Modeling the biology of forest ecosystems has been devoted to a combination of theoretical and empirical approaches representing the function of a forest ecosystem generally within an undefined spatial context. Moving to a large spatial context will require the use of theoretical representations of critical ecosystem functions that can be represented on an individual cell basis. It should then be possible to vary the size of the smallest cell from 1 m2 to 100 ha.
A forest ecosystem dynamics model is being developed that is based on the nitrogen productivity concept for forest growth; litterfall quality and microbial efficiency for forest floor decomposition, and forest regeneration based on a tree's sprouting or seed production capability. Climate and ecosystem level disturbances will be handled as restricted stochastic processes. The restriction will be based on known state factor relationships. The state factors are used to describe a broad scale classification of the landscape to define basic limitations for the randomly derived driving variables used in the model.
The model has been programed as an ARC/INFO AML within the GRID package. The current version of the model has been verified as functional from an individual tree basis (1 m2 cell size) in a number of forest types found in interior Alaska. Verification on a landscape scale (1 ha. cell size) is difficult because of a lack of detailed data that can be used from a landscape perspective.
Calculation of carbon source/sink relationships for large land areas are often based on a simple calculation of the dominant vegetation usually at a mature state for the land area. In some instances the landscape is represented by a relatively simple classification of landscape characteristics (e.g. coniferous vs. deciduous forest). In these types of calculations, differences in carbon dynamics due to potentially important factors; like topography, soils, differences in climate, or variation in vegetation community types, and the community age structure; within a region are not considered. The calculation would only be accurate if an appropriate landscape weighted average was chosen for the region's carbon factor.
A geographically referenced group of data sets that can be used to define the primary state factors that control ecosystem function across Alaska is being developed. Topography is one of the easiest and can be developed from the DEM data that is currently available. A climate classification has been developed (Hammond and Yarie, in press). A preliminary version of the land characteristics for the state has been developed (Flemming, pers comm), and work is currently in progress to develop an age structure map of the forest types within the state. These data sets will then be used to parameterize a Geographic Alaskan Forest Ecosystem Dynamics model (GAFED) and to define specific climatic changes in the defined regions that are likely to occur due to global change.
The model will be designed to work at all levels of spatial resolution which is one advantage of incorporating it into ARC/INFO. Primary analysis will be developed at the individual tree within a stand level of landscape resolution (one square meter grid cell resolution). The biogeoclimatic classification for the state of Alaska will then be used to summarize stand level results at the landscape level (one hectare or greater grid cell resolution).
The primary milestone at completion of this work will be the development of a carbon balance map for the state of Alaska with current vegetation and average climate conditions. Changes in carbon dynamics can be estimated based on climate scenarios developed from mesoscale climate models. The biogeoclimatic classification should give us the ability to describe the appropriate level of landscape summarization for Alaska.
The GAFED model is primarily a process model that will use the important limiting factors to drive forest growth, forest floor, and mineral soil dynamic routines. The model was developed as an AML within ARC/INFO GRID. The routines necessary for the model can be developed so that the grid cell size is not a limitation (Table 1). The majority of routines can be applied at either an individual tree (1 m grid cell size) or landscape representation (1 ha or above grid cell size). There are a small group of routines that also require a greater level of modeling detail if used at a small grid cell size ( 1 m ) (Table 1).
Table 1: RELATIONSHIP BETWEEN MODEL ROUTINES AND GRID CELL SIZE.| Routines valid across all grid cell sizes | Routines that have cell size dependencies |
|---|---|
| Production | Litterfall |
| Decomposition | Regeneration |
| Climate | Single Tree Mortality |
| Disturbance by Fire |
The nitrogen productivity concept (Ågren 1983, 1985; Ingestad 1977, 1980, 1981) is used to model the tree growth at both the individual tree and forest stand level (Yarie, in review). The nitrogen productivity can be defined as the amount of annual production per unit of foliar nitrogen:
where W is plant or stand biomass, t is time, Pn is the nitrogen productivity (unit production/unit nitrogen), and N is the foliar nitrogen content
At steady state nutrition (d(N/W)/dt = 0) the plants (or forest stands) growth rate is proportional to the amount of foliar nitrogen in the plant (N) and the nitrogen productivity (Pn). The nitrogen productivity is at a maximum during the exponential growth phase and depends on a number of plant properties including genotypic properties, weather conditions, self-shading and ageing. There is a decrease in the nitrogen productivity due to self shading and plant ageing (Ågren 1983) such that:
where Pnmax is the maximum nitrogen productivity, b is considered an ageing and/or light extinction parameter, the other parameters have been defined for equation 1
Equation 2 has been used to calculate the nitrogen productivity of individual seedlings (Ingestad 1979a, 1979b; Ingestad and Kahr 1985) and stands of trees (Ågren 1983). It is also being used to calculate productivity of trees and stands within interior Alaska (Yarie, in review). In both equation 1 and 2 the parameters are not developed for specific geographic unit sizes. It should then be possible to develop a simple equation (equation 2) for calculation of the nitrogen productivity for a single tree to a stand of trees (Yarie, in review).
