Browsing by Author "Katul, Gabriel G"
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Item Open Access A Hydrologic Balance Model to Predict Future Risk of Aquifer Depletion(2012-04-26) Devine, TimothyAs demand for freshwater resources rises, the importance of conservation and preservation of ground-water resources become necessary, especially in coastal areas where large-scale seawater intrusion is a risk. A hydrologic balance model that employs historic records of precipitation, reference evapotranspiration estimates and future scenarios of withdrawal rates is developed and used to forecast future groundwater levels. These model forecasts are examined with a lens on the likelihood of 'dangerous' aquifer depletion (i.e. a level that promotes sea water intrusion). This model uses the Central Coastal Plain Capacity Use Area (CCPCUA) in eastern North Carolina as a case study. This case study is selected here because of (i) ground water level data availability prior to and post- imposed reductions of groundwater withdrawal rates (per capita), (ii) long-term historic records of rainfall and estimated of reference evapotranspiration. In this first-order analysis, a logical starting point in model development is to assume that the network of regional aquifers within CCPCUA are perfectly connected and equally accessible to pumping, the water level within the aquifer is uniform (but not steady) and the aquifer hydraulic properties (such as specific yield) are uniform in space. Under those idealized conditions, the hydrologic balance at this large-scale can be treated as 'lumped' in space - so that water level redistribution in space within the aquifer is highly efficient and only temporal dynamics of the water levels in this lumped representation need to be accounted for. The impact of specific yield, initial water depth, total population and its projection, per capita consumption (and its future regulation), precipitation rates, reference evapotranspiration rates and sea level rise on aquifer depletion are examined. The MP demonstrates how various management scenarios intended to mitigate groundwater resource depletion can be examined and cross-compared via model-assisted simulations, even in such idealized model-world.Item Open Access A mathematical model to assist phytoremediation management and evaluation(2020-04-22) Wang, XinPhytoremediation is the use of plants and their associated microbes for environmental cleanup. The use of phytoremediation for soil cleanup faces a number of challenges of which leaching of soil contaminants below the rooting zone poses a significant environmental threat. Partitioning of contaminants between plant uptake and leaching is the focus of this Master’s Project (MP). An improved mathematical model to represent phytoremediation processes are developed that couple the hydrological balance and soil contaminant balance for a dynamic vegetation system (i.e. rooting zone depth and leaf area are changing in time during the remediation period). Two different measures of phytoremediation efficiency are then assessed with different water supply amount & frequency, soil & plant properties and climatic conditions. It is found that water supply pattern is a first-order factor controlling the efficiency of phytoremediation when viewed from the perspective of maximizing plant-water uptake of contaminants. Climate change could also exert significant influence by affecting growth patterns of the plant. Additionally, a geospatial analysis tool is also created with the model to locate areas where phytoremediation may be an effective management option, when the climatic and soil datasets are available. With this combined geospatial tool and the newly proposed model, phytoremediation managers can evaluate the potential phytoremediation efficiency according to their specific situation.Item Open Access Bayesian Statistical Analysis in Coastal Eutrophication Models: Challenges and Solutions(2014) Nojavan Asghari, FarnazEstuaries interfacing with the land, atmosphere and open oceans can be influenced in a variety of ways by anthropogenic activities. Centuries of overexploitation, habitat transformation, and pollution have degraded estuarine ecological health. Key concerns of public and environmental managers of estuaries include water quality, particularly the enrichment of nutrients, increased chlorophyll a concentrations, increased hypoxia/anoxia, and increased Harmful Algal Blooms (HABs). One reason for the increased nitrogen loading over the past two decades is the proliferation of concentrated animal feeding operations (CAFOs) in coastal areas. This dissertation documents a study of estuarine eutrophication modeling, including modeling of major source of nitrogen in the watershed, the use of the Bayesian Networks (BNs) for modeling eutrophication dynamics in an estuary, a documentation of potential problems of using BNs, and a continuous BN model for addressing these problems.
Environmental models have emerged as great tools to transform data into useful information for managers and policy makers. Environmental models contain uncertainty due to natural ecosystems variability, current knowledge of environmental processes, modeling structure, computational restrictions, and problems with data/observations due to measurement error or missingness. Many methodologies capable of quantifying uncertainty have been developed in the scientic literature. Examples of such methods are BNs, which utilize conditional probability tables to describe the relationships among variables. This doctoral dissertation demonstrates how BNs, as probabilistic models, can be used to model eutrophication in estuarine ecosystems and to explore the effects of plausible future climatic and nutrient pollution management scenarios on water quality indicators. The results show interaction among various predictors and their impact on ecosystem health. The synergistic eftects between nutrient concentrations and climate variability caution future management actions.
BNs have several distinct strengths such as the ability to update knowledge based on Bayes' theorem, modularity, accommodation of various knowledge sources and data types, suitability to both data-rich and data-poor systems, and incorporation of uncertainty. Further, BNs' graphical representation facilitates communicating models and results with environmental managers and decision-makers. However, BNs have certain drawbacks as well. For example, they can only handle continuous variables under severe restrictions (1- Each continuous variable be assigned a (linear) conditional Normal distribution; 2- No discrete variable have continuous parents). The solution, thus far, to address this constraint has been discretizing variables. I designed an experiment to evaluate and compare the impact of common discretization methods on BNs. The results indicate that the choice of discretization method severely impacts the model results; however, I was unable to provide any criteria to select an optimal discretization method.
