arXiv subjects

Amilcare Porporato

Publications and source records attributed to Amilcare Porporato.

At least 37 records · Page 2Linked to original sources

arXiv2020

Linear layout of multiple flow-direction networks for landscape-evolution simulations

We present an algorithm that is well suited to find the linear layout of the multiple flow-direction network (directed acyclic graph) for an efficient implicit computation of the erosion term in landscape evolution models. The time complexity of the algorithm varies linearly with the number of nodes in the domain, making it very efficient. The resulting numerical scheme allows us to achieve accurate steady-state solutions in conditions of high erosion rates leading to heavily dissected landscapes. We also establish that contrary to single flow-direction methods such as D8, D$\infty$ multiple flow-direction method follows the theoretical prediction of the linear stability analysis and correctly captures the transition from smooth to the channelized regimes. We finally show that the obtained numerical solutions follow the theoretical temporal variation of mean elevation.

physics.geo-ph↗

arXiv2020

Dynamic dependence of nonequilibrium work limits the validity of the Jarzynski Equality

The Jarzynski equality (JE) is analyzed in regard to its validity for both quasi-static transformations in the thermodynamic limit and Hamiltonian evolutions of the work protocol. In the first case, we show that the JE holds for isothermal transformations only; in the second case, we show that the work done (linked to the final state Hamiltonian) depends on the temporal dynamics of the work protocol (including its speed), thus precluding the possibility of identifying it with the free energy or any other thermodynamic state function. Even in the case of thermodynamic limit and infinitesimally slow transformations of the Hamiltonian (adiabatic invariance) following states of thermodynamic equilibrium, the resulting work expression does not default to the JE, but to the work relation for adiabatic thermodynamic transformations, W=Delta U, where W is work and U is internal energy.

cond-mat.stat-mech↗

arXiv2020

A Fast-Slow Model of Banded Vegetation Pattern Formation in Drylands

From infiltration of water into the soil during rainstorms to seasonal plant growth and death, the ecohydrological processes that are thought to be relevant to the formation of banded vegetation patterns in drylands occur across multiple timescales. We propose a new fast-slow switching model in order to capture these processes on appropriate timescales within a conceptual modeling framework based on reaction-advection-diffusion equations. The fast system captures hydrological processes that occur on minute to hour timescales during and shortly after major rainstorms, assuming a fixed vegetation distribution. These include key feedbacks between vegetation biomass and downhill surface water transport, as well as between biomass and infiltration rate. The slow system acts between rain events, on a timescale of days to months, and evolves vegetation and soil moisture. Modeling processes at the appropriate timescales allows parameter values to be set by the actual processes they capture. This reduces the number of parameters that are chosen expressly to fit pattern characteristics, or to artificially slow down fast processes by the orders of magnitude required to align their timescales with the biomass dynamics. We explore the fast-slow switching model through numerical simulation on a one-dimensional hillslope, and find agreement with certain observations about the pattern formation phenomenon, including band spacing and upslope colonization rates. We also find that the predicted soil moisture dynamics are consistent with time series data that has been collected at a banded vegetation site. This fast-slow model framework introduces a tool for investigating the possible impact of changes to frequency and intensity of rain events in dryland ecosystems.

nlin.PS↗

arXiv2020

Fluctuation-theorem and extended thermodynamics of turbulence

Turbulent flows are out-of-equilibrium because the energy supply at large scales and its dissipation by viscosity at small scales create a net transfer of energy among all scales. Here, the energy cascade is approximated by a combined contribution of a forward drift and diffusion that recover accepted phenomenological theories of turbulence. The fluctuation theorem (FT) is then shown to describe the scale-wise statistics of forward and backward energy transfer and their connection to irreversibility and entropy production. The ensuing turbulence entropy may be used to formulate an extended turbulence thermodynamics.

physics.flu-dyn↗

arXiv2020

Impacts of Solar Intermittency on Future Photovoltaic Reliability

As photovoltaic power is expanding rapidly worldwide, it is imperative to assess its promise under future climate scenarios. While a great deal of research has been devoted to trends of mean solar radiation, less attention has been paid to its intermittent character, a key challenge when compounded with uncertainties related to climate variability. Using both satellite data and climate model outputs, here we characterize solar radiation intermittency to assess future photovoltaic reliability. We find that the relation between the future power supply and long-term trends of mean solar radiation is highly nonlinear, thus making power reliability more sensitive to the fluctuations of mean solar radiation in regions where insolation is the highest. Our results highlight how reliability analysis must account simultaneously for the mean and intermittency of solar inputs when assessing the impacts of climate change on photovoltaics.

