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Because of its interaction with plants, carbon decomposition, and soil properties, soil iron cycle has been recognized as an important player in the carbon and other biogeochemical cycles. The impact of the hydrologic cycle and plants on it, however, remains largely unexplored. Here we focus on terrestrial ecosystems and develop a dynamical system to analyze the coupling between iron and carbon dynamics in the soil root zone as driven by fluctuations in soil moisture. Particular emphasis is placed on the modeling of the soil organic matter, the Fe-reducing population, the iron Fe2+-Fe3+ cycling, and the soil moisture level, which controls the redox rates. Informed by laboratory and field measurements from a tropical forest, our results suggest that soil moisture and litterfall rates are the primary drivers of iron fluctuations at daily-to-seasonal temporal scales. We also emphasize the important role of soil iron cycle in the decomposition of the organic matter.

Channel networks increase in complexity as the importance of erosion grows compared to diffusion by soil creep, giving rise to a channelization cascade. In this cascade, smaller channels join to fo...

Soil drying and wetting cycles promote carbon (C) release through large heterotrophic respiration pulses at rewetting, known as Birch effect. Empirical evidence shows that drier conditions before rewetting and larger changes in soil moisture at rewetting cause larger respiration pulses. Because soil moisture varies in response to rainfall, also these respiration pulses depend on the random timing and intensity of precipitation. In addition to rewetting pulses, heterotrophic respiration continues during soil drying, eventually ceasing when soils are too dry to sustain microbial activity. The importance of respiration pulses in contributing to the overall soil respiration flux has been demonstrated empirically, but no theoretical investigation has so far evaluated how the relative contribution of these pulses may change along climatic gradients or as precipitation regimes shift in a given location. To fill this gap, we start by assuming that rewetting pulses and respiration rates during soil drying can be treated as random variables dependent on soil moisture fluctuations, and develop a stochastic model for soil heterotrophic respiration rates that analytically links the statistical properties of respiration to those of precipitation. Model results show that both the mean rewetting pulse respiration and the mean respiration during drying increase with increasing mean precipitation. However, the contribution of respiration pulses to the total heterotrophic respiration increases with decreasing precipitation frequency and to a lesser degree with decreasing precipitation depth, leading to an overall higher contribution of respiration pulses under future more intermittent and intense precipitation. Moreover, the variability of both components of soil respiration is also predicted to increase under these conditions. Therefore, our results suggest that with future more intermittent precipitation, respiration pulses and the associated nutrient release will intensify and become more variable, contributing more to soil biogeochemical cycling.

Enhanced Weathering (EW) resulting from soil amendment with highly reactive silicate minerals is regarded as one of the most effective techniques for carbon sequestration. While in laboratory conditions silicate minerals dissolution rates are well characterized, in field conditions the rate of the dissolution reaction is more difficult to predict, not least because it interacts with soil, plant, and hydrologic processes. Here we present a dynamic mass balance model connecting biogeochemical and ecohydrological dynamics to shed light on these intertwined processes involved in EW. We focus on the silicate mineral olivine, for its faster laboratory dissolution rate, and pay particular attention to understanding the role of plants and hydrological fluctuations and their propagation into soil biogeochemical processes (including cation exchange) and EW dynamics. A companion paper Cipolla et al.(2021) presents specific applications with the main purpose of understanding the carbon sequestration potential under different climate scenarios.

Chemical weathering is one of the major processes interacting with climate and tectonics to form clays, supply nutrients to soil micro-organisms and plants, and sequester atmospheric CO2. Hydrology and dissolution kinetics have been emphasized as factors controlling chemical weathering rates. However, the interaction between hydrology and transport of dissolved inorganic carbon (DIC) in controlling weathering has received less attention. In this paper, we present an analytical model that couples subsurface water and chemical molar balance equations to analyze the roles of hydrology and DIC-transport on chemical weathering. The balance equations form a dynamical system that fully determines the dynamics of the weathering zone chemistry as forced by the transport of DIC. The model is formulated specifically for the silicate mineral albite, but it can be extended to other minerals, and is studied as a function of percolation rate and water transit time. Three weathering regimes are elucidated. For very small or large values of transit time, the weathering is limited by reaction kinetics or transport, respectively. For intermediate values, the system is transport-controlled and is sensitive to transit time. We apply the model to a series of watersheds for which we estimate transit times and identify the type of weathering regime. The results suggest that hydrologic transport of DIC may be as important as reaction kinetics and dilution in determining chemical weathering rates.

Legacies of historical land use strongly shape contemporary ecosystem dynamics. In old-field secondary forests, tree growth embodies a legacy of soil changes affected by previous cultivation. Three patterns of biomass accumulation during reforestation have been hypothesized previously, including monotonic to steady state, non-monotonic with a single peak then decay to steady state, and multiple oscillations around the steady state. In this paper, the conditions leading to the emergence of these patterns is analyzed. Using observations and models, we demonstrate that divergent reforestation patterns can be explained by contrasting time-scales in ecosystem carbon-nitrogen cycles that are influenced by land use legacies. Model analyses characterize non-monotonic plant-soil trajectories as either single peaks or multiple oscillations during an initial transient phase controlled by soil carbon-nitrogen conditions at the time of planting. Oscillations in plant and soil pools appear in modeled systems with rapid tree growth and low initial soil nitrogen, which stimulate nitrogen competition between trees and decomposers and lead the forest into a state of acute nitrogen deficiency. High initial soil nitrogen dampens oscillations, but enhances the magnitude of the tree biomass peak. These model results are supported by data derived from the long-running Calhoun Long-Term Soil-Ecosystem Experiment from 1957 to 2007. Observed carbon and nitrogen pools reveal distinct tree growth and decay phases, coincident with soil nitrogen depletion and partial re-accumulation. Further, contemporary tree biomass loss decreases with the legacy soil C:N ratio. These results support the idea that non-monotonic reforestation trajectories may result from initial transients in the plant-soil system affected by initial conditions derived from soil changes associated with land-use history.

Plants rely on water storage capacity to increase accessibility of water for transpiration, reduce competition for water with neighboring plants, and buffer water supply during dry periods. The resulting benefits, typically a decrease in plant water stress and increase in productivity, are highly climate dependent and vary with soil moisture, vapor pressure deficit, and solar radiation. This paper analyzes the effects of plant water storage capacity on the relationship between soil moisture and carbon assimilation in woody plants. A resistance-capacitance model is used to examine the role of plant water storage at various soil moisture levels. Hydraulic traits are co-varied according to empirical relationships, and effects of sapwood volume and wood density on carbon assimilation are explored. The time scales of plant water storage and withdrawal are analyzed as a function of plant hydraulic capacitance, water storage capacity, and resistance to transport between water storage tissue and xylem. The effects of plant water storage on carbon assimilation are found to depend strongly on soil moisture levels. The theoretically optimal sapwood volume lies near naturally occurring ranges and increases with increasing soil moisture. The theoretically optimal wood density also lies within expected ranges and decreases with increasing soil moisture. A large portion of sapwood volume appears to be justified by its role in buffering diurnal variability in evaporative demand. The outlined coordination between soil moisture and optimal hydraulic traits is consistent with observed increases in sapwood capacitance and decreases in wood density across increasing rainfall gradients. This coordination provides support for the drought-tolerance vs. drought-avoidance hypothesis.

