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Using near–surface temperature data to vicariously calibrate high-resolution thermal infrared imagery and estimate physical surface properties

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Thermal response of the surface to solar insolation is a function of the topography and the thermal physical characteristics of the landscape, which include bulk density, heat capacity, thermal conductivity and surface albedo and emissivity. Thermal imaging is routinely used to constrain thermal physical properties by characterizing or modeling changes in the diurnal temperature profiles. Images need to be acquired throughout the diurnal cycle – typically this is done twice during a diurnal cycle, but we suggest multiple times. Comparison of images acquired over 24 hours requires that either the data be calibrated to surface temperature, or the response of the thermal camera is linear and stable over the image acquisition period. Depending on the type and age of the thermal instrument, imagery may be self-calibrated in radiance, corrected for atmospheric effects, and pixels converted to surface temperature. We used an experimental instrumentation where the calibration should be stable, but calibration coefficients are unknown. Cases may occur where one wishes to validate the camera's calibration. We present a method to validate and calibrate the instrument and characterize the thermal physical properties for areas of interest. Finally, in situ high-temporal-resolution oblique thermal imaging can be invaluable in preparation for conducting overflight missions. We present the following: •The use of oblique thermal high temporal resolution thermal imaging over diurnal or multiday periods for the characterization of landscapes has not been widespread but poses great potential. •A method of collecting and analyzing thermal data that can be used to either determine or validate thermal camera calibration coefficients. •An approach to characterize thermophysical properties of the landscape using oblique temporally high-resolution thermal imaging, combined with in situ ground measurements.
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MethodsX 9 (2022) 1016 44
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MethodsX
j o u r n a l h o m e p a g e: w w w . e l s e v i e r . c o m / l o c a t e / m e x
Method Article
Using near–surface temperature data to
vicariously calibrate high-resolution thermal
infrared imagery and estimate physical surface
properties
Timothy N. Titus
, J. Judson Wynne, Murzy D. Jhabvala,
Nathalie A. Cabrol
U.S. Geological Survey, Northern Arizona University, Goddard Space Flight Center, SETI Institute, United States
a b s t r a c t
Thermal response of the surface to solar insolation is a function of the topography and the thermal
physical characteristics of the landscape, which include bulk density, heat capacity, thermal conductivity and
surface albedo and emissivity. Thermal imaging is routinely used to constrain thermal physical properties by
characterizing or modeling changes in the diurnal temperature profiles. Images need to be acquired throughout
the diurnal cycle –typically this is done twice during a diurnal cycle, but we suggest multiple times. Comparison
of images acquired over 24 hours requires that either the data be calibrated to surface temperature, or the
response of the thermal camera is linear and stable over the image acquisition period. Depending on the type
and age of the thermal instrument, imagery may be self-calibrated in radiance, corrected for atmospheric effects,
and pixels converted to surface temperature. We used an experimental instrumentation where the calibration
should be stable, but calibration coefficients are unknown. Cases may occur where one wishes to validate the
camera’s calibration. We present a method to validate and calibrate the instrument and characterize the thermal
physical properties for areas of interest. Finally, in situ high-temporal-resolution oblique thermal imaging can be
invaluable in preparation for conducting overflight missions. We present the following:
The use of oblique thermal high temporal resolution thermal imaging over diurnal or multiday periods for the
characterization of landscapes has not been widespread but poses great potential.
A method of collecting and analyzing thermal data that can be used to either determine or validate thermal
camera calibration coefficients.
An approach to characterize thermophysical properties of the landscape using oblique temporally high-
resolution thermal imaging, combined with in situ ground measurements.
Published by Elsevier B.V.
This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )
Corresponding author.
E-mail address: ttitus@usgs.gov (T.N. Titus).
https://doi.org/10.1016/j.mex.2022.101644
2215-0161/Published by Elsevier B.V. This is an open access article under the CC BY license
( http://creativecommons.org/licenses/by/4.0/ )
2 T.N. Titus, J.J. Wynne and M.D. Jhabvala et al. / MethodsX 9 (2022) 101644
a r t i c l e i n f o
Method name: Using nearsurface temperature data to vicariously calibrate high-resolution thermal infrared imagery and
estimate physical surface properties
Keywo rds: Pisgah lava field, QWIP, Fourier transformation, Thermal conductivity, Planetary analog
Article history: Received 7 July 2021; Accepted 20 February 2022; Available online 2 April 2022
Specifications table
Subject Area: Earth and Planetary Sciences
More specific subject area: Thermal camera calibration, thermal physical surface
properties
Method name: Using near–surface temperature data to vicariously
calibrate high-resolution thermal infrared imagery and
estimate physical surface properties
Name and reference of original method: Infrared camera calibration; H. Budzier and G. Gerlach
(2015) Calibration of uncooled thermal infrared cameras, J.
