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The virtual water (VW) trade associated to food is composed by the quantity of water utilized for the production of the crops exchanged on the global market. In assessing a country’s water abundance or scarcity when entering the international VW trade, scholars consider only physical water availability, neglecting economic water scarcity, which indicates situations in which socio-economic obstacles impede the productive use of water. We weight the global VW trade associated to primary crops with a newly proposed composite water scarcity index (CWSI) that combines physical and economic water scarcity. 39% of VW volumes is exported from countries with a higher CWSI than the one of the destination country. Such unfair routes occur both from low- to high-income countries and among low- and middle-income countries themselves. High-income countries have a predominant role in import of CWSI-weighted VW, while low- and middle-income countries dominate among the largest CWSI-weighted VW exporters. For many of them economic water scarcity dominates over physical scarcity. The application of the CWSI elicits also a status change from net exporter to net importer for some wealthy countries and viceversa for some low- and middle-income countries. The application of CWSI allows one to quantify to what extent VW exchanges flow along environmentally and economically unfair routes, and it can inform the design of compensation policies.

Many studies have shown a growing trend in terms of frequency and severity of extreme events. As never before, having tools capable to monitor the amount of rain that reaches the Earth’s surface has become a key point for the identification of areas potentially affected by floods. In order to guarantee an almost global spatial coverage, NASA Global Precipitation Measurement (GPM) IMERG products proved to be the most appropriate source of information for precipitation retrievement by satellite. This study is aimed at defining the IMERG accuracy in representing extreme rainfall events for varying time aggregation intervals. This is performed by comparing the IMERG data with the rain gauge ones. The outcomes demonstrate that precipitation satellite data guarantee good results when the rainfall aggregation interval is equal to or greater than 12 h. More specifically, a 24-h aggregation interval ensures a probability of detection (defined as the number of hits divided by the total number of observed events) greater than 80%. The outcomes of this analysis supported the development of the updated version of the ITHACA Extreme Rainfall Detection System (ERDS: erds.ithacaweb.org). This system is now able to provide near real-time alerts about extreme rainfall events using a threshold methodology based on the mean annual precipitation.

Streamflow prediction in high-altitude scarcely-gauged catchments is essential for efficient water resources management and hydropower generation. Aim of this study is to estimate water resources availability (WRA) by the application of a standard rainfall-runoff model and to study its impact on mini-hydropower production with application to Mangla basin. The Mangla basin is a scarcely gauged catchment situated in the snow- and glacier-fed Himalayan and Pir Panjal Range. Daily streamflow forecasting has been performed by the application of a GIS (Geographic Information System) based hydrological modeling system (HEC-HMS) with observed and TRMM (Tropical Rainfall Measuring Mission) rainfall data to cover the ungauged part of the catchment. The obtained results suggest that HEC-HMS can efficiently reproduce daily streamflows in snow-fed glacierized catchments with Nash-Sutcliffe (NS) coefficients in the range 0.71–0.80. The WRA was estimated at the Mangla dam to analyze its impact on mini-hydropower generation at Upper Jhelum Canal (UJC). The gross mini-hydropower potential energy on the UJC was found to be 196 and 360 GWH for average and design discharge, respectively, demonstrated that mini-hydro power generation could be a significant addition for the energy sector of Pakistan.

World freshwater ecosystems are significantly deteriorating at a faster rate than other ecosystems. Water withdrawals are recognized as one of the main drivers of growing water stress in river basins worldwide. Over the years, much effort has been devoted to quantify water withdrawals at a global scale; however, comparisons are not simple because the uneven spatiotemporal distribution of surface water resources entails that the same amount of consumed water does not have the same environmental cost in different times or places. In order to account for this spatiotemporal heterogeneity, this work proposes a novel index to assess the environmental cost of a withdrawal from a generic river section. The index depends on (i) the environmental relevance of the impacted fluvial ecosystem (e.g., bed-load transport capacity, width of the riparian belt, biodiversity richness) and (ii) the downstream river network affected by the water withdrawal. The environmental cost has been estimated in each and every river section worldwide considering a reference withdrawal. Being referred to a unitary reference withdrawal that can occur in any river section worldwide, our results can be suitably arranged for describing any scenario of surface water consumption (i.e., as the superposition of the actual pattern of withdrawals). The index aims to support the interpretation of the volumetric measure of surface water withdrawal with a perspective that takes into account the fluvial system where the withdrawal actually occurs. The application of the index highlights the river regions where withdrawals can cause higher environmental costs, with the challenge of weighting each water withdrawal considering the responsibilities that it has on downstream freshwater ecosystems.