The cycling of soil carbon (C) and nitrogen (N) is mediated by microbial organisms, the activity of which depends on soil-water availability. In this chapter, we review how water availability affects C and N cycling, starting from fine-scale microbial responses to changes in soil moisture, and moving up in scale to the dynamics of soil C and N compartments at the plot scale and finally to the climatic and stoichiometric controls on decomposition along broad climatic gradients. In arid and semiarid ecosystems, water is available only intermittently and often in limited amount, forcing microorganisms to adopt a range of physiological drought response strategies to cope with these conditions (e.g., osmoregulation). These strategies, however, do not always allow microorganisms to remain active in dry conditions because physical limits to substrate movement in dry soils reduce the supply of C to sustain their metabolism. Thus, both biological and physical constraints are at play and determine how C and N fluxes in dryland soils vary during drying and wetting cycles. A coupled soil C–N cycling model, which integrates these aspects, is then described and applied to an African savanna. The model results show a multitude of response time scales of the various organic matter compartments (faster responses of microbial biomass, slower for stabilized organic matter), and decoupled dynamics of mineral N production by microorganisms and consumption by plants under prolonged dry periods. We conclude by outlining areas of future research, including the complexities of C and N dynamics at rewetting, the propagation of extreme hydrologic events on C and N cycles, and the challenges in scaling up microbial processes from soil pore- to plot-scales.

The main control exerted by hydrological processes on vegetation in water-limited ecosystems is through the soil water content, which, in turn, results from complex interactions between precipitation, infiltration, evaporation, transpiration, and soil drainage. Soil moisture dynamics affects the occurrence, duration, and intensity of periods of water stress in vegetation (Hale and Orcutt 1987; Smith and Griffiths 1993; Porporato et al. 2001) with important effects on plant cell turgidity, on stomatal conductance, and, in turn, on photosynthesis, carbon assimilation, and ecosystem net primary productivity (Chaps. 4 and 5). The dependence of canopy conductance on soil moisture is also of foremost importance in modulating the heat and water vapor fluxes from terrestrial vegetation to the near-surface atmosphere, with important impacts on the moisture content and stability of the atmospheric boundary layer and consequent feedbacks to the process of precipitation and the water cycle (Chap. 7). Soil moisture also exerts an important control on nutrient cycling (e.g., Linn and Doran 1984; Skopp et al. 1990; Parton et al. 1998; Porporato et al. 2003), due to its effects on microbial activity and nitrogen and phosphorus leaching and uptake, as explained in Chaps. 11, 12, and 13. Other surface processes affected by the soil water content include infiltration, runoff, soil erosion, and dust emission from dryland landscapes (Chap. 9).

Photosynthesis is governed by leaf water status that depends on the difference between the rates of transpiration and water supply from the soil and through the plant xylem. When transpiration increases compared to water supply, the leaf water potential reaches a more negative equilibrium, leading to water stress. Both high atmospheric vapor pressure deficit and low soil moisture increase the water demand while decreasing the supply due to lowered soil-to-root conductance and xylem cavitation. Therefore, dry conditions may eventually reduce the leaf water potential to the point of collapsing the plant hydraulic system. This “hydraulic failure” is shown to correspond to a fold bifurcation where the environmental parameters (vapor pressure deficit and soil moisture) trigger the loss of a physiologically sustainable equilibrium. Using a minimal plant hydraulic model, coordination among plant hydraulic traits is shown to result in increased resilience to environmental stresses, thereby impeding hydraulic failure unless hydraulic traits deteriorate due to prolonged water shortage or other damages.

Soil microbes face highly variable moisture conditions that force them to develop adaptations to tolerate or avoid drought. Drought conditions also limit the supply of vital substrates by inhibiting diffusion in dry conditions. How these biological and physical factors affect carbon (C) cycling in soils is addressed here by means of a novel process-based model. The model accounts for different microbial response strategies, including different modes of osmoregulation, drought avoidance through dormancy, and extra-cellular enzyme production. Diffusion limitations induced by low moisture levels for both extracellular enzymes and solutes are also described and coupled to the biological responses. Alternative microbial life-history strategies, each encoded in a set of model parameters, are considered and their effects on C cycling assessed both in the long term (steady state analysis) and in the short term (transient analysis during soil drying and rewetting). Drought resistance achieved by active osmoregulation requiring large C investment is not useful in soils where growth in dry conditions is limited by C supply. In contrast, dormancy followed by rapid reactivation upon rewetting seems to be a better strategy in such conditions. Synthesizing more enzymes may also be advantageous because it causes larger accumulation of depolymerized products during dry periods that can be used upon rewetting. Based on key model parameters, a spectrum of life-history strategies thus emerges, providing a possible classification of microbial responses to drought.

Regional-scale drought-induced forest mortality events are projected to become more frequent under future climates due to changes in rainfall patterns. The occurrence of these mortality events is driven by exogenous factors such as frequency and severity of drought and endogenous factors such as tree water and carbon use strategies. To explore the link between these exogenous and endogenous factors underlying forest mortality, a stochastic ecohydrological framework that accounts for random arrival and length of droughts as well as responses of tree water and carbon balance to soil water deficit is proposed. The main dynamics of this system are characterized with respect to the spectrum of anisohydric-isohydric stomatal control strategies. Using results from a controlled drought experiment, a maximum tolerable drought length at the point where carbon starvation and hydraulic failure occur simultaneously is predicted, supporting the notion of coordinated hydraulic function and metabolism. We find qualitative agreement between the model predictions and observed regional-scale canopy dieback across a precipitation gradient during the 2002–2003 southwestern United States drought. Both the model and data suggest a rapid increase of mortality frequency below a precipitation threshold. The model also provides estimates of mortality frequency for given plant drought strategies and climate regimes. The proposed ecohydrological approach can be expanded to estimate the effect of anticipated climate change on drought-induced forest mortality and associated consequences for the water and carbon balances.

