis paper deals with the problem of analysing the coupling of meteorological meso-scale quantitative precipitation forecasts with distributed rainfall-runoff models to extend the forecasting horizon. Traditionally, semi-distributed rainfall-runoff models have been used for real time flood forecasting. More recently, increased computer capabilities allow the utilisation of distributed hydrological models with mesh sizes from tenths of metres to a few kilometres. On the other hand, meteorological models, providing the quantitative precipitation forecast, tend to produce average values on meshes ranging from slightly less than 10 to 200 kilometres. Therefore, to improve the quality of flood forecasts, the effects of coupling the meteorological and the hydrological models at different scales were analysed. A distributed hydrological model (TOPKAPI) was developed and calibrated using a 1x1 km mesh for the case of the river Po closed at Ponte Spessa (catchment area c. 37000 km2). The model was then coupled with several other European meteorological models ranging from the Limited Area Models (provided by DMI and DWD) with resolutions from 0.0625° * 0.0625°, to the ECMWF ensemble predictions with a resolution of 1.85° * 1.85°. Interesting results, describing the coupled model behaviour, are available for a meteorological extreme event in Northern Italy (Nov. 1994). The results demonstrate the poor reliability of the quantitative precipitation forecasts produced by meteorological models presently available; this is not resolved using the Ensemble Forecasting technique, when compared with results obtainable with measured rainfall

A Bayesian technique for conditioning radar precipitation estimates to rain-gauge measurements

International audienceThe paper introduces a new technique based upon the use of block-Kriging and of Kalman filtering to combine, optimally in a Bayesian sense, areal precipitation fields estimated from meteorological radar to point measurements of precipitation such as are provided by a network of rain-gauges. The theoretical development is followed by a numerical example, in which an error field with a large bias and a noise to signal ratio of 30% is added to a known random field, to demonstrate the potentiality of the proposed algorithm. The results analysed on a sample of 1000 realisations, show that the final estimates are totally unbiased and the noise variance reduced substantially. Moreover, a case study on the upper Reno river in Italy demonstrates the improvements in rainfall spatial distribution obtainable by means of the proposed radar conditioning technique. Keywords: Rainfall, meteorological radar, Bayesian technique, block-Kriging, Kalman filterin

Recent advances in flood forecasting and flood risk assessment

International audienceRecent large floods in Europe have led to increased interest in research and development of flood forecasting systems. Some of these events have been provoked by some of the wettest rainfall periods on record which has led to speculation that such extremes are attributable in some measure to anthropogenic global warming and represent the beginning of a period of higher flood frequency. Whilst current trends in extreme event statistics will be difficult to discern, conclusively, there has been a substantial increase in the frequency of high floods in the 20th century for basins greater than 2x105 km2. There is also increasing that anthropogenic forcing of climate change may lead to an increased probability of extreme precipitation and, hence, of flooding. There is, therefore, major emphasis on the improvement of operational flood forecasting systems in Europe, with significant European Community spending on research and development on prototype forecasting systems and flood risk management projects. This Special Issue synthesises the most relevant scientific and technological results presented at the International Conference on Flood Forecasting in Europe held in Rotterdam from 3-5 March 2003. During that meeting 150 scientists, forecasters and stakeholders from four continents assembled to present their work and current operational best practice and to discuss future directions of scientific and technological efforts in flood prediction and prevention. The papers presented at the conference fall into seven themes, as follows