The nitrogen productivity of individual trees within a stand was calculated using the 1989 tree chemistry (Yarie and Van Cleve 1996) and above-ground production dataset from the Bonanza Creek LTER program . A total of 239 white spruce, 21 aspen, 54 birch, and 107 balsam poplar trees were available. Because I was trying to estimate the maximum N-productivity for individual trees 37 white spruce, 12 aspen, 8 birch, and 15 balsam poplar were selected for analysis. Individual tree N-productivity was then calculated by dividing the above-ground production by the above-ground foliar nitrogen content.
The comparative analysis between trees and stands was handled by placing all estimates of N-productivity and foliar nitrogen content on a simple unit area basis. The space occupancy of each individual tree was based on a calculation of tree density of a fully stocked stand if the diameter of the sample tree was the average diameter of the stand. The chemical analysis of the foliar material was performed as described by Yarie and Van Cleve (1996).
Calculation of the nitrogen productivity of stands of trees was based on data sets from Van Cleve et al. (1983) and the USFS Inventory of the Porcupine River Drainage (Setzer 1987, Yarie 1983). None of these stands contained any of the trees used for the individual tree calculations. The stands represented independent measurements of the nitrogen content and nitrogen productivity. The foliage quantity per unit area for each stand was again reduced to a one meter square basis.
Foliage, root, and twig litterfall is spread equally within a 81, 81 or 121 m2, respectively, area around the tree for the 1 m2 grid cell size. Tree death and stemwood litterfall is positioned in a random direction chosen from eight (0°, 45°, 90°, · · ·, 315°) potential angles from the tree base. Tree length is calculated based on standard allometric equations relating tree height to tree diameter. In stands of trees with individual grid cell sizes larger than the height of the tallest tree, litterfall occurs within the grid cell.
The decomposition dynamics are modeled using the theoretical representation presented by Bosatta and Ågren (1985) and Ågren and Bosatta (1987). Simply, litter quality is set for the fresh litterfall after which it changes by:
where E = a scale factor, fc = % C in microbial biomass, and u(q) = microbial growth rate estimated through equation (4)
Microbial growth rate is:
where u0 = microbial growth rate parameter, q = carbon quality (equation 3), B = growth parameter
Carbon content of the litter cohort decreases at the rate:
where e(q) = microbial efficiency, and C = carbon quantity in g/m2
Nitrogen content of the litter cohort decreases at the rate:
where N = nitrogen quantity (g/m2), fn = microbial % N
Microbial efficiency is:
where e0 and e1 are simple coefficients
Model validation will be carried out by using tree growth, forest floor and mineral soil dynamic variables that have been measured in the Fairbanks area as part of the Bonanza Creek Long-Term Ecological Research (LTER) Program (see the BNZ-LTER World Wide Web home page). There is sufficient information available on tree growth and forest floor dynamics from the Bonanza Creek LTER site to evaluate the model behavior for soil temperature, moisture dynamics, carbon and nitrogen turnover, and tree growth across both upland and floodplain successional sequences.
Currently a number of data sets are available for the state of Alaska. A 90 m DEM derived from USGS data sources is available. This data set can be used to derive relevant elevation, slope and aspect groupings. This data set has been summarized to 1000m grid cell size (USGS EROS field office Anchorage) and was used to develop a topography coverage for Alaska.
The average climatic zones based on a May through September growing season have been determined using average monthly data sets available from NOAA (world wide web home page; http://www.ncdc.noaa.gov) these data sets were brought up to date and edited using locally available weather records. A total of 40 growing season eco-climatic regions and 35 annual eco-climatic regions were estimated for the state of Alaska (Hammond and Yarie, in press).