Diurnal hysteresis between evapotranspiration (ET) and vapor pressure deficit (VPD) was reported in many ecosystems, but justification for its onset and magnitude remains incomplete with biotic and abiotic factors invoked as possible explanations. To place these explanations within a holistic framework, the occurrence of hysteresis was theoretically assessed along a hierarchy of model systems where both abiotic and biotic components are sequentially added. Lysimeter evaporation (E) measurements and model calculations using the Penman equation were used to investigate the effect of the time lag between net radiation and VPD on the hysteresis in the absence of any biotic effects. Modulations from biotic effects on the ET-VPD hysteresis were then added using soil-plant-atmosphere models of different complexities applied to a grassland ecosystem. The results suggest that the hysteresis magnitude depends on the radiation-VPD lag, while the plant and soil water potentials are both key factors modulating the hysteretic ET-VPD relation as soil moisture declines. In particular, larger hysteresis magnitude is achieved at less negative leaf water potential, root water potential, and soil water potential. While plant hydraulic capacitance affects the leaf water potential-ET relation, it has negligible effects on the ET-VPD hysteresis. Therefore, the genesis and magnitude of the ET-VPD hysteresis are controlled directly by both abiotic factors such as soil water availability, biotic factors (leaf and root water potentials, which in turn depend on soil moisture), and the time lag between radiation and VPD.

Soil properties are determined by a complex arrangement of pores, particles, and aggregates, which may change in time as a result of both ecohydrological dynamics and land management processes. The soil pore size distribution (PSD), which typically is treated as a static component, is a key determinant of soil properties, and its accurate representation has the potential to improve hydrological and crop models. Following previous work by Or et al. (2000), a modeling framework is proposed for the time evolution of the PSD which takes into account processes such as tillage, consolidation, and changes in organic matter. A time-varying power law PSD is obtained as the solution of a special form of transport equation for the PSD, parameterized using data from the literature to capture, in a parsimonious and efficient manner, the changes in the PSD as a result of the soil processes considered. Alterations in soil properties brought about by tillage, consolidation, and organic matter are then discussed. The potential benefit of this method for determining soil properties over the more widely used pedotransfer functions (PTF) is that it allows for the history of the soil, rather than only its present state, to be taken into account when estimating soil properties, and it does so in a physically consistent manner, leading to the widely used power law expression for soil properties with few parameters.

Optimization theories explain a variety of forms and functions in plants. At the leaf scale, it is often hypothesized that carbon gain is maximized, thus providing a quantifiable objective for a mathematical definition of optimality conditions. Eco-physiological trade-offs and limited resource availability introduce natural bounds to this optimization process. In particular, carbon uptake from the atmosphere is inherently linked to water losses from the soil as water is taken up by roots and evaporated. Hence, water availability in soils constrains the amount of carbon that can be taken up and assimilated into new biomass. The problem of maximizing photosynthesis at a given water availability by modifying stomatal conductance, the plant-controlled variable to be optimized, has been traditionally formulated for short time intervals over which soil moisture changes can be neglected. This simplification led to a mathematically open solution, where the undefined Lagrange multiplier of the optimization (equivalent to the marginal water use efficiency, λ ) is then heuristically determined via data fitting. Here, a set of models based on different assumptions that account for soil moisture dynamics over an individual dry-down are proposed so as to provide closed analytical expressions for the carbon gain maximization problem. These novel solutions link the observed variability in λ over time, across soil moisture changes, and at different atmospheric CO2 concentrations to water use strategies ranging from intensive, in which all soil water is consumed by the end of the dry-down period, to more conservative, in which water stress is avoided by reducing transpiration.

[1] While seasonally dry conditions are typical of large areas of the tropics, their biogeochemical responses to seasonal rainfall and soil carbon (C) sequestration potential are not well characterized. Seasonal moisture availability positively affects both productivity and soil respiration, resulting in a delicate balance between C deposition as litterfall and C loss through heterotrophic respiration. To understand how rainfall seasonality (i.e., duration of the wet season and rainfall distribution) affects this balance and to provide estimates of long-term C sequestration, we develop a minimal model linking the seasonal behavior of the ensemble soil moisture, plant productivity, related C inputs through litterfall, and soil C dynamics. A drought-deciduous caatinga ecosystem in northeastern Brazil is used as a case study to parameterize the model. When extended to different patterns of rainfall seasonality, the results indicate that for fixed annual rainfall, both plant productivity and soil C sequestration potential are largely, and nonlinearly, dependent on wet season duration. Moreover, total annual rainfall is a critical driver of this relationship, leading at times to distinct optima in both production and C storage. These theoretical predictions are discussed in the context of parameter uncertainties and possible changes in rainfall regimes in tropical dry ecosystems.

Leaching of heavy metals and other contaminants from soils poses a significant environmental threat as it affects the quality of downstream water bodies. Quantifying these losses is particularly important when employing phytoremediation approaches to reduce soil contamination, as contaminant escaping the system through leaching cannot be taken up by vegetation. Despite its undoubted importance, the role of such hydrologic forcing has seldom been fully considered in models describing the long-term contaminant mass balance during phytoremediation. The partitioning of contaminants between leaching and vegetation uptake is controlled by a number of biophysical processes as well as rainfall variability. Here, we develop a novel stochastic framework that provides analytical expressions to quantify the partitioning of contaminants between leaching and plant uptake and the probability of phytoremediation duration as a function of rainfall statistics and soil and vegetation characteristics. Simple expressions for the mean phytoremediation duration and effectiveness (defined as the fraction of contaminant that is recovered in plant biomass) are derived. The proposed framework can be employed to estimate under which conditions phytoremediation is more efficient, as well as to design phytoremediation projects that maximize contaminant recovery and minimize the duration of the remediation process.

Summary 1. Quantification of stomatal responses to environmental variables, in particular to soil water status, is needed to model carbon and water exchange rates between plants and the atmosphere. 2. Models based on stomatal optimality theory successfully describe leaf gas exchange under different environmental conditions, but the effects of water availability on the key optimization parameter [the marginal water use efficiency (WUE), k = ¶A ⁄¶ E] has resisted complete theoretical treatment. Building on previous optimal leaf gas exchange models, we developed an analytical equation to estimate k from gas exchange observations along gradients of soil water availability. This expression was then used in a meta-analysis of about 50 species to investigate patterns of variation in k. 3. Assuming that cuticular water losses are negligible k increases under mild water stress but decreases when severe water stress limits photosynthesis. When cuticular conductance is considered, however, k increases monotonically with increasing water stress, in agreement with previous theoretical predictions. Moreover, the shape of these response curves to soil water availability changes with plant functional type and climatic conditions. In general, k is lower in species grown in dry climates, indicating lower marginal WUE. 4. The proposed parameterization provides a framework to assess the responses of leaf gas exchange to changes in water availability. Moreover, the model can be extended to scale leaflevel fluxes to the canopy and ecosystem level.