physics.ao-ph↗

arXiv2019

Variational Analysis of Landscape Elevation and Drainage Networks

Landscapes evolve toward surfaces with complex networks of channels and ridges in response to climatic and tectonic forcing. Here we analyze variational principles giving rise to minimalist models of landscape evolution as a system of partial differential equations that capture the essential dynamics of sediment and water balances. Our results show that in the absence of diffusive soil transport, the steady-state surface extremizes the average domain elevation. Depending on the exponent m of specific drainage area in the erosion term, the critical surfaces are either minima (0 1), with m=1 corresponding to a saddle point. Our results establish a connection between Landscape Evolution Models (LEMs) and Optimal Channel Networks (OCNs) and elucidate the role of diffusion in the governing variational principles.

physics.geo-ph↗

arXiv2019

Bridging discrete and continuous formalisms for biodiversity quantification

Several theoretical frameworks have been proposed to explain observed biodiversity patterns, ranging from the classical niche-based theories, mainly employing a continuous formalism, to neutral theories, based on statistical mechanics of discrete communities. Differences in the descriptions of biodiversity can arise due to the discrete or continuous nature of the underlying models and the way internal or external perturbations appear in their formulations. Here, we trace the effects of stochastic population dynamics on biodiversity, from the scale of the individuals to the community and based on both discrete and continuous representations of the system, by consistently using measures of community diversity like the species abundance distribution and the rank abundance curve and applying them to both discrete and continuous populations. A novel measure, the community abundance distribution, is introduced to facilitate the comparison across different levels of description, from microscopic to macroscopic. Using a simple birth and death process and an interacting population model, we highlight discrepancies in their discrete and continuous distributions and discuss relevant implications for the analysis of rare species and extinction dynamics. Quantitative consideration of these issues is useful for better understanding of the contributions of non-neutral processes and the mathematical approximations to various measures of biodiversity.

q-bio.QM↗

arXiv2019

From Turbulence to Landscapes: Universality of Logarithmic Mean Profiles in Bounded Complex Systems

The logarithmic mean-velocity profile is a key experimental and theoretical result in wall-bounded turbulence. Similarly, here we show that the topographic surface emerging between parallel zero-elevation boundaries presents an intermediate region with a logarithmic mean-elevation profile. We use model simulations, which account for growth, erosion, and smoothing processes and give rise to complex topography with channel branching and fractal river networks, as well as data from a physical landscape-evolution experiment. Dimensional and self-similarity arguments are used to corroborate this finding. Our results suggest a universality of the logarithmic scaling in bounded complex systems out of equilibrium, of which landscape topography and turbulence are quintessential examples.

physics.geo-ph↗

arXiv2019

Thermodynamics of fluctuations in small systems interacting with the environment

A few decades after Hill's work on nano-thermodynamics, the development of a thermodynamic framework, to account consistently for the fluctuations of small systems due to their interactions with the surrounding environment, is still underway. Here we discuss how, in a small system, the interaction energy with the environment may be described through a conjugate pair of intensive and extensive variables, giving rise to a Gibbs thermodynamics with an additional thermodynamic degree of freedom. The relevant thermodynamic potentials help describe the equilibrium conditions and the material properties that measure the susceptibility of the system to the interaction with the environment. The resulting generalized ensembles, which describe the non-negligible, small system fluctuations, are shown to be equivalent. Away from the average thermodynamic state, the availability describes the distance between system and the environment, in terms of the maximum work extractable from the fluctuation, and a proper definition of entropy extends the thermodynamics to the generic fluctuating state. From the latter state, entropic forces arise to restore the average thermodynamic state. Our framework unifies and extends the ensemble thermodynamics by Hill and the recent advances in statistical mechanics under strong coupling and reduces to classical macroscopic thermodynamics when the system is large. The particular case of a small ideal gas system is discussed in detail and the example of a single particle immersed in a bath is revisited in the light of the new formalism.

