2.1. The model
SORTIE is a spatially explicit, mixed-species forest dynamics model that makes population dynamic forecasts for juvenile and adult trees by predicting the fate of individuals (Pacala et al., 1996). SORTIE simulations use a mixture of mechanistically and empirically derived relationships found in five core submodels parametrized using field data that describe light availability, growth, mortality, recruitment and disturbance by windstorms. A brief description for each submodel follows.
Resources. The model focuses on light as the dominant limiting resource in forests and predicts light availability as a function of species-specific light transmission coefficients, crown geometry and the local sky brightness distribution at the sampled location (Canham et al., 1994, 1999). The model does not account for the effects of variation in soil nutrients and water on growth and mortality.
Growth. Species-specific equations predict radial growth of juvenile trees based on growing season light availability and tree size (Pacala et al., 1994). Growth of adult trees follows the constant area increment law (as in Phipps, 1967).
Mortality. For juveniles, species-specific equations predict the probability of survival for each juvenile tree as a function of recent (3–5 yr) radial growth rates (Kobe et al., 1995; Kobe and Coates, 1997). In the absence of disturbance, adult tree mortality is modelled as a random process with an annual rate of 1% (Runkle, 1981).
Recruitment. Mapped seedling traps or seed quadrats distributed at varying distances from the potential seed trees of each species provide the data to parametrize functions that describe both tree fecundity as a function of tree size and a the shape of the seed dispersal kernel (Ribbens et al., 1994).
Wind disturbance. The analysis for this submodel takes advantage of the fact that severe windstorms often contain dramatic spatial variation in intensity (e.g. Boose et al., 1994). The probability that an individual will experience any given level of damage is predicted as a logistic function of species taxonomic identity, individual tree size and local storm severity (as assessed using a relative, quantitative index) (Canham et al., 2001). The method uses maximum likelihood estimation to fit an ordinal logistic model of the form:
where pijks is the probability that individual i of species s in plot k is windthrown, and where ajs, bs and cs are species-specific parameters (s= 1.. m species), and Sk are the estimated storm severities (on a scale of 0 – 1) for the k= 1..n plots. For our analyses of wind disturbance in temperate forests, we only consider complete but not partial crown loss.
SORTIE has been parametrized for three regions where wind is a major natural disturbance agent: the transition oak-northern hardwood forests of the Northeastern U.S. (Pacala et al., 1996), the Interior Cedar–Hemlock forests of Northwestern British Columbia, Canada (Kobe and Coates, 1997; Wright et al., 1998; Canham et al., 1999; LePage et al., 2000), and the tropical forests of the Luquillo Mountains of Puerto Rico (Uriarte et al., 2004; 2005). In this paper, we use parameters obtained for nine species from transition oak-northern hardwoods forests in Northeastern North America for the first four submodels (Pacala et al. 1996). The species are (in roughly decreasing order of shade tolerance; Kobe et al., 1995): American beech (Fagus grandifolia Ehrh.), eastern hemlock (Tsuga canadensis L.), sugar maple (Acer saccharum Marsh), yellow birch (Betula allegheniensis Britton), black cherry (Prunus serotina Ehrh), red oak (Quercus rubrum), red maple (A. rubrum L.), white pine (Pinus strobus) and white ash (Fraxinus americana). These nine species are widespread in the northern hardwoods forests that stretch from the Appalachians in the south to New England in the northeast, account for approximately 50% of stems in the study region, and represent a good mix of early-mid to late successional species (Table 1). We obtained parameter estimates for the wind disturbance submodel for six of the nine species included in the analysis from Canham et al. (2001). For the remaining three species (white ash, red oak and white pine), we assigned parameter values based on similarity in canopy allometry, wood density and canopy position with the other six species. We also tested patterns of mortality generated with these parameters with existing field damage data (Foster, 1988).
Table 1. Average importance value for species x across counties in the four regions was calculated as IV (x) = 100* BA(x)/BA(all spp) + 100*No stems(x)/NoStems. We used data in the states of CT, MA, ME, NH, RI, and VT, Putnam, Rockland and Westschester County in New York. Data from Iverson & Prasad 1998. Data were not available for Long Island and urban areas surrounding New York City. A species in a monotypic stand would have an IV = 200
|Species||Region 1||Region 2||Region 3||Region 4|
Forest characteristics at the sites where the model was parametrized are those of maturing, second-growth stands that have developed following a history of agriculture and logging, typical of land use history and forest development in Southern New England (Foster, 1988; Pacala et al., 1996). Changes in forest structure since the last severe hurricane to affect the region in 1938, namely, the greater number of larger, more susceptible trees, are likely to increase impacts of future wind storms on these forest ecosystems (Boose et al., 2001).
2.2. Disturbance regimes
New England is affected by Atlantic hurricanes that approach from the south, with greatest impact from hurricanes that pass over the warm waters of the Gulf Stream (Elsner et al., 2000). Simulation parameters for hurricane severity and frequency were derived from a reconstruction of regional variation in historical damage for 67 storms that affected six New England states plus adjacent New York City and Long Island since European settlement to the present (1620–1997) (Boose et al., 2001). The authors reconstructed regional maps of damage in the Fujita scale using both historical reports of wind damage and meteorological data (HURRDAT, Ludlum, 1963; Fernandez-Partagas and Diaz, 1995; Fig. 1). Given the difficulty in obtaining direct local measurements of wind speed at a given location, we used descriptions of tree damage in the Fujita scale to develop a synthetic index of storm severity ranging from 0 to 1 representing the approximate proportion of trees killed in a storm of a given intensity (Table 2) and converted this value to correspond with the storm severity index in Canham et al. (2001, S in eq. 1). We relied on maps from Boose et al. (2001, cf. Fig. 8) to partition regional variation in hurricane frequency and severity into four separate storm regimes (Table 3). These regions contained all of Rhode Island, Connecticut and Massachussetts, the southern counties of Vermont, New Hampshire and Maine, and Putnam, Rockland and Westchester counties in New York (Fig. 1).
