Mapping attributes of Canada’s forests at moderate resolution through kNN and MODIS imagery
Publication: Canadian Journal of Forest Research
24 January 2014
Abstract
Canada’s National Forest Inventory (NFI) sampling program is designed to support reporting on forests at the national scale. On the other hand, continuous maps of forest attributes are required to support strategic analyses of regional policy and management issues. We have therefore produced maps covering 4.03 × 106 km2 of inventoried forest area for the 2001 base year using standardised observations from the NFI photo plots (PP) as reference data. We used the k nearest neighbours (kNN) method with 26 geospatial data layers including MODIS spectral data and climatic and topographic variables to produce maps of 127 forest attributes at a 250 × 250 m resolution. The stand-level attributes include land cover, structure, and tree species relative abundance. In this article, we report only on total live aboveground tree biomass, with all other attributes covered in the supplementary data (http://nrcresearchpress.com/doi/suppl/10.1139/cjfr-2013-0401). In general, deviations in predicted pixel-level values from those in a PP validation set are greater in mountainous regions and in areas with either low biomass or sparse PP sampling. Predicted pixel-level values are overestimated at small observed values and underestimated at large ones. Accuracy measures are improved through the spatial aggregation of pixels to 1 km2 and beyond. Overall, these new products provide unique baseline information for strategic-level analyses of forests (https://nfi.nfis.org).
Résumé
L’Inventaire forestier national (IFN) du Canada est un programme d’échantillonnage conçu pour appuyer la production de rapports sur les forêts à l’échelle nationale. D’autre part, les cartes continues d’attributs forestiers sont nécessaires pour appuyer les analyses stratégiques des problématiques régionales de politique et d’aménagement. Nous avons donc produit des cartes couvrant 4,03 × 106 km2 de surface forestière inventoriée en 2001 à partir d’observations normalisées provenant des placettes photos de l’IFN utilisées comme données de référence. Nous avons utilisé la méthode des k plus proches voisins (kNN) avec 26 couches de données géospatiales, y compris les données spectrales MODIS et les variables climatiques et topographiques, pour produire les cartes de 127 attributs forestiers à une résolution de 250 × 250 m. Les attributs à l’échelle du peuplement comprennent le type de couverture terrestre, la structure et l’abondance relative des espèces d’arbres. Dans cet article, nous rapportons seulement la biomasse totale aérienne et vivante des arbres. Tous les autres attributs abordés sont présentés dans la section matériel supplémentaire (http://nrcresearchpress.com/doi/suppl/10.1139/cjfr-2013-0401). En général, les écarts des valeurs prédites à l’échelle du pixel par rapport à celles des placettes photos de validation, sont plus importants dans les régions montagneuses et dans les zones où, soit la biomasse, soit le taux d’échantillonnage de placettes photos est faible. Les valeurs prédites à l’échelle du pixel sont surestimées lorsque les valeurs observées sont petites et sous-estimées lorsqu’elles sont grandes. Les mesures de précision sont améliorées grâce à l’agrégation spatiale des pixels sur 1 km2 et plus. Dans l’ensemble, ces nouveaux produits fournissent des informations de base uniques pour les analyses stratégiques des forêts (https://nfi.nfis.org). [Traduit par la Rédaction]
Introduction
Canada’s forests and wooded lands cover 40% of its territory and constitute one-tenth of the world’s forest area (National Forest Inventory 2010). Provincial and territorial governments are responsible for forested lands within their boundaries and deploy forest inventory programs with standards, intensities, and frequencies designed to fit their specific forest management needs. Differences in inventory data sets among such programs make their integration at the national level difficult. Canada’s National Forest Inventory (NFI), a collaborative effort between the federal government and the provincial and territorial forest management agencies, was therefore developed to bridge that gap (Gillis et al. 2005). One of the main NFI products is a set of photo plots (PP), 2 × 2 km square sampling units centred on the intersections of a grid of a nominal 20 × 20 km format that covers all of Canada. The PP sampling thus covers 1% of the forests of Canada. Its systematic sampling provides estimates of selected forest properties across all forested landscapes in support of forest assessment and reporting at the scale of terrestrial ecozones (Ecological Stratification Working Group 1996).
