Chapter 6
A SIMULATION MODEL OF THE RESPONSE OF
VEGETATION TO HURRICANE DISTURBANCE
Modeling is done to aid the conceptualization 
and measurement of complex systems and, sometimes, 
to predict the consequences of an action that 
would be expensive, difficult, or destructive to 
do with the real system. ... Modeling is needed 
for the understanding of nature because the 
complexity of nature is often overwhelming.
                                          C.A.S. Hall

                                 INTRODUCTION
     In this chapter, I review concepts relative to the
development of spatially-explicit simulation models of
ecosystem function, describe the development and
parameterization of a model that incorporates the results of my
study of hurricane damage and recovery, and report on the
results of initial simulation experiments.  

     Simulation models are used in ecology in a variety of
ways, to meet a variety of purposes.  Models are: formalization
of what we know about a system, simplifications of the system
under study - toward specific research goals, and tools for
investigating conditions that are difficult to observe or
create.  They may lead to: generation of hypotheses, accurate
predictions about future system states, or the discovery of
emergent properties of the system (Caswell et al. 1972, Botkin
1977, Hall & Day 1977).  Models may be mechanistic or
descriptive, deterministic or stochastic, and may vary in
spatial and temporal resolution.  

     Descriptive models include the relationship among
variables without necessarily incorporating the underlying
physiological mechanisms.  Mechanistic models tend to be more
easily transferred to a new site or to new conditions, where a
descriptive model may not be extrapolated safely beyond the
conditions for which it was developed.  However, descriptive
models can be valuable first attempts at formalizing a complex
system, and may suggest procedures for investigating the
underlying mechanisms (Hall & Day 1977).

     Deterministic models have no random component, and, in
different simulations, give the same output value for the same
input or starting conditions.  Where the model is expected to
generate values within a typical distribution, or where the
range of possible outcomes are of interest, such as in
sensitivity analysis, stochastic simulations may be preferable. 
A stochastic model incorporates the generation of random output
around a specified mean or within specified minimum and maximum
values. 

     Temporal resolution of a model should be determined by the
rates of change of the processes incorporated.  The same is
true for the spatial scale of a simulation model with respect
to the spatial scale of the system of interest (Kowal 1972). 
Spatially-explicit models, those that incorporate variation of
parameters over a landscape, are required when the system of
interest, or the processes incorporated into the model, vary
over the landscape or include interactions among landscape
components.

RECOVER: A HURRICANE DISTURBANCE AND RECOVERY MODEL
     I synthesize the empirical work of this project through
the development of a spatially-explicit landscape simulation
model of hurricane disturbance and recovery, RECOVER.  This
model simulates pattern of disturbance severity over the
landscape and the resulting vegetation response in terms of
tree community changes, biomass accumulation, and canopy
restructuring.

     RECOVER is descriptive, and fits damage and recovery
curves to field data. The portions of the model that are driven
by position in abiotic gradient space might be considered
mechanistic, although the physiological processes that result
in differential growth rates are not incorporated.  This model
has options for stochastic simulation, varying the starting
points of recovery based on the averages and standard
deviations of the field measurements of response to hurricane
disturbance (API, biomass accumulation, and canopy structure). 
The model is spatial explicit, but uses the position in the
landscape only to identify topographic positions.  Beyond that
function, each grid cell is processed as an independent unit. 
The spatial scale of the simulation can be adjusted based on
the available geographic data.  The temporal scale is set at
one time step per month.  

     Vegetation recovery from hurricane disturbance in the LEF
has been quantified in a variety of ways including: biomass
accumulation (Chapter 4, see also Crow 1980, Weaver 1986b, Hall
et al. 1992b), recovery of physical structure (Chapter 5, see
also Crow 1980, Brokaw & Grear 1991), or tree community
composition changes (Chapter 3, see also Crow 1980, Doyle 1981,
Weaver 1986b).  I include all three of these measures in this
model of recovery. 

