Using phase-state modelling for inferring forecasting uncertainty in nonlinear stochastic decision schemes

The paper introduces the use of phase-state modelling as a means of estimating expected benefits or losses when dealing with decision processes under uncertainty of future events. For this reason the phase-space approach to time series, which generally aims at forecasting the expected value of a future event, is here also used to assess the forecasting uncertainty. Under the assumption of local stationarity the ensemble of generated future trajectories can be used to estimate a probability density that represents the a priori uncertainty of forecasts conditional on the latest measurements. This a priori density can then be used directly in the optimisation schemes if no additional information is available, or after deriving an a posteriori distribution in the Bayesian sense, by combining it with forecasts from deterministic models, here taken as noise-corrupted 'pseudo-measurements' of future events. Examples of application are given in the case of the Lake Como real-time management system as well as in the case of rainfall ensemble forecasts on the River Reno

Extending the global gradient algorithm to unsteady flow extended period simulations of water distribution systems

This paper introduces an extension of the Global Gradient Algorithm (GGA) to directly solve unsteady flow problems arising from the presence of variable head water storage devices, such as tanks, in Extended Period Simulations (EPS) of looped water distribution networks (WDN). Such a modification of the original algorithm was motivated by the need to overcome oscillations and instabilities reported by several users of EPANET, a worldwide available package, which uses the GGA to solve the looped WDN equations. The set of partial differential equations describing the time and space behaviour of a water distribution system is here presented. It is shown how an unsteady flow GGA can be derived by simple modifications of the original steady-state GGA. The performances of the new algorithm, referred to as EPS-GGA, are compared with the results provided by EPANET on an extremely simplified example, the solution of which is qualitatively known. As opposed to EPANET which shows significant instabilities, the EPS-GGA is stable under a wide variety of increasing integration time intervals

History and perspectives of hydrological catchment modelling

This paper presents a brief historical excursus on the development of hydrological catchment models together with a number of possible future perspectives. Given the wide variety of available hydrological models which, according to the embedded level of prior physical information, vary from the simple input–output lumped models to complex physically meaningful ones, the paper suggests how to accommodate and to reconcile the different approaches. This can be performed by better clarifying the roles and the limitations of the different models through objective benchmarks or test-beds characterizing the diverse potential hydrological applications. Furthermore, when dealing with hydrological forecasting, the reconciliation can be obtained in terms of forecasting uncertainty, by developing Bayesian frameworks to combine together models of different nature in order to assess and reduce predictive uncertainty

Comparing Hydrological Postprocessors Including Ensemble Predictions Into Full Predictive Probability Distribution of Streamflow

AbstractAlthough not matching the formal definition of the predictive probability distribution, meteorological and hydrological ensembles have been frequently interpreted and directly used to assess flood‐forecasting predictive uncertainty. With the objective of correctly assessing the predictive probability of floods, this paper introduces ways of taking into account the measures of uncertainty provided in the form of ensemble forecasts by modifying a number of well‐established uncertainty postprocessors, such as Bayesian Model Averaging and Model Conditional Processor. The uncertainty postprocessors were developed on the assumption that the future unknown quantity (predictand) is uncertain while model forecasts (predictors) are given, which imply that they are perfectly known. With this in mind, we propose to relax this assumption by considering ensemble predictions, in analogy to measurement errors, as expressions of errors in model predictions to be integrated in the postprocessors coefficients estimation process. The analyses of the methodologies proposed in this work are conducted on a real case study based on meteorological ensemble predictions for the Po River at Pontelagoscuro in Italy. After showing how improper can be the direct use of ensemble predictions to describe the predictive probability distribution, results from the modified postprocessors are compared and discussed

An operational approach to real-time dynamic measurement of discharge

Based on the maximization of entropy, microwave sensors are becoming standard approaches for converting point surface velocity measurements into discharge. Unfortunately, this conversion is conditioned by cross-section regularity and by the need to take the surface measures above the vertical where the maximum velocity occurs. Cross-section irregularities and the presence of floodplains, vegetation and/or local bed depressions can change the theoretical applicability conditions of the proposed methods and, due to the wandering of the current, the microwave sensor must be continuously moved to track the maximum velocity. We describe the theoretical development and practical application of a new approach to operationally convert surface velocity and water level, measured using a fixed installation, into discharge. The resulting equation that links the surface point velocity measurement to the discharge is a function of two parameters describing the velocity distribution within the cross-section plus an additional correction factor which describes the non-homogeneity of the different vertical slices into which the cross-section is divided. Interesting results of the approach are shown for the gauging section of Tavagnasco on the Dora Baltea River in Italy with high performances both in terms of calibration and validation

Data Assimilation in Water Distribution Systems

Abstract Operational management of water distribution networks (WDNs) requires assimilating observations such as pressures at junction nodes, flows in pipes and, whenever available, monitored demand. Although several data assimilation techniques are today available, ranging from 1-2-3-4 DVAR to Kalman Filters, a problem is posed by the need of preserving the structural relations among state variables in a WDN, such as for instance pressure head, discharge and demand. Ensemble Kalman Filters certainly can be used to account for non-linearities but, for example, if one tries to assimilate pressure heads and pipe flows at the same time, nothing guarantees that the resulting variables after the data assimilation step, will still obey to the hydraulic structural relations mathematically describing a WDN. In this work an EnKF based procedure has been implemented, which allows to assimilate three types of observations, namely pressures at junction nodes, flows in pipes and monitored demand. The procedure allows to assimilating all the observations in three successive steps, while guaranteeing the full satisfaction of the structural relations. The results, demonstrated over an operational network, show the high performance of the chosen approach

Acople modelos numéricos de tiempo (NWP) a modelos hidrológicos distribuidos. Sistema de predicciones hidrometeorológicas en tiempo real en las cuencas de Galicia Costa. El sistema ARTEMIS

Ponencia presentada en: XXXI Jornadas Científicas de la AME y el XI Encuentro Hispano Luso de Meteorología celebrado en Sevilla, del 1 al 3 de marzo de 2010

Forecasting: theory and practice

Forecasting has always been in the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The lack of a free-lunch theorem implies the need for a diverse set of forecasting methods to tackle an array of applications. This unique article provides a non-systematic review of the theory and the practice of forecasting. We offer a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts, including operations, economics, finance, energy, environment, and social good. We do not claim that this review is an exhaustive list of methods and applications. The list was compiled based on the expertise and interests of the authors. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of the forecasting theory and practice