Ecological Archives A021-003-A1

Casey M. Ryan and Mathew Williams. 2011. How does fire intensity and frequency affect miombo woodland tree populations and biomass? Ecological Applications 21:48–60.

Appendix A. Model description and color photographs depicting fire in miombo woodlands.

 

FIG. A1. Gap model schematic. Parameters are shown in red (see Tables A2 and A3 for values, source and sensitivity of the parameters). Green shows allometric calculations based on Table A1. Model driving data is shown in blue (see Fig. A2). Stochastic processes are shown with a dashed line. The model produces annual output, but the light and C assimilation functions run on hourly time steps (see text).

The model is a 1D patch model, explicitly representing each stem and its light environment, carbon assimilation, growth and mortality. Each model patch has twenty-five 1 m vertical layers and is not spatially explicit. The model is written in FORTRAN 90.

Light and seasonal and diurnal model drivers

Within each patch, the model simulates light interception by the canopy and the resulting photosynthetic assimilation. The model is driven with a 3.5 year radiation climatology from a weather station (Skye Instruments, UK) at Chitengo, 25 km from the study site. We generated a mean diurnal cycle of downwelling PAR, at hourly resolution, for each calendar month. The model is also driven with an observed monthly fraction of peak leaf area index (LAI), determined from 3.5 years of monthly hemispherical photos at two nearby permanent sample plots.


 

FIG. A2. Data used to drive the model. A seasonal cycle of leaf area index was derived from replicated monthly hemispherical photos on two 1 ha permanent sample plots. PAR measurements are from a weather station 25 km away. 3.5 years of data were averaged by hour and month to generate a representative diurnal cycle for each month.

Plant Area Index (PAI ) was estimated from hemispherical photos (Nikon Coolpix 4500 with a FC-E8 fisheye converter) collected each month at two 1 ha permanent sample plots (PSP). Nine photos were acquired on a 20 m grid on each plot, each month. The photos were thresholded to separate plant and sky pixels using the algorithm of Ridler and Calvard (1978), implemented in MATLAB to determine gap fraction, which was converted to an PAI estimate using the method of Licor (1989), with the images segmented in a similar manner to van Gardingen et al. (1999). As the trees are fully deciduous, PAI was converted to LAI by subtracting the lowest observed PAI from each observation point. The monthly LAI fraction represents the deciduousness of the vegetation and is an explicit representation of limits of the growing season of trees in this environment (Fig. A2). Each year the vertical leaf area distribution is calculated based on functions which relate each stem’s DBH to its total height, canopy depth and leaf area (Shinozaki et al. 1964) using the allometric relationships shown in Table A1. Leaves were assumed to be spread evenly throughout the canopy depth. A simple radiative transfer scheme passes light down through the canopy layers. The amount of PAR absorbed is calculated according to leaf area density using the Beer-Lambert law (Jones 1992), with an assumed spherical leaf angle distribution (k). All radiation was assumed diffuse and the leaves had no albedo or transmittance.

Carbon assimilation and allocation

The absorbed PAR was converted to assimilated C using photosynthetic light response curves parameterised from two studies in Zimbabwean miombo (Tuohy and Choinski 1990; Tuohy et al. 1991). Two parameters describe the light response curve: the maximum rate of assimilation, Pmax and the amount of light needed to achieve half this rate, kp. For each stem, mass of photosynthate was summed for each canopy layer, for each hour of the 12 diurnal cycles representative of each month, and scaled up to a yearly total.

Carbon allocation routines are resolved each year for each stem. We assumed that 50% of assimilate is used for respiration (Waring et al. 1998, Ra in Table A2). Of the remainder, the required amount is allocated to leaves to produce the observed phytomass of peak LAI. Leaf carbon specific area (LCA gC m2) is derived from field measurements (Nottingham 2004). We assumed that allocation to fine roots, Afr, is equal to allocation to leaf mass. Any remaining C is allocated to woody growth, which is partitioned above and belowground according to a local DBH-specific root:shoot allometric. The increase in aboveground stem C is converted to a change in DBH using allometric equations (Table A1), which in turn allows the increase in height and leaf area to be calculated for the next year.

Mortality and the effect of fire

Once growth is completed, each stem is exposed to a random chance of mortality, which is either an intrinsic (non-fire) mortality or a fire-induced mortality derived from our fire experiments. These fire-induced mortality rates are DBH- and fire intensity class-specific and are based on piecewise functions of the field results (Table A3). The intrinsic mortality rate, Mi, was unknown and is very poorly constrained in this ecosystem. We used a nominal value of 2% regardless of size (similar to Desanker and Prentice 1994; Desanker 1996), and undertook sensitivity analysis (Table A2). In the model, the chance of a fire occurring was determined from a user supplied control variable, the fire return interval (FRI), and a random number generator. The chance of a fire occurring was determined as 1/FRI.

