Simulation of the carbon dynamics of a Florida slash pine plantation

Ecological Modelling, 66 (1993) 231-249

231

Elsevier Science Publishers B.V., Amsterdam

Simulation of the carbon dynamics of a Florida slash pine plantation Wendell P. Cropper, Jr. and Henry L. Gholz Department of Forestry, UniL'ersity of Florida, Gainesc'ille, FL, USA (Received 3 October 1991; accepted 5 June 1992)

ABSTRACT Cropper, W.P., Jr. and Gholz, H.L., 1993. Simulation of the carbon dynamics of a Florida slash pine plantation. Ecol. Modelling, 66: 231-249. A model of the carbon dynamics of a Florida slash pine (Pinus eUiottii) plantation was designed to use as a tool to scale up physiological data to the stand level, and to address questions about the dynamics of the labile carbon pool (starch + sugars) and fertilization responses. The model adequately simulated labile carbon dynamics, stem growth, and root respiration over a 2-year period. Measured labile carbon pool dynamics were consistent with the simulation based on a daily balance between inputs of net canopy assimilation and outputs of respiration and growth. Increased stem growth following fertilization can be simulated as a consequence of increased foliage mass; no other changes in allocation patterns or physiological responses to fertilization were evident.

INTRODUCTION

Pine flatwoods are the most extensive type of terrestrial ecosystem in Florida (Abrahamson and Hartnett, 1990). These forests, found within a matrix of lakes and cypress swamps, grow on sandy, nutrient- poor, and poorly drained soils with relatively little topographic variation. In this century, the natural, open, fire-controlled flatwoods forests, dominated by Pinus palustris, have largely been replaced by human development and plantations of the less fire resistant slash pine (Pinus elliottii). Pine plantations currently cover greater area (4 x 10 6 ha) than natural pine forests in Florida, and slash pine forests make up 69% of the coniferous forest types in Florida (Brown and Thompson, 1988). Slash pine plantations provide the Correspondence to: W.P. Cropper, Jr., Department of Forestry, University of Florida, Gainesville, FL 32611, USA. 0304-3800/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved

232

W.P. C R O P P E R A N D H.L. G H O L Z

advantage over natural forests of a relatively uniform structure dominated by a single native tree species and a relatively simple understory. These characteristics simplify ecosystem studies and model development. Process-based simulation models may be the best method available for synthesizing isolated results from parts of ecosystems into a potentially predictive framework (,~gren et al., 1991). Our simulation model of slash pine stand carbon dynamics (the SPM) was designed to meet the following specific objectives: 1. To provide a method of scaling-up an extensive data base of field measurements of physiological and ecological processes to the stand level. When integrated throughout the canopy, needle photosynthesis is expected to be closely related to biomass accumulation (Isebrands et al., 1990). 2. To test whether increased stem growth on fertilized plots is consistent with the increased foliage mass and available photosynthate, rather than a change in the allocation pattern to stems. 3. To test whether the dynamics of the labile (non-structural) carbon pool can be realistically simulated as a daily balance between assimilation, respiration and growth. The state of the labile carbon pool may be directly related to the sensitivity of the forest to stress. Previous simulations (,~gren and Axelsson, 1980; Cropper and Gholz, 1990) have demonstrated the difficulties of modeling the labile carbon pool dynamics, due in part to the small size of the pool relative to the magnitudes of assimilation, respiration, and growth. MODEL DESCRIPTION

The SPM is an annual model of a north central Florida slash pine stand. The model starts on March 1, approximating the initiation date of new foliage expansion. Model inputs are hourly air temperature and incident PAR. The SPM was parameterized (Appendix 1) based on mean values (1987) of seven control (non-treated) plots in a 60-ha block of slash pine plantation in north Florida (29°44'N, 82°9'W). The plantation was established in 1965 on a sandy, nutrient-poor soil with a high, but fluctuating, water table. The study site included seven control and eight fertilized 50 × 50-m plots. Fertilization was applied quarterly beginning in February 1987. A more detailed description of the site and treatments can be found in Gholz et al. (1991). The structural components of the SPM include "new" ( < I year old) and "old" ( > 1 year old) slash pine foliage, stem, branches, coarse roots, fine roots in the litter layer, fine roots in the mineral soil, needle litter, dead fine roots, and soil organic matter carbon (Fig. 1). Live pine components are assumed to be 45% carbon (dry weight), and litter and dead fine roots

