1.2.1 Different Scales in Forest Growth Modeling
Following Kurth (1994b), plant models can be differentiated by different approaches into 3 main categories (see Figure 1.1).
Figure 1.1: Triangle schema of different types of plant models (Figure from Kurth, 1994b, p. 300).
and sophistication of these model types has increased in the last century with the development of distribution models towards the implementation of single tree based growth models (Pretzsch, 2019). Due to the fast development of compu-tational power, the resolution of empirically based stand models has therefore increased from the population to the organism level (Pretzsch, 2019). Several single tree based growth simulators have been implemented like SILVA (Pretzsch et al., 2002), SIBYLA (Fabrika, 2005, cited in Fabrika and Pretzsch (2013)) or BWINPro (Nagel et al., 2002). A central motivation for furthering this approach were the shortcomings of simple stand level models like yield tables in estimating growth especially within mixed species forest stands with more complex stand dynamics (Pretzsch, 2019).
Coming from the organism scale, the resolution of the modeling approach can be further elaborated towards more detailed and finer organizational levels within the tree. Following the categorization by Kurth (1994b) this increase can either focus on the morphology of a tree and its components (morphological/structural models) or the functional processes and their relationships (process/functional models). Morphological models are focused on the arrangement, size and shape of a tree’s components (woody biomass like roots, stems and branches as well as foliage for example) in 3D space (referred to as geometry (Danjon and Reubens, 2008)) and the structural relations of these components (topology (Danjon and Reubens, 2008)). Important groundwork from a botanical viewpoint has been provided by Hallé et al. (1978) and their development of an architectural analy-sis of trees. Process models are more concerned with physiological questions relating for example to biomass production through photosynthesis, water uptake and balance, transpiration, nutrient balance and cycling within the plant and in interaction with the environment that surrounds the plant.
Arranging models into these categories is not mutually exclusive and no hard borders can be drawn here as models exist that combine the inherent methodolo-gies (Kurth, 1994b). Pretzsch (2019) lists for example hybrid models that combine properties of empirical stand growth models with functions that approximate the physiology of biomass production based on environmental parameters.
An approach that combines the properties and fundamentals of morphologi-cal and process models are Functional-Structural-Plant-Models (short: FSPMs) (Buck-Sorlin, 2013a). This is an integrated concept that considers the mutual
de-pendency of morphology and physiology in plants (Buck-Sorlin, 2013a). Figure 1.2 depicts the composition of an FSPM and how the different modules regarding structure and function interact.
Figure 1.2: Basic design and principles of an FSPM (Figure adapted from Figure 3 in Kurth and Anzola Jürgenson, 1997, p. 19).
The FSPM paradigm has seen a rise in application and growing interest in the last years (Vos et al., 2010; Sievänen et al., 2014). Regarding the theoretical for-malisms of how to simulate the development of plants, important groundwork has been made by the establishment of Lindenmayer-systems (short: L-systems).
These were formed by the botanist Aristid Lindenmayer who first used them to describe the development of algae (Lindenmayer, 1968). L-systems are a rule-based approach in which the latter refers to string rewriting (Buck-Sorlin, 2013b).
Through a set of rules, which are being applied in parallel, symbols are being replaced by strings (Buck-Sorlin, 2013b). The resulting string can be graphically interpreted for visualization (Buck-Sorlin, 2013b). A more extensive overview on the subject can be found in Prusinkiewicz and Lindenmayer (2004, originally pub-lished in 1990) which also introduces some extensions of L-systems like stochas-tic components. The theorestochas-tical framework has subsequently been expanded by graph theory (Buck-Sorlin, 2013b) through the introduction of growth grammars (Kurth and Sloboda, 1997; Kurth, 1994a) and later on relational growth grammars (Kurth et al., 2005). These developments were accompanied by the implementa-tion of software, modeling platforms, their associated programming/specificaimplementa-tion
and programming (Kurth et al., 2005), the programming language XL and with it the modeling platform GroIMP were implemented (Kniemeyer, 2008). Several other software solutions for functional-structural plant modeling exist currently like OpenAlea (Pradal et al., 2008). For an overview see Sievänen et al. (2014).
The question on which model to employ depends primarily on the research question that needs to be answered. Aggregated models are usually preferred for a coarser scale and can be helpful as a support tool in decision making due to their, in comparison, simplicity and easier comprehensibility. Additionally, their im-plementation has been preferred due to lack of knowledge on the more detailed, underlying processes and the lower demand in resources (like measurement ef-fort or computational power) that the more sophisticated modeling of these pro-cesses demand. Trivially, the success and growing utilization of models focusing on more detailed scales like single tree based growth models or FSPMs is con-sequentially, in part, owed to the rapid development in computer technology and the growing knowledge on plants, including their internal processes and interac-tion with their surroundings, based on findings made in plant biology and, in this special case, forest science.
The aim of this work is to demonstrate the possibilities in parameterizing a sin-gle tree based model and a structural model, both with an applied background in SRC plantations, as well as the connection of both approaches. The follow-ing Section will give an overview on the properties of SRC for modelfollow-ing along with prior work on the subject matter. Finally the concrete aims will be defined which then open for the description of the data acquisition, analysis and model implementation.