Michael Hauhs

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.

Water flow paths and residence times in a small headwater catchment at Gårdsjön, Sweden, during steady state storm flow conditions

Since April 1991 the small forested headwater catchment Gl at Gardsjon (Sweden) has been covered by a roof underneath which natural throughfall is replaced by artificial irrigation with a controlled chemical composition. Here this unique experimental setup was used for a tracer experiment with LiBr. The tracer pulse was applied to a subcatchment of approximately 1000 m2 that was maintained at steady state flow conditions throughout the experiment. Except these steady state flow conditions, the irrigation rates corresponded to a typical storm flow episode. Infiltration of event water was confined to the steep slope of a subcatchment of G1; no water was applied at the boggy valley bottom or close to the weir. An array of groundwater wells, suction lysimeters, and surface water sampling plots was used to document the soil passage of this pulse. Breakthrough in runoff (i.e., streamflow from the weir) occurred in a single peak within about 17 hours when less than 15% of the estimated total soil water in the subcatchment was replaced, indicating a relatively small fraction of mobile water. Tracer concentrations in groundwater wells and surface water in the catchment revealed some shallow, locally confined flow paths through the lower parts of the subcatchment. However, 4 days after application of the tracer the runoff concentration already reached the preevent background level for Br−. Only about 14% of the applied tracer was recovered by this time. Taking this into account, i.e., considering bromide as a nonconservative tracer, a one-dimensional model application (two-region convection-dispersion approach) successfully reproduced breakthrough curves at various places in the catchment. Thus the small portion of mobile water has intensive contact with the resident immobile water along the one-dimensional flow paths yielding an extremely long tail in the residence time distribution by back diffusion from immobile water. Results of this experiment qualitatively confirm earlier tracer studies under less controlled conditions but are virtually impossible to extrapolate quantitatively to transient flow conditions.

Ecosystem dynamics viewed from an endoperspective

The connection between ecosystems, thermodynamics and information theory is analyzed. We intend to show that the laws on computation can be applied in a much simpler and direct way than thermodynamic laws. The focus is on terrestrial ecosystems, for which boundaries are defined according to the statistical properties of energy and matter fluxes. The internal model which organisms inside ecosystems have about their environment is investigated. The evolution of an ecosystem model is considered as an alternation of model testing and model revision phases. The problem of knowledge acquisition for an observer placed inside the system and intimately connected with it (endoperspective) is discussed in detail. The bounds for the maximal information gain depending on thermodynamic conditions are derived under different assumptions. The proposed framework has not been rigorously tested yet, but it would explain much of the current dilemma in ecological modelling. Its application leads to testable predictions.

Long-Term Sulfate Dynamics at Lange Bramke (Harz) used for testing two Acidification Models

At Lange Bramke (Harz) soil solution and runoff concentrations of major elements were observed over 16 yr. During this period acid deposition was high but showed a marked decrease of H+ and SO42− both in concentrations and fluxes over the last five years. Among others, this record reveals the following patterns: seasonality in the signals for SO42− and NO3− in runoff which are synchronous; an accumulation of SO42− in the soil, initially up to 50% of the deposition fluxes; apparently no correlation between runoff and SO42− concentration, and no long-term trend in runoff concentration of SO42−.In this paper we use these patterns in the data set from Lange Bramke to test two established acidification models. The test criterion is that the algorithms employed by the SO42− modules of these models must be able to reproduce these features. To that end, both models need not to be run as it can be shown that even with completely unrestricted parameter values the two algorithms are unable to match the observed SO42− dynamics. The MAGIC model (Cosbyet al., 1985) is unable to reproduce, given the existence of net SO42− accumulation, the constant SO42− concentration in runoff during the last 16 years. The second model, BEM (Prenzel, 1986), is succesful in reconstructing the constant SC>4~ levels in runoff. However, on a monthly time scale BEM predicts a shift between the periodic maximum concentrations of SO42− and NO3− which is not observed in the data.

Diagnosing the dynamics of observed and simulated ecosystem gross primary productivity with time causal information theory quantifiers

Data analysis and model-data comparisons in the environmental sciences require diagnostic measures that quantify time series dynamics and structure, and are robust to noise in observational data. This paper investigates the temporal dynamics of environmental time series using measures quantifying their information content and complexity. The measures are used to classify natural processes on one hand, and to compare models with observations on the other. The present analysis focuses on the global carbon cycle as an area of research in which model-data integration and comparisons are key to improving our understanding of natural phenomena. We investigate the dynamics of observed and simulated time series of Gross Primary Productivity (GPP), a key variable in terrestrial ecosystems that quantifies ecosystem carbon uptake. However, the dynamics, patterns and magnitudes of GPP time series, both observed and simulated, vary substantially on different temporal and spatial scales. We demonstrate here that information content and complexity, or Information Theory Quantifiers (ITQ) for short, serve as robust and efficient data-analytical and model benchmarking tools for evaluating the temporal structure and dynamical properties of simulated or observed time series at various spatial scales. At continental scale, we compare GPP time series simulated with two models and an observations-based product. This analysis reveals qualitative differences between model evaluation based on ITQ compared to traditional model performance metrics, indicating that good model performance in terms of absolute or relative error does not imply that the dynamics of the observations is captured well. Furthermore, we show, using an ensemble of site-scale measurements obtained from the FLUXNET archive in the Mediterranean, that model-data or model-model mismatches as indicated by ITQ can be attributed to and interpreted as differences in the temporal structure of the respective ecological time series. At global scale, our understanding of C fluxes relies on the use of consistently applied land models. Here, we use ITQ to evaluate model structure: The measures are largely insensitive to climatic scenarios, land use and atmospheric gas concentrations used to drive them, but clearly separate the structure of 13 different land models taken from the CMIP5 archive and an observations-based product. In conclusion, diagnostic measures of this kind provide data-analytical tools that distinguish different types of natural processes based solely on their dynamics, and are thus highly suitable for environmental science applications such as model structural diagnostics.