In the last 80 years, a number of mathematical models of different level of complexity have been developed to describe biogeochemical processes in soils, spanning spatial scales from few μm to thousands of km and temporal scales from hours to centuries. Most of these models are based on kinetic and stoichiometric laws that constrain elemental cycling within the soil and the nutrient and carbon exchange with vegetation and the atmosphere. While biogeochemical model performance has been previously assessed in other reviews, less attention has been devoted to the mathematical features of the models, and how these are related to spatial and temporal scales. In this review, we consider ∼250 biogeochemical models, highlighting similarities in their theoretical frameworks and illustrating how their mathematical structure and formulation are related to the spatial and temporal scales of the model applications. Our analysis shows that similar kinetic and stoichiometric laws, formulated to mechanistically represent the complex underlying biochemical constraints, are common to most models, providing a basis for their classification. Moreover, a historic analysis reveals that the complexity and degree and number of nonlinearities generally increased with date, while they decreased with increasing spatial and temporal scale of interest. We also found that mathematical formulations specifically developed for certain scales (e.g., first order decay rates assumed in yearly time scale decomposition models) often tend to be used also at other spatial and temporal scales different from the original ones, possibly resulting in inconsistencies between theoretical formulations and model application. It is thus critical that future modeling efforts carefully account for the scale-dependence of their mathematical formulations, especially when applied to a wide range of scales.

Profiles of subsurface soil CO2 concentration, soil temperature, and soil moisture, and throughfall were measured continuously during the years 2005 and 2006 in 16 locations at the free air CO2 enrichment facility situated within a temperate loblolly pine (Pinus taeda L.) stand. Sampling at these locations followed a 4 by 4 replicated experimental design comprised of two atmospheric CO2 concentration levels (ambient [CO2]a, ambient + 200 ppmv, [CO2]e) and two soil nitrogen (N) deposition levels (ambient, ambient + fertilization at 11.2 gN m−2 year−1). The combination of these measurements permitted indirect estimation of belowground CO2 production and flux profiles in the mineral soil. Adjacent to the soil CO2 profiles, direct (chamber-based) measurements of CO2 fluxes from the soil–litter complex were simultaneously conducted using the automated carbon efflux system. Based on the measured soil CO2 profiles, neither [CO2]e nor N fertilization had a statistically significant effect on seasonal soil CO2, CO2 production, and effluxes from the mineral soil over the study period. Soil moisture and temperature had different effects on CO2 concentration depending on the depth. Variations in CO2 were mostly explained by soil temperature at deeper soil layers, while water content was an important driver at the surface (within the first 10 cm), where CO2 pulses were induced by rainfall events. The soil effluxes were equal to the CO2 production for most of the time, suggesting that the site reached near steady-state conditions. The fluxes estimated from the CO2 profiles were highly correlated to the direct measurements when the soil was neither very dry nor very wet. This suggests that a better parameterization of the soil CO2 diffusivity is required for these soil moisture extremes.

Despite the observed impact of water stress on photosynthesis, some of the most used models of CO2 assimilation in C3 and C4 functional types do not directly account for it. We discuss an extension of these models, which explicitly includes the metabolic and diffusive limitations due to water stress on photosynthesis. Functional relationships describing the photosynthetic processes and CO2 diffusion inside leaves are modified to account for leaf water status on the basis of experimental results available in the literature. Extensive comparison with data shows that the model is suitable to describe the reduction in CO2 assimilation rate with decreasing leaf water potentials in various species. A simultaneous analysis of photosynthesis, transpiration and soil moisture dynamics is then carried out to explore the actual impact of drought on different photosynthesis processes and on the overall plant activity. The model well reproduces measured CO2 assimilation rate as a function of soil moisture and could be useful to formulate hypotheses for detailed experiments as well as to simulate in detail transpiration and photosynthesis dynamics under water stress.

The heterogeneous distribution of nutrient-rich and nutrient-poor patches in soils strongly affects the intensity of nitrogen cycling between organic and inorganic soil compartments. In highly heterogeneous soils, observation at the core scale of large gross mineralization and immobilization fluxes has led to the development of the mineralization–immobilization turnover (MIT) modeling scheme, which maintains that all nitrogen decomposed from organic compounds is mineralized before assimilation by the microbial biomass. This hypothesis, however, neglects the endogenous nature of the ammonification reactions at the microscopic scale, where organic N is directly assimilated by the decomposers and only the surplus is released as ammonium, as better described by the direct (DIR) pathway. Here we hypothesize that, at the micro-scale, mineralization behaves according to the DIR pathway and analyze a simple two-compartment model to simulate a heterogeneous soil with two fractions of different chemical composition (i.e., C-to-N ratio) and quality (i.e., decomposition rate). We derive the effective parameters of the aggregated model as a function of micro-scale features, and show that it represents a generalization of the parallel (PAR) scheme, which in its original form was introduced to combine DIR and MIT pathways. This physically based new parameterization improves current lumped N mineralization models.

Analytical formulations of soil carbon and nitrogen cycles are used to explore the effects of model nonlinearities and feedbacks on the resulting dynamics. Two particular aspects are addressed: (i) nonlinearities in the decomposition rate of soil organic matter and (ii) nitrogen limitation feedbacks on microbial activity and plant-microbe competition. Although linear models of decomposition are more typical in the literature, nonlinear models accounting for the coupling between microbial biomass and its substrate have also been proposed. In deterministic conditions, linear models behave like exponential decay functions, while nonlinear models may also show fluctuating behavior, with dynamic bifurcations between stable-node and stable-focus equilibria as a function of the climatic parameters (e.g., soil moisture and temperature). Both data-model comparison and linear stability analysis support the conclusion that linear models are less suited to describe the soil fluctuating dynamics that arise under certain conditions. A second strong nonlinearity appears when the nitrogen-limitation feedback on decomposition is analyzed. Nitrogen limitation is often established when the substrate of the microbes is N-poor, and/or the competition with plants for mineral N is strong. Such conditions mainly occur when a large fraction of the microbial community cannot meet its nitrogen demand through organic N assimilation, so that mineral N is used. On the contrary, when the microbial community predominantly assimilates organic nitrogen, the occurrence of nitrogen-limitation is less likely and mineralization is given by microbial N surplus. The first case is traditionally modeled by the mineralization-immobilization turnover (MIT) scheme, while the second by the direct assimilation (DIR) scheme. However, since organic N assimilation and mineral N immobilization likely occur simultaneously because of soil heterogeneity and coexistence of different microbial communities, the two schemes only represent extreme cases. Thus, we combine them in a flexible model framework (parallel scheme) and explore how different efficiencies of organic nitrogen assimilation, mineral nitrogen availability and climatic factors control the outcome of plant-microbe competition. We conclude that models accounting only for the DIR pathway implicitly assume that microbes are superior competitors over plants, while models implementing only the MIT pathway might be too sensitive to N-limitation.