Sens. Sens. Syst., 4, 187–197, 2015
doi:10.5194/jsss-4-187-2015
Resource availability: (1) The data used https://doi.org/10.5066/P9PN5BMK ; (2)
Supplementary online material
Method details
Background
Remote sensing has been used to characterize landscapes (e.g., the identification of possible energy
or mineral deposits, the classification of land use) and to form a baseline for determining future
change detection (e.g., effects of climate change or urban expansion). On other planets, remote sensing
is the primary tool for understanding geological processes and landscape evolution. Typically, remote
sensing is conducted from orbital platforms where viewing angles are only a few degrees from
surface normal. However, remote sensing can also be conducted from stationary landers, rovers, and
drones, where oblique views become the norm. Wavelength ranges used for passive remote sensing
include visible and near-to thermal infrared. For oblique imagery using reflected light, knowledge
of the surface photometric function is an important component for analysis. For imagery using
thermal emission, it is usually assumed that the thermal emission is isotropic. For oblique views,
this assumption may not valid. The focus here is the use of thermal infrared oblique observations of
cave-bearing volcanic landscapes.
The use of thermal cameras to analyze landscapes has expanded over the last decade (e.g.,
[ 6 , 14 , 15 , 21 , 32–34 , 39 , 40 ]). However, depending on the type and age of the thermal cameras, the output
image may be self-calibrated in radiance, corrected for atmospheric absorption and emission, and each
pixel converted to surface temperature values. However, we used an experimental thermal camera
where the calibration is reported to be stable with a linear response, but calibration coefficients
were either unknown or poorly constrained. Proper calibration of thermal infrared cameras should be
conducted under laboratory conditions but is also a time-consuming complicated process (e.g., [4] ).
The approach presented here is a simplified method of vicarious in situ calibration, based on field
data collected using an experimental Quantum Well Infrared Photodetector (QWIP) thermal camera.
In 2010, we conducted a series of experiments using the QWIP thermal instrument, which was
an experimental precursor version of a QWIP thermal camera ([ 17 , 19 ] that has been flown on
the International Space Station and is the thermal imaging instrument onboard Landsat 8 [ 18 , 20 ]
and Landsat 9 [25] . Several experiments to analyze cave-bearing landscapes in the Mojave Desert,
California, assisted in this instrument’s maturation. Wynne et al., [ 40 , 42 ] reported thermal distinctions
between cave, tunnel cave (i.e., a subterranean feature with entrances on either end, typically with
frequent air flow) and random non-cave locations on the surface in thermal images captured at
10-minute intervals over a 24-hour period. Their results demonstrated how larger caves may be
T.N. Titus, J.J. Wynne and M.D. Jhabvala et al. / MethodsX 9 (2022) 101644 3
Tabl e 1
Regions of interest and time periods of simultaneous data acquisition (GMT -7).
ROI Start Date Start Time End Date End Time No. Images
B Cave 2010-03-23 10: 15: 04 2010-3-24 10:10: 06 288
Station 7 trench 2010-03-24 12:0 0: 06 2010-3-25 11:55:06 287
Note: Station 7 trench dataset is missing the image that was to be acquired at 3:05:06.
Therefore, the interval between 180.tif and 181.ti f is 10 min for Station 7 trench.
distinguishable from shallow alcoves and tunnel features. Using a similar dataset of thermal imagery,
Titus et al., [34] further examined multiple thermal images containing cave entrances; they found
the detectability of caves was best when multiple thermal images were acquired either at the hottest
(early afternoon) or coolest (pre-dawn) times of day. Moreover, they reported that combining multiple
images captured over a 24-hour period yielded the best results.
The methods presented here were prompted by a QWIP-based airborne thermal imagery
acquisition mission conducted in 2011 (refer to [ 41 , 42 ] for details). As the acquired imagery were not
radiometrically calibrated and atmospherically corrected, we needed to confirm the Digital Number
(DN) pixel values were valid as input into algorithms for detecting terrestrial caves. Fortunately, we
had previously collected a 2010 dataset of QWIP ground-based thermal imagery and in situ near
surface kinetic temperature data [ 34 , 35 ], as a precursor experiment to the overflight campaign [ 16 , 42 ].
We used these data to vicariously calibrate thermal infrared imagery, as well as estimate physical
surface properties. As these data were simultaneously acquired at a temporally high resolution over a
diurnal cycle, we developed and applied the techniques presented here to both extract in situ thermal
physical properties and calculate camera calibration coefficients.
