A new tasselled cap transformation based on Landsat 7 at-satellite reflectance was developed. This transformation is most appropriate for regional applications where atmospheric correction is not feasible. The brightness, greenness and wetness of the derived transformation collectively explained over 97% of the spectral variance of the individual scenes used in this study

Homer, Collin

Huang, C.

Yang, Wylie L.

Zylstra, G.

English

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USGS Staff -- Published Research US Geological Survey 
2002 
Derivation of a tasselled cap transformation based on Landsat 7 
at-satellite reflectance 
C. Huang 
USGS EROS Data Center, cqhuang@umd.edu 
Wylie L. Yang 
USGS EROS Data Center 
Collin Homer 
U.S. Geological Survey, homer@usgs.gov 
G. Zylstra 
USGS EROS Data Center 
Follow this and additional works at: https://digitalcommons.unl.edu/usgsstaffpub 
 Part of the Geology Commons, Oceanography and Atmospheric Sciences and Meteorology Commons, 
Other Earth Sciences Commons, and the Other Environmental Sciences Commons 
Huang, C.; Yang, Wylie L.; Homer, Collin; and Zylstra, G., "Derivation of a tasselled cap transformation 
based on Landsat 7 at-satellite reflectance" (2002). USGS Staff -- Published Research. 621. 
https://digitalcommons.unl.edu/usgsstaffpub/621 
This Article is brought to you for free and open access by the US Geological Survey at DigitalCommons@University of 
Nebraska - Lincoln. It has been accepted for inclusion in USGS Staff -- Published Research by an authorized 
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int. j. remote sensing, 2002, vol. 23, no. 8, 1741–1748
Derivation of a tasselled cap transformation based on Landsat 7
at-satellite re ectance
C. HUANG, B. WYLIE, L. YANG, C. HOMER and G. ZYLSTRA
Raytheon ITSS, USGS EROS Data Center, Sioux Falls, SD 57198, USA;
e-mail: huang@usgs.gov
(Received 12 March 2001; in  nal form 19 October 2001 )
Abstract. A new tasselled cap transformation based on Landsat 7 at-satellite
re ectance was developed. This transformation is most appropriate for regional
applications where atmospheric correction is not feasible. The brightness, green-
ness and wetness of the derived transformation collectively explained over 97%
of the spectral variance of the individual scenes used in this study.
1. Introduction
The tasselled cap transformation is a useful tool for compressing spectral data
into a few bands associated with physical scene characteristics (Crist and Cicone
1984). Originally constructed for understanding important phenomena of crop
development in spectral space (Kauth and Thomas 1976), the transformation has
potential applications in revealing key forest attributes including species, age and
structure (e.g. Cohen et al. 1995 ).
Essentially two tasselled cap transformations have been developed based on
Landsat Thematic Mapper (TM)–one based on digital number (DN) (Crist and
Cicone 1984) and the other on re ectance factor (Crist 1985), which for simplicity
will be referred to as DN based and re ectance factor based transformations , respect-
ively. While the similar spectral characteristics of TM and the Landsat 7 Enhanced
Thematic Mapper Plus (ETM+) might suggest direct applicability of both trans-
formations to ETM+ images (Crist and Kauth 1986), an at-satellite re ectance
based transformation is needed for large area applications for the following reasons.
First, the re ectance factor based transformation was developed based on ground
measurements with little atmospheric eVects (Crist 1985). Applying this transforma-
tion to satellite images requires the images to be corrected for atmospheric eVects.
Although several atmospheric correction algorithms have been developed (e.g. Liang
et al. 1997), for large area applications, many users are still concerned with possible
unknown errors that may arise due to lack of (or uncertainties in the) ground and
atmospheric data necessary for running these algorithms, and therefore, often choose
not to perform atmospheric correction (e.g. Cohen et al. 2001). Second, use of the
DN based transformation in multi-scene applications can be problematic, because
changing sun illumination geometry greatly aVects DN, and thus aVects the derived
tasselled cap value. As will be demonstrated in §3.1, a large part of the impact of
Internationa l Journal of Remote Sensing
ISSN 0143-1161 print/ISSN 1366-590 1 online © 2002 Taylor & Francis Ltd
http://www.tandf.co.uk/journals
DOI: 10.1080/01431160110106113
C. Huang et al.1742
illumination geometry can be normalized by converting DN to at-satellite re ectance.
Therefore, a transformation based on at-satellite re ectance is more appropriate for
regional applications where atmospheric correction is not feasible.
The purpose of this Letter is to demonstrate the necessity to convert DN to
