empirical proof of the empirical line
TRANSCRIPT
This article was downloaded by: [University of Colorado - Health Science Library]On: 11 October 2014, At: 15:46Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
International Journal of RemoteSensingPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/tres20
Empirical proof of the empirical lineW. M. Baugh a & D. P. Groeneveld aa HydroBio , Santa Fe, NM, USAPublished online: 21 Dec 2007.
To cite this article: W. M. Baugh & D. P. Groeneveld (2008) Empirical proof of the empirical line,International Journal of Remote Sensing, 29:3, 665-672, DOI: 10.1080/01431160701352162
To link to this article: http://dx.doi.org/10.1080/01431160701352162
PLEASE SCROLL DOWN FOR ARTICLE
Taylor & Francis makes every effort to ensure the accuracy of all the information (the“Content”) contained in the publications on our platform. However, Taylor & Francis,our agents, and our licensors make no representations or warranties whatsoever as tothe accuracy, completeness, or suitability for any purpose of the Content. Any opinionsand views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Contentshould not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoever orhowsoever caused arising directly or indirectly in connection with, in relation to or arisingout of the use of the Content.
This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions
Technical Note
Empirical proof of the empirical line
W. M. BAUGH* and D. P. GROENEVELD
HydroBio, Santa Fe, NM, USA
(Received 26 May 2006; in final form 12 March 2007 )
Calibrating remotely sensed data to reflectance maximizes their quantitative
utility. Many approaches exist for calibrating to reflectance (r), one of which is
the empirical line (EL) method. It offers high-quality results, often to within a
few per cent, but is demanding in terms of field work and analysis. The method
assumes there is a linear relationship between raw digital numbers (DNs) (or
radiance) and reflectance spectra of ground targets. While the EL technique is
widely accepted, we have not found an exhaustive demonstration that there is a
truly linear relationship between radiance/DN and reflectance factors. In this
paper we present an empirical demonstration of the EL method using a data set
that consists of 5304 ground spectra paired with Landsat Thematic Mapper (TM)
pixels.
1. Introduction
Satellite image digital numbers (DNs) cannot be assumed to represent actual surface
conditions because of a variety of effects, such as variable atmospheric attenuation,
illumination geometry, and sensor characteristics. Therefore, the quantitative utility
of remotely sensed data is maximized by calibrating it to a surface reflectance factor
[rsl is the ratio of directional reflected to incident radiation at the surface (s) within
the spectral band (wavelength l)] (Teillet 1986, Moran et al. 2001). The empirical
line (EL) atmospheric correction technique is a common and effective way of
correcting multispectral and hyperspectral data from raw DNs, or radiance, to
reflectance factors (Smith and Milton 1999, Clark et al. 2002, Ben-Dor et al. 2004).
It assumes that a linear relationship exists between image DNs and ground-
measured reflectance for surfaces with a range of contrasting albedo (figure 1). This
linear relationship is used to calculate gains and offsets that convert DNs to
reflectance factors (Roberts et al. 1985, Conel et al. 1987, Clark et al. 2002).
Various numbers of calibration targets have been used in the EL method, with a
trend towards using more targets in recent work. The simplest approach to EL
calibration is to use one target and assume that a dark ground surface will produce a
DN of zero. This approach neglects the contribution of atmospheric scattering, and
errors of 15–20% have been reported when using it (Freemantle et al. 1992, McArdle
et al. 1992). Using two targets of contrasting albedo allows the calibration to
account for atmospheric scattering, and improves the accuracy to better than 10%
(Schott et al. 1988, Caselles and Lopez Garcıa 1989). The two-target approach was a
generally accepted protocol in early applications of the EL method (Kruse et al.
1990, Ben-Dor et al. 1994, Van Der Meer 1994). More recently, however, studies
*Corresponding author. Email: [email protected]
International Journal of Remote Sensing
Vol. 29, No. 3, 10 February 2008, 665–672
International Journal of Remote SensingISSN 0143-1161 print/ISSN 1366-5901 online # 2008 Taylor & Francis
http://www.tandf.co.uk/journalsDOI: 10.1080/01431160701352162
Dow
nloa
ded
by [
Uni
vers
ity o
f C
olor
ado
- H
ealth
Sci
ence
Lib
rary
] at
15:
46 1
1 O
ctob
er 2
014
have used a larger number of calibration surfaces with reported accuracies
improving to within a few per cent. For example, Ferrier and Wadge (1996) used
four targets and stated that more targets reduce uncertainties; Smith and Milton
(1999) used 2–4 points and suggested that two points are not adequate to
characterize errors in the relationship; and Karpouzli and Malthus (2003) used nine
surfaces with contrasting albedo, and suggested that the error of the correction was
reduced by using a greater number of targets. All three of these examples found
linear relationships between ground spectral measurements and image DNs. As a
byproduct of field methods that we are currently developing, we have created a data
set of over 5000 points that clearly shows the linear relationship that is assumed in
the EL method.