Work is close to completion on assembling all current vegetation data bases for the state. We will try to summarize this data set at the level IV groups for the Alaska Vegetation Classification (Viereck et al. 1992). The level IV category can be further summarized to broader groupings (e.g. needle-leaf forest, broadleaf forest, etc.) for comparison to datasets derived from other areas of the country. The level IV groupings will also give us the best approach for defining the four primary components of the carbon stores on the landscape. These components are; alive and dead trees (above- and belowground), forest floor, mineral soil, and understory vegetation.
The nitrogen productivity concept represents one approach for developlment of an algorithms for expansion from individual tree to stand or landscape levels of estimation of primary production. A simple nitrogen productivity equation for trees and stands of trees on a unit area basis within interior Alaska was estimated (Figure 1, Yarie, in review).
Figure1. Relationship between nitrogen productivity and foliage biomass for aspen, birch, balsam poplar and white spruce stands and individual trees in interior Alaska. The equation is: Maximum N-Productivity = 133.191 - 0.0394 * (foliage biomass/unit area).
The model was able to acurately predict the growth of white spruce and birch trees in an old-growth white spruce forest on the floodplain in interior Alaska. Measured diameter growth for white spruce between 1989 and 1993 averaged 0.9 cm at breast heaight. The model predicted an average of 1.1 cm for the same time period. Total biomass growth for the modeled tree species in this site was approximately 270 gms/m*m. The above ground portion was then approximately 135 gms/m*m. these values are typical for mature white spruce forest stands found in interior Alaska (Yarie and Van Cleve 1983).
The model was able to predict litter decomposition for the tree foliage found on the site when compared to litterbag decomposition from the mature white spruce site (Figure 2). In both cases, the model and litterbag data, were a mixture of the tree foliage litterfall found on the validation site. The exact mixture of the litterfall in the modeled version was dependent on the movement of foliage litterfall around the tree. The model also calculated the decomposition of moss litter, tree twig litter and stemwood litter if a large tree dies and falls to the ground.
Figure 2. Comparison of foliage decomposition between the modeled cohorts and a set of litterbag data from the floodplain mature white spruce site.
The last set of results that is important to present at this time is the carbon flux, either capture or release, from the individual grid cells and the average for the entire validation plot. This can be presented as a three dimensional map of the carbon capture for the entire validation test site on a square meter basis (Figure 3). The average carbon capture for this stand was 77 grams per square meter for a single year. Total carbon capture represents 155 kg for the entire plot (45 m x 45 m). Carbon capture was found throughout the entire plot but only in the cells that contained a tree. Carbon release was found in cells in which trees were not present. Release was due to decomposition of the forest floor and mineral soil organic matter. For a mature stand this represents one of the best estimates of carbon capture for the boreal forest because of the inclusion of moss in the understory and the inclusion of root growth for the trees present in the model.
Figure 3. Graphical representation of the carbon captured in a mature white spruce stand on the floodplain of interior Alaska. The highest values reported were 5542 gms/m*m with a minimum value of -288 gms/m*m. The positive value represents carbon capture by trees and the negative value represents carbon release through decomposition of the forest floor and mineral soil organic matter. The grid cell size is one meter.
The estimates for ecosystem carbon uptake were less than those reported by Bonan (1992). He estimated that the trees captured about 1580 gms /m*m in a year and that including moss and microbial respiration the net capture was also about 1580 gms/ m*m per year. This is about 10 times higher than the estimate in the GAFED model. The GAFED model is also estimating carbon release from the forest floor and mineral soil at about 106 gms/ m*m per year (the range is 18 to 230) while Bonan (1992) estimated about 200 gms /m*m per year. The indication from this analysis is that both of the estimates are reasonably correct but neither can be accurately moved to a landscape basis without a large overestimate in one case or an underestimate in the other. The need to move to the landscape with the differences in vegetation types accurately portrayed should be obvious.
The next set of work for the GAFED model will be to verify the carbon dynamics for a number of additional sites within the Taiga LTER program. In addition a verification effort for the landscape level with the data sets that are available for the area surrounding the Bonanza Creek Experimental Forest will be put together. The final result will be the ability to start to develop accurate estimates of the carbon flux across the forested landscape of interior Alaska.
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