Study Area
Our experiment was conducted at Pisgah lava field, which is located about 175 miles northeast
of Los Angeles on Bureau of Land Management lands. Consisting of Quaternary basaltic lava and a
cinder cone superimposed on alluvial deposits and lacustrine sediments of Lavic Lake playa [8] , the
flow is approximately 21,0 0 0 years old [38] . Extending 18 km to the west and 8 km to the southeast
from the Pisgah cinder cone [13] , three eruption phases emitted both p
¯
ahoehoe and a ʻa lava, which
vary in thickness from 1 to 5 meters across the field [9] . In addition to the lava field, sections of
the landscape were punctuated by desert pavements and sand deposits, which made the area ideal
for thermal imaging across a range of thermal physical properties. We used the cinder cone as our
vantage point for acquiring oblique imagery.
Fig. 1 depicts the study area with camera location and the two regions of interest (ROI). Fig. 2
shows sensor locations within the camera’s field of view. Thermal imaging of each ROI was conducted
on consecutive days. We collected imagery of the B Cave ROI first and Station 7 trench ROI was
acquired the next day. Tables 1 and 2 describe the metadata associated with the camera and the
in situ sensors, which include GPS coordinates.
Data collected from B Cave was acquired at a high oblique angle with the center of the image
being 7.5 °, measured from the horizontal. Sensors within the image ranged from 7.5 °to 5.4 °(near
the image background). Distance between camera and sensors varied from 440m to 670m, which
would also suggest a range in air mass values (the amount of air along the line of sight) were present.
Importantly, the distance of 670 m was not far from the expected altitude for possible overflights.
Data collected from Station 7 trench were acquired the day after B Cave data were collected
( Table 1 ). However, these data were collected at a less oblique range of angles of elevation, with the
center of the image being 9 °. Sensors located within the image ( Table 2 ) ranged from 8.6 °to 9.8 °.
Distance between camera and sensors varied from 315m to 365m. Distances from the camera to the
four sensors were similar; thus, the air mass was also similar.
4 T.N. Titus, J.J. Wynne and M.D. Jhabvala et al. / MethodsX 9 (2022) 101644
Fig. 1. Pisgah lava field, Mojave Desert, California, with QWIP camera location and two regions of interest identified. Orange
vectors approximate the left and right field of view for B cave dataset, while yellow vectors approximate the left and right
limits of the field of view for Station 7 trench dataset. Blue balloons denote camera and sensor locations. The inset shows the
same scene but at an oblique angle and provides additional context. Credit: Google Earth.
Fig. 2. (a) Differenced images show location of two sensor locations in the B Cave ROI. (b) Sensor locations for all seven
sensors surrounding B Cave. (c) Differenced images show location of two sensor locations in the Station 7 trench ROI. (d)
Sensor locations for all four sensors surrounding Station 7 trench.
T.N. Titus, J.J. Wynne and M.D. Jhabvala et al. / MethodsX 9 (2022) 101644 5
Tabl e 2
Sensor and camera locations. ID is either the QWIP camera or the sensor serial number. Locations of sensors were determined
using a Garmin Etrex (Vista HCx) GPS and WGS 84 datum. Time averaging was used to increase accuracy to 3m horizontal.
Vertical errors are typically 5x the horizonal error for this type of GPS, suggesting the elevation error is 15m . Pixel sample
and line number represent coordinates of the sensor within the QWIP image. The estimated uncertainty in distance is 5 m,
while the estimated uncertainty in angle is 30%.
ID Longitude Latitude Elevation (m) Pixel Sample Pixel Line Distance (m) Elev. Angle
QWIP Camera W116.37409 N34.74651 764 n/a n/a n/a n/a
Atmospheric Temperature/Humidity
9702167 W116.37125 N34.75059 701 184 146 526.498 6.840
9702171 W116.37182 N34.74858 710 154 111 314.623 9.786
B Cave (23-24 March 2010)
9695783 W116.37192 N34.74998 707 10 3 124 437.560 7.44 3
9695779 W116.37148 N34.75037 699 164 13 8 494.978 7.50 2
9695787 W116.37125 N34.75059 701 184 146 526.498 6.840
9695785 W116.37107 N34.75039 706 272 146 515. 076 6.438
9695788 W116.37077 N34.75118 707 203 169 603.545 5.403
9695782 W116.37103 N34.75166 693 75 157 640.735 6.336
9695786 W116. 37019 N34.75157 697 265 172 669.034 5.728
Station 7 trench (24-25 March 2010)
9695781 W116.37182 N34.74858 710 154 111 314.623 9.786
2233224 W116.37173 N34.74904 709 27 137 358.665 8.752
2233225 W116.37135 N34.74885 709 205 148 365.109 8.598
2041160 W116.37160 N34.74897 707 105 145 360.402 9.024
QWIP thermal instrument specifications
The QWIP thermal infrared sensor responded to thermal infrared radiation from 7.5 to 9.1 μm with
a peak response of 8.7 μm. The detector array was cooled with a miniature Stirling cycle cryocooler
to 67K (-206 °C), which minimized both detector noise and internal field of view optical effects. The
QWIP used a standard 50mm Infrared (IR) lens and had an instantaneous field of view of 8.8 °x 11 °.
