Utilizing Agent-Based Modeling to explore the Effects of Precipitation on Vegetation and Sand Dune Activity

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1. Introduction:

The dynamism of dune morphology has captivated the research attention of scientists across numerous fields of study, including those invested in recognizing signs of climatic change in arid landscapes (Ciccarelli et. al 196). Dune modes are also highly desired for their predictive capabilities to be used for land management purposes (Bishop et. al 8).

Vegetation plays a key role in both the shape and migration of sand dunes. In arid regions where dunes lack vegetation, it is seen that over time the crest of the dune moves in the direction of the predominate wind regime; this migration phenomena classifies a dune as ‘active.’ This is caused by the continuous removal and redistribution of sand over the crest of the dune when transported by wind (Kok et. al 37). On the contrary, a dune may be classified as fixed when vegetation is introduced into a landscape, and keeps underlying sand from being eroded by wind (Sujith et. al 54).

Sand dune migration processes have been well observed and modeled in the fields of physics, and geomorphology (Worman et. al 1063). Currently, the predominant methods of modeling sand dune migration exist in discrete mathematical models that emphasize the deterministic mechanisms that take part in dune formation (Mitasova et. al 204). Though these methods capture the characteristics of sand dune migration competently in a controlled environment, these models tend to omit stochastic factors that influence dune activity such as vegetation growth, climate and seasonal weather changes (Neild and Baas 4). While field observations do account for stochastic influences, dune activity typically fluctuates over very large temporal scales ranging from weeks to decades, thus, field observations occurring over weeks or even years may neglect the ways in which patterns emerge over large temporal scales (Bishop et. al 9).

Spatial modeling then provides us with an outlet granting us technicalities that allow us to create a model that includes stochastic processes which mimic natural occurrences, while remaining abstract enough so that we can infer something about the processes themselves across appropriate spatial and temporal scales. Meanwhile, complex systems science focuses on the emergent, high-level patterns that come about due to low-level interactions between agents and their environment (Gornish et. al 2671). Capitalizing on this notion may allow us to further our understanding of sand dune migration and its interaction with vegetation distribution by focusing on modeling agent-level interactions and observing how the results of these interactions coalesce into large-scale patterns in both space and time.

Given the appropriate critique of the literature, it becomes apparent that more research is needed to understand exactly how different climate regimes affect sand dune activity. Thus, the principle objective of this study is to evaluate how dune activity is affected by precipitation regime. Specifically, I will observe how the individual interactions between discrete patches of sand and climatic variables (e.g. precipitation levels and seasonal precipitation variability) lead to emergent spatial and temporal patterns in dune activity and vegetation.

This objective will be achieved by utilizing an agent-based model that has been designed to represent specific mechanisms in the real-life system including sand transport, precipitation regime, vegetation growth and seasonality. After performing a sensitivity analysis and closely examining the output and functionality of the model, it will be critically evaluated on the conceptual design to see if this approach has been successful in deciphering the posed inquiry.

2. Methods:

 2.1 Purpose

The purpose of this model is to examine how different precipitation regimes affect dune migration over a period of years. Specifically, the model aims to show the connectivity between precipitation regimes, vegetation growth and dune migration in arid and semi-arid regions. It is known that vegetation and thus high levels of precipitation hinders a dune’s path and speed (Ping et. al 100), an agent-based modeling approach is pursued in order to create an abstract representation that capitalizes on low-level interactions of the system’s mechanisms in order to gain a clearer, more developed understanding of the system through a bottom-up approach to modeling.

 2.2 Entities, State Variables and Scales:

The model represents slabs of sand on the crest of a dune as its only entities. We model only the crest both for simplicity and clarity. Each slab of sand has two state variables: vegetation, and moisture-content. The vegetation state variable shows whether or not the slab of sand is vegetated. If an entity inhibits a vegetated state, this means that there is enough vegetation in the area to impede erosional processes from taking place. The moisture-contents of an entity may hold a range of percentage values affected by different processes in the system. This percentage value contributes to determining whether or not a patch will become vegetated in the following time step. At each time step, a random sample of sand patches are polled and may become vegetated or un-vegetated in a time step, and will migrate forward due to wind speed.

2. 3 Processes, overview and scheduling

A selection of five patches are chosen randomly at each timestep. Whether or not the sand slab will become vegetated is determined probabilistically by the moisture contents of the sand. If the condition is favorable, it becomes vegetated and halts its movement. While a patch is vegetated, it increases the vegetation probability of the surrounding patches by diffusing its moisture content to the surrounding patches. At every 10th timestep, the environment changes seasonality (from a dry season to a wet season), and due to an input parameter indication seasonal variety, the precipitation may be additionally altered.