In addition to national or ecozone-level reporting, many applications such as evaluations of timber losses from forest fires or the spread of invasive insects based on host tree species abundance require a spatially explicit coverage of forest attributes with units and definitions harmonized across jurisdictional boundaries. A decision was therefore made to develop forest attribute map products using the attribute values from the PPs as the source of reference information and remote sensing data sets as the main source of predictor variables. The design criteria for the output product were that (i) the spatial resolution and accuracy would be sufficient to support strategic-level reporting at regional to national scales and (ii) the resulting spatial data sets would be updatable between NFI re-measurements of PPs. We therefore selected the 250 × 250 m pixel (250 m hereafter) of the satellite-borne moderate resolution imaging spectroradiometer (MODIS) as the resolution of the output map product.
Following a preliminary trial on a pilot region (Beaudoin et al. 2011), we also chose to use the nonparametric k nearest neighbours (kNN) method as our basic mapping method because it met three basic criteria: (i) the capacity to predict simultaneously a large set of attributes while preserving their among-attribute functional relationships, (ii) a relative simplicity and cost effectiveness to implement across a large country such as Canada, and, importantly, (iii) a successful track record of application within national forest inventory programs. This choice is also supported by Brosofske et al. (2014) for application to forest inventory mapping.
The kNN method is a multivariate nonparametric prediction procedure that uses a set of predictor feature variables (X) to match each target pixel to a number (k) of most similar (nearest neighbours or NN) reference pixels for which values of response variables (Y) are known (McRoberts 2012). Feature variables are predictor variables for which values are known for both target and reference units and are used to match one to the other. The similarity measure between a target pixel and reference pixels can be given by any of several distance metrics such as the Euclidian distance (McRoberts 2009). First proposed for application in forestry using satellite data by Tomppo (1991), this method and its many variants have now been tested or applied successfully within forest inventory programs in many countries (Tomppo 2006; McRoberts 2012; Wilson et al, 2013). As a consequence, there is now a relatively large body of knowledge related to kNN application to forestry that can be drawn upon for our specific needs.
The objectives of this work were therefore (1) to produce forest attribute maps for the baseline year 2001 using an optimized kNN procedure for a broad suite of PP attributes across the well-inventoried forests of Canada and (2) to quantify the accuracy of the predicted attribute values relative to a reserved PP validation set of attribute values at spatial scales from pixels to ecozones.
Materials and methods
Mapping area, NFI PPs, and response variables
The potential mapping area for the present exercise covers the 12 forested ecozones of Canada for a total area of about 7.4 × 106 km2 (Fig. 1; Table 1). The NFI PP data, which were established, collected, and compiled over a 7-year period between 2000 and 2006, form a large sampling set across these ecozones in which definitions and units of forest attributes are harmonized across all jurisdictions. The PP sampling intensity and the completeness and quality of NFI information within PPs are far greater within the managed forests because of existing forest inventory programs and much lower in the unmanaged forests located mostly in northern Canada. The current mapping effort is therefore based on the 8202 PPs with complete forest attribute information of the 18 720 PPs across Canada (Fig. 1; Table 1). Although predictions were made for all 12 forested ecozones, the mapping effort is nominally limited to the 4.03 × 106 km2 of six well-inventoried ecozones within which accuracy measures can be generated. Predicted values in other ecozones should be used with caution.
Fig. 1.
Table 1.
Note: Ecozones are sorted by decreasing area size, with the shaded ones being poorly inventoried.
*
Mountainous ecozones.
†
Within the NFI PP establishment database: X, extensive (g, significant spatial gaps; i, variable areal intensity); x, poor (sparse or local); 0, practically nonexistent.
§
With full suite of attributes.
