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Simulation techniques for a stochastic model of the growth of douglas-fir Goulding, Christopher John

Abstract

This study is part of the overall problem of determining the most suitable management practises for second growth stands of Douglas-fir, Pseudotsuga menzesii (Mirb.) Franco, in British Columbia. A stochastic simulation model of the growth of a Douglas fir stand was constructed capable of providing yield and stand tables in response to various conditions of site, Initial density and thinning regime. The model is suitable for incorporation as the growth module of a larger systems model of a forest estate. Execution time is in the order of seconds for 80 years of simulated growth on an IBM 36O/67 computer. The programme is written in Fortran IV. The basic component of the simulation model is a list representing the dbh's of individual trees in a sample plot. The model does not consider inter-tree distances, hence is restricted to simulating stands with no large, irregular gaps in tree cover. A black box approach was taken in formulating the components of the system of growth. The major components are two difference equations which predict mortality end dbh growth over a short increment period, six years or less. Growth over longer periods is obtained by using the output of one forecast as the input to the next. A stochastic addition to the mortality component was constructed. Random mortality had an interaction with the growth functions so that the complete model had smaller values of expected volume yield when compared to a model with the random component removed. The model is capable of generating artificial data for stands at age 20, of being thinned to various regimes, and of predicting both total and merchantable volumes. The concept of validation was discussed. A three phase approach was taken: testing the individual components; direct comparison of the model's predictions with actual permanent sample plots; analysing and criticising the Inferences derived from the behaviour of the model as a whole. The average error in the prediction of total volume growth of 14 plots measured over an average of 35 years was 10 cu. ft. per acre. The average error in numbers of trees was -7 per acre. No trends in errors with respect to age, site index and density were found. The problems of multiple response and experimental size were important in designing experiments on the simulation model. Response surface techniques were used to obtain maximum mean annual increment of total gross volume as a function of site index and initial density for simulated unthinned stands and as a function of thinning intensity, site index and initial density for a specific thinning regime. The response of merchantable volume was also examined. The model's behaviour was such that initial densities affected volume yield more than did thinning intensity. Both factors interacted with site. More space was required per tree for the optimal development of the stand on poor sites than on good sites, where there was a strong tendency to lose production if the density of the stand became low. The inferences derived from this partial analysis were compared to selected references of summaries of spacing and thinning trials. It was concluded that the confidence in the model's ability to predict growth and yield was fairly good.

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