Modeling Nitrogen Fixation Rates in Dead Wood

by

William T. Hicks, Mark E. Harmon, and Steven L. Garman

Chapter 5 from Hicks, William T. 2000. Modeling nitrogen fixation in dead wood. Corvallis, OR: Oregon State University. 160 p. Ph.D. dissertation.

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Table of Contents

Abstract

Introduction

Model Description

Layer Surface Area, Volume, and Mass

Difference Equations for Nitrogen Fixation and Respiration

Log Temperature

Temperature Effects

Log Moisture Content

Moisture Effects

Log Oxygen Content

Oxygen Index for Nitrogen Fixation

Oxygen Index for Respiration

Oxygen Diffusion

Methods

Results and Discussion

Uncertainty Analysis

Model Validation

Model Experiments

Relative Importance

Conclusions

Acknowledgments

Literature Cited

Figures

Tables

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Abstract

We developed a mechanistic simulation model of nitrogen fixation in dead wood to synthesize current knowledge, develop hypotheses, and estimate nitrogen fixation rates in the Pacific Northwest. Our model is a system of difference equations that estimate the annual amount of nitrogen fixed in a log of defined length and diameter and divided into five concentric layers. In our model nitrogen fixation is constrained by log substrate, temperature, moisture, and oxygen content. Respiration and diffusion of oxygen indirectly affect nitrogen fixation and respiration by regulating log oxygen content. Oxygen diffusion is influenced by log density, moisture, and oxygen content. Uncertainty analysis indicates that the focus of future research should be on improving estimates of the maximum nitrogen fixation rate, parameters involved in regulating log moisture content, and parameters involved in estimating oxygen diffusion rates. In comparison to independent data, our model reasonably estimated seasonal patterns of log temperature, moisture, oxygen content, and respiration rate. Our model estimates an annual nitrogen fixation rate of 0.7 kg N�ha-1�yr-1 for an old-growth stand at the H. J. Andrews, which is reasonably close to an independent estimate of 1.0 kg N�ha-1�yr-1 made for the same stand. Model output indicates that a decay class two, Tsuga heterophylla log fixes the most nitrogen in warm wet sites such as those near the coast, and the least in dry sites east of the Cascades and in the Klamaths. Raising the annual temperature by 2�C and decreasing precipitation by 10% caused nitrogen fixation rates to increase at all sites. Increases were greatest in warm wet sites and least in dry sites. Despite low annual rates of asymbiotic nitrogen fixation in wood, soil, and litter, asymbiotic nitrogen fixation can contribute 9% to 42% of a stands nitrogen inputs over succession when symbiotic fixers such as Alnus rubra and Lobaria oregana are present and absent, respectively. Managed stands with reduced levels of woody debris and litter may be losing a significant nitrogen input.

Introduction

In the highly productive forest ecosystems of the Pacific Northwest, both tree growth and fungal wood decay are limited by nitrogen (Cowling and Merrill, 1966; Gessel, 1973; Spano et al., 1982). Nitrogen fixation is an important input of this key nutrient, but little attention has been given to this process in woody debris because of its relatively low annual input. However, a significant portion of a forest ecosystem's nitrogen can be provided by asymbiotic fixation in woody debris when inputs are summed over succession and/or when symbiotic nitrogen fixers are absent (Cromack et al., 1979; Sollins et al., 1987).

Past attempts at elucidating the controlling mechanisms and the magnitude of nitrogen fixation in dead wood were preliminary. Most studies examined one to several of the factors controlling fixation in woody debris (e.g., Roskoski, 1980; Sollins et al., 1987; Griffiths, 1993), but none attempted to synthesize all major mechanisms. For example, past estimates of the annual amount of nitrogen fixed in dead wood in the Pacific Northwest involved extrapolation from a few substrates at one point in time (Sylvester et al., 1982) or at most a few substrates at two points during a year (Sollins et al., 1987). A model of nitrogen fixation in woody debris incorporating the primary controlling variables integrated over a year would greatly expand our understanding of this process.

To this end we developed a mechanistic simulation model of nitrogen fixed in woody debris that synthesized our current knowledge of this process. Comparisons of model results with independent data were used to evaluate the accuracy of our model. The model was then used to examine situations that have not been or that would be difficult to assess experimentally (e.g., annual and successional changes at log or stand scales; changing climate regimes). Finally, uncertainty analysis of model parameters was used to help direct future research towards areas that can be improved most.

Model Description

Our model is a system of difference equations that estimate the annual amount of nitrogen fixed in a log of defined length and diameter. A log is represented by five concentric layers of varying thickness with each layer corresponding to a wood tissue: bark, sapwood, and three layers of heartwood. All equations are solved on a daily time step. The model is programmed in BASIC. We scale up annual fixation rates from logs to stands by running the model for each decay class of each species present. Maximum nitrogen fixation and respiration rates, and densities for each species, tissue, and decay class are included in the model (Chapter 3; Griffiths et al., 1993; Harmon and Sexton, 1996). These maximum rates are adjusted by daily air temperature and precipitation data provided by the user. The model also requires mean monthly temperature to calculate evaporation potential. For stand level estimates, woody debris masses by species and decay class are required.

