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A general method to normalize Landsat reflectance data to nadir BRDF
adjusted reflectance
D.P. Roy
a,
⁎,H.K.Zhang
a
,J.Ju
b,c
, J.L. Gomez-Dans
d,e
,P.E.Lewis
d,e
, C.B. Schaaf
f
,Q.Sun
f
,J.Li
a
,
H. Huang
a
, V. Kovalskyy
a
a
GeospatialScience Center of Excellence, South Dakota State University, Brookings, SD 57007, USA
b
Universities Space Research Association, 7178 Columbia Gateway Dr, Columbia, MD 21046, USA
c
NASA Goddard Space Flight Center, 8800 Greenbelt Rd, Greenbelt, MD 20771, USA
d
NERC National Centre for Earth Observation (NCEO), UK
e
Department of Geography, University College London, Gower Street, London WC1E 6BT, UK
f
School for the Environment, University of Massachusetts Boston, Boston, MA 02125, USA
abstractarticle info
Article history:
Received 31 October 2015
Received in revised form 23 January 2016
Accepted 28 January 2016
Available online xxxx
The Landsat satellites have been providing spectacular imagery of the Earth's surface for over40 years. However,
they acquire images at view angles ±7.5° from nadir that cause small directional effects in the surface reflec-
tance. There are also variations with solar zenith angle over the year that can cause apparent change in reflec-
tance even if the surface properties remain constant. When Landsat data from adjoining paths, or from long
time series are used, a model of the surface anisotropy is required to adjust all Landsat observations to a uniform
nadir view (primarily for visual consistency, vegetation monitoring, or detection of subtle surface changes). Here
a generalized approach is developed to provide consistent view angle corrections across the Landsat archive.
While this approach is not applicable for generationof Landsat surface albedo, which requires a full characteriza-
tion of the surface bidirectional reflectance distribution function (BRDF), or for correction to a constant solar
illumination angle across a wide range of sun angles, it provides Landsat nadir BRDF-adjusted reflectance
(NBAR) for a range of terrestrial monitoring applications.
The Landsat NBAR is derivedas the product of the observed Landsat reflectance and the ratio of the reflectances
modeled using MODIS BRDF spectral model parameters for the observed Landsat and for a nadir view and fixed
solar zenith geometry. In this study, a total of 567 conterminous United States (CONUS) January and July 2010
Landsat 5 Thematic Mapper (TM) and Landsat 7 Enhanced Thematic Mapper (ETM+) images that have swath
edge overlapping paths sensed in alternating backscatter and forward scattering orientations were used. The av-
erage difference between Landsat 5 TM and Landsat 7 ETM+ surface reflectance in the forward and backward
scatter directions at the overlapping Landsat scan edges was quantified. The CONUSJuly view zenith BRDF effects
were about 0.02 in the Landsat visible bands, and about 0.03, 0.05 and 0.06, in the 2.1 μm, 1.6 μm and near-
infrared bands respectively. Comparisons of Landsat 5 TM and Landsat 7 ETM + NBAR derived using MODIS
BRDF spectral model parameters defined with respect to different spatial and temporal scales, and defined
with respect to different land cover types, were undertaken. The results suggest that, because the BRDF shapes
of different terrestrial surfaces are sufficiently similar over the narrow 15° Landsat field of view, a fixed set of
MODIS BRDF spectral model parameters may be adequate for Landsat NBAR derivation with little sensitivity to
the land cover type, condition, or surface disturbance. A fixed set of BRDF spectral model parameters, derived
from a global year of highest quality snow-free MODIS BRDF product values, are provided so users may
implement the described Landsat NBAR generation method.
© 2016 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords:
Bidirectional reflectance distribution function
(BRDF)
Landsat
NBAR
MODIS
1. Introduction
Landsat data offer a unique 40+ year record of theterrestrial surface
(Roy et al., 2014). Recently, there has been a significant increase in the
development of techniques using dense Landsat time series to describe
surface landcover type, condition and dynamics (Boschetti, Roy, Justice,
& Humber, 2015; Brooks, Thomas, Wynne, & Coulston, 2012; Hansen &
Loveland, 2012; Hansen et al., 2014; Yan & Roy, 2014; Zhu, Woodcock, &
Olofsson, 2012) and the development of spatially mosaiced and tem-
porally composited Landsat reflectance products that use a signifi-
cant proportion of the available Landsat data (Griffiths, van der
Linden, Kuemmerle, & Hostert, 2013; Lindquist, Hansen, Roy, &
Remote Sensing of Environment 176 (2016) 255–271
⁎Corresponding author.
http://dx.doi.org/10.1016/j.rse.2016.01.023
0034-4257/© 2016 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Contents lists available at ScienceDirect
Remote Sensing of Environment
journal homepage: www.elsevier.com/locate/rse
Justice, 2008; Roy et al., 2010). This has been made possible by the
free availability of systematically geolocated (Lee, Storey, Choate, &
Hayes, 2004; Storey, Choate, & Lee, 2014) and radiometrically cali-
brated (Markham & Helder, 2012) Landsat data and also in some
cases by algorithms for Landsat atmospheric correction (Masek
et al., 2006; Ouaidrari & Vermote, 1999) and cloud detection (Irish,
Barker, Goward, & Arvidson, 2006; Scaramuzza, Bouchard, &
Dwyer, 2012; Zhu & Woodcock, 2012). Algorithms for the correction
of the directional dependency of Landsat reflectance have received less
attention however. Arguably this is because directional reflectance ef-
fects, commonly described by the bidirectional reflectance distribution
function (BRDF) (units of sr
−1
), are relatively small in Landsat data,
due to the narrow 15° sensor field of view and also because the acquisi-
tion view zenith angle is usually less than the solar zenith angle and so
Landsat reflectance hot-spot effects do not occur (Zhang et al. in press).
Most terrestrial surfaces are not Lambertian and so directional
reflectance effects are present in satellite reflectance retrievals due to var-
iable solar-surface-sensor geometry. Terrestrial reflectance anisotropy
varies with the physical arrangement, structural variability, and optical
properties of the surface components (soil, grass, trees, etc.) and nominal-
ly may vary with the land cover type and condition (Gao, Schaaf, Strahler,
Jin, & Li, 2003; Roberts, 2001). The BRDF of terrestrial surfaces can be
broadly described by dome-bowl anisotropic reflectance shapes (basis
functions) with a retro-reflectance peak (hot spot) that describes the in-
creased directional reflectance associated with shadow hiding that occurs
when the solar and view direction coincide (Hautecœur & Leroy, 1998;
Jackson et al., 1990; Li & Strahler, 1992; Maignan, Bréon, & Lacaze,
2004; Rahman, Verstraete, & Pinty, 1993; Roujean, Leroy, & Deschamps,
1992). Models of the BRDF of terrestrial surfaces are commonly inverted
against multiple cloud-cleared, atmospherically-corrected directional re-
flectance values that sufficiently sample this anisotropy. Inversion over
snow covered surfaces may be less reliable because snow can exhibit sig-
nificant forward scattering particularly in the near and short wave infra-
red (Aoki et al., 2000; Warren, Brandt, & Hinton, 1998). Bacour and Bréon
(2005) observed that only a limited number of archetypal BRDF shapes
(typically five in the red and near infrared) capture most of the variability
of the directional reflectance observed in snow-free coarse resolution PO-
Larization and Directionality of the Earth's Reflectances (POLDER) data
(view zenith angles up to 70°). Similarly, Jiao et al. (2014) and Zhang
et al. (2015) observed that six archetypal BRDF shapes can be generally
identified in snow-free Moderate Resolution Imaging Spectroradiometer
(MODIS) data (view zenith angles up to 65°).
Empirical statistical correction methods to minimize Landsat BRDF
effects have been developed and they require the presence of similar
land cover types or pseudo-invariant features located across each
image (Broich et al., 2011; Hansen et al., 2008; Toivonen, Kalliola,
Ruokolainen, & Malik, 2006). However, such features are not always
available and images normalized in this manner are only comparable
reliably to other images within the normalized data set. More global-
ly applicable approaches that employ external BRDF information de-
rived from the MODIS BRDF/Albedo product suite (Schaaf, Liu, Gao, &
Strahler, 2011; Schaaf et al., 2002) have been advocated (Flood,
Danaher, Gill, & Gillingham, 2013; Gao et al., 2014; Li et al., 2010;
Roy et al., 2008). They normalize observed Landsat reflectance to
nadir (0° view zenith) and a specified solar zenith angle to generate
Landsat nadir BRDF adjusted reflectance (NBAR). A c-factor approach,
similar to that proposed by Flowerdew and Haigh (1995) and first
described for Landsat application by Roy et al. (2008), is used, whereby
Landsat NBAR is derived as the product of the observed Landsat reflec-
tance and the ratio of the reflectances modeled using contemporaneous
MODIS BRDF spectral model parameters for the observed Landsat and
for a nadir view and fixed solar zenith geometry. The c-factor approach
is applied on a per-pixel basis and is unaffected by the presence of miss-
ing or contaminated neighboring Landsat pixels, does not require the
presence of pseudo-invariant features or similar land cover types across
each image, accommodates spatial and temporal surface dynamics that
are observable at the 500 mMODIS BRDF/Albedo gridded product reso-
lution, and may be automated without the need for tuning parameters
(Roy et al., 2008). Note that the c-factor BRDF normalization is not
applicable to sensors with large view angle variations, such as the
MODIS and Visible Infrared Imaging Radiometer Suite (VIIRS) scanning
instruments, nor for the normalization of significant solar illumination
variations.
Recently, researchers have suggested, based on examination of lim-
ited amounts of satellite data, that spatially and temporally explicit
MODIS BRDF spectral model parameters used to c-factor normalize
Landsat imagery perform no better than using a fixed set of BRDF spec-
tral model parameters (Flood, 2013; Flood et al., 2013). Claverie et al.
(2015) demonstrated similar findings over sample land covers using a
sample of 28.0° maximum viewing zenith angle Satellite Pour
l'Observation de la Terre (SPOT-4) images. Potentially, the BRDF shapes
of terrestrial surfaces may be sufficiently similar over the 15° Landsat
field of view that a c-factor BRDF normalization approach may be ap-
plied reliably using only a single fixed set of MODIS BRDF spectral
model parameters. If this is the case then Landsat NBAR can be derived
in a computationally efficient manner for all the Landsat global long-
term record and not just from February 2000 onwards when the
MODIS products became first available (Justice et al., 2002).
In this paper the MODIS BRDF/Albedo model parameter and MODIS
land cover products, and Landsat5 Thematic Mapper (TM) and Landsat
7 Enhanced Thematic Mapper Plus (ETM+) data, are used to derive and
examine the utility of a single fixed set of BRDF spectral model parame-
ters for Landsat NBAR generation. The satellite data and pre-processing
are described, and then the evaluation methods and results, including a
quantification of the magnitude of Landsat view zenith BRDF effects ob-
served across the conterminous United States (CONUS), are presented.
