Multiple Equilibrium States Multiple Equilibrium States and the Abrupt Transitions in a and the Abrupt Transitions in a Dynamical System of Soil Water Dynamical System of Soil Water Interacting with VegetationInteracting with Vegetation

David X.D. Zeng1, Xubin Zeng1, Samuel S.P. Shen2, and Robert E. Dickinson3

1. Department of Atmospheric Sciences, University of Arizona 2. Department of Mathematical and Statistical Sciences, University of Alberta3. 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

• Gz, Dz, and Cz are the accumulation, decomposition, and consumption of the wilted leaves

• P is the precipitation (through fall), Ev is the soil evaporation, Et is the vegetation transpiration, and R is runoff

)()(),(

),,(),(),,(

)(),(),(

zCzDyxGdtdz

zyxRyxEzyxEPdtdy

xCyxDyxGdtdx

zzz

tv

The Three-Variable Dynamical Grassland Model

Living Grass

Wilted Grass

Run-off

precipitation

Sketch of the Sketch of the Water BalanceWater Balance

transpiration

Soil Wetness

evaporationshading

evaporation

The processes of the living and wilted biomass:

0)1(

)1)(1(

)1)(1(

1

z

zzz

zz

yx

yx

CCeD

DGeeD

eeG

dz

dydx

gygx

)1()1(1 )1(

)1( )1(

)1(1)1( )1(

zrz

xrf

y

xtf

ytt

xvff

zyvv

rzrxry

txty

vxvzvy

eeePR

eeeE

eeeeE

The processes of the soil wetness:

The Equilibrium StatesThe 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 Sensitivity to model to model parametersparameters(3 categories)(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 rateDG zz

The transformation functionIn 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) fmax

The functional forms in the following terms will be replaced by other transformation functions

Sensitivity to the transformation function Sensitivity to the transformation function ff((uu))

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

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

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

SummarySummary

• 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:10.1029/2003GL018910, 2004

Focus in the near futureFocus 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?