A conceptual diagram of modeled factors influencing nitrogen fixation in a log is shown in Figure 5.1. Nitrogen fixation is directly controlled by log substrate, temperature, moisture, and oxygen content. Respiration and diffusion of oxygen indirectly affect nitrogen fixation by regulating log oxygen content. Respiration is directly controlled by log substrate, temperature, moisture, and oxygen content. In our model oxygen diffusion is influenced by log substrate, moisture, and oxygen content.

Layer Surface Area, Volumes, and Mass

Several geometric quantities are necessary for calculating the temperature, moisture, and oxygen contents of the log layers. Log layers correspond to tissues: bark, sapwood, and heartwood. Radial tissue thicknesses are determined using equations relating log radius to tissue thickness (Lassen and Okkonen, 1969; Wilson et al., 1987). The outer most log layer is composed of both outer and inner bark. Outer bark is ten percent of the log radius (Figure 5.2). Inner bark thickness (IBTHIK, cm) is determined from the following equation:

IBTHIK = IBTMAX*((1-EXP(-IB1*RADIUS))^IB2)

where IBTMAX is the maximum inner bark thickness, RADIUS is the log radius, and IB1 and IB2 are parameters that determine the shape of the curve (Table 5.1). Sapwood thickness (SWTHIK, cm) is determined from the following equation:

SWTHIK = SWTMAX*((1-EXP(-SW1*RADIUS))^SW2)

where SWTMAX is the maximum sapwood thickness, and SW1 and SW2 are parameters that determine the shape of the curve (Table 5.1). Heartwood thickness (HWTHIK, m) is calculated as any remaining thickness after subtracting the other tissue thicknesses from RADIUS. The surface area of a log layer (LOGSA, m2) is given by:

LOGSA = 2p*ROUT*LENGTH

where ROUT is the outer radius of the layer and LENGTH is the log length. The projected surface area (i.e. the effective area available to collect precipitation; PROSA; m2) of the log is equal to:

PROSA = 2*ROUT*LENGTH

Layer volume (LOGV, l) is defined as:

LOGV = LENGTH*1000*p*(ROUT2-RIN2)

where RIN is the inner radius of the layer. The mass of a log layer (LMASS, kg) is equal to:

LMASS = LOGV*DENSE.

where DENSE (kg�l-1) is the density of the layer. The maximum gas volume (GASVM, l) and maximum water volume (H2OVM; l) for a layer are equivalent and given by:

GASVM = H2OVM=LOGV*DENSE*(MAXMST/100)

where MAXMST is the maximum moisture content of the layer (the determination of MAXMST is described later in the Log Moisture Content section).

Difference Equations for Nitrogen Fixation and Respiration

Nitrogen fixation and respiration rates are directly controlled by log temperature, moisture and oxygen content:

DNFIX = NFIXMAX*TMPIDN*MSTIDN*O2IDXN

DRESP = RESPMAX*TMPIDR*MSTIDR*O2IDXR

where NFIXMAX (nmol N2�g-1�d-1) and RESPMAX (mmol CO2�g-1�hr-1) are the maximum nitrogen fixation and respiration rates for a given decay class, tissue, and species. Indices are included that describe the effect of log temperature (TMPIDN, TMPIDR), moisture (MSTIDN, MSTIDR) and oxygen content (O2IDXN, O2IDXR) on the nitrogen fixation and respiration rates, respectively. These indices are used to adjust NFIX and RESP from the maximum values to actual values for a given log temperature, moisture and oxygen content.

Log Temperature

Daily log temperatures (TEMP, �C) are estimated from the average daily air temperature and Fourier's Law of Heat Conduction. The temperature of the outer layer of the log is assumed to be the same as air temperature allowing us to ignore heat convection, radiation, and absorption. Heat conduction moves heat between layers within the log as described by Fourier's Law:

QCON = K*LOGSA*DTEMPK*TIME/THIK

where QCON is the amount of heat in Joules moved between two layers in a day, DTEMPK is the temperature difference in Kelvin between the two layers, TIME is the number of seconds in a day, and THIK is the radial thickness between the midpoints of the layers. The thermal conductivity coefficient (K, W�m-1�K-1) is affected by wood density and moisture according to the following equation (U.S. Forest Products Laboratory, 1974):

K = 0.14*(DENSE*(1.39+0.028*MOIST)+0.165).

The total heat in the layer is calculated with:

HEAT = ((LMASS+H2OV)*C*TEMPK)+QCON

where HEAT is the amount of heat in Joules in the layer, and H2OV is the volume of water in liters in the layer (the determination of H2OV is described later in the Log Moisture Content section). The heat capacity (C; J�kg-1�K-1) is affected by wood moisture and temperature according to the following equation (U.S. Forest Products Laboratory; 1974):

C = (M + (0.27+0.0011*TEMP))/(1+M)+0.05

where M is the fractional wood moisture content. The temperature of the layer is then calculated from the amount of heat in the layer using:

TEMPK = HEAT/((LMASS+H2OV)*CTOT).