Finally, I propose a continuous variable Bayesian Network methodology and demonstrate its application for water quality modeling in estuarine ecosystems. The proposed method retains advantageous characteristics of BNs, while it avoids the drawbacks of discretization by specifying the relationships among the nodes using statistical and conditional probability models. The Bayesian nature of the proposed model enables prompt investigation of observed patterns, as new conditions unfold. The network structure presents the underlying ecological ecosystem processes and provides a basis for science communication. I demonstrate model development and temporal updating using the New River Estuary, NC data set and spatial updating using the Neuse River Estuary, NC data set.
Item Open Access Bridging Hydrology, Ecology, and Reservoir Management to Address Environmental Flow Specifications from Dams in a Changing Climate(2019-04-26) Abib, Nicole; Erfurth, SophieWater resource management has altered the natural flow regime of rivers around the globe. Buffers to environmental risk and uncertainty, dams balance competing demands for water storage and release for human needs. While dams have served as a cornerstone for human development, they have historically been tied to river exploitation, jeopardizing ecological health and species richness of streams and rivers. This project seeks to assess the impacts of current reservoir management practices on downstream ecological integrity in a changing climate with a focus on rainfall distribution shifts. We assess these impacts in a ‘model-world’ that captures some of the complexities existing in natural systems while enabling various dam management scenarios to operate under controlled conditions. For this reason, a lumped three-part mathematical model was developed to represent the impacts of precipitation and dam management on the stability of a simplified food web operating downstream from the dam. First, a watershed routing model was derived to link precipitation statistics and watershed land cover properties using a prescribed unit hydrograph. Second, a nonlinear reservoir model linking inflow, outflow and storage behind the dam was used to generate distinct patterns of streamflow variability downstream of the dam. Last, the dynamics of a three species food web were coupled to the aforementioned flow downstream from the dam so as to determine whether reservoir operations can sustain the downstream food web stability. This three-part lumped model was operated under five reservoir management scenarios: Natural flow variability, run of river, minimum flow management, drought management, and flood management. Using predictions from the IPCC AR5 Report (2013), changes in precipitation frequency and depth due to long term shifts in the climate were evaluated assuming long-term annual precipitation is not altered. By simulating multiple reservoir management scenarios, it is envisaged that reservoir operators can accommodate ecological integrity explicitly. As expected, flow variability was found to decrease substantially in each of the four dammed scenarios when compared to an unregulated flow regime, with the range of flows shifting from 105-108 to 4-5 105 m3/day. With less frequent and more intense storms, the outflow from the reservoir shifted towards less frequent, higher magnitude flow rates in each scenario. None of the scenarios tested maintain populations in all trophic levels for the duration of the modeling period when faced with high variability in rainfall inter-arrival times. Presently, reservoir managers operating their dams under run of river or flood management will achieve the greatest downstream ecological integrity. However, as precipitation patterns shift from more frequent and less intense to less frequent and more intense storms, these reservoir types are most at risk to ecological degradation. The downstream food web appeared to be resilient to a changing precipitation pattern in a minimum flow management scenario, indicating that current management practices that preserve “ecological integrity” may be advantageous in an uncertain climate future. While the study’s findings support that minimum flow regulation may be one of the best management approaches in a changing climate, the top trophic level is only maintained during 33.6% of the modeling time period for said management scenario. Continued efforts should be made to optimize reservoir management practices so as to improve ecological integrity in an uncertain future. Serving as a first attempt at linking shifts in precipitation statistics, hydrology, reservoir management, and ecology, this study provides new insight into the effects of dam management on downstream food web dynamics, allowing reservoir managers to assess the impacts of their management decisions to preserve ecological integrity.Item Open Access Bridging the Scale Gap from Leaf to Canopy in Biosphere-Atmosphere Gas and Particle Exchanges(2016) Huang, ChengWeiTerrestrial ecosystems, occupying more than 25% of the Earth's surface, can serve as
`biological valves' in regulating the anthropogenic emissions of atmospheric aerosol
particles and greenhouse gases (GHGs) as responses to their surrounding environments.
While the signicance of quantifying the exchange rates of GHGs and atmospheric
aerosol particles between the terrestrial biosphere and the atmosphere is
hardly questioned in many scientic elds, the progress in improving model predictability,
data interpretation or the combination of the two remains impeded by
the lack of precise framework elucidating their dynamic transport processes over a
wide range of spatiotemporal scales. The diculty in developing prognostic modeling
tools to quantify the source or sink strength of these atmospheric substances
can be further magnied by the fact that the climate system is also sensitive to the
feedback from terrestrial ecosystems forming the so-called `feedback cycle'. Hence,
the emergent need is to reduce uncertainties when assessing this complex and dynamic
feedback cycle that is necessary to support the decisions of mitigation and
adaptation policies associated with human activities (e.g., anthropogenic emission
controls and land use managements) under current and future climate regimes.