The Landsat BRDF normalization sensitivity to the use of MODIS BRDF
spectral model parameters defined with respect to different spatial
(CONUS and global) and temporal (weekly and annual) scales, and
defined with respect to different land cover types, is reported. A general
method to normalize Landsat reflectance data to NBAR is suggested and
the recommended MODIS BRDF derived spectral model parameters are
provided for users to implement. The paper concludes with a discussion
and the implications of the research.
2. Data
2.1. Landsat TM and ETM+ data
The Landsat 5 and 7 satellites are in thesame approximately 710 km
sun-synchronous circular 98.2° inclined orbit and overpass every Earth
location every 16 days but are offset from each other by 8 days
(Loveland & Dwyer, 2012; Teillet et al., 2001). The Landsat 5 TM and
Landsat 7 ETM+ sensors have 15° field of view and their data are avail-
able in approximately 185 km × 180 km scenes defined in a Worldwide
Reference System (WRS) of path (groundtrack parallel) and row
(latitude parallel) coordinates (Arvidson, Goward, Gasch, & Williams,
2006). In May 2003 the Landsat 7 ETM + scan line corrector failed,
reducing the usable data in each Landsat ETM + image by 22%
(Markham, Storey, Williams, & Irons, 2004). The Landsat 5 TM has no
such missing data issue. The Landsat 5 sensor acquired data from 1984
until 2012 while the Landsat 7 instrument is still operational. The
Landsat 5 and 7 acquisitions are nominally processed to Level 1 terrain
corrected (L1T) level with processing that includes radiometric correc-
tion, systematic geometric correction, precisioncorrection using ground
control, and the use of a digital elevation model to correct parallax error
due to local topographic relief (Lee et al., 2004). The Landsat 5 TM and 7
ETM+ radiometric calibration uncertainties are reported as 7% and 5%
respectively (Markham & Helder, 2012) and over the CONUS their
geolocation error is less than one 30 m pixel (Lee et al., 2004).
All the Landsat 5 and Landsat 7 acquisitions for a CONUS winter
week (8th to 14th January 2010) and summer week (2nd to 8th July
256 D.P. Roy et al. / Remote Sensing of Environment 176 (2016) 255–271
2010) were obtained from the U.S. Landsat archive. Summer and winter
images were used to capture phenological surface differences and
therefore a range of surface anisotropy. Only Landsat acquisitions proc-
essed to L1T and with metadata GEOMETRIC_RMSE_MODEL values
≤30 m were used to ensure the high geolocation accuracy needed for
a pixel-level Landsat5 and 7 data comparison.In addition, only daytime
acquisitions, defined as those with metadata SUN_ELEVATION values
N5°, were used. This resulted in 270 Landsat 5 TM images (124 winter,
146 summer) and 297 Landsat 7 ETM+ images (139 winter, 158
summer), a total of 567 images.
Fig. 1 illustrates the geographic locations of the Landsat data. There is
an across-track acquisition overlap that increases further north due to
the poleward convergence of the Landsat orbits (Kovalskyy & Roy,
2013). Because the TM and ETM+ are in the same orbit but offset by
8 days the western and eastern sides of a sensor acquisition are over-
lapped by the eastern and western sides respectively of the other sensor
acquisition, and areacquired with only a one-day separation. This is im-
portant for the analysis in this paper as the overlapping area is sensed in
the forward scattering direction from one sensor and the backward
scattering direction from the other, and this pattern alternates across
the CONUS. The one-day separation is advantageous as surface changes
are less likely to occur within such a short period, although atmospheric
conditions may change.
2.2. MODIS BRDF/Albedo product
The 16-day 500 m MODIS BRDF model parameter product
(MCD43A1) was used to compute the directional reflectance at any
Fig. 1. Geographiclocations of the Landsat5 TM (blue) and Landsat7 ETM + (red) imagesfor the winter January 8th to 14th, 2010(top) and summer July2nd to 8th, 2010 (bottom)weeks.
Locationswere derived fromthe latitude andlongitude scene corner coordinate image metadata. (Forinterpretationof the references tocolor in this figure legend, the readeris referred to
the web version of this article.)
257D.P. Roy et al. / Remote Sensing of Environment 176 (2016) 255–271
desired viewing and solar geometry. The product defines Ross-Thick/Li-
Sparse-Reciprocal spectral model parameters determined as those that
best fit all of the cloud-cleared, atmospherically-corrected MODIS
Terra and Aqua reflectance values observed at each pixel location over
a 16 day period (Schaaf et al., 2002, 2011). The Ross-Thick/Li-Sparse-
Reciprocal BRDF model defines reflectance as a weighted sum of an
isotropic parameter and two functions (or kernels) of viewing and illu-
mination geometry (Roujean et al., 1992), where one kernel is derived
from radiative transfer models (Ross, 1981) and the other is based on
surface scattering and geometric shadow casting theory (Li & Strahler,
1992)as:
ρλ
MODIS;Ω;Ω0
¼fiso λMODIS
ðÞþfvol λMODIS
ðÞKvol Ω;Ω0
þfgeo λMODIS
ðÞKgeo Ω;Ω0
ð1Þ
where ρðλMODIS;Ω;Ω0Þis the MODIS spectral reflectance for wavelength
λ
MODIS
,forviewingvectorΩ(view zenith and azimuth angles) and solar
illumination vector Ω′(solar zenith and azimuth angles), K
vol
(Ω,Ω′)
and K
geo
(Ω,Ω′) are the volumetric scattering and geometric-optical
model kernels respectively which depend only on the sun-view geom-
etry (Ω,Ω′), andf
iso
(λ
MODIS
), f
vol
(λ
MODIS
), f
geo
(λ
MODIS
) are spectrally de-
pendent BRDF model parameters (Schaaf et al., 2002, 2011). Generally,
the volumetric scattering kernels represent bowl BRDF shapes while the
geometric-optical kernels represent more domed BRDF shapes. The
volumetric scattering and geometric-optical model kernels are quite
uniform and comparatively similar over the near-nadir portions of the
bi-directional reflectance distribution (Lucht, Schaaf, & Strahler, 2000).
This is illustrated in Fig. 2 which shows for different solar zenith angles
(colored lines) the very high degree of correlation between these
kernels derived over the Landsat ± 7.5° view zenith range (values
along lines). This linear relationship implies that over such a narrow
view angle range, the two kernels effectively collapse to a single kernel.
The gridded 500 m Collection 5 MCD43A1 and MCD43A2 products
were used in this study. They were generated with a quasi-rolling pro-
duction strategy, whereby each 16-day product is produced every
8 days on an 8-day overlapping basis to minimize global data processing
constraints (Roy, Lewis, Schaaf, Devadiga, & Boschetti, 2006). The three
MCD43A1 BRDF spectral model parameters, i.e.f
i=1…3
(λ
MODIS
), for the
MODIS 500 m land surface reflectance bands: blue (0.459–0.479 μm),
green (0.545–0.565 μm), red (0.620–0.670 μm), near-infrared (0.841–
0.876 μm) and shortwave infrared (1.628–1.654 μm and 2.105–
2.155 μm) were used; the spectral parameters for the MODIS 1.230-
1.250 μm band were not used since this band has no corresponding
Landsat 5 or 7 band (Roy et al., 2008). The MODIS BRDF/Albedo quality
product (MCD43A2) corresponding to each MCD43A1 product was
used to remove poor quality product values. These MODIS products
are defined in 10° × 10° tiles in the equal area sinusoidal projection
(Wolfe, Roy, & Vermote, 1998). All of the MODIS MCD43A1 and
MCD43A2 products for 2010 over the CONUS and globally were used.
This corresponded to a total of 11 MODIS tiles (CONUS) and an average
of 310 tiles (globally) every 8 days for all of 2010.
2.3. MODIS land cover product
The Collection 5 annual 500 m MODIS land cover product
(MCD12Q1) (Friedl et al., 2010) was used for land cover type specific
BRDF normalization analyses. The MCD12Q1 International Geosphere–
Biosphere Program (IGBP) scheme, which classifies each 500 m pixel
into one of the 17 classes (Table 1) and has a reported 75% overall
land cover classification accuracy, was used. The classes are mutually
exclusive and every land pixel is either classified into one class or is
unclassified. Associated with this classification scheme is a per-pixel
classification confidence estimate (range 0–100) (McIver & Friedl,
2001) that was used in this study to remove pixels with low classifica-
tion confidence. Eleven years (2002 to 2012) of MCD12Q1 over the
CONUS was used to identify regions of relatively little surface land
cover change. This corresponded to a total of 11 MODIS tiles per year de-
fined in the equal area sinusoidal projection.
3. Data pre-preprocessing
3.1. Overview
A number of pre-processing steps were undertaken to enable mean-
ingful BRDF normalization of the Landsat 5 TM and 7 ETM+ data using
the MODIS BRDF spectral model parameters. The Landsat data were
converted to top of atmosphere (TOA) reflectance and then atmospher-
ically corrected to surface reflectance. The Landsat data were projected
into the MODIS sinusoidal projection.Only spatially overlapping pairs of
Landsat 5 TM and Landsat 7 ETM+ reflectance values sensed one day
apart were considered; the pairs have similarsolar geometry but differ-
ent viewing geometries. Only pairs that were cloud-free, snow-free,
unsaturated, and that had no significant change in their one day separa-
tion, were considered. Only one 30 m Landsat 5 and 7 reflectance pair
Fig. 2. Plots of the MODIS Ross-Thick/Li-Sparse-Reciprocal BRDF geometric kernel (K
geo
) as a function of the volumetric kernel (K
vol
) for Landsat view zenith angles from −7.5° to 7.5°
(colored lines) in the principal plane (0° relative azimuth) for solar zenith angles 0° (red), 15° (green), 30° (blue), 45° (yellow), and 60° (purple). The Pearson correlation between the
K
geo
and K
vol
data in each colored line is greater than 0.99. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
258 D.P. Roy et al. / Remote Sensing of Environment 176 (2016) 255–271
per MODIS 500 m pixel wasused to reduce the data volume and to pro-
vide a convenient way to investigate the use of MODIS BRDF spectral
model parameters for different land cover types. The normalization
was undertaken using only the highest quality snow-free MODIS
spectral BRDF model parameters.
3.2. Landsat reflectance data pre-processing
The CONUS Landsat L1T data were converted to top of atmosphere
reflectance and then atmospherically corrected to surface reflectance
using the Landsat Ecosystem Disturbance Adaptive Processing System
(LEDAPS) code (Masek et al., 2006). It is well established that atmo-
spheric correction is required prior to BRDF correction because atmo-
spheric gases and aerosols scatter and absorb radiation anisotropically
(Franch, Vermote, Sobrino, & Fédèle, 2013; Hu, Lucht, & Strahler,
1999). Moreover, atmospheric gases and aerosols are highly variable
in space andtime and may have significant impacts on Landsat top of at-
mosphere reflectance (Masek et al., 2006; Roy et al., 2016)thatcanbe
greater than the BRDF effects found in this paper.