Temperature Effects

The response of nitrogen fixation and respiration to temperature has two components. The first component simulates the increase in activity that occurs as temperature rises from 0�C to the optimum temperature. We use a modified Q10 equation to describe the increase. Instead of a constant value for Q10, we used the following exponential equations that allow Q10 to vary with temperature:

Q10N = RATEQN*EXP(-SHPQN*TEMP)

Q10R = RATEQR*EXP(-SHPQR*TEMP)

where Q10N and Q10R are the Q10 values at a given temperature for nitrogen fixation and respiration respectively. RATEQN, RATEQR, SHPQN, and SHPQR are parameters that determine the height and steepness of the curve, and are generated from data collected on various substrates (Chapter 1; Table 5.1). The equations relating nitrogen fixation and respiration to temperature are given by:

TMPN1 = Q10N^((TEMP-REFTMP)/10)

TMPR1 = Q10R^((TEMP-REFTMP)/10)

where TMPN1 and TMPR1 are the first components of the temperature index for nitrogen fixation and respiration respectively. For these analyses we used our most common incubation temperature (15�C) for the reference temperature (REFTMP). The second component of the temperature response describes the lethal effect of rising temperature on the fixing and respiring organisms. We used the following Chapman-Richards equations:

TMPN2 = 1-((1-EXP(-SHPTN2*TEMP))^LAGTN2)

TMPR2 = 1-((1-EXP(-SHPTR2*TEMP))^LAGTR2)

where TMPN2 and TMPR2 are the second components of the temperature index for nitrogen fixation and respiration respectively. SHPTN2, SHPTR2, LAGTN2, and LAGTR2 are parameters that determine the shape of the curve and are generated from data collected on various substrates (Chapter 2, Table 5.1). The overall effect of temperature on nitrogen fixation and respiration is given by combining the two components (Figure 5.3):

TMPIDN = TMPN1*TMPN2

TMPIDR = TMPR1*TMPR2.

Log Moisture Content

Daily log moisture content (MOIST) is estimated for each layer from precipitation data (PRECIP, mm), evaporation, and diffusion rates. The approach for each daily time- step is to wet the log with throughfall, calculate water loss from drying, and then estimate diffusion of water between layers. First, we wet the log using precipitation data. Before precipitation can enter the log, canopy interception and runoff eliminate some of the water (Figure 5.4). The fraction of throughfall water (THRUFL) that is not intercepted by the canopy increases as the amount of precipitation increases (Rothacher, 1963; Figure 5.5a) as described by the following Chapman-Richards equation:

THRUFL = MAXFAL*((1-EXP(-SHPINT*PRECIP))^LAGINT)

where MAXFAL is the maximum fraction for THRUFL. SHPINT and LAGINT are parameters that alter the shape of the curve. The fraction of throughfall that runs off the log surface (RUNOFF) is related to layer density according to the following equation:

RUNOFF = (1-EXP(-SHPRUN* DENSE))^LAGRUN

where SHPRUN and LAGRUN are parameters which determine the shape of the curve and are generated from Harmon and Sexton's data (1995; Figure 5.5b). Thus, the water that enters the outermost log layer (H2OIN, l�d-1) is determined from the following equation:

H2OIN = PRECIP*PROSA*THRUFL*(1-RUNOFF)

where PROSA is used to convert PRECIP from mm/area to liters. We use a "tipping bucket" approach to move excess water in the outer layer into internal layers. Conceptually, each layer is a bucket. If the amount of water entering the outermost bucket is greater than the bucket can hold, the excess (OVFLO, l�d-1) moves into the next layer or leaches out of the log. The amount of overflow that leaches out is determined using the same equation as used for runoff except for sound heartwood. When heartwood is at 80 to 100% of its initial density, all overflow runs off and leaches from the log. We model heartwood in this manner because field observations indicate that sound heartwood does not wet up to its maximum moisture content even when exposed to saturated sapwood (Harmon and Sexton, 1995). Possibly, heartwood does not reach maximum moisture contents until decomposition produces cracks and channels in the heartwood. The amount of water that enters the next inner layer is then determined by subtracting leachate from overflow. For the innermost layer, all overflow is considered leachate.

Second, we dry the log. Evaporation (EVAP, l�d-1) only occurs in the outer layer. We used the evaporation component of the soil moisture model of Huang et al. (1996) to determine evaporation:

EVAP = EVAPPOT*(MOIST/MAXMST).

where EVAPPOT is the potential evaporation in liters per day and MAXMST is the maximum moisture content of a layer as described below. EVAPPOT is determined using a model of soil evaporation that requires mean monthly temperature and day length (Thornthwaite, 1948).

Next, we diffuse water between layers. Moisture diffusion (MDIFF, l�d-1) is expressed as:

MDIFF = MDMX*MGID*MDDIX*MDTIX*LOGSA

where MDMX is the maximum moisture diffusion rate (l�m-2�d-1), MGID is the moisture gradient between layers, MDDIX and MDTIX are the indices relating moisture diffusion and wood density and temperature, respectively. MGID is determined by comparing the fractions of actual to potential water stores for two adjacent layers. Figure 5.6a demonstrates the linear relationship of density and moisture diffusion as described by:

MDDIX = 1-MDDIXA*DENSE

where MDDIXA is a constant (Table 5.1). Figure 5.6b demonstrates the relationship between temperature and moisture diffusion that is expressed as:

MDTIX = MDTIXA*(TEMP^MDTIXB)^0.5

where MDTIXA and MDTIXB are constants (Table 5.1). When TEMP is less than zero MDTIX is assumed to be zero. MDMX, MDDIXA, MDTIXA, and MDTIXB were determined from an unpublished experiment of moisture movement between wood blocks (Harmon, unpublished data). Because of the manner in which this experiment was performed, the effect of wood thickness on moisture diffusion rate could not be determined. The equations should be valid as long as layer thickness is 8mm or greater.