With the goal to improve the predictions for the biosphere-atmosphere exchange
of biologically active gases and atmospheric aerosol particles, the main focus of this
dissertation is on revising and up-scaling the biotic and abiotic transport processes
from leaf to canopy scales. The validity of previous modeling studies in determining
iv
the exchange rate of gases and particles is evaluated with detailed descriptions of their
limitations. Mechanistic-based modeling approaches along with empirical studies
across dierent scales are employed to rene the mathematical descriptions of surface
conductance responsible for gas and particle exchanges as commonly adopted by all
operational models. Specically, how variation in horizontal leaf area density within
the vegetated medium, leaf size and leaf microroughness impact the aerodynamic attributes
and thereby the ultrane particle collection eciency at the leaf/branch scale
is explored using wind tunnel experiments with interpretations by a porous media
model and a scaling analysis. A multi-layered and size-resolved second-order closure
model combined with particle
uxes and concentration measurements within and
above a forest is used to explore the particle transport processes within the canopy
sub-layer and the partitioning of particle deposition onto canopy medium and forest
oor. For gases, a modeling framework accounting for the leaf-level boundary layer
eects on the stomatal pathway for gas exchange is proposed and combined with sap
ux measurements in a wind tunnel to assess how leaf-level transpiration varies with
increasing wind speed. How exogenous environmental conditions and endogenous
soil-root-stem-leaf hydraulic and eco-physiological properties impact the above- and
below-ground water dynamics in the soil-plant system and shape plant responses
to droughts is assessed by a porous media model that accommodates the transient
water
ow within the plant vascular system and is coupled with the aforementioned
leaf-level gas exchange model and soil-root interaction model. It should be noted
that tackling all aspects of potential issues causing uncertainties in forecasting the
feedback cycle between terrestrial ecosystem and the climate is unrealistic in a single
dissertation but further research questions and opportunities based on the foundation
derived from this dissertation are also brie
y discussed.
Item Open Access Energetics of Turbulence Explains Physical Transport Processes in the Environment(2023) Li, ShuolinThe indispensability of turbulent transport processes in environmental flows for a broad spectrum of applications, such as river restoration, sediment transport, and wetland design, is a widely acknowledged fact. Notably, turbulent eddies exert a substantial influence on transport phenomena, warranting novel approaches that account for their energetic impact on bulk flow variables. In this vein, the present study endeavors to explore and expound upon such approaches, with a specific focus on the transport of sediments in turbulent flows.
This dissertation consists of six chapters, with Chapter 1 serving as an introduction and overview. Chapter 2 focuses on the development of a co-spectral budget model to account for the pressure-redistribution effect in modeling turbulent shear stress. The model proposed incorporates a modified spectral linear Rotta scheme that considers isotropization of production and interactions between turbulent eddies and bed roughness. The result is a mathematical derivation of a modified Nikuradse curve that links the friction factor to Reynolds number and wall roughness.
Chapter 3 extends the co-spectral budget model to link the incipient motion of sediments to turbulent eddies. A mathematical derivation is presented to elucidate the scaling properties of an empirical diagram between a densimetric Froude number and relative roughness, connecting sediment motion to turbulent energetics.
Chapter 4 centers on representing the energetics of multiple turbulent eddies in modeling the suspended particle distribution in turbulent flows. A noval formulation is developed that considers all characteristic scales, Reynolds number, and Schmidt number effects, based on established spectral shapes of the turbulent vertical velocity and closure model constants.
Chapter 5 examines the turbulent settling velocity of suspended particles, accounting for two often-neglected effects: the unsteady vortices caused by grain movement (Basset history term) and the displacement of water mass due to grain movement (virtual mass term). The inclusion of these terms addresses inconsistencies between resent laboratory experiments and previous theories on grain settling velocities in turbulence where density contrasts between water and grain is not too large.
The findings of this research have potential to enhance the design and management of river systems and other flow-related infrastructure. Some of these applications are discussed in the concluding Chapter 6.