SIMULATIONOF CARBONDYNAMICS CO 2

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Fig. 1. Diagram of the model. MR is maintenance respiration; DEC is decomposition; Mort is mortality; NCA is net canopy assimilation; GR is growth respiration; TMR is total pine maintenance respiration; and Temp is temperature. The dashed lines represent summed variables from several compartments.

are assumed to be 50% carbon. The labile carbon pool is operationally defined to be the sum of soluble sugar and starch carbon contents of the seven slash pine tissue types. Simulated processes include assimilation, maintenance respiration, growth and growth respiration, decomposition, mortality/litterfall, soil CO 2 evolution, and labile carbon dynamics. Biomass components are simulated with a daily time step, and physiological processes are calculated hourly.

234

w.P. C R O P P E R AND H.L. G H O L Z

Biomass dynamics of the non-foliage structural components of the slash pine trees are simulated as follows:

as, dt = GRi - tz( i ) "Xi

(1)

where X,. is the biomass of compartment i (g- m -2) at time t; GR(i) is the daily growth (g. m -2. day-~); and ~(i) is the mortality rate (day-~). GR is allocated to the pine tree structural components based on partitioning available carbon (net canopy carbon gain-total maintenance respiration) on a daily basis:

pc(i)" A V A I L GRi =

(2)

fc(i)

where pc(i) is the partitioning coefficient; AVAIL is the daily total carbon available for growth (g C O : . m-Z); and fc(i) is a constant that incorporates the fraction of the dry weight of compartment i that is composed of carbon and the conversion of g CO 2 to g C. Partitioning is simulated according to the following rules: 1. When total stand daily maintenance respiration is greater than net canopy assimilation and the labile carbon pool is greater than a lower limit (35 g C - m - Z ) , maintenance respiration of all tissues and new needle growth and growth respiration are supplied from the labile carbon pool and no growth of other structural components occurs. If the labile carbon pool is below the lower limit no needle growth occurs either. We assume that foliage growth has the highest priority for carbon partitioning as a consequence of the relatively short needle retention time ( 2 years). Reduced needle growth of a single cohort can dramatically limit the tree's capacity for assimilation and growth. 2. When daily maintenance respiration is less than net canopy assimilation for the whole stand, available carbon is partitioned to the stem, branches, coarse roots, and fine roots according to the partitioning coefficients. The daily available carbon supplies all new growth and growth respiration of these components. New foliage growth and growth respiration is supplied from the remainder of the daily available carbon, or the labile C pool when the available carbon is insufficient to meet the foliage growth requirement. The seasonal timing (phenology) of simulated woody tissue growth depends on the dynamics of the daily available pool. Available carbon is calculated as: AVAIL = ( NCA - TMR

for NCA > T M R for NCA < TMR

(3)

235

SIMULATION OF CARBON DYNAMICS 24

6

TMR = Y'. Y'. MRESPi" X i h=l

(4)

i=1

where NCA is the daily net canopy assimilation (g CO 2 • m-Z); TMR is the daily total slash pine maintenance respiration (g CO 2- m-2); MRESP, is the hourly maintenance respiration rate (g CO 2 • g-~ tissue • h-t); X i is the tissue dry weight (g. m 2) for living slash pine component i; and h is the hour. During the 2-year simulation period TMR was greater than NCA for 10 days, but the total labile pool was never reduced to the lower threshold limit. The peak of available carbon occurs in October (Fig. 2), after the summer peaks in net canopy assimilation and maintenance respiration, because maintenance respiration declines more rapidly than assimilation with cooler autumn temperatures. Measured slash pine stem radial growth is highest in April to May (Grissom, 1985). To test the significance of this difference, an alternate growth formulation is also simulated. The second method depends on phenology functions (Cropper, 1988), consisting of interpolated tables of relative growth rates of each pine tissue throughout the year and specified net annual growth ( g - m -2) for each tissue. The partitioning scheme tends to produce flatter growth rates than the phenology functions (presumably the actual growth phenology) (Fig. 3). The alternate methods of simulating growth do not greatly influence simulated respiration (Fig. 4), but the labile carbon dynamics are sensitive to the growth formulation (see below, Model Evaluation). We base all of the following simulations in this paper on the dynamic partitioning scheme 12

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Fig. 2. Simulated available carbon (net canopy assimilation - total maintenance respiration) for 2 years.

