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The dynamics of soil development and erosion is studied through a stochastic soil mass balance in which the soil production by bedrock weathering is expressed as a state-dependent deterministic function, while the erosion by landslides is modeled as a marked Poisson process. For a range of values of the parameters the dynamics is bistable and the noise drives the transitions from a state to another through a potential barrier. The rates of such a transition are analytically estimated and their dependence on the system parameters is briefly discussed.

This work looks into the existing links between conditional sampling techniques for coherent structure identification and methods for state space reconstruction which come up in the field of nonlinear time series analysis. It is shown that the sampling condition used by the VITA method corresponds to a round hyper-cylinder, having as its axis the main diagonal of an embedding space reconstructed with the delay method. Such a geometrical interpretation allows us to better understand certain typical characteristics of the method and to see bursting events as excursions of the system leaving the high-dimension basic turbulence.

This Brief Communication presents a simple second-order differential equation extracted from experimental data, which can mimic the velocity fluctuations that are typical of bursting. The starting time series concerns the longitudinal component of turbulent velocity measured near the wall in a hydraulically smooth pipe flow. By means of standard conditional sampling techniques, we found the typical behavior of velocity fluctuations during the bursting events, to which we then applied the trajectory method in order to extract the equation of motion. The resulting equation, containing quadratic and cubic nonlinearities, follows the original time series very well, and may represent a useful starting point for the construction of more complex models of this phenomenon. (C) 1998 American Institute of Physics. [S1070-6631(98)03211-5].

Studying the hypothetical case of a trend superimposed on a random stationary variable, we highlight the strong influence of possible non-stationarities on exceedance probability. After a general outline, the subject is analytically developed using the Gumbel distribution, emphasizing the quick increase of the exceedance probability over time in the presence of weak rising trends, and its sensitive underestimation where the non-stationarity goes unnoticed or is considered negligible. Finally the work is applied to hydrological series of rainfall and river flow.

We present the results of the nonlinear analysis of a near-wall turbulence signal, measured using a Laser Doppler Anemometer. Despite being preliminary in part, the results highlight some interesting aspects of the dynamics of coherent structures. Careful reconstruction of the dynamics from the scalar time series highlight particular phases of the bursting cycle, corresponding to the VITA detections, immersed in the overall high-dimension dynamics: the possibility to distinguish these trajectories in the embedding space provides indications for conditional sampling techniques on the reconstructed attractor. The application of nonlinear prediction to a system of high-dimension produces forecasts of rapidly decreasing quality over time, with no consequences for practical applications. Much more interesting instead is the analysis of the forecast errors for very short forecast intervals, where we observed a greater difficulty to predict the beginning of coherent structure instability probably due to the quasi-random forcing of the outer flow.

It is widely accepted that the wall turbulent flows are globally high dimensional (e.g. Keefe, Kim & Moin 1992). Therefore the system is not globally treatable either theoretically or in experiments and, at best, we can only focus our study on the main features of the dynamics. Fortunately this approach is not in actual fact restrictive, since it is also naturally suggested by the presence of coherent structures which, in a certain sense, constitute the skeleton of the near-wall turbulence. Because of their coherency and simplicity in relation to the rest of the dynamics, it is likely that in phase space such organized flow structures correspond to distinct and fairly simple orbits that, at random intervals, leave and suddenly reconnect to the large dimensional part of the attractor (Newell et al., 1988). In particular, in the low dimensional model of Aubry et al. (1988), the bursting phenomenon is shown to correspond in phase space to heteroclinic excursions (see also Sanghi & Aubry, 1993, and references therein). These theoretical studies, as well as certain ad hoc simplified numerical simulations (Hamilton et al. 1995), can capture the main features of the near-wall dynamics and are very important for highlighting the physical origin of the bursting process. However, they still have too little contact with the real turbulence. From the experimental and numerical point of view, the bursting process is quantitatively studied by means of conditional sampling techniques (e.g. Luchik & Tiederman, 1987), that unfortunately suffer from a certain subjectivity in the choice of the threshold values.

Generalized Langevin equations (GLE) with multiplicative white Poisson noise pose the usual prescription dilemma leading to different evolution equations (master equations) for the probability distribution. Contrary to the case of multiplicative Gaussian white noise, the Stratonovich prescription does not correspond to the well-known midpoint (or any other intermediate) prescription. By introducing an inertial term in the GLE, we show that the Itô and Stratonovich prescriptions naturally arise depending on two time scales, one induced by the inertial term and the other determined by the jump event. We also show that, when the multiplicative noise is linear in the random variable, one prescription can be made equivalent to the other by a suitable transformation in the jump probability distribution. We apply these results to a recently proposed stochastic model describing the dynamics of primary soil salinization, in which the salt mass balance within the soil root zone requires the analysis of different prescriptions arising from the resulting stochastic differential equation forced by multiplicative white Poisson noise, the features of which are tailored to the characters of the daily precipitation. A method is finally suggested to infer the most appropriate prescription from the data.