Integration time was 0.0164 sec. The camera was preset to remotely capture one 16- bit image every 5
minutes for a 24-hour period (or 288 images total). Each image is in a 320 ×256 pixel format where
each detector pixel within the array is a 30 μm square. Although the imagery was not radiometrically
calibrated, the instrument had the ability to resolve signals from objects where temperature variations
are less than 0.02 °C. Calibration tests on QWIP thermal infrared cameras have been documented to
be stable for months, even years [20] .
Ground-based temperature instrumentation
We used ONSET Hobo logger U23-003 to measure surface kinetic temperatures. Accuracy was
±0.21 °C from 0 °to 50 °C with a resolution of 0.02 °C. Sensor response time when located in soil
and rock was not provided but was reported to be 30 seconds when located in stirred water or
three minutes in air moving at 1 m/sec ( https://www.onsetcomp.com/products/data- loggers/u23- 003/
) . Tempe ra tu re sensors used to measure the atmosphere were ONSET Hobo logger U23-001. The
accuracy of the U23-001A is ±0.2 °C from 0 to 70 °C, with a resolution of 0.04 °C. Response time
was reported to be 10 minutes in air moving at 1 m/sec. The accuracy of the U23-001A for relative
humidity (RH) is typically ±2.5% between 10% and 90% RH, with a maximum of ±3.5% including
hysteresis at 25 °C. At HR below 10% and above 90%, the accuracy is typically ±5%. ( https://www.
onsetcomp.com/products/data- loggers/u23- 001/ )
Experimental design
Proper experimental design is key to success. This section describes our methodology, but we
also provide both recommendations and sampling improvements for guiding similar studies. We
believe that possible applications of high temporal resolution diurnal oblique thermal imaging include
6 T.N. Titus, J.J. Wynne and M.D. Jhabvala et al. / MethodsX 9 (2022) 101644
landscape characterization on other planets (e.g., Mars) using a rover-mounted camera, collection of
data that can be used for overflight planning (such as the original purpose of this study), and thermal
physical characterization of landscapes where overflights, even by drones, are either not practical or
not allowed.
When collecting long term thermal infrared imagery (i.e., over a 24-hour period) in backcountry
settings, the following considerations should be applied. The camera should be mounted in a stable
location and in a secure manner to ensure all imagery in the sequence can be co-registered. As
imagery is acquired, the camera’s field of view (FoV) should not shift by more than a fraction of
a pixel to avoid having to register the images. Thus, the mounting apparatus must be stable and
data acquisition during gusty wind events should be avoided. Importantly, care should be taken
when personnel are moving around the instrument to avoid any accidental jostling –as this could
compromise data collection and quality. When capturing data over a diurnal period, we recommend a
frame acquisition rate of every 5 to 10 minutes. Our experiment showed a rate of every five minutes
was temporally sufficient ([ 34 , 35 ]; this study). Higher rates of image acquisition could be used to test
this assertion and/or for better characterization of the instrument properties, such as signal-to-noise
ratio (SNR) or Noise Equivalent Delta Tempe ra ture (NEDT).
Instrumentation for ground measurements should be deployed in areas within the camera’s FoV.
Sensors should minimally sample temperature at the same frame acquisition rate, but ideally at
least every minute. For our study, temperature probes were inserted into the soil (or rock) so that
the base of the sensor was flush with the surface. When installing into rock, we used a hammer
drill with a bit the same diameter as the temperature probe (5mm). Te mp er at ure data acquired
effectively represented the near surface temperature at the midpoint of the probe. By inserting the
probe into the soil or rock, we minimized the effect of direct insolation on the probe. However, this
introduced a time lag and a small amount of attenuation between the actual surface temperature
(as captured by the camera) and the ground temperature measured by the probe. However, this
time delay can be used to estimate both the surface thermal physical properties (e.g., thermal
diffusivity) and the attenuation of actual surface temperature. Additionally, the time delay and the
calculated attenuation can be used to correct the measured ground temperature to the actual surface
temperature. Thereafter, this corrected surface temperature can be directly compared to a thermal
camera’s digital number (DN) output for the pixels containing ground instrument locations.
