Spatial distribution of tracers for optical sensing of stream surface flow

River monitoring is of particular interest for our society that is facing increasing complexity in water management. Emerging technologies have contributed to opening new avenues for improving our monitoring capabilities, but also generating new challenges for the harmonised use of devices and algorithms. In this context, optical sensing techniques for stream surface flow velocities are strongly influenced by tracer characteristics such as seeding density and level of aggregation. Therefore, a requirement is the identification of how these properties affect the accuracy of such methods. To this aim, numerical simulations were performed to consider different levels of particle aggregation, particle colour (in terms of greyscale intensity), seeding density, and background noise. Two widely used image-velocimetry algorithms were adopted: i) Particle Tracking Velocimetry (PTV), and ii) Large-Scale Particle Image Velocimetry (LSPIV). A descriptor of the seeding characteristics (based on density and aggregation) was introduced based on a newly developed metric π. This value can be approximated and used in practice as π = ν0.1 / (ρ / ρ1) where νρ, and ρcν1 are the aggregation level, the seeding density, and the converging seeding density at ν = 1, respectively. A reduction of image-velocimetry errors was systematically observed by decreasing the values of π; and therefore, the optimal frame window was defined as the one that minimises π. In addition to numerical analyses, the Basento field case study (located in southern Italy) was considered as a proof-of-concept of the proposed framework. Field results corroborated numerical findings, and an error reduction of about 15.9 and 16.1 % was calculated – using PTV and PIV, respectively – by employing the optimal frame window.

Numerical simulation of clustered tracers.

How to cite: Pizarro, A., Dal Sasso, S. F., Perks, M., and Manfreda, S.: Spatial distribution of tracers for optical sensing of stream surface flow, Hydrol. Earth Syst. Sci. Discuss.,, in review, 2020. [pdf]


L’approccio statistico rappresenta uno dei principali strumenti di analisi per lo studio dei fenomeni naturali. Eventi estremi e processi di base sono stati analizzati e caratterizzati utilizzando diversi metodi statistici quali: teoria dei valori estremi, distribuzioni di probabilità teoricamente derivate, processi di Poisson, e equazioni differenziali stocastiche. Questi metodi sono stati utilizzati per fornire strumenti di calcolo in diversi ambiti delle costruzioni idrauliche, dell’idrologia e dell’ecoidrologia. Tra questi è opportuno menzionare i modelli per la caratterizzazione spazio-temporale del contenuto idrico del suolo, le distribuzioni derivate per la stima delle piene e dell’erosione localizzata, ed i modelli interpretativi sulla organizzazione spaziale della vegetazione.

An ecohydrological framework to explain shifts in vegetation organization across climatological gradients

Spatial patterns found in vegetated ecosystems exhibit different degrees of organization in stand density that can be interpreted as an indicator of ecosystem health. In semiarid environments, it is possible to observe transitions from over-dispersed individuals (e.g., an ordered lattice) to under-dispersed individuals (e.g., clumped points). These configurations correspond to different strategies of adaptation or optimization, whose understanding may help to predict some of the consequences of environmental changes for both ecosystem services and water resources. For this reason, we have developed a theoretical framework that characterizes the dispersion of individuals through a generalized double Poisson distribution and estimates the landscape-wide statistics using a soil moisture model accounting for tree canopies and root systems overlapping. Considering both the shading effect (light interception) of the canopies and the partitioning of water fluxes due to the presence of multiple individual root systems in one point, the optimum spacing between individuals at a given stand density is determined. This framework allows identifying the climatic boundaries for different landscape patterns in terms of optimal water use and stress. This simple scheme explains well the observed patterns of vegetation in arid and semiarid ecosystems.

How to cite: Manfreda, S., K. K. Caylor, S. Good, An Ecohydrological framework to explain shifts in vegetation organization across climatological gradientsEcohydrology, 10(3), 1-14, (doi: 10.1002/eco.1809), 2017. [pdf]

On the importance of accurate depiction of infiltration processes on modelled soil moisture and vegetation water stress

The description of soil moisture dynamics is a challenging problem for the hydrological community, as it is governed by complex interactions between climate, soil and vegetation. Recent research has achieved significant advances in the description of temporal dynamics of soil water balance through the use of a stochastic differential equation proposed by Laio et al. (2001). The assumptions of the Laio et al. model simplify the mathematical form of the soil water loss functions and the infiltration process. In particular, runoff occurs only for saturation excess, the probability distribution function (PDF) of which is well represented by a simple expression, but the model does not consider the limited infiltration capacity of soil. In the present work, we extend the soil moisture model to include limitations on soil infiltration capacity with the aim of understanding the impact of varying infiltration processes on the soil water balance and vegetation stress. A comparison between the two models (the original version and the modified one) is carried out via numerical simulations. The limited infiltration capacity influences the soil moisture PDF by reducing its mean and variance. Major changes in the PDFs are found for climates characterized by storms of short duration and high rainfall intensity, as well as in humid climates and in cases where soils have moderate permeability (e.g. loam and clay soils). In the case of limited infiltration capacity, modifications to the dynamics of soil moisture generally lead to higher amounts of vegetation water stress. An investigation of the role of soil texture on vegetation water stress demonstrates that loam soil provides the most favorable condition for plant-growth under arid and semi-arid conditions, while vegetation may benefit from the presence of more permeable soils (e.g. loamy sand) in humid climates.

