modelling vegetation patterns in semiarid environments

1/21 FOUR DECADES OF PROGRESS IN MONITORING AND MODELING OF PROCESSES IN THE SOIL-PLANT-ATMOSPHERE SYSTEM: APPLICATIONS AND CHALLENGES – 19-20 June 2013 Napoli

Salvatore Manfreda1, Teresa Pizzolla1, Kelly K. Caylor2

1) University of Basilicata, Italy. 2) Princeton University, USA.

Modelling Vegetation Patterns in Semiarid Environments

e-mail: [email protected]


Spatial Pattern of Vegetation Landscape ecology emphasizes the interaction between spatial pattern and ecological process (movement of plants & animals; edge/interior effects, isolation) that is the causes and consequences of spatial heterogeneity across a range of scales.

“Two fundamental and interconnected themes in ecology are the development and maintenance of spatial and temporal pattern, and the consequences of that pattern for the dynamics of populations and ecosystems.” – Simon A. Levin, 1992

(Photo by Yann Arthus-Bertrand)


Motivation

Global precipitation projections for December, January, and February (top map) and June, July, and August (bottom map.) Blue and green areas are projected to experience increases in precipitation by the end of the century, while yellow and pink areas are projected to experience decreases.

Source: Christensen et al. (2007)

How climate change will impact on vegetation patterns?

How this will modify water resources?


The Study Case

Sevilleta LTER

(Caylor et al., AWR 2005)

Upper Rio Salado Catron County, NM Cibola National Forest Basin Area: 681 km2 Mean Annual Rainfall: 218±84 mm


! Couple patterns of vegetation, soil, and climate to generate patterns of steady state water balance and soil moisture distribution within the basin

! Use existing stochastic model of soil moisture:

( ) ( )stsdtdsnZr χϕ −= ,

Input is a poisson process of rainfall events with a characteristic

distribution of storm depths

(Rodriguez-Iturbe et al., 1999; Laio et al., 2001; Manfreda et al, 2010)

Losses are determined according to a loss function that includes

evaporation, transpiration, and leakage

0

0.5

1

1.5

2

2.5

3

3.5

0 shsw s* sfc 1

χ (s)

cm

/d

Emax

Evap

Soil Water Balance


Basin Water Stress

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.2

0.4

0.6

0.8

1

x

θʹ′

1.0 0.0

⎪⎩

⎪⎨

⎧<⎟

⎟⎠

⎞⎜⎜⎝

⎛=

otherwise

kTTifkTT

seass

n

seas

ss

1

''

*

*

*

/1

ζζ

θ

t

s(t)

Duration of the growing season, Tseas

ξ

Duration of an excursion below ξ

(Porporato et al., AWR – 2001)

Frequency of crossing Number of crossing Mean time of crossing )()(

)()(ξξρ

ξνξ

ξ

ξp

PPT ==

Dynamic water stress defined as a function of frequency of crossing, number of crossing, mean time of crossing, etc.


Potential evapotranspiration

Rn = Ra 1−α( )−εsσTs4 +εaσTa4

Rdir

Rdif Rem

αRdir Rrif

Ra atmosphere

target

Ra =GSCd2

cos θ( )dωω1

ω2

∫

Net solar radiation


DWS Tree

km

km

1 10 20 30 40 50 60 70 80 90 100

1

10

20

30

40

50

60

70

80 0

0.2

0.4

0.6

0.8

1

DWS Shrub

km

km

1 10 20 30 40 50 60 70 80 90 100

1

10

20

30

40

50

60

70

80 0

0.1

0.2

0.3

0.4

DWS Grass

km

km

1 10 20 30 40 50 60 70 80 90 100

1

10

20

30

40

50

60

70

80 0

0.2

0.4

0.6

0.8

1

DWS Tree

km

km

1 10 20 30 40 50 60 70 80 90 100

1

10

20

30

40

50

60

70

80 0

0.2

0.4

0.6

0.8

1

DWS Shrub

km

km

1 10 20 30 40 50 60 70 80 90 100

1

10

20

30

40

50

60

70

80 0

0.1

0.2

0.3

0.4

0.5

DWS Grass

km

km

1 10 20 30 40 50 60 70 80 90 100

1

10

20

30

40

50

60

70

80 0

0.2

0.4

0.6

0.8

1

T ! s! = T!! s! − T ! s + 1ν s − 1

ν s! + γ 1ν u !− T! u

!!

!du

θ′ = T!"#! − T ! s!T!"#! θ

Dynamic Water Stress Dynamic water stress computed including initial conditions

The mean first passage time (in days) of the stochastic process between s0 (initial condition) and <s>

Basin morphology modifies dynamic water stress allowing the existence of some species.