After accounting for infiltration, evaporation, and diffusion, the moisture content of a layer (MOIST) is calculated by:

MOIST=(H2OV/LMASS)*100.

The maximum moisture content for a layer (MAXMST) is a function of layer density as described by the following negative exponential equation:

MAXMST = MMHITE*(EXP(-DENSE*MAXCOM))

where MMHITE and MAXCOM are parameters that determine the height and steepness of the curve, respectively, based on data from Harmon & Sexton (1995, Table 5.1, Figure 5.7). This relationship reflects the fact that as wood density increases the amount of pore space that can store water decreases.

Moisture Effects

The moisture effects indices determine the effect of daily log moisture content on nitrogen fixation and respiration. A lack of moisture generally prevents respiration and nitrogen fixation in wood when levels fall below the fiber saturation point (Griffin, 1977, Figure 5.8). At this point microorganisms cannot overcome the matric potential of water stored in wood fibers. High log moisture content can also indirectly inhibit respiration presumably by slowing diffusion of oxygen (Boddy, 1983; Flanagan & Veum, 1974; Griffin, 1977). However, by incorporating an oxygen index for nitrogen fixation in our model, we directly account for the latter effect (see Log Oxygen Content section). The nitrogen fixation and the respiration moisture indices are solved using Chapman-Richards equations:

MSTIDN = (1-EXP(-SHPMN*MOIST))^LAGMN

MSTIDR = (1-EXP(-SHPMR*MOIST))^LAGMR

where SHPMN, LAGMN, SHPMR and LAGMR are parameters that determine the shape of the curve and are generated from data collected on various substrates (Chapter 2; Table 5.1).

Log Oxygen Content

Daily log oxygen content (O2, %) is needed to alter the indices which control the effect of oxygen on nitrogen fixation and respiration (see Oxygen Effects). We modeled oxygen content mechanistically using respiration and oxygen diffusion. These processes are most accurately described using molar quantities. Thus, we keep track of daily changes in the oxygen content in a layer in moles, and use this molar value to determine percent oxygen content for each time step.

We determine the moles of oxygen (O2MOL, mol) present in a layer on a daily basis with the following equation:

O2MOL = MO2GAS+MO2H2O+DIFF-RESPC

where RESPC is the moles of oxygen respired per day, DIFF is the moles of oxygen diffusing into the layer per day (see Oxygen Diffusion section), MO2GAS is the moles of oxygen in gaseous form, and MO2H2O is the moles of oxygen dissolved in water. MO2H2O is determined from the amount of water in the layer (H2OV) and the concentration of oxygen in the water (CO2H2O). CO2H2O is calculated with Henry's Law using the partial pressure of oxygen and the Henry's Law constant (k, mol�l-1�atm-1) which varies with temperature (Weast, 1973):

k = (-2.5*10-5)*TEMP+0.002.

MO2GAS is determined from the ideal gas equation. The volume of gas in the layer (GASV) used in the ideal gas equation is the difference of H2OVM and H2OV.

Finally, we backcalculate O2 from O2MOL. First, we determine the amount of O2MOL that is contained in gas (XMOL) using Henry's Law and the ideal gas equation.

OCON = (R*TEMPK*k*H20V)/GASV

where R is the ideal gas constant and TEMPK is the temperature in Kelvin. Then:

XMOL = O2MOL/(OCON+1).

Log oxygen content (O2) can then be determined from the ideal gas equation.

Oxygen Index for Nitrogen Fixation

This function describes the effect of daily log oxygen concentration (O2, %) on nitrogen fixation rate (Figure 5.9a). The response of nitrogen fixation to oxygen has two components. The first portion describes the increase in activity as oxygen concentration rises due to the demands of these aerobically respiring nitrogen fixers for energy. This index rises from zero when oxygen is absent to one at an optimum. The following Chapman-Richards equation describes this increase:

O2N1 = (1-EXP(-SHPON1*O2))^LAGON1

where O2N1 is the first component of the oxygen index for nitrogen fixation; SHPON1 and LAGON1 are parameters that determine the shape of the curve and are generated from data collected on various substrates (Chapter 2, Table 5.1). The second component of the oxygen response describes the inactivating effect of rising oxygen concentrations on nitrogenase (Silvester et al., 1982). The index starts at one then declines to zero after reaching the optimum:

O2N2 = 1-((1-EXP(-SHPON2*O2))^LAGON2)

where O2N2 is the second component of the oxygen index for nitrogen fixation. SHPON2 and LAGON2 are parameters that determine the shape of the curve and are generated from data collected on various substrates (Chapter 2, Table 5.1). The nitrogen fixation response to oxygen index results from combining these two components:

O2IDXN = O2N1*O2N2.