How to cite: Manfreda, S., T.M. Scanlon, K.K. Caylor, On the importance of accurate depiction of infiltration processes on modelled soil moisture and vegetation water stressEcohydrology, 3, 155-165, (doi: 10.1002/eco.79), 2010. [pdf]

Runoff generation dynamics within a humid river basin

The present paper introduces an analytical approach for the description of the soil water balance and runoff production within a schematic river basin. The model is based on a stochastic differential equation where the rainfall is interpreted as an additive noise in the soil water balance and is assumed uniform over the basin, the basin heterogeneity is characterized by a parabolic distribution of the soil water storage capacity and the runoff production occurs for saturation excess. The model allowed to derive the probability density function of the produced surface runoff highlighting the role played by climate and physical characteristics of a basin on runoff dynamics. Finally, the model have been tested over a humid basin of Southern Italy proposing also a strategy for the parameters estimation.

How to cite: Manfreda, S., Runoff Generation Dynamics within a Humid River BasinNatural Hazard and Earth System Sciences, 8, 1349-1357, (doi:10.5194/nhess-8-1349-2008), 2008. [pdf]

A stochastic approach for the description of the water balance dynamics in a river basin

The present paper introduces an analytical approach for the description of the soil water balance dynamics over a schematic river basin. The model is based on a stochastic differential equation where the rainfall forcing is interpreted as an additive noise in the soil water balance. This equation can be solved assuming known the spatial distribution of the soil moisture over the basin transforming the two dimensional problem in a one dimensional one. This assumption is particularly true in the case of humid and semihumid environments, where spatial redistribution of soil moisture becomes dominant producing a well defined pattern. The model allowed to derive the probability density function of the saturated portion of a basin and of its relative saturation. This theory is based on the assumption that the water storage capacity varies across the basin following a parabolic distribution and the basin has homogeneous soil texture and vegetation cover. The methodology outlined the role played by the basin shape in the soil water balance. In particular, the resulting probability density functions of the relative basin saturation were found to be strongly controlled by the maximum water storage capacity of the basin, while the probability density functions of the relative saturated portion of the basin are strongly influenced by the spatial heterogeneity of the soil water storage capacity. Moreover, the saturated areas reach their maximum variability when the mean rainfall rate is almost equal to the soil water loss coefficient given by the sum of the maximum rate of evapotranspiration and leakage loss in the soil water balance. The model was tested using the results of a continuous numerical simulation performed with a semi-distributed model in order to validate the proposed theoretical distributions.

How to cite: Manfreda, S., M. Fiorentino, A Stochastic Approach for the Description of the Water Balance Dynamics in a River BasinHydrology and Earth System Sciences, 12, 1189-1200, (doi:10.5194/hess-12-1189-2008), 2008.  [pdf]

Space-time modeling of soil moisture: Stochastic rainfall forcing with heterogeneous vegetation

The present paper complements that of Isham et al. (2005), who introduced a space-time soil moisture model driven by stochastic space-time rainfall forcing with homogeneous vegetation and in the absence of topographical landscape effects. However, the spatial variability of vegetation may significantly modify the soil moisture dynamics with important implications for hydrological modeling. In the present paper, vegetation heterogeneity is incorporated through a two dimensional Poisson process representing the coexistence of two functionally different types of plants (e.g., trees and grasses). The space-time statistical structure of relative soil moisture is characterized through its covariance function which depends on soil, vegetation, and rainfall patterns. The statistical properties of the soil moisture process averaged in space and time are also investigated. These properties are especially important for any modeling that aggregates soil moisture characteristics over a range of spatial and temporal scales. It is found that particularly at small scales, vegetation heterogeneity has a significant impact on the averaged process as compared with the uniform vegetation case. Also, averaging in space considerably smoothes the soil moisture process, but in contrast, averaging in time up to 1 week leads to little change in the variance of the averaged process.

How to cite: Rodríguez-Iturbe, I., V. Isham, D.R. Cox, S. Manfreda, A. Porporato, Space-time modeling of soil moisture: stochastic rainfall forcing with heterogeneous vegetationWater Resources Research, 42, W06D05, (doi:10.1029/2005WR004497), 2006. [pdf]

Representation of space–time variability of soil moisture

A simplified spatial-temporal soil moisture model driven by stochastic spatial rainfall forcing is proposed. The model is mathematically tractable, and allows the spatial and temporal structure of soil moisture fields, induced by the spatial-temporal variability of rainfall and the spatial variability of vegetation, to be explored analytically. The influence of the main model parameters, reflecting the spatial scale of rain cells, the soil storage capacity, the rainfall interception and the soil water loss rate (representing evaporation and deep infiltration) is investigated. The variabilities of the spatially averaged soil moisture process, and that averaged in both space and time, are derived. The present analysis focuses on spatially uniform vegetation conditions; a follow-up paper will incorporate stochastically heterogeneous vegetation.

How to cite: Isham, V., D.R. Cox, I. Rodríguez-Iturbe, A. Porporato, S. Manfreda, Representation of Space-Time Variability of Soil MoistureProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461(2064), 4035 – 4055, (doi:10.1098/rspa.2005.1568), 2005. [pdf]