Figure 1. Composite map of maximum wind damage from 1620 to 1997 in the Fujita scale in 0.5 increments. Regional gradient shows most severe impacts along the southern coastline and lesser damage to the north and west. Figure from Boose et al. (2001). Reprinted with permission from the Ecological Society of America. We limited our analyses to areas that have historically been subject to F1 damage.
Download figure to PowerPoint
Table 2. Return intervals for windstorms in Southern New England (region 1 in Fig. 1) and description of likely forest damage
|Fujita index||Mean Return Interval (yr)||Sustained wind speed (m s−1)||Damage||Estimated Mortality (proportion)|
|F0||5||18–25||Leaves & fruits broken||0|
|F1||10||26–35||Trees blown down||0.05–0.1|
|F3||0||48–62||Most trees down||0.5–0.7|
Table 3. Estimated hurricane return intervals (storm severity index) for four regional areas in Northeastern US. Data from Boose et al. (2001). These four storm regimes were used in simulations for four regions. Technically, it corresponds to the expected mean probability of mortality of a well-mixed stand with a full size distribution of trees. The actual mortality of an individual storm will depend on what species are present and what the size distribution is. In each 5-yr time step, we evaluate the occurrence of a hurricane by the probability of it occurring. A 10 yr severity storm has a 50% chance of happening. An 80 yr severity storm has a 6.25% chance of occurring. These storm regime is then used in the wind disturbance submodel to estimate probability of mortality for all trees in the stand
|Return interval (yr)||Region 1||Region 2||Region 3||Region 4|
To simulate the observed multi-decadal pattern in windstorm severity in the North Atlantic (Goldenberg et al., 2001), we calculated the probability of occurrence of a hurricane of a given intensity, Pr(H), as a function of the average frequency (B) determined from Boose et al. (2001), (Table 3) and Y, a sine function that generates the periodicity observed in the historical record.
Y takes the form:
where x= 4t/A, A is the duration of the multi-decadal cycle in years, and t is the number of years since the start of the cycle. We used A= 40 yr based on recent published data (Goldenberg et al., 2001).
We explored the implications of an increase in the return interval of severe hurricanes concurrent with the multi-decadal pattern by adding a trend to eq. 3a as follows:
Since two recent studies have reported a near doubling in destructive potential of hurricanes in the record (Emmanuel, 2005; Webster et al., 2005), we used a value of m= 0.125 which causes a doubling in hurricane regime severity over the length of two complete cycles (i.e. 80 yr). Technically, storm severity corresponds to the expected mean probability of mortality of a well-mixed stand with a full size distribution of trees (Table 3).
For each of these two scenarios (baseline & increased storm severity), we performed 10 simulations of 300 yr. Initial conditions for runs in each region had seedling numbers available for recruitment that were proportional to the average relative abundance of each species in the four storm disturbance regions (Table 1). These initial abundances were selected to create forest stands that were representative of 100-yr old conditions in each region. Abundance figures were calculated using US Forest Service inventory data (Iverson and Prasad, 1998) and were adjusted to produce an initial density of 225 seedlings ha−1, which generate observed adult densities (Pacala et al., 1996). Seedlings were distributed randomly in a 300 × 300 m simulated stand. The initial 100 yr of the simulations were used to generate forest stands representative of conditions (e.g. diameter distributions) observed in the region. Windstorm scenarios were applied starting at 100 yr through the end of the simulations (300 yr). At each time step, we calculated total number of trees for each species. Aboveground biomass was estimated using US Forest Service dimension analysis equations (Jenkins et al., 2003) and average percent carbon in tree biomass was assumed to be 50% (Koch, 1989). Carbon sequestration over the 300 yr of the simulations was calculated as net annual growth in biomass minus rate of biomass loss through mortality or wind damage (Brown and Schroeder, 1999). We also calculated total biomass in aboveground woody production downed in storms. Carbon in this pool may be incorporated into the soil through decomposition, although dead wood in these temperate forests may take many decades to decompose (Harmon et al., 1986). Alternatively, carbon in felled timber may be respired, salvaged for commercial uses or burned to the atmosphere due to increased susceptibility to fires (Foster et al., 1997; McNulty, 2005). Total aboveground productivity was calculated as net annual growth in biomass plus annual dead biomass (Brown and Schroeder, 1999).
To ensure that the range of carbon sequestration predicted by our model was within the range observed in other studies, we compared it with other independent estimates. However, the last severe storm to affect forests in the study region was the 1938 hurricane. Since independent data used to estimate biomass storage in aboveground biomass in the region (e.g. US Forest Service Inventory analyses in the NE) were collected in periods free of hurricanes (1970–1990), we used the model in a hurricane-free scenario to calibrate rates carbon sequestration in aboveground biomass. Estimates of carbon storage for 100, 150 and 200 yr periods in the absence of hurricanes were 1.69, 1.45 and 1.11 tons Cha−1 yr−1 well within the 1–4 tons Cha−1 yr−1 range measured from forest inventory data (Birdsey, 1992) and from eddy covariance methods (Goulden et al., 1996).