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Compaction and salinization of soils reduce croplands fertility, affect natural ecosystems, and are major concerns worldwide. Soil compaction alters soil structure and affects the soil's hydraulic properties, and it therefore may have a significant impact on evaporation and solute transport processes in the soil. In this work, we investigated the combined processes of soil compaction, bare soil evaporation, and salt precipitation. X-ray computed microtomography techniques were used to study the geometrical soil pore and grain parameters influenced by compaction. The impact of compaction on evaporation and salt precipitation was studied using column experiments. We found that compaction reduced the average grain size and increased the number of grains, due to the crushing of the grains and their translocation within the compacted soil profile. Changes in pore and grain geometry and size were heterogeneously distributed throughout the soil profile, with changes most apparent near the source of compaction, in our case, at the soil surface. The column experiments showed that the presence of small pores in the upper layer of the compacted soil profile leads to higher evaporation loss and salt precipitation rates, due to the increase of hydraulic connectivity to the soil surface and the prolongation of the first stage of evaporation.

Extreme heatwave events can impose great stress on plant functioning, including desiccation, over-heating, and the risk of irreversible damage to tissues. We study here the resilience of pine trees in a semi-arid forest in Israel to heatwaves. The backdrop of the heatwaves is a long dry season, along which average water and carbon fluxes decrease, as plants adjust to atmospheric and soil drought. The harsh and short heatwaves, characterized by vapor-pressure deficit exceeding the 85th percentile for the season, punctuate the long dry-down period, and their effect on the trees is monitored through plant water status indicators such as sap flow and stem diameter. First, we developed an index, the cumulative heatwave unit, to quantify heatwaves and compare between them (e.g., heatwave A is 50% harsher than the one that came before it). We then defined two resilience metrics for our non-stationary indicators, that quantify the immediate decrease in water status, and the typical recovery time. Our main result is the identification of compounding effects of heatwaves on tree resilience, showing that long-lasting damage accumulates non-linearly, i.e., the total damage over the drydown is greater than the sum of damage from all individual heatwaves. Plotting the temporal changes in resilience of the trees on the 2-dimensional impact-recovery space, we see a typical loop over the hydrological year, indicating the months when the trees are especially vulnerable to long-lasting damage. We hope that the conceptual tools developed to quantify heatwave disturbances and to quantify resilience are useful to the community in other contexts, especially with expected increases in climatic variability and extreme weather events.

Species-specific hydraulic traits play a critical role in determining the response of ecosystem carbon and water fluxes to water stress. Improving the representation of plant hydraulic behavior in vegetation and land-surface models is critical for improving our predictions of the impacts of water stress on ecosystem carbon and surface fluxes given that biodiverse representation of forest canopies remain challenging for land-surface models. Here, we use FETCH3.14, a multispecies, canopy-level, hydrodynamic transpiration model which builds upon the previous versions of the Finite-difference Ecosystem-scale Tree Crown Hydrodynamics model (FETCH). FETCH3.14 is parameterized by our newly developed package, Bayesian Optimization for Anything (BOA), which facilitates and eases hyperparameter optimization using multi-scale and multi-variate observations. BOA incorporates multiple sources of data easily, reduces optimization setup time, and eases advanced use cases such as High-Performance Computing (HPC) parallelization and optimization restarting. BOA facilitates multi-source data assimilation for FETCH3.14 from a disparate range of sources including ET observations, soil and stem water potential observations, and carbon flux observations to provide insights about species-specific hydraulic traits. We use flux data from representative model trees that get scaled to the plot level based on the composition of species and structure of the canopy in the plot, which allows parameterization using tree level observations (sap flux, stem water storage) and plot level observations (eddy covariance evapotranspiration). We use BOA to set up a multi-objective optimization inverse problem with little overhead or extra boilerplate code. This approach allows us to utilize multi-scale observations to resolve information about species-specific hydraulic parameters, including parameters that are difficult or impossible to measure in the field.

Declining soil-saturated hydraulic conductivity (Ks) as a result of saline and sodic irrigation water is a major cause of soil degradation. While it is understood that the mechanisms that lead to degradation can cause irreversible changes in Ks, existing models do not account for hysteresis between the degradation and rehabilitation processes. We develop the first model for the effect of saline and sodic water on Ks that explicitly includes hysteresis. As such, the idea that a soil's history of degradation and rehabilitation determines its future Ks lies at the center of this model. By means of a “weight” function, the model accounts for soil-specific differences, such as clay content. The weight function also determines the form of the hysteresis curves, which are not restricted to a single shape, as in some existing models for irreversible soil processes. The concept of the weight function is used to develop a reversibility index, which allows for the quantitative comparison of different soils and their susceptibility to irreversible degradation. We discuss the experimental setup required to find a soil's weight function and show how the weight function determines the degree to which Ks is reversible for a given soil. We demonstrate the feasibility of this procedure by presenting experimental results showcasing the presence of hysteresis in soil Ks and using these results to calculate a weight function. Past experiments and models on the decline of Ks due to salinity and sodicity focus on degradation alone, ignoring any characterization of the degree to which declines in Ks are reversible. Our model and experimental results emphasize the need to measure “reversal curves”, which are obtained from rehabilitation measurements following mild declines in Ks. The developed model has the potential to significantly improve our ability to assess the risk of soil degradation by allowing for the consideration of how the accumulation of small degradation events can cause significant land degradation.

