Multiple Equilibrium States and the Abrupt Transitions in a Dynamical System of Soil Water Interacting with Vegetation David X.D. Zeng 1, Xubin Zeng 1, Samuel S.P. Shen 2, and Robert E. Dickinson 3 1. Department of Atmospheric Sciences, University of Arizona 2. Department of Mathematical and Statistical Sciences, University of Alberta 3. School of Earth and Atmospheric Sciences, Georgia Institute of Technology

We develop an analytically tractable simple model and show that in the land system, soil water-vegetation interaction alone (with prescribed precipitation) could explain the coexistence of multiple ecosystems over arid and semi-arid regions in Inner Mongolia of China. Our overall research goal is to use such simple models and data to help interpret, understand, and improve dynamic vegetation/BGC models.

The distribution of vegetation is determined by climate condition (e.g. precipitation), and the boundary between different ecosystems (e.g., forest, grassland, shrub, desert) can be abrupt. Africa: Sahara/Sahel Amazonia: forest/savanna Inner Mongolia: steppe/desert The distribution of vegetation zone and moisture index in Inner Mongolia.

G, D, and C are the growth, wilting, and grazing of the living grass G z, D z, and C z are the accumulation, decomposition, and consumption of the wilted leaves P is the precipitation (through fall), E v is the soil evaporation, E t is the vegetation transpiration, and R is runoff The Three-Variable Dynamical Grassland Model

Living Grass Wilted Grass Run-off precipitation Sketch of the Water Balance transpiration Soil Wetness evaporation shading evaporation

The processes of the living and wilted biomass: The processes of the soil wetness:

The Equilibrium States Desert if moisture index  <  1 Stable grassland if  >  2 Transition region, grassland/desert, if  1 <  <  2 Moisture Index  : The ratio of precipitation to potential evaporation.

Sensitivity to model parameters (3 categories) (a) changes in  1 only (b) changes in both  1 and  2

The system dynamics change significantly with the wilted-biomass- related parameters, i.e., the accumulation rate, decomposition rate, and shading effect coefficient. (c) changes in dynamics accumulation rate

The transformation function In general, the dependences of terms on any particular state variable u, f(u), need to satisfy two constraints: The linear limit: f(u~0)~ku The saturated limit: f(u  )  f max The functional forms in the following terms will be replaced by other transformation functions

Sensitivity to the transformation function f(u) Changes in  1 and slightly in  2, The bifurcation diagram is preserved

A: The more wilted biomass, the less living biomass Q: Under the given soil wetness, what is the required minimum amount of living biomass for the recovery of a grassland from the desert state?

Q: What is the maximum grazing that can be taken from a grassland without leading it into desertification?

Q: What temporal sequence of drought is needed to drive a grassland to desert?

Summary The land system with soil water-vegetation interaction alone can possess multiple ecosystems over arid and semi-arid regions. The transition between ecosystems can occur in both spatial and temporal domains. The wilted biomass can provide the benefits of shading to help conserve the soil water which is essential to vegetation in the semi-arid regions. Reference: Zeng, X., S. fS. P. Shen, X. Zeng, and R. E. Dickinson (2004), Multiple equilibrium states and the abrupt transitions in a dynamical system of soil water interacting with vegetation, Geophys. Res. Lett., 31(5), 5501, doi: /2003GL018910, 2004

Focus in the near future Use such simple models and data to help interpret, understand, and improve the dynamic vegetation/BGC model in the CCSM. Do similar bifurcation and transition phenomena occur in the dynamic vegetation/BGC model? Its sensitivity to model parameters and functional forms? The minimum requirement of living biomass for vegetation maintenance? How does grazing influence vegetation maintenance? The impact of the time sequence of drought on vegetation?