Planning and verification of hydraulic infrastructures require a design estimate of hydrologic variables, usually provided by frequency analysis, and neglecting hydrologic uncertainty. However, when hydrologic uncertainty is accounted for, the design flood value for a specific return period is no longer a unique value, but is represented by a distribution of values. As a consequence, the design flood is no longer univocally defined, making the design process undetermined. The Uncertainty Compliant Design Flood Estimation (UNCODE) procedure is a novel approach that, starting from a range of possible design flood estimates obtained in uncertain conditions, converges to a single design value. This is obtained through a cost–benefit criterion with additional constraints that is numerically solved in a simulation framework. This paper contributes to promoting a practical use of the UNCODE procedure without resorting to numerical computation. A modified procedure is proposed by using a correction coefficient that modifies the standard (i.e., uncertainty-free) design value on the basis of sample length and return period only. The procedure is robust and parsimonious, as it does not require additional parameters with respect to the traditional uncertainty-free analysis. Simple equations to compute the correction term are provided for a number of probability distributions commonly used to represent the flood frequency curve. The UNCODE procedure, when coupled with this simple correction factor, provides a robust way to manage the hydrologic uncertainty and to go beyond the use of traditional safety factors. With all the other parameters being equal, an increase in the sample length reduces the correction factor, and thus the construction costs, while still keeping the same safety level.

Plant rooting systems affect slope stability through the soil reinforcement given by the root network. The vertical root distribution in particular is crucial for the assessment of the critical slip surface in slope stability analyses. We propose here an expeditious way to assess the major characteristics of the root system at landslide slopes. More in detail, we extend and validate an ecohydrological model proposed for flat terrain and water-dependent ecosystems by Laio et al. (2006). This model has the merit to use readily available climatic and pedologic descriptors to predict the mean root depth, but its extension to hillslopes in semi-humid environments requires validation. The model has been improved and then tested on a case study in northern Tuscany (Italy) which considers 17 landslide sites where the tree rooting systems have been measured. The results show a quite good match between observed and modeled mean root depths. The accuracy of the results largely depends on the improvements brought to the model in the parameters estimation phase, in particular through the application of the Curve Number method and through the refinement of the definition of the growing season. The results show that in 14 cases out of 17 the error is lower than 30%. Furthermore, the error becomes lower than 30% at all sites if we take into account differences among soils in the estimation of the portion of precipitation which infiltrates into the soil. These results prove the potential of the proposed method: using few and quite readily available parameters, it allows one to determine the mean root depths of vegetation with good accuracy: an important parameter for stability assessment of vegetated slopes on a large scale.

[1] Through the international trade of food commodities, countries virtually export or import the water used for food production, known as “virtual water.” The international trade network thus implies a network of virtual water flows from exporting to importing countries. The purpose of this study is to identify some controlling factors of the virtual water network by means of multivariate regression analyses, or gravity laws, as often named in economics. Starting from the FAOSTAT database, we reconstruct 25 years (1986–2010) of international virtual water trade values; we then analyze the dependence of the exchanged fluxes on: population, gross domestic product, arable land, virtual water embedded in agricultural production and dietary demand, and geographical distance between countries. Significant drivers are identified for each country considering separately export and import fluxes; temporal trends are outlined and the relative importance of drivers is assessed by a commonality analysis. Results indicate that population, gross domestic product and geographical distance are the major drivers of virtual water fluxes, with a minor (nonnegligible) contribution given by the agricultural production of exporting countries. Such drivers have become relevant for an increasing number of countries throughout the years, with an increasing variance explained by the distance between countries and a decreasing role of the gross domestic product. The worldwide adjusted coefficient of determination of fitted gravity-law model is 0.57 (in 2010), and it has increased in time, confirming the good descriptive capability of selected drivers for the virtual water trade.