Ground temperature sensors should be placed in areas uniform in slope, composition, and texture,
and correspond to several neighboring pixels within the camera’s FoV. This will help reduce possible
errors with sensor location within the imagery. For this study, we also restricted the slopes to within
a few degrees of zero (i.e., flat or horizontal surfaces). Refer to figures S1 through S11 for examples of
terrain types where sensors were installed.
To directly compare measured ground temperatures to thermal DN levels, ground sensor locations
within the thermal images were needed, i.e., image line and sample. We used the observed heat
from our own bodies in images to mark locations of sensors in a few of the pre-dawn images. When
these images were acquired, field personnel straddled the sensor, with the instrument between their
feet. This was repeated for all instruments and was quite effective. The contrast between the “warm
bodies” and the surrounding area can be enhanced by taking the difference between the image of
interest and either the previous or the next image in the sequence. Fig. 2 is an example of this method
where two sensor locations can be identified.
While not needed for the near surface temperature corrections, atmospheric temperature and
humidity was required for our in situ calibration technique to be most effective. Therefore, we
collocated the temperature/humidity (U23-001) sensors proximal to the in situ near surface sensors.
These additional sensors were positioned approximately one meter above ground (see Figure S3 for
example image). A makeshift sunshade, constructed with aluminum foil, was used in an attempt to
minimize the effect from direct sunlight and surface radiance on the temperature probe. In retrospect,
we should have sampled atmospheric temperature at a height of 1. 5 to 2 meters above the ground
surface and used commercially available sunshades. This would have optimally minimized the effects
from both direct sunlight and surface emission and reduced the presumably large temperature effects
of the dark-colored and thermally conductive iron rebar – used as the mounting apparatus for the
surface temperature probes.
T.N. Titus, J.J. Wynne and M.D. Jhabvala et al. / MethodsX 9 (2022) 101644 7
Fig. 3. Thermal profile examples: (a) Temperature vs. time at several depths, z. The black line represents the surface. Red,
green, and blue lines show temperature at one, two, and three diurnal skin depths, respectively. (b) Diurnal minimum and
maximum temperatures shown as a function of depth. Black curve is the temperature profile at noon (local daylight time). Blue
and red dashed lines represent the minimum and maximum temperature envelopes, respectively.
Another methodological refinement would have been to place two instruments at different
heights to ascertain the appropriate height for these sorts of experiments. While tracking the
atmospheric temperature at one location per ROI was valuable, additional locations (e.g., foreground
and background) would have allowed for a more complete characterization of the different air masses.
Thermal diffusion theory
Near surface temperature, as a function of depth, can be determined by solving the thermal
diffusion equation:
dT
dt = α
2
T
z
2
(1)
where α= k/ ρc , αis the thermal diffusivity, k is thermal conductivity, ρc is the density times the heat
capacity, T is temperature and z is depth into the subsurface.
Since surface temperature is cyclic, one convenient and useful solution to this 2
nd order PDE is:
T
(
t, z
)
= T
o
+
i
e
z/ δi A
i
cos
(
θi
(
t, z
) + ϕ
i
) (2)
where θi
( t,z ) = (2 πi/P ) t - z/ δi
and ϕi
is the initial phase shift of the surface temperature, t is time,
T
o is the diurnal mean surface temperature, and A
i
is the amplitude of the temperature variation of
the i
th harmonic. Thermal skin depth, δi
, is a measure of how far a surface temperature cycle of an
arbitrary period penetrates the regolith. The exact definition is the depth at which the amplitude of
the thermal wave (over a given period) is attenuated by a factor 1/ e .
δ=
P
π
k
ρc =
αP
π(3)
where δis skin depth, and P is the period of the cycle (86,400 sec for the terrestrial diurnal cycle).
An example of this is shown in Fig. 3 .
Thermal diffusion analysis
Once a diurnal cycle of data has been acquired, pixels corresponding to in situ sensor locations
should be identified. By plotting each identified pixel’s DN levels and in situ near surface temperature
versus time (see Fig. 4 ), a quick estimate of the time lag between image signals and measured
8 T.N. Titus, J.J. Wynne and M.D. Jhabvala et al. / MethodsX 9 (2022) 101644
Fig. 4. Sensor 9695781 thermal profile of raw data before and after the Fourier transform (FT) correction. (a) Temperature
vs. time with curves shown as measured rock temperature (red), the FT corrected temperature (green), and atmospheric
temperature (blue). Black line represents the thermal image pixel DN values. (b) Temperature vs DN, with the red line
representing the uncorrected temperature vs. thermal image pixel DN values. The green line represents the FT corrected
temperature values vs. thermal image pixel DN values. The green line demonstrates hysteresis between measured temperature
and observed radiance. The green line is better represented by a best-fit line,
as much of the hysteresis has been removed.