Resprouting

Because of the importance of resprouting in fire-prone ecosystems (Bond and Midgley 2001; Chidumayo 2004; Mlambo and Mapaure 2006), aboveground stem mortality (top-kill) was decoupled from belowground rootstock mortality. Stems > 2 cm DBH (parameter Sresprout) which are killed, have a probability or resprouting (1 - Smort), which is based on data from the fire experiments, and we assume they achieve a 2 cm DBH in their first year. In addition, every year there is a nominal 3% chance (parameter Precruit) of a recruitment event occurring and 200 new seedlings (parameter Snew) being established in the patch. We justify this low level of recruitment from studies which show that most regeneration is from sprouts and that seedling survival is low in these woodlands (Chidumayo 1992, 1997).

Model output and initiation

After calculating mortality, the patch LAI (for stems > 1.5 m tall), basal area, aboveground C stock, and stocking density (for stems > 5 cm DBH), and stem size distribution are calculated for all live stems.

The model was initiated from bare ground with 200 seedlings and tended to reach equilibrium after ~200 years. All model runs in this study used 50 patches of 0.02 ha (based on an 8 m crown radius for a typical large stem) and were 1000 years long. Output for the final 500 years is reported as the 50-patch 500-year mean with the standard deviation between the 50 patches.

Model sensitivity analysis

Method

We ran a sensitivity test of all model parameters. Each parameter was varied in turn by a factor of 0.5, 0.75, 1.5, and 2 from its nominal value (Table A2). The sensitivity, S, is defined as Sx = ([Radj - Rn]/ Rn) / ([Padj - Pn]/ Pn), where x is the factor by which the nominal value is changed, Radj is the response for the model run with the adjusted value, Rn is the response with the nominal value, and Pn and Padj are the parameter values for the nominal and adjusted cases respectively. Patch basal area was used as the response variable. The parameters used in the model and their source, magnitude and sensitivity, are shown in Table A2.

Results

The model output were much more sensitive to the growth parameters compared to those controlling regeneration (Table A2). In order of sensitivity, they were: the maximum rate of photo synthesis (Pmax); the fraction of assimilate allocated to respiration (Ra); the half-saturation rate of photosynthesis (kp); carbon mass per unit leaf area (LCA); allocation to fine roots (Afr); the leaf angle distribution (k); and the leaf area:basal area ratio (LA:BA). These are basic physiological parameters, which are well constrained by local field observations (Pmax, and kp, by Tuohy et al. 1991; LCA and LA:BA by our data) or to a lesser degree, globally (Ra, Waring et al. 1998 and k, Norman and Campbell 1989). Afr is badly constrained, particularly in savanna environments. Of the mortality and regeneration parameters, the intrinsic mortality rate (Mi) was the only one that significantly affected the final patch basal area.

TABLE A1. Allometric equations used in the model and derived from local field data. Equation forms are defined as follows: power, Y = aXb; linear, Y = aX ± b. n is the number of samples of field data used to fit the function.

Dependent (Y) variable

Independent (X) variable

Form

a

b

n

r2

min X

max X

Notes

C stock of stem (kg C)

DBH, m

power

4222

2.6

29

0.93

0.05

0.72

 

C stem : C root+stem

DBH, m

linear

0.32

0.6

23

0.26

0.05

0.72

 

Height of top of tree (m)

DBH, m

linear, with saturation

42.6

 

80

0.67

0.07

0.86

where DBH > 60 cm, ht = 25 m

Height of base of canopy (m)

DBH, m

linear, with saturation

22.3

 

80

0.58

0.07

0.86

where DBH > 67 cm, canopy base = 15 m

Leaf area, m2

Basal area, m2

linear

1330

 

10

0.29

4.4

13.9

plot level data

 

TABLE A2. Parameters in the model, their source, nominal value and sensitivity, Sx, see text for symbol definitions. For the sensitivity analysis, we use the 50-patch mean basal area as the response variable. Each variable was changed in turn.

Parameter description

Parameter name

Nominal parameter value, Pn

S0.5

S0.75

S1.5

S2

Source of nominal parameter value

Growth parameters

Fraction of GPP used for autotrophic respiration

Ra

0.5

-1.8

-1.9

-2.4

-1.0

Waring et al. (1998)

Extinction coefficient for Beer-Lambert law

k

0.5

0.0

-0.6

-0.2

0.1

Norman and Campbell (1989)

Amount of C allocated to fine roots, as a fraction of allocation to leaves

Afr

1

-0.4

-0.2

-1.0

-0.6

Consistent with Castellanos et al. (2001). Similar to Table 5 of Hendricks et al. (2006), which is for temperate systems.