We develop and compare two hydraulically-based schemes of the xylem structure of an individual plant. The dynamics of water uptake are analyzed under random conditions through the modeling of rainfall as a stochastic process. The two hydraulic schemes differ in the modeling of the root ability to cooperate, i.e., the capacity of roots to increase the water uptake from the wetter soil layers when other parts of the soil are dry (compensation effect) and to transfer water from moister into drier soil layers (water redistribution effect). Both compensation and water redistribution are direct consequences of the hydraulic structure of the root system, which is modeled here considering two contrasting cases corresponding to non-interacting uptake paths from different soil layers, and converging uptake paths. Only the latter hydraulic architecture allows for compensation and water redistribution. Another important difference between the hydraulic schemes is the stomatal response to soil dryness. When the soil water is unevenly distributed in the soil layers, the differences in the hydraulic schemes emerge. In semi-arid climates, plants characterized by a cooperative root system are shown to be less prone to water stress. In contrast, plants with non-interacting roots result to be better fit to humid climates, where the probability of droughts is small.

The flow duration curve (FDC) is a fundamental signature of the hydrological cycle to support water management strategies. Despite many studies on this topic, its estimation in ungauged basins is still a relevant issue as the FDC is controlled by different types of processes at different time-space scales, thus resulting quite sensitive to the specific case study. In this work, a regional spatially-smooth procedure to evaluate the annual FDC in ungauged basins is proposed, based on the estimation of the L-moments (mean, L-CV and L-skewness) through regression models valid for the whole case study area. In this approach, homogeneous regions are no longer required and the L-moments are allowed to continuously vary along the river network, thus providing a final FDC smoothly evolving for different locations on the river. Regressions are based on a set of topographic, climatic, land use and vegetation descriptors at the basin scale. Moreover, the model ensures that the mean annual runoff is preserved at the river confluences, i.e. the sum of annual flows of the upstream reaches is equal to the predicted annual downstream flow. The proposed model is adapted to incorporate different "sub-models" to account for local information within the regional framework, where man-induced alterations are known, as common in non-pristine catchments. In particular, we propose a module to consider the impact of existing/designed water withdrawals on the L-moments of the FDC. The procedure has been applied to a dataset of daily observation of about 120 gauged basins on the upper Po river basin in North-Western Italy.

We propose a method for assessing root profiles by means of hydrological, pedological and above-ground vegetation information. The method is analytical and allows one to relate the vertical distribution of plant roots to the local climatic and pedological conditions. The model does not require calibration and employs only data that are easily available. The model has been applied to two case studies in central Italy and proved effective for assessing both root area and average rooting depth as functions of depth. Plant rooting systems turn out to be closer to the soil surface where the soils are clay-textured and where the evaporation/precipitation ratio is large (intensive water use). The proposed methodology would be useful for slope ecosystem restoration, non-destructive analysis of the stability of vegetated slopes, and planning soil bio-engineering works.

Known as "the hidden half", plant roots are fundamental contributors to the riparian ecosystem functioning. Roots show an extraordinary architectural complexity that recalls their remarkable ability to adapt to environmental heterogeneity, resources availability, and climate. In fluvial environments, phreatophytes and hydrophytes cope with flow and sediment processes, and hydrotropism and aerotropism are the main drivers for root growth. In this work, we show how the vertical root density distribution in riparian plants is the result of how plants respond to the random fluctuations of river flows. A root data set from field and controlled outdoor experiments is used in combination with a physically based analytical model to demonstrate that the root vertical density distribution can be ascribed to the interplay of randomness and determinism in a simple mathematical form. The shape of the distribution reflects the profitability of plant roots to grow in different soil layers depending on the soil moisture availability. For the first time, this model helps understanding in an analytical manner the adaptation strategy of plant roots to different scenarios, paving the way for the comprehension of the effects of future changes in climate and environmental conditions.

Univariate shot noise models for streamflow generation at short time scales are examined in detail, to reconsider the verification of the basic hypotheses behind the models, the problem of objectively evaluating their performances, and the importance of model parsimony. The classical approach to model estimation is shown to produce some inconsistencies in the inverse evaluation of the model input, in particular regarding the assumed independence and Poissonianity of the pulses; an alternative procedure for pulses identification is proposed, which enables the mentioned hypotheses to be respected. To evaluate model performances, two indices are proposed, respectively based on the comparison of real and generated flow duration curves (I1) and annual maxima statistics (I2). A method for explicitly accounting for the dependence of I1 and I2 on the number of model parameters is described. An application to seven daily streamflow time series in northern Italy demonstrates the validity of the proposed procedure for the identification of the input and the usefulness of the performance indices in discerning among competing models.