A simplified, vertically-averaged model of soil moisture interpreted at the daily time scale and forced by a stochastic process of instantaneous rainfall events is compared with a vertically-averaged model which uses a non-overlapping rectangular pulse rainfall model and a more physically based description of infiltration. The models are compared with respect to the importance of short time-scale (intra-storm) variable infiltration in determining the probabilistic structure of soil-moisture dynamics at the daily time-scale. Differences in approach to infiltration modelling show only minor effects on the probabilistic structure of soil-moisture dynamics as simulated in the two models. The partitioning of losses during a single rainfall event are examined closely and the conditions under which surface-controlled runoff is significant, as a proportion of total losses, are delineated.

The nitrogen and carbon dynamics of water-limited ecosystems are significantly controlled by the soil water content, which in turn depends on soil properties, climate, and vegetation characteristics. Because of its impact on soil aeration, microorganism environmental stress, and ion transport within the pore spaces, the soil water content controls the activity of microbial biomass with important effects on the rates of decomposition, mineralization, nitrification, and denitrification. Mineral nitrogen is mainly lost in the leaching and plant uptake processes, which are both controlled by the soil water content. To assess both the long-term and the short-term impact of soil moisture dynamics on the soil nitrogen and carbon budgets, models of the N and C cycles need to operate at daily resolutions (or higher). On the other hand, long-term projections require a stochastic modeling of the climate forcing to generate long replicates of the climate signal as well as to assess the system response to climate change. This paper reviews a modeling framework developed by the authors [Proc. R. Soc. Lond. A 455 (1999a) 3789; Adv. Water. Res. 26 (2003) 45; Adv. Water Resour. 26 (2003) 59; Sci. J. 5 (2003) 781] for the process-based analysis of soil moisture, nitrogen, and carbon dynamics, presenting a synthesis of the main results of those investigations.

The governing equations of soil moisture dynamics, photosynthesis, and transpiration are reviewed and coupled to study the dependence of plant carbon assimilation on soil moisture. The model follows the scheme of the soil‐plant‐atmosphere continuum (SPAC) and uses a simplified model of the atmospheric boundary layer to arrive at an upscaled, parsimonious representation at the daily time scale. The analysis of soil moisture, transpiration, and carbon assimilation dynamics provides an assessment of the role of soil, plant, and boundary layer characteristics on the diurnal courses of photosynthesis and transpiration rates, while the subsequent upscaling at the daily level provides a functional dependence of stomatal conductance on soil moisture that is in good agreement with field experiments. The upscaled dependence of transpiration and carbon assimilation on soil moisture is used in Part II of this paper to explore the impact of soil moisture dynamics on plant conditions when rainfall variability is explicitly considered.

The coupled dynamics of soil moisture, transpiration, and assimilation are studied at the daily time scale by temporally upscaling the hourly time scale results obtained in a companion paper. The effects of soil and vegetation characteristics on soil moisture dynamics at the daily time scale and the parameters characterizing the dependence of transpiration and assimilation on soil water content are analyzed and discussed. The daily leaf carbon assimilation is then coupled to a stochastic soil moisture model to obtain a probabilistic description of the carbon assimilation during a growing season. The rainfall regime, in terms of both frequency and amount of precipitation, controls the mean assimilation during a growing season that reaches a maximum for an intermediate range of daily rainfall probabilities, indicating the existence of a rainfall regime that is most effective for plant productivity. The analysis of the duration and frequency of periods of no assimilation provides a measure of plant water stress as a function of the soil, vegetation, and climate characteristics. The results are in good agreement with the dynamic water stress defined in Porporato et al. on the basis of the crossing properties of the stochastic soil moisture dynamics.

The spatial and temporal dynamics of soil water content along a hillslope is the result of a number of complex and mutually interacting processes. This paper deals with the role of subsurface, unsaturated, lateral water flow and its links to climate, soil, and hillslope characteristics. The analysis focuses on the soil moisture dynamics at the daily time scale, averaged over the plant rooting depth, and accounts for the stochastic nature of precipitation as well as for the non-linear dependence of transpiration and hydraulic conductivity on soil moisture. The lateral fluxes of soil moisture are described by means of the one-dimensional Richards equation, and the probabilistic soil moisture dynamics is numerically investigated considering different conditions of climate, pedology, vegetation, and hillslope geometry. From the analysis two different regimes emerge: a humid one, characterized by an unsaturated lateral flow with significant spatial gradients of soil moisture along the hillslope, and a dry one, in which the topography does not affect the spatial distribution of the soil moisture. In the humid regime, the long-term average spatial pattern of soil water content is studied at different points along the hillslope using the mean, rms, and pdfs of soil moisture, as well as the components of the long-term water balance. All these analyses show how the soil moisture dynamics is the result of complex and non-local interactions between climate, soil, vegetation, and hillslope shape.

The influence of soil moisture dynamics on soil carbon and nitrogen cycles is analyzed by coupling an existing stochastic soil moisture model [Adv. Water. Resour. 24 (7) (2001) 707; Proc. R. Soc. Lond. A 455 (1999) 3789] to a system of eight nonlinear differential equations that describe the temporal evolution of the organic matter and the mineral nitrogen in the soil at the daily to seasonal time scales. Special attention is devoted to the modeling of the soil moisture control on mineralization and immobilization fluxes, leaching losses, and plant nitrogen uptake, as well as to the role played by the soil organic matter carbon-to-nitrogen ratio in determining mineralization and immobilization. The model allows a detailed analysis of the soil nitrogen cycle as driven by fluctuations in soil moisture at the daily time scale resulting from the stochastic rainfall variability. The complex ensuing dynamics are studied in detail in a companion paper [Adv. Water Resour. 26 (1) (2003) 59], which presents an application to the Nylsvley savanna in South Africa. The model accounts for the soil moisture control on different components of the nitrogen cycle on a wide range of time scales: from the high frequency variability of leaching and uptake due to the nitrate flushes after persistent rainfall following a period of drought, to the low frequency temporal dynamics of the soil organic matter pools. All the fluctuations in the various pools are statistically characterized in relation to their dependence on climate, soil, and vegetation characteristics.

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.

Soil texture is a key variable in the coupled relationship between climate, soil, and vegetation. This coupling and its dependence on soil texture are studied in this paper using analytical descriptions for soil moisture dynamics and the corresponding vegetation water stress. Results confirm the importance of soil texture in partitioning rainfall into the mean values of the water balance loss components, namely, evapotranspiration, leakage, and runoff, and in determining vegetation water stress for the vegetation and climatic regimes of the La Copita Research Area in Texas. Two separate mechanisms by which this sensitivity to soil texture can impact the ecological structure at La Copita are illustrated. First, dynamics similar to the inverse texture effect, whereby the optimal soil texture for a given vegetation type changes with rainfall amount, are demonstrated for the two most common species at this site. Second, it is shown that soil texture plays a major role in the modulation of the impact that interannual rainfall fluctuations have on the fitness and coexistence of trees and grasses.