     RECOVER can be used to investigate assumptions about the
dynamics of recovery, or the impacts of changing the hurricane
disturbance regime on landscape patterns and ecosystem
processes.  Typically, ecosystem processes, such as biomass
accumulation, have been viewed as following an asymptotic curve
during recovery from disturbance.  This has been the approach
used for many models applied to the LEF (Hall et al. 1992b,
Everham et al. 1993).  Bormann and Likens (1979a, 1979b)
suggest an alternative perspective on the phases of recovery in
a temperate hardwood forest: reorganization, aggradation,
transition, and steady state (see Figure 6, Preface).  The
reorganization phase is characterized by a continuing decline
in ecosystem structure or function (e.g biomass) immediately
following disturbance.  Foster (1988b) observed periods of
decline in biomass followed by rapid increases after a series
of disturbances to a forest in Massachusetts.  This appears
consistent with the concept of a reorganization phase.  In
Bormann and Likens' model, the system goes through aggradation
and transition phases to reach a sustainable (steady) state. 
The four-phase model of recovery is similar to the pattern of a
perturbation-dependent system as described by Vogl (1980; his
Figure 1), and the "stationary process" suggested by Loucks
(1970; his Figure 7).  

     I developed recovery algorithms based on Bormann and
Likens' phases that include the delayed mortality associated
with hurricane disturbance (Walker 1995).  If the LEF follows
this pattern of recovery, the timing of any subsequent
disturbances may be particularly critical.

      Lugo and Scatena (1994) stated the LEF is in a "continued
state of adjustment from the last major disturbance event". 
Basnet (1992) predicted that "a steady state is not possible". 
These predictions are dependent on the spatial scale of
analysis.  At a fine spatial resolution individual stands of
forest may reach an equilibrium, but this may not occur for the
landscape as a whole.  These views are supported by Weaver's
(1986b, 1989) and Crow's (1980) data for the tabonuco forest
which shows a convex but not yet flat biomass recovery curve,
and the colorado forest where the recovery is described as
linear.  Again, the slope of the curve of recovery will
influence the impacts of subsequent disturbance, particularly
if the disturbance regime changes.  RECOVER allows adjustment
of both the endpoint of recovery (i.e. the assumed biomass
levels with a steady state) and the time required to reach this
endpoint.

     Therefore, RECOVER is used to examine three questions:

     1. What would be the implications of recovery that follows
        the four-phase Bormann and Likens model?

     2. What is the impact of the assumption that recovery time
        is less than the return time for hurricane disturbance
        as opposed to the assumption that the forest is in a
        constant state of recovery?

     3. What are the possible impacts of changes in the
        hurricane disturbance regime?  


                              MODEL DEVELOPMENT
     The simulation model RECOVER includes specific subroutines
to: determine topographic position (TOPOGRPH), determine
exposure and simulate damage to a given storm event (EXPOSE,
DAMAGE), and to simulate recovery of community composition
(SUCCESS), biomass (BIOMASS), and canopy structure (CANOPY)
(see Figure 5, Preface).  Recovery dynamics can be manipulated
based on projected endpoints, length of time to recover, and
the presence of a reorganization period defined by additional
mortality following the disturbance event.  The output options
include:  hurricane damage variables for each grid cell
following each hurricane in the simulation, recovery variables
for selected grid cells for all time steps, and recovery
variables for all grid cells for selected time steps during
recovery.  Directions for use of the model can be found in
Appendix E - RECOVER Version 1.0.

             Topographic position

     One assumption of this modeling effort is that ecosystem
properties vary along gradients of abiotic factors, and that
topographic position is a strong determinant of the variation
in these abiotic factors.  Vegetation properties (species
composition, diversity, biomass, productivity, canopy
structure), have been demonstrated to vary with topographic
position in the LEF (Crow & Weaver 1977, Crow & Grigal 1979,
Weaver 1986b, Heaton & Letourneau 1989, Weaver 1991, Johnston
1992, Basnet 1992, 1993; Scatena et al. 1993, Scatena & Lugo in
press).  To expand assumptions regarding vegetation dynamics
over the landscape requires the ability to convert readily
available geographic data - elevation, slope, and aspect - into
a map of topographic positions - ridges, slopes, valleys, and
benches.  Towards this goal I developed the subroutine
TOPOGRPH.  This program module uses elevation differences to
identify topographic features.  