Optimality principles have been used to explain stomatal behavior, assuming that plants maximize carbon assimilation, while minimizing water expenditures. This optimization is often realized in models under arbitrary time horizons, from instantaneous optimization to unknown time periods of days and weeks. Here we introduce the concept of “discounting” to the optimization framework. Simply put, discounting makes the assumption that a plant cares more about its fluxes of carbon and water at the present moment than those in the future, where a “discount rate” is used to quantify the amount by which the present is more valued than the future. We explore how the plant continually updates its prior density functions (in the Bayesian sense) regarding future climatic conditions, and how this mechanism relates to memory. We also show that instantaneous optimization and the usual optimization over a fixed period of time are but the extremes in a rich spectrum of behavior in the discount rate axis. Finally, we discuss how to link the idea of discounting to risk attitudes and isohydricity.

Soil salinity and sodicity present serious risks to agriculture, in the face of dwindling freshwater resources and changing rainfall patterns. As a finite resource of crucial importance, soils must be protected from irreversible degradation. However, very little is known about how soils respond to adverse conditions in the long run, in particular regarding salinity and sodicity. As a proxy for soil stability and health, we will discuss what (little) is known about the irreversible deterioration of saturated hydraulic conductivity (Ks), subjected to water of varying levels of salinity and sodicity. We present novel soil column experiments measuring Ks hysteresis, for three soils of varying clay content. We then present a mathematical framework that allows us to make sense of the hysteresis in Ks, and that helps us understand the pivotal role of a soil's history of salinization and sodification in determining future Ks behavior. Most importantly, our model gives specific guidelines of what to measure in order to best characterize a soil's partial decline in Ks. We will focus on the role of reversal curves as the key to unlock a full characterization of the Ks hysteresis. With the help of weighting functions, we will show that our modeling framework is able to describe soils of any texture and clay mineralogy, making it both versatile and useful.

If not carefully managed, use of saline and sodic irrigation waters, a common practice in dryland regions, has the potential to cause significant harm to soils. Application of saline and sodic irrigation waters can lead to reductions in hydraulic conductivity, Ks, the mechanisms of which (e.g., slaking, swelling, clay dispersion) have been the focus of a vast body of scientific literature. The rehabilitation process, by contrast, is far less understood. Despite experimental evidence showing a significant degree of irreversibility, traditionally models have treated the degradation and rehabilitation processes as reversible. We demonstrate how this assumption obfuscates our ability to analyze the risk of long-term degradation and to estimate the resources and time required to rehabilitate. We achieve this by using the SOTE model — a minimalistic model that can be used to study dynamics of soil water content, salinity, and sodicity, as driven by irrigation practices and climatic conditions. Crucially, SOTE also accounts for the feedback between changing salinity and sodicity and soil Ks. This feedback includes irreversible changes in hydraulic conductivity, such that a soil’s history of degradation and rehabilitation informs its future state. We compare SOTE to existing models, which do not include hysteresis in Ks, and demonstrate that SOTE predicts more gradual rehabilitation of degraded soils, in line with the limited experimental evidence that has examined this question. For the test case of a degraded soil in a typical Mediterranean climate, SOTE forecasts that rehabilitation requires 50% more time and water resources, in comparison to models without hysteresis. This difference underscores the need to limit the risk of potential degradation, which SOTE also shows increases by 50% when hysteresis is accounted for. A sensitivity analysis indicates that SOTE is most sensitive to parameters connected to soil texture. The sensitivity analysis further indicates that our results are robust -- under all ranges of parameter values SOTE continues to forecast greater time requirements for rehabilitation and increased risk of soil degradation.

