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Complex topographies exhibit universal properties when fluvial erosion dominates landscape evolution over other geomorphological processes. Similarly, we show that the solutions of a minimalist landscape evolution model display invariant behavior as the impact of soil diffusion diminishes compared to fluvial erosion at the landscape scale, yielding complete self-similarity with respect to a dimensionless channelization index. Approaching its zero limit, soil diffusion becomes confined to a region of vanishing area and large concavity or convexity, corresponding to the locus of the ridge and valley network. We demonstrate these results using 1D analytical solutions and 2D numerical simulations, supported by real-world topographic observations. Our findings on the landscape self-similarity and the localized diffusion resemble the self-similarity of turbulent flows and the role of viscous dissipation. Topographic singularities in the vanishing diffusion limit are suggestive of shock waves and singularities observed in nonlinear complex systems.

While the warming trends of the Earth's mean temperature are evident at climatological scales, the local temperature at shorter timescales are highly fluctuating. In this letter we show that the probabilities of such fluctuations are characterized by a special symmetry typical of systems out of equilibrium. Their nearly universal properties are linked to the fluctuation theorem and reveal that the progressive warming is accompanied by growing asymmetry of temperature distributions. These statistics allow us to project the global temperature variability in the near future, in line with predictions from climate models, providing valuable information about future extremes., Comment: 13 pages, 4 figures

For 1D Hamiltonian systems with periodic solutions, Helmholtz formalism provides a tantalizing interpretation of classical thermodynamics, based on time integrals of purely mechanical quantities and without need of statistical description. Here we extend this approach to include heat flux and pressure at the walls, thereby enabling it to describe actual thermodynamic transformations, such as isothermal compressions and expansions. The presence of hard walls, which gives rise to non zero pressure, is justified by means of the virial theorem, while the heat fluxes are introduced as quasi-static limits of suitably thermostatted Hamiltonians. Particular attention is paid to generalizing the minimalist cases of the harmonic oscillator and elastic bouncer, which afford clear physical interpretations. With such extensions, a complete picture of thermodynamics emerges, amenable to cyclic transformations capable of producing mechanical work from heat, like the Carnot cycle.

Mangrove canopy height is a key metric to assess tidal forests' resilience in the face of climate change. In terrestrial forests, tree height is primarily determined by water availability, plant hydraulic design, and disturbance regime. However, the role of water stress remains elusive in tidal environments, where saturated soils are prevalent, and salinity can substantially affect the soil water potential. Here, we use global observations of maximum canopy height, species richness, air temperature, and seawater salinity -- a proxy of soil water salt concentration -- to explain the causal link between salinity and Mangrove stature. Our findings suggest that salt stress affects Mangrove height both directly, by reducing primary productivity and increasing the risk of xylem cavitation, and indirectly favoring more salt-tolerant species, narrowing the spectrum of viable traits, and reducing biodiversity. Yet, salt tolerance comes to a price. Highly salt-tolerant mangroves are less productive and generally shorter than more sensitive species, suggesting a causal nexus between salinity, biodiversity, and tree height. As sea-level rise enhances coastal salinization, failure to account for these effects can lead to incorrect estimates of future carbon stocks in Tropical coastal ecosystems and endanger preservation efforts.

While it is well known that water availability controls vegetation growth and soil microbial activity, how aridity affects ecosystem carbon patterns is not completely understood. Towards a more quantitative assessment of terrestrial carbon stocks, here we uncover a remarkable self-similar behavior of the global carbon stock. Using international survey and remote sensing data, we find that the key statistics (e.g., mean, quantiles, and standard deviation) of carbon stock tend to scale with the hydrological regime (i.e., aridity) via a universal exponent. As a result, when normalized by its averages in the corresponding hydrological regime, the carbon stock distributions collapse onto a single curve. Such a scaling reflects the strong coupling between hydrological cycle and biogeochemical process and enables robust predictions of carbon stocks as a function of aridity only., Comment: 18 pages, 10 figures, 1 table

Anthropogenic emissions of CO2 must soon approach net-zero to stabilize the global mean temperature. Although several international agreements have advocated for coordinated climate actions, their implementation has remained below expectations. One of the main challenges of international cooperation is the different degrees of socio-political acceptance of decarbonization. Here we interrogate a minimalistic model of the coupled natural-human system representing the impact of such socio-political acceptance on clean energy investments and the path to net-zero emissions. We show that incentives and carbon pricing are essential tools to achieve net-zero before critical CO2 concentrations are reached, and deep international coordination is necessary for a rapid and effective transition. Although a perfect coordination scenario remains unlikely, as investments in clean energy are ultimately limited by myopic economic strategies and a policy system that promotes free-riding, more realistic decentralized cooperation with partial efforts from each actor could still lead to significant emissions cuts.