Applications of Algebra and Coalgebra in Scientific Modelling

In computer science, the algebra-coalgebra duality serves as a formal framework for connecting the perspectives of state-based and behavior-based models. In other sciences such as ecology, these perspectives are seemingly harder to reconcile. We explore modelling paradigms, in the sense of philosophy of science, as an intermediate step in translating the (co)algebraic framework from computer science into applications in ecology. We illustrate the application potential of this approach with a simple model from theoretical ecology: the logistic map. Several versions of algebraic models with progressively more sophisticated carriers and operations are introduced and finally contrasted with a corresponding coalgebraic model. We illustrate two modelling paradigms with these examples. Only one of these has traditionally been used in ecology. The second one, which is based on a coalgebraic dualisation, offers new modelling perspectives in ecology and environmental science.

Distributive-law semantics for cellular automata and agent-based models

We present an effort to give formal semantics to the popular but theoretically rather unreflected scientific modelling paradigm of agent- or individual-based models. To this end, we give a generic formalization of two-dimensional cellular automata with flexible topology as the abstract basis of such models. The semantic approach of structural operational semantics a la Turi and Plotkin [7], based on bialgebras and distributive laws, leads in this case to a natural separation of the concerns of spatial structure, temporal behavior and local interaction. We give a generic distributive law for local behavior of automata and prove the equivalence to a more traditional, array-based formalization.

Sustainability in Forestry: Theory and a historical case study

The concept of sustainable development contains two independent goals: The connotation of unlimited economic growth in the term “development” and the perpetual conservation of natural resources implied by the concept of sustainable management. These two goals have been difficult to reconcile. Traditionally, sustainability is connected to the search for truly renewable resources in the realm of natural sciences and to the search for truly human needs in the realm of social sciences. Here we argue that in order to operationalize the concept of sustainable development it is necessary to distinguish two fundamentally different types of technologies by which humans develop and utilise resources. The proposed dualism of technologies is based on the respective historical contexts of their origin. One type of technology, exemplified by European forestry, depends on systems derived from natural history, but empirically by trial and error changed into an ahistoric, i.e. sustainable management system that may be extended infinitely. The second type of technology depends on scientific understanding of ahistoric material building blocks that can be recombined and developed into a virtually infinite technical potential through (open-ended) cultural history. The current dilemma of ecological problems becomes one of learning which of the technical potentials and traditions belongs to which category and how to organise the interface between them. We present and discuss a historic example were the interdependent use of the two types of technologies is exceptionally well-documented: The Rammelsberg mine at Goslar, Germany. Delineating a technical culture into realms organised by one or the other type of technology remains a non-trivial problem, but the continuous updating and learning process can be organised in a straight-forward manner. The proposed concept generalises lessons from the example of European forest history and suggests an operational implementation of sustainable ecosystem utilisation.

Chemical reactiveness of soil water pathways investigated by point source injections of chloride in a peat bog at Birkenes

Abstract At Birkenes, in southernmost Norway, cation exchange processes in peat bogs were investigated under saturated water flow conditions. Previous studies in this catchment have shown the importance of dynamic transport patterns of soil solution as the key to understanding streamwater chemistry. End-Member-Mixing Analysis (EMMA), developed on data from the Birkenes catchment and other sites, has so far been a useful concept in explaining the dynamics of stream chemistry. To obtain further information on the effect of water saturation on the degree of cation exchange during transport of soil solution, sodium chloride was injected into those parts of the peat soils along the main stream that are hydrologically saturated during rainstorms. The active buffer system of the soil matrix was effective in maintaining the level of the cations that were not added as a tracer. The tracer cation was fairly mobile under the experimental conditions, and only limited mobilization of other cations occurred. It is well known, from previous studies, that precipitation entering the catchment may reside there for days before leaving through discharge. The magnitude of cation exchange was less than might have been expected from the previous studies, which also considered hydrologically unsaturated conditions. The residence time during our experiments was probably insufficient for exchange that can be ascribed to classical equilibrium exchange. The extent of hydrodynamic dispersion is important for the magnitude of cation exchange.

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.