Exploiting the information content of hydrological "outliers" for goodness-of-fit testing.

Abstract. Validation of probabilistic models based on goodness-of-fit tests is an essential step for the frequency analysis of extreme events. The outcome of standard testing techniques, however, is mainly determined by the behavior of the hypothetical model, FX(x), in the central part of the distribution, while the behavior in the tails of the distribution, which is indeed very relevant in hydrological applications, is relatively unimportant for the results of the tests. The maximum-value test, originally proposed as a technique for outlier detection, is a suitable, but seldom applied, technique that addresses this problem. The test is specifically targeted to verify if the maximum (or minimum) values in the sample are consistent with the hypothesis that the distribution FX(x) is the real parent distribution. The application of this test is hindered by the fact that the critical values for the test should be numerically obtained when the parameters of FX(x) are estimated on the same sample used for verification, which is the standard situation in hydrological applications. We propose here a simple, analytically explicit, technique to suitably account for this effect, based on the application of censored L-moments estimators of the parameters. We demonstrate, with an application that uses artificially generated samples, the superiority of this modified maximum-value test with respect to the standard version of the test. We also show that the test has comparable or larger power with respect to other goodness-of-fit tests (e.g., chi-squared test, Anderson-Darling test, Fung and Paul test), in particular when dealing with small samples (sample size lower than 20–25) and when the parent distribution is similar to the distribution being tested

Effects of disregarding seasonality on the distribution of hydrological extremes

Abstract. This paper deals with the seasonality of hydroclimatic extremes and with the problem of accounting for their non-homogeneous character in determining the design value. To this aim we devise a simple stochastic experiment in which extremes are produced by a non-homogeneous extreme value generation process. The design values are estimated in closed analytical form both in a peak over threshold framework and by using the standard annual maxima approach. In this completely controlled world of generated hydrological extremes, a statistical measure of the error associated to the adoption of a homogeneous model is introduced. The sensitivity of this measure, named return period ratio, to the typology and strength of seasonality is investigated. We find that neglecting seasonality induces a downward bias in design value estimators. The magnitude of the bias may be large when the peak over threshold approach is adopted, while the return period distortion is limited when the annual maxima are considered. An application to rainfall data from a 30 000 km2 region located in North-Western Italy is presented to better clarify the effects of disregarding seasonality in a real case

Virtuous and Vicious Virtual Water Trade with Application to Italy

The current trade of agricultural goods, with connections involving all continents, entails for global exchanges of ‘‘virtual’’ water, i.e. water used in the production process of alimentary products, but not contained within. Each trade link translates into a corresponding virtual water trade, allowing quantification of import and export fluxes of virtual water. The assessment of the virtual water import for a given nation, compared to the national consumption, could give an approximate idea of the country’s reliance on external resources from the food and the water resources point of view. A descriptive approach to the understanding of a nation’s degree of dependency from overseas food and water resources is first proposed, and indices of water trade virtuosity, as opposed to inefficiency, are devised. Such indices are based on the concepts of self-sufficiency and relative export, computed systematically on all products from the FAOSTAT database, taking Italy as the first case study. Analysis of time series of the self-sufficiency and relative export can demonstrate effects of market tendencies and influence water-related policies at the international level. The goal of this approach is highlighting incongruent terms in the virtual water balances by the viewpoint of single products. Specific products, which are here referred to as ‘‘swap products’’, are in fact identified as those that lead to inefficiencies in the virtual water balance due to their contemporaneously high import and export. The inefficiencies due to the exchanges of the same products between two nations are calculated in terms of virtual water volumes. Furthermore, the cases of swap products are investigated by computing two further indexes denoting the ratio of virtual water exchanged in the swap and the ratio of the economic values of the swapped products. The analysis of these figures can help examine the reasons behind the swap phenomenon in trade

Runoff regime estimation at high-elevation sites: a parsimonious water balance approach

Abstract. We develop a water balance model, parsimonious both in terms of parameterization and of required input data, to characterize the average runoff regime of high-elevation and scarcely monitored basins. The model uses a temperature threshold to partition precipitation into rainfall and snowfall, and to estimate evapotranspiration volumes. The role of snow in the transformation of precipitation into runoff is investigated at the monthly time scale through a specific snowmelt module that estimates melted quantities by a non-linear function of temperature. A probabilistic representation of temperature is also introduced, in order to mimic its sub-monthly variability. To account for the commonly reported rainfall underestimation at high elevations, a two-step precipitation adjustment procedure is implemented to guarantee the closure of the water balance. The model is applied to a group of catchments in the North-Western Italian Alps, and its performances are assessed by comparing measured and simulated runoff regimes both in terms of total bias and anomalies, by means of a new metric, specifically conceived to compare the shape of the two curves. The obtained results indicates that the model is able to predict the observed runoff seasonality satisfactorily, notwithstanding its parsimony (the model has only two parameters to be estimated). In particular, when the parameter calibration is performed separately for each basin, the model proves to be able to reproduce the runoff seasonality. At the regional scale (i.e., with uniform parameters for the whole region), the performance is less positive, but the model is still able to discern among different mechanisms of runoff formation that depend on the role of the snow storage. Because of its parsimony and the robustness in the approach, the model is suitable for application in ungauged basins and for large scale investigations of the role of climatic variables on water availability and runoff timing in mountainous regions

Vegetation and Topographic Control on Spatial Variability of Soil Organic Carbon

Soil organic carbon (SOC) is one of the most important parameters affecting the hydraulic characteristics of natural soils. Despite being rather easy to measure, SOC is known to be highly variable in space. In this study, vegetation, climate, and morphology factors were used to reproduce the spatial distribution of SOC in the mineral horizons of forest and grassland areas in north-western Italy and the feasibility of the approach was evaluated. When the overall sample (114 samples) was analyzed, average annual rainfall and elevation were significant descriptors of the SOC variability. However, a large part of the variability remains unexplained. Two stratification criteria were then adopted, based on vegetation and topographic properties. We obtained an improvement of the quality of the estimates, particularly for grasslands and forests in the absence of local curvatures. These results indicate that the spatial variability of soil organic matter is scarcely reproducible at the regional scale, unless an a-priori reduction of the heterogeneity is applied. A discussion on the feasibility of applying stratification criteria to deal with heterogeneous samples closes the pape