2.4 Design Concepts:

 

2. 4. 1 Basic Principles

This model design is based loosely off of Neild and Baas’ cellular-automata model of parabolic dune formation. The cellular automata model has been grossly simplified; discrete sand patches have been turned from cells to acting agents for the ease in designing in the chosen modeling platform.

2. 4. 2 Emergence

Two major emergent patterns are presented in the model. These include vegetation abundance, and sand dune movement.

2. 4. 3 Objectives

The only objective presented in the model is for a patch of sand to move through the environment in the windward direction. If a sand patch’s moisture content increases, the likelihood of the sand becoming vegetated increases as well, and may inhibit the sand from moving in the environment. Movement may only begin again once enough time has passed, and the moisture level has dropped low enough so that the sand’s vegetation may die off.

2. 4. 4 Sensing

Agents are able to sense the moisture-levels and vegetation histories of their adjacent neighbors. Both moisture content and vegetation history influences the likelihood of a sand slab becoming vegetated. These mechanisms implemented to replicate the continuity of sand and vegetation in the real-world system (Bauer et. al 89). 

2. 4. 5 Stochasticity

Stochasticity is implemented in the model at each timestep when five randomly selected sand slabs are tested to see whether or not they will become vegetated. This is implemented to represent variability in seed distribution (Nield and Bass).

2. 4. 6 Observation

The key observation to be gathered from the model will be the average location of sand slabs at the end of some determined time interval. Since all other mechanisms in the system either aid or hinder the migration of sand slabs through the environment, this output will represent the collective output of the system. 

2. 5 Initialization

Upon initialization, user-defined parameters including precipitation amount and seasonal precipitation variability are defined and incorporated into the system. The sand patches are aligned at the top of the environment, near the perceived wind source. No patches are vegetated at this time, and the moisture content of each sand patch is set equal to the initial precipitation amount with regards to its seasonal variation.

2. 6 Approach to a sensitivity analysis

A sensitivity analysis will be conducted on this model to recognize the systems sensitivity to different parameter entries. Two separate parameter sweeps will be ran on the model. The first will explore the model’s sensitivity to seasonal precipitation variability. The second parameter sweep will explore the contrary – the model’s sensitivity to initial precipitation amount.  Each sweep will be ran at 20 different values for the parameter at focus, and at three values for the other parameter. The end location of sand patches in the environment will be our desired output.

2. 7 Approach to evaluation

Because this model is a highly abstracted version of reality, I will not evaluate this model based on operational validity nor its calibration to existing field data, as its utility outside of research is unlikely, and as an understatement, unadvised. Instead, I will focus my evaluation on its conceptual validity, and hone in on realistic patterns that have been brought to attention through the literature to evaluate the model’s utility for answering the question at hand as well as the validity of this approach.

 

3. Results:

To better explain how the emergent processes come about in this model, I engage a narrative explanation to show how agent-level interactions result in higher-level patterns.

The mechanisms of a single patch helps explain the thresholds and feedbacks presented in the output of this model, so I focus the attention of this explanation to a single patch. The environment contains agents that are represented as discrete slabs of sand meant to represent subsections of a dune positioned perpendicular to the prevailing wind. This can be described as an aerial view of an extremely simple sand dune, with the line of agents representing a section of moving sand.

 

 

At each time step, a series of implicit and explicit interactions occur between agents. Explicitly, a slab of sand advance towards the bottom of the environment, in the direction of the perceived wind, and the sand’s advancement is impeded if the sand slab becomes vegetated (turns green). When this happens, an agent halts movement until the vegetation dies off. A sand patch may advance once the vegetation has receded, however, the likelihood of the patch becoming vegetated again is increased due to probabilistic calculations.

 

Another factor that increase an agent’s likelihood of becoming vegetated is moisture content which is dictated by user-defined parameters including precipitation amount and seasonal precipitation variability. A sand patches moisture content is initially equal to the precipitation amount and is affected time goes on. The moisture content of a sand patch is diffused to its neighbors, and is lessened if the precipitation value (which is subject to seasonal variation) becomes less than the sands’ own moisture content level.

The higher the moisture content is of a single sand patch, the more likely that patch is to become vegetated, retain its moisture content, and thus raises the likelihood of the surrounding sand to become vegetated as well. This results in a positive feedback shown in the videos below:

The results of a sensitivity analysis is shown below in the following box plots:

The most captivating aspect of the parameter sweep is the nonlinearities presented in the output of both parameter sweeps. In particular, we find that as precipitation increases, the average location of sand patches at time t remains high, meaning the dune became vegetated and slowed its movement early on in the simulation. Stochasticity and probability takes more of a stronghold as the precipitation parameter decreases as we see the greatest variability in dune location as the parameter’s value drops, that is, until we approach values close to zero. In this case, there is a low likelihood that the vegetation feedback will exist, and thus the sand settles at the bottom of the environment, resulting in a average location of -15 with respect to y coordinates.

