The emergence of periodic spatial patterns in arid ecosystems has been linked to catastrophic shifts of arid grasslands to deserts. However, this link remains controversial and poorly understood. At our arid grassland field site in southern Colorado, climate change has reduced water availability, resulting in a periodic pattern of alternating vegetated and bare stripes emerging since 2015. Watering experiments showed that the bare stripes are providing water runoff to the vegetated patches, where plants increase water infiltration rate and decrease surface water flow.
The broad objective is to create a locally parameterized model for our field system. The current study aims to incorporate our field findings of the impacts of vegetation density on the speed of sheet water flow into a partial differential model.
Using the ReacTran package in R, we adapted the model developed by Hille Ris Lambers (2001), which simulates coupled spatial and temporal dynamics of the vegetation cover, surface, and soil water, where vegetation cover enhances infiltration. We augmented the model by explicitly including the impact of vegetation on sheet flow speed observed in the field. The resulting spatial patterns were analyzed using Fast Fourier Transform (FFT) and compared to those in the field.
Results/Conclusions
When the vegetation did not slow down the sheet flow, the system created periodic patterns that were along the direction of the water flow (west to east at 180°). FFT analysis showed the three dominant waves direction were at 166°, 14°, and 153°, and the wavenumbers ranged from 4.08 to 4.42. Radial analysis showed the highest signal at 4-5 wavenumbers while the dominant directions of the angular spectrum were at 165° and 4°. When vegetation did slow down the sheet flow, the system created patterns that were significantly askew to the flow. FFT analysis showed the three dominant waves direction were at 45°, 53°, and 150° with wavenumbers ranging from 2.2 to 5. Radial analysis showed the highest signal to be at 4-5 and 2-3 wavenumbers. The single dominant direction of the angular spectrum was at 45°.
Periodic patterns askew to the slope of the terrain are commonly found in nature, including at our field site. However, current theoretical literature does not provide a sufficient explanation for these patterns. Here we show that askew patterns can originate from the decrease of the water flow speed caused by the friction from vegetation.
