Biomedical subjects

Amilcare Porporato

Publications and source records attributed to Amilcare Porporato.

7 recordsLinked to original sources

PubMed2006

State-dependent fire models and related renewal processes.

We introduce a general class of stochastic processes forced by instantaneous random fires (i.e., jumps) that reset the state variable x to a given value. Since in many physical systems the fire activity is often dependent on the actual value of the state variable, as in the case of natural fires in ecosystems and firing dynamics in neuronal activity, the frequency of fire occurrence is assumed to be state dependent. Such dynamics leads to independent interfire statistics--i.e., to renewal point processes. Various functions relating the frequency of fire occurrence to x(t) are analyzed and compared. The relation between the probabilistic dynamics of x(t) and the interfire statistics is derived and some exact probability distribution of both x(t) and the interfire times are obtained for systems with different degrees of complexity. After studying processes in which the fire activity is coupled only to a deterministic drift, we also analyze processes forced by either additive or multiplicative Gaussian white noise.

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PubMed2006

Probabilistic dynamics of some jump-diffusion systems.

Some exact solutions to the forward Chapman-Kolmogorov equation are derived for processes driven by both Gaussian and compound Poisson (shot) noise. The combined action of these two forms of white noise is analyzed in transient and equilibrium conditions for different jump distributions and additive Gaussian noise. Steady-state distributions with power-law tails are obtained for exponentially distributed jumps and multiplicative linear Gaussian noise. Two applications are discussed: namely, the virtual waiting-time or Takàcs process including Gaussian oscillations and a simplified model of soil moisture dynamics, in which rainfall is modeled as a compound Poisson process and fluctuations in potential evapotranspiration are Gaussian.

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PubMed2004

Similarity solutions of nonlinear diffusion problems related to mathematical hydraulics and the Fokker-Planck equation.

Similarity solutions of the shallow-water equation with a generalized resistance term are studied for open channel flows when both inertial and gravity forces are negligible. The resulting model encompasses various particular cases that appear, in addition to mathematical hydraulics, in diverse physical phenomena, such as gravity currents, creeping flows of Newtonian and non-Newtonian fluids, thin films, and nonlinear Fokker-Planck equations. Solutions of both source-type and dam-break problems are analyzed. Closed-form solutions are discussed, when possible, along with a qualitative study of two phase-plane formulations based on two different variable transformations.

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PubMed2004

Soil water balance and ecosystem response to climate change.

Some essential features of the terrestrial hydrologic cycle and ecosystem response are singled out by confronting empirical observations of the soil water balance of different ecosystems with the results of a stochastic model of soil moisture dynamics. The simplified framework analytically describes how hydroclimatic variability (especially the frequency and amount of rainfall events) concurs with soil and plant characteristics in producing the soil moisture dynamics that in turn impact vegetation conditions. The results of the model extend and help interpret the classical curve of Budyko, which relates evapotranspiration losses to a dryness index, describing the partitioning of precipitation into evapotranspiration, runoff, and deep infiltration. They also provide a general classification of soil water balance of the world ecosystems based on two governing dimensionless groups summarizing the climate, soil, and vegetation conditions. The subsequent analysis of the links among soil moisture dynamics, plant water stress, and carbon assimilation offers an interpretation of recent manipulative field experiments on ecosystem response to shifts in the rainfall regime, showing that plant carbon assimilation crucially depends not only on the total rainfall during the growing season but also on the intermittency and magnitude of the rainfall events.

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PubMed2004

Preferential states in soil moisture and climate dynamics.

Summer precipitation in continental midlatitude regions is significantly contributed by local recycling, i.e., by moisture returning to the atmosphere through evapotranspiration from the same region. On the other hand, reduced soil moisture availability may limit evapotranspiration rates with effects on the planetary boundary layer dynamics through the partitioning between sensible and latent heat fluxes. Thus, a dependence may exist between precipitation and antecedent soil moisture conditions. Here we provide theoretical and experimental evidence in support of the hypothesis that in continental regions summer soil moisture anomalies affect the probability of occurrence of subsequent precipitation. Owing to these feedbacks, two preferential states may arise in summer soil moisture dynamics, which thus tend to remain locked either in a "dry" or a "wet" state, whereas intermediate conditions have low probability of occurrence. In this manner, such land-atmosphere interactions would explain the possible persistence of summer droughts sustained by positive feedbacks in response to initial (spring) surface moisture anomalies.

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PubMed2004

Phase transitions driven by state-dependent poisson noise.

Nonlinear systems driven by state-dependent Poisson noise are introduced to model the persistence of climatic anomalies in land-atmosphere interaction caused by the soil-moisture dependence of the frequency of rainfall events. It is found that these systems may give rise to bimodal probability distributions, while the state variable randomly persists around the preferential states because of transient dynamics that are opposite to the long-term behavior. Mean-field analysis and numerical simulations of the spatially distributed systems reveal a symmetry-breaking bifurcation for sufficiently strong spatial diffusive couplings and intermediate noise intensities. In such conditions, the initial development of spatial patterns is followed by a stable configuration, selected on the bases of the initial conditions in correspondence of the remnants of the modes of the uncoupled system.

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PubMed2004

Water pulses and biogeochemical cycles in arid and semiarid ecosystems.

The episodic nature of water availability in arid and semiarid ecosystems has significant consequences on belowground carbon and nutrient cycling. Pulsed water events directly control belowground processes through soil wet-dry cycles. Rapid soil microbial response to incident moisture availability often results in almost instantaneous C and N mineralization, followed by shifts in C/N of microbially available substrate, and an offset in the balance between nutrient immobilization and mineralization. Nitrogen inputs from biological soil crusts are also highly sensitive to pulsed rain events, and nitrogen losses, particularly gaseous losses due to denitrification and nitrate leaching, are tightly linked to pulses of water availability. The magnitude of the effect of water pulses on carbon and nutrient pools, however, depends on the distribution of resource availability and soil organisms, both of which are strongly affected by the spatial and temporal heterogeneity of vegetation cover, topographic position and soil texture. The 'inverse texture hypothesis' for net primary production in water-limited ecosystems suggests that coarse-textured soils have higher NPP than fine-textured soils in very arid zones due to reduced evaporative losses, while NPP is greater in fine-textured soils in higher rainfall ecosystems due to increased water-holding capacity. With respect to belowground processes, fine-textured soils tend to have higher water-holding capacity and labile C and N pools than coarse-textured soils, and often show a much greater flush of N mineralization. The result of the interaction of texture and pulsed rainfall events suggests a corollary hypothesis for nutrient turnover in arid and semiarid ecosystems with a linear increase of N mineralization in coarse-textured soils, but a saturating response for fine-textured soils due to the importance of soil C and N pools. Seasonal distribution of water pulses can lead to the accumulation of mineral N in the dry season, decoupling resource supply and microbial and plant demand, and resulting in increased losses via other pathways and reduction in overall soil nutrient pools. The asynchrony of resource availability, particularly nitrogen versus water due to pulsed water events, may be central to understanding the consequences for ecosystem nutrient retention and long-term effects on carbon and nutrient pools. Finally, global change effects due to changes in the nature and size of pulsed water events and increased asynchrony of water availability and growing season will likely have impacts on biogeochemical cycling in water-limited ecosystems.

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