Resilience and vulnerability of co-evolving systems such as soils and vegetation, vegetation and climate, etc. are strongly dependent on the balance of the positive and negative feedbacks of interactions. Under stress, these feedbacks breakdown and result in runaway dynamics until new equilibrium is established. While these notions are now well-understood, quantitative characterization of both resilience and vulnerability remain elusive, or are only available for deterministic systems. Our study focus takes a broad look at the concepts of resilience and vulnerability from a stochastic framework to develop general principles to guide sustainable decision-making.
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Emergent and divergent resilience behavior in catastrophic shift systems
Often, individuals and small groups collect scientific data that are targeted to address specific scientific issues and have limited geographic or temporal range. However, a large number of such collections together constitute a large database that is of immense value to the scientific community. Such data are complex in that they encompass a heterogeneous collection with many dimensions, coordinate systems, scales, variables, providers, users and scientific contexts. These data have been defined as long-tail data.
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Rainfall is the most important driving variable for all hydrologic models. To provide the most appropriate representation at the scale of the model it is important to identify and represent its properties at various scales. We developed new analysis techniques using wavelet transforms to study the multi-scale properties of rainfall variability in space and time. We established that the rainfall may be separated into two components - an underlying large-scale component representing the morphological organization resulting from the influences particular to the dynamical system, and smaller scale fluctuations, representing stochastic influence, that are scale invariant for a wide range of scales. We argued that our ability to identify multiple scale patterns is strongly dependent on our (mathematical) system of interpretation. Wavelet packets, which provide a richer set of tools for multi-scale studies were more suited for the study of rainfall patterns. Further analysis showed again that there were distinct scales of variation in rainfall patterns. We have also used wavelet spectra to study the variability in streamflow over the continental United States. Distinct modes were found which indicate the existence of regions with similar scales of fluctuations that are located geographically apart, as well as regions located geographically close with dissimilar scales of fluctuations. A Reviews of Geophysics article and an edited book on the broad topic of wavelet applications in geophysics have been widely used in research and classroom.
While ample evidence exists that observed hydrographs have a non-linear relationship to rainfall, its phenomenological explanation has been lacking. Research in our group has helped close this gap in our understanding by coupling a statistical model of self-similar stream organization with channel hydraulic geometry relations. We have demonstrated that the basin-wide spatial variation of velocities resulting from the systematic hydraulic geometry variations induce a dispersive effect, termed as kinematic dispersion. This effect at all scales is comparable in significance to that introduced by the heterogeneity of flow paths, previously identified as geomorphologic dispersion, and significantly larger than the hydrodynamic dispersion. The kinematic dispersion arises from the non-linear dependence of flow velocities on discharge captured through the hydraulic geometry relationships. These important theoretical results explain how the self-similar stream network and the systematic variation of hydraulic geometry in a basin impacts the formation of flow hydrographs. We also showed that velocity variation introduced by surface flow in hillslopes can either enhance or counteract the dispersion effects of the network, depending on the variability of the velocity. These results address long standing, fundamental challenges in hydrogeomorphology.
Terrestrial hydrology in climate models has been simulated traditionally using one dimensional land-surface models, that is, lateral sub-surface moisture flux is ignored. Our research group has made significant advancement by developing basin scale models that better represent the topographic control on soil-moisture flux, including lateral transport, and evapotranspiration dynamics. Using this new formulation, we established that the slower moisture dynamics of terrestrial hydrology act as a memory in modulating the impact of climate variability on processes such as runoff, water table dynamics, soil water deficit, and surface temperature. We further established that long-wavelength climate signals, particularly temperature, generated from ENSO (El Niño Southern Oscillation), penetrate into deep layers of the land through the dynamics of soil-moisture and soil-temperature. The sub-surface heat storage, or enthalpy, shows significant inter-annual variation that is important for understanding the impact of climate change. To better represent these processes for climate scale predictions at the regional and local scales we have developed new and significantly improved formulations for modeling the lateral transport in soil-moisture dynamics. These are currently being implemented in the Climate Weather Research Forecast Model. We have established that there exist two mechanisms by which the inter-annual variability of the deep layer soil-moisture impacts surface energy fluxes and, consequently, climate dynamics. First, the temporal variability sets the lower boundary condition for the transfer of downward moisture and heat fluxes from the surface. Second, this temporal variability influences the uptake of moisture by plant roots leading to the variability of the transpiration, and therefore the entire energy balance. These results emphasize that deep-rooted, vegetative environments may play a critical role in regulating the climate and this issue is under investigation.
We have also shown that the spatial modes of atmospheric moisture transport associated with floods and droughts are not opposite to each other, i.e., synoptic patterns causing the two are very different from each other. Moreover, they cannot always be attributed to one of the known climate patterns. Further, the moisture storage in the atmospheric column from daily to seasonal scales (a budget component previously ignored) regulates the recycling of local evaporation and serves as another memory to be included in land-atmosphere interaction studies and may influence the modes associated with floods and droughts.
We have approached the study of the interaction between water cycle and vegetation functions and patterns broadly from two perspectives: informatics and modeling. The informatics theme is motivated by the need to extract reliable quantitative characteristics of process interaction from large volumes of ecohydrologic datasets that are rapidly becoming available. Our research group is making fundamental contributions in this field both in representations of data to facilitate appropriate analyses, as well as in developing innovative data mining methods. Our study using satellite data over the entire contiguous US has shown that the spatial heterogeneity of the dynamic response of terrestrial vegetation to inter-annual climate fluctuations, such as ENSO (El Niño - Southern Oscillation), is closely linked to the heterogeneity induced by the topographic attributes such as elevation, slope and aspect. Using detailed study of remote sensing data over the Blue Ridge ecoregion, and Central Basin and Range and Northern Rockies ecoregion we have further shown that during the growing season the combination of topographic attributes, soil properties and climate variables induce formation of coherent regions of vegetation productivity. These patterns evolve over the growing season as principal controls determining the vegetation productivity change. These results provide quantitative characterization of the factors influencing vegetation response at such large scales. Through ongoing research we are exploring the factors controlling vegetation growth in specific ecosystems.
The modeling theme is motivated by the question: How do vegetation function and patterns interact with below-ground processes as well as climate systems to create an environment for their own sustenance. We have developed models of hydraulic redistribution by plant roots (i.e., movement of water by plant roots from moist to dry soil layers during periods of no transpiration) to understand how deep rooting systems of vegetation meet transpiration demands during periods of water stress. We found that this process also induces significant inter-annual variability in soil-moisture that can be correlated to climatic fluctuations such as ENSO. We have also studied precipitation recycling at short time scales from the perspective of mapping source and sink regions of evapotranspired water. This study established a negative feedback stabilizing mechanism between vegetation-atmosphere interactions that contributes to the sustenance of ecosystems. We show that in the North American Monsoon Region this mechanism sustains ecosystem health during the midsummer drought of long monsoons.