Project

Statistical analysis of spatial hydrologic variables: a problem-solving approach

Goal: Statistical analysis of extreme rainfall over the Italian territory.

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Paola Mazzoglio
added a research item
Regional rainfall frequency analyses are based on rain gauge data that are affected by spatio-temporal discontinuities and gaps that can significantly influence the results of the statistical analyses. Neglecting the shorter series leads to ignore an amount of information that can be essential to correctly understand the spatial variability of the extremes. In this work we present an application of the patched kriging technique, a year-by-year application of ordinary kriging equations, that overcomes the data inconsistency by considering all the records, independently on the length of the time series. The methodology is applied to short-duration (1 to 24 hours) annual maximum rainfall depths recorded by rain gauges coming from the recently-released Improved Italian-Rainfall Extreme Dataset (I2-RED). The trend with elevation is removed and, for each duration, the sample variogram is evaluated as the mean of the annual variograms weighted on the number of active rain gauges for any year. The sequential application of the ordinary kriging allows to reconstruct a "rainfall data cube" and a "variance data cube" in the (x, y, t) space. By coring the cube along the taxis , a complete series of measured and estimated values is obtained at each location. The cored series are then analyzed using the L-moments, weighted on the related series of kriging variance, to consider the different nature of the data (measured and estimated). To overcome inconsistency of the L-moment statistics, a bias-correction procedure is introduced, that preserves the coefficient of variation from the smoothing effect induced by the spatial interpolation. The methodology is applied to short-duration annual maximum rainfall depths in the whole NorthWest of Italy, that includes areas affected by the most severe extremes on record. The dataset used in this study covers the period 1928-2021, including the all-time Italian record events up to now, some of which observed in 2021 (377.8 mm / 3h, 496 mm / 6h, 740.6 mm / 12h).
Paola Mazzoglio
added a research item
The availability of large data samples can be useful in several research areas, including rainfall/flood frequency analysis, hydrological modelling and quantification of the hydrologic effects of catchment heterogeneities. In recent years, considerable efforts have been spent to build nationwide databases of basin attributes, with catalogs or web repositories in USA, England,, Brazil and Chile. We present here FaBI (Floods and attributes of Basins in Italy) i.e. the first collection of hydrologic data and gauged basin attributes encompassing the whole of Italy, that counts 631 basins and their flood records. The collection puts together flood data and other hydrological indices on one side, and many basin geo-morpho-climatic and soil-related attributes. In terms of hydrologic data, the starting base is that of two recent databases, i.e. the Improved Italian-Rainfall Extreme Dataset (I2-RED) and the Catalogo delle Piene dei Corsi d'acqua Italiani. The latter was the main source for identification of the watersheds to consider, that are those for which extremes of daily or of peak discharges are available. On this set of 631 basins a consistent effort has produced the computation of spatially relevant attributes and indices with the condition that each variable derives from a uniform nationwide coverage. Many attributes are related to the geomorphology of the river network, as Horton ratios, shape and amplitude factors. They were computed by processing a digital elevation model with a 30-meters spatial resolution, through the implementation of the r.basin R algorithm. On these values several quality-control procedures have been applied, starting with a check of consistency with previously published data. The raster river network extracted has been compared with a vector reference one provided by the Istituto Superiore per la Ricerca e Protezione Ambientale (ISPRA), allowing us to identify areas where it was necessary to manually force the digital elevation model. The relation between the length of the main channel and its longest path has been investigated and the Hack's law was used to double-check the computed main channel length. Several spatial average values of climatological indices have been computed, privileging data gathered from ground stations, that are subsequently interpolated in the space. This attains average values of temperature and precipitation at different time scales, for the first time available in a unique repository. The FaBI collection provides a vast range of new opportunities to perform regional and national-scale hydrological analyses, taking advantage of the hydro-climatologic and morphologic variety of the Italian basins, that represent a vast range of transitions between Alpine and semi-arid geographic environments in a Mediterranean context.