Saturated reflectance values (associated mainly with pure snow ac-
quisitions and residual cloud effects) were flagged based on the Landsat
L1T digital numbers in each band, with saturation generally varying
spectrally and with the illumination geometry (Bindschadler et al.,
2008; Roy et al., 2010). Two per-pixel cloud masks were used, the her-
itage Landsat project automatic cloud cover assessment algorithm
(ACCA) (Irish et al., 2006) and a decision tree cloud mask algorithm
that generally performs better than ACCA for Landsat 7 ETM+ over
the CONUS (Roy et al., 2010). Snow pixels were flagged in a way that
is consistent with the MODIS snow detection algorithm (Hall, Riggs,
Salomonson, DiGirolamo, & Bayr, 2002), specifically, snow was flagged
if the normalized difference snow index (NDSI) N0.4, near-infrared re-
flectance N0.11, and green reflectance N0.10, where the NDSI is the
green minus shortwave infrared (1.65 μm) reflectance divided by their
sum.
The Landsat per-pixel solar geometry was computed using an astro-
nomical model (Blanco-Muriel, Alarcón-Padilla, López-Moratalla, &
Lara-Coira, 2001) parameterized with each Landsat pixel latitude and
longitude, date, and the Landsat acquisition time. The astronomical
model is sufficiently accurate for the purposes of this study with a re-
ported average and standard deviation solar zenith prediction error of
0.001 and 0.114 min of arc (Blanco-Muriel et al., 2001). The Landsat
per-pixel viewing geometry was calculated using the Landsat Image As-
sessment System geometric libraries developed to monitor, character-
ize, and calibrate sensor and platform specific aspects of the Landsat
satellite ETM+ sensor (Lee et al., 2004). The viewing vector was com-
puted for each output pixel by first computing a vector normal to the
surface of the WGS84 Earth model for the geodetic pixel coordinate,
then the unit vector from the geodetic coordinate to the modeled satel-
lite position, adjusting for the sensor-satellite attitude, and then the
viewing vector zenith and azimuth components derived using standard
trigonometric formulae (Roy et al., 2008).
3.3. Landsat projection to MODIS sinusoidal equal area projection and
quality filtering
The pre-processed Landsat data (Section 3.2) were projected
with nearest neighbor resampling into fixed 5295 × 5295 30 m
pixel tiles in the MODIS sinusoidal equal area projection using the
Web Enabled Landsat Data (WELD) processing software (Roy et al.,
2010). In this way the projected Landsat data were aligned with
the MODIS BRDF and land cover products. Each winter and summer
week of Landsat 5 TM and 7 ETM+ data were projected indepen-
dently because at CONUS latitudes each Landsat sensor observes a
30 m pixel location no more than once per week, but the edges of
the Landsat 5 TM and 7 acquisitions ETM + overlap with only a
one-day separation (Fig. 1).
For the January and July Landsat data every pair of Landsat 5 and 7
reflectance values defined in the overlap (Fig. 1) at the same sinusoidal
30 m pixel location was examined. Only pairs that had values that were
not flagged as cloudy, snow contaminated, or saturated (Section 3.2)
were used. To remove any 30 m land cover and surface condition
changes that may have occurred in the one day difference between
the two Landsat sensors (due to abrupt disturbances such as fire,
flooding, agricultural harvesting, and residual ephemeral snowfall) a
filter was applied to their TOA blue reflectance and TOA Normalized
Difference Vegetation Index (NDVI) values as:
NDVIETMþ−NDVITM
NDVIETMþþNDVITM
jj
.2
N0:15 OR ρETMþ
blue −ρTM
blue
ρETMþ
blue þρTM
blue
jj
.2
N0:51:ð2Þ
The filter (Eq. (2)) rejects pixel values where the relative change in
one day between sensors is greater than the average effect of the atmo-
sphere on the Landsat NDVI or blue reflectance. The blue band is the
shortest wavelength Landsat band and is the most sensitive to atmo-
spheric effects. In a recent study considering approximately 53 million
30 m pixel locations sampled systematically across the CONUS for
12 months, the mean absolute difference between Landsat ETM+ sur-
face and TOA reflectance expressed as percentages of the surface reflec-
tance, and considering good quality atmospheric corrections only, was
15% for the NDVI and 51% for the blue band (Roy et al., 2014). This filter-
ing is quite aggressive, but given the large amount of Landsat data
considered and the study goals, this is preferable to retaining Landsat
TM and ETM + pairs that contained any change. The corresponding
remaining pairs of Landsat surface reflectance values were then identi-
fied and used in the subsequent analysis.
3.4. Selection of colocated 500 m and 30 m pixels with the same land cover
Only one 30 m Landsat 5 and 7 reflectance pair per MODIS 500 m
pixel was used to reduce the data volume and to provide a conve-
nient way to investigate the use of MODIS BRDF spectral model pa-
rameters for different land cover types. The MODIS land cover
product (MCD12Q1) was used to select 500 m pixel locations across
the CONUS that were classified consistently as the same land cover
class and with classification confidence N50% over eleven years
(2002 to 2012). This increased the likelihood that only reliably clas-
sified pixels were considered and that the land cover was unchanged
at 500 m resolution in 2010 (the year with the winter and summer
weeks of Landsat data). Often this filtering eroded the edges of re-
gionsthathadthesamelandcover.Fig. 3 illustrates the impact of
this filtering for a single 2010 MCD12Q1 tile (left) and the reduced
number of 500 m pixels with consistently high confidence land cover
types (middle).
For each selected MODIS 500 m pixel a single 30 m pixel location
with the same land cover type was selected. This was not straightfor-
ward because the spatial arrangement of land cover may be different
at 500 m and 30 m and the only available CONUS 30 m land cover
Table 1
The 17 MODIS MCD12Q1 IGBP land cover classes (Friedl et al., 2010).
Class Name Class Name
0 Water 9 Savannas
1 Evergreen needleleaf forest 10 Grasslands
2 Evergreen broadleaf forest 11 Permanent wetlands
3 Deciduous needleleaf forest 12 Croplands
4 Deciduous broadleaf forest 13 Urban and built-up
5 Mixed forest 14 Cropland/natural vegetation mosaic
6 Closed shrublands 15 Snow and ice
7 Open shrublands 16 Barren or sparsely vegetated
8 Woody savannas
259D.P. Roy et al. / Remote Sensing of Environment 176 (2016) 255–271
products do not have the same class nomenclature as MCD12Q1
(Hansen et al., 2014; Homer et al., 2015). Consequently, the following
selection process was implemented by examination of the pairs of
Landsat 5 and 7 data, and was undertaken independently for the winter
and summer Landsat data.
First, the spectral centroid of all the 30 m Landsat pixel values falling
within the selected 500 m MODIS pixel was defined as:
ρc¼X
n
i¼1
ρi=n
ρi¼ρETMþ1
i;ρETMþ2
i;ρETMþ3
i;ρETMþ4
i;ρETMþ5
i;ρETMþ7
i;ρTM1
i;ρTM2
i;ρTM3
i;ρTM4
i;ρTM5
i;ρTM7
i
ð3Þ
where ρ
c
is the spectral centroid (a vector of six Landsat 5 TM and six
Landsat 7 ETM+ surface reflectance values) of the npixels with over-
lapping pairs of Landsat 5 and 7 reflectance values that fall within the
500 m pixel.
Second, the 30 m pixel that was closest to the spectral centroid was
selected as the one with the minimal value of:
Δ¼X
12
j¼1
ρj
i−ρj
c
ð4Þ
where ρ
c
is the spectral centroid vector and ρ
i
are the reflectance values
as Eq. (3). If several 30 m pixels had the same value of Eq. (4) then one
was selected at random. The underlying assumption of Eqs. (3) and (4)
is that the majority of the 30 m pixels have the same land cover as the
500 m pixel. Consequently, only MODIS 500 m pixels that were more
than 50% covered by valid (cloud-free, snow-free, unsaturated) overlap-
ping pairs of Landsat 5 and 7 reflectance values were considered. Fig. 3
(right) illustrates the 500 m MODIS pixels that had corresponding se-
lected 30 m pixels. The diagonal stripe pattern is due to the geometry
of the overlapping Landsat 5 and 7 observations (Fig. 1).
Fig. 4. Scatterplots of observed surface reflectance difference (Landsat 5 TM −Landsat 7 ETM+) versus Landsat 5 TM view zenith angle for the red (left column) and NIR (right column)
bands, for the summer (top row) and winter (bottom row) weeks of CONUS data for January and July 2010 (Fig. 1). The colors show the relative frequency of occurrence of similar
reflectance difference values (with a log
2
scale); the numbers of overlapping pairs of sensor 30 m reflectance values are summarized in Table 2. The solid lines show ordinary least
squares linear regression fits of these data (see Table 3).
Fig. 3. Illustration of selection of colocated 500 m and 30 m pixelswith the same land cover. Left: example MCD12Q1 500 m land cover product (colors correspondto different land cover
classes,Table 1) for 2010 MODIS landtile h11v05 (coveringapproximately1200 × 1200 km, 91.3785° to 69.2724°W, 30.0000° to 40.0000°N), Middle:same as left but only showing500 m
pixelsthat had the same MCD12Q1land cover classlabel over elevenyears (2002 to 2012)and classificationconfidence N50%; Right: same as middlebut showing the 500m MODIS pixels
with a selected summer Landsat 30 m pixel.
260 D.P. Roy et al. / Remote Sensing of Environment 176 (2016) 255–271
3.5. MODIS spectral BRDF model parameter pre-processing to select only
high-quality parameters
Only the highest quality snow-free MODIS spectral BRDF model
parameters were used. The MODIS spectral BRDF model parameter
quality depends on a number of factors including the number and the
angular sampling of the reflectance values used in the MODIS BRDF
model inversion and the constancy of the surface conditions (Lucht &
Lewis, 2000; Schaaf et al., 2002, 2011). The 500 m band-specificBRDF
model inversion quality is stored in the Collection 5 MODIS BRDF/
Albedo quality product (MCD43A2) and coded 0, 1, 2, 3, or 4 indicating
decreasing inversion quality. In this study, only the very highest quality
BRDF full inversions, i.e., coded as 0 in the MCD43A2 product were used.
In addition, only snow-free MODIS BRDF inversions labeled in the
MCD43A2 product were used.
4. Analysis methodology
4.1. Quantification of observed Landsat directional reflectance effects
Before any BRDF normalization was undertaken the surface reflec-
tance differences between the pairs of Landsat 5 TM and Landsat 7
ETM+ values were examined to provide insights into the magnitude
of Landsat BRDF effects. The mean absolute reflectance difference and
also the relative absolute percentage reflectance difference, were de-
rived for each band as:
Δρλ¼X
n
i¼1
ρTM;λ
i−ρETMþ;λ
i
nð5Þ
Δρ
λ¼X
n
i¼1
2ρTM;λ
i−ρETMþ;λ
i
jj
.ρTM;λ
iþρETMþ;λ
i
jj
n
0
B
B
B
B
@
1
C
C
C
C
A
100 ð6Þ
where Δρλand Δρ
λare the mean absolute and the relative absolute
percentage reflectance differences respectively, ρ
i
TM, λ
and ρ
i
ETM+ ,λ
is a
pair of Landsat 5 TM and Landsat 7 ETM+ surface reflectance values,
and there are npairs for spectral band λ. As each pair is sensed with sim-
ilar solar geometry but different viewing geometry, specifically the re-
flectance is sensed in the forward scattering direction from one sensor
and the backward scattering direction from the other sensor (Fig. 1),
these measures provide an indication of view zenith Landsat BRDF ef-
fects. We note that there are several other sources of between sensor
difference that may vary spectrally and also with the surface reflectance.
