Elena Ridolfi

Ensemble Entropy for Monitoring Network Design

Information-theory provides, among others, conceptual methods to quantify the amount of information contained in single random variables and methods to quantify the amount of information contained and shared among two or more variables. Although these concepts have been successfully applied in hydrology and other fields, the evaluation of these quantities is sensitive to different assumptions in the estimation of probabilities. An example is the histogram bin size used to estimate probabilities to calculate Information Theory quantities via frequency methods. The present research aims at introducing a method to take into consideration the uncertainty coming from these parameters in the evaluation of the North Sea’s water level network. The main idea is that the entropy of a random variable can be represented as a probability distribution of possible values, instead of entropy being a deterministic value. The method consists of solving multiple scenarios of Multi-Objective Optimization Problem in which information content is maximized and redundancy is minimized. Results include probabilistic analysis of the chosen parameters on the resulting family of Pareto fronts, providing additional criteria on the selection of the final set of monitoring points.

An entropy approach for the optimization of cross-section spacing for river modelling

Abstract An accurate definition of river geometry is essential to implement one-dimensional (1D) hydraulic models and, in particular, appropriate spacing between cross-sections is key for capturing a river’s hydraulic behaviour. This work explores the potential of an entropy-based approach, as a complementary method to existing guidelines, to determine the optimal number of cross-sections to support 1D hydraulic modelling. To this end, given a redundant collection of existing cross-sections, a location subset is selected minimizing total correlation (as a measure of redundancy) and maximizing joint entropy (as a measure of information content). The problem is posed as a multi-objective optimization problem and solved using a genetic algorithm: the Non-dominated Sorting Genetic Algorithm (NSGA)-II. The proposed method is applied to a river reach of the Po River (Italy) and compared to standard guidelines for 1D hydraulic modelling. Cross-sections selected through the proposed methodology were found to provide an accurate description of the flood water profile, while optimizing computational efficiency. Editor D. Koutsoyiannis Citation Ridolfi, E., Alfonso, L., Di Baldassarre, G., Dottori, F., Russo, F., and Napolitano, F., 2013. An entropy approach for the optimization of cross-section spacing for river modelling. Hydrological Sciences Journal, 59 (1), 126–137.

An Entropy Method for Floodplain Monitoring Network Design

In recent years an increasing number of flood-related fatalities has highlighted the necessity of improving flood risk management to reduce human and economic losses. In this framework, monitoring of flood-prone areas is a key factor for building a resilient environment. In this paper a method for designing a floodplain monitoring network is presented. A redundant network of cheap wireless sensors (GridStix) measuring water depth is considered over a reach of the River Dee (UK), with sensors placed both in the channel and in the floodplain. Through a Three Objective Optimization Problem (TOOP) the best layouts of sensors are evaluated, minimizing their redundancy, maximizing their joint information content and maximizing the accuracy of the observations. A simple raster-based inundation model (LISFLOOD-FP) is used to generate a synthetic GridStix data set of water stages. The Digital Elevation Model (DEM) that is used for hydraulic model building is the globally and freely available SRTM DEM.

Accuracy Analysis of a Dam Model from Drone Surveys

This paper investigates the accuracy of models obtained by drone surveys. To this end, this work analyzes how the placement of ground control points (GCPs) used to georeference the dense point cloud of a dam affects the resulting three-dimensional (3D) model. Images of a double arch masonry dam upstream face are acquired from drone survey and used to build the 3D model of the dam for vulnerability analysis purposes. However, there still remained the issue of understanding the real impact of a correct GCPs location choice to properly georeference the images and thus, the model. To this end, a high number of GCPs configurations were investigated, building a series of dense point clouds. The accuracy of these resulting dense clouds was estimated comparing the coordinates of check points extracted from the model and their true coordinates measured via traditional topography. The paper aims at providing information about the optimal choice of GCPs placement not only for dams but also for all surveys of high-rise structures. The knowledge a priori of the effect of the GCPs number and location on the model accuracy can increase survey reliability and accuracy and speed up the survey set-up operations.

Optimal cross-sectional sampling for river modelling with bridges: An information theory-based method

The description of river topography has a crucial role in accurate one-dimensional (1D) hydraulic modelling. Specifically, cross-sectional data define the riverbed elevation, the flood-prone area, and thus, the hydraulic behavior of the river. Here, the problem of the optimal cross-sectional spacing is solved through an information theory-based concept. The optimal subset of locations is the one with the maximum information content and the minimum amount of redundancy. The original contribution is the introduction of a methodology to sample river cross sections in the presence of bridges. The approach is tested on the Grosseto River (IT) and is compared to existing guidelines. The results show that the information theory-based approach can support traditional methods to estimate rivers’ cross-sectional spacing.