Paola Mazzoglio
added a research item
The dependence of rainfall on elevation has frequently been documented in the scientific literature and may be relevant in Italy, due to the high degree of geographical and morphological heterogeneity of the country. However, a detailed analysis of the spatial variability of short-duration annual maximum rainfall depths and their connection to the landforms does not exist. Using a new, comprehensive and position-corrected rainfall extreme dataset (I2-RED, the Improved Italian-Rainfall Extreme Dataset), we present a systematic study of the relationship between geomorphological forms and the average annual maxima (index rainfall) across the whole of Italy. We first investigated the dependence of sub-daily rainfall depths on elevation and other landscape indices through univariate and multivariate linear regressions. The results of the national-scale regression analysis did not confirm the assumption of elevation being the sole driver of the variability of the index rainfall. The inclusion of longitude, latitude, distance from the coastline, morphological obstructions and mean annual rainfall contributes to the explanation of a larger percentage of the variance, even though this was in different ways for different durations (1 to 24 h). After analyzing the spatial variability of the regression residuals, we repeated the analysis on geomorphological subdivisions of Italy. Comparing the results of the best multivariate regression models with univariate regressions applied to small areas, deriving from morphological subdivisions, we found that “local” rainfall–topography relationships outperformed the country-wide multiple regressions, offered a uniform error spatial distribution and allowed the effect of morphology on rainfall extremes to be better reproduced.
Paola Mazzoglio
added a research item
L’influenza della morfologia e della quota sulla distribuzione delle piogge estreme, sebbene ampiamente documentata in letteratura, non è ancora stata analizzata approfonditamente sull’intero territorio italiano. In questo studio proponiamo alcune analisi delle relazioni fra morfologia e valori medi degli estremi annui di pioggia di durata sub-giornaliera (da 1 a 24 ore), usando un nuovo dataset di misure pluviometriche (Improved Italian – Rainfall Extreme Dataset, I2-RED). I2-RED contiene osservazioni di più di 5000 pluviometri dal 1916 al 2019, ottenute dall’unione di molte banche dati indipendenti. La dipendenza degli estremi di pioggia dalla quota e da altre variabili geomorfologiche è stata analizzata complessivamente a scala nazionale mediante relazioni di regressione multipla. Tale analisi ha dimostrato che la quota del terreno non è la sola variabile che influenza la variabilità degli estremi: longitudine, latitudine, distanza dalla costa, ostruzioni morfologiche e pioggia media annua influiscono infatti significativamente, con un contributo che varia a seconda della durata degli eventi (da 1 a 24 ore). Significative distorsioni locali in aree con morfologia complessa hanno fatto poi emergere l’utilità di scorporare l’analisi delle relazioni usando una scala di maggiore dettaglio e criteri morfologici di segmentazione del territorio nazionale. Sono state usate classificazioni geomorfologiche di letteratura e, nelle aree omogenee da esse definite, si è indagata la variabilità della pioggia estrema con la sola quota. I risultati ottenuti hanno dimostrato che l’uso di relazioni locali fra pioggia e quota produce livelli locali di distorsione molto bassi e ottima efficienza di stima, risultando quindi più rappresentative delle relazioni multivariate ottenute a scala nazionale.
Paola Mazzoglio
added a research item
Regionalization techniques have been developed to estimate design rainfall in ungauged sites and to support ordinary data-based frequency analysis of areal rainfall or in presence of short records. Regional techniques use principles of data augmentation based on hydrologic similarity, trying to overcome limitations due to low rain gauge density or to any other data inadequacy, which hamper the estimation of high return period quantiles. This chapter intends to summarize the state of the art of regionalization techniques applied to rainfall data, starting from the identification of today’s problems in data availability, and then highlighting the differences between traditional and more innovative approaches aimed to provide intensity – duration – frequency rainfall curves everywhere in a large area. In line with the frequent changes observed in station density over large areas, the chapter deals with the advantages of interpolation methods over the homogeneous region paradigm, addressing the valorization of the local information deriving from short or intermittent records. With the overall aim of providing a guide to regional model building based on updated datasets, considerations on applicability and evolution of the models are finally made on the methods currently adopted in the practice, based also on a case study in North-Western Italy.