Three water-controlled ecosystems are studied here using the stochastic description of soil moisture dynamics and vegetation water stress proposed in Part II (F. Laio, A. Porporato, L. Ridolfi, I. Rodriguez-Iturbe, Adv. Water Res. 24 (7) (2001) 707-723) and Part III (A. Porporato, F. Laio, L. Ridolfi, I. Rodriguez-Iturbe, Adv. Water Res. 24 (7) (2001) 725-744) of this series of papers. In the savanna of Nylsvley (South Africa) the very diverse physiological characteristics of the existing plants give rise to different strategies of soil moisture exploitation. Notwithstanding these differences, the vegetation water stress for all the species turns out to be very similar, suggesting that coexistence might be attained also through differentiation of water use. The case of the savanna of Southern Texas points out how rooting depth and interannual rainfall variability can impact soil moisture dynamics and vegetation water stress. Because of the different responses to water stress of trees and grasses, external climatic forcing could be at the origin of the dynamic equilibrium allowing coexistence in this ecosystem. Finally, the analysis of a short grass steppe in Colorado provides an interesting example of the so-called inverse texture effect, whereby preferential conditions for vegetation are dependent on soil texture and rainfall. Sites which are more favorable during wet conditions may become less suitable to the same vegetation type during drier years. Such an effect is important to explain the predominance of existing species, as well as to investigate their reproductive strategies.

In the study of the evolutionary dynamics of soil moisture at a site, it is particularly important to define some characteristic properties of the temporal structure of the periods in which the soil water content is below certain levels indicative of water stress conditions in vegetation. The analysis of such properties provides an approach to establish some hydrologic basis for the understanding and modeling of ecosystems functioning in water-limited environments. This paper deals with a stochastic point process model of soil water balance. Expressions for both the mean number and the mean duration of time intervals during which the soil moisture is below a given threshold are analytically derived as a function of climate, soil, and vegetation. The seasonal mean value of water deficit is also analytically obtained. These properties are used to characterize the state of water stress in plants and to study its dependence on the interrelated dynamics. Estimates are included for the probability distributions of the frequency and duration of the stress and soil water deficit, for different hypotheses on climate, soil, and vegetation. Both the hydrologic and the ecologic implications of the results are briefly outlined.

An important parameter in the assessment of the impact that conditions of limited soil water availability have on vegetation is the average length of the intervals during the growing season in which soil moisture is below some critical levels. These levels are related to the plant tolerance to water stress. The interannual rainfall variability induces important fluctuations on the average duration and frequency of the periods of water stress with important effects on the spatial and temporal structure of plant ecosystems. It is shown that the nonlinearities embedded in the dynamics controlling the soil water balance may drastically enhance the effects of the fluctuations present in the climatic forcing. Interannual climate variability leads to stronger year-to-year changes on the mean duration and frequency of periods of soil water deficit as well as to the emergence of preferential states in the probability distributions of these two variables. The sensitivity of these statistical properties is studied with respect to the characteristics of climate, soil, and vegetation.

The impact of climate fluctuations can be observed in the dynamics of vegetation and most particularly in the sensitive environment of savannas. In this paper we present a model for the local competition for soil moisture among neighboring vegetation. The initial condition for the model is a random field where at each point the soil moisture is the mean water content when there are no spatial interactions between sites. The mean soil moisture values account for stochasticity of climate and losses from evapotranspiration and leakage which depend on the existing water content. A spatial dynamics is then implemented based on the explicit minimization of the global water stress over the region. This approach explains the coexistence of herbaceous and woody plants in savannas as well as the changes in canopy density that have been documented in the southwest of the United States as a function of regional climatic fluctuations.

The soil moisture dynamics under seasonally fixed conditions are studied at a point. The water balance is described through the representation of rainfall as a marked Poisson process which in turn produces an infiltration into the soil dependent on the existing level of soil moisture. The losses from the soil are due to evapotranspiration and leakage which are also considered dependent on the existing soil moisture. The steady–state probability distributions for soil moisture are then analytically obtained. The analysis of the distribution allows for the assessment of the role of climate, soil and vegetation on soil moisture dynamics. Further hydrologic insight is obtained by studying the various components of an average water balance. The realistic representation of the processes acting at a site and the analytical tractability of the model make it well suited for further analyses which consider the spatial aspect of soil moisture dynamics.

Summary � Soil and plant hydraulics constrain ecosystem productivity by setting physical limits to water transport and hence carbon uptake by leaves. While more negative xylem water potentials provide a larger driving force for water transport, they also cause cavitation that limits hydraulic conductivity. An optimum balance between driving force and cavitation occurs at intermediate water potentials, thus defining the maximum transpiration rate the xylem can sustain (denoted as Emax). The presence of this maximum raises the question as to whether plants regulate transpiration through stomata to function near Emax. � To address this question, we calculated Emax across plant functional types and climates using a hydraulic model and a global database of plant hydraulic traits. � The predicted Emax compared well with measured peak transpiration across plant sizes and growth conditions (R= 0.86, P < 0.001) and was relatively conserved among plant types (for a given plant size), while increasing across climates following the atmospheric evaporative demand. The fact that Emax was roughly conserved across plant types and scales with the product of xylem saturated conductivity and water potential at 50% cavitation was used here to explain the safety–efficiency trade-off in plant xylem. � Stomatal conductance allows maximum transpiration rates despite partial cavitation in the xylem thereby suggesting coordination between stomatal regulation and xylem hydraulic characteristics.

