1. Abstract Background Yiwei Cheng 1, Marc Stieglitz 1,2, Greg Turk 3 and Vic Engel 4 1 Department of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA, USA 2 School of Earth Atmospheric Sciences, Georgia Institute of Technology, Atlanta, GA, USA 3 School of Interactive Computing, Georgia Institute of Technology, Atlanta, GA, USA 4 Everglades National Park, Homestead, FL, USA gtg985z@mail.gatech.edu, marc.stieglitz@ce.gatech.edugtg985z@mail.gatech.edu, marc.stieglitz@ce.gatech.edu, turk@cc.gatech.edu, vic_engel@nps.govvic_engel@nps.gov Bog Patterning Model We employ an existing spatially explicit, advection-reaction-diffusion type model to describe the formation of regularly spaced vegetation stripes parallel to flow direction from hydrologic interactions. Such vegetation patterns are, for example, characteristic of the ridge and slough system in the Florida Everglades. To our knowledge, this is the first time that a spatially explicit model encompassing the nutrient accumulation mechanism is used to demonstrate the formation of parallel stripes. We explore the conditions under which the different patterns will form and demonstrate how changes in plant transpiration, slope and strength of plant induced advective nutrient transport orthogonal to slope direction affect the resulting vegetation pattern. Our results highlight the ability of the short distance facilitation and long distance competition mechanism to explain the formation of the different vegetation patterns beyond semi-arid regions. Therefore, we propose that the parallel stripes, like the other periodic patterns observed in both isotropic and anisotropic environments, are self-organized and form as a result of scale dependent feedback. Fig.1. Left: Labyrinth vegetation patterns in Sahel. Center: Regular vegetation stripes near Niamey, Niger. Right: String patterns in Western Siberian Bogs. Rietkerk et al (2004) developed a spatially explicit, advection reaction-diffusion type model (henceforth called the Rietkerk model) to describe the formation of vegetation patterns common to the surface of bogs in North America and Eurasia. They proposed that self-organization is caused by convective transport of nutrients in the groundwater toward areas with higher vascular plant biomass, driven by differences in transpiration rate. 1 2 3 7 6 Parallel Vegetation Stripe Formation Through Hydrologic Interactions Conclusion Paper No NG43B-1212 Various hypotheses have been invoked to explain the formation of vegetation patterns: selective grazing by herbivores, fire and anisotropic environmental conditions such as slope. Recently, short distance facilitation and long distance competition between vegetation (a.k.a scale dependent feedback) has been proposed as a generic mechanism for vegetation pattern formation. 9 Parallel Stripe Simulation Short distance facilitation and long distance inhibition between vegetation is a plausible mechanism for the formation of parallel stripes Synergetic effects of plant transpiration, slope and anisotropic hydraulic conductivity led to the formation of various vegetation patterns. Effect of Plant Transpiration and Slope Fig 4. Formation of vegetation stripes parallel to flow direction. Left column: Plant biomass; darker green indicate higher biomass. Middle column: Nutrient concentration; darker red indicate higher nutrient concentration. Right column: Flow field visualization using Line Integral Convolution (LIC). 10 Rietkerk et al., 2004. A Putative Mechanism for Bog Patterning. The American Naturalist, 163(5), 699-708. Klausmeier C.A., 1999: Regular and irregular patterns in semiarid vegetation. Science, 284,1826-1828. References Objectives Test the generality of this mechanism by employing an existing spatially explicit, advection-reaction-diffusion type model to describe the formation of regularly spaced vegetation stripes parallel to flow direction from hydrologic interactions. Explore the conditions under which the different patterns will form and demonstrate how changes in plant transpiration, slope and strength of plant induced advective nutrient transport orthogonal to slope direction affect the resulting vegetation pattern. The Rietkerk model describes the dynamics of three state variable in x (left-right) and y (top-bottom) direction: vascular plant biomass (B), hydraulic head (H) and nutrient concentration in groundwater (N): [Nutrient limited growth][Mortality][Diffusion] [Ppt][Transpiration][Evaporation] [Advection] [Anthropogenic input, plant uptake, recycling of dead biomass, nutrient loss] [Advection][Diffusion] 4 Model Modification We retained the basic equations of the Rietkerk model and modify the advection of water and nutrients to (1) include anisotropic hydraulic conductivity, and (2) allow for constant advection of water and nutrients in y-direction: (1) (2) (3) k x is the hydraulic conductivity in the x-direction, k y is the hydraulic conductivity in the y-direction and SL is the constant head difference between two adjacent points on a slope. (4) Advection (5) Nutrient Advection Simulations All simulations are initialized by randomly seeding 10% of the simulation grids with plant biomass peak. The computational domain consists of 70 x 70 grids. Three sets of simulations were conducted: a)Parallel stripes simulation b)A suite of simulations to explore interactive effect of plant transpiration and slope on vegetation pattern. Plant transpiration parameter, t v (Eqn 2), and SL were gradually increased from 0 to 2.8 x 10 -5 m 3 g B day -1 and 0 to 0.025 m respectively. c) A suite of simulations to explore interactive effect of anisotropic hydraulic conductivity and slope on vegetation pattern. Ratio of hydraulic conductivity in x-direction to hydraulic conductivity in y- direction, k x /k y, and SL were gradually increased from 0 to 1 and 0 to 0.025 m respectively. Fig.3. Convective transport of nutrients in the groundwater toward areas with higher vascular plant biomass, driven by differences in transpiration rate. Fig 5. Vegetation patterns for 7 <t v < 28 (x10 -6 m 3 g B d -1 ) and 0 <SL< 0.025 m Effect of Anisotropic Hydraulic Conductivity and Slope 8 Fig 6. Vegetation patterns for 0<k x /k y <1 and 0<SL<0.025m. tvtv SL 0 0.005 0.015 0.025 7x10 -6 8x10 -6 11x10 -6 14x10 -6 28x10 -6 k x /k y SL 0 0.005 0.015 0.025 0 0.05 0.5 0.75 1 t = 5000 t = 32000 t = 0 Flow direction 5 To date, most of the mathematical models focus mainly on simulating spots and labyrinth patterns, and stripes perpendicular to flow direction in semi-arid systems. Formation of regularly spaced vegetation stripes parallel to flow direction has received far less attention. Such vegetation patterns are, for example, characteristic of the ridge and slough system in the Florida Everglades. Fig.2. Ridge and slough system in the Everglades, Fl.