Soil salinization and sodification can cause detrimental effects to soil structure, with important implications to irrigated agriculture. Knowledge of the extent to which degradation in soil structure due to salinization and sodification is reversible is still lacking, however. The objective of our study is to examine the effects of the history of solute composition on the degree of reversibility in saturated hydraulic conductivity (Ksat). We systematically investigate the effects of salinity (electrolyte concentration) and sodicity (sodium adsorption ratio) on Ksat, for three soils of varying clay content. The soil column experiments yielded hysteresis graphs, in which Ksat does not go back to its original values after initial decay. We developed indices to quantify the degree of Ksat degradation and reversibility, and found that contrary to our expectations, high susceptibility to degradation does not always correlate with low capability of rehabilitation. Measurements of soil swelling helped us discern when degradation was mainly caused by swelling or clay dispersion. Our findings underscore the need of understanding hysteresis caused by salinity and sodicity, aiming at a better management of agricultural soils for sustainable long-term use., Comment: 21 pages, 6 figures

Humans play major roles in shaping and transforming the ecology of Earth. Unlike natural drivers of ecosystem change, which are erratic and unpredictable, human intervention in ecosystems generally involves planning and management, but often results in detrimental outcomes. Using model studies and aerial-image analysis, we argue that the design of a successful human intervention form calls for the identification of the self-organization modes that drive ecosystem change, and for studying their dynamics. We demonstrate this approach with two examples: grazing management in drought-prone ecosystems, and rehabilitation of degraded vegetation by water harvesting. We show that grazing can increase the resilience to droughts, rather than imposing an additional stress, if managed in a spatially non-uniform manner, and that fragmental restoration along contour bunds is more resilient than the common practice of continuous restoration in vegetation stripes. We conclude by discussing the need for additional studies of self-organization modes and their dynamics., Author summary Human intervention in ecosystems is motivated by various functional needs, such as provisioning ecosystem services, but often has unexpected detrimental outcomes. A major question in ecology is how to manage human intervention so as to achieve its goal without impairing ecosystem function. The main idea pursued here is the need to identify the inherent response ways of ecosystems to disturbances, and use them as road maps for conducting interventions. This approach is demonstrated mathematically using two contexts, grazing management and vegetation restoration, and compared to remote sensing data for the latter. Among the surprising insights obtained is the beneficial effect of grazing, in terms of resilience to droughts, that can be achieved by managing it non-uniformly in space.

We study the reclamation process of a sodic soil by irrigation with water amended with calcium cations. In order to explore the entire range of time-dependent strategies, this task is framed as an optimal control problem, where the amendment rate is the control and the total rehabilitation time is the quantity to be minimized. We use a minimalist model of vertically averaged soil salinity and sodicity, in which the main feedback controlling the dynamics is the nonlinear coupling of soil water and exchange complex, given by the Gapon equation. We show that the optimal solution is a bang–bang control strategy, where the amendment rate is discontinuously switched along the process from a maximum value to zero. The solution enables a reduction in remediation time of about 50%, compared with the continuous use of good-quality irrigation water. Because of its general structure, the bang–bang solution is also shown to work for the reclamation of other soil conditions, such as saline–sodic soils. The novelty in our modeling approach is the capability of searching the entire “strategy space” for optimal time-dependent protocols. The optimal solutions found for the minimalist model can be then fine-tuned by experiments and numerical simulations, applicable to realistic conditions that include spatial variability and heterogeneities.

Ecosystems are highly nonlinear dissipative systems characterized by multiplicity of stable and unstable states. Two major concerns are associated with multistable ecosystems in variable environments. The first is related to the increased likelihood of extreme climate events at regional scales, such as droughts, floods, and heat waves, that may result in abrupt transitions to malfunctioning ecosystem states. The second concern is related to the dominant role played by humans in shaping and transforming the ecology of the Earth, and to the detrimental effects that such transformations often have. Using mathematical models of dryland ecosystems as a case study, we discuss recent advances that shed new light on these concerns. We first argue that state transitions can be gradual or incomplete rather than abrupt, providing opportunities for prevention and recovery. We further argue that analyzing the unstable states that exist along with the stable ones, identifying their existence ranges and their stable and unstable manifolds, can help to devise human intervention forms that direct ecosystems towards desired functional ecosystem states, without impairing ecosystem function. We conclude by presenting open problems and delineating further research directions.

Soil salinity and sodicity impose severe constrains to agriculture, especially in arid and semi-arid regions, where good-quality water for irrigation is scarce. While detailed models have been proposed in the past to describe the dynamics of salt and sodium in the soil, they typically require cumbersome calculations and are not amenable to theoretical analysis. Here we present an analytical model for the dynamics of salinity and sodicity in the root zone. We determine the dependence of steady-state salinity and sodicity levels on irrigation water quality and derive the trajectories in the phase space. The only stationary solution the equations admit is a stable node. Through numerical integration and analysis of the eigenvalues of the derived two-dimensional system of equations, the slower time scale associated with sodification is quantified with respect to the faster time scale associated to salinization. The role of different cation exchange equations (Gapon and Vanselow conventions) are shown to be practically the same with regard to the phase-space dynamics and the time scales. The results can be applied in controlling for low levels of salinity and sodicity, and in planning remediation strategies that are timely and economical.

