Browsing by Author "Porporato, Amilcare M"

Society-induced changes to the environment are altering the effectiveness of existing management strategies for sustaining natural and agricultural ecosystem productivity. At the watershed scale, natural and agro-ecosystems represent complex spatiotemporal stochastic processes. In time, they respond to random rainfall events, evapotranspiration and other losses that are spatially variable because of heterogeneities in soil properties, root distributions, topography, and other factors. To quantify the environmental impact of anthropogenic activities, it is essential that we characterize the evolution of space and time patterns of ecosystem fluxes (e.g., energy, water, and nutrients). Such a characterization then provides a basis for assessing and managing future anthropogenic risks to the sustainability of ecosystem productivity.

To characterize the space and time evolution of watershed scale processes, this dissertation introduces a mean field approach to watershed hydrology. Mean field theory (also known as self-consistent field theory) is commonly used in statistical physics when modeling the space-time behavior of complex systems. The mean field theory approximates a complex multi-component system by considering a lumped (or average) effect of all individual components acting on a single component. Thus, the many body problem is reduced to a one body problem. For watershed hydrology, a mean field theory reduces the numerous point component effects to more tractable watershed averages resulting in a consistent method for linking the average watershed fluxes (evapotranspiration, runoff, etc.) to the local fluxes at each point.

The starting point for this work is a general point description of the soil moisture, rainfall, and runoff system. For this system, we find the joint PDF that describes the temporal variability of the soil water, rainfall, and runoff processes. Since this approach does not account for the spatial variability of runoff, we introduce a probabilistic storage (ProStor) framework for constructing a lumped (unit area) rainfall-runoff response from the spatial distribution of watershed storage. This framework provides a basis for unifying and extending common event-based hydrology models (e.g. Soil Conservation Service curve number (SCS-CN) method) with more modern semi-distributed models (e.g. Variable Infiltration Capacity (VIC) model, the Probability Distributed (PDM) model, and TOPMODEL). In each case, we obtain simple equations for the fractions of the different source areas of runoff, the spatial variability of runoff and soil moisture, and the average runoff value (i.e., the so-called runoff curve). Finally, we link the temporal and spatial descriptions with a mean field approach for watershed hydrology. By applying this mean field approach, we upscale the point description with the spatial distribution of soil moisture and parameterize the numerous local interactions related to lateral fluxes of soil water in terms of its average. With this approach, we then derive PDFs that represent the space and time distribution of soil water and associated watershed fluxes such as evapotranspiration and runoff.

The topographical properties of a landscape and their time evolution are key features of the Earth's surface, regulating ecosystem functioning in terms of soil properties as well as water and energy budgets, and creating visually diverse and striking patterns across various spatial scales. Furthermore, the natural evolution of a topography under the influence of geologic erosion can be greatly altered by anthropogenic disturbances (e.g., through agriculture, mining, deforestation), with the potential of accelerating soil erosion, causing land degradation and soil fertility losses. Hence, understanding the geomorphological processes driving the evolution of landscapes under natural and disturbed conditions is key not only to define the main factors and feedbacks shaping the Earth's topography, but also to foresee the consequences of intensive land use and implement optimal strategies of land management and recovery.

This dissertation addresses some key aspects of landscape evolution and stability, with a focus on the statistical description and modeling of hillslope morphologies under natural and disturbed conditions, the theoretical definition of drainage area at regular and non-regular points of the watershed, and the formation of spatially organized ridge and valley patterns.

We start from the analysis of topographic slopes under natural and accelerated soil erosion. Using large topographic datasets from mountain ranges worldwide, we show that the approximate age of a landscape is fingerprinted in the tails of its slope distributions. We then explore the role of the different processes driving this dynamic smoothing over geologic time scales by means of numerical experiments, showing that the relaxation process is mainly dominated by diffusion. The effect of agricultural-driven soil erosion on hillslope morphology is then investigated, highlighting how the natural aging process can be altered by intensive land use which, at smaller scales, produces key differences in the slope distribution tails. Furthermore, theoretical solutions are derived for the hillslope profile and the associated soil creep and runoff erosion fluxes, and used to link the observed differences in the morphological features of disturbed and undisturbed areas to a disruption of the natural balance between soil creep and runoff erosion mechanisms.

We then move the analysis to the drainage area, an important nonlocal morphometric variable used in a large number of geomorphological and ecohydrological applications. A nonlinear differential equation whose validity is limited to regular points of the watershed is obtained from a continuity equation, and the theory is then extended to critical and singular points by means of both Gauss' theorem and dynamical systems concepts. Such a link between the drainage area and a continuity equation sets the basis for the subsequent analysis of organized ridge and valley patterns and channel forming instability. The formation of ridge/valley patterns is analyzed by means of numerical experiments in detachment limited conditions, with the identification of various regimes as a function of diffusive soil creep, runoff erosion, and tectonic uplift as well as the specific geomorphic transport law assumed. Lastly, a linear stability analysis of the coupled water and landscape evolution dynamics is outlined to investigate the critical conditions triggering channel formation and the emergence of characteristic valley spacings in relation to the main geomorphological processes involved.