Collecting and processing field spectra to use for the EL method has traditionally
been a time-consuming and labour-intensive task, requiring both field studies and
laboratory analyses. Ground target surfaces are required that are: (i) homogeneous,
(ii) at least 565 pixels in size, (iii) of contrasting albedo, and (iv) ideally spectrally
featureless (Clark et al. 2002, Ben-Dor et al. 2004). Calculated reflectance factor
values are typically considered valid only between the bright and dark target
extremes, and extrapolation outside this range is usually avoided (Smith and Milton
1999, Karpouzli and Malthus 2003). If, however, the EL relationship is truly linear,
then a well-established calibration curve should be good for the range beyond the
calibration data.
In general, the process is: (i) homogeneous areas are identified on existing imagery
of the field site; (ii) the target areas are visited by a field crew with a spectrometer to
collect a suite of representative spectra; (iii) field spectra are matched with
corresponding image pixels; and (iv) the EL is calculated. Acquisition of spectra is
best undertaken simultaneously with the overpass of the sensor. Where this is not
Figure 1. Example of an empirical line using two targets of contrasting albedo.
666 W. M. Baugh and D. P. Groeneveld
Dow
nloa
ded
by [
Uni
vers
ity o
f C
olor
ado
- H
ealth
Sci
ence
Lib
rary
] at
15:
46 1
1 O
ctob
er 2
014
possible, targets should remain invariant through time (i.e. devoid of vegetation). In
addition, to minimize the influence of atmospheric path length, calibration sites
should be at an elevation similar to the areas of interest in the image. Examples
include: playas, lava flows, rock outcrops, bare dirt and gravel areas, or dam faces
(Clark et al. 2002).
A major limiting factor for the EL correction is accessing suitable homogeneous
calibration sites. Topography, water bodies and private land are examples of factors
restricting access. We have dramatically improved our ability to collect spectra of
ground targets by mounting an Analytical Spectral Devices (ASD) Fieldspec Pro
FR (350–2500 nm) spectrometer on a single-engine Cessna 185. This system allows
us to collect about 5000 hyperspectral reflectance spectra over a field site during one
hour of flying.
The benefits of this approach include: (i) the ability to collect field spectra
simultaneously with the satellite image acquisition; (ii) nearly unlimited access to the
field region; (iii) measurement of very bright and dark targets; and (iv) highly precise
determination of the line that describes the relationship between raw DN and
reflectance factors.
2. Methods
Aircraft data (5304 spectral points) were collected on 9 April 2006, between 1000
and 1100 h local time under cloud-free skies. Data were collected over the Owens
Lake dry lakebed in eastern California, USA. As a result of dust mitigation efforts,
parts of this lakebed are artificially flooded, providing a variety of surfaces ranging
from bright salt flats and playa to saturated soils and standing water. This variety of
targets gives an ideal range from very bright to dark. The degree of wetness of these
surfaces relates directly to how well they are protected from wind-entrainment – a
fact that prompted these studies. Flight lines and spectral sampling points are shown
in figure 2.
Downlooking spectral measurements were taken through a nadir-pointing ASD
1u lens mounted on the bottom of a Cessna 185 aircraft, near the aircraft centre of
mass. Irradiance measurements were taken through an uplooking flat-surfaced
Teflon port that was mounted on the top of the aircraft. Both ports accept the
standard ASD fibre optic cable. Position information was recorded by a Global
Positioning System (GPS), and stored with each spectral measurement by ASD
software. GPS positions were reported once every 2 s, while spectra were acquired at
a higher rate of about five every 2 s. Position information was interpolated during
postprocessing to give a unique position for each spectrum. The spectrometer was
switched on about 30 min before collecting data to allow the instrument to warm up
and stabilize.