Item Open Access Feasibility Study of the Ken Betwa Project using a Super Reservoir Hydrological Model(2009-08-31T19:19:00Z) Mysore, MalavikaA modeling framework for integrated water resource management at the sub-basin scale for the Ken – Betwa water transfer link (hereafter referred to as KB-link), a part of the Greater Ganges river basin (in India), is presented. A Super Reservoir Model (hereafter referred to as SRM) was developed to explore the adequacy of the combined storage capacity of the linked reservoir system when rainfall, evapo-transpiration, and irrigation demands are considered at sub-annual time scales. Previous official feasibility studies only considered the variability of these same processes at annual time scales. The irrigation demands here are formulated as scenarios and include a number of cropping configuration and planned increases in agricultural production. The SRM assumes that the entire network of reservoirs function as a monolithic storage collection mechanism (or super-reservoir), thereby allowing a simplified mass balance analysis to be conducted. This project demonstrated that the integrated storage volume proposed in the feasibility report for the KB-link is inadequate with probabilities of complete ‘dry-downs’ ranging from 15% to 35%, depending on the scenario. On the practical side, the resulting integrated model of the watershed developed in this project can be used as a tool to facilitate debates and consultations between stakeholders and thus enhance the participatory process. In this sense, this simplified ‘simulator’ is an effective tool to explore the individual and cumulative impacts of water – resource management at sub- basin scale. The Matlab source code is provided upon request.Item Open Access Interior pathways of the North Atlantic meridional overturning circulation.(2011) Gary, Stefan FrancoisFor decades, oceanographers have hypothesized that the Deep Western Boundary Current (DWBC) is the dominant export pathway for the deep limb of the Atlantic Meridional Overturning Circulation (AMOC). However, more recent observations and theoretical work lend evidence for the existence of a second, interior, pathway for the AMOC deep limb. In order to assess the impact of the interior pathway relative to the DWBC pathway, this work seeks to quantify the AMOC deep limb pathways in ocean circulation models, compare the pathway signatures of these models to observations, and identify a mechanism driving the interior pathway. The partitioning of the AMOC deep limb into interior and DWBC pathways is observed in several ocean models. Furthermore, there is a good agreement between the structure of the export pathways in models and observations. Both Eulerian and Lagrangian techniques, in models and observations, are used to identify the DWBC and interior pathways and these two perspectives are shown to be compatible with one another. Finally, deep, eddy-driven, recirculation gyres are shown to be a mechanism driving the interior pathway and the existence of the interior pathway is consistent with the vorticity balance at depth. The interior pathway makes a significant contribution to the total transport of the deep limb of the AMOC. Since the interior pathway is much broader and slower than the DWBC pathway, the large-scale transport of climate signals, heat, and anthropogenic CO2 associated with the AMOC are slower and mixed more broadly throughout the ocean than once thought.Item Open Access Investigating Biosphere-Atmosphere Interactions from Leaf to Atmospheric Boundary Layer Scales(2007-03-14T16:05:01Z) Juang, Jehn-YihThe interaction between terrestrial ecosystems and the atmosphere continues to be a central research theme within climate, hydrology, and ecology communities. This interest is stimulated by research issues pertinent to both the fundamental laws and the hierarchy of scales. To further explorer such topics over various spatial and temporal domains, in this study, biosphere-atmosphere interactions are studied at two different scales, leaf-to-canopy and canopy-to-atmospheric boundary-layer (ABL) scales, by utilizing both models and long-term measurements collected from the Duke Forest AmeriFlux sites. For the leaf-to-canopy scale, two classical problems motivated by contemporary applications are considered: (1) ‘inverse problem’ – determination of nighttime ecosystem respiration, and (2) forward problem – estimation of two-way interactions between leaves and their microclimate ‘’. An Eulerian inverse approach was developed to separate aboveground respiration from forest floor efflux using mean CO2 concentration and air temperature profiles within the canopy using detailed turbulent transport theories. The forward approach started with the assumption that canopy physiological, drag, and radiative properties are known. The complexity in the turbulent transport model needed for resolving the two-way interactions was then explored. This analysis considered a detailed multi-layer ecophysiological and radiative model embedded in a hierarchy of Eulerian turbulent closure schemes ranging from well-mixed assumption to third order closure schemes with local thermal-stratification within the canopy. For the canopy-to-ABL scale, this study mainly explored problems pertinent to the impact of the ecophysiological controls on the regional environment. First, the possible combinations of water states (soil moisture and atmospheric humidity) that trigger convective rainfall were investigated, and a distinct ‘envelope’ of these combinations emerged from the measurements. Second, an analytical model as a function of atmospheric and ecophysiological properties was proposed to examine how the potential to trigger convective rainfall shifts over different land-covers. The results suggest that pine plantation, whose area is projected to dramatically increase in the Southeastern US (SE), has greater potential to trigger convective rainfall than the other two ecosystems. Finally, the interplay between ecophysiological and radiative attributes on surface temperature, in the context of regional cooling/warming, was investigated for projected land-use changes in the SE region.Item Open Access Land Surface-Convective Precipitation Feedbacks: Theory and Application(2011) Konings, AlexandraIn this thesis, an intermediate-level complexity model of a coupled land-surface and atmospheric boundary layer is developed. The model is used to investigate the controls on soil moisture-precipitation feedbacks and vegetation biomass-precipitation feedbacks. The diurnal evolution of a well-mixed boundary layer with piece-wise linear profiles of potential temperature and specific humidity is modeled. Rainfall can (though is not guaranteed to) occur if the boundary layer height crosses the lifting condensation level and if the boundary layer height is sufficiently high relative to the Obukhov length. The model illustrates that precipitation occurrence is more sensitive to the free atmospheric humidity profile than to the free atmospheric temperature profile. The precipitation model is also coupled to a model of spatial vegetation patterns in the Sahel to investigate the timescales of vegetation pattern response to changes in rainfall regime. Land surface-precipitation feedbacks increase the sensitivity and rate of change of vegetation pattern morphology.