Some hysteresis remained at the lower DN values, which could be a result of atmospheric radiance as shown in the blue line.
temperatures can be calculated. Once the time lag has been determined, the following equation can
be used to derive the thermal diffusivity,
α=
P
4 πz
0
t
2
=
k
ρc
(4)
where P is the number of seconds in a diurnal cycle, tis the time delay between the image
acquisition and the corresponding ground instrument temperature, and z
o is the depth to the
midpoint of the temperature probe.
A few assumptions should be considered with this calculation. First, a possible source of error may
occur between the thermal contact between the probe and the surrounding material. Poor thermal
contact will increase the observed time lag, and therefore decrease the estimated thermal diffusivity.
Sensor lag is another potential source of error, 30 seconds based on the sensor specifications.
Therefore, our estimates may represent the lower limits of these values and have the most effect
for smaller time lags (higher thermal diffusivity).
Robertson [31] provided a review of thermal physical properties for rock including those relevant
to lava fields. Typically, basalt has an αof 9 ×10
7 m
2
/s. Our highest estimated coefficient of
diffusion was 18 ×10
7 m
2
/s, which was closer to granite than to p
¯
ahoehoe. It is unlikely that
an error in the time delay estimate could compensate for a factor of two increase in measured
diffusivity when compared to laboratory measurements. Perhaps the deployed in situ sensor estimated
temperature is not representative of the radiance as observed by the QWIP at this location. Because
the U23-003 sensors are equipped with two external probes, future deployments should acquire two
in situ temperatures instead of just one.
While α, the thermal diffusivity, is the physical property that we directly estimate from the t,
the time delay between the imaging and the sensor probes’ reaction to changing insolation, thermal
inertia ( ) is the thermal physical property most used to characterize landscapes [37]
k = αρc (5)
=
kρc =
αρc (6)
where ρis density and c is the heat capacity for basalt. The product ( ρc ) of density ( ρ) and heat
capacity ( c ) typically only varies by a factor of two or less for most surface materials [ 22 , 27 , 30 , 36 ].
However, thermal conductivity can vary by several orders of magnitude. If one either knows or can
T.N. Titus, J.J. Wynne and M.D. Jhabvala et al. / MethodsX 9 (2022) 101644 9
Tabl e 3
Derived thermal physical properties at sensor locations. ID is the sensor number. Time delay represents the temporal shift
applied between the DN profile and the sensor temperature profile.
αis the coefficient of diffusion, while k is the derived
thermal conductivity (assuming that
ρc volumetric heat capacity is 2.08 ×10
6 J m
3 K
1
).
is the estimated thermal
inertia in standard SI units. Figure number (#) refere nces supplementary online material that includes images of each
sensor site. An asterisk indicates this was also the location where air temperature and humidity data were collected.
Sensor ID Number Time delay (mins) α(x 10
7
m
2
/s) Normalized Diffusivity
α/ αmax k Figure #
B Cave ROI
9695783 36 3.71384 0.197531 0.172102 282.407 S1
9695779 75 0.85567 0.0455111 0.00913591 31.2 319 S2
9695787 22 9.94451 0.528926 1.23397 1237.41 S3
9695785 41 2.86326 0.15229 0.102297 191.175 S4
9695788 46 2.27464 0.120983 0.0645603 135.366 S5
9695782 71 0.954799 0.0507836 0.0113753 36.8135 S6
9695786 34 4.16362 0.221453 0.216312 335.23 2 S7
Station 7 trench ROI
9695781 77 0.811797 0.0431776 0.00822307 28.8609 S8
2233224 47 2.17888 0.11589 0.0592387 126.908 S9
2233225 16 18 .8 013 1 4.41079 3216.79 S10
2041160 19 13.3328 0.709141 2.21811 1920.97 S11
reasonably estimate the surface material density and heat capacity, then both thermal conductivity ( k,
Eq. 5 ) and thermal inertia ( , Eq. 6 ) can be determined. We used these relationships, combined with
Eq. 4 , to estimate thermal conductivity and inertia values presented Table 3 . We assumed a density
and heat capacity consistent with basalt [31] . Estimated values were derived from the time-delay
shown in Table 3 . Unfortunately, we were not able to ground truth these properties.