These include the slightly different spectral response functions between
the Landsat 5 TM and Landsat 7 ETM+ sensors (Steven, Malthus, Baret,
Xu, & Chopping, 2003;Teillet et al., 2001) and the different sensorradio-
metric calibration uncertainties (7% for Landsat 5 TM and 5% for Landsat
7ETM+)(Markham & Helder, 2012). In addition, although surface
changes are unlikely to occur within the one day separation between
the Landsat 5 TM and Landsat 7 ETM+ observations, and the majority
of changes will be removed by the filtering of Eq. (2), the atmosphere
may change in one day. This may inflate values of Δρλand Δρ
λbecause
the Landsat surface reflectance correction is imperfect; for example, the
mean relative residual in Landsat 7 ETM + LEDAPS atmospherically
corrected data was reported as 5.9% and 4.8% in the red and NIR bands
respectively (Ju, Roy, Vermote, Masek, & Kovalskyy, 2012).
Spectral scatter plots and ordinary least regression (OLS) fits of the
difference between the observed Landsat 5 TM and Landsat 7 ETM+ re-
flectance pairs as a function of the view zenith angle were generated for
the winter and summer Landsat data independently for each band
(blue, green, red, near-infrared and the two shortwave infrared bands).
The slopes of the OLS regressions were derived to quantify the average
spectral BRDF effect across the Landsat 15.0° field of view. The goodness
of fitoftheOLSregressionsweredefined by the coefficient of determina-
tion (r
2
) and the significance of the OLS regressions was defined by exam-
ination of the regression overall F-statistic p-value. The average
maximum magnitude of Landsat view zenith BRDF effects was derived
by multiplying the OLS slope term by 15.0° and is termed for convenience
the B–F difference. The B–F difference captures the average difference
between Landsat surface reflectance in the forward and backward scatter
directions at the Landsat scan edges.
4.2. Landsat 30 m NBAR derivation using different MODIS spectral BRDF
model parameters
The c-factor approach (Roy et al., 2008) that can adjust Landsat reflec-
tance to a specified viewing and solar geometry was used to independent-
ly normalize the pairs of Landsat 5 TM and Landsat 7 ETM+ reflectance
values to nadir BRDF adjusted reflectance (NBAR) equivalents as:
NBARsensor
λθv¼0;θs¼θTM
sþθETMþ
s
2
!
¼cλ
ðÞ
ρLandsat
λθsensor
v;θsensor
s
cλðÞ¼
ρ̂MODIS
λθv¼0;θs¼θTM
sþθETMþ
s
2
!
ρMODIS
λθsensor
v;θsensor
s
ð7Þ
Table 3
Summaryof the ordinary least squares (OLS) linearregressions illustrated in Fig.3 and for the other Landsat bandsconsidered in thisstudy. Δ= (Landsat 5 TM −Landsat 7 ETM+ surface
reflectance), θ
v
= Landsat5 TM view zenith angle.The OLS regressioncoefficient of determination (r
2
), the OLS regression F-test p-value, and the B–Fdifference are shown.The number of
data points, i.e., number of pairs of sensor 30 m reflectance values for each band, are summarized in Table 2.
Landsat band July January
OLS equation OLS r
2
(p-value) B–F difference OLS equation OLS r
2
(p-value) B–F difference
1 (blue) Δ=−0.0024 + 0.0013 θ
v
0.3380 (b0.0001) 0.0202 Δ=−0.0064 + 0.0011 θ
v
0.2824 (b0.0001) 0.0176
2 (green) Δ= 0.0019 + 0.0013 θ
v
0.3033 (b0.0001) 0.0208 Δ=−0.0050 + 0.0007 θ
v
0.1223 (b0.0001) 0.0113
3 (red) Δ= 0.0009 + 0.0013 θ
v
0.2221 (b0.0001) 0.0197 Δ=−0.0053 + 0.0007 θ
v
0.1112 (b0.0001) 0.0107
4 (NIR) Δ=−0.0110 + 0.0040 θ
v
0.2753 (b0.0001) 0.0623 Δ=−0.0082 + 0.0012 θ
v
0.1734 (b0.0001) 0.0188
5 (1.6 μm) Δ=−0.0036 + 0.0033 θ
v
0.2647 (b0.0001) 0.0505 Δ= 0.0019 + 0.0012 θ
v
0.1133 (b0.0001) 0.0184
7 (2.1 μm) Δ= 0.0034 + 0.0022 θ
v
0.2203 (b0.0001) 0.0335 Δ= 0.0048 + 0.0008 θ
v
0.0742 (b0.0001) 0.0126
Table 2
Total number (n) of pairs of Landsat-5TM and Landsat-7 ETM+ surface reflectance values
for the CONUSJuly and January data (locations shownin Fi g.1 ),and the Landsat-5TM and
Landsat-7ETM + mean absolute surfacereflectance differences (Δρλ,Eq.(5)) and relative
percentage differences (Δρ
λ,Eq.(6)). All data subjectto the filteringdescribed in Section3.
Landsat band July January
nΔρλΔρ
λnΔρλΔρ
λ
1 (blue) 1,279,827 0.0098 19.13 185,783 0.0100 14.76
2 (green) 1,375,321 0.0109 14.62 187,409 0.0095 11.22
3 (red) 1,353,843 0.0114 18.13 186,264 0.0091 8.76
4 (NIR) 1,401,725 0.0309 10.73 185,257 0.0129 6.68
5 (1.6 μm) 1,400,499 0.0251 13.08 182,866 0.0136 6.91
7 (2.1 μm) 1,395,513 0.0179 14.96 183,292 0.0121 9.87
261D.P. Roy et al. / Remote Sensing of Environment 176 (2016) 255–271
where sensor is TM or ETM+ to denote the Landsat 5 TM or Landsat 7
ETM+ sensors respectively, and each pair of NBAR
λ
TM
and NBAR
λ
ETM+
values was defined with a solar zenith angle set as the mean of the ob-
served solar zenith angles of the Landsat 5 TM (θ
s
TM
) and 7 ETM+
(θ
s
ETM+
) observations (that typically have only a 0.2° solar zenith differ-
ence for the Landsat pairs used in this study due to their one day separa-
tion) and nadir view zenith angle (θ
v
=0°). Definition of the azimuthal
angles is unimportant because at nadir the BRDF is independent of the
azimuthal geometry. The NBAR values were derived for the Landsat
blue, green, red, near-infrared and two shortwave infrared bands. The
spectrally corresponding MODIS BRDF model parameters, f
iso
(λ
MODIS
),
f
vol
(λ
MODIS
), andf
geo
(λ
MODIS
), were used to predict MODIS spectral reflec-
tance (ρMODIS ) for the prescribed viewing and solar geometry as Eq. (1).
The MODIS spectral BRDF parameters were defined in a number of differ-
ent ways described below.
4.2.1. Conventional Landsat NBAR derivation
Each pair of Landsat 5 TM and Landsat 7 ETM+ winter and summer
reflectance values was normalized to NBAR as Eq. (7) in theconvention-
al manner (Roy et al., 2008) using the local spatially and temporally con-
temporaneous 500 m MODIS spectral BRDF model parameters. Only the
highest quality snow-free Collection 5 MODIS spectral BRDF model pa-
rameters defined on the closest day to the Landsat 5 and 7 pixel acqui-
sition days were used. If there were no high quality snow-free MODIS
spectral BRDF model parameters within 8 days then the NBAR deriva-
tion was not undertaken (note that the Collection 6 MODIS BRDF pa-
rameters will be retrieved daily, simplifying this methodology in the
future).
4.2.2. Landsat NBAR derivation using fixed MODIS spectral BRDF model
parameters
Rather than use the local spatially and temporally contemporaneous
MODIS spectral BRDF model parameters (as in Section 4.2.1), fixed
spectral BRDF model parameters were defined in four different
ways by averaging the 500 m MODIS BRDF spectral parameters over dif-
ferent spatial and temporal periods. Specifically, the mean values of
f
iso
(λ
MODIS
), f
vol
(λ
MODIS
), and f
geo
(λ
MODIS
) were calculated considering
the highest quality and snow-free value extracted from all of the:
(a) global MCD43 500 m product pixels for 12 months of 2010,
(b) CONUS MCD43 500 m product pixels for 12 months of 2010,
(c) CONUS MCD43 500 m product pixels with colocated 30 m pairs
of Landsat 5 and 7 summer (July) reflectance values,
(d) CONUS MCD43 500 m product pixels with colocated 30 m pairs
of Landsat 5 and 7 winter (January) reflectance values.
To provide insights into the BRDF shapes and magnitudes provided
by the above four sets of spectral BRDF model parameters, plots of
ρMODIS ((1))andc(λ)((7)) as a function of view zenith angle and differ-
ent solar zenith angles (0°, 30° or 45°) were examined. To save space,
the plots were derived for only the red and near-infrared (NIR) bands.
The red and NIR bands were selected as they in particular capture
vegetation and soil reflectance differences.
4.3. Landsat NBAR evaluation
If the BRDF normalization is reliable then the NBAR values of each
pair of Landsat 5 TM and Landsat 7 ETM+ observations should be sim-
ilar. To examine this, the mean and relative absolute percentage NBAR
differences were derived as:
ΔNBARλ¼X
n
i¼1
NBARTM;λ
i−NBARETMþ;λ
i
nð8Þ
ΔNBAR
λ¼X
n
i¼1
2NBARTM;λ
i−NBARETMþ;λ
i
jj
.NBARTM;λ
iþNBARETMþ;λ
i
jj
n
0
B
B
B
B
@
1
C
C
C
C
A
100 ð9Þ
where ΔNBARλis the mean absolute NBAR difference derived for spec-
tral band λfrom npairs of Landsat 5 and Landsat 7 NBAR values derived
as (7) from the pairs of Landsat 5 TM and Landsat 7 ETM+ reflectance,
and ΔNBAR
λis the mean absolute relative percentage NBAR difference.
We do not expect ΔNBARλand ΔNBAR
λto be zero valued because of the
sensor calibration, spectral response function, and atmospheric correc-
tion differences described earlier (Section 4.1) and because of any errors
in the MODIS BRDF retrieval.