The local extremes (i.e., peaks and pits) of the landscape-elevation field play a critical role in energy, water, and nutrient distribution over the region, but the statistical distributions of these points in relation to landscape advancing towards maturity have received limited research attention. In this work, we first explain how the spatial correlation structure of the elevation field affects the counts and frequency distributions of local extremes. We then analyze local extremes statistics for 8 mountainous landscapes worldwide with diverse hydroclimatic forcings and geologic histories using 24 Digital Elevation Models (DEMs) and compare them with complex terrain of the Erythraeum Chaos region on Mars. The results reveal that the spherical covariance structure captures the observed spatial correlation in these cases with the peak frequency distribution agreeing well with the elevation frequency distribution. The ratio of the pit-over-peak (POP) count is linked to the degree to which the pit and peak frequency distributions match, and carries the mark of landscape aging. The relationship between the geomorphic development stage (quantified by the reduced fatness of the slope-distribution tail) and the deviation of POP values from unity in old mountainous landscapes confirms that the evolution towards smoother topographies is atypically accompanied by reduced pit counts typical of organized valley and ridge patterns.

Interesting analogies between shallow water dynamics and astrophysical phenomena have offered valuable insight from both the theoretical and experimental point of view. To help organize these efforts, here we analyze systematically the hydrodynamic properties of backwater profiles of the shallow water equations with 2D radial symmetry. In contrast to the more familiar 1D case typical of hydraulics, %already for {even in} isentropic conditions, a solution with minimum-radius horizon for the flow emerges, similar to the black hole and white hole horizons, where the critical conditions of unitary Froude number provide a unidirectional barrier for surface waves. Beyond these time-reversible solutions, a greater variety of cases arises, when allowing for dissipation by turbulent friction and shock waves (i.e., hydraulic jumps) for both convergent and divergent flows. The resulting taxonomy of the base-flow cases may serve as a starting point for a more systematic analysis of higher-order effects linked, e.g., to wave propagation and instabilities, capillarity, variable bed slope, and rotation.

Dengue fever impacts populations across the tropics. Dengue is caused by a mosquito transmitted flavivirus and its burden is projected to increase under future climate and development scenarios. The transmission process of dengue virus is strongly moderated by hydro-climatic conditions that impact the vector's life cycle and behavior. Here, we study the impact of rainfall seasonality and moisture availability on the monthly distribution of reported dengue cases in Sri Lanka. Through cluster analysis, we find an association between seasonal peaks of rainfall and dengue incidence with a two-month lag. We show that a hydrologically driven epidemiological model (HYSIR), which takes into account hydrologic memory in addition to the nonlinear dynamics of the transmission process, captures the two-month lag between rainfall and dengue cases seasonal peaks. Our analysis reveals a non-monotonic dependence of dengue cases on moisture, whereby an increase of cases with increasing moisture is followed by a reduction for very high levels of water availability. Improvement in prediction of the seasonal peaks in dengue incidence results from a seasonally varying dependence of transmission rate on water availability.

Numerous complex systems, both natural and artificial, are characterized by the presence of intertwined supply and/or drainage networks. Here we present a minimalist model of such co-evolving networks in a spatially continuous domain, where the obtained networks can be interpreted as a part of either the counter-flowing drainage or co-flowing supply and drainage mechanisms. The model consists of three coupled, nonlinear partial differential equations that describe spatial density patterns of input and output materials by modifying a mediating scalar field, on which supply and drainage networks are carved. In the 2-dimensional case, the scalar field can be viewed as the elevation of a hypothetical landscape, of which supply and drainage networks are ridges and valleys, respectively. In the 3-dimensional case, the scalar field serves as the chemical signal strength, in which vascularization of the supply and drainage networks occurs above a critical 'erosion' strength. The steady-state solutions are presented as a function of non-dimensional channelization indices for both materials. The spatial patterns of the emerging networks are classified within the branched and congested extreme regimes, within which the resulting networks are characterized based on the absolute as well as the relative values of two non-dimensional indices.

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.

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., Comment: 19 pages, 10 figures, 1 table

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., Comment: 35 pages, 21 figures, 2 tables, 2 appendices

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., Comment: We request to withdraw the manuscript because it contains a conceptual mistake that affects our conclusions. Thanks

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 (01), 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.

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.

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.

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.

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.

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., Comment: 20 pages and 8 figures

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.

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.

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.

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 It\^o 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., Comment: 22 pages, 6 figures

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.

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., Comment: 12 pages, 7 figures

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., Comment: 15 pages, 5 figures

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., Comment: 24 pages, 19 figures, 1 table

By reflecting solar radiation and reducing longwave emissions, clouds regulate the earth's radiation budget, impacting atmospheric circulation and cloud dynamics. Given the diurnal fluctuation of shortwave and longwave radiation, a shift in the cloud cycle phase (CCP) may lead to substantial feedbacks to the climate system. While most efforts have focused on the overall cloud feedback, the response of CCP to climate change has received much less attention. Here we analyze the variations of CCP using both long-term global satellite records and general circulation models (GCM) simulations to evaluate their impacts on the earth's energy budget. Satellite records show that in warm periods the CCP shifts earlier in the morning over the oceans and later in the afternoon over the land. Although less marked and with large inter-model spread, similar shifting patterns also occur in GCMs over the oceans with non-negligible CCP feedbacks. Over the land, where the GCM results are not conclusive, our findings are supported by atmospheric boundary layer models. A simplified radiative model further suggests that such shifts may in turn cause reduced reflection of solar radiation, thus inducing a positive feedback on climate. The crucial role of the cloud cycle calls for increased attention to the temporal evolution of the cloud diurnal cycle in climate models., Comment: 38 pages, 18 figures