Human societies are increasingly altering the water and biogeochemical cycles to both improve ecosystem productivity and reduce risks associated with the unpredictable variability of climatic drivers. These alterations, however, often cause large negative environmental consequences, raising the question as to how societies can ensure a sustainable use of natural resources for the future. Here we discuss how ecohydrological modeling may address these broad questions with special attention to agroecosystems. The challenges related to modeling the two-way interaction between society and environment are illustrated by means of a dynamical model in which soil and water quality supports the growth of human society but is also degraded by excessive pressure, leading to critical transitions and sustained societal growth-collapse cycles. We then focus on the coupled dynamics of soil water and solutes (nutrients or contaminants), emphasizing the modeling challenges, presented by the strong nonlinearities in the soil and plant system and the unpredictable hydroclimatic forcing, that need to be overcome to quantitatively analyze problems of soil water sustainability in both natural and agricultural ecosystems. We discuss applications of this framework to problems of irrigation, soil salinization, and fertilization and emphasize how optimal solutions for large-scale, long-term planning of soil and water resources in agroecosystems under uncertainty could be provided by methods from stochastic control, informed by physically and mathematically sound descriptions of ecohydrological and biogeochemical interactions.

We consider simple systems driven multiplicatively by white shot noise, which appear in the modeling of the dynamics of soil nutrients and contaminants. The dynamics of these systems is analyzed in two ways: solving a hierarchy of linear ordinary differential equations for the moments, which gives a time scale of convergence of the stationary probability density function; and characterizing the crossing properties, such as the mean first-passage time and the mean frequency of level crossing. These results are readily applicable to the study of geophysical systems, such as the problem of accumulation of salt in the root zone, i.e., soil salinization.

An important environmental application of pattern control by periodic spatial forcing is the restoration of vegetation patterns in water-limited ecosystems that went through desertification. Vegetation restoration is often based on periodic landscape modulations that intercept overland water flow and form favorable conditions for vegetation growth. Viewing this method as a spatial resonance problem, we show that plain realizations of this method, assuming a complete vegetation response to the imposed modulation pattern, suffer from poor resilience to rainfall variability. By contrast, less intuitive realizations, based on the inherent spatial modes of vegetation growth and involving partial vegetation implantation, can be highly resilient and equally productive. We derive these results using two complementary models, a realistic vegetation model, and a simple pattern formation model that lends itself to mathematical analysis and highlights the universal aspects of the behaviors found with the vegetation model. We focus on reversing desertification as an outstanding environmental problem, but the main conclusions hold for any spatially forced system near the onset of a finite-wave-number instability that is subjected to noisy conditions.

Spatial periodic forcing can entrain a pattern-forming system in the same way as temporal periodic forcing can entrain an oscillator. The forcing can lock the pattern's wave number to a fraction of the forcing wave number within tonguelike domains in the forcing parameter plane, it can increase the pattern's amplitude, and it can also create patterns below their onset. We derive these results using a multiple-scale analysis of a spatially forced Swift-Hohenberg equation in one spatial dimension. In two spatial dimensions the one-dimensional forcing can induce a symmetry-breaking instability that leads to two-dimensional (2D) patterns, rectangular or oblique. These patterns resonate with the forcing by locking their wave-vector component in the forcing direction to half the forcing wave number. The range of this type of 2:1 resonance overlaps with the 1:1 resonance tongue of stripe patterns. Using a multiple-scale analysis in the overlap region we show that the 2D patterns can destabilize the 1:1 resonant stripes even at exact resonance. This result sheds new light on the use of spatial periodic forcing for controlling patterns.

Spatial periodic forcing of pattern-forming systems is an important, but lightly studied, method of controlling patterns. It can be used to control the amplitude and wave number of one-dimensional periodic patterns, to stabilize unstable patterns, and to induce them below instability onset. We show that, although in one spatial dimension the forcing acts to reinforce the patterns, in two dimensions it acts to destabilize or displace them by inducing two-dimensional rectangular and oblique patterns.

We show that spiral vortices in oscillatory systems can lose stability to secondary modes to form dual-mode spiral vortices. The secondary modes grow at the vortex core where the oscillation amplitude vanishes but are nonlinearly damped by the oscillatory mode away from the core. Gradients of the oscillation phase, induced by the hosted secondary mode, can lead to additional hosting events that culminate in periodic core oscillations or in a novel form of spatiotemporal chaos. The results of this study apply to physical, chemical, and biological systems that go through cusp-Hopf, fold-Hopf, and Hopf-Turing bifurcations.