     For each grid cell, the subroutine searches the eight
surrounding cells.  This is similar to the approaches used by
Zevenbergen and Thorne (1987) and Bevacqua and Floris (1987),
but does not include tracking of linear features (Bevacqua &
Floris 1987, Jenson & Dominque 1988).  Since this search window
operates on cells surrounding the target cell in all
directions, additional algorithms were developed for the edges
of a map.  The window is searched for the lowest and highest
elevations, and identified using an aspect code (Figure 45). 
The location of these maximum and minimum elevations in the
window are used as references to search for and identify
topographic features.


Figure 45 - Topographic position search window.  The highest
and lowest elevations in the nine grid cell window are
identified using the codes 0 - 8.


     After the high and low elevation points in the window are
identified, the topographic position for the grid cell in the
center of the window is checked as a valley, ridge, bench, or
slope, in that order.  A valley is identified when the cells to
either side of the low point in the search window are higher in
elevation than the cell in the center of the search window
(Figure 46).  A ridge is identified when the cells to either
side of the high point in the search window are lower in
elevation than the cell in the center of the search window. 
The difference in elevation required to identify a ridge or
valley is set with the variable SLPCHG, the change in elevation
(as a percent slope) required.  The setting for this variable
is critical, as it acts as a filter to elevation changes.  For
either valleys or ridges, the aspect of the topographic
feature, which may differ from the aspect of the center cell,
is determined based on the direction of the low or high point,
respectively.  A bench is identified when the difference      
between the maximum and minimum elevations is less than the
elevation change required to identify a slope (set at 15% for
my simulations).  All cells that are not identified as valleys,
ridges, or benches (in that order) are assumed to fall into the
slope category.  These search and selection algorithms account
for 30% of code in RECOVER.


Figure 46 - Examples of cells used to identify valleys or
ridges.  A is the grid cell of interest.  B is the minimum or
maximum point of the search window.  Cells 1, 2, 3, and 4 are
checked for higher elevation, indicating A is a valley; or for
lower elevations, indicating A is a ridge.  Note that cells 3
and 4 are outside the search window and may not be available
near the edge of the map.


     With this approach, the spatial resolution is critical and
must be matched to the variation in both the topography and the
process (hurricane damage) of interest.  A scale that is too
gross will miss fine scale variation in the landscape that
affects patterns of damage.  Spatial resolution at too fine a
scale results in a misidentification of topographic features
since the search is limited to five times the grid cell size
(the grid cell and two cells in each direction).  For example,
a ridge top might be identified as a bench if the sides of the
ridge are not captured by the search window.  Preliminary data
exploration indicates that modeling the landscape at a scale of
a 10 m square grid cell should capture the variation in
topography, and spatial pattern analysis of hurricane damage
indicates that a spatial resolution of 10 m should capture the
pattern of damage over the landscape (see Chapter 2).  However,
a grid cell of 10 m square may be impacted by damage in
adjacent cells.  This fine scale simulation is not expected to
simulate damage accurately for all cells at that scale.

    Storm Intensity and Severity of Damage

     The subroutine STORM reads in, or simulates times and
storm characteristics (intensity and path), for hurricanes
impacting the forest.  The presence of a storm for a given year
is determined based on the probability for each year, 0.0517
(based on 15 storms per 290 years; Salivia 1972, Weaver 1987). 
The exact month for a hurricane in a given year is distributed
from June to November based on the frequency of occurrence for
storms in each month (Salivia 1972, Weaver 1987).  The path of
the storm: south, west, north, east of, or directly over, the
LEF; and the direction of the storm track: west, northwest,
north, or northeast, also are simulated based on the
probabilities as determined by the hurricane history. 

     Once the data for a given storm are read in, or simulated,
the exposure for each grid cell is determined.  This value is
calculated at two scales, large-scale exposure (LSE) and small-
scale exposure (SSE).  LSE is determined by the side of the
mountain (south, northeast or northwest) relative to the path
of the storm.  A value of 1 to 4 (increasing exposure) is
assigned based on the position of side of the mountain relative
to the path of the storm.