at-satellite re ectance when atmospheric correction is not feasible, and to derive an
at-satellite re ectance based tasselled cap transformation. Full explanation of the
basic tasselled cap concept and its characteristics was provided in Kauth and Thomas
(1976) and Crist and Cicone (1984).
2. Data and methods
A set of 5 pairs of clear and near cloud-free ETM+ scenes representing both
leaf-on and leaf-oV conditions for a variety of landscapes of the United States were
used in this study (table 1). These images were radiometrically and geometrically
corrected in the EROS Data Center of the US Geological Survey using standard
methods (Irish 2000). Raw digital number was converted to at-satellite re ectance
according to Markham and Barker (1986) and the Landsat 7 Science Data Users
Handbook (Irish 2000).
The impact of sun illumination geometry was demonstrated using pseudo-
invariant objects including large  at building roofs, airport runways, large parking
lots and deep water. These objects were identi ed visually from each of the  ve pairs
of ETM+ scenes.
The at-satellite re ectance based tasselled cap transformation was derived using
the method described in Crist and Cicone (1984). About 2000 random samples were
selected from each of the 10 ETM+ scenes. A principal component analysis was
performed on all random samples to de ne the initial principal axes. With the
orthogonality of all six axes preserved, the transformation was derived through a
Table 1. Landsat 7 ETM+ images used in this study.
Geographic Acquisition Variance
Path Row location date (all in 1999 ) explained (%)*
15 34 Virginia, east 28 July 99.50
15 34 Virginia, east 17 November 99.12
16 34 Virginia, west 19 July 99.35
16 34 Virginia, west 8 November 98.82
31 30 Nebraska 12 July 98.37
31 30 Nebraska 17 November 97.96
39 31 Utah 4 July 99.31
39 31 Utah 24 October 99.42
46 29 Oregon 22 August 99.36
46 29 Oregon 28 December 99.19
*Percentage of the variance of all six spectral bands explained by the  rst three axes of
the at-satellite re ectance based tasselled cap transformation.
Figure 1. Pseudo-invariant objects selected from the Nebraska scene (path 31/row 30) have
quite diVerent DN values between summer and fall/winter. Many of the diVerences
are removed by converting the DN to at-satellite re ectance. The units for both
x- and y-axis are (a) DN value and (b) at-satellite re ectance ×400. Each point
represents a pseudo-invariant object. The plots for pseudo-invariant objects selected
from the other four pairs of ETM+ scenes are similar.
Remote Sensing L etters 1743
C. Huang et al.1744
Table 2. Tasselled cap coeYcients for Landsat 7 ETM+ at-satellite re ectance.
Index Band 1 Band 2 Band 3 Band 4 Band 5 Band 7
Brightness 0.3561 0.3972 0.3904 0.6966 0.2286 0.1596
Greenness ­ 0.3344 ­ 0.3544 ­ 0.4556 0.6966 ­ 0.0242 ­ 0.2630
Wetness 0.2626 0.2141 0.0926 0.0656 ­ 0.7629 ­ 0.5388
Fourth 0.0805 ­ 0.0498 0.1950 ­ 0.1327 0.5752 ­ 0.7775
Fifth ­ 0.7252 ­ 0.0202 0.6683 0.0631 ­ 0.1494 ­ 0.0274
Sixth 0.4000 ­ 0.8172 0.3832 0.0602 ­ 0.1095 0.0985
sequence of rotations. Several hundreds of soil, impervious surface, dense vegetation
and water samples were selected from the 10 scenes to guide the rotations.
3. Results and discussion
3.1. Impact of illumination geometry and its normalization
Figure 1(a) compares the DN values of the selected pseudo-invariant objects
between summer and fall/winter. The values diVered substantially between summer
and fall/winter, though the re ective properties of those objects should be relatively
stable over time. While the diVerences may be attributed to diVerent atmospheric
conditions or possible changes in the re ective property of the selected pseudo-
invariant objects, the fact that most of them were removed by converting DN to
at-satellite re ectance suggests that, for the  ve pairs of clear and near cloud-free
images, the diVerences were mostly caused by changing illumination geometry
( gure 1(b)). If the DN based transformation is applied to DN images, these pseudo-
invariant objects likely will have diVerent tasselled cap values between summer and
fall/winter. Such impact of illumination geometry can confuse the analysis of real
change signals that are characteristic of ground targets. Figure 1(b) suggests that for
clear and cloud-free images, it is possible to remove much of this confusion by
converting DN to at-satellite re ectance. The conversion method is physically based
and easy to automate . Though it is also possible to normalize such impact by  tting
a line between summer and fall/winter images using the pseudo-invariant objects
(e.g. Schott et al. 1988), selecting pseudo-invariant objects can be time consuming
and is often impractical for regional applications involving large numbers of scenes.
3.2. T he tasselled cap transformation
Table 2 gives the coeYcients for the derived tasselled cap transformation based