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Fig. 3. Simulated stem growth based on phenology functions and prescribed annual growth increment, or based on a daily carbon partitioning scheme.

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Fig. 4. Total slash pine maintenance respiration based on biomass calculated by phenology" functions and prescribed annual growth increment or through a daily carbon partitioning scheme (7-day means). because it represents the observed range of the labile carbon pool much more accurately than the simulations based on forced growth rates. Labile carbon dynamics are simulated as a balance of inputs and outputs to the labile carbon pool:

dLC ~- N C A - T M R dt

6 6 E G R i - E GRESPI i=l i=l

(5)

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Fig. 5. Relative vertical distribution of old and new foliage in the canopy and the mean relative gap frequency (h) within the canopy. where LC is the total slash pine labile carbon pool (g C m -2) at time t; and G R E S P i is the daily growth respiration. All units are converted from dry weight or CO 2 to carbon before summing. N e e d l e assimilation is simulated with the following equation (Landsberg, 1986): ap" P A R ' k c" Ci ASSIM =

ap- P A R + k c " Ci

(6)

w h e r e P A R is the photon flux density (/zmol • m -2. s - l) of photosynthetically active radiation, ap is the q u a n t u m efficiency ( m o l / m o l ) , k¢ is the mesophyll conductance ( / z m o l - m -2. s - 1 . > b a r - l ) , and Ci is the internal leaf CO 2 concentration (/zbar). Ci is treated as a constant equal to the m e a n calculated from field data. The assimilation rates of new and old foliage cohorts are simulated separately. The vertical distribution of old and new foliage biomass (Fig. 5) is based on destructive harvest of 120 trees in 6 D B H classes (Gholz et al., 1991). The vertical distribution of the two age classes are similar, with new foliage slightly higher in the canopy. Light attenuation through the canopy follows a modified B e e r - L a m b e r t formulation: P A R x = P A R 0 • exp( - k . F x • h / S E )

(7)

where P A R x is the P A R incident at the midpoint of canopy layer x, P A R 0 is the above-canopy PAR, Fx is the cumulative projected LAI above the midpoint of canopy layer x, h is the relative canopy gap frequency (Sinclair and Knoerr, 1982), SE is the sine of the solar elevation angle, and k is a

238

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Fig. 6. Specific leaf mass function for the new needle cohort (from Gholz et al., 1991).

constant. The adjustment for relative gap frequency (A) is necessary because foliage clumping allows more light penetration than predicted by the standard Beer-Lambert formulation (McKelvey, 1990). The solar elevation angle is calculated hourly using the method of Brock (1981). Foliage biomass is converted to all-sided LAI using a constant specific leaf mass of 118 g- m -2 for old foliage and a function for new foliage (Fig. 6). All-sided LAI is converted to projected LAI by dividing by rr (Grace, 1987). Hourly net canopy assimilation is calculated as follows: 9

NCA = E [ASSIM(n, new) • N F A . + ASSIM(n, old). OFA~]

(8)

n=l

where NFA is the new foliage all-sided area (m-2); OFA is old foliage all-sided area (m-E); and n is the canopy layer. In an earlier, more aggregated, version of this model (Cropper, 1988;Cropper and Gholz, 1990), simulated canopy photosynthesis was modified by soil water and phosphorus terms, but more than 2 years of physiological measurements have indicated that short-term assimilation responses are primarily controlled by incident solar radiation. Fertilization did not alter assimilation rates, and pre-dawn water potentials have remained relatively constant. Mid-day stomatal closure has not been observed, and it has not been possible to relate assimilation rates to vapor pressure deficit or leaf water potential (Teskey et al., unpublished data). We believe that the relatively high water table normally allows avoidance of water stress by slash pines growing on typical flatwoods sites. The biomass dynamics of old and new foliage cohorts are simulated with

