State & Transition Models: Moving Beyond Boxes and Arrows. Steve Archer University of Arizona

Transcription

1 State & Transition Models: Moving Beyond Boxes and Arrows Steve Archer University of Arizona Beyond Boxes and Arrows - Assessing Climate Change/Variability and Ecosystem Impacts/Responses in Southwestern Rangelands San Carlos - January 25, 2006

2 S & T Approach POSITIVE ATTRIBUTES Robust conceptual framework Flexible Allows for event driven change Accommodates cyclic & directional change Forces us to explicitly state conditions and assumptions Explicitly links management and research

3 Beyond Boxes and Arrows

4 Early Warning Threshold A B Axis II D C Axis I (from NRC 1994)

5 S & T Approach LIMITATIONS Heurisic states Transition mechanisms poorly understood Probability and rate of change seldom known State longevity? Likelihood of change to alternate states? What drives or triggers transitions?

6 S & T Approach Beyond Boxes and Arrows ~ Markov Models ~ Transition Matrix Models ~ Matrix Projection Models T1 IV Recently burnt, many shrub seedlings or resprouts T7 I Grassland, scattered woody plants From Westoby et al T6 II T2 Grassland, with many shrub seedlings T5 III Dense shrub cover, little grass T4 T3

7 Compute P(change) from a given state to another state(s) Change Matrix x Matrix of Current States = New State Matrix

8 Change Matrix x Matrix of Current States = New State Matrix pproach: Classify vegetation in 20 x 20 m grids on 1941 aerial photo W Wm G Gm MC PC HZ = Woodlands = W margins = Groves = G margins = Mature Clusters = Pioneer Clusters = Herbaceous zones

9 Change Matrix x Matrix of Current States = New State Matrix Approach: Compare 20 x 20 m grids on 1960 aerial photo with those on 1941 aerial photo W Wm G Gm M P H W Wm G Gm M P H

10 Change Matrix x Matrix of Current States = New State Matrix W Wm G Gm M P H W Wm G Gm M P H x = (Wm and Cm not shown)

11 Stationarity Assumption Transitions between states are constant over time Alternatives Develop a mean transition Develop time-specific transitions

12 Computed transitions for >1960 (DRY) >1983 (WET)

13 DRY MATRIX W Wm C Cm M P H W Wm C Cm M P H WET MATRIX W Wm C Cm M P H W Wm C Cm M P H

14 Matrix of Current States x Wet Change Matrix or Dry Change Matrix = New State Matrix 20 y time-steps

15 Where are we headed? Forward projections 20 y time-steps WET vs DRY transitions randomly selected Constraint: P(WET) = 0.40

16 How did we get where we are today? Compute reverse transitions ( >1960 and > > 1941) Run model backwards in time - How long did it take us to get here? - What did things look like pre-settlement?

17 Proportion of Landscape P(WET) = Year (from Scanlan & Archer 1992) Herbaceous Woodland

18 Early Warning & Theshold States? Proportion of Landscape P(WET) = Year (from Scanlan & Archer 1992) Herbaceous Woodland

19 What if we. Change the P(WET)? Change the sequencing of WET and DRY? Compute new transition matrices based on new photo dates? Compute transition probabilities based on composition of neighboring cell(s)? Incorporate episodic events

20 S & T Approach Beyond Boxes and Arrows Dynamic Simulation Models

21 S & T Approach Beyond Boxes and Arrows Dynamic Simulation Models Data intensive Highly complex Difficult to customize for specific needs unless model developer is available Even then, very time consuming; requires expertise in high-level programming Research vs management models

22 Model Maker

23 T1 T7 IV Recently burnt, many shrub seedlings or resprouts I Grassland, scattered woody plants From Westoby et al T6 II T2 Grassland, with many shrub seedlings Grassland Patch-Level T5 III Dense shrub cover, little grass T4 T3 Grazing Rainfall Increaser Intermediate Decreaser Landscape-Level Herbaceous Biomass Annual Turnover Fire Intensity Fire Frequency Intra-spp. Competition Source Size 1 Size 2 Size 3 Size 4 Size 5 Dispersal Production Mortality Sink

24 Grassland Patch-Level Grazing Rainfall Increaser Intermediate Decreaser Landscape-Level Herbaceous Biomass Annual Turnover Fire Intensity Fire Frequency Intra-spp. Competition Source Size 1 Size 2 Size 3 Size 4 Size 5 Dispersal Production Mortality Sink

25 Grassland Patch-Level Grazing Rainfall Increaser Intermediate Decreaser Landscape-Level Herbaceous Biomass Annual Turnover Fire Intensity Fire Frequency Intra-spp. Competition Source Size 1 Size 2 Size 3 Size 4 Size 5 Dispersal Production Mortality Sink

26 Grassland Patch-Level Grazing Rainfall Increaser Intermediate Decreaser Landscape-Level Herbaceous Biomass Annual Turnover Fire Intensity Fire Frequency Intra-spp. Competition Source Size 1 Size 2 Size 3 Size 4 Size 5 Dispersal Production Mortality Sink

27 Grassland Patch-Level Grazing Rainfall Increaser Intermediate Decreaser Landscape-Level Herbaceous Biomass Annual Turnover Fire Intensity Fire Frequency Intra-spp. Competition Source Size 1 Size 2 Size 3 Size 4 Size 5 Dispersal Production Mortality Sink

28 Grassland Patch-Level Grazing Rainfall Increaser Intermediate Decreaser Landscape-Level Herbaceous Biomass Annual Turnover Fire Intensity Fire Frequency Intra-spp. Competition Source Size 1 Size 2 Size 3 Size 4 Size 5 Dispersal Production Mortality Sink

29 Fuhlendorf et al. in prep. Canopy Area (m 2 ) High low productivity Productivity Site high MAP productivity = 850 mm Year Low Productivity Site MAP = 600 mm 50

30 Grassland Patch-Level Grazing Rainfall Increaser Intermediate Decreaser Landscape-Level Herbaceous Biomass Annual Turnover Fire Intensity Fire Frequency Intra-spp. Competition Source Size 1 Size 2 Size 3 Size 4 Size 5 Dispersal Production Mortality Sink

31 Density (trees / ha) With no fire, increases regard- less of grazing history or grazing regime Ungrazed Moderate- 1y rest Heavy- 1y rest Year Fuhlendorf et al.,, in prep.

32 Biomass (% of max) Herbaceous Production No Fire Ungrazed Moderate Heavy Year Fuhlendorf et al.,, in prep.

33 100 Ungrazed Potential Herbaceous Production (%) low productivity high productivity uhlendorf, et al. in prep. No fire Fire Frequency (y)

34 Potential Herbaceous Production (%) Moderate grazing low productivity high productivity Fuhlendorf et al.,, in prep. No fire Fire Frequency (y)

35 Beyond Boxes and Arrows