The nitrogen and carbon cycles in the broad-leafed savanna at Nylsvley (S. Africa) are modeled using the stochastic approach presented by Porporato et al. [Adv Water Res (this issue)]. An accurate representation of the hydrological mechanisms that control the nitrogen cycle at the daily time scale is shown to be necessary to capture the impact of the high-frequency variability of the soil moisture on the nitrogen and carbon dynamics. The fluctuations of the random precipitation forcing propagate to soil moisture, carbon, and nitrogen dynamics, giving rise to a gamut of fluctuations at different time scales. Long simulations are carried out to achieve a probabilistic characterization of the dynamics of the state variables under different rainfall regimes.

Population growth, socio-economic development and climate changes are placing increasing pressure on water resources. Crop water footprint is a key indicator in the quantification of such pressure. It is determined by crop evapotranspiration and crop yield, which can be highly variable in space and time. While the spatial variability of crop water footprint has been the objective of several investigations, the temporal variability remains poorly studied. In particular, some studies approached this issue by associating the time variability of crop water footprint only to yield changes, while considering evapotranspiration patterns as marginal. Validation of this Fast Track approach has yet to be provided. In this Letter we demonstrate its feasibility through a comprehensive validation, an assessment of its uncertainty, and an example of application. Our results show that the water footprint changes are mainly driven by yield trends, while evapotranspiration plays a minor role. The error due to considering constant evapotranspiration is three times smaller than the uncertainty of the model used to compute the crop water footprint. These results confirm the suitability of the Fast Track approach and enable a simple, yet appropriate, evaluation of time-varying crop water footprint.

Three water-controlled ecosystems are studied here using the stochastic description of soil moisture dynamics and vegetation water stress proposed in Part II (F. Laio, A. Porporato, L. Ridolfi, I. Rodriguez-Iturbe, Adv. Water Res. 24 (7) (2001) 707-723) and Part III (A. Porporato, F. Laio, L. Ridolfi, I. Rodriguez-Iturbe, Adv. Water Res. 24 (7) (2001) 725-744) of this series of papers. In the savanna of Nylsvley (South Africa) the very diverse physiological characteristics of the existing plants give rise to different strategies of soil moisture exploitation. Notwithstanding these differences, the vegetation water stress for all the species turns out to be very similar, suggesting that coexistence might be attained also through differentiation of water use. The case of the savanna of Southern Texas points out how rooting depth and interannual rainfall variability can impact soil moisture dynamics and vegetation water stress. Because of the different responses to water stress of trees and grasses, external climatic forcing could be at the origin of the dynamic equilibrium allowing coexistence in this ecosystem. Finally, the analysis of a short grass steppe in Colorado provides an interesting example of the so-called inverse texture effect, whereby preferential conditions for vegetation are dependent on soil texture and rainfall. Sites which are more favorable during wet conditions may become less suitable to the same vegetation type during drier years. Such an effect is important to explain the predominance of existing species, as well as to investigate their reproductive strategies.

This study investigates the uncertainty in the estimation of the design flood induced by errors in flood data. We initially describe and critically discuss the main sources of uncertainty affecting river discharge data, when they are derived using stage-discharge rating curves. Then, different error structures, recently proposed by the literature, are used to investigate the effects of flood data errors on design flood estimation. Annual maxima values of river discharge observed on the River Po (Italy) at Pontelagoscuro are used as application example. The study demonstrates that observation errors may have a significant impact on the uncertainty of design flood, especially when rating curve is affected by systematic errors.

[1] Wetlands are crucial ecosystems which provide several functions, beneficial both to human beings and to the environment. Despite such importance, quantitative approaches to many aspects of wetlands are far from being adequate, above all the interaction between rainfall, vegetation, soil moisture and groundwater depth. Starting from a previously developed model for below-ground stochastic water level fluctuations, we extend it to consider the case of waterlogging. The extended model is now suitable for describing the long-term probability distribution of water table depth in temporarily inundated wetland sites, whose hydrologic input is dominated by stochastic rainfall. The extended model performs well when compared to real data collected in the Everglades National Park (Florida, US), confirming its capability to capture the stochastic variability of wetland ecosystems.