Several methods exist for the detection of nonlinearity in univariate time series. In the present work we consider riverflow time series to infer the dynamical characteristics of the rainfall-runoff transformation. It is shown that the non-Gaussian nature of the driving force (rainfall) can distort the results of such methods, in particular when surrogate data techniques are used. Deterministic versus stochastic (DVS) plots, conditionally applied to the decay phases of the time series, are instead proved to be a suitable tool to detect nonlinearity in processes driven by non-Gaussian (Poissonian) noise. An application to daily discharges from three Italian rivers provides important clues to the presence of nonlinearity in the rainfall-runoff transformation.

We study the dynamics of systems with deterministic trajectories randomly forced by instantaneous discontinuous jumps occurring according to two different compound Poisson processes. One process, with constant frequency, causes instantaneous positive random increments, whereas the second process has a state-dependent frequency and describes negative jumps that force the system to restart from zero (renewal jumps). We obtain the probability distributions of the state variable and the magnitude and intertimes of the jumps to zero. This modelling framework is used to describe snow-depth dynamics on mountain hillsides, where the positive jumps represent snowfall events, whereas the jumps to zero describe avalanches. The probability distributions of snow depth, together with the statistics of avalanche magnitude and occurrence, are used to explain the correlation between avalanche occurrence and snowfall as a function of hydrologic, terrain slope and aspect parameters. This information is synthesized into a ‘prediction entropy’ function that gives the level of confidence of avalanche occurrence prediction in relation to terrain properties.

Intensive agricultural land use can have detrimental effects on landscape properties, greatly accelerating soil erosion, with consequent fertility loss and reduced agricultural potential. To quantify the effects of such erosional processes on hillslope morphology and gain insight into the underlying dynamics, we use a twofold approach. First, a statistical analysis of topographical features is conducted, with a focus on slope and gradient distributions. The accelerated soil erosion is shown to be fingerprinted in the distribution tails, which provide a clear statistical signature of this human-induced land modification. Theoretical solutions are then derived for the hillslope morphology and the associated creep and runoff erosion fluxes, allowing us to distinguish between the main erosional mechanisms operating in disturbed and undisturbed areas. We focus our application on the landscape at the Calhoun Critical Zone Observatory in the US Southern Piedmont, where severe soil erosion followed intensive cotton cultivation, resulting in highly eroded and gullied hillslopes. The observed differences in hillslope morphologies in disturbed and undisturbed areas are shown to be related to the disruption of the natural balance between soil creep and runoff erosion. The relaxation time required for the disturbed hillslopes to reach a quasi-equilibrium condition is also investigated. © 2019 John Wiley & Sons, Ltd.

Due to their high water use efficiency, Crassulacean acid metabolism (CAM) plants are of environmental and economic importance in the arid and semiarid regions of the world. Moreover, many CAM plants (e.g., Agave tequilana) have attractive qualities for biofuel production such as a relatively low lignin content and high amount of soluble carbohydrates. However, the current estimates of CAM productivity are based on empirical stress indices that create large uncertainties. As a first step towards a more accurate quantification of CAM productivity, this paper introduces a new model that couples both soil and atmosphere conditions to CAM photosynthesis. The new CAM model is based upon well established C3 photosynthesis models coupled to a nonlinear circadian rhythm oscillator for the control of the photosynthesis carbon fluxes. The leaf-level dynamics are coupled to a simple, yet realistic description of the soil-plant-atmosphere continuum, including a plant water capacitance module. The resulting model reproduces the four phases of CAM photosynthes is and the evolution of their dynamics during a soil moisture drydown, as a function of soil type, plant features, and climatic conditions. The results help quantify the impact of soil water availability on CAM carbon assimilation and transpiration flux.

Water controls the dynamics of terrestrial ecosystems directly, as a resource for the biota, and indirectly, as a driver for abiotic processes on the Earth's surface, in the atmosphere, and belowground. The biota, in turn, modulate several hydrological processes and the rate of the water cycle. Here we review recent advances related to fundamental processes and feedbacks emerging from the interactions among hydrologic processes and ecosystems, with a particular focus on soil moisture dynamics and river flow. Most terrestrial vegetation interacts with hydrological processes through the soil-water balance, which is affected by soil properties, random climate drivers, and feedbacks with the biota. River flow enhances the ecohydrological connectivity of the landscape, spreading sediments, nutrients, propagules, and waterborne disease through waterways.

The objective of this comment is to correct two sets of statements in Litwin et al. (2022, https://doi.org/10.1029/2021JF006239), which consider our research work (Bonetti et al., 2018, https://doi.org/10.1098/rspa.2017.0693; Bonetti et al., 2020, https://doi.org/10.1073/pnas.1911817117). We clarify here that (a) the specific contributing area is defined in the limit of an infinitesimal contour length instead of the product of a reference contour width (Bonetti et al., 2018, https://doi.org/10.1098/rspa.2017.0693), and (b) not all solutions obtained from the minimalist landscape evolution model of Bonetti et al. (2020, https://doi.org/10.1073/pnas.1911817117) are rescaled copies of each other. We take this opportunity to demonstrate that the boundary conditions impact the obtained solutions, which has not been considered in the dimensional analysis of Litwin et al. (2022, https://doi.org/10.1029/2021JF006239). We clarify this point by using dimensional analysis and numerical simulations for a square domain, where only one horizontal length scale (the side length l) enters the physical law.