     SSE is based on the topographic position and the aspect of
the topographic position.  For example, valleys are generally
sheltered from the wind.  A valley grid cell with an aspect
away from the hurricane winds would have a SSE value of 1. 
However, a valley with an aspect in line with hurricane winds
is scored as a 10.  The LSE and SSE are combined to one
exposure rating.  The model provides three options for the
combination: 1) equal weight, 2) LSE weighted twice as much as
SSE, or 3) SSE weighted twice as much as LSE.

     Finally, exposure is used to simulate damage values of
both structural damage and mortality.  Both ways of quantifying
damage are calculated using exposure and intensity of the
storm; and allows modification of these values based on soil
type, tree community, or disturbance history:

 Structural                       Storm        Soil     History
   Damage   = (Exposure * 10) * Category/5 * Modifier * Modifier 

Compositional                     Storm        Soil      History
   Damage   = (Exposure * 3.5) * Category/5 * Modifier * Modifier 

     A review of the literature on catastrophic wind impacts
indicates that although structural damage may reach extremely
high levels, mortality seldom exceeds 35% in tropical forests
(see Chapter 1).  Therefore, compositional damage is set at a
maximum of 35% (exposure of 1 to 10 multiplied by 3.5).  This
value for mortality may be too low at finer spatial scales
where a small plot might experience 100% mortality.

     The soil modifier is defined by a look-up table that
specifies each soil type's impact on damage.  Then, maps of
soil types for the area are input.  A similar approach is used
for the disturbance history of the site; defining the extent to
which previous disturbance facilitates or mitigates subsequent
hurricane damage, then inputing a map of the disturbance
history.  In subsequent disturbances in the same simulation,
Average Pioneer Index (API) values are used to modify damage,
replacing the history modifier.

           Community Dynamics

     Community dynamics are quantified as changes in API. 
Damage levels are used to categorize each grid cell as above or
below 1.33 API (see Chapter 3).  Within each category, the API
value is stochastically simulated based on the average and
standard deviation of the field measurements.  The API value
established after the disturbance is held constant for 40
years, then gradually moves to a value of 1.0 (all primary
forest species) over the next 20 years.  This pattern is
thought to reflect the life span of the pioneer species that
establish after the disturbance (Silander 1979, Weaver 1983). 
If the recovery dynamics are set to include a reorganization
period as in the four-phase recovery model, this period is set
at five years.  During this five-year reorganization period,
additional hurricane-induced mortality occurs (Walker 1995,
Everham unpublished data).  For each time step a new API is
generated stochastically, and the additional mortality is
reflected as an additional decline in biomass.  If the plot has
an API value of less than 1.33 and the additional mortality
results in a shift across the line in the gradient space of
compositional and structural damage, the API value shifts to
greater than 1.33.  This shift then impacts the dynamics of
canopy restructuring.  At the end of five years the API
stabilizes for the next 35 years, then again begins to shift
toward 1.0.

               Biomass Recovery

     Initial biomass levels are set based on topographic
position using values from Scatena and Lugo (In press), who
found predictable trends in standing biomass based on position
along a catena.  These values are decreased proportionally
based on the percent structural damage.  Recovery to the
original values is based on asymptotic curves, and is set to
complete recovery in 60 years (Crow 1980).  Maximum biomass
levels are based on topographic position (Scatena & Lugo in
press) and the steepness of the recovery curve is based on the
growth rate as defined by position in the gradient space of
available water and solar radiation.  This results in 12
different recovery curves (three growth rates and four
endpoints).  These recovery curves can be manipulated further
by adjusting either the endpoints or the length of time
required to reach them.

         Recovery of Canopy Structure

     Canopy structure, the amount and distribution of plant
biomass (Chapter 5), is quantified as LAI and percent cover for
each of the canopy layers.  These values are initialized before
disturbance based on values from Brokaw and Grear (1991).  The
data of Brokaw and Grear, for the tabonuco forest, was not
collected based on differences in topographic position, and
Weaver (1991) found no variation in canopy closure based on
topography.  So, I assume that the values are constant across
the landscape, except for the impacts of ridges and valley on
the lowest two canopy layers (see Chapter 5). 

