This project will investigate the relationship between spatiotemporal variation of vegetation patterns and desertification probabilities in systems exhibiting patterned vegetation for current and projected future climates. Three hypotheses frame the scientific scope of the project:
H1: In isolation, a) increased CO2 concentrations shift patterns towards a homogeneous vegetated condition; b) increased vapor pressure deficit shift patterns towards desertified conditions. H2: A length-scale threshold exists below which spatial variability (e.g. in soil patterns) acts as additive noise to vegetation patterns. Above this threshold, the properties of the vegetation pattern depend on both the dynamics of the pattern forming processes, and the wavelength of the spatial variation. H3: Temporal stochasticity in rainfall will blur sharp transitions to desertification predicted by mean-field theory into a "basin" of desertification probabilities. Three tasks are proposed to address these three hypotheses: Task 1: Model Development and Forward Modeling, intended to extend existing models and evaluate them at four data-rich study locations in Africa, the USA and Australia, along with assessing the implications of spatiotemporal variability on pattern morphology and desertification risk; Task 2: Remote Sensing Imagery Acquisition, Processing and Analysis, intended to support the modeling efforts in Tasks 1 and 3, and to assess the drivers of spatial variation in pattern morphology; Task 3: Inverse Modeling, incorporating the development of parameter estimation techniques, their application to synthetic pattern time series and ultimately to observations from case study sites.
As a proof of concept, the investigators will initially develop an inverse modeling methodology using a phenomenological model (c.f. Lefever and Lejeune) with a reduced parameter space. They will then proceed to a full mechanistic inverse model that will draw on a detailed meta-analysis from the literature on stomatal and biochemical responses of plants under soil moisture stress to strongly constrain the physiological parameters. The proposed image analysis task (Task 2 above, initially focused on spectral techniques) will be extended to evaluate the suitability of a range of pattern identification techniques (including methods that rely on dimension reduction such as POD and wavelet thresholding) to discriminate different features of vegetation patterning over multiple spatial scales. The kernel-based approaches proposed here are non-Fickian and permit heavy-tailed seed dispersal kernels. Time delays can be explored by allowing the seed source function to become time dependent. The researchers have conducted extensive simulations using simplified routing schemes to identify key processes and sensitivities (which relate largely to surface roughness as a means of sustaining vegetation patterning). Extensive literature searches indicate a number of suitable datasets examining flow velocities, runoff coefficients and runoff scaling in patchy landscapes. We will draw on these datasets for model validation.
General summary of project outcomes: This project is to develop a framework for linking mathematical models of vegetation patterning to remote sensing products thereby allowing land management planners to identify potential threats to arid ecosystems and to prioritize management interventions to avoid irreversible damage. More broadly, this project was a proof of concept for the interpretation of remote-sensing derived information about vegetation patterns in terms of what these patterns reveal about the biological and physical functioning of ecosystems. Direct inference of the parameters describing these hydrological and ecological processes from observations of vegetation spatial patterns has not been attempted. Such inference facilitates the parameterization and predictive use of vegetation pattern models. Key Findings: A major criticism of patterned vegetation models is of their treatment of overland flow as a diffusive process. The findings from the activities indicated above suggest that this representation may be reasonable for estimating water redistribution during storms provided infiltration rates are correlated with ponded depth and the overland flow maintains a turbulent state. Another finding is that when the infiltration rate is independent of ponded depth, no clear simplifications to the full shallow water equations capture the water redistribution. However, the subsidy of water provided to the vegetated patches seems to have occurred over a hydraulic length scale whose importance may not have been appreciated. We anticipate that the length scales of self-organization may be commensurate with this hydraulic length scale. When the vegetation patterning models were employed over flat terrain, lateral redistribution did occur driven primarily by the gradient in ponded depth. The ponded water depth gradient appears to be primarily controlled by the infiltration contrast between the bare soil and vegetated surfaces, not the contrast in their roughness. Even though our preliminary results shows that lateral redistribution occurs over flat terrain, the amounts of redistributed water are much smaller than the amounts observed over sloping terrain. Hence, the lateral redistribution hypothesis may not be sufficient to explain the persistence of patterned vegetation. Seed dispersal in overland flow has been hypothesized to stabilize vegetation patterns in drylands. Spatially and temporally resolved coupled flow – seed transport models suggest that such stabilization is feasible under conditions when (i) multiple runoff events occur and (ii) vegetated bands are effective at trapping seed. High-resolution aerial photography was used to explore the spatial associations between changes in pattern morphology and changes in soil type, or topographic transitions (ridgelines, streamlines etc). While this analysis confirmed some aspects of theory, it has also posed challenges to theoretical predictions. We found that vegetation patterns became more coherent (smaller band width, more uniform directionality and wavelength) on soils with a shallow petrocalcic layer, and more diffuse (wide bands, poorly resolvable directionality and wavelength) on deeper clay soils. We also found that pattern wavelength increased with proximity to stream channels. Both findings point to processes that are not addressed by contemporary theories, including an explicit role of soil depth in altering vegetation pattern morphology, and the potential for downslope accumulation of moisture. This project also explored the feasibility of directly estimating ecosystem parameters from the vegetation pattern using nonlinear filtering theory coupled to a suitable model of pattern formation. The results from this project established a needed link between field observations and theoretical models of vegetation patterns, setting the stage for improved data and model assimilation for ecological forecasting. The work demonstrated for the first time the feasibility of inferring quantitative ecological information from spatial observations of vegetation distributions. The findings from this project were instrumental to the training of a female graduate student and the completion of her PhD in eco-hydrology. The results from this project were presented in a number of seminars, and contributed to her attaining four offers (University of Western Sydney, North Western University, Penn. State University, and U.C. Berkeley). Pieces of this research were also instrumental in the completion of a Masters Project. This female graduate student (Professor Sally Thompson) is now a faculty member at U.C. Berkeley (the sub-contract to U.C. Berkeley issued via this NSF grant is to allow Thompson to complete the work she commenced at Duke University as a student). As part of this subcontract, Thompson has now involved graduate students in the detailed spatial analysis of high-resolution imagery of vegetation patterns, including collaboration with non-linear physicists and publication in a respected journal. Moreover, at U.C. Berkeley, Thompson has involved a graduate student in the analysis of spatially distributed surface climate and hydrological datasets gathered across the grass-treeline transition in a Mediterranean oak woodland, which was presented at the AGU Fall Meetings, and another student has been engaged in developing hydrological theory to analyze the implications of these spatial variations for seasonal baseflow recession.