Each 2 km × 2 km PP is composed of forest polygons (stands) delineated from photo interpretation. Each stand has been assigned values for land use, land cover, and forest structure attributes from which 127 forest attributes were selected as a set of response variables (Y) to be predicted across target pixels (Supplementary Table S1).1 This set includes (1) four land cover attributes derived from photo interpretation related to vegetated and treed proportions, (2) 11 stand structures (age, height, and crown closure derived from photo interpretation, as well as merchantable volume provided by provinces used by NFI staff to estimate total volume and aboveground biomass based on Boudewyn et al. (2007) models), and (3) 112 forest species composition as percent abundance. For the sake of simplicity, in this paper, we report on only one of these attributes, total live aboveground tree biomass (AGB, tonnes (t) per hectare). The accuracy measures of the resulting kNN predictions are available for all attributes in Supplementary Table S2.
The stands within the selected PPs along with their suite of 127 attributes were first rasterized to a 25 × 25 m grid using NN interpolation. The resulting 127 raster layers were then aggregated to the 250 m MODIS grid through spatial averaging. Averaging was done with biomass weighting for some of the structural attributes to retain the original functional relationships among the PP attributes (Supplementary Table S1). Only the 250 m pixels fully within a PP boundary were retained as potential kNN samples (Fig. 2). Spatial analyses based on semivariograms had shown that spatial autocorrelation became negligible at distances greater than about 1.5 km. We therefore retained only the four corner pixels within each PP for further analyses (Fig. 2). Pixels were also removed if they had been affected by fire or harvesting after 2001, our kNN mapping year (for the change detection method, see Guindon et al. 2011).
Fig. 2.
The remaining corner pixels (N = 30 092) were split into a reference and validation (ref–val) set. Tests carried out within a commonly used range (Picard and Berk 1990) of percent ref–val splits (50%–50%, 70%–30%, and 80%–20%) randomly replicated 30 times each revealed a maximum difference of 1.2% among the mean values of two kNN accuracy measures (see description below) across the three splits. As a consequence, we retained the commonly used 70%–30% data split (Nref = 21 037 and Nval = 9055) to carry out the analysis (Table 1).
Selecting feature variables
We assembled a set of 31 Canada-wide continuous geospatial layers covering all 12 forested ecozones to be used as predictor X feature variables. This set included 18 spectral reflectance variables, nine climatic variables, three topographic variables, and one permanent land cover class (Table 2) as in similar studies (e.g., Brosofske et al. 2014). All variables were standardized to values between –1 and 1 (Z score) to avoid scale effects (LeMay and Temesgen 2005).
Table 2.
Note: Shaded feature layers along with labels represent the five variables (four winter ones for spectral variables) not retained for the kNN prediction, as per the criteria described in the text.
Scenes from TERRA MODIS level 1.B geolocated top-of-atmosphere radiance data (MOD02) for 2001 summer (July–August) and winter (January–February) were processed by the Canada Centre for Remote Sensing to produce orthorectified seasonal mosaics of composite surface reflectance at 250 m resolution (Pouliot et al. 2009). Each seasonal mosaic is based on two averaged monthly (5 × 10 day) composites (Luo et al. 2008) with various geometric and radiometric corrections applied, including the downscaling of band 6 from 500 m to 250 m resolution (Trishchenko et al. 2006). The resulting spectral features (Table 2) include the summer and winter reflectance data in bands 1, 2, and 6 at 250 m resolution (see colour composites in Supplementary Fig. S1), as well as six spectral indices derived from summer and winter reflectance data (Pouliot et al. 2009).
Climatic data (30-year normals, 1970–2000) were obtained from 1 × 1 km resolution interpolated meteorological data (McKenney et al. 2011) re-sampled to the 250 m MODIS pixel grid using cubic interpolation to generate appropriate climatic feature variables. These include three variables related to temperature, three related to precipitation, two indices of soil moisture availability, and mean annual incoming shortwave radiation. Slope, cosine of aspect angle, and elevation were derived from a SRTM-based 90 m digital elevation model (DEM) (Farr et al. 2007) re-sampled at the 250 m MODIS grid using cubic interpolation. Finally, the percent water cover by pixel was extracted from a 2000 Canada-wide 25 × 25 m resolution land cover map (Wulder et al. 2008) aggregated to 250 m through spatial averaging.