Dynamics of Organization within River Networks Initial Condition

Neighbor model: Interactions can occur between all 8 neighbors

Network model: Interactions constrained by flow path – only

downstream neighbors can be replaced

2

1

Cells replace neighbor pixels if it lowers the local amount of water stress with a probability p

How well do each of these interactions represent the observed distribution of water

stress? (Caylor et al., GRL 2004)

⎟⎟⎠

⎞⎜⎜⎝

⎛

+−=

21

11θθ

θp

Cell becomes bare when θ is 1 for all vegetation types


Neighbor Model

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.2

0.4

0.6

0.8

1

xθʹ′

Network modelActual

Steady-State Condition

Model calibration


Vegetation Pattern obtained including the Effects of Morphology on Solar Radiation

The hypothesis of feasible optimality is explored using four cellular automata approaches. The initial random vegetation mosaic is modified through the iteration of local interactions that occur between adjacent locations. These interactions are defined such that the replacement probabilities (P ) adopted combine both the dynamic water stress (𝜃′ ) and the plant transpiration (T ). The schemes proposed are the following:


(Manfreda et al., Procedia Environ. Sci. 2013)

Vegetation Pattern obtained including the Effects of Morphology on Solar Radiation

Among all considered cases, the second and third schemes (see Fig. 5 B and C) provide spatial patterns that replicate more closely the actual distribution of vegetation in the Rio Salado basin.


Vegetation Pattern obtained including the Effects of Morphology on Solar Radiation Initial Condition

Cells replace neighbor pixels if it lowers the local amount of water stress with a probability p

⎟⎟⎠

⎞⎜⎜⎝

⎛

+⎟⎟⎠

⎞⎜⎜⎝

⎛

+−=

21

1

21

11TT

Tpθθ

θ

Vegetation strategy is: •  to minimize of stress •  and maximize transpiration


Ecohydrological Model: Simulation Results (Hurvitz, 2002)

The proposed model has been used to predict 256 scenario defined changing both the mean rainfall rate (λ) and the mean rainfall depth (α).

Increasing mean annual rainfall

200 400 600 800 1000 1200

100

200

300

400

500

600

700

800

900

1000

(A) (B) (C) Bare soil

Grass

Shrub

Tree

Maps are obtained using the measured rainfall rate (λ = 0.284 day−1) and changing the parameter α that assumes the following values: 0.474cm (A), 0.517cm (B), 0.631cm (C).


Shannon’s Entropy – Diversity Index

0.4

0.5

0.6

0.70.2

0.250.3

0.350.4

0.450.5

0

0.5

1

1.5

λ

α

Shan

non'

s en

tropy

SHDI = − pi *ln pi( )i=1

m

∑

SHDI increases as the number of different patch types increases and/or the proportional distribution of area among patch types becomes more comparable

pi = proportion of landscape occupied by the class i.

The Shannon’s evenness index (SHDI) represents a well-known landscape metric that accounts for both abundance and evenness of species in the landscape. This index has the same expression of the informational entropy and is defined by

(Manfreda and Caylor, Water 2013)


Same Rainfall with Different Rate or Mean Depth

…changes in α provides sharper modifications of landscape.


Same Rainfall with Different Rate or Mean Depth

Land

scap

e D

iver

sity

Annual rainfall

Changing α

Changing λ


Results on a Mediterranean Area

Aridity Index (De Martonne) Basin Subasins

(Manfreda, Ann Arid Zone 2013)


Conclusions The main outcomes of the present work can be summarized in following points:

i)  The algorithm that seems to explain the actual structure of vegetation observed in the Upper Rio Salado basin is the one that tend to minimize dynamic water stress and maximize vegetation water use;

ii)  The landscape analyses, based on the modeling applications, show that reduction of landscape diversity (described by the Shannon’s Index) may occur rapidly for small changes in the rainfall characteristics;

iii)  These changes are exacerbated when rainfall modifications are due to reduction in the mean rainfall depth;

iv)  The impact of climate change on the vegetation pattern depends on the vulnerability of a system with respect to the expected changes.


References ! Manfreda, S., K.K. Caylor, On The Vulnerability of Water Limited Ecosystems to

Climate Change, Water, 5, 819-833; doi:10.3390/w5020819, 2013. ! Manfreda, S., T. Pizzolla, K.K. Caylor, Modeling Vegetation Patterns in Semiarid

Environment, Procedia Environmental Science, 2013. ! Pizzolla, T., S. Manfreda, K.K. Caylor, M. Fiorentino, Il ruolo dell’esposizione e della

pendenza dei versanti sullo stress idrico della vegetazione, Atti del Convegno di idraulica e Costruzioni Idrauliche - IDRA2012, 9-14 settembre 2012, Brescia, 2012.

! Acampora, A., T. Pizzolla, S. Manfreda, Effects of Morphology on Solar Radiation and Evapotranspiration, 3rd International Meeting on Meteorology and Climatology of the Mediterranean - IMCM 2011.

! Acampora, A., A. Sole, M. T. Carone, T. Simoniello, S. Manfreda, Le Metriche del Paesaggio come Strumento di Analisi del Territorio, in Informatica e Pianificazione Urbana e Territoriale a cura di Las Casas G., Pontrandolfi P., Murgante B., Atti della Sesta Conferenza Nazionale INPUT 2010, Libria, pp 221-231, vol.1, 2010.

! Manfreda, S., Ecohydrology: a New Interdisciplinary Approach to Investigate on Climate-Soil-Vegetation Interactions, Annals of Arid Zones, 48 (3 & 4), 219-228, 2009.


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modelling vegetation patterns in semiarid environments

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