4.4. Sensitivity of Landsat NBAR derivation to land cover
Each pair of Landsat 5 TM and Landsat 7 ETM+ surface reflectance
values, located at 30 m pixel location iwith MODIS land cover class u
(u=0,1,…,or16)(Table 1), was normalized to NBAR using the follow-
ing MODIS spectral BRDF parameters:
i) the conventional, local spatially and temporally contemporane-
ous, MODIS spectral BRDF parameters (which by definition
have the same land cover class as the Landsat 5 and 7 pair); the
resulting NBARs are denoted NBAR
i,u,u
TM, λ
and NBAR
i,u,u
ETM+ ,λ
,
ii) the MODIS spectral BRDF parameters defined by a randomly
sampled pixel that had a different land cover class v(v=0,1,
…, or 16, v≠u); the resulting NBARs are denoted NBAR
i,u,v
TM, λ
and NBAR
i,u,v
ETM+ , λ
,
iii) three sets of fixed spectral BRDF model parameters; the resulting
NBARs are denoted NBAR
i,u,set
TM, λ
and NBAR
i,u,set
ETM+ , λ
(set =a,b,orc;
as defined in Section 4.2.2);
In this way each pair of Landsat 5 TM and Landsat 7 ETM+ surface
reflectance values iwas normalized to NBAR once as (i), 16 times as
(ii), and three times as (iii). Given the very large number of
Table 5
Global 12 month fixed MODIS spectral BRDF model parameters for all the bands. The nvalues
show the number of 500 m highest quality and snow-free MODIS BRDF spectral parameters
pixel values considered; nvaries spectrally because of the number of high-quality parame-
ters in the MODIS BRDF/Albedo quality product (MCD43A2) varies spectrally.
Landsat band nf
iso
f
geo
f
vol
1 (blue) 15,551,077,545 0.0774 0.0079 0.0372
2 (green) 16,362,112,402 0.1306 0.0178 0.0580
3 (red) 16,095,103,393 0.1690 0.0227 0.0574
4 (NIR) 16,260,280,058 0.3093 0.0330 0.1535
5 (1.6 μm) 16,176,131,413 0.3430 0.0453 0.1154
7 (2.1 μm) 16,149,440,059 0.2658 0.0387 0.0639
Table 4
Fixed MODIS spectral BRDF model parameters (see Section 4.2.2 for details) for the Red
and NIR bands derived by averaging the 500 m MODIS BRDF (MCD43) highest quality
and snow-free spectral parameters over different spatial and temporal periods.
MODIS spectral BRDF model
parameter set
Red band NIR band
f
iso
f
geo
f
vol
f
iso
f
geo
f
vol
(a) Global 12 months 0.1690 0.0227 0.0574 0.3093 0.0330 0.1535
(b) CONUS 12 months 0.1131 0.0247 0.0462 0.2869 0.0367 0.1833
(c) CONUS July 0.1059 0.0233 0.0409 0.3155 0.0420 0.2108
(d) CONUS January 0.1159 0.0229 0.0296 0.2345 0.0373 0.0979
262 D.P. Roy et al. / Remote Sensing of Environment 176 (2016) 255–271
combinations generated, only 1400 pairs of summer Landsat 5 TM and
Landsat 7 ETM+ surface reflectance pairs were considered. The 1400
pairs were selected randomly without replacement from the CONUS
July filtered data (Section 3).
The mean and relative absolute percentage NBAR differences be-
tween the sensors were derived as (8) and (9) but considering each
land cover type independently and for (i), (ii) and (iii). This provided
quantitative insights into the magnitude of NBAR sensor differences
Fig. 5.ρMODIS derivedas (1) for red (leftcolumn) and NIR (rightcolumn) surfacereflectance modeled for MODIS viewing zenith angles(± 60°)and for three fixed solarzenith angles (0°top
row, 30° middle row, 45 ° bottom row). The colored lines show the modeled reflectance values for the four sets of fixe d MODIS spectral BRDF model parameters (Table 4). (For
interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
263D.P. Roy et al. / Remote Sensing of Environment 176 (2016) 255–271
with respect to land cover type and using different spectral BRDF model
parameters.
Nominally the local spatially and temporally contemporaneous
MODIS spectral BRDF parameters are expected to most appropriate
for Landsat NBAR generation. To investigate this, the statistical
significance of differences between the NBAR values generated
as (i) and as (ii), and between the values generated as (i) and
(iii), was quantified. The Landsat 5 and 7 NBAR values derived as
(i) (NBAR
i,u,u
TM, λ
and NBAR
i,u,u
ETM+ , λ
) was subtracted from the corresponding
NBAR values derived as (ii) (NBAR
i,u,v
TM, λ
and NBAR
i,u,v
ETM+ , λ
where v=0,1,
Fig. 6. c-factors derivedas (7) over the Landsat view zenithangle range (±7.5°) for three fixedsolar zenith angles(0° top row, 30° middle row,45° bottom row). The colored lines showthe
modeled reflectance valuesfor the four sets of fixed MODIS spectral BRDF model parameters (Table 4).
264 D.P. Roy et al. / Remote Sensing of Environment 176 (2016) 255–271
…, or 16, v≠u) to provide a list of NBAR difference values. A two-
tailed matched-pairs t-test (Freund & Wilson, 1993) was performed
with the null hypothesis that the mean NBAR difference was zero
and the alternative hypothesis that the mean difference was not
zero. This was undertaken for each spectral band. Similarly, the
Landsat 5 and 7 NBAR values derived as (i) (NBAR
i,u,u
TM, λ
and NBAR
i,u,u
ETM+ , λ
)
were subtracted from the corresponding NBAR values derived as
(iii) (NBAR
i,u,set
TM, λ
and NBAR
i,u,set
ETM+ , λ
where set =a,b,orc;asdefined in
Section 4.2.2) and the NBAR difference values were tested for significant
differences.
Fig. 7. Scatterplotsof NBAR difference(Landsat 5 TM−Landsat 7 ETM+) versus Landsat5 TM view zenithangle for the red (leftcolumn) and NIR (rightcolumn) bands. Results for the July
data (Fig. 1). TheNBAR values derived as (7) usingMODIS spectral BRDFmodel parametersderived using the local spatiallyand temporally contemporaneous 500 m MODISspectral BRDF
model parameters (top row),and derived using the fixed meanCONUS July (2nd row), CONUS12 month (3rd row) and Global12 month (bottom row) modelparameters (Table 4). The
colors show the relativefrequency of occurrence of similarNBAR differencevalues (with a log
2
scale);the numbers of overlapping pairs of sensor30 m reflectance valuesare summarized
in Table 2. Thesolid lines show ordinary leastsquares regressionlinear regressionfits of these data. (For interpretationof the references to colorin this figure legend, the readeris referred
to the web version of this article.)
265D.P. Roy et al. / Remote Sensing of Environment 176 (2016) 255–271
5. Results
5.1. Quantification of observed Landsat bi-directional reflectance effects
Fig. 4 shows scatterplots of Landsat 5 TM and Landsat 7 ETM+ red
surface reflectance difference (left column) and NIR surface reflectance
difference (right column) as a function of view zenith angle. The plots
were generated using all the filtered CONUS data (Section 3)and
show more than 1.35 million July (top row) and 185,000 January
(bottom row) pairs of Landsat 5 TM and 7 ETM + surface reflectance
values (Table 2). There are fewer Landsat 5 TM and Landsat 7 ETM +
pairs in January than in July because there were fewer winter images
available (Fig. 1) and because of greater winter snow and cloud cover.
Recall that due to the Landsat sensor overlap acquisition geometry
(Fig. 1), each pair of values includes one observed in the forward scat-
tering direction and the other observed in the backward scattering di-
rection. Fig. 4 illustrates an evident view zenith BRDF effect with
greater reflectance in the backscatter (shown as positive view zenith
angles) than the forwardscattering direction. There are no data with ab-
solute view zenith |view zenith| b0.87° and b1.91° in July and January
respectively. This is not because the Landsat 5 and 7 orbits overlap dif-
ferently in these months but rather because the Landsat orbits overlap
more progressively northward (Fig. 1), and further north in the winter
the CONUS is predominantly snow covered (Sheng et al., 2015)and
generally more cloudy at the time of Landsat overpass (Ju & Roy, 2008).
Table 2 summarizes the mean CONUS absolute (Δρλ) and relative
percentage (Δρ
λ) differences between the pairs of Landsat-5 TM
and Landsat-7 ETM+ surface reflectance values. For each band the
mean (Δρλ) differences are all approximately 0.01 in January data and
are greater in July. The mean differences are smallest for the visible
bands, greatest for theNIR and intermediate for the shortwave infrared
(SWIR) bands. Unsurprisingly, the Δρλvalues are greater in July than
January suggesting that on average CONUS vegetated surfaces are
more anisotropic than winter senescent vegetation and soil dominated
surface conditions. The mean relative differences (Δρ
λ) are easier to
compare between the spectral bands asthey are normalized for spectral
reflectance differences, whereby, for example, healthy vegetation has
low red reflectance but high NIR reflectance. The Δρ
λdifferences are
greatest for the visible bands and smallest for the NIR band and reflect
primarily atmospheric correction errors which are greater at shorter
Landsat wavelengths (Ju et al., 2012; Maiersperger et al., 2013).
The solid black lines in Fig. 4 show ordinary least squares (OLS) linear
regression fits of the displayed data and are summarized for all the bands
in Table 3. The regressions have low r
2
values due to the scatter in the data
but are statistically significant (p b0.0001) and all have positive slope
terms. The B–F difference, i.e., the OLS slope term multiplied by the
Landsat 15.0° field of view, quantifies the average difference between
Landsat surface reflectance in the forward and backward scatter
directions at the Landsat scan edges. As expected, the B–F differences
(Table 3)aregreaterthanΔρλ(Table 2)and,asfortheΔρλvalues, are
smaller in January than July. In January the B–F differences are similar
spectrally and vary from around 0.011 to 0.019 whereas in July the B–F
differences are about 0.02 in the visible bands, and about 0.03, 0.05 and
0.06, in the 2.1 μm, 1.6 μm and NIR bands respectively (Table 3). These
Landsat view zenith BRDF effects are not insignificant and are about an
order of magnitude greater than the mean absolute residual due to
Landsat 7 ETM+ LEDAPS atmospheric correction errors (Ju et al., 2012).
5.2. Preliminary analysis of fixed MODIS spectral BRDF model parameters
The four sets of fixed MODIS spectral BRDF model parameters
(Section 4.2.2) were derived considering more than 15,500,000,000
(global 12 months), 1,200,000,000 (CONUS 12 months), 41.7 million
(CONUS July), and 12.9 million (CONUS January) highest quality and
snow-free MODIS 500 m pixel values. Table 4 shows the resulting spec-
tral parameters for the red and NIR bands. The f
vol
and f
geo
terms act to
weight volumetric scattering and geometric-optical BRDF kernels re-
spectively ((1)) and have no direct physical meaning, although they
can be conceptualized as describing the directional reflectance effects
of inter-leaf and inter-crown canopy gaps respectively (Lucht et al.,
2000). The f
iso
parameter provides an additive reflectance term that re-
flects nadir viewing and solar geometry ((1)), and so f
iso
(red) and f
iso
(NIR) can be considered as average BRDF-independent (i.e., isotropic)
red and NIR surface reflectance values. As expected, when considering
the three CONUS sets of fixed parameters, the greatest f
iso
(NIR) and
smallest f
iso
(red) values occur for the July data when vegetation is de-
veloped and conversely the smallest f
iso
(NIR) and greatest f
iso
(red)
values occur for the January data when vegetation is mainly senescent.
