Predicting effects of different harvesting intensities with a model of nitrogen limited forest growth

Abstract

The anticipated increasing utilisation of forest biomass necessitates improved understanding of its long-term consequences on forest productivity. We have used a model of carbon and nitrogen fluxes to predict effects of different management regimes in Norway spruce stands at three levels of fertility. Stands with high production are the least sensitive to intensified harvesting, partly because these stands occur in regions with high nitrogen deposition which compensates for the removal in nitrogen in harvests. Intensified thinning with stem-only removal is the management that affects productivity least followed by whole-tree harvesting at clear-fellings. Whole-tree thinnings are less beneficial and shortened rotation times the least desirable from a production point of view. Increases in total biomass harvests are at the expense of stem harvest, which can mean a conflict between volume and value. The importance of secondary vegetation as is also discussed.

Introduction

In the last decades there has been a rapid increase in the interest for forest products as energy source. This trend is expected to be further accentuated in the coming century. As a consequence, there will be a demand on the forests of the world for more biomass per unit of area and time. This will inevitably lead to a more intensified forest utilisation. Utilisation of felling residues and shorter rotation times have been suggested as means of increasing harvests. The impact of such practices on the nutrient circulation and the soil micro-climate are poorly understood. There is evidence of second generation decline in productivity following whole tree harvest, i.e. intensified utilisation of branches and needles in thinnings or final harvest (Andersson, 1983, Tveite, 1983, Björkroth, 1984, Proe and Dutch, 1994) although this is not always found (Smith et al., 1994, Egnell and Leijon, 1997). To experimentally estimate the effects on a long term basis (e.g. 100–500 years) is not possible, if decisions are to be made today. Mathematical modelling to increase the understanding of disturbances in the nutrient cycling of different stands provides an alternative approach. It can also help interpreting trends in experimental data and facilitate extrapolations from these.

A review of approaches to forest ecosystem modelling was given by Ågren et al. (1991). Several realisations of these approaches exist. Bossel and Schäfer (1989) developed a rather detailed generic ecophysiological model of carbon and nitrogen cycling in a single species forest. This model was given a higher temporal and structural resolution by Bossel (1996). A ‘single plant ecosystem’ model of a pine stand on raw humus was presented by Chertov (1990). This model provides a simpler representation of the forest carbon and nitrogen cycles. King (1995) demonstrated how an equilibrium approach can show the importance of plant physiological processes relative to soil processes in determining forest yield. Aber et al. (1997) used a generalised, lumped parameter model to discuss nitrogen saturation and recovery in response to land use and atmospheric deposition. Regeneration and succession can be important determinants for forest development. A model combining such aspects with carbon and nitrogen cycling is Hybrid (Friend et al. 1997). A number of additional models can be found in Mohren and Kienast (1991) and a comparison of 16 forest-soil atmosphere models was made by Tiktak and Van Grinsven (1995). A problem emphasised by reviewers of models (van Oene and Ågren, 1995, Tiktak and Van Grinsven, 1995) is that few of the models are well-balanced, describing all aspects of the system in comparable detail.

A model (NITMOD, NITrogen MODel, for later versions the name Q is used, Ryan et al., 1996a, Ryan et al., 1996b) is presented in this paper for use as a tool to understand the dynamics of nitrogen circulation in managed Scandinavian Norway spruce stands. It is a simple model, with equal emphasis on vegetation and soil, based on a few theoretical principles of nitrogen productivity and decomposition developed by Ågren and Bosatta (1998 and references therein). In contrast to several other forest growth models, NITMOD includes not only a tree layer but also a secondary vegetation, which we will show to be important for nitrogen conservation after harvests. We will show that NITMOD can reproduce observed growth patterns. A sensitivity analysis of NITMOD will indicate that a few parameters dominate the model behaviour. Three case studies will show the influence of soil history, secondary vegetation and nutrient depletion on second and third generation growth.

Nitrogen is normally considered to be the most limiting growth factor for plant growth (Vitousek and Howarth, 1991) and Scandinavian stands of Norway spruce in particular (Nilsson et al., 1995). We have therefore constructed a model specifically on this basis. The model operates at stand level without individual trees and with annual updating of all state variables. The nitrogen processes included in NITMOD are mineralisation, immobilisation, atmospheric deposition, fertilisation, uptake by vegetation and litterfall. Modelled carbon flows are net primary production, litterfall and decomposition. These processes are schematically shown in Fig. 1. The restriction on growth from nitrogen availability is expressed through the nitrogen productivity concept. Limitation of growth by other factors as light and climate is not modelled directly in NITMOD but contained in the parameters of the nitrogen productivity and assumed not to vary during stand development. The nitrogen available for uptake by the plants is derived from two sources, mineralisation of soil organic matter and external inputs like atmospheric deposition and fertilisation (Fig. 1).