Soil water limitations cause water-stressed conditions in vegetation because of temporary and/or permanent damage to plant tissues. Vegetation water stress is here assumed to increase when soil moisture is below a threshold level, s*, and to decrease otherwise. The crossing properties of s* allow one to describe the temporal evolution of water stress, Φ, as a dichotomic Markov process. The available analytical solutions for dichotomic processes are used to determine the probability density function of Φ and the mean first-passage times (MFPT) of a water stress threshold. MFTP is used as a measure of the variability of water stress. The use of MFPT in conjunction with the average stress levels allows us to provide a more complete characterization of health/stress conditions in vegetation. We investigate the influence on the dynamics of vegetation water stress of different climatic, pedological, and plant physiological parameters. From these analyses, we find, for example, that resistant species are favoured in relatively humid environments, whereas resilient shallow-rooted plants have an advantage in drier conditions.

[1] Areas with a relatively shallow water table are environments where the groundwater plays a key role on the ecosystem function, and important interactions exist between hydrology and ecosystem processes. We propose here an analytical model to study the interactions between rainfall, water table, and vegetation in groundwater-dependent ecosystems. The water table dynamics are studied as a random process stochastically driven by a marked Poisson noise representing rainfall events. Infiltration, root water uptake, water flow to/from an external water body, and capillary rise are accounted for in a probabilistic description of water table fluctuations. We obtain analytical expressions for the steady state probability distribution of water table depth, which allows us to investigate the long-term behavior of water table dynamics, and their sensitivity to changes in climate, vegetation cover, and water management.

[1] The effect of temperature on the flood frequency distribution in mountainous basins is examined through a minimalist analytical model. The conceptual hypothesis on which the model is grounded is the existence of a subtractive mechanism that reduces the basin-contributing area in flood formation to the fraction of basin laying below the freezing elevation at the time of occurrence of each precipitation event. This fraction depends on the watershed hypsometric curve and on the seasonal evolution of temperatures. Under this hypothesis, the probability distribution of the annual maximum discharge is analytically derived, based on simple assumptions on the stochastic process of precipitation. The shape and the moments of this distribution explicitly relate to basin hypsometry and to the seasonality of temperatures. Qualitative results show that the simple causative mechanisms can explain the attenuation of flood quantiles in high-elevation basins. Model application to 57 watersheds in the Northwestern Italian Alps effectively demonstrates the role of the hypsography in explaining the spatial variability of the mean of the flood distribution.

[1] The soil water content plays a fundamental role in a number of important environmental processes, including those involved in the water cycle, vegetation dynamics, soil biogeochemical cycles, and land-atmosphere interactions. Despite the recent efforts spent in the analytical modeling of the stochastic soil moisture dynamics in dryland ecosystems, the probabilistic characterization of the soil water balance in groundwater dependent environments is still missing, due to the complexity arising from the existence of shallow aquifers and capillary rise. This paper makes a first step in the direction of studying the stochastic soil water balance in groundwater dependent systems. An analytic probabilistic framework is developed for the modeling of soil moisture dynamics at the daily timescale for the case of bare soil conditions and in the presence of a shallow water table. This framework accounts for random rainfall occurrence, water table fluctuations, capillary rise, and soil evaporation. The stochastic soil water balance equation is analytically solved in the steady state, and the probability density functions of water table depth, soil moisture (as a function of depth), and evaporation are obtained and discussed for a variety of climate conditions and soil properties.

[1] Soil water content is a key determinant of the health of terrestrial ecosystems. It plays a fundamental role in the feedbacks between the Earth and the atmosphere, as well as in all aspects of vegetation growth and composition. The dynamics of soil water in humid areas, and especially in wetlands, presents particularly challenging features for its quantitative description, since it needs to be linked to the intertwined stochastic fluctuations of the water table and the soil moisture of the unsaturated zone. These fluctuations are themselves dependent on the climate, soil, and vegetation of the region. The paper describes some of the most important problems that need to be considered in attempting to develop a quantitative framework for the ecohydrology of humid areas. The avenues of research suggested here will play a keystone role in the understanding of the complex dynamics of humid lands as well as in their scientifically based management in the face of a changing climate.