Combining decomposition data with process-based biogeochemical models is essential to quantify the turnover of organic carbon (C) in surface litter and soil organic matter (SOM). Long-term decomposition may be suitably analyzed by linear models (i.e., all fluxes defined by first-order kinetics), which allow the derivation of analytical expressions to estimate the loss of C and the overall apparent decay rate (kapp) through time. Here we compare eight linear models (four discrete-compartment models with one or two C pools, two models with a single time-dependent decay rate, and two models based on a continuous distribution of decay rates) and report their analytical solutions for two types of decomposition experiments: i) studies that evaluate the decomposition of a single input of fresh litter (i.e., a single cohort, as in litterbag and C labeling experiments), and ii) studies that evaluate the decomposition of soil samples with compounds of different ages (i.e., multiple cohorts, as in long-term incubations or isotope dilution experiments). We fitted analytical mass loss functions to both types of datasets and evaluated the performance of the models. For single-cohort data, continuous-decay models provide the best balance between accuracy and parsimony (R2 ¼ 0.99, lowest Akaike and Bayesian information criteria), while for multiple-cohort data the two-pool models tend to perform better (R2 ¼ 0.96), perhaps because of the strong separation of time scales in the decomposition data considered. Differences among some models are marginal, suggesting that decomposition data alone do not point to a single ‘best’ model. All models resulted in apparent decay rates that decreased markedly through time, in contrast with the assumption of constant k adopted in the single-pool exponential decay model. We also show how model parameters estimated from single cohort samples can be used to model multiple cohort decomposition, unifying both types of experimental data in one theory. Based on our results, it is possible to distinguish the temporal changes in C loss that are attributable to initial chemical composition or abiotic factors, from those associated with the presence of multiple ages in the substrate. Fil: Manzoni, Stefano. University Of Duke. Nicholas School Of Environment; Estados Unidos Fil: Piñeiro, Gervasio. University Of Duke. Nicholas School Of Environment; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura. Universidad de Buenos Aires. Facultad de Agronomía. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura; Argentina Fil: Jackson, Robert B.. University Of Duke. Nicholas School Of Environment; Estados Unidos Fil: Jobbagy Gampel, Esteban Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis ; Argentina Fil: Kim, John H.. University Of Duke; Estados Unidos Fil: Porporato, Amilcare. University Of Duke. Nicholas School Of Environment; Estados Unidos

[1] Drought-related tree mortality at a regional scale causes drastic shifts in carbon and water cycling in Southeast Asian tropical rain forests, where severe droughts are projected to occur more frequently, especially under El Nino conditions. We examine how the mortality of a Bornean tropical rain forest is altered by projected shifts in rainfall, using field measurements, global climate model (GCM) simulation outputs, and an index developed for drought-induced tree mortality (Tree Death Indexη) associated with a stochastic ecohydrological model. All model parameters have clear physical meanings and were obtained by field observations. Rainfall statistics as primary model forcing terms are constructed from long-term rainfall records for the late 20th century, and 14 GCM rainfall projections for the late 21st century. These statistics indicate that there were sporadic severe droughts corresponding with El Nino events, generally occurring in January–March, and that seasonality in rainfall will become more pronounced, e.g., dry (January–March) seasons becoming drier and wet (October–December) seasons becoming wetter. The computedη well reflects high tree mortality under severe drought during the 1997–1998 El Nino event. For the present, model results demonstrate high and low probabilities of mortality in January–March and October–December, respectively, and they predict that the difference in such probabilities will increase in the future. Such high probability of mortality in the dry season is still significantly high, even considering the beneficial effect of increased soil water storage in the wet season (which is projected to increase in the late 21st century).

Forested soils are being increasingly transformed to agricultural fields in response to growing demands for food crop. This modification of the land use is known to result in deterioration of soil properties, in particular its fertility. To reduce the impact of the human activities and mitigate their effects on the soil, it is important to understand the factors responsible for the modification of soil properties. In this paper we reviewed the principal processes affecting soil quality during land use changes, focusing in particular on the effect of soil moisture dynamics on soil carbon (C) and nitrogen (N) cycles. Both physical and biological processes, including degradation of litter and humus, and soil moisture evolution at the diurnal and seasonal time scales were considered, highlighting the impact of hydroclimatic variability on nutrient turnover along with the consequences of land use changes from forest to agricultural soil and vice-versa. In order to identify to what extent different models are suitable for long-term predictions of soil turn-over, and to understand whether some simulators are more suited to specific environmental conditions or ecosystems, we enumerated the principal features of the most popular existing models dealing with C and N turnover. Among these models, we considered in detail a mechanistic compartment-based model. To show the capabilities of the model and to demonstrate how it can be used as a predictive tool to forecast the effects of land use changes on C and N dynamics, four different scenarios were studied, intertwining two different climate conditions (with and without seasonality) with two con-trasting soils having physical properties that are representative of forest and agricultural soils. The model incorporates synthetic time series of stochastic precipitation, and therefore soil moisture evolu-tion through time. Our main findings in simulating these scenarios are that 1) forest soils have higher concentrations of C and N than agricultural soils as a result of higher litter decomposition; 2) high frequency changes in water saturations under seasonal climate scenarios are commensurate with C and N concentrations in agricultural soils; and 3) due to their different physical properties, forest soils attenuate the seasonal climate-induced frequency changes in water saturation, with accompanying changes in C and N concentrations. The model was shown to be capable of simulating the long term effects of modified physical properties of agricultural soils, being thus a promising tool to predict future consequences of practices affecting sustainable agriculture, such as tillage (leading to erosion), ploughing, harvesting, irrigation and fertilization, leading to C and N turnover changes and in conse-quence, in terms of agriculture production.

[1] Rainfall variability occurs over a wide range of time scales owing to processes initiated by cloud microphysics and sustained by atmospheric circulation. A central topic in rainfall research is to determine whether rainfall variability at a given scale is caused by dynamics acting at some other scales. Random multiplicative cascades (RMCs) are standard approaches for describing rainfall variability across such a wide range of time scales. Their popularity stems from their ability to reproduce rainfall self-similarity and long-range correlations as well as intermittency buildup at finer scales. However, standard RMCs only predict instantaneous flow of variance (energy or activity) from large to fine scales and cannot account for scale-wise causal relationships. Such relationships reveal themselves through noninstantaneous cascade mechanisms, namely, large-scale events influencing finer-scale events at later times (i.e., forward causal cascade) or conversely (inverse causal cascade). The presence of causal cascade signatures within the rainfall process is explored here using both continuous wavelet decomposition (CWT) and scale-by-scale causality measures such as cross-scale correlation and linearized transfer entropy. The causality hypothesis is further tested against results from toy models, surrogate data, and a scalar turbulence time series (water vapor) to ensure that rainfall causality is not an artifact of the estimation method or resulting from the redundancy in CWT. The analysis demonstrates the presence of causal cascades (mainly forward) in rainfall series when sampled at fine temporal resolutions (seconds). These causal relationships tend to vanish when rainfall is aggregated at coarser time scales (hours and longer).

[1] Microtopography, consisting of small-scale excursions in the elevation of the land surface on millimeter to centimeter scales, is ubiquitous on hillslopes, but its effects are rarely incorporated into hydrological analyses of rainfall-runoff partitioning. To progress toward a hydrological theory that accounts for microtopography, two research questions are considered: (1) Does microtopography change the partitioning of rainfall into runoff and infiltration compared to a background case that lacks these small-scale excursions? and (2) how do soil, mean slope, storm properties, and microtopographic geometric attributes influence this partitioning? To address these questions, a simplified one-dimensional hillslope with uniform sinusoidal microtopography is considered, and several rainfall-runoff scenarios are examined with a numerical model. The results indicate that for a range of realistic conditions, microtopography increases the proportion of rainfall infiltrating by 20–200% relative to an equivalent “background state” in which microtopography is absent. Additional theoretical development addressing issues of connectivity and improved representations of flow hydraulics over microtopographic surfaces are needed to refine these estimates and extend them to less idealized conditions. If confirmed, the results suggest that microtopography may have a significant impact on streamflow generation, plant water availability and the co-evolution of geomorphic, hydrological and ecological systems, with important implications for land management, especially in arid ecosystems.