on at-satellite re ectance. This transformation is not directly comparable to the DN
based one because the two transformations are derived based on measurements of
diVerent physical units. The re ectance factor based transformation developed by
Crist (1985), however, can be compared to the at-satellite re ectance based trans-
formation because they are based on measurements of the same physical units.
Generally, the three major axes—brightness, greenness and wetness, are de ned by
similar concepts for the two transformations , though the coeYcients are not exactly
the same. The relative locations of the soil, impervious surface, dense vegetation and
water samples selected from the 10 ETM+ scenes in the two transformed spaces
are also similar ( gure 2). However, there is a major problem with applying directly
the re ectance factor based transformation to at-satellite re ectance images: the
greenness value of soil increases as its brightness value increases, making it diYcult
to diVerentiate bright soil pixels from some dark green vegetation pixels using the
Remote Sensing L etters 1745
Figure 2. Soil (‘s’), impervious surface (‘i’), dense vegetation (‘g’) and water (‘w’) in the spaces
of (a) at-satellite re ectance based and (b) re ectance factor based transformations.
Both transformations were applied to at-satellite re ectance images rescaled by 400
(see  gure 1(b)). The radial lines have a slope interval of 10 degrees and are used for
visual aids.
C. Huang et al.1746
Figure 3. Greenness calculated by applying directly the re ectance factor based transforma-
tion to an at-satellite re ectance image might not be able to diVerentiate dark green
vegetation from bright soil. The at-satellite re ectance based greenness image, however,
is similar to the NDVI image, and they both reveal the spatial pattern of green
vegetation. The 5.4 km×5.4 km image window was selected from an ETM+ scene
(path 38/row 32, acquired on 17 October 1999 ) not used in deriving the at-satellite
re ectance based transformation.
greenness alone ( gure 3). This problem is probably due to a stronger brightening
eVect of the atmosphere in the visible bands on dark soil than on bright soil
(Kaufman 1989), which reduces the greenness value of dark soil more severely than
does bright soil. The at-satellite re ectance based transformation does not have this
problem when applied to at-satellite re ectance images. Figure 2 suggests that the
at-satellite re ectance based transformation can diVerentiate water from land targets
in the brightness-wetness space slightly better than the re ectance factor based
transformation.
Many applications often use the  rst three components of the tasselled cap
transformation and are concerned with the information content of the three compon-
ents. The last column of table 1 shows that very high percentages of the spectral
variance of individual images were explained by the  rst three components of the
Remote Sensing L etters 1747
developed transformation. Considering the variety of landscapes represented by the
10 scenes, this at-satellite re ectance based transformation is probably applicable to
clear and near cloud-free images for both leaf on and leaf oV seasons over the
conterminous United States.
4. Conclusions
An at-satellite re ectance based tasselled cap transformation was developed based
on 10 Landsat 7 ETM+ scenes representing a variety of landscapes of the United
States in both leaf-on and leaf-oV seasons. This transformation is most appropriate
for regional remote sensing applications where atmospheric correction is not feasible.
The DN based transformation is often not appropriate for this type of application,
because DN value is strongly aVected by changing illumination geometry. A large
part of the impact of illumination geometry can be normalized by converting DN
to at-satellite re ectance. Applying the ground re ectance factor based transforma-
tion directly to at-satellite re ectance images is not appropriate because it may result
in unreasonable tasselled cap values. The at-satellite re ectance based transformation
generally does not have this problem when applied to clear and near cloud-free
at-satellite re ectance images. The brightness, greenness and wetness of the derived
transformation collectively explained over 97% of the spectral variance of individual
scenes used in this study.
Acknowledgment
This study was made possible in part by the Raytheon Corporation under US
Geological Survey contract 1434-CR-97-CN-40274 .
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Derivation of a tasselled cap transformation based on Landsat 7
at-satellite reflectance

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Derivation of a tasselled cap transformation based on Landsat 7 at-satellite reflectance

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