Hi,

Greenness is only one of the three dimensions of the Tasseled Cap transformation. The other two dimensions, orthogonal to Greenness, and orthogonal to one another are Brightness and Wetness. These dimensions contain information that is not conveyed by a vegetation index. Brightness is an albedo-like measure, that quantifies how bright-dark a given surface is. Wetness, as the name reveals, provides information on the moisture content of sols and vegetation, and its values are strongly influenced by the DN of the SWIR channels.

The following Google Scholar search provides you links to several papers about the Tasseled Cap: http://scholar.google.pt/scholar?hl=en&q=Tasseled+Cap+transformation&btnG=&as_sdt=1%2C5&as_sdtp=

Remote sensing is not only about measuring vegetation amount. Soils, water bodies, rock outcrops, urban areas are also environmentally important targets and working with three independent dimensions of information in the optical domain will allow for richer land surface analysis.

Thanks a lot dear Prof. Pereira for such a detailed reply which resolved my troubles.

Regards,

Dear Muhammad

I include here some of my thoughts on indices.

There are problems with the blind use of indices whether they be Tasseled Cap Greenness or NDVI or any of the other myriad of spectral indices. All spectral variation has to map somewhere onto any index scale. If you have a requirement to map vegetation amount  then you require an index where variation in vegetation amount maps as unique variation on the vegetation index scale. All variations associated with other landscape/atmospheric dimensions should ideally map to fixed points (not necessarily zero) on that vegetation index scale. For example the effects of shade and brightness should not map as variation on the vegetation index scale. Variation in brightness should be orthogonal to the index scale. Similarly, variation in soil dampness should not project as variation on the  vegetation index scale. There are fundamental problems with the design of Tasseled cap indices. The indices might have been designed to be orthogonal by using an orthogonal principal component transformation process but that process did not properly account for the ratio-scaled nature of the spectral data. The orthogonality of the chosen method (principal components/ factor rotation) has not resulted in the indices being truly orthogonal indices for brightness greenness and wetness.

With uni-dimensional spectral indices such as NDVI and EVI there are no other-dimensional, companion indices like brightness or wetness to assist with understanding how the other landscape variations map onto a reduced spectral space. Some uni-dimensional indices perform better at high levels of cover, some at low levels of cover. Most are sensitive to brightness variation, smoke haze, cloud shadow, terrain shadow and background soil variation.

When developing vegetation change maps using a vegetation index like TC Greenness one needs those detected changes over time to be vegetation changes, not some other change like soil moisture changes . In other words you don't want soil moisture variation to appear as though it is vegetation variation. (This example might only apply to some special landscapes)

If you were mapping change in vegetation over a rainforest you would want the vegetation index scale to be sensitive to small changes in vegetation at high levels of vegetation cover but insensitive to changes in brightness and shade. I suspect, in general, that indices are used by researchers without checking whether they have the desired properties for the application at hand.

http://www.sciencedirect.com/science/article/pii/S092427160900104X

Trevor, very very interesting observations.

I substantially agree with you that "All variations associated with other landscape/atmospheric dimensions should ideally map to fixed points (not necessarily zero) on that vegetation index scale".

Some years ago I tried to develop an index for monitoring quarries revegetation so that index is 0 in naked rock sites and 1 in mature undisturbed vegetation sites in the same area.

https://www.researchgate.net/publication/233369023_Analysis_of_Landsat_5_TM_Images_for_Monitoring_the_State_of_Restoration_of_Abandoned_Quarries

Article Analysis of Landsat 5 TM Images for Monitoring the State of ...

Thanks Ivan for your agreement. Much appreciated.

Since this question attracts many views I will extend my answer in relation to tasseled cap indices.

Vegetation indices are generally regarded as having limited usefulness. Part of this lack of confidence in them is due to a lack of understanding of them. I will focus on the poor understanding of principal components analysis used to produce the tasseled cap indices.

