Development of potential height growth and diameter increment models for the parameterisation of an individual tree growth model for Pinus elliottii plantations in South Africa

Lindner, Gerard Eckard (2014-04)

Thesis (MScFor)--Stellenbosch University, 2014.

Thesis

ENGLISH ABSTRACT: Individual tree models, as opposed to stand models, have the potential to greatly improve sensitivity of forest growth models to changing conditions such as silvicultural amendments, irregular stand structures, etc. It was the purpose of this study to extend two sub-components of a European individual tree growth model to introduce individual tree growth modelling concepts in South Africa using Pinus elliottii as a study species. Two main objectives were established: Modelling the potential height of stands across different site qualities and modelling diameter increment using a potential modifier approach with a combination of competition indices that change in importance according to the edaphic conditions of the site. Potential height modelling used three steps in order to achieve this objective. The first was to compare site index models based on different model fitting techniques, namely nonlinear least squares, generalised nonlinear least squares and nonlinear mixed effects models. The nonlinear mixed effects model proved to be superior in terms of achieving the principles of regression assumptions and model fit for the data range observed. The second step was to fit potential height using nonlinear quantile regression on observed spacing trial height measurements. This proved to be a robust technique able to capture potentials according to the defined Chapman-Richards model structure. The final step was to use the predicted site index as a site classification variable in order to predict potential height. While some small deviation occurred, potential height seems to be well correlated to site index and validation on selected sites suggested that site index can be used to model potential height until a more sophisticated site classification model is used for future improvement of the model. Diameter increment modelling followed six major steps in order to apply the full parameterisation methodology of an age-independent diameter increment model dependent on tree diameter and competition. Diameter increment potentials were fit using site index as a predictor of the potential height curves. Multiple competition indices were tested on two sites to obtain a combination of two indices, which can capture overtopping and local crowding effects. Principle components analysis and variance inflation factors calculation were applied to test for collinearity between indices. Suitable combinations were tested resulting in a combination of the KKL and Local Basal Area competition indices. Changing importance of the two indices were observed on the two sites tested indicating a shift in the mode of competition according to a water gradient. These were combined in a deterministic potential modifier model, which mimicked competitive stages over age; however the validation showed a skewed distribution, which was not sensitive to stand density gradients. A stochastic model was constructed to model variance from observed residual plots using linear quantile regression to determine bounds for a truncated normal distribution which generates random deviates for a predicted increment. The stochastic element significantly improved the performance and sensitivity of the model, however the model was still not sensitive enough at very high and very low spacing densities. All in all two key models for an adaptation of an individual tree growth simulator to South African conditions were successfully demonstrated. The two main objectives were achieved; however some indicated improvements could be made, especially for the competition indices where the sensitivity of competition to changing resource limitation according to site and temporal scales needs to be further investigated. Furthermore, the full set of models for simulating individual tree growth still needs to be applied. Overall, as a methodological approach, the study outlined problems and future improvements, introduced new concepts and can serve as a guideline for future parameterisation of an individual tree growth model.