We explored the possibility of reducing the number of feature variables to avoid detrimental effects on kNN prediction accuracy due to the inclusion of X variables unrelated to Y response variables (McRoberts et al. 2002). We used the hybrid least absolute shrinkage and selection operator (hybrid-LASSO (HL); Efron et al. 2004) method to rank all feature variables according to the strength of their relationship to each Y of a subset of 27 of 127 response variables including all four land cover and 11 stand structure attributes along with 12 tree species abundance attributes representing key broad-leaved – needle-leaved and tolerant–intolerant species combinations and close to 60% of total biomass in the PP data set. These rankings based on adjusted R2 (adj. R2) values for individual Y variables were then merged into a single set, and X variables with consistently low ranking were deleted from the set. The adj. R2 quantifies the strength of the relationship between the feature variable and PP attribute and has a range of 0 to 1. Redundant X variables were also removed from the set when their marginal contribution to adj. R2 was less than 1% to provide a reduced X set.
Optimizing kNN parameters
As mentioned above, the application of the kNN method entails identifying the k nearest reference pixels in the feature space for each target pixel. Values of each Y within these k nearest pixels are then averaged and assigned to the target pixel. Formally, the estimate 
, the resulting mean value of variable Y for target pixel i, is calculated as in McRoberts (2012):
, the resulting mean value of variable Y for target pixel i, is calculated as in McRoberts (2012):(1)
where 
is the set of observations for the k reference set pixels nearest in feature space to the ith target set pixel, as calculated using a given distance metric (dm). The weights 
used for each of the k pixels in the averaging process are calculated as
is the set of observations for the k reference set pixels nearest in feature space to the ith target set pixel, as calculated using a given distance metric (dm). The weights used for each of the k pixels in the averaging process are calculated as(2)
where dij is the distance in feature space between the ith target pixel and the jth nearest reference pixel calculated using a given dm, and exponent t is used to modulate the impact of distance in the weighting (usually t = 0, 1, or 2).
Optimized selection of the three kNN parameters (dm, t, and k) was performed through the analysis of kNN predictions using the yaImpute R package (Crookston and Finley 2008) and the ref–val set. Predictions using the reduced set of X feature variables were done only for the Euclidian (EUC) dm as our privileged approach and were compared against predictions with the complete X set (31 feature variables) along with four popular distance metrics (Hudak et al. 2008), i.e., EUC, Mahalanobis (MAH), gradient nearest neighbour (GNN), and most similar neighbour (MSN), using the k neighbours version as in Packanen and Maltamo (2007). The Mahalanobis dm handles covariance among Xs, while the two other variants handle X–Y correlations and provide ranking and weighting to features, respectively, through canonical correspondence and canonical correlation analyses. For all of these combinations, t values were restricted to 0 or 1 and k values were between 1 and 15 based on preliminary results from application to a pilot region (Beaudoin et al. 2011).
For each of the five X–dm–t combinations, we computed the multivariate goodness of fit criterion T (McRoberts 2012) across the range of k values using the following equation based on the sample reference set:
(3)
where y represents one of the 27 (Y) response variables used in the HL procedure, wy is a set of weights that sums to 1 (here all set equally to 1/Y), and 
is the fractional amount of variance in response variable y explained by the kNN prediction. The choice of the best X–dm–t combination was based on a comparison of T values among curves. In addition, graph of root mean square deviation vs. k derived from the validation set (eq. 5) was used as a univariate accuracy measure (McRoberts 2012) to further assess the choice of the optimal combination for AGB. For a given X–dm–t combination, the value of k was deemed optimal when its corresponding value of T reached 0.95 of Tmax, where Tmax is the maximal value of T on the curve. This result was further checked against the one found using RMSD% curve for AGB (value of k when RMSD% equalled 1.05 of RMSD%min). The optimization exercise was repeated for the 30 random replicates, yielding values of means and standard errors of T, RMSD%, and optimal k values. These values were then used to compare the EUC kNN using the reduced X set with other dm–t combinations using the complete X set.
