Ann Arbor, Michigan, USA
The application of multispectral scanner data to vegetation and soils studies can be facilitated by use of data transformations which reduce the number of channels to be considered, provide a more direct association between signal response and physical processes on the ground, and highlight the particular types of information of greatest interest to the user. This paper describes one such transformation, the TM Tasseled Cap transformation and both summarizes previously reported results and presents the results of new analyses pertaining to vegetation, soils, and external effects information contained in the TM Tasseled Cap feature space.
Keywords: Tasseled Cap, transformations, spectral features, Thematic Mapper, vegetation, soils
Because of the complexities involved with display and extraction of information contained in multispectral scanner data, a variety of approaches have been taken to combining multiple band responses into a lesser number of features which reduce the overall data volume and/or enhance the ability to extract particular types of scene class information. Many of these approaches are discussed by Perry and Lautenschlager (Ref. 1). The Tasseled Cap transformations of MSS (Refs. 2,3) and TM data (Refs. 4,5) accomplish the above goals by providing linear combinations of the original sensor bands which respond primarily to particular physical scene class characteristics and capture 95% or more of the total data variability (in scenes dominated by vegetation and soils) in one-half the original number of channels.
2. BASIC CONCEPTS
As a result of characteristic reflectance properties of scene classes (e.g. green vegetation), sensor data tend to be concentrated in particular portions of the total data volume defined by the sensor bands .
The TM Tasseled Cap transformation is simply an adjustment of viewing perspective (rotation of those data space) such that the concentrations of data within the total data volume are most readily observed (Ref. 6). For example, in the three bands of a hypothetical sensor, the data of interest primarily occupy a plane as shown in Figure 1a. Rotation of the data cube (defined by the three bands) causes the data plane to be most fully presented to view (Figure 1b). Two processes of interest are observed to cause spectral variation primarily in the directions labeled A and B in Figure 1c, so another rotation is applied to align these directions of spectral change with the x- and y-axes (Figure 1d). Now the features defined by the x- and y-axes contain the majority of important data variation, and can be directly related to the physical processes of interest. However, euclidean distances are unaffected, i.e. the three-dimensional data dispersions are exactly as they were -- only the position of the viewer has changed. Further, if the data from which the rotations were determined are representative of their populations, the same rotations should apply to all data from similar climates and scene types (e.g. primarily vegetated), since the driving factors are the spectral expressions of actual physical scene class characteristics (e.g. chlorophyll absorption).
Analyses of simulated and actual TM data (Refs. 4,5) have revealed that vegetation and soils data in the six reflective TM bands (excluding the thermal band) primarily occupy three dimensions. Within these three dimensions two planes are defined which are occupied by fully vegetated and bare soil samples, along with a "transition zone" between the two which is occupied by partially vegetated samples (Figure 2). The three features corresponding to the three data dimensions are named Brightness, Greenness, and Wetness. Brightness, a weighted sum of all six bands, is a measure of overall reflectance (e.g. differentiating light from dark soils). Greenness is a contrast between near-infrared and visible reflectance, and is thus a measure of the presence and density of green vegetation. Wetness is a contrast between shortwave-infrared (SWIR) and visible/ near-infrared (VNIR) reflectance, providing a measure of soil moisture content, vegetation density, and other scene class characteristics. Figure 3 illustrates general locations of some important scene classes in the TM Tasseled Cap feature space. More detailed discussion of the vegetation and soil distributions is provided in later sections.
3. TRANSFORMATION MATRICES
The Landsat-4 TM Tasseled Cap transformation matrix, provided in Table 1, was derived using simulated and actual data results (Ref. 5). In order to facilitate use of the transformation for Landsat-5 TM data, a second matrix was derived by applying the Landsat-5 to Landsat-4 conversion equations of Metzler and Malila (Ref. 7) to the Landsat-4 matrix. Because the conversion equations include both multiplicative and additive terms, the Landsat-5 equivalent transformation consists of a 6x6 matrix of multiplicative coefficients as well as a vector of additive coefficients (Tables 2 and 3). The multiplicative matrix alone produces the proper rotations such that, for example, the Greenness direction is the same for both sensors but the Tasseled Cap features derived will not have the same range of values as do those derived for Landsat-4 data by the original transformation matrix. The additive vector must also be applied (to the computed Tasseled Cap features) in order to obtain signal range equivalence. Note also that without the additive vector, the features are not technically orthogonal.