SIMULATION

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239

DYNAMICS

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logistic equations to model the phenology of relative needle elongation and cumulative litterfall (Dougherty et al., 1990; Gholz et al., 1991): Yt = K / J 1 +exp(C-R.t)]

(9)

where Yt is the relative (0-1) state of needle elongation or cumulative litterfall at time t; K, C, and R are parameters fit from nonlinear regression; and t is time in days elapsed from March 1. North Florida slash pines have a normal needle life span of 2 years (Gholz et al., 1991), but retention of needle mass into a third year can sometimes occur and can be simulated by adding a residual value to the old needle mass. Old needle mass on March 1 is an initial value input to the model. New needle production is either an initial input or can be simulated based on a relationship with stand basal area, A p r i l - J u n e Growing Degree Days (base 10°C) and total incoming solar radiation (April-June) (Gholz et al., 1991). The climate data are measured during the spring that needles are developing. Simulated foliage mass using the logistic phenology functions compares favorably with foliage mass estimates based on destructive harvest and measured litterfall and needle growth rates (Fig. 7). Long-term litterfall records can provide the foliage biomass data necessary for input, assuming that the current year's litterfall reflects the previous year's foliage production (Gholz et al., 1991). Outputs from the labile carbon pool include maintenance respiration, carbon used to form new structural tissue, and growth respiration. Maintenance respiration is simulated as a function of temperature and tissue mass: MRESP~ = B R ( i ) ' X i • QIO((TEMP-z°)/I°) (10)

240

w.P. C R O P P E R AND H.L. G H O L Z

where MRESPi is the maintenance respiration rate (g CO 2 • g-1 tissue • h -1) of pine component i, Q10 is the rate of change of respiration per 10-degree change in temperature, TEMP is air temperature (°C), X i is the tissue mass ( g - m - 2 ) , and BR(i) is the respiration rate at 20°C. Maintenance respiration for foliage is calculated only at night (assimilation is the net result of photosynthesis and foliage day time respiration). Estimates of base respiration rate (BR(i)) and Q10 are based on in situ measurements we made on slash pine tissues with a controlled temperature cuvette for needles and fine roots (Cropper and Gholz, 1991), and ambient temperature cuvettes for woody tissues (M. Ryan, pers. comm.). Fine root respiration was measured in the litter layer only; the mineral layer fine root base respiration BR was adjusted according to the ratio of annual forest floor and mineral soil fine root respiration reported in Ewel et al. (1987b). Growth respiration is calculated as: (11)

GRESPi = c(i) . GR i

where c(i) is the growth respiration coefficient (g CO z. g - l ) new tissue growth) for living slash pine component i. Estimates for c(i) values were obtained from Chung and Barnes (1977). The needle litter and fine root litter compartments are simulated as follows:

dX, d----~ = • l . t ( j ) ' X j - k d ( i ) ' X

i

(12)

where Xj is the living slash pine component(s) producing litter (g. m-2); X i is the litter compartment mass (g- m-2); and k d ( i ) is the decomposition coefficient (day-l). Decomposition coefficients are based on litterbag measurements for needles (Gholz et al., 1985) and fine roots (Gholz et al., 1986). Soil organic matter dynamics are based on the following equation: dSOM d--'--~ = rd" D F R - kd(som)" SOM

(13)

where SOM is the soil organic matter (g C" m-2); rd the rate that dead fine roots become amorphous soil organic matter (day-l); D F R is the dead fine root mass (g. m-2); and kd(som) is the decomposition rate of the soil organic matter (day-1). The flux from dead fine roots to soil organic matter is converted to units of g C" m-2 before summing. The simulated annual carbon budget for the mean control stand (Table 1) demonstrates the importance of maintenance respiration in slash pines growing in a relatively warm environment. Annual maintenance respiration is 47% of the net canopy assimilation. Fine root maintenance respiration (246 g C- m -2) comprises nearly half of the total. The high maintenance

2~1

SIMULATION OF CARBON DYNAMICS

TABLE 1 Simulated annual carbon budget (g C" m -2) for mean control stand (1987-1988) Net canopy assimilation Maintenance respiration a Growth respiration Mortality b New growth increment c Labile C pool increment