is the fractional amount of variance in response variable y explained by the kNN prediction. The choice of the best X–dm–t combination was based on a comparison of T values among curves. In addition, graph of root mean square deviation vs. k derived from the validation set (eq. 5) was used as a univariate accuracy measure (McRoberts 2012) to further assess the choice of the optimal combination for AGB. For a given X–dm–t combination, the value of k was deemed optimal when its corresponding value of T reached 0.95 of Tmax, where Tmax is the maximal value of T on the curve. This result was further checked against the one found using RMSD% curve for AGB (value of k when RMSD% equalled 1.05 of RMSD%min). The optimization exercise was repeated for the 30 random replicates, yielding values of means and standard errors of T, RMSD%, and optimal k values. These values were then used to compare the EUC kNN using the reduced X set with other dm–t combinations using the complete X set.kNN mapping, diagnostic, and accuracy measures
Following this selection process (see Results), the Euclidian kNN with t = 0 and k = 6 using the reduced X set was implemented across Canada for mapping all 127 response variables using a single realization of the ref–val set. No a priori stratification of the country was used to geographically restrain the recruitment of neighbours, but the use of climatic features promoted the recruitment of neighbours from climatically similar areas. Maps of attributes were produced using an in-house C++ kNN routine (kNNMapping) that provides very fast and exact kNN prediction using the approximate nearest neighbor (ANN) library (Mount and Arya 2010).
The kNNMapping routine also produces maps of three diagnostic variables for evaluating sampling representativeness and deficiencies. The first of them is a variance estimator 
in the absence of spatial autocorrelation (McRoberts et al. 2007) among the k neighbours for each attribute:
in the absence of spatial autocorrelation (McRoberts et al. 2007) among the k neighbours for each attribute:(4a)
where yi,j is the value of the PP attribute for neighbour j to pixel i and 
is the predicted mean of the k neighbours. This estimator was computed for each pixel i and was used to calculate a coefficient of variation (CV, %):
is the predicted mean of the k neighbours. This estimator was computed for each pixel i and was used to calculate a coefficient of variation (CV, %):(4b)
where 
is the kNN predicted value. The two other diagnostic variables are the Euclidian (Deuc) and geographic (Dgeo) recruitment distances of the k neighbours for each target pixel to assess sampling distances in the feature space and in the geographical space, respectively.
is the kNN predicted value. The two other diagnostic variables are the Euclidian (Deuc) and geographic (Dgeo) recruitment distances of the k neighbours for each target pixel to assess sampling distances in the feature space and in the geographical space, respectively.Pixel-level accuracy of predicted values relative to “observed” PP attribute values of the 30% validation set was assessed graphically through an observed vs. predicted graph by binned groups of n = 100 samples ranked in order of increasing observed value as in McRoberts (2009). Commonly used accuracy measures were also computed: pseudo coefficient of determination R2 (hereafter R2, equation not shown), relative root mean-squared deviation (RMSD%) (Crookston and Finley 2008), and relative mean deviation (MD%):
(5)
(6)
where for a validation set m containing n pixels indexed i, 
is the kNN predicted value, and yi and 
are, respectively, the pixel value and mean value of the observed PP attribute. Means and standard errors of these measures were obtained with the 30 replicates to take into account the impact of random sample realizations of the ref–val split (LeMay and Temesgen 2005).
is the kNN predicted value, and yi and are, respectively, the pixel value and mean value of the observed PP attribute. Means and standard errors of these measures were obtained with the 30 replicates to take into account the impact of random sample realizations of the ref–val split (LeMay and Temesgen 2005).The calculations were also performed for AGB on 3 × 3, 5 × 5, and 7 × 7 pixel windows (750, 1250, and 1750 m, respectively) centred on PP centroids to test the effect of spatial aggregation on prediction accuracy. This last procedure was applicable only to 379 of the 8202 PPs available due to PP boundary effects (Fig. 2).
Finally, ecozone-level estimates of total AGB (tonnes (t)) obtained by kNN were compared with PP-based total AGB estimates. For our comparison, AGB values were summed across tiles within each ecozone. A tile is the 20 × 20 km2 square centred on a given 2 × 2 km2 PP that it represents (1% sample). Tile-level kNN AGB is the sum of the within-tile pixel estimates, whereas tile-level PP AGB is the mean AGB value in the original PP data expanded to the tile, with the value of the expansion factor nominally equal to 100.
