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

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

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

The role of predictive uncertainty in the operational management of reservoirs

The present work deals with the operational management of multi-purpose reservoirs, whose optimisation-based rules are derived, in the planning phase, via deterministic (linear and nonlinear programming, dynamic programming, etc.) or via stochastic (generally stochastic dynamic programming) approaches. In operation, the resulting deterministic or stochastic optimised operating rules are then triggered based on inflow predictions. In order to fully benefit from predictions, one must avoid using them as direct inputs to the reservoirs, but rather assess the "predictive knowledge" in terms of a predictive probability density to be operationally used in the decision making process for the estimation of expected benefits and/or expected losses. Using a theoretical and extremely simplified case, it will be shown why directly using model forecasts instead of the full predictive density leads to less robust reservoir management decisions. Moreover, the effectiveness and the tangible benefits for using the entire predictive probability density instead of the model predicted values will be demonstrated on the basis of the Lake Como management system, operational since 1997, as well as on the basis of a case study on the lake of Aswan

Corrigendum to "A mass conservative and water storage consistent variable parameter Muskingum-Cunge approach" published in Hydrol. Earth Syst. Sci., 11, 1645–1659, 2007

No abstract available

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

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

Reply to Comment on "A dynamic rating curve approach to indirect discharge measurement by Dottori et al. (2009)" by Koussis (2009)

No abstract available

Recent developments in predictive uncertainty assessment based on the model conditional processor approach

Abstract. The work aims at discussing the role of predictive uncertainty in flood forecasting and flood emergency management, its relevance to improve the decision making process and the techniques to be used for its assessment. Real time flood forecasting requires taking into account predictive uncertainty for a number of reasons. Deterministic hydrological/hydraulic forecasts give useful information about real future events, but their predictions, as usually done in practice, cannot be taken and used as real future occurrences but rather used as pseudo-measurements of future occurrences in order to reduce the uncertainty of decision makers. Predictive Uncertainty (PU) is in fact defined as the probability of occurrence of a future value of a predictand (such as water level, discharge or water volume) conditional upon prior observations and knowledge as well as on all the information we can obtain on that specific future value from model forecasts. When dealing with commensurable quantities, as in the case of floods, PU must be quantified in terms of a probability distribution function which will be used by the emergency managers in their decision process in order to improve the quality and reliability of their decisions. After introducing the concept of PU, the presently available processors are introduced and discussed in terms of their benefits and limitations. In this work the Model Conditional Processor (MCP) has been extended to the possibility of using two joint Truncated Normal Distributions (TNDs), in order to improve adaptation to low and high flows. The paper concludes by showing the results of the application of the MCP on two case studies, the Po river in Italy and the Baron Fork river, OK, USA. In the Po river case the data provided by the Civil Protection of the Emilia Romagna region have been used to implement an operational example, where the predicted variable is the observed water level. In the Baron Fork River example, the data set provided by the NOAA's National Weather Service, within the DMIP 2 Project, allowed two physically based models, the TOPKAPI model and TETIS model, to be calibrated and a data driven model to be implemented using the Artificial Neural Network. The three model forecasts have been combined with the aim of reducing the PU and improving the probabilistic forecast taking advantage of the different capabilities of each model approach

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