Item Open Access Plant water transport and photosynthesis in water-limited environments(2020) Mrad, AssaadTerrestrial ecosystems depend on vegetation for many indispensable services including carbon fixation from the atmosphere, food production, and the maintenance of the global water and carbon cycles. As the climate changes, temperature and precipitation patterns shift and extreme climatic events become more frequent. In many areas, droughts are increasing in intensity and frequency, posing a challenge to ecosystem health and food security. Plants depend on water for physiological functioning including photosynthesis. The ability of plants to continue supplying water to the leaves from the soil during droughts depends on the anatomy and structure of its vascular network, the xylem. Droughts cause gas bubbles, or embolisms, to spread within the xylem, blocking water movement.
A combination of modeling water flow in xylem of flowering plants and theoretical considerations derived from graph theory is used to explain the response of different xylem functional types to droughts. An open-source model of plant xylem hydraulics was developed with which it was shown how 'network' effects, such as the spatial distribution of anatomy throughout growth rings, alter the response of Maples to drought.
The xylem of similar flowering plants was further investigated through the model in addition to the the physics of percolation. This was the first instance percolation theory has ever been applied to embolism spread inside xylem. It was shown how embolism spread inside the xylem can be represented by an edge percolation process. The results indicate that an increased connectivity among the conduits in the xylem is a necessary feature in plant organs that are resistant to droughts.
The detrimental effects of droughts on plant water translocation cascade to inhibit photosynthesis. Soil-to-leaf resistance to drought is represented by a vulnerability to embolism curve (VC) that plots the percent loss in plant hydraulic conductivity as water potential declines. The whole-plant VC affects plant CO2 fixation under drought. The results show how different VC shapes give rise to typical isohydric and anisohydric plant responses to drought. To arrive at this conclusion, the calculus of variations is used to integrate plant hydraulics into the trade-off between CO2 fixation and transpiration during a drought.
Item Open Access Reducing Uncertainty in The Biosphere-Atmsophere Exchange of Trace Gases(2010) Novick, Kimberly AnnA large portion of the anthropogenic emissions of greenhouse gases (GHGs) are cycled through the terrestrial biosphere. Quantifying the exchange of these gases between the terrestrial biosphere and the atmosphere is critical to constraining their atmospheric budgets now and in the future. These fluxes are governed by biophysical processes like photosynthesis, transpiration, and microbial respiratory processes which are driven by factors like meteorology, disturbance regimes, and long term climate and land cover change. These complex processes occur over a broad range of temporal (seconds to decades) and spatial (millimeters to kilometers) scales, necessitating the application of simplifying models to forecast fluxes at the scales required by climate mitigation and adaptation policymakers.
Over the long history of biophysical research, much progress has been made towards developing appropriate models for the biosphere-atmosphere exchange of GHGs. Many processes are well represented in model frameworks, particularly at the leaf scale. However, some processes remain poorly understood, and models do not perform robustly over coarse spatial scales and long time frames. Indeed, model uncertainty is a major contributor to difficulties in constraining the atmospheric budgets of greenhouse gases.
The central objective of this dissertation is to reduce uncertainty in the quantification and forecasting of the biosphere-atmosphere exchange of greenhouse gases by addressing a diverse array of research questions through a combination of five unique field experiments and modeling exercises. In this first chapter, nocturnal evapotranspiration -- a physiological process which had been largely ignored until recent years -- is quantified and modeled in three unique ecosystems co-located in central North Carolina, U.S.A. In the second chapter, more long-term drivers of evapotranspiration are explored by developing and testing theoretical relationships between plant water use and hydraulic architecture that may be readily incorporated into terrestrial ecosystem models. The third chapter builds on this work by linking key parameters of carbon assimilation models to structural and climatic indices that are well-specified over much of the land surface in an effort to improve model parameterization schemes. The fourth chapter directly addresses questions about the interaction between physiological carbon cycling and disturbance regimes in current and future climates, which are generally poorly represented in terrestrial ecosystem models. And the last chapter explores effluxes of methane and nitrous oxide (which are historically understudied) in addition to CO2 exchange in a large temperate wetland ecosystem (which is an historically understudied biome). While these five case studies are somewhat distinct investigations, they all: a) are all grounded in the principles of biophysics, b) rely on similar measurement and mathematical modeling techniques, and c) are conducted under the governing objective of reducing measurement and model uncertainty in the biosphere-atmosphere exchange of greenhouse gases.