The global 12 month MODIS spectral BRDF model parameters are
providedfor all the bands in Table 5. They are more complexto interpret
than the CONUS parameters as they include a much greater diversity of
BRDFs representing a larger number of land cover types and conditions
and both northern and southern hemisphere vegetation phenology and
soil moisture variations. However, they are indicative of a generally soil
and vegetation dominated spectra with monotonically increasing f
iso
values from the blue to 1.6 μm wavelengths and then decreased reflec-
tance at 2.1 μm(Table 5). By averaging all the varying BRDF shapes
across the globe or the CONUS, we recognize that we are reducing the
BRDF to a single shape.
To provide insights into the BRDF shapes and magnitudes provided
by the four sets of spectral BRDF model parameters, plots of ρMODIS
((1)) as a function of MODIS ±60° view zenith angle and for different
fixed solar zenith angles (0°, 30° or 45°) were generated for the red
and NIR (Fig. 5). With the sun directly overhead (Fig. 5,toprow)
ρMODIS is symmetrical around nadir (view zenith = 0°) whereas for
the 30° and 45° solar zenith angles the surface reflectance anisotropy
is apparent (Fig. 5, middle and bottom rows) with increased reflectance
in the backscatter direction and a hot-spot when the view and solar
zenith angles coincide. Two salient observations can be made: (i) the
magnitudes of ρMODIS are different between the four spectral BRDF
model parameters, but their shapes are similar, and (ii) the ρMODIS values
vary in an approximately linear manner near-nadir over the narrow
Landsat ±7.5° view zenith angle range. This is apparent in Fig. 6 which
shows the c-factor values for the four sets of spectral BRDF model param-
eters and for the different fixed solar zenith angles (0°, 30° or 45°) derived
over the Landsat ± 7.5° view zenith angle range. Recall that the c-factor is
used to adjust directional reflectance to nadir as (7). Over the narrow
Landsat field of view the c-factor varies linearly and there is only a
marginal difference (no more than 3.20% and 1.81% at the scan edge for
Table 6
CONUS July mean absolute NBAR difference (ΔNBARλ,Eq.(8)) and relative absolute per-
centage NBAR diffe rence (ΔNBAR
λ,Eq.(9)) values between the npairs (Table 2)of
Landsat-5 TM and Landsat-7 ETM+ surface reflectance values normalized to NBAR. The
ΔNBAR
λvalues are shown in parentheses under the ΔNBARλvalues. The NBAR was de-
rived for each band using local spatially and temporally contemporaneous 500 m MODIS
spectral BRDF model parameters (1st results column) and using different fixed MODIS
spectral BRDF model parameters (Table 4) (other result columns).
Landsat
band
MODIS spectral BRDF model parameter source
Local spatially and
temporally
contemporaneous
Fixed CONUS
July mean
Fixed CONUS
12 month
mean
Fixed Global
12 month
mean
1 (blue) 0.0075 (15.22) 0.0077 (15.68) 0.0078 (15.83) 0.0083 (16.74)
2 (green) 0.0077 (10.76) 0.0080 (11.33) 0.0080 (11.30) 0.0086 (12.06)
3 (red) 0.0089 (15.37) 0.0091 (15.87) 0.0091 (15.83) 0.0096 (16.42)
4 (NIR) 0.0227 (7.77) 0.0231 (8.00) 0.0233 (8.05) 0.0241 (8.38)
5 (1.6 μm) 0.0164 (8.79) 0.0171 (9.32) 0.0174 (9.52) 0.0189 (10.24)
7 (2.1 μm) 0.0125 (10.99) 0.0129 (11.57) 0.0130 (11.64) 0.0141 (12.46)
266 D.P. Roy et al. / Remote Sensing of Environment 176 (2016) 255–271
the red and NIR bands respectively) among the c-factor values derived
using the four sets of spectral BRDF model parameters.
5.3. Landsat 30 m NBAR derived using both local spatially and temporally
contemporaneous and fixed MODIS spectral BRDF model parameters
Fig. 7 shows scatterplots of the July Landsat 5 TM and Landsat 7
ETM+ NBAR differences as a function of view zenith. Tables 6 and 7
summarize the CONUS mean absolute NBAR differences ( ΔNBARλ)
and the relative absolute percentage NBAR differences (ΔNBAR
λ) for
the July and January data respectively. The NBAR values were defined
in four different ways using: the local spatially and temporally contempo-
raneous 500 m MODIS spectral BRDF model parameters (Fig. 7 top row),
and using the fixed mean CONUS model parameters (one month and
12 months, Fig. 7 middle rows) and the fixed mean Global 12 month
model parameters (Fig. 7 bottom row).
The BRDF effects apparent in the July surface reflectance sensor dif-
ference scatterplots (Fig. 4 top row) appear greatly reduced in the
equivalent NBAR results (Fig. 7 all rows). The OLS regressions illustrated
in Fig. 7 all have low r
2
values (b0.1) but are statistically significant
(p b0.0001). The magnitude of the B–F NBAR differences were, for all
bands and for both the July and January (not plotted) data, smaller
than the corresponding B–F differences for the uncorrected surface re-
flectance data reported in Table 3. Comparison of the NBAR difference
statistics reported in Tables 6 and 7 with the uncorrected surface reflec-
tance sensor difference statistics reported in Table 2 reveals that, for all
bands and BRDF parameter sources, the July NBAR differences are
always less than the corresponding uncorrected surface reflectance dif-
ferences. This is also the case for the January NIR and SWIR bands, and
the January NBAR differences are comparable to the uncorrected surface
Table 8
JulyredbandmeanCONUSabsoluteNBARdifference(
ΔNBARλ) and relative absolute percentage NBAR difference (ΔNBAR
λ) values between the Landsat-5 TM and Landsat-7 ETM+ surface
reflectance values normalized to NBAR for different land cover types. The ΔNBAR
λvalues are shown in parentheses under the ΔNBARλvalues. The Landsat 5 TM and Landsat 7 ETM+ NBAR
values were derived using different spectral BRDF model parameters (table rows): the local MODIS BRDF parameters, the three fixed spectral BRDF model parameters (Table 4), and using the
incorrect MODIS BRDF parameters defined randomly at other 500 m pixel locations that had different land cover types. The values in bold indicate the smallest ΔNBARλand ΔNBAR
λin each
land cover class column. The red asterisks (*) denote matched-pairs t-test p-values N0.05 i.e., no significant difference between the set of Landsat 5 and 7 NBAR values derived using the local
MODIS BRDF parameters and the corresponding set of NBAR values derived using the tabulated spectral BRDF model parameter source.
Spectral BRDF model
parameter source
Land cover class
0
Water
1
Evergreen
needleleaf
forest
4
Deciduous
broadleaf
forest
5
Mixed
forest
6
Closed
shrublands
7
Open
shrublands
8
Woody
savannas
9
Savannas
10
Grasslands
12
Croplands
13
Urban and
built-up
14
Cropland
/natural veg.
mosaic
16
Barren or
sparsely
vegetated
Local 0.0143*
(54.34)
0.0067*
(22.53)
0.0086*
(34.82)
0.0081*
(30.72)
0.0077*
(9.96)
0.0138*
(6.85)
0.0062*
(12.42)
0.0052*
(5.53)
0.0095*
(8.34)
0.0091*
(14.55)
0.0072*
(10.30)
0.0074*
(15.53)
0.0221*
(7.08)
Random Class 0 0.0085
(27.80)
0.0102
(38.76)
0.0084
(31.41)
0.0094*
(12.05)
0.0142
(7.05)
0.0078*
(14.57)
0.0074
(8.07)
0.0135
(11.59)
0.0120
(17.45)
0.0077
(10.83)
0.0078
(16.34)
0.0227
(7.28)
Random Class 1 0.0164
(56.32)
0.0087
(35.06)
0.0081*
(30.46)
0.0052
(6.63)
0.0167
(8.21)
0.0063
(12.58)
0.0051
(5.22)
0.0092*
(8.17)
0.0094
(14.72)
0.0087*
(11.39)
0.0079
(16.44)
0.0235
(7.30)
Random Class 4 0.0180
(58.82)
0.0072*
(24.32)
0.0081
(30.83)
0.0107
(13.88)
0.0159
(7.78)
0.0064
(12.59)
0.0057
(6.07)
0.0189
(15.25)
0.0091
(14.28)
0.0073*
(10.34)
0.0075
(15.69)
0.0393
(12.27)
Random Class 5 0.0143
(53.60)
0.0071
(24.10)
0.0086
(34.88)
0.0063
(8.10)
0.0200
(9.80)
0.0061
(12.20)
0.0037
(3.87)
0.0107
(9.32)
0.0090
(14.58)
0.0073
(10.53)
0.0085
(17.63)
0.0248
(7.65)
Random Class 6 0.0155*
(55.07)
0.0072*
(24.29)
0.0085
(34.59)
0.0081*
(30.58)
0.0177*
(8.67)
0.0063*
(12.50)
0.0040*
(4.27)
0.0092*
(8.11)
0.0093
(14.47)
0.0075*
(10.43)
0.0075*
(15.73)
0.0290
(8.98)
Random Class 7 0.0144*
(53.75)
0.0082
(27.08)
0.0082
(33.66)
0.0080*
(30.48)
0.0095
(12.13)
0.0064*
(12.62)
0.0052*
(5.58)
0.0097
(8.57)
0.0091*
(14.59)
0.0073*
(10.43)
0.0072*
(15.14)
0.0217
(6.86)
Random Class 8 0.0153*
(54.93)
0.0073
(24.67)
0.0085
(34.53)
0.0080
(30.32)
0.0107
(13.80)
0.0150*
(7.51)
0.0045
(4.82)
0.0092
(8.14)
0.0091
(14.42)
0.0075*
(10.69)
0.0072
(15.17)
0.0218
(6.84)
Random Class 9 0.0146*
(53.97)
0.0076*
(25.47)
0.0083
(34.08)
0.0081
(30.51)
0.0098
(12.56)
0.0149*
(7.38)
0.0067*
(12.92)
0.0092*
(8.16)
0.0091*
(14.51)
0.0074*
(10.38)
0.0072*
(15.27)
0.0218*
(6.83)
Random Class 10 0.0152*
(54.87)
0.0075*
(25.28)
0.0085
(34.69)
0.0081
(30.56)
0.0083
(10.70)
0.0153*
(7.52)
0.0062*
(12.24)
0.0067*
(7.13)
0.0090
(14.30)
0.0074*
(10.38)
0.0073*
(15.46)
0.0214*
(6.74)
Random Class 12 0.0147*
(54.21)
0.0072*
(24.30)
0.0082
(33.68)
0.0081
(30.83)
0.0110
(14.22)
0.0157
(7.72)
0.0066
(12.83)
0.0098
(10.50)
0.0108
(9.43)
0.0076*
(10.98)
0.0078*
(16.49)
0.0231
(7.16)
Random Class 13 0.0145*
(53.83)
0.0076*
(25.58)
0.0083
(33.97)
0.0081*
(30.69)
0.0102
(13.05)
0.0134
(6.65)
0.0064*
(12.58)
0.0048
(5.11)
0.0097*
(8.53)
0.0090*
(14.42)
0.0073*
(15.43)
0.0245
(7.58)
Random Class 14 0.0153*
(54.98)
0.0067
(22.89)
0.0083*
(33.99)
0.0080
(30.19)
0.0083
(10.63)
0.0136
(6.86)
0.0074
(13.97)
0.0125*
(13.25)
0.0121
(10.39)
0.0101*
(15.81)
0.0074
(10.36)
0.0221
(6.97)
Random Class 16 0.0147*
(54.09)
0.0087
(28.51)
0.0084
(34.32)
0.0080*
(30.41)
0.0130
(16.52)
0.0131*
(6.60)
0.0074*
(13.95)
0.0102*
(10.89)
0.0143*
(12.04)
0.0098*
(15.46)
0.0079*
(11.40)
0.0072*
(15.22)
Fixed CONUS July
mean
0.0144*
(53.71)
0.0080*
(26.72)
0.0082
(33.82)
0.0080*
(30.42)
0.0113
(14.50)
0.0135*
(6.79)
0.0068*
(13.10)
0.0069
(7.44)
0.0105*
(9.18)
0.0092*
(14.63)
0.0073*
(10.53)
0.0072
(15.17)
0.0217*
(6.86)
Fixed CONUS 12
month mean
0.0146*
(54.06)
0.0078*
(26.09)
0.0083
(34.08)
0.0080*
(30.46)
0.0103
(13.20)
0.0139*
(6.95)
0.0065*
(12.72)
0.0060
(6.45)
0.0100*
(8.77)
0.0091*
(14.50)
0.0073*
(10.42)
0.0072*
(15.25)
0.0214
(6.71)
Fixed Global 12 month
mean
0.0140
(53.26)
0.0084
(27.69)
0.0082
(33.61)
0.0080*
(30.48)
0.0126
(16.02)
0.0132*
(6.68)
0.0072*
(13.72)
0.0081
(8.73)
0.0114*
(9.86)
0.0094*
(14.94)
0.0075*
(10.87)
0.0072*
(15.20)
0.0220
(6.99)
Table 7
As Table 6 but for the CONUS January data, the ΔNBAR
λvalues are shown in parentheses
under the ΔNBARλvalues.