     The initial canopy structure values are decreased by a
proportion based on the percent structural damage.  LAI then
recovers based on an asymptotic curve within 24 months (F.
Scatena personal communication).  Recovery of the canopy
structure varies based on the category of API.  In plots with
API less than 1.33 recovery of the upper canopy levels is based
on asymptotic curves to pre-disturbance levels (Figure 47A).   


Figure 47 - Simulated pattern of canopy structure dynamics
following hurricane disturbance in plots dominated by regrowth
of primary forest species (API > 1.33) (A) and plots dominated
by recruitment of pioneer species (API < 1.33) (B).


The lower canopy levels respond to the initially higher solar
radiation penetration and the percent cover exceeds pre-
disturbance levels.  As the stucture increases in the upper
canopy levels, the lower canopy levels are shaded out and the
percent cover drops back down to initial conditions. 

     The recovery of the plots with API greater than 1.33 is
more complex (Figure 46B).  The recovery of the top two canopy
layers are delayed, as the principally newly-established
pioneer species grow up to these levels.  As with the plots
with API less than 1.33, the lower canopy levels first increase
in cover rapidly, then decrease.  As the pioneer species grow
up into the canopy, a temporary, dense, lower canopy is
established which shades out the levels below it.  Therefore,
the percent cover of the lower two canopy levels in plots with
API greater than 1.33 first increase rapidly, then rapidly
decrease as they are shaded out.  This decrease lowers the
percent cover below pre-disturbance levels, then as the canopy
moves higher and self-thinning occurs, percent cover of these
lowest levels comes back up to the pre-disturbance levels. 
These complex patterns of recovery are extrapolated from my
measured canopy structure values in the first five years. 

                      SIMULATION METHODOLOGY
     Validations - As both BEW and HRP data were utilized in
developing this model, comparisons with this data can not be
viewed as a true validation of the model.  However, RECOVER
links topographic classification, determination of exposure to
a given storm, simulated damage values, and uses damage,
topographic, and additional primary abiotic gradients to
determine recovery dynamics.  Simulations that accurately
reproduce the complex dynamics in both the HRP and BEW should
demonstrate the integrity of this synthesis.

     To compare the completed model to empirical results at
both sites, I initially simulated the storm impacts and
recovery for the first four years after Hurricane Hugo.  This
simulation provides several opportunities to validate the
model.  For the HRP, which has been completely classified for
topographic position (Zimmerman et al. 1994, also see Chapter
2), the results of the topographic classification generated by
TOPOGRPH are compared to the previous description.  For both
the HRP and the BEW, the empirical measures of damage at each
plot are compared to the simulated values.  Finally the
simulated recovery for each plot are compared to the empirical
data.

     Simulation Experiment 1 - Recovery dynamics - I ran a 200
year simulation at both study sites, using historical data on
the paths of 12 hurricanes from 1807 up to and including Hugo
in 1989.  Then the simulation ran for 18 years following Hugo. 
Hurricane intensity data (Simpson Index) were not available for
storms before this century, so I used simulated values based on
the distribution of storms of known intensity.  

     Simulation 1A - (baseline) using a 60 year recovery period
          and an asymptotic recovery curve

     Simulation 1B - (four-phase) including a reorganization
          period of five years with additional mortality of 50%
          of initial hurricane mortality.  

     Simulation 1C - (recovery time) using a period of
          recovery of 100 years and multiplying the starting
          biomass (and therefore maximums of the asymptotic
          curves) by 1.67 (100 yrs/ 60 yrs).

     Simulation Experiment 2 - Disturbance Regime - 
Next I simulated a hurricane disturbance regime for 1000 yrs using
current frequency and intensity probabilities.  I then doubled
the storm probability from 0.0517 to 0.1034 per year resulting
in a change from 48 storms in 1000 years to 104 storm in the
same period.  Finally, I changed the probability of storm
intensities (Emanuael 1987), doubling the probability of more
intense storms (category 3, 4 and 5 storms) and correspondingly
decreasing the probability of category 1 and 2 storms (one half
and one third respectively) (Table 20).  This provided four
scenarios to examine the third question: What are the
implications of a changing disturbance regime?  