The biomass of the trees in the stand is divided into six different parts: needles (B₁), stems (B₂), branches (B₃), large roots and stumps (B₄), medium roots (B₅), and fine roots (B₆). In addition, the needle biomass is separated into age cohorts. For each of the biomass components (B₁–B₆) there is also a corresponding state variable for nitrogen (N₁–N₆). The production (P) of new tree biomass for all components i (1–6) is described by , , :

$$\text{P}{}_1\text{(t+1)=(a}\text{−}\text{bB}{}_1\text{(t))}\text{N}{}_1\text{(t),}$$

$$\text{P}{}_{\mathrm{i}}\text{(t+1)=[α}{}_{\mathrm{i}}\text{−}\text{β}{}_{\mathrm{i}}\text{B}{}_{\mathrm{i}}\text{(t)]N}{}_1\text{(t),}\text{(i=2}\text{–5}\text{),}$$

$$\text{P}{}_6\text{(t+1)=δN}{}_1\text{(t)t(α}{}_{\mathrm{i}}\text{−}\text{β}{}_{\mathrm{i}}\text{(N}{}_1\text{(t)/B}{}_1\text{(t)))}\text{B}{}_6\text{(t)}$$

where:a and b≥0 are parameters for the nitrogen productivity (Ågren, 1983), and δ, α_i and β_i≥0 are fitted parameters from observed stands.

These formulations of the tree growth produce realistic stands for sites of different productivities but contains no mechanistic information, except for needle production. Growth of all components except needles occurs at fixed nitrogen concentrations. The nitrogen concentration in litter is also set to a fixed value for each litter type, but lower than that of the corresponding living tissue. The difference in nitrogen between the living and dead plant components is recycled inside the plant. The difference between the amount of nitrogen available for tree growth and the one used by the woody tissues (B₁–B₆) is added to the needle nitrogen. Should this difference be negative, the growth of the woody tissues is scaled down until the difference is zero. The production of fine root biomass Eq. (3) is a sum of new production and retained fine root biomass from the previous year. Increased retention of fine roots with decreasing needle nitrogen concentration (Eq. (3) the second part) generates a reduced turnover rate of fine roots with deteriorating needle nitrogen status. All other vegetation (‘secondary vegetation’) in the stand besides the spruce trees are lumped into a state variable called ‘grass’.

Litter formation is described by simply assuming that for every time step a constant fraction of each biomass component is transferred to the soil organic matter; for the needles this is at present approximated by assuming a fixed life span (number of cohorts). The carbon concentration in the fresh litter is set to be 50%.

Uptake of nitrogen occurs from the inorganic pool of nitrogen in the soil, which is the sum of the mineralisation and external inputs of the current year. The fine root biomass of the trees determines how much of this pool is taken up. Since ammonium, which is the dominating inorganic nitrogen species in the types of soils of interest, is relatively immobile, the root efficiency in uptake can be treated as an occupancy problem. The soil is viewed as a three-dimensional grid of cells. The probability for an additional root-tip to find a cell that is not already occupied by other roots is decreasing with increasing number of root cells (i.e. fine root biomass). The decreasing probability of finding an ‘empty’ soil cell is interpreted as a decrease in the efficiency of additional root growth with increasing fine root biomass. Since the number of cells is large, this can be generalised as an exponential function

The nitrogen that is not taken up by tree roots is taken up by the secondary vegetation up to a given amount (maximally observed nitrogen amount in secondary vegetation). If there is still an excess of mineral nitrogen, this is leached out of the system. The secondary vegetation produces a biomass proportional to the amount of nitrogen taken up (fixed nitrogen concentration). This biomass and its associated nitrogen are turned into litter the same year.

