Abstract:

Objective: This study was carried out to compare different effects of multiple source data on forest dynamic forecasting. The patterns of parametric uncertainty and predictive uncertainty were analysed and quantified to illustrate the processes of information fusion. Changes in model accuracy and reliability were also assessed to reveal the differences in the characteristics of data, which also was expected to provide directions for further data collection. Method: Multi-period (i.e. 1990, 2005 and 2012) and multi-type (i.e. temporary plots, permanent plots and stem analysis) of inventory data of Pinus tabulaeformis were collected in Qinling Mountains. A simple variable-density stand-level model with a low data requirement was selected. Under a Bayesian framework of information fusion, we analysed the relations between traditional forest inventory data and empirical growth and yield models. The joint posterior parametric distributions were constructed using MCMC sampling technique in order to quantify the uncertainty in the forecasts of forest dynamics. On the one hand, the changes in the probability distributions of both parameters and predictions were compared for multi-period inventory data; on the other hand, the multi-type data were tested considering their impacts on model performances. The data-model updating loop was achieved by the relation between the priori and the posteriori, which meant that the joint posterior parametric distribution in the former experiment was continuously used as the prior information for the latter experiment. The integration of multiple source data was based on the assumptions of the independent likelihood for sampling and observing error in each dataset. To avoid the biases from erratic observations and outliers, the likelihood of error structure applied a heavy-tailed normal distribution. The heteroscedasticity of errors was considered using an automatically changing variance in likelihood during iterations. Result: With the new dataset continuously obtained, the marginal and joint parametric distribution kept changing. In general, the parametric uncertainty decreased along with the increase of the kurtosis in the probability distribution, resulting in a decreasing predictive uncertainty. In comparison with parameterization from inventory in 1990, the model calibrated with data from 2005 and 2012 showed an obvious lower predictive uncertainty during the mature stage, while the asymptotic parameter was shifted to higher values. The distinctions of predictions among various datasets revealed the advantages and drawbacks of different inventory datasets. The information from stem analysis tended to a higher prediction of average height for mature stand, when compared with plot sampling. The temporary plots and permanent plots differed in the sampling method and the observation quantity, which made the forecasts of stand basal area present distinctively. The model based on continuously updating and multi-source data performed the highest precision and accuracy. Conclusion: One challenge of forest growth and yield modeling is that sampling and observing errors vary with datasets. Even with the same set of optimal parameters, the advantages and drawbacks in different datasets might lead to a distinctive pattern of uncertainty. The probabilistic information could demonstrate both the accuracy of models and the lacking information of data, which would reveal the further direction of model development and data collection. The case study chose a specific Bayesian approach to demonstrate the complete logic of data-model loop and processes of information fusion.

Key words: Bayesian analysis, growth and yield, model update, multi-source data, uncertainty quantification