In field spectroradiometry, a Spectralon reference panel is typically scanned every
10 min (more or less often depending on weather conditions) (ASD 2006), and used
as an irradiance reference for calculating reflectance. As this was impractical in the
aircraft platform, the uplooking Teflon port, which has been calibrated to the
Spectralon panel, was used for an irradiance measurement approximately every
20 min. The Teflon port was calibrated prior to the experiment by collecting
uplooking measurements through the port (in level flying configuration), and then
collecting Spectralon measurements as quickly as possible afterwards (about 3 min).
Averages of these two sets of measurements were ratioed (Spectralon/uplooking),
and multiplied by the uplooking irradiance measurements collected while flying.
Empirical proof of the empirical line 667
Dow
nloa
ded
by [
Uni
vers
ity o
f C
olor
ado
- H
ealth
Sci
ence
Lib
rary
] at
15:
46 1
1 O
ctob
er 2
014
(This produced the Spectralon, or irradiance reference, component in the reflectance
equation.) Absolute reflectance (accounting for non-perfect Spectralon reflection)
was not used for this work.
Each uplooking irradiance measurement (collected while flying) was an average of
20 rapidly acquired spectra. Interpolations were made between each of the 20-min
Figure 2. Flight lines and sampling points over the Owens Lake dry lakebed in easternCalifornia. Available in colour online.
668 W. M. Baugh and D. P. Groeneveld
Dow
nloa
ded
by [
Uni
vers
ity o
f C
olor
ado
- H
ealth
Sci
ence
Lib
rary
] at
15:
46 1
1 O
ctob
er 2
014
uplooking averages to help account for systematic changes in solar elevation (before
solar noon). The result was that each downlooking spectrum was paired with an
irradiance value that was interpolated between 20-min measurements. This
approach assumes relatively stable meteorological conditions, which were present
during both days of the study (table 1). The aircraft was operated at 152.4 m
(500 feet) above ground level, and atmospheric effects operating beneath the aircraft
were assumed to be negligible.
The spectrometer’s footprint, or instantaneous field of view (IFOV), through the
1u lens, at 152.4 m (500 feet) and with a forward motion of 56.6 m/s (110 knots) was
2.7 m wide and 14.0 m long [56.6 m/s60.2 s + 2.7 m] due to along-track ‘smear’
during the time of the acquisition (about 0.2 s). The motion of the aircraft due to
light turbulence (3–4u of pitch or roll) increased the uncertainty of the IFOV to an
area about 20 m wide by 30 m long – about the same size as a Thematic Mapper
(TM) pixel.
The Landsat 5 TM image was acquired on 8 April 2006, one day before the
aircraft mission, at 1119 h local time. Both 8 April and 9 April were similar cloud-
free days. We estimated that horizontal visibility was better than 75 km on both
days. Solar radiation data from two California Irrigation Management Information
System (CIMIS) pyranometer sensors located at the north and south ends of the
study area, mounted 2 m above the lakebed, showed that there was only about 3%
difference in solar radiation between the two days, and less than 2% difference
across the study site each day (table 1, CIMIS 2006).
A subset of the TM image was registered to UTM zone 11 (NAD83) using eight
ground control points, with first-order polynomial equations and nearest-neighbour
resampling, resulting in a root mean squared error (RMSE) of 0.177. For
comparison to the Landsat 5 image, the spectrometer data were resampled to
Landsat equivalence using Landsat 5 band response curves (RSI 2003). GPS
information was used to match aircraft spectra with corresponding TM pixels.
To reduce the effects of pointing uncertainty, homogeneous areas on the satellite
image were identified and used to select aircraft-sampled points within areas of low
spectral variability. To do this, the satellite image was filtered with a 363 kernel,
producing mean, standard deviation, and coefficient of variation (stdev/mean6100). From the set of 5304 spectral measurements, 2652 were selected (50% of the
data in the most homogeneous ground locations).
The results were combined in an ArcGIS shape file with points showing the
aircraft sampling locations, and a database containing: (i) GPS location, (ii) ASD
spectra (resampled to TM5 bands), (iii) corresponding TM pixel values, and (iv)
homogeneity values. The TM-equivalent spectrometer values from the 2652
Table 1. Solar radiation (W/m2) from two California Irrigation Management InformationSystem (CIMIS) sensors located at the north and south ends of the study area. Values are anhourly average (60 minute-by-minute readings) for the time period 1000–1100 h, measuredusing pyranometers at a height of 2.0 m above the ground (CIMIS 2006). The rows show thatthere was about 3% difference in solar radiation between the two sampling days, and thecolumns show that there was less than 2% difference in solar radiation across the study area.