Item Open Access Sedimentation analysis on steep slope areas development: Western North Carolina(2008-08-29T16:46:27Z) Li, LinThis project focuses on the rapid development and its concomitant environmental consequences that threaten water resources and the quality of life in Western North Carolina (WNC). The growing popularity of WNC, coupled with the region's topography means that builders are increasingly developing on steep slopes. The influence of steep slope development on sedimentation pollution and corollary hazards is investigated. In particular, the focus is on land development and its potential link to the probability of landslides. . A detail analysis was conducted for potential factors that induce landslides, particularly concentrating on Macon County and Watauga County. Most of the analysis applies Geographic Information System (GIS) technology, therefore gathering data, analyzing them, making them compatible to ArcGIS and developing intuitive map making for ease of visualization. How to expand the conclusions from this project to other steep slope areas are briefly described. Slope is analyzed by different percent degree categories, with a lens on the current legislation of 40 percent degree as the initial point of steep slope definition.Item Open Access Spatial Patterns in Dryland Vegetation and the Significance of Dispersal, Infiltration and Complex Topography(2010) Thompson, SalDrylands, comprising arid and semi-arid areas and the dry subtropics, over some 40% of the world's land area and support approximately 2 billion people, including at least 1 billion who depend on dryland agriculture and grazing. 10-20% of drylands are estimated to have already undergone degradation or desertification, and lack of monitoring and assessment remains a key impediment to preventing further desertification. Change in vegetation cover, specifically in the spatial organization of vegetation may occur prior to irreversible land degradation, and can be used to assess desertification risk. Coherent spatial structures arise in the distribution of dryland vegetation where plant growth is localized in regular spatial patterns. Such "patterned vegetation" occurs across a variety of vegetation and soil types, extends over at least 18 million ha, occurs in 5 continents and is economically and environmentally valuable in its own right.
Vegetation patterning in drylands arises due to positive feedbacks between hydrological forcing and plant growth so that the patterns change in response to trends in mean annual rainfall. Mathematical models indicate that vegetation patterns collapse to a desertified state after undergoing a characteristic set of transformations so that the condition of a pattern at any point in time can be explicitly linked to ecosystem health. This dissertation focuses on the mathematical description of vegetation patterns with a view to improving such predictions. It evaluates the validity of current mathematical descriptions of patterning for the specific case of small-scale vegetation patterns and proposes alternative hypotheses for their formation. It assesses the significance of seed dispersal in determining pattern form and dynamics for two cases: vegetation growing on flat ground with isotropic patterning, and vegetation growing on slopes and having anisotropic (i.e. directional) patterning. Thirdly, the feedbacks between local biomass density and infiltration capacity, one of the positive feedbacks believed to contribute to patterning, are quantified across a wide range of soil and climatic conditions, and new mathematical descriptions of the biomass-infiltration relationship are proposed. Finally the influence of land surface microtopography on the partitioning of rainfall into infiltration and runoff is assessed.
Item Open Access Sucrose transport in osmotically driven laminar flow: going from slender tubes to plant phloem(2023) Nakad, MazenThe transport of photosynthates within plants from the production sites (mainly leaves) to areas of consumption or storage (for example the roots) is drawing attention in plant physiology, eco-hydrology, and earth systems models. The phloem, one of the plant's hydraulic systems, provides the necessary pathway for this transport mechanism. Its structure and function have been conjectured to be optimized for the efficient transport of soluble organic matter (mostly sucrose). The implications of efficient sucrose transport range from local impacts on plant growth and survival, because of a potential link between phloem failure and plant mortality under extreme weather conditions such as drought, to ecosystem-scale effects on carbon and water cycling because of the possible link between stomatal control of photosynthesis and sucrose (a main product of photosynthesis) transport within the phloem. Many models for phloem transport and their possible deficiencies have been formulated and discussed. The most commonly used and accepted hypothesis under which most of these models rely on is the pressure-flow hypothesis, commonly known as the M$\rm{\ddot{u}}$nch mechanism. In the pressure-flow hypothesis, sucrose and other photosynthates are loaded in the phloem at the production site (leaves). This high sugar concentration draws water from the xylem, which is another hydraulic system that provides the necessary water reservoir for the M$\rm{\ddot{u}}$nch mechanism, by osmosis towards the phloem. This inflow of water molecules builds the required pressure gradient along the phloem pathway to drive sugars and water molecules through the phloem's complex network of narrow, elongated, interconnected, and cylindrical living cells (the sieve tubes). Once sugars arrive at the desired location, sugar molecules are unloaded from the phloem for consumption or storage by the cells and water is released back to the xylem or other surrounding tissues. The difference in sugar concentration at the production and consumption sites builds the pressure gradient along the phloem needed for solute transport over long distances without any active pumping. Experimental challenges in measuring sugar fluxes within the phloem have led to the reliance on theoretical models to understand and predict sucrose transport. These models usually simplify physics to allow mathematical tractability. As expected when using such models, calculated sucrose mass fluxes are not in agreement with data, especially for long-distance transport. In addition, the theory of the M$\rm{\ddot{u}}$nch mechanism has been under criticism where some argue that the sieve tubes seem to have low hydraulic conductance along the phloem which makes it nearly impossible for sucrose to be transported in the longest of plants.