Characterising prediction error as a function of scale in spatial surfaces of tree productivity

Abstract Background Two indices, the 300 Index and Site Index, are commonly used to quantify productivity of Pinus radiata D.Don within New Zealand. Although maps of these indices exist, availability of new data and modifications to underlying models makes a refit of these prediction surfaces desirable. Prediction errors of such surfaces have only been reported at a plot-level scale, but their application is invariably at a larger scale where prediction accuracy should be better. The objectives of this study were to: (i) develop updated predictive surfaces for the 300 Index and Site Index; and (ii) characterise the relationship between prediction error and spatial scale for both surfaces. Methods Models were developed using a dataset of 4108 permanent sample plots from throughout New Zealand. Productivity indices were estimated from plot measurements and environmental variables extracted for each plot. Data were randomly split into fitting and validation datasets and surfaces developed from the fitting dataset for the 300 Index and Site Index using partial least squares regression, ordinary kriging and regression kriging. Prediction accuracy across a range of scales from 0.2 to 200 km was evaluated using the validation dataset. Results Regression kriging was found to be the most accurate method for describing spatial variation in the 300 Index and Site Index across New Zealand. Examination of changes in prediction error with spatial scale demonstrated a gradual decline in error from the plot level with increasing scale. Conclusions This study provides accurate maps of both the 300 Index and Site Index across New Zealand. Analysis of the effects of scale on prediction accuracy indicates that 95% confidence intervals of predictions for the 300 Index based on these maps averaged over an area of about 700 ha are half those of plot-level predictions and halve again at a scale of about 20,000 ha. For the Site Index, the improvement in precision with increasing scale is more gradual with 95% confidence intervals halving at a scale of about 20,000 ha and halving again at a scale of about 250,000 ha.