[1] We propose an analytical model to relate the vertical distribution of plant roots in water controlled ecosystems to the local climatic and pedologic conditions. We find that the shape of the root profile is determined by the distribution of the incoming rainfall pulses, and that the rooting systems are deeper where the soils are coarse-textured and the evaporative demand slightly exceeds precipitation.

[1] The interaction of vegetation with the groundwater is one of the key mechanisms affecting the dynamics of wetland plant ecosystems. The main feature of these interactions is the feedback between the downward shift of the water table caused by riparian vegetation and the emergence of soil aeration conditions favorable to plant establishment, growth, and survival. We develop a conceptual framework to explain how vegetation–water table feedbacks may lead to the emergence of multiple stable states in the dynamics of wetland forests and riparian ecosystems. This framework is used to investigate the sensitivity of these ecosystems to vegetation disturbances and changes in water table depth. As a result of these feedbacks, such ecosystems are prone to catastrophic shifts to an unvegetated state. Because of their competitive advantage, water-tolerant and shallow-rooted species can replace the original vegetation, contributing to the occurrence of vegetation succession in riparian zones and to the existence of alternative vegetation states between areas with shallow and deep water tables.

[1] Well-defined vegetation patterns are a widespread feature of dryland landscapes, where spotted, banded, or other organized systems of vegetation patches are bordered by bare soil. A number of different mechanisms have been invoked to explain the emergence of these patterns and to associate their geometrical features to the driving (biotic and abiotic) processes. A commonly accepted theory of pattern formation is based on the interplay between mechanisms of short-range facilitation and long-range competition with surrounding vegetation. Recently associated with the emergence of vegetation patterns, these short- and long-range interactions have been seldom interpreted as a means for plants to enhance their chances of survival in arid environments. Here we develop a simplistic facilitation-competition model to show how these spatial interactions increase the productivity of dryland ecosystems. Stable (sparsely) vegetated states are shown to occur even in systems in which unvegetated conditions are the only stable state of the local dynamics (i.e., in the absence of spatial interaction). Pattern emergence is also interpreted as an easily detectable sign of the occurrence of highly effective resource allocation and use due to spatial interactions. Moreover, the resilience of vegetated states is qualitatively related to pattern geometry.

[1] We present an analysis of water balance and plant water stress along the Kalahari precipitation gradient using a probabilistic model of soil moisture. The rainfall statistical characteristics, obtained from daily data of four stations along the transect, show that the rainfall gradient (from 950 to 300 mm/year) is mostly due to a decrease in the mean rate of storm arrivals (from 0.38 to 0.09 1/day) rather than to a change in the mean storm depth (practically constant at 10 mm). Using this information and typical vegetation and soil parameters, the analysis relates the vegetation properties along the transect with those of climate and soil. It is shown that differences in water balance and plant water stress between trees and grasses generate varying preferences for vegetation types along the transect, with deeper-rooted trees favored in the more mesic regions of the northern Kalahari and grasses favored in the drier zones of the southern Kalahari. The point of equal plant water stress is found at about 420 mm of rainfall during the growing season (October–April), indicating the possibility of tree-grass coexistence in the central sector of the Kalahari. These findings are consistent with patterns of vegetation distribution across the Kalahari transect.

Ecosystem dynamics in arid and semiarid climates are strongly dependent on the soil water availability which, in turn, is the result of a number of complex and mutually interacting hydrologic processes. This motivates the development of a process-based framework for the analysis of the soil water content in the root zone at the daily time scale. This paper reviews the results that the authors have obtained using a probabilistic–mechanistic model of soil water balance for the characterization of the seasonal regimes of soil moisture with different combinations of climate, soil, and vegetation. Average seasonal soil water content and level-crossing statistics have been used to study conditions of water stress in vegetation. The same framework has been applied to the analysis of the impact of interannual climate fluctuations on the seasonal regime of soil moisture and water stress.

[1] Starting from a stochastic model of the water balance at a point proposed by Rodriguez-Iturbe et al. [1999], the unsteady dynamics of mean soil moisture under varying climatic conditions is analyzed. The exact differential equations that describe the evolution of the mean soil moisture are obtained, and the simplifications that are needed to solve these equations are detailed. Within this framework we are able to study the importance of the seasonal variations in precipitation and evapotranspiration and the role of the root depth and soil characteristics, as well as the possible occurrence and relevance of steady state conditions for the soil moisture process during the growing season.