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.

Reducing the Uncertainty of Radiata Pine Site Index Maps Using an Spatial Ensemble of Machine Learning Models

“…Comparative studies of model performance undertaken in P. radiata plantations have highlighted the precision of regression kriging and more advanced non-parametric models, but as with other forest species, have not included a comprehensive comparison of models. Within New Zealand plantations, regression kriging was found to be marginally more precise than ordinary kriging, which in turn was more precise than Partial Least Squares [2,15], with the best Regression Kriging model accounting for 82% of the variance in Site Index [15]. Using a regional New Zealand dataset multiple regression models of Site Index were found to have a slightly superior precision to those created using Random Forests [22].…”

“…Environmental surfaces have been widely used through a range of modelling approaches to develop maps of Site Index for P. radiata [2,15] and many other coniferous tree species [16][17][18][19][20][21]. Compared to direct measurements of Site Index made using plot data, which are typically averaged to the stand level, predictions of Site Index from environmental surfaces open up a range of applications that are not available from traditional inventory.…”

“…Compared to direct measurements of Site Index made using plot data, which are typically averaged to the stand level, predictions of Site Index from environmental surfaces open up a range of applications that are not available from traditional inventory. The resulting spatial description of Site Index provides insight into the key environmental drivers of productivity and allows managers to understand how productivity is likely to vary across the landscape and where the optimal productivity will occur at range of resolutions from the intra-stand to the regional level [2,15]. In contrast to spatial predictions of Site Index from remotely sensed data, such as LIDAR, [22], surfaces of productivity, created from environmental surfaces can also be used to estimate productivity for unplanted areas, providing managers with insight into the potential value of land that they intend to purchase.…”

“…Parametric methods that utilise the spatial correlation between the underlying plot data describing Site Index have been less frequently used to develop models and surfaces of Site Index. Amongst these geostatistical methods the most commonly used techniques are ordinary kriging and regression kriging [2,15]. As predictions are made by ordinary kriging through interpolating values between measured plots this method is most precise when plots are located in relatively close proximity [2].…”

Aplicación de imágenes de satélites y datos LiDAR en la modelización de recursos forestales

“…También existe relación entre la precisión de los modelos y la escala de trabajo. Kimberley et al (2017) estudiaron la caracterización del error de predicción en función de la escala en la productividad del Pinus radiata D. Don. en Nueva Zelanda y concluyeron que la precisión mejora gradualmente a medida que aumenta la escala.…”