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

Time-Dependent Z-R Relationships for Estimating Rainfall Fields from Radar Measurements

Abstract. The operational use of weather radars has become a widespread and useful tool for estimating rainfall fields. The radar-gauge adjustment is a commonly adopted technique which allows one to reduce bias and dispersion between radar rainfall estimates and the corresponding ground measurements provided by rain gauges. This paper investigates a new methodology for estimating radar-based rainfall fields by recalibrating at each time step the reflectivity-rainfall rate (Z-R) relationship on the basis of ground measurements provided by a rain gauge network. The power-law equation for converting reflectivity measurements into rainfall rates is readjusted at each time step, by calibrating its parameters using hourly Z-R pairs collected in the proximity of the considered time step. Calibration windows with duration between 1 and 24 h are used for estimating the parameters of the Z-R relationship. A case study pertaining to 19 rainfall events occurred in the north-western Italy is considered, in an area located within 25 km from the radar site, with available measurements of rainfall rate at the ground and radar reflectivity aloft. Results obtained with the proposed method are compared to those of three other literature methods. Applications are described for a posteriori evaluation of rainfall fields and for real-time estimation. Results suggest that the use of a calibration window of 2–5 h yields the best performances, with improvements that reach the 28% of the standard error obtained by using the most accurate fixed (climatological) Z-R relationship

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

Measuring economic water scarcity in agriculture: a cross-country empirical investigation

High water availability enhances agricultural performance and food security. However, many countries where water is abundant according to hydrological indicators face difficulties in the utilization of water in agriculture, being in a situation of economic water scarcity (EWS), due to lack of institutional and material means for water management and governance. EWS faces a stronger challenge of measurability, if compared to physical water scarcity. Since the Sustainable Development Goal Indicator on Integrated management of domestic and transboundary water resources (IWRM) is a unique attempt to quantify information on water management at a national level, we explore whether it can represent a valid metric for EWS measurement. We first show that a high level of water management is neither necessarily associated to high economic power of the country nor to low physical water availability. Then, we analyze whether the indicator can predict typical EWS situations such as low agricultural productivity and inefficient water use. Although the importance of water institutions for agriculture is well known through case studies at the local level, we make the first attempt to quantify the strengths of this relation at a global scale for different crops in climatic diverse countries. We detect a positive and significant association between IWRM level and yield, and consequently a negative and equally significant association between the IWRM level and the crop water footprint. Statistical significance holds also when potentially confounding variables are included in a multiple regression analysis. We infer from this analysis that good water management, as detectable through the IWRM indicator, improves land productivity and water saving, in turn mitigating EWS. Our findings pave the way toward the use of the IWRM indicator as a valuable tool for measuring EWS in agriculture, bridging the measurability gap of economic water scarcity, with straightforward policy implications in favour of investments in water management as a lever for enhancing food security and development

Propagation of crises in the virtual water trade network

The international trade of agricultural goods is associated to the displacement of the water used to produce such goods and embedded in trade as a factor of production. Water virtually exchanged from producing to consuming countries, named virtual water, defines flows across an international network of “virtual water trade” which enable the assessment of environmental forcings and implications of trade, such as global water savings or country dependencies on foreign water resources. Given the recent expansion of commodity (and virtual water) trade, in both displaced volumes and network structure, concerns have been raised about the exposure to crises of individuals and societies. In fact, if one country had to markedly decrease its export following a socio-economical or environmental crisis, such as a war or a drought, many -if not all- countries would be affected due to a cascade effect within the trade network. The present contribution proposes a mechanistic model describing the propagation of a local crisis into the virtual water trade network, accounting for the network structure and the virtual water balance of all countries. The model, built on data-based assumptions, is tested on the real case study of the Argentinean crisis in 2008-09, when the internal agricultural production (measured as virtual water volume) decreased by 26% and the virtual water export of Argentina dropped accordingly. Crisis propagation and effects on the virtual water trade are correctly captured, showing the way forward to investigations of crises impact and country vulnerability based on the results of the model propose