When a principal component analysis is used to transform multidimensional data to fewer "more meaningful dimensions" the data should ideally be multivariate normal prior to transformation. That is, each dimension of the original data should have a normal distribution. Only then will the principal components transformation have a chance of producing a set of orthogonal axes that have meaning in the reduced dimension space, even after rotation of the axes.

A major problem with the tasseled cap indices occurs because the original reflectance data are not multivariate normal. Why? Reflectance has a common true zero reflectance as a lower bound in each of the spectral bands. Data which have a lower bound are not normally distributed (unless the data are far removed from the bound). When a principal component analysis is applied to bound data, instead of seeing a football or oval shape in the bivariate-scatterplot of principal component scores you will see a funnel shape or the tasseled cap shape that gives rise to the name to the “tasseled cap” indices. The funneling pattern is due to all components funneling towards a common zero reflectance. Technically however, pairs of principal component axes are still mathematically orthogonal for the given dataset, no matter the type of data. However, they are not practically orthogonal in the way that researchers interpret or want them to be. What does this mean? A researcher would want greenness and brightness to be orthogonal to each other (independent of each other) so that only greenness alone would be necessary to relate to or describe a vegetation amount. The greater the greenness the greater should be the vegetation amount irrespective of brightness. Greenness should be independent of brightness when describing foliage cover. For the tasseled cap indices, vegetation cover cannot be described by greenness alone even though that is what researchers want to believe.

How can this be tested? If you have a large dataset of foliage cover measurements made in the field that can be directly related to the pixels of the spectral image, colour code the principal component scores (or tasseled cap greenness brightness values) in the bivariate scatterplot and you will see that constant vegetation amount is not parallel to the brightness axis at a constant value of greenness. Constant vegetation amount is oblique to both axes. The angle of obliqueness changes with the amount of vegetation cover. If you use the tasseled cap indices, both greenness and brightness are needed to specify a vegetation amount. For example, for the same level of foliage cover, the greenness index is lower at low brightness and higher at high brightness.

In summary, the tasseled cap indices are built on a wrong premise or misunderstanding of orthogonality and how it relates to vegetation cover. Given this understanding about the meaning of orthogonality, one would also need to question the validity of the rotation that was applied to the orthogonal axes that produced the final tasseled cap indices. One would also need to question whether creating an initial “universal” dataset is the best method for developing spectral indices.

In contrast to the tasseled cap indices, the Principal Polar Spectral indices are calculated on a single image for which the variation in the landscape was essentially one of brightness and greenness. There was no attempt to include all types of landscape variation including snow and water. No rotation was required to realign the principal component axes with a perceived “superior” plane of greenness and brightness. The greenness index is called Principal Polar Spectral Greenness PPSG. The brightness index is called Principal Polar Spectral Brightness. Polar refers to a polar transformation of the principal components whereby the greenness index is an angle in principal component space and the brightness index is a radial distance. The angle represents a change in spectral profile due to a change in the mixture of soil and vegetation components. The brightness represents the amplitude of a spectral profile. This was tested by simulation in my thesis.

A colour coding test of PPSG against PPSB can be used to demonstrate that PPSG is orthogonal to PPSB. Vegetation cover can be specified by PPSG independently of PPSB.

Some advantages of the PPSG index are.

• PPSG values are confined between zero and 1. PPSG values can be used as a direct estimate of foliage cover proportion particularly when the foliage cover is reasonably high (greater than 50%).
• For topographically complex landscapes with relatively high levels of foliage cover, PPSG will perform better as a direct predictor of foliage cover over complex terrain than any other methods that require topographic correction of the reflectance.
• The PPSG index appears to have a greater dynamic range than any of the other indices. In other words PPSG would be better at discerning small differences in foliage cover, particularly at high levels of foliage cover, than other indices.

The basics of my work have been published in

• a conference paper “Modelling of foliage projected cover using Landsat-7 spectral imagery: Spectral indices for greenness and brightness”,
• my thesis
• and “Motivation, development and validation of a new spectral greenness index:A spectral dimension related to foliage projective cover”

I will expand my explanations, and release some of my unpublished work, in Research Gate over time.