Landsat
band
MODIS spectral BRDF model parameter source
Local spatially and
temporally
contemporaneous
Fixed CONUS
January mean
Fixed CONUS
12 month
mean
Fixed Global
12 month
mean
1 (blue) 0.0096 (14.27) 0.0095 (14.08) 0.0095 (14.01) 0.0095 (14.13)
2 (green) 0.0095 (11.32) 0.0093 (11.09) 0.0094 (11.23) 0.0092 (11.05)
3 (red) 0.0092 (8.83) 0.0090 (8.66) 0.0092 (8.84) 0.0090 (8.59)
4 (NIR) 0.0125 (6.57) 0.0123 (6.44) 0.0124 (6.50) 0.0122 (6.38)
5 (1.6 μm) 0.0116 (6.28) 0.0110 (5.96) 0.0113 (6.07) 0.0108 (5.91)
7 (2.1 μm) 0.0112 (9.24) 0.0107 (9.22) 0.0109 (9.30) 0.0106 (9.27)
267D.P. Roy et al. / Remote Sensing of Environment 176 (2016) 255–271
reflectance differences in the visible wavelength bands. These results
confirm previous research that the MODIS BRDF spectral parameters
can be used to reduce Landsat BRDF effects (Flood et al., 2013; Gao
et al., 2014; Li et al., 2010; Roy et al., 2008).
The ΔNBARλand ΔNBAR
λvalues reported in Tables 6 and 7 are not
zero-valued because of the sensor calibration, spectral response function,
and atmospheric correction differences described earlier (Section 4.1)
and because of any errors in the MODIS BRDF retrieval. The smallest
July ΔNBARλand ΔNBAR
λvalues are found using the local, then the
CONUS July, then the CONUS 12 month, and then the Global 12 month,
MODISspectralBRDFmodelparameters.Thisisexpectedasusinglocal
spatially and temporally specific MODIS spectral BRDF model parameters
should better capture surface reflectance anisotropy than generalized
fixed parameters. Of specific interest however is that the ΔNBARλand
ΔNBAR
λvalues, in any given spectral band, are only marginally different
for the NBAR results generated using the different MODIS spectral BRDF
model parameter sources. This suggests that a fixed parameter set may
be adequate for Landsat NBAR derivation. This is investigated in the
next section.
5.4. Sensitivity of Landsat NBAR derivation to land cover
The sensitivity of the Landsat NBAR derivation to the use of MODIS
BRDF spectral model parameters defined with respect to different land
cover types was quantified. The purpose was not to examine the aver-
age BRDF of different land cover classes, which is expected to depend
on several factors, not least the land cover class nomenclature used
and the surface condition, but rather to assess if different land cover
specific MODIS BRDF spectral model parameters would provide signifi-
cantly different Landsat BRDF n ormalization capabilities than th ose pro-
vided by the local parameters. Recall that to manage the considerable
number of combinations (Section 4.4) only pairs of Landsat 5 TM and
Landsat 7 ETM+ values with at least 1400 July reflectance values per
land coverclass were considered. For the evergreen broadleaf forest, de-
ciduous needle leaf forest, snow and ice, and permanent wetland classes
(Table 1) there were fewer than 1400 Landsat reflectance pairs avail-
able, due to the strict filtering used to define the colocated MODIS
500 m and Landsat 30 m pixels (Section 3.4) and because of their rela-
tively sparse occurrence relative to the July Landsat data locations
(Fig. 1), and these classes were not considered in this land cover sensi-
tivity analysis. We recognize that evergreen broadleaf and deciduous
needle leaf forests (such as certain tropical forest and taiga ecosystems)
are not represented in this CONUS land cover sensitivity analysis, but
feel that the lessons learned from the other forest classes, that also
have typically geometric-optical shadowing (dome) BRDF shapes, are
sufficiently illustrative.
To summarize the large number of comparisons, two way matrices
were generated with rows and columns defined by the spectral BRDF
model parameter types and the land cover class respectively. Tables 8
and 9 summarize for the red and NIR bands respectively the mean
CONUS absolute NBAR difference (ΔNBARλ) and relative absolute per-
centage NBAR difference (ΔNBAR
λ). The water class has the greatest
ΔNBAR
λvalues (about 50%) and reflect the inability of the MODIS
Table 9
As Table 8 but ΔNBARλand ΔNBAR
λvalues (in parentheses) for the NIR band.
Spectral BRDF model
parameter source
Land cover class
0
Water
1
Evergreen
needleleaf
forest
4
Deciduous
broadleaf
forest
5
Mixed
forest
6
Closed
shrublands
7
Open
shrublands
8
Woody
savannas
9
Savannas
10
Grasslands
12
Croplands
13
Urban and
built-up
14
Cropland
/natural veg.
mosaic
16
Barren or
sparsely
vegetated
Local 0.0172*
(48.33)
0.0119*
(5.65)
0.0313*
(8.58)
0.0292*
(9.62)
0.0132*
(6.69)
0.0120*
(4.14)
0.0282*
(9.67)
0.0096*
(4.43)
0.0184*
(7.70)
0.0342*
(9.67)
0.0162*
(5.76)
0.0286*
(8.01)
0.0216*
(5.72)
Random Class 0 0.0205
(9.55)
0.0537
(14.27)
0.0367
(11.95)
0.0116
(5.84)
0.0144*
(4.95)
0.0363
(12.77)
0.0131
(6.03)
0.0238
(10.10)
0.0374*
(10.51)
0.0179
(6.39)
0.0343
(9.53)
0.0308
(7.92)
Random Class 1 0.0177
(48.54)
0.0296*
(8.16)
0.0304*
(9.97)
0.0115*
(5.88)
0.0130*
(4.48)
0.0259*
(8.85)
0.0069
(3.15)
0.0181*
(7.60)
0.0335*
(9.42)
0.0175*
(6.22)
0.0295*
(8.20)
0.0272
(7.09)
Random Class 4 0.0170
(47.55)
0.0152
(7.30)
0.0293*
(9.64)
0.0194
(9.76)
0.0130*
(4.58)
0.0291*
(10.07)
0.0121*
(5.56)
0.0188*
(7.88)
0.0335*
(9.48)
0.0166*
(5.91)
0.0277
(7.75)
0.0228
(5.96)
Random Class 5 0.0172
(47.91)
0.0152*
(7.29)
0.0294
(8.16)
0.0170
(8.55)
0.0140*
(4.88)
0.0287*
(9.89)
0.0123
(5.68)
0.0192*
(8.03)
0.0333*
(9.45)
0.0164*
(5.82)
0.0290*
(8.09)
0.0206
(5.39)
Random Class 6 0.0176
(48.44)
0.0149
(7.06)
0.0293*
(8.10)
0.0293*
(9.61)
0.0131*
(4.59)
0.0260*
(8.89)
0.0071
(3.26)
0.0181*
(7.57)
0.0339*
(9.53)
0.0171*
(6.07)
0.0275*
(7.67)
0.0259
(6.73)
Random Class 7 0.0172
(47.88)
0.0159*
(7.58)
0.0334*
(9.12)
0.0281*
(9.26)
0.0178
(8.96)
0.0279*
(9.61)
0.0090
(4.13)
0.0184*
(7.72)
0.0338*
(9.55)
0.0166*
(5.87)
0.0290*
(8.11)
0.0213
(5.57)
Random Class 8 0.0171*
(47.68)
0.0156*
(7.48)
0.0297*
(8.2)
0.0296*
(9.74)
0.0180
(9.06)
0.0123*
(4.29)
0.0092*
(4.23)
0.0184*
(7.68)
0.0333*
(9.43)
0.0167*
(5.92)
0.0284*
(7.94)
0.0209*
(5.47)
Random Class 9 0.0170*
(47.63)
0.0148*
(7.09)
0.0303*
(8.36)
0.0292*
(9.60)
0.0172*
(8.65)
0.0127
(4.40)
0.0290*
(10.02)
0.0185*
(7.77)
0.0335*
(9.45)
0.0164*
(5.82)
0.0278*
(7.76)
0.0210*
(5.50)
Random Class 10 0.0171
(47.78)
0.0142*
(6.81)
0.0307
(8.46)
0.0299
(9.81)
0.0171*
(8.60)
0.0127*
(4.45)
0.0304*
(10.52)
0.0122
(5.61)
0.0335*
(9.47)
0.0163*
(5.79)
0.0286*
(7.98)
0.0219
(5.72)
Random Class 12 0.0170*
(47.41)
0.0167*
(8.02)
0.0365*
(9.93)
0.0311
(10.20)
0.0233
(11.66)
0.0129*
(4.55)
0.0316*
(10.96)
0.0152
(7.02)
0.0209*
(8.77)
0.0166*
(5.92)
0.0307*
(8.56)
0.0218
(5.74)
Random Class 13 0.0173
(48.17)
0.0154*
(7.39)
0.0300*
(8.27)
0.029*
(9.54)
0.0187
(9.42)
0.0124*
(4.31)
0.0275*
(9.45)
0.0108*
(5.00)
0.0184*
(7.74)
0.0330*
(9.35)
0.0278*
(7.78)
0.0207*
(5.43)
Random Class 14 0.0170*
(47.15)
0.0185
(8.86)
0.0304
(8.36)
0.0304*
(9.96)
0.0162
(8.17)
0.0129*
(4.57)
0.0302*
(10.45)
0.0140*
(6.48)
0.0197*
(8.25)
0.0345*
(9.77)
0.0174*
(6.15)
0.0210*
(5.53)
Random Class 16 0.0169*
(47.21)
0.0189
(9.00)
0.0338*
(9.24)
0.031
(10.18)
0.0240
(12.03)
0.0138*
(4.93)
0.0323*
(11.22)
0.0183*
(8.42)
0.0239*
(10.06)
0.0355*
(10.03)
0.0188
(6.66)
0.0300*
(8.37)
Fixed CONUS July
mean
0.0170*
(47.48)
0.0155*
(7.41)
0.0308*
(8.46)
0.0291*
(9.57)
0.0186
(9.37)
0.0125*
(4.38)
0.0288*
(9.92)
0.0104
(4.82)
0.0188*
(7.85)
0.0336*
(9.50)
0.0164*
(5.82)
0.0282*
(7.87)
0.0207*
(5.45)
Fixed CONUS 12
month mean
0.0170*
(47.44)
0.0158*
(7.55)
0.031*
(8.53)
0.0292*
(9.60)
0.0191
(9.60)
0.0125
(4.39)
0.0291*
(10.03)
0.0109*
(5.03)
0.0189*
(7.92)
0.0337*
(9.54)
0.0165*
(5.84)
0.0283*
(7.91)
0.0208
(5.46)
Fixed Global 12 month
mean
0.0169*
(47.23)
0.0174
(8.32)
0.033*
(9.03)
0.0297*
(9.78)
0.0217
(10.90)
0.0131*
(4.62)
0.0308*
(10.69)
0.0130*
(6.01)
0.0197*
(8.27)
0.0342*
(9.69)
0.0171
(6.07)
0.0294*
(8.21)
0.0212*
(5.59)
268 D.P. Roy et al. / Remote Sensing of Environment 176 (2016) 255–271
BRDF parameters to reliably model water specular reflectance. In the
red band (Table 8), the water, evergreen needleleaf forest, deciduous
broadleaf forest, and mixed forest classes have ΔNBAR
λvalues greater
than the approximately 15% all-class ΔNBAR
λvalue (Table 6). In the
NIR band (Table 8), the water, deciduous broadleaf forest, mixed forest,
woody savanna and cropland classes have ΔNBAR
λvalues greater than
the approximately 8% all-class ΔNBAR
λvalue (Table 6). The table values
in bold denote the smallest ΔNBARλand ΔNBAR
λfor each land cover
class (i.e., the smallest values in each table column). Of the 13 land
cover classes considered, the local parameters provide NBAR with the
smallest differences between Landsat 5 TM and Landsat 7 ETM+ for
only the evergreen needleleaf forest and urban/built-up classes (red
band) and only for the evergreen needleleaf forest, open shrubland,
and urban/built-up classes (NIR band), which is unsurprising as these
are the more structurally dominated (geometric-optically governed)