Oxygen Index for Respiration

This index describes the effect of oxygen on respiration rate by simulating the increase and subsequent leveling of aerobic respiration activity that occurs as oxygen concentration rises (Figure 5.9b). Unlike nitrogen fixation, respiration is not inhibited by atmospheric oxygen concentrations. Thus, the index starts at zero when oxygen is absent and rises to one. The following Chapman-Richards equation describes this effect:

O2IDXR = (1-EXP(-SHPOR*O2))^LAGOR

where SHPOR and LAGOR are parameters that determine the shape of the curve and are generated from data collected on various substrates (Chapter 2; Scheffer, 1985; Table 5.1). We modified the response of respiration to oxygen to include the additional inhibiting effect of CO2, by limiting respiration below 5% O2 (Highley, 1983).

Oxygen Diffusion

We incorporate oxygen concentration and diffusion in our model to provide a mechanistic means for evaluating the effect of oxygen on nitrogen fixation and respiration. High wood moisture has been shown to indirectly inhibit respiration by reducing oxygen diffusion, and this moisture effect could be used to estimate the inhibitory effect of low oxygen concentration on respiration (Boddy, 1983; Chen et al., 2000). Because nitrogen fixation and respiration respond differently to oxygen concentration, we could not use an inhibiting effect of high moisture to model both responses to oxygen.

The oxygen diffusion rate (DIFF, mol�d-1) is controlled by log moisture, density and oxygen content:

DIFF = DIFMAX*LOGSA/THIK*MSTIDD*DENIDD*O2IDXD

where DIFMAX (mol O2�m-1�d-1) is the maximum diffusion rate of oxygen through wood (Chapter 4). Three indices describe the effect of log moisture (MSTIDD), density (DENIDD) and oxygen content (O2IDXD) on the oxygen diffusion rate. Indices range from zero to one and are used to reduce DIFMAX when any conditions controlling diffusion are limiting.

Moisture Index for Oxygen Diffusion

Increasing wood moisture decreases oxygen diffusion rates for two reasons. Wood fibers and decomposed material swell as their moisture content increases up to the fiber saturation point. Cracks and air spaces shrink, decreasing the area of air space available for diffusion. Once wood fibers become saturated additional water fills the remaining pore spaces. Oxygen moves slower in wood saturated in this manner, because the oxygen diffusion rate constant is four orders of magnitude lower in water compared to air (Harmon et al., 1986; Bird, 1960).

We modeled the effect of water on diffusion in the following way. The moisture index for oxygen diffusion (MSTIDD) is assumed to remain at one as long as log moisture content is below the fiber saturation point. As moisture content increases above the fiber saturation point, MSTIDD is related to the fraction of pore space filled with air (FPSA, Figure 5.10a) as expressed by:

MSTIDD = 10^(-MIDDA+MIDDB*FPSA)

where MIDDA determines the y-intercept and MIDDB controls the rate of increase of the curve. Parameter values were determined from measurements of oxygen diffusion through wood cores of varied moisture (Chapter 4, Table 5.1). FPSA is determined from the following equation:

FPSA = (GASVM-H2OV)/GASVM.

FPSA is used as a metric of wood moisture because it is independent of wood density.

Density Index for Oxygen Diffusion

As wood density increases, oxygen diffusion rates decrease because denser wood has less pore space available for oxygen diffusion (Figure 5.10b). We used a negative exponential equation to estimate the effect of wood density on oxygen diffusion:

DENIDD = 10^(DIDDA-DIDDB*DENSE)

where DIDDA and DIDDB are parameters that alter curve height and slope steepness respectively. Parameter values were determined from measurements of oxygen diffusion through wood cores of varied density (Chapter 4, Table 5.1).

Oxygen Gradient Index for Oxygen Diffusion

According to Fick's Law, oxygen diffusion should decrease linearly as the oxygen gradient from the outside to the inside of the log decreases. The following equation is used to describe this effect:

O2IDXD=(O2OUT-O2)/O2OUT

where O2OUT is the oxygen concentration external to the log.

Methods

Uncertainty Analysis

We used uncertainty analysis to evaluate the sensitivity and degree of confidence in parameters. Our goal was to identify parameters that are estimated with low confidence and to which the model is highly sensitive (Table 5.2). Parameters that have low estimate confidence and low sensitivity are not as critical, because they have little influence on model output. Precise parameters that have high sensitivity are also of less concern given the resolution of estimates. Finally, the parameters of least interest are those with low sensitivity and high estimate confidence.

We tested the relative influence of all model parameters on the estimate of the amount of nitrogen fixed annually (NFIX) in a decay class two, Tsuga heterophylla log by recording the percent change in NFIX after increasing the parameter by 10%. After identifying sensitive parameters with a low estimate confidence, we further tested model sensitivity to these parameters by increasing and decreasing parameters by 5, 10, and, 20% to see if the response was linear or curvilinear.

The uncertainty of the parameter estimate was crudely estimated by assigning parameters to the low or high uncertainty category. If we felt the parameter estimate was within 10% of the real value, the parameter was assigned to the low uncertainty category, while parameters that were not estimated this well were assigned to the high uncertainty category.