\par %These studies also report lower leaf concentration in tall trees compared to crops thereby contradicting the M$\rm{\ddot{u}}$nch hypothesis that requires higher loaded concentration to allow larger driving force over long distances. To solve the issue of decreased conductance in long-distance transport, it has been conjectured that rather than loading and unloading sugars only at the sources and sinks, sugars can be exchanged at different locations along the phloem forming a "relay" system to increase efficiency. Another reason for this theory is the existence of sieves plates that connect the sieve tubes, where their main role is still not fully understood. While this theory is plausible, there is no clear evidence of the loading and unloading of sugars along the pathway. However, there is an increasing amount of evidence that water is being exchanged between the phloem and the xylem along the pathway. This dissertation provides theoretical and experimental contributions toward modeling sucrose transport within the phloem. Note that specific notations, definitions and literature reviews are provided within each chapter. In chapter \ref{chap:1}, we propose a new one-dimensional model that includes Taylor dispersion for osmotically driven laminar flows. In previous studies, this effect has been overlooked when simplifying the problem into a one-dimensional model where radial variations in the solute (in this case sucrose) concentration are negligible. However, as earlier noted by G.I. Taylor that these small radial solute concentration variations lead to a new correction to the flow in closed pipes. This correction is modeled as a new dispersion term that is added in the advection-diffusion equation (or the conservation of solute mass equation), hence the name Taylor dispersion. This is not the case for osmotically driven laminar flows because the radial inflow of water molecules due to osmosis dictates a position-dependent (in the axial direction) pressure gradient instead of a constant one as in closed pipe application. This will lead to a new correction in the advection-diffusion equation where a new term is formulated and modeled as an advective term. In this chapter, we showed the mathematical derivation and required assumptions to develop this new model with these corrections. We also showed their impact on the flow from a general perspective and in the plant application specifically. In chapter \ref{chap:2}, we re-address the problem by studying viscosity variations in the flow. Previously, most studies simplify the physics by assuming a constant dynamic viscosity that does not depend on the sucrose concentration. Other studies have included viscosity variations along the tube (i.e. the phloem) in the one-dimensional model or in a globally averaged model where dynamic viscosity is set equal to loading sucrose concentration. In this chapter, we consider viscosity variations due to sucrose concentration variations in the radial and axial directions using a simple numerical model by re-considering the Navier-Stokes equations. We showed that the sucrose speed increases when viscosity variations are included because of the pull-push mechanism of water molecules where the efficiency of pushing water outside the phloem increases due to lower frictional forces. This result has an impact on understanding the M$\rm{\ddot{u}}$nch mechanism and its ability to model sucrose transport within the phloem, especially for tall trees. This result can also be generalized for other applications, especially where solute concentration variations in the radial direction are higher because of lower near-wall frictional losses. In chapter \ref{chap:3}, we conducted experiments on osmotically driven laminar flows using idealized elastic membranes. In these experiments, the membrane is allowed to expand in the radial direction depending on the osmotic potential that has been injected within the membrane where dextran has been used as the solute to drive the flow. These experiments have allowed us to shape an idea of the interaction between solute front speeds and membrane elasticity which was not studied before. For phloem studies, the membrane (i.e. the sieve elements) is usually assumed to be rigid with the exception of some studies that include membrane elasticity by using the phloem elasticity predicted from field data. These data are collected from plants that already have low elasticity because of the existence of sieve plates, where their main role is still not fully understood. In these experiments, we showed that by allowing the membrane to expand, the solute front speed decreases because some of the osmotic potential was lost to expand the membrane, and by dilution of the injected concentration (increasing the volume while maintaining the same amount of solute). These results have allowed us to formulate a different theory regarding the role of sieve plates where their existence might enhance phloem rigidity and hence transport efficiency. Chapter \ref{chap:4} summarizes the under-studied effects in previous chapters where we developed a two-dimensional numerical model. In this study, we included membrane elasticity using a simple formulation for the evolution of the membrane radius in time. This formulation was included by studying the data collected from the experiments in chapter \ref{chap:3} where an exponential increase of the membrane radius in time was apparent. The results of this study showed the impact of membrane elasticity on the front speed beyond the experiments where two membrane properties were changed, the rate of increase, and the maximum value for the radius. They also showed the interplay between membrane elasticity and concentration-dependent viscosity. These results reinforce the new role of sieve plates and provided a new comprehensive model for sucrose transport which can be eventually simplified to be included in any vegetation model that connects the phloem to the leaf-xylem-root system. Finally, in the conclusions and future development chapter \ref{conclusion}, we summarize the findings of this thesis and discuss the possibility of implementing our model in future climate studies.
Item Open Access The Effects of Land Surface Heating and Roughness Elements on the Structure and Scaling Laws of Atmospheric Boundary Layer Turbulence(2017) Ghannam, KhaledThe atmospheric boundary-layer is the lowest 500-2000 m of the Earth's atmosphere where much of human life and ecosystem services reside. This layer responds to land surface (e.g. buoyancy and roughness elements) and slowly evolving free tropospheric (e.g. temperature and humidity lapse rates) conditions that arguably mediate and modulate biosphere-atmosphere interactions. Such response often results in spatially- and temporally-rich turbulence scales that continue to be the subject of inquiry given their significance to a plethora of applications in environmental sciences and engineering. The work here addresses key aspects of boundary layer turbulence with a focus on the role of roughness elements (vegetation canopies) and buoyancy (surface heating) in modifying the well-studied picture of shear-dominated wall-bounded turbulence. A combination of laboratory channel experiments, field experiments, and numerical simulations are used to explore three distinct aspects of boundary layer turbulence. These are:
\begin{itemize}
\item The concept of ergodicity in turbulence statistics within canopies: It has been long-recognized that homogeneous and stationary turbulence is ergodic, but less is known about the effects of inhomogeneity introduced by the presence of canopies on the turbulence statistics. A high resolution (temporal and spatial) flume experiment is used here to test the convergence of the time statistics of turbulent scalar concentrations to their ensemble (spatio-temporal) counterpart. The findings indicate that within-canopy scalar statistics have a tendency to be ergodic, mostly in shallow layers (close to canopy top) where the sweeping flow events appear to randomize the statistics. Deeper layers within the canopy are dominated by low-dimensional (quasi-deterministic) von K{\'a}rm{\'a}n vortices that tend to break ergodicity.