Data selection to assess bias in rainfall radar estimates: An entropy-based method

Miscalibration of radar determines a systematic error (i.e., bias) that is observed in radar estimates of rainfall. Although a rain gauge can provide a pointwise rainfall measurement, weather radar can cover an extended area. To compare the two measurements, it is necessary to individuate the weather radar measurements at the same location as the rain gauge. Bias is measured as the ratio between cumulative rain gauge measurements and the corresponding radar estimates. The rainfall is usually cumulated, taking into account all rainfall events registered in the target area. The contribution of this work is the determination of the optimal number of rainfall events that are necessary to calibrate rainfall radar. The proposed methodology is based on the entropy concept. In particular, the optimal number of events must fulfil two conditions, namely, maximisation of information content and minimisation of redundant information. To verify the methodology, the bias values are estimated with 1) a reduced number of events and 2) all available data. The proposed approach is tested on the Polar 55C weather radar located in the borough area of Rome (IT). The radar is calibrated against rainfall measurements of a couple of rain gauges placed in the Roman city centre. Analysing the information content of all data, it is found that it is possible to reduce the number of rainfall events without losing information in evaluating the bias.Miscalibration of radar determines a systematic error (i.e., bias) that is observed in radar estimates of rainfall. Although a rain gauge can provide a pointwise rainfall measurement, weather radar can cover an extended area. To compare the two measurements, it is necessary to individuate the weather radar measurements at the same location as the rain gauge. Bias is measured as the ratio between cumulative rain gauge measurements and the corresponding radar estimates. The rainfall is usually cumulated, taking into account all rainfall events registered in the target area. The contribution of this work is the determination of the optimal number of rainfall events that are necessary to calibrate rainfall radar. The proposed methodology is based on the entropy concept. In particular, the optimal number of events must fulfil two conditions, namely, maximisation of information content and minimisation of redundant information. To verify the methodology, the bias values are estimated with 1) a reduced number of...

Joint probabilities of demands on a water distribution network: A non-parametric approach

This paper proposes aprocedure to determine the probability of a specific water demand scenario in a Water Distribution Network (WDN). Stochastic correlated demands are generated for each node of the network using scaling laws. In particular, each demand fits a normal probability density function (PDF). To determine the joint probability of water demands at all nodes of the network, each nodal demand is divided in class intervals and a multidimensional contingency table is built. The joint probability represents the occurrence probability of a specific water demand scenario. The presented approach produces valuable information about demand scenarios and their probability of occurrence in a network. This method can find a further application in the robust optimization models for the design and management of WDN.

A comparison of two rainfall disaggregation models

Whitin the context of flood management, and generally for performing environmental, climate, hydrological, and water resources analysis, it is useful and reliable to provide scenarios by rainfall simulation, in order to overcome data limitations in terms of time and spatial resolution. Generally, it is required that the stochastic model preservesimportant properties of the rainfall process, such as intermittency, seasonality and scaling behavior in space and time, so that there will be no substantial differences between historical rainfall data and synthetic records. In this work, two rainfall disaggregation models are evaluated in terms of their ability to reproduce rainfall hourly statistics in four sites in Central Italy. The considered models are an entropy based disaggregation model and Hyetos-R (Bartlett-Lewis rectangular pulses rainfall)

A methodology to estimate flow duration curves at partiallyungauged basins

The flow duration curve (FDC) of streamflow at a specific site has a key role in the knowledge on the distribution and characteristics of streamflow at that site. The FDC gives information on the water regime, providing information to optimally manage the water resources of the river. In spite of its importance, because of the lack of streamflow gauging stations, the FDC construction can be a not straightforward task. In partially gauged basins, FDCs are usually built using regionalization among the other methods. In this paper we show that the FDC is not a characteristic of the basin only, but of both the basin and the weather. Different weather conditions lead to different FDCs for the same catchment. The differences can often be significant. Similarly, the FDC built at a site for a specific period cannot be used to retrieve the FDC at a different site for the same time window. In this paper, we propose a new methodology to estimate FDCs at partially gauged basins (i.e., target sites) using precipitation data gauged at another basin (i.e., donor site). The main idea is that it is possible to retrieve the FDC of a target period of time using the data gauged during a given donor time period for which data are available at both target and donor sites. To test the methodology, several donor and target time periods are analyzed and results are shown for different sites in the USA. The comparison between estimated and actually observed FDCs shows the reasonability of the approach, especially for intermediate percentiles.

A bivariate analysis of temperature and rainfall series for snowfall return period estimation

The lack of snowfall observations makes snow return period estimation a relevant issue in areas characterized by the absence of snow gauges. Therefore, in these regions, the post-event effects regarding electrical, hydraulic, and road infrastructures become difficult to evaluate. The issue of the estimation for the return period of snow events is solved by analysing pairs of rainfall and temperature data. First, the statistical dependence of the three variables (i.e. snow, rainfall and temperature) is analysed. Second, the return period of a selected rainfall sample, with values conditioned to a specific range of temperatures, is evaluated (i.e., indirect snow return period). Then, the corresponding snow return period (i.e., direct snow return period) is estimated. Finally, the equivalence of both return periods is investigated. The results obtained with the two approaches are compared, presenting encouraging perspectives in terms of return period value equivalence.