Histogram matching for the calibration of kNN stem volume estimates

The k-nearest neighbours (kNN) methods have been used successfully in many countries for the production of spatially comprehensive raster databases of forest attributes, made from the combination of National Forest Inventory (NFI) and satellite data. In Sweden, country-wide kNN estimates of forest variables have been produced to represent the forest condition in the years 2000 and 2005 by using a combination of Système Pour l'Observation de la Terre 5 (SPOT 5) satellite data and field data from the Swedish NFI. The resulting products are wall-to-wall raster maps with estimates of total stem volume, stem volume per tree species, tree height and stand age and a 25 × 25 m² pixel resolution. However, probability-based kNN stem volume estimates tend to have a suppressed variation range as large values are usually underestimated and small values are overestimated. One way to handle this problem is to calibrate the kNN stem volume estimates to the reference distribution of stem volume observations by histogram matching (HM) for a defined geographic area.

In this study, we have tested HM for the calibration of kNN total stem volume raster maps to the reference distribution captured by a forest inventory (FI) from 106 stands in Strömsjöliden, in the north of Sweden. The available field FI data set comprises 1084 circular plots, divided into a reference data set and an evaluation data set of total stem volume observations. The reference data set was used for the creation of a cumulative frequency histogram of total stem volume and the evaluation data set was used to assess the accuracy of volume estimates, before and after HM. The HM adjusted the cumulative distribution of the kNN data set to the distribution of the reference observations and resulted in a distribution of kNN estimates of total stem volume, which corresponded closely to that of the evaluation data set. The results show that the variation range of the kNN stem volume estimates can be extended by HM both on the pixel and stand levels. The extension of the range of estimates towards the range provided by the field observations allows improvement of kNN volume estimation for use in forest management planning based on stand-level analysis, given that the reference stem volume distribution can be estimated accurately, for example, using field data from NFI.