Paola Mazzoglio
added a research item
Italy is a mountainous country with peculiar exposure to severe rainstorms. With the aim of improving the rainstorm hazard assessment over ungauged areas, the spatial variability of the relationship between rainfall and elevation is investigated over Italy, using local linear regression analysis. The analysis focuses on annual precipitation extremes in 1 and 24 hours. Data are taken from the recently released Improved Italian – Rainfall Extreme Dataset (I2-RED), a collection of rainfall measurements acquired from 1916 until now by 5265 rain gauges. In this analysis, only the series with at least 10 years of data are considered, for a total of more than 3700 time series. Starting from a knowledge base of general multivariate modeling, we have addressed local simple linear regression models between elevation and the average of extremes for any of the 1-km size pixels that cover Italy. The analysis is carried out by selecting, for each pixel, rain gauges available within a radius ranging from 1 to 50 km, with a progressive increase of 1 km. Regression constraints are set so to include only cases with at least 5 rain gauges and > 100 m of difference in elevation. Statistical significance is set at the 5% level. To avoid excessive extrapolation effects in high elevations (i.e., where snow is often recorded in place of rainfall), only the cases in which a tolerance of +/- 100 m between the estimation pixel elevation and that of the considered rain gauge stations are retained. Further constraints, as a higher minimum search radius or a constraint on the persistence of the significance of the regression as function of the radius, have been also tested. The results obtained for the 1-hour duration highlight a different sign of the “orographic effect” between rainfall and elevation in different areas: an inverse effect is noticed over the Alps, Liguria region and central Apennines, where rainfall decreases with elevation. For 24-hours rainfall the spatial distribution of the trend is different: for the most of the Italian territory the 24-hours extremes increase with elevation. The advantages of the high spatial detail granted by the proposed approach are finally demonstrated by the error assessment analysis, showing low absolute bias and very limited error clustering effects.
Paola Mazzoglio
added 2 research items
The dependence of rainfall on elevation has frequently been documented in the scientific literature and may be relevant in Italy, due to the high degree of geographical and morphological heterogeneity of the country. However, a detailed analysis of the spatial variability of short-duration rainfall extremes and their connection to the landforms does not exist. Using a new, comprehensive and position-corrected rainfall extreme dataset (I2-RED), we present a systematic study of the relationship between geomorphological forms and the average of rainfall extremes (index rainfall) across the whole of Italy. We first investigated the dependence of sub-daily rainfall depths on elevation and other landscape indices through univariate and multivariate linear regressions. After analyzing the results, we repeated the analysis on geomorphological subdivisions of Italy. The results of the national-scale regression analysis did not confirm the assumption of elevation being the sole driver of the variability of rainfall extremes. The longitude, latitude, distance from the coastline, morphological obstructions and mean annual rainfall resulted to be significantly related to the index rainfall, and to play different roles for different durations (1- to 24-hours). However, when comparing the results of the best multivariate regression models with univariate regressions for morphological subdivisions, we found that “local” rainfall-topography relationships within the geomorphological subdivisions outperformed the country-wide multiple regressions and offered a reasonable representation of the effect of morphology on rainfall extremes.
Paola Mazzoglio
added a research item
The collection and management of hydrological data in Italy has been dealt with at national level, initially, by the National Hydrological Service (SIMN), and at regional level in the last 40 years. This change has determined problems in the availability of complete and homogeneous data for the whole country. As of 2020, an updated and quality-controlled dataset of the historical annual maxima rainfall in Italy is still lacking. The Italian Rainfall Extreme Dataset (I-RED) has recently been created to allow studies to be performed with a homogeneous dataset at a national level. In this paper, the methodological approach adopted to build an improved and quality-controlled version of I-RED (in terms of both the rainfall depth values and the position of the rain gauges) is presented. The new database can be used as a more reliable research support for the frequency analysis of the rainfall extremes. This new I2-RED database contains rainfall annual maxima rainfall of 1, 3, 6, 12 and 24 h from 1916 until 2019, counts 5265 rain gauges and has been corroborated by a re-positioning and elevation-checking of 15% of the stations. A descriptive analysis of the maximum values of the stations, which provides an additional quality check and reveals different intriguing spatial features of Super-Extreme rainfall events, is also presented.
Paola Mazzoglio
added a project goal
Statistical analysis of extreme rainfall over the Italian territory.