8 April 2006 9 April 2006 % difference by day
OL North (#183) 852 882 3.521OL South (#189) 869 891 2.532% difference by site 1.995 1.020
Empirical proof of the empirical line 669
Dow
nloa
ded
by [
Uni
vers
ity o
f C
olor
ado
- H
ealth
Sci
ence
Lib
rary
] at
15:
46 1
1 O
ctob
er 2
014
homogeneous locations were plotted against the corresponding raw Landsat DN
values. Plots and EL calculation results are shown in figure 3.
3. Results and conclusion
As shown in figure 3, there is a good linear relationship between raw Landsat DN
values and the corresponding ASD values for Landsat bands 1–5 and 7. The RMSE
and coefficient of determination (R2) values are (RMSE/R2, respectively): 3.39/0.90
for band 1, 3.36/0.93 for band 2, 3.30/0.93 for band 3, 2.98/0.96 for band 4, 1.95/0.99
for band 5, and 1.59/0.99 for band 7. The regression lines in figure 3 represent the
‘empirical line’ that would be used for EL correction for each band. While the
linearity of the empirical line has not been questioned in the literature, these data
offer empirical proof of its existence.
Note that the positive offset on the x-axis is representative of the atmospheric
path radiance (additive scattering) contribution, which is addressed in atmospheric
correction methods such as dark object subtraction (Chavez 1996). Also note that
the RMSE values are smaller (and R2 larger) for longer wavelengths, showing less
Figure 3. Plots showing calculation of empirical lines for Landsat TM bands 1–5 and 7.Aircraft reflectance values are paired with corresponding TM pixels for 2652 points in themost homogeneous areas of the image. The following number of points were deleted due tosaturated Landsat TM pixels (DN5255): band 15147, band 3515, band 554.
670 W. M. Baugh and D. P. Groeneveld
Dow
nloa
ded
by [
Uni
vers
ity o
f C
olor
ado
- H
ealth
Sci
ence
Lib
rary
] at
15:
46 1
1 O
ctob
er 2
014
variance in the data. This is probably due to reduced Rayleigh scattering at longer
wavelengths. The large sample size used here should reduce uncertainty considerably
in the derivation of the EL, as opposed to using a handful of points recorded on the
ground (Ferrier and Wadge 1996, Karpouzli and Malthus 2003).
The scatter in this data set is well balanced on either side of the calibration curves,
and is probably due to: (i) atmospheric effects between the ground and aircraft, (ii)
20-min interpolation of irradiance measurements, and (iii) positional and pointing
uncertainty.
Acknowledgements
We thank The Great Basin Unified Air Pollution Control District, Bishop
California, the City of Los Angeles Department of Water and Power, and especially
Ted Schade, Air Pollution Control Officer, for their support and interest in
developing these analyses. We also thank the anonymous reviewers for their editorial
guidance and comments on the manuscript.
ReferencesASD, 2006, FieldSpecH 3 User Manual (Boulder, CO: Analytical Spectral Devices Inc.).
BEN-DOR, E., KINDEL, B. and GOETZ, A.F.H., 2004, Quality assessment of several methods to
recover surface reflectance using synthetic imaging spectroscopy data. Remote Sensing
of Environment, 90, pp. 389–404.
BEN-DOR, E., KRUSE, F.A., LEFKOFF, A.B. and BANIN, A., 1994, Comparison of three
calibration techniques for the utilization of GER 63-channel scanner data of
Makhtesh Ramon, Negev, Israel. Photogrammetric Engineering and Remote Sensing,
60, pp. 1339–1354.
CASELLES, V. and LOPEZ GARCIA, M.J., 1989, An alternative simple approach to estimate
atmospheric correction in multitemporal studies. International Journal of Remote
Sensing, 10, pp. 1127–1134.
CHAVEZ, P.S., 1996, Image-based atmospheric corrections revisited and improved.
Photogrammetric Engineering and Remote Sensing, 62, pp. 1025–1036.
CIMIS, 2006, California Irrigation Management Information System, Office of Water Use
Efficiency and Transfers, California Department of Water Resources. Available
online at: www.cimis.water.ca.gov/cimis/welcome.jsp (accessed 22 August 2006).