Maximum rate of photosynthesis (µmol C·m-2·s-1)

Pmax

10

2.0

2.0

2.5

2.3

Tuohy and Choinski (1990); Tuohy et al. (1991)

PAR intensity at which 0.5 Pmax is obtained (µmol·s-1·m-2)

kp

250

-1.7

-1.7

-1.1

-0.7

Tuohy and Choinski (1990); Tuohy et al. (1991)

Leaf carbon per leaf area (g C/m2)

LCA

50

-1.5

-1.1

-1.7

-0.9

Nottingham (2004); Chidumayo (1997)

Leaf area per unit basal area (m2/m2)

LA:BA

1330

0.0

-0.6

-0.1

-0.1

See Table A1

Mortality and Regeneration parameters

Intrinsic mortality rate

Mi

0.02

-0.8

-1.3

-1.3

-0.5

Estimated, similar to Desanker and Prentice (1994)

Diameter, m, at which a seedling is considered to have developed a rootstock and the ability to resprout

Sresprout

0.02

0.0

-0.2

-0.1

0.0

estimated

Number of seedlings per ha established in a recruitment year

Snew

100

0.0

-0.5

0.2

0.1

estimated

Probability of a recruitment year occurring

Precruit

0.03

0.1

0.1

-0.2

0.0

estimated

Probability of a root stock failing to resprout after fire

Smort

0.04

-0.2

-0.3

0.1

0.0

this study

 

TABLE A3. Piecewise parameterisation of fire-induced mortality rates shown in Fig. A3. These are used to calculate stem mortality in the model in years when a fire occurs.

 

Fire intensity (TA tercile)

 

High

Med

Low

ax

-70

-70

-60

bx

5

4

2

bx_sat

-2

-3

-3.8


Where:

DBH < 10 cm

Log odds of top-kill  = -ax DBH+ bx

DBH > 10 cm

Log odds of top-kill = b x_sat


 

TABLE A4. Metrological conditions during each burn. The values are the mean for the period of the fire.

Plot No.

1

2

3

4

5

6

7

8

Temp (°C)

no burn

31.4 29.9 35.4 25.0 33.3 32.8 33.3

Relative Humidity (%)

33 32 23 55 15 28 21

Wind speed (m/s) -1

2.4 1.4 0.9 1.1 1.7 1.6 0.9

Where:

DBH < 10 cm

Log odds of top-kill = -ax DBH+ bx

DBH > 10 cm

Log odds of top-kill = bx_sat


 

TABLE A5. Metrological conditions during each burn. The values are the mean for the period of the fire.

Plot No.

1

2

3

4

5

6

7

8

Temp (°C)

no burn

31.4 29.9 35.4 25.0 33.3 32.8 33.3

Relative Humidity (%)

33 32 23 55 15 28 21

Wind speed (m/s)

2.4 1.4 0.9 1.1 1.7 1.6 0.9

 

TABLE A6. Tree and sapling species composition on the experimental plots. Trees are defined as live standing woody species > 5 cm DBH. Saplings are defined as woody species < 5 cm DBH and > 0.3 cm D10. Species names area abbreviated as follows: Brachystegia boehmii (Bb), Brachystegia spiciformis (Bs), Burkea africana (Ba), Combretum adenogonium (Ca), Crossopteryx febrifuga (Cf), Dalbergia boehmii subsp. boehmii (Dbb), Diplorhynchus condylocarpon (Dc), Erythrophleum africanum (Ea), Julbernardia globiflora (Jg), Lannea schimperi (Ls), Millettia stuhlmannii (Ms), Ormocarpum trichocarpum (Ot), Pterocarpus angolensis (Pa), Pterocarpus rotundifolius subsp. Polyanthus (Prp), Sclerocarya birrea subsp. caffra (Sbc), Xeroderris stuhlmannii (Xs). Blanks indicate unidentified saplings.

Large tree data

Top 5 species by basal area. 1.

Bb

Bb

Bb

Bb

Bb

Bb

Bb

Jg

2.

Dc

Dc

Dc

Dc

Dc

Dc

Ba

Dc

3.

Jg

Ba

Ba

Jg

Jg

Sbc

Bs

Bb

4.

Ba

Bs

Sbc

Prp

Prp

Prp

Dc

Bs

5.

Ea

Jg

Ea

Pa

Xs

Ca

Ea

Pa

Top 5 spp % of total basal area

76%

90%

81%

82%

92%

85%

84%

77%

Sapling data

Top 5 species by basal area. 1.

Bb

Bb

Dc

Dc

Bb

Dc

Dc

Dc

2.

Dc

Jg

Ot

Ca

Dc

Jg

Jg

Ba

3.

Jg

Dc

Ls

Bb

Ba

Dbb

Bb

Xs

4.

Ca

Ls

Bb

Jg

 

Cf

Ba

Ms

5.

Ba

 

Ba

 

Ms

Bb

Pa

Ca

Top 5 spp % of total basal area

86%

78%

95%

86%

92%

70%

87%

93%

 



 

FIG. A3. Model output of patch characteristics for a low-fire scenario (FRI = 100, low-intensity fires) from initiation with bare ground at year zero to 1000 years. The mean of the 50 patches is shown with a black line. One standard deviation of the 50 patches is shown above and below the mean with a gray shade. The white triangles on the right Y axis indicate the field data for the Marrameu forest plot (Site 2), the gray triangles indicate the 50-patch mean of the final 500 model years.




 

FIG. A4. A damaged tree bursts into flames.




 

FIG. A5. Another collapses after the bole has combusted.



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