Model Validation

Unfortunately, there is little available data for direct validation of predicted nitrogen fixation rates; however, we compared predictions of respiration rate, temperature, moisture, and oxygen concentration to independent field data (Chapter 4). Studies of nitrogen fixation in dead wood are relatively scarce, with only two estimates of the annual amount of nitrogen fixed in wood at the stand scale in the Pacific Northwest (Silvester et al., 1982; Sollins et al., 1987). In addition, no method has been developed to measure absolute nitrogen fixation rates in logs in the field without removing a portion of the sample and incubating it in conditions that probably do not resemble those of the log. Thus, even if the data on nitrogen fixation in dead wood existed, we would be limited to relative comparisons.

Model Experiments

Climate sensitivity

To begin understanding how variations in climate in the Pacific Northwest and possible future changes in climate would affect nitrogen fixation rates in dead wood, we simulated annual nitrogen fixation rates in a 50 cm diameter, decay class two, Tsuga heterophylla log in a variety of Pacific Northwest locations (Table 5.3). We used a decay class two, Tsuga heterophylla log because it has relatively high activity and sensitivity to changes in precipitation. To simulate climate change we ran the model with adjusted meteorological data from each site. Daily temperatures were increased by 2�C and daily precipitation was decreased by 10%.

Log level

To gain an understanding of the contribution of nitrogen fixation to the nitrogen budget of a log, we used our model to estimate how much nitrogen is fixed over the 200 year lifetime of a 1.5 Mg, 50 cm, Pseudotsuga menziesii log decaying at a rate of 0.02 yr-1. The log was assumed to initially contain 0.1% nitrogen or a store of 1.5 kg N (Harmon and Sexton, 1995).

Stand level

We estimated the amount of nitrogen fixed at the stand level for the three sites where wood was sampled to parameterize our model (Chapter 3). We used woody debris biomass estimates for the H. J. Andrews from Sollins et al. (1987) while biomass estimates from Wind River and Cascade Head are from Harmon (unpublished). Woody debris biomass was 143 Mg, 167 Mg, and 153 Mg for H. J. Andrews, Wind River, and Cascade Head, respectively. Woody debris biomass was primarily Pseudotsuga menziesii and Tsuga heterophylla at H. J. Andrews and Wind River, while Cascade head also had substantial amounts of Picea sitchensis.

Relative Importance

We used model output for estimating nitrogen fixation rates in wood over a hypothetical 500-year succession and literature values to estimate nitrogen fixation inputs from other sources. In this analysis we assumed Alnus rubra and Ceanothus velutinus only occurred early in succession, lichens only after 150 years, and wood, soil, and litter were present throughout. Nitrogen inputs from precipitation and soil were assumed to remain constant throughout succession (2.5 and 0.5 kg N ha-1 yr-1, respectively).

Results and Discussion

Uncertainty Analysis

Model output was relatively insensitive (ie., less than a 5% change in NFIX) to most of the parameters (Table 5.1). We have high confidence in some parameter estimates that the model was sensitive to (e.g., REFTMP and RESPMAX). The remaining parameters, that the model is sensitive to and we are not highly confident in our estimate of, fall into three groups: 1) the maximum nitrogen fixation rate (NFIXMAX), 2) parameters related to generating log moisture content (SHPRUN, MMHITE, MAXCOM, and EVAPOT), and 3) parameters related to oxygen diffusion (DIFMAX, MIDDB, and DIDDB). Altering these parameters of most concern by various amounts generally produced linear changes in NFIX, although EVAPOT and DIDDB produced slightly curvilinear changes in NFIX (Figure 5.11). As expected, altering NFIXMAX by a given percent results in the same relative change in NFIX (Figure 5.11). Nitrogen fixation rates are highly variable and vary with the woody tissue, degree of decay, and species (Chapter 3; Sollins et al., 1987). Despite the many logs we sampled to generate our table of NFIXMAX values, we are not highly confident in our values. The accuracy and applicability of our model would therefore improve with additional data from different species and sites. In general, altering the parameters that influence log moisture content increases NFIX if it leads to greater log moisture, and decreases NFIX if it leads to lower log moisture (Figure 5.11a). Changing the parameters that influence log moisture content produces a similar magnitude change in NFIX when compared to altering NFIXMAX.

Unfortunately, very little is known about evaporation and runoff of water from logs (Harmon and Sexton, 1995). The parameters involved in generating the maximum moisture content (MMHITE and MAXCOM) of logs are relatively accurate; however, logs early in decay do not seem to reach these moisture contents under field conditions. Future research should focus on developing better estimates of evaporation and runoff, as well as evaluating the discrepancy between lab generated maximum moisture contents and the maximum moisture contents observed in the field. In general, altering the parameters that influence oxygen diffusion increases NFIX if it leads to lower rates of oxygen diffusion, and decreases NFIX if it leads to higher rates of oxygen diffusion (Figure 5.11a). Changing the parameters that influence rates of oxygen diffusion produces a similar magnitude change in NFIX when compared to altering NFIXMAX except for DIDDB, which produced a greater change. DIDDB determines the exponential rate of decrease in the diffusion rate as wood density increases, thus changes in DIDDB can have a proportionately greater effect on NFIX than other parameters. Future research should focus on improving our estimates of MIDDB and DIDDB, as well as investigating the role of longitudinal oxygen diffusion, which we did not include in our model.