Thermal diffusion correction for surface temperature
While the thermal diffusivity ( α) is a constant, skin depth is a function of the period over which
change occurs. This means the temperature attenuation correction must be conducted over a range
of time periods. The most direct approach is to use a discrete Fourier transform (DFT) to identify
amplitudes and phase shifts (which can be represented as a complex number) for the entire range of
periods represented in the temperature time sequence. These amplitudes and phase shifts should be
corrected using Eq. 7 .
f
i
= DF T
T
p
f
i
= f
i
(cos
z
0
δi
+ j sin
z
0
δi 
e
z
0
δi
T
s
= DF T
1
f
(7)
Where T
p is the temperature measured by the sensor probe, T
s is the corrected surface temperature,
and an inverse Fourier transform (DFT
1
) can then be used to convert the corrected spectrum back to
the temperature time sequence. d
i
is the harmonic specific skin depth and is defined by Eq. 3 , except
the period, P , is replaced by P / i . Fig. 4 illustrates this technique applied to field data. This approach
also amplifies higher frequency noise contained in the data, so this technique should only be applied
if probe depth is less than the diurnal skin depth.
A comparison of measured surface temperatures and corrected surface temperatures compared
the observed QWIP DNs are shown in Figs. 4 , S1-S11. A hysteresis effect is clear in the uncorrected
temperature data, but some residual hysteresis remains even in the corrected surface data. One
possible cause for this residual hysteresis could be that the corrected surface temperature may not
be completely representative of the entire surface area within a pixel’s FOV. For example, scattered
rocks could alter observed radiance by casting shadows or having different temperatures than the
surrounding flat surface. Another possible cause is that the QWIP DN observations have not been
corrected for atmospheric effects in these plots. The atmosphere is warmer during the morning and
cooler during the night for the same corresponding surface temperatures, causing the observed DN
levels to be higher in the morning and lower during the night.
10 T.N. Titus, J.J. Wynne and M.D. Jhabvala et al. / MethodsX 9 (2022) 101644
Tabl e 4a
Atmospheric characteristic water column equivalent, h
0
.
Wavel en gth (um) 7.5 8 8.5 9 9.5
h
o
(mm/km) 3.67950 19.8340 34.7064 60.5592 73.8088
Tabl e 4b
Atmospheric coefficients to calculate water column equivalent, h.
Coefficient c
0 c
1 c
2 c
3
Value 5 3.8333 ×10
1 10
2 1.6667 ×10
4
Fig. 5. QWIP spectral window, Planck functions, and atmospheric absorption. (a) Blackbody radiance for the QWIP’s spectral
window as a function of temperature. The black line is h
0
, the characteristic water column used to estimate atmospheric
transparency. (b) Radiance vs. wavele ngth as a function of temperature. Solid lines are the radiance levels for a blackbody
and the dashed lines are the attenuated radiance of the blackbody radiance if looking through a 1mm/km equivalent water
column. For reference,
the range of an equivalent water column, h, for this data set was between 0.5 and 2 mm/km.
Atmospheric absorption
Even in an arid desert environment, the atmosphere contains water vapor that absorbs and re-
emits thermal radiation. The amount of absorption and emission is a function of temperature, relative
humidity, and distance between the thermal source and the detector. Using the formula in Minkina
and Kleccha [24] and water vapor opacity tables from [ 10 , 28 ] (as used by Minkina and Kleccha [24] ),
we estimated atmospheric transmissivity ( τ) as a function of air temperature, relative humidity, and
distance using the standard exponential decay function
τ= e
h/ h
o (8)
The coefficient, h
o
, is weighted assuming a top hat spectral response for the QWIP (8.5 –9.1 μm)
and are shown in Table 4a . Absorption due to atmospheric CO
2
is negligible at these wavelengths
[ 10 , 28 ]. Fig. 5 contains absorption coefficients and the Planck function for a range of temperatures
and humidity within the QWIP spectral window. h is a function of temperature, relative humidity,
and distance.
h =
c
0
+ c
1
T + c
2
T
2
+ c
3
T
3
rd (9)
where h is the water column in mm/km, T is temperature (in degrees Celsius), r is relative humidity
(from 0 to 1), and d is the distance in km. Coefficients c
0
thru c
3
are presented in Table 4b .
As previously mentioned, atmospheric temperature data were acquired one meter above the
surface. In retrospect, a minimum of two meters may have improved our results. As it currently
stands, a comparison of the Fourier transforms’ phase shifts of atmospheric and surface data suggested
that “atmospheric” temperatures represented a significant component of surface radiance. We posit
that acquiring temperature data at a height at or above two meters and the use of commercially
available sunshades would have reduced this effect. Additional air temperature sensors along the line
T.N. Titus, J.J. Wynne and M.D. Jhabvala et al. / MethodsX 9 (2022) 101644 11
of sight should also be considered. The largest uncertainty in our calibration is due to an incomplete
characterization of the line-of-sight atmosphere.
Camera calibration
Once near surface temperatures have been corrected for both time delay and attenuation effects,
these values can be converted to radiance using the Planck function – assuming the top hat spectral
response function (i.e., uniform response across the spectral band-pass) ranges between 7.5 and 9.1
μm. These values can be compared directly to the corresponding DNs within the imagery. Fig. 4 b
illustrates a direct comparison where lower temperatures (corresponding to nighttime imagery) and
higher temperatures (corresponding to daytime imagery) are depicted as lines with different slopes.