1102 513 79 89 435 - 14

a Foliage maintenance respiration is night only. b Old foliage litterfall is not included because the carbon source was from the previous year's assimilation. ¢ Includes new foliage production. respiration rate is due both to the relatively warm air t e m p e r a t u r e (mean annual t e m p e r a t u r e is 21.7°C) and to the lack of any dormant period. Slash pines are normally harvested at age 2 0 - 2 5 years; this rotation-age stand is still accumulating biomass, but at a lower rate than in previous years (Gholz and Fisher, 1982; Gholz et al., 1991). A younger stand would have a much higher proportion of growth and growth respiration. MODEL EVALUATION The SPM o u t p u t can be c o m p a r e d with data collected in the field for stem growth, root respiration, and labile carbon dynamics. D a t a used for evaluation of root respiration (estimated from soil C O z evolution) and labile carbon dynamics were b a s e d on control plot means for March 1987 through April 1989. M e a n values are used b e c a u s e there was little difference b e t w e e n plots or treatments in soil C O z evolution or the labile carbon pool (Gholz and Cropper, 1991). R o o t respiration in Florida slash pine plantations has b e e n estimated from soil CO z evolution based on litter removal and trenched plot experiments (Ewel et al., 1987b). These" experiments led to an estimate that 62% of the total soil CO 2 evolution Of a 29-year-old slash pine plantation was attributable to live root respiration. For evaluation of simulated root respiration, we use a static technique (soda lime) to m e a s u r e soil CO 2 evolution. Because static techniques u n d e r e s t i m a t e actual CO 2 evolution at high rates (Cropper et al., 1985; Ewel et al., 1987a), we use the following equation to predict actual soil C O z evolution: ln(FT) -- 3.98 + 0.00653. SL

(14)

where FT (mg C O z • m - z . h -1) is the corrected soil C O 2 evolution; and SL is the measured rate with soda lime (mg CO 2 • m -2" h - l ) . The correction

242

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DAYS ELAPSED FROM MARCH i, 1987 Fig. 8. Simulated live root respiration and estimates based on soil C O z evolution measurements.

has little effect on rates below 250 mg CO 2 • m - z . h -1 (most of our data). The simulated root (fine + coarse) respiration (Fig. 8) matches the estimated values (62% of corrected soil CO 2 evolution) well in both magnitude and seasonality. The soil and litter moisture status may also be important variables in controlling soil C O / evolution under some conditions, but are not included in the model. Simulated root respiration includes both maintenance and growth respiration, but maintenance respiration is 95% of the total root respiration. The balance of the total soil CO z evolution consists of needle, dead fine root and soil organic matter decomposition. Estimations of the actual size of the labile carbon pool in 1988 and 1989 are based on measurements of starch and sugar concentrations in foliage, branches, stems, coarse roots, and fine roots (Gholz and Cropper, 1991). Concentrations were multiplied by simulated biomass components and s u m m e d to estimate the total labile carbon pool (Fig. 9). The simulated labile carbon pool for the mean control stand decreased by 14 g C" m -2 from March 1, 1987 through February 29, 1988, and increased by 7 g C- m -2 for 1988-1989. This relative stability of the simulated labile carbon pool is significantly different than results from simulations based on the phenology functions with prescribed annual growth increments (see also Cropper and Gholz, 1990). Slight imbalances between net canopy carbon gain and labile carbon pool outputs can cause large variation in the labile carbon pool in the phenologically forced simulations which lack the stabilizing factor of growth reduction or cessation when available carbon is limiting.

SIMULATION

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CARBON

243

DYNAMICS

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Fig. 9. Simulated and measured labile (non-structural) carbon pool.