Seasonally dry ecosystems cover large areas over the world, have high potential for carbon sequestration, and harbor high levels of biodiversity. They are characterized by high rainfall variability at timescales ranging from the daily to the seasonal to the interannual, and water availability and timing play key roles in primary productivity, biogeochemical cycles, phenology of growth and reproduction, and agricultural production. In addition, a growing demand for food and other natural resources in these regions renders seasonally dry ecosystems increasingly vulnerable to human interventions. Compounded with changes in rainfall regimes due to climate change, there is a need to better understand the role of climate variabilities in these regions to pave the way for better management of existing infrastructure and investment into future adaptations.

In this dissertation, the ecohydrological responses of seasonally dry ecosystem to climate variabilities are investigated under a comprehensive framework. This is achieved by first developing diagnostic tools to quantify the degree of rainfall seasonality across different types of seasonal climates, including tropical dry, Mediterranean, and monsoon climates. This global measure of seasonality borrows from information theory and captures the essential contributions from both the magnitude and concentration of the rainy season. By decomposing the rainfall signal from seasonality hotspots, increase in the interannual variability of rainfall seasonality is found, accompanied by concurrent changes in the magnitude, timing, and durations of seasonal rainfall, suggesting that increase in the uncertainty of seasonal rainfall may well extend into the next century. Next, changes in the hydrological partitioning, and the temporal responses of vegetation resulting from these climate variabilities, are analyzed using a set of stochastic models that accounts for the unpredictability rainfall as well as its seasonal trajectories. Soil water storage is found to play a pivotal role in regulating seasonal soil water hysteresis, and the balance between seasonal soil water availability and growth duration is found to induce maximum plant growth for a given amount of annual rainfall. Finally, these methods are applied in the context of biodiversity and the interplay of irrigation and soil salinity, which are prevailing management issues in seasonally dry ecosystems.

This dissertation addresses feedbacks between vegetation dynamics and land surface response to rainfall events, particularly in Mediterranean climates. Specifically, we ask how a saturated hydraulic conductivity value (ks) that is tied to vegetation biomass affects how water is divided into infiltration and runoff under a range of conditions. First, a field campaign in Sardinia was conducted in which a 4 m by 4 m rainfall simulator was constructed and deployed on a number of dates. Measurements of surface runoff from the plot and soil moisture within the plot informed estimates of the effective ks for each experimental run, and a comparison between ks and vegetation height measurements revealed a monotonically increasing relationship between the two. We then fit a logistic equation to this relationship and incorporated it into the calculations of a coupled vegetation dynamics and land surface model. Using the model, which is calibrated for the Sardinia field site, we investigated the effect of the variable ks by comparing the model results of biomass, saturation, and runoff to results using a static ks. We then used the same model to investigate the effects of a variable ks on drought recovery by simulating drought severity through a range of biomass levels relative to a no-drought condition. Our modeling results revealed that the primary result of a variable ks is modification of the quantity and mechanism of surface runoff; specifically, runoff increased over the constant ks case and shifted from saturation excess runoff to infiltration excess runoff. These effects are more pronounced in drier conditions and when rainfall intensities are in a critical region similar to the ks value. We conclude that a dynamic ks value is relevant for prediction of surface runoff and may improve the performance of land surface models.

Topography, vegetation, nutrient dynamics, soil features and hydroclimatic forcing are inherently coupled, with feedbacks occurring over a wide range of temporal and spatial scales. Vegetation growth may be limited by soil moisture, nutrient or solar radiation availability, and in turn influences both soil moisture and nutrient balances at a point. These dynamics are further complicated in a complex terrain, through a series of spatial interactions. A number of experiments has characterized the feedbacks between soil moisture and vegetation dynamics, but a theoretical framework linking short-term leaf-level to interannual plot-scale dynamics has not been fully developed yet. Such theory is needed for optimal management of water resources in natural ecosystems and for agricultural, municipal and industrial uses. Also, it complements the current knowledge on ecosystem response to the predicted climate change.