Results
Feature selection and parameter optimization
Results of the HL procedure show that among all 26 feature variables, spectral feature variables explain the most variance in the land cover and structural attribute categories, whereas climatic feature variables generally explain the most variance in the 10 species abundance attributes due to their relationship to climate. Topographic and land cover (WATER) features have only a modest contribution for all attributes (Supplementary Fig. S2a). Depending on the attribute category, best predictor spectral features were B1w and B6s bands and NDVIs and RSRs/w indices, indicative of the usefulness of winter MODIS imagery combined with the summer one. Best climatic features were related to precipitation (PCQ and PWQ) and temperature (MMIN and MAT) (Supplementary Fig. S2b). Merging of all HL-selected feature sets relative to each PP attribute and removal of redundant features enabled us to identify and remove four spectral feature variables and one topographic feature variable. We thus retained 26 feature variables of the complete set of 31 (Table 2).
The analysis of mean T values resulting from the five X–dm–t combinations (Fig. 3A) shows that the best fit is obtained with the complete set using the MSN dm (31X-MSN-t0) followed closely by the combination of the reduced set and the Euclidian dm (26X-EUC-t0). Other combinations using the MAH dm and GNN dm have smaller values of T. Analyses based on the 30 random replicates show the 31X-MSN-t0 variant to be only slightly better than the simpler 26X-EUC-t0 variant, with differences of –2.1% in mean T values and of +1.75% in mean RMSD% values (Fig. 3B) between the two variants (average across all k values). Finally, each combination above was tested for t = 1 relative to t = 0, and in all cases, differences were found to be negligible for both T and RMSD% (results not reported). Given its interpretive advantages, we therefore selected the 26X-EUC-t0 variant for the rest of the study. We also selected k = 6 based on the optimal values of 5.5 ± 0.1 and 4.4 ± 0.1 obtained from T and RMSD% curves, respectively (Figs. 3A and 3B).
Fig. 3.
NFI attribute prediction and diagnostics
Maps of predicted AGB (Fig. 4A) along with three diagnostic variables (Figs. 4B, 4C, and 4D) are reported with their ecozone-level mean values (Fig. 5a). For the six well-inventoried ecozones, values of CV% are large in the mountainous ecozones of western Canada and in areas of low biomass such as recently disturbed or unproductive forests and agriculture areas (Figs. 4B and 5A), suggesting a greater uncertainty in their predicted AGB values. To the contrary, values of CV% are small across the Boreal Shield ecozone with its moderately flat topography and moderate AGB levels. Values of Deuc of the k neighbours from target pixels show a trend similar to that of CV%, further revealing sampling issues in the X feature space for mountainous or low biomass areas (Figs. 4C and 5A). Finally, values of Dgeo predictably increase in areas where the PP sampling is locally sparse or missing (Figs. 1, 4D, and 5A). Across the six well-inventoried ecozones, mean Dgeo is of 161 km.
Fig. 4.
Fig. 5.
Accuracy assessment at various scales
At the pixel level, binned AGB kNN predictions show an overestimation (positive MD%) of smaller values and an underestimation (negative MD%) of larger ones (Fig. 6). The pattern and magnitude of the deviation varies among ecozones and attributes (analysis not shown). When calculated using the complete validation data set across its 30 replicates, mean pixel-level values of MD%, RMSD%, and R2 for AGB are 1.47% ± 0.14%, 69.22% ± 0.18%, and 0.62 ± 0.002, respectively. These mean accuracy measures vary substantially across the six managed ecozones and are the best for the large Boreal Shield ecozone (Fig. 5B). Accuracy measures for all attributes (Supplementary Table S2) show that values of R2 > 0.30, RMSD% < 100%, or absolute MD% < 10% were achieved for land cover and structure attributes, as well as for the abundance of the more common tree species.
Fig. 6.
Pixel aggregation substantially improves all accuracy measures for AGB. Values of R2 increase by 25% and MD% and RMSD% decrease by about 40% when pixels are spatially aggregated beyond a 1 km2 window (Fig. 7). At the level of the six well-inventoried ecozones for totals in AGB, the relative difference between predicted kNN-derived AGB and the “measured” expanded PP AGB totals is within ±4% for all but the two mountainous Boreal Cordillera and Montane Cordillera ecozones and is best for the Boreal Shield ecozone. Overall, relative difference for the six well-inventoried ecozones is –1.83% (Table 3).