     Simulation 2A - (baseline) 1000 years with 48 storms using
          current distribution of intensity 

     Simulation 2B - (doubled intensity) 1000 years with 48
          storms using new distribution of intensity

     Simulation 2C - (doubled frequency) 1000 years with 104
          storms using current distribution of intensity

     Simulation 2D - (doubled frequency and intensity) 
          1000 years with 104 storms using new distribution of
          intensity


TABLE 20 - Probabilities and resulting storm intensity distributions for
     simulation Experiment 2.  Simulation using STORM subroutine.
Simpson's Historical  Simulated    Doubled   Climate  Simulated    Doubled
 Index   Probability Distribution Frequency  Change  Distribution Frequency
Category                N=48        N=104  Probability   N=48       N=104
   1       0.40          19          39     0.20 (-50%)      9         20
   2       0.30          12          29     0.20 (-33%)      8         19
   3       0.15           8          21     0.30 (+100%)    15         34
   4       0.10           6          11     0.20 (+100%)    11         22
   5       0.05           3           4     0.10 (+100%)     5          9



                                   RESULTS
     RECOVER appears to capture the spatial variation in
hurricane impacts and recovery and accurately quantifies these
values when averaged over the landscape, but does not predict
these variables accurately for all points on the forest at a
resolution of 10 m by 10 m.

     Validations - The empirical data and simulated values for
all 43 plots are listed in Appendix C-XVII.  Aggregate
simulated values for each site tend to correspond well to
empirical averages, but the deterministic algorithms do not
capture the variance between individual plots.  In addition,
simulated mortality, and percent cover in the upper two canopy
levels (Surviving 20-30 m, and Canopy 12-20 m) are consistently
higher than empirical values.  Even with higher average
mortality values, the simulated API is consistently lower than
the empirical values.  Simulated compositional damage values do
not reach the extremely high levels found in some of these
small plots.  This may explain the rarer occurrence of plots
with simulated API greater than 1.33. 

     Problems with topographic classification may also minimize
the variance of simulated damage values.  Both ridges and
valleys were under-identified in the classification of the HRP. 
Slopes, the default topographic feature, had the highest number
of grid cells incorrectly placed in that category (Figure 48).
Overall, 75% of the grid cell classification from subroutine
TOPOGRPH matched the classifications established for the HRP.


Figure 48 - Validation of topographic classification subroutine
in RECOVER.  For each topographic position, the number of grid
cells correctly identified and the number classified as that
topographic position, but actually belonging to another
category (based on previous classification; Zimmerman et al.
1994), are displayed.  N = 1600. 


Figure 49 - Simulated recovery of Leaf Area Index during the
first four years after Hurricane Hugo in both the Bisley
Experimental Watersheds (BEW) and the Hurricane Recovery Plot
(HRP).


Figure 50 - Simulated changes in biomass during the first four
years after Hurricane Hugo in both the Bisley Experimental
Watersheds (BEW) and the Hurricane Recovery Plot (HRP).


Figure 51 - Canopy dynamics during the first four years after
Hurricane Hugo in both the Bisley Experimental Watersheds (A)
and the Hurricane Recovery Plot (B).


TABLE 21 - Results of long-term simulations of both Bisley
Experimental Watershed and Hurricane Recovery Plot.  Simulation
Experiment 1 investigates dynamics of recovery, using the historical
hurricane record from 1807-2007.  Simulation 1A used an expected
recovery time of 60 years.  1B included a five-year reorganization
period incorporating delayed mortality.  1C used a 100 year recovery
time and elevated endpoints for biomass.  Simulation Experiment 2
investigates the impacts of changing the disturbance regime, over a
1000 year time frame.  2A used historical patterns of frequency and
intensity.  2B used a distribution of storm intensities resulting in
twice the number of category 3 and larger hurricanes, and
correspondingly fewer mild storms. 2C used an increased storm
probability resulting in twice the number of storms. 2D combined 2B
and 2C, using both increased frequency and increased intensity of
hurricanes.   
  Simulation  API  Biomass Surviving  Canopy  Subcanopy   Shrub    Herb
                   (Kg/m2)a (20-30m)  (12-20m)  (4-12m)   (1-4m)   (0-1m)
                              (%)       (%)       (%)      (%)      (%)
     1A      1.24    17.97     37.1     73.8     75.0     71.9    59.3
     