\item Scaling laws of turbulent velocity spectra and structure functions in near-surface atmospheric turbulence: the existence of a logarithmic scaling in the structure function of the longitudinal and vertical velocity components is examined using five experimental data sets that span the roughness sub-layer above vegetation canopies, the atmospheric surface-layer above a lake and a grass field, and an open channel experiment. The results indicate that close to the wall/surface, this scaling exists in the longitudinal velocity structure function only, with the vertical velocity counterpart exhibiting a much narrower extent of this range due to smaller separation of scales. Phenomenological aspects of the large-scale eddies show that the length scale formed by the friction velocity and energy dissipation acts as a dominant similarity length scale in collapsing experimental data at different heights, mainly due to the imbalance between local production and dissipation of turbulence kinetic energy.
\item Nonlocal heat transport in the convective atmospheric boundary-layer: Failure of the mean gradient-diffusion (K-theory) in the convective boundary-layer is explored. Using large eddy simulation runs for the atmospheric boundary layer spanning weakly to strongly convective conditions, a generic diagnostic framework that encodes the role of third-order moments in nonlocal heat transport is developed and tested. The premise is that these nonlocal effects are responsible for the inherent asymmetry in vertical transport, and hence the necessary non-Gaussian nature of the joint probability density function (JPDF) of vertical velocity and potential temperature must account for these effects. Conditional sampling (quadrant analysis) of this function and the imbalance between the flow mechanisms of ejections and sweeps are used to characterize this asymmetry, which is then linked to the third-order moments using a cumulant-discard method for the Gram-Charlier expansion of the JPDF. The connection between the ejection-sweep events and the third-order moments shows that the concepts of bottom-up/top-down diffusion, or updraft/downdraft models, are accounted for by various quadrants of this joint probability density function.
\end{itemize}
To this end, future research directions that build upon this work are also discussed.
Item Open Access Turbulence in Natural Environments(2015) Banerjee, TirthaProblems in the area of land/biosphere-atmosphere interaction, hydrology, climate modeling etc. can be systematically organized as a study of turbulent flow in presence of boundary conditions in an increasing order of complexity. The present work is an attempt to study a few subsets of this general problem of turbulence in natural environments- in the context of neutral and thermally stratified atmospheric surface layer, the presence of a heterogeneous vegetation canopy and the interaction between air flow and a static water body in presence of flexible protruding vegetation. The main issue addressed in the context of turbulence in the atmospheric surface layer is whether it is possible to describe the macro-states of turbulence such as mean velocity and turbulent velocity variance in terms of the micro-states of the turbulent flow, i.e., a distribution of turbulent kinetic energy across a multitude of scales. This has been achieved by a `spectral budget approach' which is extended for thermal stratification scenarios as well, in the process unifying the seemingly different and unrelated theories of turbulence such as Kolmogorov's hypothesis, Heisenberg's eddy viscosity, Monin Obukhov Similarity Theory (MOST) etc. under a common framework. In the case of a more complex scenario such as presence of a vegetation canopy with edges and gaps, the question that is addressed is in what detail the turbulence is needed to be resolved in order to capture the bulk flow features such as recirculation patterns. This issue is addressed by a simple numerical framework and it has been found out that an explicit prescription of turbulence is not necessary in presence of heterogeneities such as edges and gaps where the interplay between advection, pressure gradients and drag forces are sufficient to capture the first order dynamics. This result can be very important for eddy-covariance flux calibration strategies in non-ideal environments and the developed numerical model can be used in related dispersion studies and coupled land atmosphere interaction models. For other more complex biosphere atmosphere interactions such as greenhouse gas emissions from wetlands, the interplay between air and water, often in presence of flexible aquatic vegetation, controls turbulence in water, which in turn affect the gas transfer processes. This process of wind shear induced wave-turbulent-vegetation interaction is studied for the first time in the laboratory and the state of turbulence as well as the bulk flow is found to be highly sensitive to environmental controls such as water height, wind speed, vegetation density and flexibility. This dissertation describes and gradually develops these concepts in an increasing order of complexity of boundary conditions. The first three chapters address the neutral and thermally stratified boundary layers and the last two chapters address the canopy edge problem and the air-water-vegetation experiments respectively.