A test of the Landsat-5 matrix on a single data set (Scene 5020116173, Cedar Rapids, Iowa, Path 25, Row 31, 18 Sept. 84) indicated no gross errors although a more comprehensive analysis including several scenes and, if possible, coincident Landsat-4 and -5 acquisitions would be desirable. While the limited scope of the analysis to date leaves open the possibility that some fine tuning of the Landsat-5 matrix should be done, the transformation as presented produces better results for Landsat 5 data than does the original Landsat-4 transformation matrix, and is thus the best available choice for Landsat 5 data.
4. CULTIVATED VEGETATION CHARACTERISTICS
Figure 4 illustrates the spectral paths followed by a typical cultivated crop over the growing cycle. Among the types of information contained in the TM Tasseled Cap data is the percentage of the pixel covered by green vegetation. Using TM Tasseled Cap Greenness and Wetness (Figure 4c) a simple angle can be defined (Figure 5) which shows strong correlation to the percentage of vegetative cover of three different crops (Figure 6). These results were derived using spectral data from experimental field plots whose physical characteristics were also measured and recorded in detail (Ref. 8).
Secondly, the Wetness dimension offers promise of improved delineation between fields which are greening-up (emerging and developing vegetation) and those which are senescing. Because combinations of green vegetation and bare soil closely resemble combinations of green and brown vegetation in the Brightness and Greenness projection, these classes have been difficult to distinguish in Landsat-MSS data (where Brightness and Greenness capture nearly all the important vegetation and soil information). However, analyses of both field-measured and actual Landsat TM data suggest that the two classes will be more separable in the Greenness/Wetness projection, since senescing vegetation remains in the "plane of Vegetation" until the process of senescence is well advanced. During this time, it can be readily distinguished both from fully green vegetation (based on Greenness), and from developing green vegetation (based on Wetness).
5. FOREST/NATURAL VEGETATION CHARACTERISTICS
The distinction between forest/natural vegetation and cultivated vegetation is enhanced in the third TM Tasseled Cap dimension (Wetness). In the Greenness/Brightness projection comparable to MSS data (Figure 3a), some separation occurs, with the particular location of the forest data distribution giving rise to the term "badge of trees" (i.e. on the front of the "cap" -- Ref. 2). The added information in the Greenness/Wetness projection (Figure 3c) results in clearer separation which is particularly striking in color composite imagery.
The most likely explanation for the Tasseled Cap Wetness difference is the increase in visible shadows in forest stands as compared to cultivated crop or grass canopies. Kimes et al. (Reference 9) indicate that while relatively dense forest stands tend to behave much as agricultural crops or grasslands with respect to scattering less dense stands are characterized by higher probability of gap (i.e. Likelihood of observing lower canopy layers) and increased occurrence of low transmitting clumps, both of which will increase the total amount of shadowing and the proportion of shadow in the sensor field of view. In addition, any forest stand will contain a higher percentage of opaque stems, as compared to a grass or crop canopy, thus increasing the incidence of deep shadows both on the lower layers of the canopy and on the leaves/needles in the tree crowns.
The hypothesis that increased shadowing should cause increased signal in the Wetness feature finds support on theoretical grounds as well as in simulated and actual data. The inverse relationship between scattering and wavelength suggests that areas lit only by skylight (i.e. shadowed areas) should receive relatively more illumination in the visible and near-infrared wavelength regions than in the SWIR, which would result in higher Wetness values than would be observed for the identical area illuminated directly. A second piece of evidence comes from simulation of the sensor signals produced from uniform reflecting panels across the 0.4 to 2.5 um wavelength range. TM Tasseled Cap Wetness values from low reflecting panels ("shadow-like") fall at the extreme high end of values for TM data simulated in the same way from reflectance spectra of crops and soils. Finally observation of actual data supports the hypothesis. Horler and Ahern (Reference 10) indicate a strong sensitivity to shadow in their third principal component, whose coefficients are essentially identical to TM Tasseled Cap Wetness. Further, cloud shadows in TM Tasseled Cap imagery are virtually indistinguishable from forest stands in the Wetness feature. Thus the available evidence strongly suggests that the Wetness difference between forest and crop/grass canopies is in large part due to shadowing.