The seasonal dynamics of the labile carbon pool were primarily due to variation in tissue starch concentrations (Gholz and Cropper, 1991); sugar concentrations were relatively constant. The SPM simulations indicate that the seasonal variation in labile carbon storage is consistent with the hypothesis that the dynamics are due to the balance between net canopy assimilation and the outputs of respiration and growth on a daily basis. Stem growth from each of the seven control and eight fertilized plots was estimated through increment coring of ten representative trees in 1990. Leaf biomass for the new and old cohorts for 1987-1989 was estimated from litterfall collections on each plot. We then used the SPM to test the hypothesis that the increased stem growth on the fertilized plots reflected the increase in net canopy assimilation due to higher leaf areas (Gholz et al., 1991). Simulated annual stem growth for the 15 plots (over 2 years) generally corresponded well with the measured data (Fig. 10), but three of the 30 plot estimates (two fertilized and one control) had substantially highei" measured stem growth than simulated by the SPM. These differences may be attributed to sampling errors in increment coring or leaf biomass, or they may indicate that other fertilizer responses were significant in t h e s e plots. We found no significant difference in in situ respiration (Cropper and Gholz, 1991) or assimilation rates between fertilized and control plots, however, we estimate that a difference of 15% or less would not be detectable under field conditions. A 15% increase in Otp and k c can increase simulated annual stem growth by 100 g" m -2, assuming no change in foliage mass dynamics (Fig. 11). Although the SPM is primarily intended to simulate carbon dynamics over a single growing season, it is also useful to examine the model

244 T

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W.P. CROPPER AND H.L. G H O L Z

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MEASURED ANNUAL STEM G R O W T H (g m -z)

Fig. 10. Annual stem growth for seven control and eight fertilized plots during 2 years. The solid line represents 1 : 1.

behavior over longer time periods. The model should not be applied to young stands prior to closed canopy (approximately 14 years old) because the canopy structure might be significantly different from mature stands. To accomplish this examination, chronosequence data from similar unfertilized stands in this area (Gholz and Fisher, 1982) were used to initialize the model at age 14 and provide comparison points through age 35 years. As a

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245

SIMULATION OF CARBON DYN,,MMICS

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Fig. 12. Simulated and measured stem biomass of a slash pine chronosequence (age 14 through 34 years). Simulations included: 1987 climate with 1987 leaf biomass (87/87), 1989 climate and biomass (89/89), 1987 climate and 1989 leaf biomass (unlabeled), and 1989 climate with 1987 biomass (unlabeled).

simple test of the hypothesis that increasing maintenance respiration is primarily responsible for decreased growth of mature stands, combinations of 2 years of climate and corresponding control plot mean leaf biomass data for 1987 and 1989 were used as repeated inputs for each year of the simulation. The simulated stand development (Fig. 12) is clearly sensitive to both climate and leaf biomass. The model does not reflect the observed reduction in stem biomass accumulation in post-rotation aged stands, indicating that the hypothesis of growth limitation due to increasing maintenance respiration is not consistent with the simulated stand carbon budget. However, it should be noted that the large variation in the measured stands might reflect differences in site quality and leaf biomass among the measured chronosequence stands, and that the stem mortality coefficient was set at zero (reflecting the history of our study plots, but probably not an accurate representation of post-harvest age stands). A potentially important aspect of our simulations was the choice of the lower limit for the labile carbon pool of 35 g C" m -2, which is clearly arbitrary. An alternate assumption might be a lower limit of 90 g C. m-2, approximating the observed lower limit of the labile carbon pool during 2 years of sampling (Fig. 9). Although neither limit has a significant impact on normal 1-year simulations, a small decrease in the labile carbon pool (e.g., 1987 control, Table 1) can limit growth over long-term simulations, or potentially if temperature increases lead to significantly increased maintenance respiration rates (Ryan, 1991).