AFRIKAANSE OPSOMMING: In vergelyking met vakgroeimodelle, het individuele-boomgroeimodelle die potensiaal om die sensitiwiteit van plantasiegroeimodelle vir veranderende omstandighede soos aanpassings in boskultuur, onreëlmatige vakstrukture, ensovoorts, drasties te verbeter. Die doel van hierdie studie was om twee subkomponente van ‘n Europese individuele-boomgroeimodel uit te brei om sodoende individuele-boomgroei modelleringskonsepte in Suid-Afrika bekend te stel. Pinus elliottii is gebruik as studiespesie. Twee hoofdoelstellings is bepaal. Eerstens, die modellering van hoogtegroei potensiaal van opstande oor verskeie vlakke van groeiplek kwaliteit. Tweedens, die modellering van deursnee-aanwas deur gebruik te maak van ‘n potensiaal matigingsbenadering “potential modifier approach“ met ‘n kombinasie van kompetisie-indekse waarvan die belangrikheid verander volgens die edafiese toestande van die groeiplek. Die hoogtepotensiaalmodellering bestaan uit drie stappe. Tydens die eerste stap word groeiplek bonniteitsmodelle vergelyk op grond van verskillende modelpassingstegnieke, naamlik nie-lineêre minimum kwadrate, algemene nie-lineêre minimum kwadrate en nie-lineêre gemengde effek modelle. Laasgenoemde het die beste gevaar in terme van die beginsels van regressiemodelle asook die mate waarin die model die waargeneemde data pas. Tweedens is hoogtegroei potensiaal gemodelleer deur nie-lineêre kwantielregressie op waargeneemde hoogtes van spasiëringseksperimente toe te pas. Die metode is robuust en in staat om potensiale volgens die gedefinieerde Chapman Richards modelstruktuur vas te vang. Laastens is die voorspelde bonniteits indeks as ‘n groeiplek klassifasie veranderlike gebruik om sodoende die hoogtegroei potensiaal te voorspel. Alhoewel klein afwykings voorgekom het, blyk hoogtegroei potensiaal goed gekorreleer te wees met bonniteits indeks. Uit validasie op geselekteerde groieplekke blyk dit dat bonniteits indeks gebruik kan word om hoogtegroei potensiaal te modelleer totdat ‘n meer gesofistikeerde groeiplek klassifikasiemodel beskikbaar is wat die model verder sal kan vebeter. Die volledige parametriseringsmetodiek van ‘n ouderdoms-onafhanklike deursnee-aanwas model wat afhanklik is van boomdeursnee en kompetisie bestaan uit ses hoof prosesse. Nie-lineêre kwantielregressie is gebruik om deursnee-aanwaspotensiale te pas vir verskeie groeiplekke. Dié is gekombineer met ‘n bonniteits indeks om ‘n nuwe model te vorm waarmee hoogtegroeipotensiaal kurwes voorpel kon word. Daar is met veelvuldige kompetisie-indekse op twee groeiplekke geëksperimenteer om ‘n kombinasie van slegs twee indekse te vind wat die effekte van oorskaduwing en plaaslike verdringing kan vasvang, te vind. Hoof komponent analise “Principle components analysis” en variansie inflasie faktore berekening “variance inflation factors calculation” is gebruik om vir kollineariteit tussen die indekse te toets. Gepaste indekskombinasies is getoets. ‘n Kombinasie van die KKL en plaaslike basale oppervlakte “Local Basal Area” kompetisie-indekse het die beste resultate gelewer. Die twee indekse is as volg geselekteer. Veranderings in die belangrikheid van elk van die indekse is waargeneem op die twee toetspersele. Dit dui op ‘n verskuiwing in die modus van kompetisie afhangend van ‘n watergradiënt. Die twee indekse is gekombineer in ‘n deterministiese potensiaal matigings model wat die kompeterende stadiums oor ouderdom naboots. Validasie het egter ‘n skewe verdeling wat nie sensitief vir opstandsdigtheidsgradiënte is nie, gewys. ‘n Stogastiese model is ontwikkel om variansie in die residuele grafieke te modelleer. Lineêre kwantielregressie is gebruik om grense vir ‘n afgestompte normaalverdeling wat ewekansige afwykings vir ‘n voorspelde aanwas te bepaal. Die stogastiese element het die prestasie van die deterministiese model merkbaar verbeter. Selfs met die stogastiese element, is die model egter steeds nie sensitief genoeg vir baie hoë en baie lae opstandsdigthede nie. Ter opsomming is twee modelle vir ‘n aanpassing van ‘n individuele-boomgroeisimuleerder vir Suid- Afrikaanse toestande suksesvol gedemonstreer. Die twee hoofdoelstellings is bereik. Daar is egter steeds ‘n paar aangeduide verbeterings wat aangebring kan word. Die sensitiwiteit van die kompetisie-indekse op hulpbronbeperkings wat verander op grond van die ruimtelike en temporale skale moet veral verder bestudeer word. Verder moet die volle stel modelle wat benodig word om individuele-boomgroei te modelleer nog toegepas word. As ‘n metodologiese benadering, het die studie probleme uitgewys en toekomstige verbeterings aangedui, nuwe konsepte bekendgestel en kan dus dien as ‘n riglyn vir toekomstige parametrisering van individuele-boomgroeimodelle.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/86621
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