     1B      1.41    17.89     31.5     65.9     77.1     65.6    54.9

     1C      1.24    27.98     37.1     73.8     75.0     71.9    59.3
     2A      1.19    17.95     43.0     77.4     75.6     67.1    55.1

     2B      1.27    17.65     40.2     75.1     76.9     62.8    52.1

     2C      1.26    16.64     30.0     67.0     75.5     74.9    63.2

     2D      1.31    15.88     27.4     60.3     76.5     71.2    61.2
     a standing biomass given as Kg/m2 in tables, text, and figures to 
facilitate shifts in spatial scale of simulation. Multiple by 10 to
convert to t/ha.

     
     The simulated patterns of recovery during the first four
can be illustrated by several of the parameters.  LAI recovers
at both sites in the first two years (Figure 49).  Biomass 
levels are higher in the BEW (Figure 50), even though this site
was impacted more by the hurricane (simulated average
structural damage of 21.3 compared to 16.0 for the HRP).  Both
sites show a steady increase in biomass levels.  Canopy
dynamics are more complex (Figure 51) and illustrate the
difference between the two sites.  The percent cover of the
surviving layer (20-30 m) and the canopy layer (12-20 m) are
the lowest in the BEW, but are much higher in the HRP.  The
percent cover in the lowest two levels (Shrub and Herb) are
decreasing in the BEW as the subcanopy established by
recruiting pioneer species shades out the lower levels.


Figure 52 - Simulated changes in Average Pioneer Index in the
Bisley Experimental Watersheds over 200 years comparing the
impacts of including a five year reorganization period that
includes additional mortality. 
      

Figure 53 - Simulated changes in biomass over 200 years in the
Bisley Experimental Watersheds, comparing the impacts of
including a five year reorganization period with additional
mortality, and changing the maximum biomass and length of
recovery. 

     Simulation Experiment 1 - Recovery dynamics - The results
for the investigation of the impacts of different assumptions
about recovery dynamics are shown in Table 21.  When a
reorganization period is included (1B), the API value for the
entire simulation increases (from 1.24 to 1.41).  The
additional mortality elevates the API for many storms where the
API without a reorganization period stayed below 1.33 (Figure
52).  These changes in API influence the dynamics of the
recovery of the canopy structure, lowering the percent cover in
the Surviving and Canopy layers.  The reorganization period had
little impact on biomass, lowering it slightly (Table 21 and
Figure 53).

     Increasing the length of recovery and the endpoint for
biomass (1C) raises the average biomass significantly, and
appears to increase the slope of the recovery curve.  Otherwise
the pattern of disturbance and recovery follows that of a
shorter recovery period.

     Simulation Experiment 2 - Disturbance Regime - The results
for the investigation of the impacts of changing the
disturbance regime are shown in Table 21.  Increasing either
the frequency or intensity of the hurricane disturbance regime
increases API, decreases average biomass, and decreases the  
percent cover in the upper canopy layers.  These results are
similar to those of O'Brien et al (1992), but at much lower,
and more realistic disturbance levels.  O'Brien et al. (1992)
demonstrated significant impacts on forest structure and
composition, but ran simulations with intensities up to 100%
mortality, and frequencies up to one storm every year. 


Figure 54 - Simulated changes in Average Pioneer Index over
1000 years in the Hurricane Recovery Plot, comparing the
impacts of: A - increasing the intensity of hurricanes, B -
increasing the frequency of hurricanes, or C - increasing both
frequency and intensity of hurricanes.