Compliance with EAT–Lancet dietary guidelines would reduce global water footprint but increase it for 40% of the world population

The EAT–Lancet Commission has proposed a global benchmark diet to guide the shift towards healthy and sustainable dietary patterns. Yet it is unclear whether consumers’ choices are convergent with those guidelines. Applying an advanced statistical analysis, we mapped the diet gap of 15 essential foods in 172 countries from 1961 to 2018. We found that countries at the highest level of development have an above-optimal consumption of animal products, fats and sugars but a sub-optimal consumption of legumes, nuts and fruits. Countries suffering from limited socio-economic progress primarily rely on carbohydrates and starchy roots. Globally, a gradual change towards healthy and sustainable dietary targets can be observed for seafood, milk products, poultry and vegetable oils. We show that if all countries adopted the EAT–Lancet diet, the water footprint would fall by 12% at a global level but increase for nearly 40% of the world’s population

Charting out the future agricultural trade and its impact on water resources

International agricultural trade triggers inter-dependency among distant countries, not only in economic terms but also under an environmental perspective. Agricultural trade has been shown to drive environmental threats pertaining to biodiversity loss and depletion and pollution of freshwater resources. Meanwhile, trade can also encourage production where it is most efficient, hence minimizing the use of natural resources required by agriculture. In this study, we provide a country-level assessment of the future international trade for 6 primary crops and 3 animal products composing 70% of the human diet caloric content. We set up four variegate socio-economic scenarios with different level of economic developments, diets habits, population growth dynamics, and levels of market liberalization. Results show that the demand of agricultural goods and the correspondent trade flow will increase with respect to current levels by 10–50% and 74–178% by 2050, respectively. The largest increase in the amount of traded goods is expected under the Economic Optimism scenario that will see an average trade flow of 2830 kcal/cap/day (i.e., nearly doubling the current per-capita flow). Most of the increase will be driven by the trade of crops for animal feeding, particularly maize will be the most traded crop. The trade networks architecture in 2050 and 2080 will be very different from the one we actually know, with a clear shift of the trade pole from the Western toward the Eastern economies. The dramatic changes of global food-sources and trade patterns will jeopardize the water resources of new regions while exacerbating the pressure in those areas that will continue serving food also in the future. In spite of this, trade may annually save around 40–60 m3 of water per person, compared to a situation where countries are self-sufficient

International corporations trading Brazilian soy are keystone actors for water stewardship

Transnational corporations play a major, but poorly constrained, role in reallocating global water resources. Here, we couple high-resolution, company-specific trade data with hydrological and crop models to estimate the virtual water trade of the top 9 transnational corporations that trade Brazilian soy. We identify 4429 virtual water flows connecting 1620 Brazilian municipalities with the top-10 soy importing countries and find that the total virtual water flow increased from 43 billion m3 to 100 billion m3 between 2004 and 2018. We find that the largest soy traders displace on average twice as much virtual water as top-importing countries, excluding China. For example, in 2018 one transnational corporation exported 15 Gm3, almost tripling the Netherlands’s virtual water import (the second largest importer at about 5 Gm3). Our findings highlight the importance of transnational corporations for achieving water stewardship and sustainable supply chains to support water resource security at municipal and international scales

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

Systematic Improvement of Classical Nucleation Theory

We reconsider the applicability of classical nucleation theory (CNT) to the calculation of the free energy of solid cluster formation in a liquid and its use to the evaluation of interface free energies from nucleation barriers. Using two different freezing transitions (hard spheres and NaCl) as test cases, we first observe that the interface-free-energy estimates based on CNT are generally in error. As successive refinements of nucleation-barrier theory, we consider corrections due to a non-sharp solid-liquid interface and to a non-spherical cluster shape. Extensive calculations for the Ising model show that corrections due to a non-sharp and thermally fluctuating interface account for the barrier shape with excellent accuracy. The experimental solid nucleation rates that are measured in colloids are better accounted for by these non-CNT terms, whose effect appears to be crucial in the interpretation of data and in the extraction of the interface tension from them.Comment: 20 pages (text + supplementary material