In this dissertation, the response of vegetation dynamics to unpredictable environmental fluctuations at multiple space-time scales is explored in a modeling framework from sub-daily to interannual time scales. At the hourly time scale, a simultaneous analysis of photosynthesis, transpiration and soil moisture dynamics is carried out to explore the impact of water stress on different photosynthesis processes at the leaf level, and the overall plant activity. Daily soil moisture and vegetation dynamics are then scaled up to the growing season using a stochastic model accounting for daily to interannual hydroclimatic variability. Such stochastic framework is employed to explore the impact of rainfall patterns and different irrigation schemes on crop productivity, along with their implications in terms of sustainability and profitability. To scale up from point to landscape, a probabilistic representation of local landscape features (i.e., slope and aspect) is developed, and applied to assess the effects of topography on solar radiation. Finally, a minimalistic ecosystem model, including soil moisture, vegetation and nutrient dynamics at the year time scale, is outlined; when coupled to the proposed probabilistic topographic description, the latter model can serve to assess the relevance of spatial interactions and to single out the main biophysical controls responsible for ecohydrological variability at the landscape scale.

The hydrologic cycle may be described in essence as the process of water rising and falling in its various phases between land and atmosphere. In this minimal description of the hydrologic cycle two features come into focus: intermittency and irreversibility. In this dissertation intermittency and irreversibility are investigated broadly in the soil-plant-atmosphere system. The theory of intermittency and irreversibility is addressed here in three ways: (1) through its effect on components of the soil-plant-atmosphere system, (2) through development of a measure of the degree of irreversibility in time-series, and (3) by the investigation of the dynamical sources of this intermittency. First, soil infiltration and spring frost risk are treated as two examples of hydrologic intermittency with very different characters and implications for the soil plant system. An investigation of the water budget in simplified soil moisture models reveals that simple bucket models of infiltration perform well against more accurate representation of intra-storm infiltration dynamics in determining the surface water partitioning. Damaging spring frost is presented as a ``biologically-defined extreme event'' and thus as a more subtle form of hydrologic intermittency. This work represents the first theoretical development of a biologically-defined extreme and highlights the importance of the interplay between daily temperature mean and variance in determining the changes in damaging frost risk in a warming climate. Second, a statistical measure of directionality/asymmetry is developed for stationary time-series based on analogies with the theory of nonequilibrium thermodynamics. This measure is then applied to a set of DNA sequences as an example of a discrete sequence with limited state-space. The DNA sequences are found to be statistically asymmetric and further that the local degree of asymmetry is a reliable indicator of the coding/noncoding status of the DNA segment. Third, the phenomenology of rainfall occurrence is compared with canonical examples of dynamical intermittency to determine whether these simple dynamical features may display a dominant signature in rainfall processes. Summer convective rainfall is found to be broadly consistent with Type-III intermittency. Following on this result we studied daytime atmospheric boundary layer dynamics with a view toward developing simplified models that may further elucidate the interaction the interaction between land surface conditions and convective rainfall triggering.

Human activities are shifting hydrological and biogeochemical cycles further from their natural states, often resulting in negative impacts on the environment. Because of increased pressures due to climate change and population growth, it is important to understand how human activities affect soil and water resources and how these resources can be managed sustainably. This dissertation presents a series of works which relate to the sustainable management of soil and water resources. In general, we make use of parsimonious ecohydrological models to describe key components of the soil and water system, and random hydroclimatic variability is accounted for with stochastic forcing. Methods from dynamical systems theory are also applied to further the analysis of these systems.

Initially we focus on soil resources, the impacts of vegetation on soil production and erosion and the feedbacks between soil formation and vegetation growth are ex- plored with a minimal model of the soil-plant system, which includes key feedbacks, such as plant-driven soil production and erosion inhibition. Vegetation removal re- duces the stabilizing effect of vegetation and lowers the system resilience, thereby increasing the likelihood of transition to a degraded soil state. We then turn our at- tention to water resources. Rainwater harvesting (RWH) has the potential to reduce water-related costs by providing an alternate source of water, in addition to relieving pressure on other water sources and reducing runoff. An analytical formulation is developed for the optimal cistern volume as a function of the roof area, water use rate, climate parameters, and costs of the cistern and of the external water source, and an analysis of the rainfall partitioning characterizes the efficiency of a particular RWH system configuration. Then we consider nutrient management in addition to sustainable soil and water resources. Crop models, though typically constructed as a set of dynamical equations, are not often analyzed from a specifically dynamical systems point of view, and so we develop a minimal dynamical systems framework for crop models, which describes the evolution of canopy cover, soil moisture, and soil nitrogen. Important crop model responses, such as biomass and yield, are calcu- lated, and optimal yield and profitability under differing climate scenarios, irrigation strategies, and fertilization strategies are examined within the developed framework. Important in the use of crop and other ecohydrological models and studies on soil and water resources is the representation of soil properties. 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) is a key determinant of soil properties, and its accurate representation has the potential to improve hydrological and crop models. 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. This model is used to show how soil properties such as the water retention curve and the hydraulic conductivity curve evolve in time. Finally, in order to explore the coupled evolution of soil properties, ecohydrological processes, and crop growth, we couple a dynamic crop model with a soil biogeochemistry model and the previously developed model for the evolution of the soil PSD.