Model Validation

Our model produced a seasonal pattern of wood respiration rate similar to observed rates obtained from soda lime measurements of respiration by logs at Wind River Experimental Forest in Washington (Figure 5.12, Figure 5.13a, Chapter 4). Both curves peak in summer when temperatures both are warmest and are lowest in the winter months. The relationship of the predicted and observed data is significant despite the low correlation coefficient (p = 0.01, r2 = 0.35). The low degree of correlation is not surprising because the soda lime respiration measurements were highly variable and are not an absolute measure of respiration rate.

Model estimates of average daily log temperature closely track daily air temperature in 50 cm diameter logs (Figure 5.14). Unpublished data of log temperature measurements in logs close to 50 cm in diameter indicates that log temperatures are generally within 1�C of average daily air temperature. In 100 cm diameter logs, modeled log temperatures are often up to 5�C different from air temperature. The larger ratio of mass to surface area as log diameter increases should produce similar results in actual logs. Thus, our model appears to reasonably estimate log temperature.

Our model produced a comparable pattern of seasonal changes in wood moisture content in comparison to moisture contents obtained from time domain reflectometry (TDR) in logs at Wind River Experimental Forest in Washington (Figure 5.13b, Figure 5.15, Chapter 4). Average annual moisture contents were similar and increased with decay class for actual and modeled results (Table 5.4). In addition, seasonal fluctuations in moisture content in decay classes four and five are similar in magnitude and timing. However, our model does predict greater seasonal fluctuations in moisture content than observed for decay classes one through three. The greatest practical difference between our model and actual data is in decay class one, where the lower average predicted moisture contents might produce underestimates of respiration and nitrogen fixation throughout much of the year. Harmon and Sexton (1995) also found little seasonal variation in the moisture content of sound heartwood. The wetting and moisture diffusion characteristics of sound heartwood may explain the discrepancy between modeled and actual data.

Average and seasonal oxygen concentrations were similar for modeled and actual data from oxygen monitoring tubes placed in logs at Wind River Experimental Forest in Washington (Figure Figure 5.13c, Figure 5.16, Table 5.4). Average log oxygen concentrations are very close in magnitude and increase with decay class for both actual and modeled data. The only differences of consequence occurred in decay class one logs where the model underestimates of oxygen concentration from Julian dates 10-100 could result in overestimates of nitrogen fixation. Respiration would not be affected, as it is not inhibited in our model until oxygen falls below 5%.

Model Experiments

Climate sensitivity

Nitrogen fixation rates in a decay class two Tsuga heterophylla log varied among the different sites (Table 5.3). The highest nitrogen fixation rate was in the warm and wet Cascade Head Experimental Forest, and the lowest fixation rate was in the cool and dry Pringle Falls Experimental Forest east of the Cascades. Despite the high annual temperature for Ashland, OR, nitrogen fixation rates were relatively low because of the dry climate in the Klamath Range. We would expect the highest nitrogen fixation rates in woody debris in the Pacific Northwest to be in warm, moist site near the coast such as Cascade Head. The model simulations indicate that dry interior sites east of the Cascades and in the Klamaths probably have the lowest rates of nitrogen fixation per gram of woody debris.

Predicted changes in the climate may affect nitrogen fixation rates. It is estimated that the Pacific Northwest will become warmer and drier (Hanson et al., 1988). Their models indicate a temperature rise of 2-5�C in mean temperature and little change in precipitation. In addition, the annual pattern of relatively dry summers and mild, wet winters will persist. In our simulation of climate change, log level nitrogen fixation rates in woody debris increased at all sites (Table 5.3). Increases were greatest at sites with abundant precipitation (e.g., Cascade Head), while in the dry interior regions east of the Cascades and in the Klamaths rates only increased slightly (e.g., Ashland and Pringle Falls). Changes in the amount of nitrogen fixed per hectare are more difficult to predict because this depends on the amount of woody debris available. Changes in disturbance regime and tree productivity will undoubtedly affect woody debris biomass and these changes have the potential to alter nitrogen fixation rates to a greater degree than changes in temperature and precipitation (Franklin et al., 1991).

Log level

Over the 200-year lifetime of the simulated Pseudotsuga menziesii log, 0.4 kg of nitrogen were fixed, which was equivalent to 28% of the initial amount of nitrogen in the log. Considering the limiting role nitrogen plays in wood decay (Cowling and Merrill, 1966), our results suggest that nitrogen fixation is playing a significant role in the nitrogen cycle and decomposition of logs.