[1] The long-term soil carbon dynamics may be approximated by networks of linear compartments, permitting theoretical analysis of transit time (i.e., the total time spent by a molecule in the system) and age (the time elapsed since the molecule entered the system) distributions. We compute and compare these distributions for different network configurations, ranging from the simple individual compartment, to series and parallel linear compartments, feedback systems, and models assuming a continuous distribution of decay constants. We also derive the transit time and age distributions of some complex, widely used soil carbon models (the compartmental models CENTURY and Rothamsted, and the continuous-quality Q-Model), and discuss them in the context of long-term carbon sequestration in soils. We show how complex models including feedback loops and slow compartments have distributions with heavier tails than simpler models. Power law tails emerge when using continuous-quality models, indicating long retention times for an important fraction of soil carbon. The responsiveness of the soil system to changes in decay constants due to altered climatic conditions or plant species composition is found to be stronger when all compartments respond equally to the environmental change, and when the slower compartments are more sensitive than the faster ones or lose more carbon through microbial respiration.

Nonlinear storage-discharge relations may explain important hydrologic features frequently observed under a variety of environmental conditions. In this paper the catchment dynamic storage problem is addressed by incorporating nonlinear storage-discharge relations in a stochastic framework to derive the statistical distribution and the duration curve of streamflows in river basins. Such a goal is achieved by extending recent analytical solutions for the seasonal probability distribution of discharges derived from the stochastic description of soil moisture dynamics at basin scales. Long-term probability density functions (pdf's) and flow duration curves are expressed through climatic, ecohydrologic, and geomorphic parameters of the basin by relaxing the linear reservoir assumption of subsurface flow components conveniently made in previous studies. In particular, this paper focuses on three different types of nonlinear, algebraic relationships between instantaneous discharges and storage volumes (concave and convex power laws and hyperbolic). Exact expressions of the streamflow pdf are derived in all cases, which are also tested by numerical simulations. Streamflow statistics and duration curves, estimates of catchment dynamic storages, recession timescales, and sensitivity to the underlying rainfall regime are then discussed. The model shows that different shapes of the streamflow pdf (bell shaped, monotonously decreasing, and bimodal) arise depending on the degree of nonlinearity of the storage-discharge relation, providing a new approach to catchment hydrology characterization.

[1] Local topographic features such as slope and aspect play a crucial role in a number of morphological, ecological, and hydrological processes. We propose a simple yet realistic probabilistic description of local slope and aspect as a function of properties of the field of elevation changes. We consider different classes of models of elevation changes and obtain the theoretical distribution of slope and aspect. We relate the features of the obtained distributions to large-scale landscape structures, such as regional trends and anisotropy. We find that the theoretical distribution of slope is strongly impacted by the parameters used to represent the distribution of elevation changes, while large-scale features play a secondary role. Conversely, the distribution of aspect is also controlled by regional trends and anisotopy, even when they are weak. The proposed statistical description of slope and aspect is applied to assess the effects of topographic features on direct solar radiation mean and standard deviation. The main control on direct solar radiation is exerted by the partial derivative variance. We consider four different landscapes across the continental United States and compare the proposed theoretical description of slope and aspect distributions to the observed histograms.

[1] Estimation of water uptake by plants and subsequent water stress are complicated by the need to resolve the soil-plant hydrodynamics at scales ranging from millimeters to meters. Using a simplified homogenization technique, the three-dimensional (3-D) soil water movement dynamics can be reduced to solving two 1-D coupled Richards’ equations, one for the radial water movement toward rootlets (mesoscale, important for diurnal cycle) and a second for vertical water motion (macroscale, relevant to interstorm timescales). This approach allows explicit simulation of known features of root uptake such as diurnal hysteresis in canopy conductance, hydraulic lift, and compensatory root water uptake during extended drying cycles. A simple scaling analysis suggests that the effectiveness of the hydraulic lift is mainly controlled by the root vertical distribution, while the soil moisture levels at which hydraulic lift is most effective is dictated by soil hydraulic properties and surrogates for atmospheric water vapor demand.

[1] A continuum-scale mathematical model which couples water flow and bacterial dynamics explores the process of biological clogging in unsaturated soils. The impact of biomass dynamics on soil water flow is assumed to take place through the changes in porosity and the structural properties of the medium by suitable modifications of the pore size distribution, water retention, and hydraulic conductivity functions. The feedback of soil moisture on biomass is taken into account by including the effect of water stress on microbial growth. The model is calibrated against existing laboratory experimental data for an artificial porous medium in saturated conditions, and it is used to analyze the hydraulic behavior of unsaturated soils when subject to biological clogging and plant water uptake. The results of this analysis show that this feedback may have a substantial impact on the net water flow, the soil water-holding capacity, and the soil moisture and biomass space-time distributions.

[1] The spectrum of soil moisture content at scales ranging from 1 hour to 8 years is analyzed for a site whose hydrologic balance is primarily governed by precipitation (p), and evapotranspiration (ET). The site is a uniformly planted loblolly pine stand situated in the southeastern United States and is characterized by a shallow rooting depth (RL) and a near-impervious clay pan just below RL. In this setup, when ET linearly increases with increasing root zone soil moisture content (θ), an analytical model can be derived for the soil moisture content energy spectrum (Es(f), where f is frequency) that predicts the soil moisture “memory” (taken as the integral timescale) as β1−1 ≈ ηRL/ETmax, where ETmax is the maximum measured hourly ET and η is the soil porosity. The spectral model suggests that Es(f) decays at f−2−α at high f but almost white (i.e., f0) at low f, where α is the power law exponent of the rainfall spectrum at high f (α ≈ 0.75 for this site). The rapid Es(f) decay at high f makes the soil moisture variance highly imbalanced in the Fourier domain, thereby permitting much of the soil moisture variability to be described by a limited number of Fourier modes. For the 8-year data collected here, 99.6% of the soil moisture variance could be described by less than 0.4% of its Fourier modes. A practical outcome of this energy imbalance in the frequency domain is that the diurnal cycle in ET can be ignored if β1−1 (estimated at 7.6 days from the model) is much larger than 12 hours. The model, however, underestimates the measured Es(f) at very low frequencies (f ≪ β1) and its memory, estimated from the data at 42 days. This underestimation is due to seasonality in ETmax and to a partial decoupling between ET and soil moisture at low frequencies.