Predictive mapping of soil organic carbon in wet cultivated lands using classification-tree based models: the case study of Denmark.

Soil organic carbon (SOC) is one of the most important carbon stocks globally and has large potential to affect global climate. Distribution patterns of SOC in Denmark constitute a nation-wide baseline for studies on soil carbon changes (with respect to Kyoto protocol). This paper predicts and maps the geographic distribution of SOC across Denmark using remote sensing (RS), geographic information systems (GISs) and decision-tree modeling (un-pruned and pruned classification trees). Seventeen parameters, i.e. parent material, soil type, landscape type, elevation, slope gradient, slope aspect, mean curvature, plan curvature, profile curvature, flow accumulation, specific catchment area, tangent slope, tangent curvature, steady-state wetness index, Normalized Difference Vegetation Index (NDVI), Normalized Difference Wetness Index (NDWI) and Soil Color Index (SCI) were generated to statistically explain SOC field measurements in the area of interest (Denmark). A large number of tree-based classification models (588) were developed using (i) all of the parameters, (ii) all Digital Elevation Model (DEM) parameters only, (iii) the primary DEM parameters only, (iv), the remote sensing (RS) indices only, (v) selected pairs of parameters, (vi) soil type, parent material and landscape type only, and (vii) the parameters having a high impact on SOC distribution in built pruned trees. The best constructed classification tree models (in the number of three) with the lowest misclassification error (ME) and the lowest number of nodes (N) as well are: (i) the tree (T1) combining all of the parameters (ME=29.5%; N=54); (ii) the tree (T2) based on the parent material, soil type and landscape type (ME=31.5%; N=14); and (iii) the tree (T3) constructed using parent material, soil type, landscape type, elevation, tangent slope and SCI (ME=30%; N=39). The produced SOC maps at 1:50,000 cartographic scale using these trees are highly matching with coincidence values equal to 90.5% (Map T1/Map T2), 95% (Map T1/Map T3) and 91% (Map T2/Map T3). The overall accuracies of these maps once compared with field observations were estimated to be 69.54% (Map T1), 68.87% (Map T2) and 69.41% (Map T3). The proposed tree models are relatively simple, and may be also applied to other areas.

The fundamentals of average local variance--Part I: Detecting regular patterns.

The method of average local variance (ALV) computes the mean of the standard deviation values derived for a 3 x 3 moving window on a successively coarsened image to produce a function of ALV versus spatial resolution. In developing ALV, the authors used approximately a doubling of the pixel size at each coarsening of the image. They hypothesized that ALV is low when the pixel size is smaller than the size of scene objects because the pixels on the object will have similar response values. When the pixel and objects are of similar size, they will tend to vary in response and the ALV values will increase. As the size of pixels increase further, more objects will be contained in a single pixel and ALV will decrease. The authors showed that various cover types produced single peak ALV functions that inexplicitly peaked when the pixel size was 1/2 to 3/4 of the object size. This paper reports on work done to explore the characteristics of the various forms of the ALV function and to understand the location of the peaks that occur in this function. The work was conducted using synthetically generated image data. The investigation showed that the hypothesis originally proposed in is not adequate. A new hypothesis is proposed that the ALV function has peak locations that are related to the geometric size of pattern structures in the scene. These structures are not always the same as scene objects. Only in cases where the size of and separation between scene objects are equal does the ALV function detect the size of the objects. In situations where the distance between scene objects are larger than their size, the ALV function has a peak at the object separation, not at the object size. This work has also shown that multiple object structures of different sizes and distances in the image provide multiple peaks in the ALV function and that some of these structures are not implicitly recognized as such from our perspective. However, the magnitude of these peaks depends on the response mix in the structures, complicating their interpretation and analysis. The analysis of the ALV Function is, thus, more complex than that generally reported in the literature.

The fundamentals of average local variance--Part II: Sampling simple regular patterns with optical imagery.

In this investigation, the characteristics of the average local variance (ALV) function is investigated through the acquisition of images at different spatial resolutions of constructed scenes of regular patterns of black and white squares. It is shown that the ALV plot consistently peaks at a spatial resolution in which the pixels has a size corresponding to half the distance between scene objects, and that, under very specific conditions, it also peaks at a spatial resolution in which the pixel size corresponds to the whole distance between scene objects. It is argued that the peak at object distance when present is an expression of the Nyquist sample rate. The presence of this peak is, hence, shown to be a function of the matching between the phase of the scene pattern and the phase of the sample grid, i.e., the image. When these phases match, a clear and distinct peak is produced on the ALV plot. The fact that the peak at half the distance consistently occurs in the ALV plot is linked to the circumstance that the sampling interval (distance between pixels) and the extent of the sampling unit (size of pixels) are equal. Hence, at twice the Nyquist sampling rate, each fundamental period of the pattern is covered by four pixels; therefore, at least one pixel is always completely embedded within one pattern element, regardless of sample scene phase. If the objects in the scene are scattered with a distance larger than their extent, the peak will be related to the size by a factor larger than 1/2. This is suggested to be the explanation to the results presented by others that the ALV plot is related to scene-object size by a factor of 1/2-3/4.