CLARK, R.N., SWAYZE, G.A., LIVO, K.E., KOKALY, R.F., KING, T.V.V., DALTON, J.B.,
VANCE, J.S., ROCKWELL, B.W., HOEFEN, T. and MCDOUGAL, R.R., 2002, Surface
reflectance calibration of terrestrial imaging spectroscopy data: a tutorial using
AVIRIS. In Proceedings of the 10th Airborne Earth Science Workshop, R. O. Green
(Ed.), JPL Publication 02-1, 2002 (Pasadena, CA: Jet Propulsion laboratory).
CONEL, J.E., GREEN, R.O., VANE, G., BRUEGGE, C.J., ALLEY, R.E. and CURTISS, B.J., 1987,
Airborne imaging spectrometer-2: radiometric spectral characteristics and com-
parison of ways to compensate for the atmosphere. Proceedings of SPIE, 834,
pp. 140–157.
FERRIER, G. and WADGE, G., 1996, The application of imaging spectrometry data to mapping
alteration zones associated with gold mineralization in southern Spain. International
Journal of Remote Sensing, 17, pp. 331–350.
FREEMANTLE, J.R., PU, R. and MILLER, J.R., 1992, Calibration of imaging spectrometer data
to reflectance using pseudo-invariant features. In Proceedings of the 15th Canadian
Symposium on Remote Sensing (Toronto: Canadian Remote Sensing Society and
Canadian Aeronautics and Space Institute), pp. 452–455.
KARPOUZLI, E. and MALTHUS, T., 2003, The empirical line method for the atmos-
pheric correction of IKONOS imagery. International Journal of Remote Sensing, 24,
pp. 1143–1150.
Empirical proof of the empirical line 671
Dow
nloa
ded
by [
Uni
vers
ity o
f C
olor
ado
- H
ealth
Sci
ence
Lib
rary
] at
15:
46 1
1 O
ctob
er 2
014
KRUSE, F.A., KIEREIN-YOUNG, K.S. and BOARDMAN, J.W., 1990, Mineral mapping at
Cuprite, Nevada with a 63-channel imaging spectrometer. Photogrammetric
Engineering and Remote Sensing, 56, pp. 83–92.
MCARDLE, S.S., MILLER, J.R. and FREEMANTLE, J.R., 1992, Airborne image acquisition
under cloud: preliminary comparisons with clear-sky scene radiance and reflectance
imagery. In Proceedings of the 15th Canadian Symposium on Remote Sensing
(Toronto: Canadian Remote Sensing Society and Canadian Aeronautics and Space
Institute), pp. 446–449.
MORAN, M.S., BRYANT, R., THOME, K., NI, W., NOUVELLON, Y., GONZALEZ-DUGO, M.P.,
QI, J. and CLARKE, T.R., 2001, A refined empirical line approach for reflectance
factor retrieval from Landsat-5 TM and Landsat-7 ETM + . Remote Sensing of
Environment, 78, pp. 71–82.
ROBERTS, D.A., YAMAGUCHI, Y. and LYON, R.J.P., 1985, Calibration of airborne imaging
spectrometer data to percent reflectance using field spectral measurements. In
Proceedings of the 19th International Symposium on Remote Sensing of Environment
(Ann Arbor, MI: ERIM), pp. 295–298.
RSI, 2003, ENVI User’s Guide, ENVI Version 4.0 (Boulder, CO: Research Systems Inc.).
SCHOTT, J.R., SALVAGGIO, C. and VOLCHOK, W.J., 1988, Radiometric scene normalization
using pseudoinvariant features. Remote Sensing of Environment, 26, pp. 1–16.
SMITH, G.M. and MILTON, E.J., 1999, The use of the empirical line method to calibrate
remotely sensed data to reflectance. International Journal of Remote Sensing, 20,
pp. 2653–2662.
TEILLET, P.M., 1986, Image correction for radiometric effects in remote sensing. International
Journal Remote Sensing, 7, pp. 1637–1651.
VAN DER MEER, F., 1994, Extraction of mineral absorption features from high-spectral
resolution data using non-parametric geostatistical techniques. International Journal
of Remote Sensing, 15, pp. 2193–2214.
672 Empirical proof of the empirical line
Dow
nloa
ded
by [
Uni
vers
ity o
f C
olor
ado
- H
ealth
Sci
ence
Lib
rary
] at
15:
46 1
1 O
ctob
er 2
014