We show that similarly to the logarithmic mean-velocity profile in wall-bounded turbulence, the landscape topography presents an intermediate region with a logarithmic mean-elevation profile. Such profiles are present in complex topographies with channel branching and fractal river networks resulting from model simulation, controlled laboratory experiments, and natural landscapes. Dimensional and self-similarity arguments are used to corroborate this finding. We also tested the presence of logarithmic profiles in discrete, minimalist models of networks obtained from optimality principles (optimal channel networks) and directed percolation. The emergence of self-similar scaling appears as a robust outcome in dynamically different, but spatially bounded, complex systems, as a dimensional consequence of length-scale independence.

Manning’s empirical formula in conjunction with Strickler’s scaling is widely used to predict the bulk velocity$V$from the hydraulic radius$R_{h}$, the roughness size$r$and the slope of the energy grade line$S$in uniform channel and pipe flows at high bulk Reynolds numbers. Despite their importance in science and engineering, both Manning’s and Strickler’s formulations have waited for decades before finding a theoretical explanation. This was provided, for the first time, by Gioia & Bombardelli (Phys. Rev. Lett., vol. 88, 2002, 014501), labelled as GB02, using phenomenological arguments. Perhaps their most remarkable finding was the link between the Strickler and the Kolmogorov scaling exponents, the latter pertaining to velocity fluctuations in the inertial subrange of the turbulence spectrum and presumed to be universal. In this work, the GB02 analysis is first revisited, showing that GB02 employed severalad hocscaling assumptions for the turbulent kinetic energy dissipation rate and, although implicitly, for the mean velocity gradient adjacent to the roughness elements. The similarity constants arising from the GB02 scaling assumptions were presumed to be independent of$r/R_{h}$, which is inconsistent with well-known flow properties in the near-wall region of turbulent wall flows. Because of the dependence of these similarity constants on$r/R_{h}$, this existing theory requires the validity of the Strickler scaling to cancel the dependence of these constants on$r/R_{h}$so as to arrive at the Strickler scaling and Manning’s formula. Here, the GB02 approach is corroborated using a co-spectral budget (CSB) model for the wall shear stress formulated at the cross-over between the roughness sublayer and the log region. Assuming a simplified shape for the spectrum of the vertical velocity$w$, the proposed CSB model (subject to another simplifying assumption that production is balanced by pressure–velocity interaction) allows Manning’s formula to be derived. To substantiate this approach, numerical solutions to the CSB over the entire flow depth using different spectral shapes for$w$are carried out for a wide range of$r/R_{h}$. The results from this analysis support the simplifying hypotheses used to derive Manning’s equation. The derived equation provides a formulation for$n$that agrees with reported values in the literature over seven decades of$r$variations. While none of the investigated spectral shapes allows the recovery of the Strickler scaling, the numerical solutions of the CSB reproduce the Nikuradse data in the fully rough regime, thereby confirming that the Strickler scaling represents only an approximate fit for the friction factor for granular roughness.

We run a comparative study of ecohydrological models of streamflow probability distributions (pdfs), p(Q), derived by Botter et al. (2007a, 2009), against field data gathered in different hydrological contexts. Streamflows measured in several catchments across various climatic regions of northeastern Italy and the United States are employed. The relevance of the work stems from the implied analytical predictive ability of hydrologic variability, whose role on stream and riparian ecological processes and large‐scale management schemes is fundamental. The tools employed are analytical models of p(Q) (and of the related flow duration curve, D(Q)) derived by coupling suitable storage‐discharge relations with a stochastic description of streamflow production through soil moisture dynamics, and are expressed as a function of few macroscopic rainfall, soil, vegetation and geomorphological parameters. In this work we compare the performances of a recent version of the model (which includes the effects of nonlinear subsurface storage‐discharge relations) to those provided by the linear version through the application of the models to 13 test catchments belonging to various climatic and geomorphic contexts. A general agreement between predicted and observed daily streamflows pdfs is shown, though differences emerge between the linear and the nonlinear approaches. In particular, by including the effects of a nonlinear storage‐discharge relation the model accuracy is shown to increase with respect to the linear scheme in most examined cases. We show that this is not simply attributable to the added parameter but corresponds to a proper likelihood increase. The nonlinear model is shown to exhibit three basic forms for p(Q) (monotonically decreasing with an atom of probability in Q = 0, bell‐shaped with the mode close to zero, bell‐shaped with the mode close to the mean), corresponding to different hydrologic regimes which are clearly detectable in field data. Inferences on the nonlinear character of the relation between subsurface storage and discharge from observed p(Q) are finally drawn.