With regard to forest stand information, Horler and Ahern (Reference 10) suggest that the SWIR bands provide an improved ability to estimate stand density. This suggestion also finds support in our analysis of TM imagery. U.S. Forest Service stand maps were obtained for a 72 square-mile area of the Upper Pensinsula of Michigan, and were compared to Landsat-5 TM imagery transformed to TM Tasseled Cap features. In that area, the highest Wetness values were associated with three planted stands, approximately 25 years old, of red pine and black spruce. Based on the fact that these are planted rather than natural stands and that the common practice at least for red pine plantations is to plant at a high density, we can assume that these stands are among the most dense in the scene. Their high Wetness response suggests that stand density is indeed expressed in the Tasseled Cap Wetness feature.
One other note of interest concerns discrimination of coniferous from deciduous stands. In the color composite TM Tasseled Cap image of the Michigan scene, many maple/beech or aspen stands are readily distinguishable from conifer stands or, in some cases, oak stands. This difference, however, is not apparent in the Wetness image, but rather is the result of higher Brightness and Greenness values for the maple and aspen stands. The specific reasons for these spectral differences are not known.
6. SOIL CHARACTERISTICS
In TM data as in MSS data, the Brightness direction is correlated to texture and moisture content of soils. However additional information is available in the Wetness direction. Analysis of lab-measured soils over a range of moisture contents (Ref. 11, data from Ref. 12) showed a strong correlation between changes in moisture content (wet to dry) and direction of spectral change in the Brightness/Wetness projection (Figure 7). Additional analysis of a smaller set of soils data collected specifically for this purpose showed a similar correlation (Figure 8, Ref. 13), although the correlation between spectral location in the Brightness/Wetness projection and absolute moisture content (percent by weight) was poor. However. Wetness was found to be well correlated, within broad soil texture classes, to pF (a measure of soil moisture tension), which is in fact a more relevant datum for soil and vegetation management purposes. Figure 9 illustrates this correlation. The slope of the steeply ascending portion of the curves shows a consistent relationship to the broad textural classifications of the soils.
Thus is appears that TM Tasseled Cap Wetness, combined with broad textural classification, can yield useful information with respect to soil moisture status. Such textural information could be derived from either spectral data or historic soil maps.
7. ATMOSPHERIC HAZE CHARACTERISTICS
Figure 10 illustrates the general effects of haze on the overall vegetation and soils distributions in the three primary projections of the TM Tasseled Cap feature space (Ref. 14). These figures were derived using simulated Landsat-4 TM Tasseled Cap data (based on field-measured spectra), and the Dave atmospheric model, with the difference between "clear" and "hazy" being a five-fold increase in aerosol density (Ref. 15).
Since most of the scene-class-related spectral variation is contained in the first three features, an additional feature defined in the direction of maximum haze-related variation in the fourth through sixth dimensions of the data volume should provide a means of measuring atmospheric haze without the confounding influence of scene content. Figure 11 illustrates the distribution of this haze feature (the fourth TM Tasseled Cap feature) for a large set of simulated Landsat-4 TM data and the same two conditions of the Dave atmospheric model (Ref. 14). The clear and hazy distribution means are separated by more than four standard deviations, with no overlap at the 2 level. The other two distributions in Figure 10 represent partial atmospheres in the Dave model, neither of which has any aerosol component. Between these two distributions and the clear (i.e. very small aerosol component) distribution, an average shift of 1 occurs. Applied to a Landsat-4 TM scene near Mobile Alabama which contains a large smoke plume, the haze feature clearly delineates the smoke plume while smoothing out nearly all of the scene class variation (Figure 12, Ref. 15). However, the feature is sensitive to senescent vegetation, manmade materials (e.g. roads), some soils, and water. Thus in its current form, the use of this feature for haze detection must be restricted to scenes dominated by green vegetation, and used in combination with a screening algorithm to flag and ignore confusion classes.
The TM Tasseled Cap transformation provides a convenient method for reorienting TM data such that vegetation and soils information can be more easily extracted, displayed, and understood. The transformation applied as is to any temperate climate scene will produce invariant features which can be directly compared (i.e. between scenes or sensors), thereby simplifying the development of automatic signal processing algorithms and minimizing the need for re-calibration of either algorithms or expectations (i.e. of human interpreters).
In the TM Tasseled Cap feature space, information on vegetation type, stage of development, and condition, and soil type and moisture status, is readily available. In addition, estimation of atmospheric condition can be made from the data themselves, with minimal impact from ground class response differences.
Neither the TM Tasseled Cap transformation nor any other transformation can create information which was not present in the original data. However, by capturing the majority of data variation in the fewest possible number of features, and aligning the data such that direct association can be made between feature response and physical characteristics of scene classes, the TM Tasseled Cap transformation greatly facilitates extraction of the information contained in the multi-dimensional, multispectral data.
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