Figure 55 - Simulated changes in biomass 1000 years in the
Hurricane Recovery Plot, comparing the impacts of: A -
increasing the intensity of hurricanes, B - increasing the
frequency of hurricanes, or C - increasing both frequency and
intensity of hurricanes.


Figure 56 - Simulated changes in percent cover of the Surviving
canopy layer (20-30m) over 1000 years in the Hurricane Recovery
Plot, comparing the impacts of: A - increasing the intensity of
hurricanes, B - increasing the frequency of hurricanes, or C -
increasing both frequency and intensity of hurricanes.


     For changes in API, increasing frequency or intensity has
equal impact, each increasing the API from 1.19 to 1.26 and
1.27, respectively (Table 21).  However, the increased
frequency of storms results in no periods between storms long
enough to allow the forest to return to an API of 1.0 (Figure
54B).

     Biomass values (kg/m2) also are impacted more by changing
the frequency than the intensity of storms (lowering the
biomass from 17.95 to 16.04 or 17.65 respectively) (Table 21). 
Figure 55 represents these differences graphically.  Increased
intensity (Figure 55A) still results in periods of the biomass
reaching a steady state, but this steady state is 
not reached if the frequency of storms is doubled  (Figure 55B).

     A similar pattern exists for the percent cover of the top
canopy layer (20-30m).  The disturbance regime of doubled
intensity of storms decreases the percent cover to a greater
extent following the more intense storms, but the canopy is
able to recover to pre-disturbance levels (Figure 56). 
Doubling the frequency of disturbance results in the canopy
cover never recovering completely.

                                 DISCUSSION
     The comparison of empirical data to the simulated values
of the recovery following Hurricane Hugo indicates that RECOVER
is a successful synthesis of the dynamics of hurricane
disturbance and recovery, and may be a valuable tool for
generating hypotheses about this process.   

     Simulation Experiment 1 indicated little impact from
incorporating a reorganization period following hurricane
disturbance, at least if this period is defined and quantified
by additional mortality.  Changing the time required for
recovery also had little impact.  The higher biomass levels
seemed due to the elevated end points only.  However, the
simulated results for both recovery times (60 and 100 years)
seem to support the statement by Lugo and Scatena (1994) that
the forest is in a constant state of recovery.  In both the
historical simulations and the 1000 year projections, biomass
rarely reaches a steady state and never remains there for long. 
A steady state is possible, with a long period between storms,
but these long periods seldom occur.

     Simulation Experiment 2 indicates that changes in storm
frequency would have more of an impact than changes in storm
intensity.  The forest can recover from more intense storms if
given enough time before the next intense storm.  When storms
become more common, the vegetation is held in a continual state
of recovery.

     Future research, and modification and applications of
RECOVER should include:

expansion of simulations to the entire tabonuco forest zone
validation with independent data sets
additional data collection 
modifications to the model structure related to 
vegetation dynamics
incorporating faunal dynamics 

     Expanding the simulations to the entire tabonuco forest
should be relatively simple.  Elevation and soil data exists,
so the topographic features can be determined and the soil
water and solar radiation gradients can be simulated.  This
expansion would allow validation with independent data sets.

     Additional data collection should focus on validating the
simulated abiotic gradients of solar radiation and soil
moisture.  If these gradients do quantify the impacts of
disturbance and control the dynamics of recovery, we must be
able to represent the variation of these gradients over the
landscape accurately.  In addition, monitoring the recovery of
biomass and canopy structure, and the changes in community
composition, should continue.  This will allow future
validation and modifications of the extrapolation of RECOVER
beyond the four years of empirical data.

     Nutrient availability should be incorporated into the
abiotic gradient quantification.  The CENTURY model is
available for simulating nutrient levels in the LEF (Sanford et
al. 1991, Everham et al. 1993) and requires only its
modification to a spatially-explicit structure.

     Finally, the simulated canopy structure can be correlated
to population dynamics of the faunal species, allowing
simulation of the dynamics of recovery over the landscape of
these organisms.  

     RECOVER incorporates the empirical results of this study
into a simulation tool which may be used to further investigate
the dynamics of hurricane disturbance and recovery.

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