land covertypes. The red asterisks (*) denote where there was no signif-
icant difference between the set of Landsat 5 and 7 NBAR values derived
using the local MODIS BRDF parameters and derived using the tabulated
spectral BRDF model parameter source. Therefore for the majority of the
land cover classes there was no significant difference between NBAR
values derived usingthe local MODIS BRDFparameters and using the in-
correct MODIS BRDF parameters (ones that were selected randomly at
other 500 m pixel locations that had different land cover types). In the
NIR band (Table 9) only the deciduous broadleaf forest, closed shrub-
land, and barren land cover types provided predominantly significant
land cover type differences between using the local and other land
cover parameters. In the red band (Table 8) only the water, closed
shrubland, savannaand barren land cover types provided predominant-
ly significant land cover type differences between using the local and
other land cover parameters.
Considering the fixed MODIS BRDF parameters (bottom rows of
Tables 8 and 9), for all the land cover classes, except closed shrubland
(red) and closed shrubland and savanna (NIR), there was no significant
difference between NBAR values derived using the local and the fixed
parameters. In fact in several cases in the NIR the smallest ΔNBARλ
and ΔNBAR
λvalues were found using the fixed rather than the local
or random land class parameters.
6. Conclusion and discussion
The need for consistent Landsat data records over space and time for
both research and applications is well established and a number of
studies have suggested the need for and methods to minimize near-
nadir Landsat bidirectional reflectance (BRDF) effects to provide more
consistent reflectance data (Broich et al., 2011; Flood et al., 2013; Gao
et al., 2014; Hansen et al., 2008; Li et al., 2010; Nagol et al., 2015; Roy
et al., 2008; Toivonen et al., 2006). In this comprehensive paper the
magnitude of the view zenith BRDF effects observed across a range of
surfaceconditions was quantified and then a general method to normal-
ize Landsat reflectance data to nadir BRDF adjusted reflectance (NBAR)
was developed.
A total of 567 CONUS Landsat images acquired over a week in Janu-
ary and July 2010 were examined. The average difference between
Landsat 5 TM and Landsat 7 ETM+ surface reflectance in the forward
and backward scatter directions at the Landsat scan edges were found
to be greater in July than in January. In January the differences are
about 0.01 in all bands and in July the differences were about 0.02 in
the visible bands, and 0.03, 0.05 and 0.06, in the 2.1 μm, 1.6 μmand
NIR bands respectively. Thus the magnitude of these Landsat view ze-
nith BRDF effects may constitute a significant source of noise for many
Landsat applications, although we note that for certain mapping appli-
cations, for example, deforestation (Kennedy, Yang, & Cohen, 2010;
Kim et al., 2014; Potapov, Turubanova, & Hansen, 2011) or burned
area (Bastarrika, Chuvieco, & Martin, 2011; Boschetti et al., 2015)
mapping,these effects maybe negligible compared to thesurface reflec-
tance signal of interest. The proposed general method to normalize
Landsat reflectance to NBAR was found to reduce the average difference
between Landsat 5 TM and Landsat 7 ETM+ surface reflectance in the
forward and backward scatter directions. In July the differences were
approximately 0.01 in the visible bands, and 0.01, 0.02 and 0.02, in the
2.1 μm, 1.6 μm and NIR bands respectively. These average differences
are not zero valued because of differences imposed by sensor calibra-
tion, spectral response function, and atmospheric correction differences
between the Landsat 5 and 7 sensors, and because of any errors in the
MODIS BRDF product retrieval.
The main finding of this study is that appropriate Landsat NBAR can
be generated using a c-factor BRDF normalization approach without
needing to use local spatially and temporally contemporaneous
MODIS BRDF spectral model parameters. The c-factor BRDF normaliza-
tion approach is based on the shape and not the magnitude of the
BRDF (Roy et al., 2008). Previous researchers have observed that only
a limited number of archetypal BRDF shapes capture most of the vari-
ability of the directional reflectance observed in snow-free wide field
of view satellite data (Bacour & Bréon, 2005; Jiao et al., 2014; Zhang
et al. 2015) and there is little variation in these archetypal shapes in
the near-nadir region. Landsat data have a narrow 15° field of view
and the results of this study indicate that the BRDF shapes of different
terrestrial surfaces are sufficiently similar over this narrow field of
view that a c-factor BRDF normalization approach may be applied
using only a single fixed set of MODIS BRDF spectral model parameters.
This has several implications. First, Landsat NBAR can be generatedwith
little sensitivity to the land cover type, condition, or surface disturbance.
Thus, Landsat data observed at anylocation or date can beBRDF normal-
ized in the same way, including surfaces that underwent significant
change, for example, due to deforestation or due to fire that can change
both the BRDF shape and magnitude (Roy, Lewis, & Justice, 2002; Trigg,
Roy, & Flasse, 2005). This is important as the surface state and condition
may change due to anthropogenic factors (e.g., urbanization, agricultural
crop harvesting and rotation) and due to natural factors (e.g., phenology,
wind, fire and other natural disturbances) that are often difficult to detect
reliably using Landsat time series (Boschetti et al., 2015; Hansen et al.,
2014; Huang et al., 2010; Kennedy et al., 2010; Yan & Roy, 2015; Zhu &
Woodcock, 2014). Second, Landsat NBAR can be derived in a computa-
tionally efficient manner for all the Landsat global long-term record
and prior to the year 2000 availability of the MODIS BRDF/Albedo
product. Third, the application of a fixed set of MODIS BRDF spectral
model parameters means that the NBAR correction can be removed
should a user prefer non-view-angle corrected reflectances.
A general and computationally simple method to normalize snow-
free Landsat reflectance data to NBAR is suggested. Namely, the c-factor
BRDF normalization approach (Eq. (7)) applied using fixed BRDF model
parameters (f
iso
,f
vol
and f
geo
)defined for each Landsat band for a speci-
fied solar zenith. The global 12 month parameters (Table 5) are recom-
mended as they provide NBAR results sufficiently similar to the other
fixed parameters but were derived from more than 15,500,000,000
MCD43 500 m product pixels and so are generally applicable. The pro-
posed method is untested for Landsat NBAR derivation withsolar zenith
angles that are different from the Landsat overpass solar geometry. Con-
sequently, it is not recommended that the method be used to derive
Landsat NBAR with solar zenith angles that are very different from
those at the time of Landsat overpass. For large area and multi-
temporal applications a smooth predictable parameterization of the ob-
served Landsat 5 and 7 solar zenith for any location and date has been
developed (Zhang et al. in press). This approach has been implemented
to generate global coverage 30 m Landsat 5 and 7 NBAR surface reflec-
tance data sets that are now available at (http://globalweld.cr.usgs.
gov/collections/).
We do not advocate that this method be applied to scanningsensors
with wide view angle variations or for the determination of surface
albedo, both of which require accurate characterization of the surface
269D.P. Roy et al. / Remote Sensing of Environment 176 (2016) 255–271
anisotropy which is particularly important in areas of structural com-
plexity where geometric-optical shadowing dominate. However, we
note that the general method to normalize Landsat reflectance data to
NBAR may be adapted to other sensors that have spectral band passes
similar to MODIS and narrow fields of view similar to Landsat. For
example, future research to investigate the utility of the method for
application to the Sentinel-2 Multi Spectral Instrument (MSI) that has
MODIS-like spectral bands and a narrow near-nadir 20.6° field of view
only slightly greater than that of Landsat (Drusch et al., 2012)is
planned.
Acknowledgments
This research was funded by the U.S. Department of Interior, U.S.
Geological Survey (USGS) under grant G12PC00069, by the NASA
Making Earth System Data Records for Use in Research Environments
(MEaSUREs) program under Cooperative Agreement NNX13AJ24A,
and by the NASA MODIS BRDF/Albedo/NBAR product generation grant
NNX12AL38G. The U.S. Landsat project management and staff at USGS
Earth Resources Observation and Science (EROS) Center, Sioux Falls,
South Dakota, are thanked for provision of the Landsat data.
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