Towards a comprehensive physically-based rainfall-runoff model

International audienceThis paper introduces TOPKAPI (TOPographic Kinematic APproximation and Integration), a new physically-based distributed rainfall-runoff model deriving from the integration in space of the kinematic wave model. The TOPKAPI approach transforms the rainfall-runoff and runoff routing processes into three ?structurally-similar' non-linear reservoir differential equations describing different hydrological and hydraulic processes. The geometry of the catchment is described by a lattice of cells over which the equations are integrated to lead to a cascade of non-linear reservoirs. The parameter values of the TOPKAPI model are shown to be scale independent and obtainable from digital elevation maps, soil maps and vegetation or land use maps in terms of slope, soil permeability, roughness and topology. It can be shown, under simplifying assumptions, that the non-linear reservoirs aggregate into three reservoir cascades at the basin scale representing the soil, the surface and the drainage network, following the topographic and geomorphologic elements of the catchment, with parameter values which can be estimated directly from the small scale ones. The main advantage of this approach lies in its capability of being applied at increasing spatial scales without losing model and parameter physical interpretation. The model is foreseen to be suitable for land-use and climate change impact assessment; for extreme flood analysis, given the possibility of its extension to ungauged catchments; and last but not least as a promising tool for use with General Circulation Models (GCMs). To demonstrate the quality of the comprehensive distributed/lumped TOPKAPI approach, this paper presents a case study application to the Upper Reno river basin with an area of 1051 km2 based on a DEM grid scale of 200 m. In addition, a real-world case of applying the TOPKAPI model to the Arno river basin, with an area of 8135 km2 and using a DEM grid scale of 1000 m, for the development of the real-time flood forecasting system of the Arno river will be described. The TOPKAPI model results demonstrate good agreement between observed and simulated responses in the two catchments, which encourages further developments of the model. Keywords: rainfall-runoff modelling, topographic, kinematic wave approximation, spatial integration, physical meaning, non-linear reservoir model, distributed and lumped</p

Flood forecasting using a fully distributed model: application of the TOPKAPI model to the Upper Xixian Catchment

International audienceTOPKAPI is a physically-based, fully distributed hydrological model with a simple and parsimonious parameterisation. The original TOPKAPI is structured around five modules that represent evapotranspiration, snowmelt, soil water, surface water and channel water, respectively. Percolation to deep soil layers was ignored in the old version of the TOPKAPI model since it was not important in the basins to which the model was originally applied. Based on published literature, this study developed a new version of the TOPKAPI model, in which the new modules of interception, infiltration, percolation, groundwater flow and lake/reservoir routing are included. This paper presents an application study that makes a first attempt to derive information from public domains through the internet on the topography, soil and land use types for a case study Chinese catchment - the Upper Xixian catchment in Huaihe River with an area of about 10000 km2, and apply a new version of TOPKAPI to the catchment for flood simulation. A model parameter value adjustment was performed using six months of the 1998 dataset. Calibration did not use a curve fitting process, but was chiefly based upon moderate variations of parameter values from those estimated on physical grounds, as is common in traditional calibration. The hydrometeorological dataset of 2002 was then used to validate the model, both against the outlet discharge as well as at an internal gauging station. Finally, to complete the model performance analysis, parameter uncertainty and its effects on predictive uncertainty were also assessed by estimating a posterior parameter probability density via Bayesian inference

Orographic effects on convective precipitation and space-time rainfall variability: preliminary results

International audienceIn the EFFS Project, an attempt has been made to develop a general framework to study the predictability of severe convective rainfall events in the presence of orography. Convective activity is embedded in orographic rainfall and can be thought as the result of several physical mechanisms. Quantifying its variability on selected area and time scales requires choosing the best physical representation of the rainfall variability on these scales. The main goal was (i) to formulate a meaningful set of experiments to compute the oscillation of variance due to convection inside model forecasts in the presence of orography and (ii) to give a statistical measure of it that might be of value in the operational use of atmospheric data. The study has been limited to atmospheric scales that span the atmosphere from 2 to 200 km and has been focused on extreme events with deep convection. Suitable measures of the changing of convection in the presence of orography have been related to the physical properties of the rainfall environment. Preliminary results for the statistical variability of the convective field are presented

A Bayesian decision approach to rainfall thresholds based flood warning

International audienceOperational real time flood forecasting systems generally require a hydrological model to run in real time as well as a series of hydro-informatics tools to transform the flood forecast into relatively simple and clear messages to the decision makers involved in flood defense. The scope of this paper is to set forth the possibility of providing flood warnings at given river sections based on the direct comparison of the quantitative precipitation forecast with critical rainfall threshold values, without the need of an on-line real time forecasting system. This approach leads to an extremely simplified alert system to be used by non technical stakeholders and could also be used to supplement the traditional flood forecasting systems in case of system failures. The critical rainfall threshold values, incorporating the soil moisture initial conditions, result from statistical analyses using long hydrological time series combined with a Bayesian utility function minimization. In the paper, results of an application of the proposed methodology to the Sieve river, a tributary of the Arno river in Italy, are given to exemplify its practical applicability

Stochastic rainfall interpolation and downscaling

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