Fig. 7.
Table 3.
Note: Ecozones are sorted in decreasing number of PP tiles.
*
Mountainous ecozones.
†
Total number of PP tiles is lower than number of PP reported in Table 1 (N = 7689) as PP tiles including large water bodies (AGB = 0) were removed.
Discussion
The PP data set was successfully used with MODIS spectral information and other auxiliary feature variables within an optimized Euclidean-based kNN prediction method to produce maps of forest attributes across provincial and territorial boundaries for managed forests of Canada. Previously in Canada, various projects have produced land cover maps using either LANDSAT (Wulder et al. 2008) or MODIS imagery (Latifovic et al. 2012), as well as maps of selected forest attributes such as volume and biomass (Hall et al. 2010). However, the present effort is the first to produce a coherent set of quantitative values for such a large suite of forest attributes across Canada’s well-inventoried forests.
As mentioned earlier, Finland has been producing kNN-based national maps of forest properties but has been using LANDSAT multispectral data (Tomppo et al. 2008) because of its relatively small forest domain and dense field plot system as compared with Canada. We successfully used MODIS data as a cost-effective alternative to LANDSAT to cover much larger areas at the expense of decreased resolution, similarly to the kNN-based mapping carried on in the US (Wilson et al. 2012, 2013). Although these studies share their basic NN method with ours, the details of the analyses and resulting accuracies are strongly conditioned by their respective national circumstances.
Accuracy was assessed and analyzed at various scales using a reserved validation set of NFI PP. At the pixel level, the pattern of overestimation of small values and underestimation of large ones (Fig. 6) is typical of kNN (Magnussen et al. 2010) and explains the relatively large and variable values of RMSD% (Fig. 5B; Supplementary Table S2). Sources of errors at the pixel level are diverse but certainly include the use of stand-level photo-interpreted or modeled values of forest attributes as “ground truth” in PPs (Magnussen and Russo 2012) compared with actual field plot data such as used in Wilson et al. (2013). Compounding this problem is the use of older aerial photos for extracting values of forest attributes and their resulting temporal mismatch with the 2001 MODIS mosaics. Ongoing updating of PP information by provincial partners should lead to improved kNN predictions.
Various geometric and radiometric issues related to the MODIS-based spectral feature variables also contribute to the overall uncertainty. Winter reflectance data, an important predictor of forest cover attributes, are sensitive to the variability in snow cover depth and persistence. Larger CV% values at the prairie–forest ecotone in western Canada (Fig. 4b) were found to result from discontinuous snow cover in this low-precipitation area (red patches in Supplementary Fig. S1). Overall, spectral features are prone to radiometric imbalance and residual haze effects within the MODIS mosaic (Pouliot et al. 2009), to decreased geolocation accuracy and increased radiometric distortions in high relief areas (Brosofske et al. 2014), and to spectral saturation (Lu et al. 2012) in areas of large values of forest attributes, particularly in the Pacific Maritime ecozone. Inclusion of additional remotely sensed features such as PALSAR L-band radar backscatter mosaics (Shimada and Ohtaki 2010) could help to reduce the overall uncertainty, particularly for the underestimation of larger biomass values as the L-band signal saturates at a larger biomass level than optical data (Dobson et al. 1992).
The level of uncertainty in the attribute predictions at the pixel level compares favourably with the stand-level uncertainty found by Bernier et al. (2010) for a large operational inventory program in eastern Canada. The highest accuracy was achieved for the Boreal Shield ecozone (Fig. 5B), which represents about 53% of the forest in the six well-inventoried ecozones (Table 1) and 38% of the forest in Canada. The substantial and asymptotic drop in MD% and RMSD% when aggregating pixels beyond a 1 km2 window (Fig. 7) supports the use of the kNN-predicted spatial data sets for small-area estimation (Katila 2006; McRoberts 2012) for which poor inference statistics are expected using the 1% NFI PP samples. The mass balance of AGB totals is generally well preserved at the ecozone level at the cost of decreased resolution, therefore supporting its use for regional reporting (Table 3).