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CONCLUSIONS The S P M successfully simulates the seasonal labile carbon dynamics, stem growth, and root respiration of a flatwoods slash pine stand. The model would not be appropriate to use under conditions of water limitation, but those conditions seem to be rare on these sites. The simulations for 1987-1989 support the hypothesis that seasonal variation in the labile carbon pool can be explained as a result of the daily balance b e t w e e n net canopy assimilation and outputs of respiration and growth. Fertilization responses in the slash pine plots are consistent with the hypothesis that increased stem growth is due to the higher leaf biomass on the fertilized plots. Poor nutrient availability clearly limits foliage production (Gholz et al., 1991), b u t there is no evidence of a response in physiology or allocation patterns (other than foliage) in slash pine. ACKNOWLEDGMENTS Funding for this research was provided by National Science Foundation grant No. B S R 8106678 from the Ecosystem Studies Program and from Environmental Protection Agency cooperative agreement CR817538 from the E P A Global Change R e s e a r c h program. The stands for this research were used with the permission of the Jefferson-Smurfit Company. W e wish to thank Drs. K.C. Ewel and J. Jones for providing useful comments on this paper. This is Journal Series N u m b e r R-01919 of the Institute of F o o d and Agricultural Sciences, University of Florida, Gainesville, Florida 32611. REFERENCES Abrahamson, W.G. and Hartnett, D.C., 1990. Pine flatwoods and dry prairies. In: R.L. Myers and J.J. Ewei (Editors), Ecosystems of Florida. University of Central Florida Press, Orlando, FL, pp.103-149. ,~gren, G.I. and Axelsson, B., 1980. PT-A tree growth model. In: T. Persson (Editor), Structure and Function of Northern Coniferous Forests - An Ecosystem Study. Ecol. Bull., 32: 525-536. ,~gren, G.I., McMurtrie, R.E., Parton, W.J., Pasto, J. and Shugart, H.H., 1991. State-of-theart of models of production-decomposition linkages in conifer and grassland ecosystems. Ecol. Applic., 1: 118-138. Brock, T.D., 1981. Calculating solar radiation for ecological studies. Ecol. Modelling, 14: 1-19. Brown, M.J. and Thompson, M.T., 1988. Forest statistics for Florida, 1987. United States Department of Agriculture Forest Service Resource Bulletin SE-101. Chung, H.H. and Barnes, R.L., 1977. Photosynthate allocation in Pinus taeda. I. Substrate requirements for synthesis of shoot biomass. Can. J. For. Res., 7: 106-111. Cropper, W.P. Jr., 1988. Labile carbon dynamics in a Florida slash pine plantation. In: A.R. Ek, S.R. Shirley and T.E. Burk (Editors), Forest Growth Modelling "and Prediction. Proceedings of the IUFRO conference, August 1987, Minneapolis, MN. USDA Forest

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Service North Central Forest Experiment Station General Technical Report NC-I20, pp. 278-284. Cropper, W.P. Jr. and Gholz, H.L., 1990. Modelling the labile carbon dynamics of a Florida slash pine plantation. Silva Carelica, 15: 121-130. Cropper, W.P., Jr. and Gholz, H.L., 1991. In situ needle and fine root respiration in mature slash pine trees. Can. J. For. Res., 21: 1589-1595. Cropper, W.P., Jr., Ewe, K.C. and Raich, J.W., 1985. The measurement of soil CO, evolution in situ. Pedobiologia, 28: 35-40. Dougherty, P.M., Oker-Blom, P., Hennessey, T.C., Wittwer, R.F. and Teskey, R.O., 1990. An approach to modeling the effects of climate and phenology on the leaf biomass dynamics of a loblolly pine stand. Silva Carelica, 15: 133-143. Ewel, K.C., Cropper, W.P., Jr. and Gholz, H.L., 1987a. Soil CO 2 evolution in Florida slash pine plantations. I. Changes through time. Can. J. For. Res., 17: 325-329. Ewel, K.C., Cropper, W.P., Jr. and Gholz, H.L., 1987b. Soil CO 2 evolution in Florida slash pine plantations. II. Importance of root respiration. Can. J. For. Res., 17: 330-333. Gholz, H.L. and Cropper, W.P., Jr., 1991. Carbohydrate dynamics in mature Pinus elliottii var elliottii trees. Can. J. For. Res., 21: 1742-1747. Gholz, H.L. and Fisher, R.F., 1982. Organic matter production and distribution in slash pine (Pinus elliottii) plantations. Ecology, 63: 1827-1839. Gholz, H.L., Perry, C.S., Cropper, W.P., Jr. and Hendry, L.C., 1985. Litterfall, decomposition and N and P immobilization in a chronosequence of slash pine (Pinus elliottii) plantations. For. Sci., 31:463-478 Gholz, H.L., Hendry, L.C. and Cropper, W.P., Jr., 1986. Organic matter dynamics of fine roots in plantations of slash pine (Pinus elliottii) in north Florida. Can. J. For. Res., 16: 529-538. Gholz, H.L., Vogel, S.A., Cropper, W.P., Jr., McKelvey, K., Ewel, K.C. and Teskey, R.O., 1991. Dynamics of canopy structure and light interception in Pinus elliottii stands of north Florida. H.L. Ecol. Monogr., 61: 33-51. Grace, J.C., 1987. Theoretical ratio between "one-sided" and total surface area for pine needles. N.Z.J. For. Sci., 17: 292-295. Grissom, J.E., 1985. Effect of crown scorch on water status and growth of slash pine trees. Thesis, Univ. of Florida, Gainesville, FL, USA. Isebrands, J.G., Rauscher, H.M., Cro, T.R. and Dickmann, D.I., 1990. Whole-tree growth process models based on structural-functional relationships. In: R.K. Dixon, R.S. Meldahl, G.A. Ruark and W.G. Warren (Editors), Process Modeling of Forest Growth Responses to Environmental Stress. Timber Press, Portland, OR, pp. 96-112. Landsberg, J.J., 1986. Physiological Ecology of Forest Production. Academic Press, London, 198 pp. McKelvey, K.S., 1990. Modeling light penetration through a slash pine (Pinus elliottii) canopy. Ph.D. dissertation, University of Florida, 136 pp. Ryan, M.G., 1991. Effects of climate change on plant respiration. Ecol. Applic., 1: 157-167. Sinclair, T.R. and Knoerr, K.R., 1982. Distribution of photosynthetically active radiation in the canopy of a loblolly pine plantation. J. Appl. Ecol., 19: 183-191. APPENDIX 1

