Modelling the statistical dependence of rainfall event variables by a trivariate copula function

In many hydrological models, such as those derived by analytical probabilistic methods, the precipitation stochastic process is represented by means of individual storm random variables which are supposed to be independent of each other. However, several proposals were advanced to develop joint probability distributions able to account for the observed statistical dependence. The traditional technique of the multivariate statistics is nevertheless affected by several drawbacks, whose most evident issue is the unavoidable subordination of the dependence structure assessment to the marginal distribution fitting. Conversely, the copula approach can overcome this limitation, by dividing the problem in two distinct parts. Furthermore, goodness-of-fit tests were recently made available and a significant improvement in the function selection reliability has been achieved. Herein the dependence structure of the rainfall event volume, the wet weather duration and the interevent time is assessed and verified by test statistics with respect to three long time series recorded in different Italian climates. Paired analyses revealed a non negligible dependence between volume and duration, while the interevent period proved to be substantially independent of the other variables. A unique copula model seems to be suitable for representing this dependence structure, despite the sensitivity demonstrated by its parameter towards the threshold utilized in the procedure for extracting the independent events. The joint probability function was finally developed by adopting a Weibull model for the marginal distributions

Multivariate statistical analysis of flood variables by copulas: two italian case studies

Multivariate statistics are important to determine the flood hydrograph for the design of hydraulic structures and for the hydraulic risk assessment. In the last decade, the copula approach has been investigated in hydrological practice to assess the design flood hydrograph in terms of flood peak, volume and duration. In this paper, the copula approach is exploited to perform pair analyses of these three random variables for two Italian watersheds, in the Apennine and the Alps respectively. The criterion to separate continuous flow series into independent events is discussed along with its implications on the dependence structure. The goodness-of-fits of the proposed copulas are then assessed by non-parametric tests. Marginal distributions to derive joint distributions are briefly suggested. The possibility of generating flood events according to the proposed model and potential applications to hydraulic structure design and flood management are finally examined

Deriving a practical analytical-probabilistic method to size flood routing reservoirs

In the engineering practice routing reservoir sizing is commonly performed by using the design storm method, although its effectiveness has been debated for a long time. Conversely, continuous simulations and direct statistical analyses of recorded hydrographs are considered more reliable and comprehensive, but are indeed complex or seldom practicable. In this paper a handier tool is provided by the analytical-probabilistic approach to construct probability functions of peak discharges issuing from natural watersheds or routed through on-line and off-line reservoirs. A simplified routing scheme and a rainfall-runoff model based on a few essential hydrological parameters were implemented. To validate the proposed design methodology, on-line and off-line routing reservoirs were firstly sized by means of a conventional design storm method for a test watershed located in northern Italy. Their routing efficiencies were then estimated by both analytical-probabilistic models and benchmarking continuous simulations. Bearing in mind practical design purposes, adopted models evidenced a satisfactory consistency

Land cover changes since the 19th century detected from historic maps for environmental applications: toward a “CORINE 1800” project?

The value of cartographic heritage for environmental applications is demonstrated with a test case in the Central Italian Alps. Land cover changes since the early 19th century are detected from sample maps of the Second Military Survey of the Habsburg Empire in Lombardy (1818-1829), available on the portal www.mapire.eu. They are compared with 1954 areal sur-veys and successive land cover classification until 2018. Issues as land use classes homogeni-zation, data vectorization, georeferencing errors are addressed. The dynamics of main land cover classes (woods, bush, meadows, crops) are investigated on sample areas and the potential use of this exercise for hydrological applications is explored. In fact, the impact of the observed natural afforestation on changes in hydrological losses due to evapotranspiration and its influ-ence as a likely cause for the decrease in runoff monitored since 1845 in the Adda river basin and needs to be assessed in a systematic way. The proposed test case can pave the road for a project extended at European scale, a sort of “CORINE 1800 land cover” Geographic Infor-mation System, which could have several environmental, cartographic and socio-economic ap-plications

Failure Probability Analysis of Levees Affected by Mammal Bioerosion

Mammal bioerosion is an emergent threat to the functionality of levees. In the present paper, the problem of assessing the failure probability of levees affected by mammal bioerosion is addressed. A fully bivariate description of peak flow discharge and flood duration is combined with a deterministic unsteady seepage flow model to obtain a suitable model of variably disturbed levee response to the observed natural variability of floods. Monte Carlo analysis is also implemented to evaluate the epistemic uncertainty connected to the description of the river system. The obtained model is tested with respect to a real-world levee located along the Secchia River in northern Italy, which underwent a disastrous failure caused by mammal bioerosion in 2014. The convex linear combination of two Archimedean copulas is found to fit the empirical dependence structure between peak flow discharge and flood duration. The reliability of the unsteady seepage flow model is tested against detailed numerical simulations of the seepage occurring through the levee body. A limit state function is obtained by comparing the maximum extent of the seepage front to the distance between the den end and the riverside levee slope, and the corresponding levee safety and failure regions are delimited. Results obtained from the developed model reveal a significant impact of mammal dens located near the levee crest in terms of failure probability and related return period. This impact is consistent with failures observed in the study area

Nutrient delivery efficiency of a combined sewer along a lake challenged by incipient eutrophication

Although sewage diversion outside of a lake's watershed is now ordinary practice in the restoration of eutrophic lakes, often the observed recovery is slower than expected and the internal load from the lake anoxic sediments is identified as a possible reason. However, in the case of combined sewer, the quantification of the residual nutrient load discharged from sewer spillways must also be questioned. In this paper, the diversion efficiency of the sewer system along the east coast of Lake Iseo, a prealpine Italian lake where eutrophication effects are still severe, is investigated. To this purpose, a representative part of the sewer system was modelled by PCSWMM and calibrated by using an extensive series of discharge measurements. Water quality monitoring during wet weather periods reveals that the first flush is common in tributary sewers, whereas it is absent along the main collector. Moreover, flow discharges are strongly affected by infiltration waters, which are controlled by the lake water level. The calibrated model, including infiltration modeling, was used to assess the annual overflow volumes and the nutrient load through a continuous 10-year simulation. Simulations were conducted both with regard to the current conditions and to a climate change scenario. Results show that the discharged residual load is at least 7 times larger than the design value, with the water infiltration contributing to 17% to the overflow volume and that non-structural practices could considerably reduce the overall impact of the sewer. This research thus provides important insight into the potential impact of combined sewer overflows on lacustrine environments and addresses effective mitigation measures in similar contexts