Stand level

Nitrogen fixation rates at the stand level varied among the different sites. The annual amount of nitrogen fixed was highest at Cascade Head (1.2 kg N�ha-1�yr-1), followed by Wind River (0.8 kg N�ha-1�yr-1), and the H. J. Andrews (0.7 kg N�ha-1�yr-1). The warmer and wetter climate at Cascade Head probably explains most of the difference between Cascade Head and the other two sites as the biomass of logs and nitrogen fixation activity of species was not so different. These results are somewhat lower than two estimates of the amount of nitrogen fixed in woody debris at the H. J. Andrews of 1.0 kg N�ha-1�yr-1 and 1.4 kg N�ha-1�yr-1 by Sollins et al. (1987) and Silvester et al. (1982), respectively. Sollins et al. (1987) sampled the range of log species and decay classes to a much greater degree than Silvester et al. (1982) and is probably a more realistic estimate.

Relative Importance

The low annual rates of nitrogen fixation in woody debris we have predicted have to be evaluated in a successional and landscape context to understand the relative importance of this process as a nitrogen input. Although the maximum annual rates of symbiotic nitrogen fixers are higher, asymbiotic nitrogen fixers in wood and soil can contribute significant amounts of nitrogen because of their wide extent. Nitrogen fixation is carried out by asymbiotic microorganisms in wood, litter, and soil, and by microorganisms in symbiotic relationships with plants and other organisms. Asymbiotic nitrogen fixers generally contribute up to 1 kg N ha-1 yr-1, while symbiotic fixers such as Alnus rubra and Ceanothus velutinus can contribute 100 kg N ha-1 yr-1 or more (Table 5.5). However, symbiotic fixers are restricted to certain stages of succession and areas of the landscape, whereas asymbiotic fixers are not. In our analysis, nitrogen inputs from Alnus and Ceanothus peak early in succession at 100 and 50 kg N ha-1 yr-1, respectively, then rapidly decline (Figure 5.17). These species fix nitrogen rapidly as biomass increases initially. Then biomass and fixation rates decline rapidly as the species are shaded and are outcompeted by larger, longer-lived conifers. Lichen nitrogen inputs are assumed to begin after 100 years, rise to a maximum of 4 kg N ha-1 yr-1 at 200 years, and then remain constant (Neitlich, 1993).

Lobaria biomass follows this same pattern. Woody debris nitrogen inputs also follow the pattern of woody debris biomass with a peak near 4 kg N ha-1 yr-1 early in succession created by the death of the previous stand; a decrease as the initial wood mass decomposes and tree death is negligible; and a final leveling off at 1 kg N ha-1 yr-1 as aging trees die and are replaced.

During one cycle of secondary succession, a hypothetical stand in the central Cascades of Oregon received 7090 kg N ha-1 over 500 years from the following sources: precipitation and dry deposition (18%); symbiotic fixation by Alnus rubra (48%) and by lichens (21%); and asymbiotic fixation in woody debris (9%) and in soil and litter (4%). In stands without symbiotic fixers, however, asymbiotic inputs provide 42% of total nitrogen inputs. Given that, across the landscape Alnus rubra occurs only in low elevation, recently disturbed sites; Ceanothus velutinus occurs primarily in high elevation, recently disturbed sites; and nitrogen fixing lichens occur in low elevation stands over 150 years old, their inputs at the landscape scale may be quite restricted (Sollins et al., 1987). Because asymbiotic nitrogen fixation occurs in all forests, their relative nitrogen contribution must be greater than maximum annual rates would suggest.

Conclusions

At this point, our model is primarily a synthesis and learning tool. Therefore our model is best used for examining relative differences, developing theory, synthesizing, and directing research. Our model is not recommended at this point for determining absolute values for nitrogen fixation rates. Current methods for estimating actual nitrogen fixation rates in woody debris are also limited in their absolute accuracy. Thus, any model of this process will be limited in this manner. However, as a synthesis and learning tool our model is a useful step towards understanding and predicting nitrogen fixation rates in dead wood and the controlling mechanisms. Key areas for future research include further surveying of nitrogen fixation activity, and investigations of the processes that control oxygen diffusion and log moisture content. We need to verify the relationships of oxygen diffusion with wood density and moisture content. In addition, better methods for estimating evaporation and runoff of water from logs are needed. Low-level chronic nitrogen inputs from asymbiotic nitrogen fixation in woody debris, soil, and litter may be important to nitrogen deficient Pacific NW forests. Managed stands with reduced levels of woody debris may be losing a significant nitrogen input.

Acknowledgments

Significant funding for this research was provided by the Kaye and Ward Richardson endowment, the United States Department of Agriculture (USDA-CSRSNRICGP contract number 9537109-2181), and the National Science Foundation Long-Term Ecological Research program (NSF grant number DEB-96-32929). Meteorological data sets from the H. J. Andrews Experimental Forest were provided by the Forest Science Data Bank, a partnership between the Department of Forest Science, Oregon State University, and the U.S. Forest Service Pacific Northwest Research Station, Corvallis, Oregon. Significant funding for these data was provided by the National Science Foundation Long-Term Ecological Research program (NSF grant numbers BSR-90-11663 and DEB-96-32921). This research was also funded in part by the Western Regional Center (WESTGEC) of the National Institute for Global Environmental Change (NIGEC) through the U.S. Department of Energy (Cooperative Agreement No. DE-FC03-90ER61010). Any opinions, findings and conclusions or recommendations expressed herein are those of the authors and do not necessarily reflect the view of the DOE.

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