Assimilation parameters a p = 0.0111 m o l / m o l k c ( n e w foliage) = 0.01 / z m o l . m - 2 . s -1 • / z b a r -1

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k c (old foliage) = 0.007 ~ m o l • m - 2 . s -1 • p.bar -1 Ci (new foliage) = 2 3 8 / x b a r Ci (old foliage) --- 245 ~ b a r k ( B e e r - L a m b e r t , p r o j e c t e d L A D = 0.468 latitude = 30°N

Maintenance respiration Q10 (needles) = 2.09 Q10 (fine roots) = 1.94 Q10 (woody tissues) = 2.00 B R (needles) = 0.00027 g C O z • g - 1 . h - 1 B R (fine roots, litter layer) = 0.0004 g C O 2 • g - l . h-1 B R (fine roots, m i n e r a l soil) = 0.00008 g C O 2 • g - 1 . h-1 B R (woody tissues) = 0.00000367 g C O 2 • g - 1 . h - 1

Growth respiration (g C O 2 • g - l tissue growth) c(needles) --- 0.294 c ( w o o d y tissues) = 0.226 c(fine roots) = 0.240

Decomposition (day

- 1)

k d ( n e e d l e litter) = 0.000411 k d ( d e a d fine r o o t s ) - - 0 . 0 0 0 4 7 9 rd = 0.0019 kd(som) = 0.0000782

Mortality (day - 1) ~ ( s t e m ) -- 0 ~ ( b r a n c h e s ) = 0.000224 tz(coarse roots) = 0.0000384 ~ ( f i n e roots, litter layer) = 0.000932 ~ ( f i n e roots, m i n e r a l soil) = 0.000685

Partitioning coefficients pc(stem) -- 0.42 p c ( b r a n c h ) --- 0.07 p c ( c o a r s e root) = 0.101

S I M U L A T I O N O F C A R B O N DYNAMICS

p c ( f i n e root, litter l a y e r ) = 0.054 p c ( f i n e root, m i n e r a l soil) = 0.044

Cumulative needle litterfaU K = 1.1083 R = 0.0161 C = 3.5684

Relative needle elongation K = 1.0118 R = 0.0313 C = 4.0036

Initial values of state variables (1987, g . m - 2) old foliage = 416 new foliage = 371 s t e m = 10309 b r a n c h = 582 c o a r s e r o o t = 2238 fine r o o t (litter) = 191 fine r o o t ( m i n e r a l soil) = 212 n e e d l e litter = 2890 d e a d fine r o o t s --- 134 soil o r g a n i c c a r b o n = 7492 labile c a r b o n p o o l = 175

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