In the soil, each litter cohort (litter type and year of formation) is treated individually with respect to its carbon content, nitrogen content and quality; i.e. six new cohorts are created every year. Quality, which is the key factor for the description of the soil processes, describes the degradability of the litter cohort and decreases with time, t. The turnover of the soil organic matter is based on the assumption that the micro-organisms responsible for the processes are basically carbon limited. The equations for quality, q(t,t′), carbon, C(t,t′), and nitrogen, N(t,t′), for a litter cohort formed at time t′ are (indices for litter types are left out)

$$\text{q(t,}\text{t′)=}\text{q}{}_0\text{1+(β−1)η}{}_{10}\text{f}{}_{\mathrm{c}}\text{u}{}_0\text{q}{}_0{}^{\mathrm{\beta -1}}\text{(t−t′)}{}^{\mathrm{<mtext>1</mtext><mtext>\beta -1</mtext>}}\text{,}$$

where β is a parameter controlling the rate at which the microbial growth rate changes with substrate quality, η₁₀ is a parameter describing the decrease in quality for each cycle of a substrate through the microbes, e₁ is a parameter describing the rate of change in microbial efficiency (production-to-assimilation ratio) with quality, u₀ is the microbial growth rate per unit of carbon, f_C is the carbon concentration in the microbes, f_N is the nitrogen concentration in the microbes, q₀ is the initial litter quality (dependent upon litter type), and r₀ is the initial litter nitrogen concentration (dependent upon litter type).

A fuller description and discussion of these equations and parameter values can be found in Bosatta and Ågren, 1991, Bosatta and Ågren, 1994 and Ågren and Bosatta (1998, model I). The transformation of the soil organic matter occurs continuously and therefore no distinction is necessary between humus and litter. Humus is simply a late stage in a decay continuum.

Rates of mineralisation of carbon and nitrogen are calculated as the difference between the total amounts (sum over all litter types and all ages of , of the previous year and the current year but before the litter of the current year is added to the soil. An important aspect of the model is that f_N has been defined as a linear function of the annually available soil inorganic nitrogen. In this way, the mineralisation-immobilisation of nitrogen can respond to changes in inorganic nitrogen availability (Bosatta and Ågren, 1995). It requires, however, a recursive calculation of the annual nitrogen mineralisation.

In its present format NITMOD runs for 300 years with a 1-year time step. It is initialised with a litterfall file of 300 years and seedling-sized trees. The litterfall file is generated by running the model over 300 years and using the generated litterfall to define the soil system from which the next generation of runs should be started. By changing management regimes and nitrogen deposition scenarios as well as scaling the nitrogen content of the ‘old soil’ it is possible to create different initial soil fertililties.

The model has been tested for stability of algorithms and sensitivity to individual parameters. To test the stability of the model a number of critical parameters such as nitrogen productivity and decomposition parameters were replaced with fairly short cycled (5–10 years) time dependent sinus functions oscillating (±10–20%) around the normal values. The purpose of this was to see if the period and amplitude of the disturbance could be recognised in the output (total biomass production). A chaotic or significantly different pattern in the output would be interpreted as an inability of the model to adapt to rapid changes. The model did however follow the perturbations smoothly, although this was not tested in a strict way (e.g. Fourier analysis) but only by measuring the cycle lengths and amplitudes of the curves.

To test the sensitivity of individual parameters every parameter (57 excluding management options) was altered±10%. The integral of the absolute difference between total tree biomass production for a reference and an altered system over a rotation period was calculated. This integral was then divided by the integral of the total tree biomass production for the reference system. The quotient was interpreted as the relative sensitivity of the whole system to changes in the altered parameter.

If the quotient is less than 10% the effect of the parameter is damped by the model. A value of more than 10% is an amplification, a value of around 10% is a proportional effect and values around 0 show a complete insensitivity in the model to changes in that parameter. No parameter disturbances caused the model to react violently or chaotically. No parameter disturbances failed to affect output. Most parameter disturbances gave an effect of equal magnitude (10%) in the output as in the input. In this group were the parameters α_2–5 and β_2–5 controlling internal carbon allocation functions Eq. (3) of the woody tissues of the tree. They affect their respective biomass component in proportion to the disturbance. A few parameter disturbances generated amplifications (10–25%). In this group were the parameters of , , affecting the soil nitrogen dynamics. The nitrogen productivity parameters a and b of Eq. (1) have a strong effect on productivity. The scaling of nitrogen availability in Eq. (4) makes the model sensitive to the parameter k₆ of that equation. Consequently the parameters α₆, β₆ and δ regulating fine root growth and turnover have an affect that amplifies a disturbance. This indicates that these processes are most likely to determine the behaviour of the system. The most sensitive parameters are those most central to the theories presented in Ågren, 1983, Bosatta and Ågren, 1991. Since these theories are also the theoretical hard core of the model it stands to reason that these parameters should to a great extent determine the response to changes in input.