For species abundance, accuracy measurements for the needle-leaved species group are relatively good but accuracy measures for individual species decrease with decreasing species abundance (Supplementary Fig. S3 and Supplementary Table S2). In spite of all their shortcomings, the kNN species-level products provide an improvement in spatial distribution over the existing species composition data set at a 10 × 10 km resolution from the previous Canadian forest inventory (CanFI) (Gillis et al. 2005) or its enhancement to 250 × 250 m resolution through randomized predictions (Yemshanov et al. 2011).
One of the strengths of the kNN approach is that it supports the identification of undersampled areas or forest types through the use of various diagnostic variables (McRoberts 2009, 2012). Our results show that the geographic recruitment distances of the k pixels increase with a decrease in the density of PP, a situation that also increases the probability of recruiting neighbour pixels with incorrect presence of low-abundance species. The mountainous areas of western Canada, as well as areas with low biomass, also pose a particular recruitment challenge in both the spatial and feature domains. Results indicate that the set of reference pixels in these areas is not sufficiently representative of the pixel population and is a source of significant bias (Magnussen et al. 2010). Such information provides valuable feedback to inventory programs and can be used to target areas for further investments in monitoring, which in turn will improve kNN predictions.
Additional avenues for improvement include the use of radar backscatter (Holmström and Fransson 2003), forest stratification (Wilson et al. 2013), a priori information such as coarse species distribution or land cover maps (Tomppo and Halme 2004), and bias correction (Magnussen et al. 2010). Current work priorities also include the generation of 2011 maps of forest attributes, as well as validation and eventually improvements of these products in the unmanaged northern ecozones (Taiga Shield, Taiga Plains, and Taiga Cordillera). The latter is an area of high priority for NFI and for carbon accounting.
In summary, the coupling of PP data with an array of feature variables through the use of the nonparametric kNN method can be used to produce moderate-resolution maps of forest attributes across Canada. The error structure of these products at first analysis appears close to that of regular forest inventories in Canada for key attributes. However, the continuous coverage of quantitative variables harmonized across provincial and territorial boundaries, increased timeliness through assimilation of current information at small incremental cost, and small area estimation are distinct innovations and advantages of these products in the Canadian context. As they stand, these moderate-resolution NFI map products for Canada’s forest are the first of their kind and already have strategic applications in analyses that require timely spatially explicit forest information across provincial boundaries.
Acknowledgements
This project would not have been possible without the high-quality MODIS mosaics provided graciously by Darren Pouliot and Rasim Latifovic (Canada Centre for Remote Sensing of Natural Resources Canada). We also acknowledge the contribution of Dan McKenney and his team (Canadian Forest Service, Natural Resources Canada) for providing the climate-related feature variables and thank both Dan McKenney and Ron McRoberts for their reviews of this manuscript. In addition to our regular operating funds, this project was supported by the Forest Change Initiative of the Canadian Forest Service, whose confidence in this project is deeply appreciated, as well as indirectly by the National Forest Inventory (NFI) and its provincial partner agencies who provided the data foundation for this research. Finally, we express our thanks to Canadian Forest Service specialist Rémi St-Amant for the creation of the fast and efficient C++ kNNMapping code, without which the task of performing Canada-wide analyses would have been a significantly greater challenge.
Footnote
1
Supplementary data are available with the article through the journal Web site at http://nrcresearchpress.com/doi/suppl/10.1139/cjfr-2013-0401.
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Supplementary Material
Supplementary data (cjfr-2013-0401suppl.pdf)
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Published In
Canadian Journal of Forest Research
Volume 44 • Number 5 • May 2014
Pages: 521 - 532
History
Received: 25 September 2013
Accepted: 24 January 2014
Published online: 24 January 2014
Copyright
© 2014.
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BeaudoinA., BernierP.Y., GuindonL., VillemaireP., GuoX.J., StinsonG., BergeronT., MagnussenS., and HallR.J.. Mapping attributes of Canada’s forests at moderate resolution through kNN and MODIS imagery. Canadian Journal of Forest Research.
44(5): 521-532. https://doi.org/10.1139/cjfr-2013-0401
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