In the parameter sweep that regards seasonal variability in precipitation results vary much more as we approach large seasonal variabilities. This is likely due to the probabilistic mechanisms that occur over seasonal, temporal intervals. With large seasonal precipitation variability, a sand patch is offered numerous different opportunities to become vegetated, and thus to raise the likelihood of those around them becoming vegetated and causes the dune to become fixed.

While evaluating the model’s output, it is important to take into account that this model has disregarded important processes and variations, such as vegetation types, climate variation, dune topography, replacing these complex processes with probability. This hinders the robustness and validity of our output for practical use, but not necessarily the model itself; we still gain a deeper understanding about connection between individual processes and the emergent pattern that is revealed in nonlinearities that occur in the real-world system.

4. Discussion and Conclusion:  

By running the model, and examining its dynamics through both a narrative approach and a sensitivity analysis, we begin to gain a deeper understanding of the system as a complex system that produces nonlinearities and emergent patterns.Through the positive feedback we observe in vegetation growth and sand transport, we are able to examine how the lower-level interactions between sand slabs and climatic variables give rise to larger, emergent patterns that are seen in the real-world system (Partelli et. al 2087). In particular, we view how the characteristics of sand slabs influence the probablitlity of their neighbors to become vegetated and how this affects the amount of time a dune stays active. This is considered to be a nonlinearity because changes in parameter values have surprising outputs that are not proportional to input values.

The principle goal of this study was to examine how precipitation level affects dune activity through means of vegetation growth. Through an agent-based modeling approach, I emphasized how individual characteristics and interactions between discrete sand patches and climatic variables gave rise to unexpected, high-level patterns. After a brief introduction to the natural system of dune migration, and current progress that has been made on the subject, I introduced a simple spatial model that has been designed to symbolize the interactions between different acting agents in the system. This model highlighted the existence of positive feedbacks that occur in vegetation growth, and how this feedback contributes to the fixation of a sand dune.

6. Works Cited

Bauer, Bernard O., and Robin G.d. Davidson-Arnott. “A General Framework for Modeling Sediment Supply to Coastal Dunes including Wind Angle, Beach Geometry, and Fetch Effects.” Geomorphology49.1-2 (2003): 89-108. JSTOR. Web.

Bishop, Steven R., Hiroshi Momiji, Ricardo Carretero-González, and Andrew Warren. “Modelling Desert Dune Fields Based on Discrete Dynamics.” Discrete Dynamics in Nature and Society 7.1 (2002): 7-17.UO Libraries. Web.

Ciccarelli, Daniela. “Mediterranean Coastal Sand Dune Vegetation: Influence of Natural and Anthropogenic Factors.” Environmental Management 54.2 (2014): 194-204. JSTOR. Web.

Gornish, Elise S., and Thomas Miller. “Effects of Storm Frequency on Dune Vegetation.” Global Change Biology 16.1o (2010): 2668-675. Wiley. Web.

Mitasova, Helena, Margery Overton, and Russell S. Harmon. “Geospatial Analysis of a Coastal Sand Dune Field Evolution: Jockey’s Ridge, North Carolina.” Geomorphology 72.1-4 (2005): 204-21. JSTOR [JSTOR]. Web.

Nield, A., and C. Baas. “Modeling Vegetated Dune Landscapes.”Geophysical Reseach Letters 57.10 (2007): 1029. UO Libraries. Web.

Parteli, E. J. R., O. Duran, H. Tsoar, V. Schwammle, and H. J. Herrmann. “Dune Formation under Bimodal Winds.” Proceedings of the National Academy of Sciences 106.52 (2009): 22085-2089. Wiley. Web.

Ping, Lü, Clément Narteau, Zhibao Dong, Zhengcai Zhang, and Sylvain Courrech Du Pont. “Emergence of Oblique Dunes in a Landscape-scale Experiment.” Nature Geosci Nature Geoscience 7.2 (2014): 99-103. Wiley. Web.

Ravi, Sujith, David D. Breshears, Travis E. Huxman, and Paolo D’Odorico. “Land Degradation in Drylands: Interactions among Hydrologic-aeolian Erosion and Vegetation Dynamics.” Geomorphology and Vegetation: Interractions, Dependencies, and Feedback Loops 4th ser. 116.3 (2010): 236-45. Wiley. Web.

Worman, S. L., A. B. Murray, R. Littlewood, B. Andreotti, and P. Claudin. “Modeling Emergent Large-scale Structures of Barchan Dune Fields.”Geology 41.10 (2013): 1059-062. JSTOR [JSTOR]. Web.