cond-mat.stat-mech↗

arXiv2019

Channelization cascade

The hierarchy of channel networks in landscapes displays features that are characteristic of non-equilibrium complex systems. Here we show that a sequence of increasingly complex ridge and valley networks is produced by a system of partial differential equations coupling landscape evolution dynamics with a specific catchment area equation. By means of a linear stability analysis we identify the critical conditions triggering channel formation and the emergence of characteristic valley spacing. The ensuing channelization cascade, described by a dimensionless number accounting for diffusive soil creep, runoff erosion, and tectonic uplift, is reminiscent of the subsequent instabilities in fluid turbulence, while the structure of the simulated patterns is indicative of a tendency to evolve toward optimal configurations, with anomalies similar to dislocation defects observed in pattern-forming systems. The choice of specific geomorphic transport laws and boundary conditions strongly influences the channelization cascade, underlying the nonlocal and nonlinear character of its dynamics.

physics.geo-ph↗

arXiv2019

Energy Constraints for Climate Models from Hydrologic Partitioning

It is well known that evaporative cooling of Earth's surface water reduces the amount of radiation that goes into sensible heat, namely the portion of radiation that produces higher temperatures. However, a rigorous use of long-term hydrologic measurements and the related theories of hydrologic partitioning have not yet been fully exploited to quantify these effects on climate. Here, we show that the Budyko's curve, a well-known and efficient framework for water balance estimation, can be effectively utilized to partition the surface energy fluxes by expressing the long-term evaporative fraction as a function of the dryness index. The combination of this energy partitioning method with hydrological observations allows us to estimate the surface energy components at watershed and continental scales. Analyzing climate model outputs through this new lens reveals energy biases due to inaccurate parameterization of hydrological and atmospheric processes, offering insight into model parameterization and providing useful information for improving climate projections.

physics.geo-ph↗

arXiv2019

Unified representation of the C3, C4, and CAM photosynthetic pathways with the Photo3 model

Recently, interest in crassulacean acid metabolism (CAM) photosynthesis has risen and new, physiologically based CAM models have emerged. These models show promise, yet unlike the more widely used physiological models of C3 and C4 photosynthesis, their complexity has thus far inhibited their adoption in the general community. Indeed, most efforts to assess the potential of CAM still rely on empirically based environmental productivity indices, which makes uniform comparisons between CAM and non-CAM species difficult. In order to represent C3, C4, and CAM photosynthesis in a consistent, physiologically based manner, we introduce the Photo3 model. This work builds on a common photosynthetic and hydraulic core and adds additional components to depict the circadian rhythm of CAM photosynthesis and the carbon-concentrating mechanism of C4 photosynthesis. This allows consistent comparisons of the three photosynthetic types for the first time. It also allows the representation of intermediate C3-CAM behavior through the adjustment of a single model parameter. Model simulations of *Opuntia ficus-indica* (CAM), *Sorghum bicolor* (C4), and *Triticum aestivum* (C3) capture the diurnal behavior of each species as well as the cumulative effects of long-term water limitation. The results show potential for use in understanding CAM productivity, ecology, and climate feedbacks and in evaluating the tradeoffs between C3, C4, and CAM photosynthesis.

q-bio.QM↗

arXiv2018

Origin of Negative Temperatures in Systems Interacting with External Fields

The controversial existence of negative temperatures has stirred interesting debates that have reached the foundations of thermodynamics, including questions on the second law, the Carnot efficiency and the statistical definition of entropy. Here we show that for systems interacting with an external field, negative temperatures arise from an energy mis-attribution in which the interaction energy with the field is treated as a form of internal energy. We discuss how negative temperatures are avoided when using a proper thermodynamic formalism, which accounts for the intensive and extensive variables associated to the external field. We use the paramagnetic system and a perfect gas in a gravitational field to illustrate these ideas. Considerations about the isothermal and adiabatic work done by the field or the system also shed light on the inconsistency of super-Carnot efficiencies.

cond-mat.stat-mech↗

arXiv2018

Thermodynamic relations among isotropic material properties in conditions of plane shear stress

