Alois Kastner-Maresch

A model relating forest growth to ecosystem-scale budgets of energy and nutrients

In this model of a forest ecosystem the height growth strategy of individual trees is linked to ecosystem-scale budgets of energy and a growth-limiting nutrient. The model spans from the individual tree to stand scales up to one hectare with a yearly time resolution. Competition among trees above-ground for light and below-ground for nutrients is used to model adaptation to external input fluxes over several tree generations. The competition among leaves and roots is modelled by a representation of the geometrical structures and a functional balance among the corresponding biomass compartments of trees. Dead biomass is decomposed in relation to its initial quality and nutrients are thus recycled into the root zone. The model is used (i) to reconstruct biomass accumulation and stand structure for even-aged and thinned stands and (ii) to study the evolutionary stability of observed height growth curves as a function of external input fluxes characterizing the physical environment of the stand in an abstract manner. Empirically, height growth has been widely established as a site-specific growth potential index for Norway spruce stands (Picea abies Karst.) in Germany. The model is used to reconstruct typical height growth curves. Such an assessment of the initial potential in growth responses is a prerequisite for studying the transient growth response to an external disturbance in the nutrient budget of the stand, e.g. in stands receiving atmospheric deposition.

Implicit Runge-Kutta methods for differential inclusions

This paper is concerned with the application of implicit Runge-Kutta methods suitable for stiff initial value problems to initial value problems for differential inclusions with upper semicontinuous right-hand sides satisfying a uniform one-sided Lipschitz condition and a growth condition. The problems could stem from differential equations with state discontinuous right-hand sides. It is shown that there exist methods with higher order of convergence on intervals where the solution is smooth enough. Globally we get at least the order one.

Difference methods with selection strategies for differential inclusions

The objective of this paper is to investigate convergence properties of multistep methods applied to differential inclusions. These multistep methods are combined with selection strategies, especially strategies based on optimization, forcing convergence to solutions with additional differentiability properties. For selection with respect to a reference trajectory an error estimate is proved.

Modelling optimal plant biomass partitioning

Abstract A theoretical framework is presented to quantitatively describe the dynamics of biomass partitioning in plants. The approach is based on the assumption that nitrogen supply is limiting plant growth, and hence the nitrogen concentration of leaves is adjusted in such a way that the relative growth rate of the plant is maximized. Special emphasis is put on the incorporation of time-varying environmental conditions and on the inclusion of a stem compartment. Furthermore, the nitrogen concentrations may vary between leaves, stems and roots. Simulations show that the qualitative behaviour of the model is consistent with empirical and theoretical results.

The implicit midpoint rule applied to discontinuous differential equations

The numerical solution of initial value problems with state-discontinuous right-hand sides by the well known implicit midpoint rule is discussed. The differential equations are transformed into differential inclusions following an approach of Filippov. The results are a theoretical foundation of the numerical treatment of problems arising in vehicle dynamics, mechanical systems with dry and Coulomb friction or population biology. An algorithm together with numerical tests is presented.ZusammenfassungIn dieser Arbeit wird die Konvergenzordnung der impliziten Mittelpunktsregel angewandt auf Anfangswertprobleme mit unstetigen rechten Seiten untersucht. Die Differentialgleichungen werden nach der Theorie von Filippov in Differentialinklusionen transformiert. Die erzielten Resultate stellen eine theoretische Fundierung für die numerische Behandlung von Problemen aus der Fahrzeugdynamik, der Mechanik von Systemen mit trockener und Coulombscher Reibung oder aus der Populationsökologie dar. Ein Algorithmus und numerische Tests werden präsentiert.

Complexity and Simplicity in Ecosystems: The case of forest management

There are numerous examples of systems, natural as well as technical, which are considered as rather complex from a scientific viewpoint, but are amenable to successful management and control nevertheless. The approaches towards these systems of scientists on one hand and practitioners on the other are vastly different. Taking ecosystems as typical example, scientists usually rely on observations of the current status of the system, while management traditions are based on augmented memory derived from past interference and utilisation patterns. The usual attitude of scienti sts, to analyze the system and then transfer the gained knowledge to system “users” to explain its behavior to them, has not worked out for this example. We therefore try to reverse the direction of the information flow between scientists and ecosystem practitioners for Mid-European forestry as a case study for which long-term experiences as well as high-resolution data are available. To this end, we use a sophisticated tree growth simulator based on current information technologies and demonstrate two complementary views on the system: the data view may be used by scientists to validate the model against empirical observations; the management view allows foresters to interactively perform thinning and harvesting operations according to their experiences through a 3-D graphical interface (here used as an input device to the model) and visualize them. The presented framework allows an assessment of the relative appropriateness of the two perspectives. It also offers a twofold validation scheme for the model: its calibration against measurements on one hand and its evaluation in practical forestry on the other.

The Direct Response of Photosynthesis to Climate Change

In this simulation study we based two very different forest stand simulation models, TRAGIC and TREEDYN3, on the same biochemical description of photosynthesis at the leaf scale, thus eliminating one source of uncertainty in model structure. We examined long-term predictions of net primary productivity and cumulative standing biomass as well as height growth curves under the hypothetical influence of climate change for a Pinus pinaster Ait. stand at Bray. Both models predicted comparable NPP and cumulative standing biomass dynamics and also changes with respect to given climate change scenarios were similar. Predictions of climate change effects converge despite very different model philosophy. Differences in height growth reflect different resolution of the models with respect to uptake and competition.