We present new general relationships among the material properties of an isotropic material kept in homogeneous stress conditions with hydrostatic pressure and plane shear. The derivation is not limited to the proximity of the zero shear-stress and -strain condition, which allows us to identify the relationship between adiabatic and isothermal shear compliances (inverse of the moduli of rigidity) along with new links, among others, between isobaric and isochoric shear thermal expansion coefficients, heat capacities at constant stress and constant shear strain. Such relationships are important for a variety of applications, including characterization of nanomaterials as well as identification of properties related to earthquakes precursors and complex media (e.g., soil) behaviors. The results may be useful to investigate the behavior of materials during phase transitions involving shear or in non-homogeneous conditions within a local thermodynamic equilibrium framework.

cond-mat.soft↗

arXiv2018

State dependent jump processes: Itô-Stratonovich interpretations, potential, and transient solutions

The abrupt changes that are ubiquitous in physical and natural systems are often well characterized by shot noise with a state dependent recurrence frequency and jump amplitude. For such state dependent behavior, we derive the transition probability for both the Itô and Stratonovich jump interpretations, and subsequently use the transition probability to pose a master equation for the jump process. For exponentially distributed inputs, we present a novel class of transient solutions, as well as a generic steady state solution in terms of a potential function and the Pope-Ching formula. These new results allow us to describe state dependent jumps in a double well potential for steady state particle dynamics, as well as transient salinity dynamics forced by state dependent jumps. Both examples showcase a stochastic description that is more general than the limiting case of Brownian motion to which the jump process defaults in the limit of infinitely frequent and small jumps. Accordingly, our analysis may be used to explore a continuum of stochastic behavior from infrequent, large jumps to frequent, small jumps approaching a diffusion process.

cond-mat.stat-mech↗

arXiv2018

Reinforcement of Climate Hiatus by Decadal Modulation of Daily Cloud Cycle

Based on observations and climate model results, it has been suggested that the recent slowdown of global warming trends (climate hiatus), which took place in the early 2000s, might be due to enhanced ocean heat uptake. Here we suggest an alternative hypothesis which, at least in part, would relate such slowdown to unaccounted energy reflected or reemitted by clouds. We show that the daily cloud cycle is strongly linked to pacific decadal oscillation (PDO) and that its decadal variations during the climate hiatus have an overall cooling effect. Such an effect may have partially, and temporarily, counteracted the greenhouse warming trends.

physics.ao-ph↗

arXiv2018

Radiative effects of daily cloud cycle: general methodology and application to cloud fraction

The daily cloud cycle (DCC) and its response to global warming are critical to the Earth's energy budget, but their radiative effects have not been systematically quantified. Toward this goal, here we analyze the radiation at the top of the atmosphere and propose a measure of the DCC radiative effect (DCCRE) as the difference between the total radiative fluxes with the full cloud cycle and its uniformly distributed cloud counterpart. We apply it to the cloud fraction from four climate models that participated in the second phase of the Cloud Feedback Model Inter-comparison Project. The results allow us to objectively compare inter-model differences in the daily cycle of cloud fraction and their influences on the global energy balance. In particular, the spatial patterns of the DCC response to global warming obtained in our analysis suggest possible impacts on large-scale circulation. Such a framework can be used for conducting a more systematic evaluation of the DCC in climate models and observations with the goal to reduce uncertainty in climate projections.

physics.ao-ph↗

arXiv2017

Hidden Warming Effects of Cloud Cycle Errors in Climate Models

Clouds' efficiency at reflecting solar radiation and trapping the terrestrial one is strongly modulated by their diurnal cycle. Much attention has been paid to mean cloud properties due to their critical role in climate projections; however, less research has been devoted to their diurnal cycle. Here, we quantify the mean, amplitude, and phase of the cloud cycles in current climate models and compare them with satellite observations and reanalysis data. While the mean values appear to be reliable, the amplitude and phase of the diurnal cycles of clouds show marked inconsistencies, especially over land. We show that, to compensate for the increased net radiation input implied by such errors, an overestimation of the cloud liquid water path may be introduced during calibration of climate models to keep temperatures in line with observations. These discrepancies are likely to be related to cloud parametrization problems in relation to atmospheric convection.

physics.ao-ph↗