This effect is likely due to atmospheric absorption (and lower thermal re-emission) along the line
of sight. Assuming the detector array is linear and uniform in response, we used Eqs. 10 and 11 to
determine both the camera’s calibration coefficients and the surface emissivity at each sensor location.
N = N
1
R
obs
+ N
0 (10)
where N is the image DN, N
1
is the calibration coefficient (gain) in DN per W
sr
1
m
3 (described
below), N
0
is the corresponding calibration offset, and R
obs
is the observed radiance. These equations
did not account for the effects from the camera optics, but because the QWIP is cooled and used a
standard IR lens, we assumed these effects were minimal.
R
obs
=
9 . 1
7 . 5
τε βs
+
(
1 τ)
βa dμ(11)
where τis the atmospheric transparency along the line of sight between the camera ( Eq. 8 ) and
the surface, εis the surface emissivity, βs is the Planck function radiance as determined from the
corrected surface temperature ( Eq. 7 ), and βa is the atmospheric radiance. All terms are functions of
wavelength and must be integrated across the QWIP spectral response function, which we assume is
a top hat for this analysis.
Eqs. 10 and 11 can be combined:
N = N
1
9 . 1
7 . 5
τε βs
+
(
1 τ)
βa dμ+ N
0 (12)
This Eq. must be solved where the calibration coefficients, N
0
and N
1
, are constant for all sites,
and εis a function of each site and should be restricted to physically reasonable values. In retrospect,
using a TIR field spectrometer on site or returning samples to the lab for characterization to determine
surface emissivity at oblique viewing angles would have further improved our calculations.
The use of multivariate linear regression techniques proved to be unwieldy, so Amoeba (an IDL
minimization function based on the downhill simplex method [ 26 , 29 ]) was used to determine N
0
and
N
1
, as well as individual emissivity values for each of the 11 sites. We applied this process on the
complete dataset. We also ran this procedure individually for both the B Cave and Station 7 trench
ROIs.
Method validation
The best fit calibration coefficients using the entire dataset were -9,304.05 DN and 1,838.57
DN/radiance unit for N
0
and N
1
, respectively. Derived surface emissivity for the 11 sites, which were
also free parameters where the solution was constrained to be between 0.55 and 1.0, ranged between
0.69 and 0.78, which were lower than previous laboratory measures of basaltic emissivity when
observed at oblique angles (e.g., ε0.86 at 10 °viewing angle, [2] ). Unfortunately, we were not
able to ground truth these properties. For future experiments, we recommend using a field thermal
infrared (TIR) spectrometer or returning samples to laboratory facilities to measure surface emissivity,
especially at oblique angles. In addition, because emissivity was the only free parameter specific to
each of the 11 sites, it is possible that any systematic lateral variations in atmospheric conditions or
12 T.N . Titus, J.J. Wynne and M.D. Jhabvala et al. / MethodsX 9 (2022) 101644
Tabl e 5
Calibration coefficients as defined in Eq. 6 . ID is the sensor ID number. Change in the estimated camera calibration
coefficient between the two days was 11%. RU stands for radiance unit in
MKS.
ID N
0
(DN) N
1
(DN/RU) e (All) e (ROI Only)
All -9304.05 1838.57
B Cave
9695783 -8727.04 186 4. 02 0.729765 0.677238
9695779 0.719626 0.656209
9695787 0.724459 0.668035
9695785 0.702367 0.64 4 497
9695788 0.693667 0.635248
9695782 0.734 4 46 0.675343
9695786 0.721647 0.648719
Station 7 trench
9695781 -10521.1 2077.23 0.773473 0.739183
2233224 0.760042 0.730661
2233225 0.728786 0.70 0 086
2041160 0.746743 0.715206
Fig. 6. Calibration model compared to observations. The black line is the estimated observed radiance derived from the DN
profiles at the 11 pixels (sensor sites), using the N
0 (DN offset) and N
1 (DN gain). The red line is the estimated radiance as
derived from the corrected surface temperature, estimated emissivity, atmospheric absorption, and emission. The green line is
the difference between these two estimates. Zero line has been offset to 6 Wm
2
sr
1
μm
1
.
non-uniformity of the surface (e.g., scattered rocks) could be compensated for by altering the apparent
effective emissivity. This is further discussed in the next section.
Calibration coefficients for the QWIP as determined for B Cave ROI had values of -8,727.04 DN and
1,864.02 DN/radiance unit. This was a change of 6.2% and 1.4 % for N
0
and N
1
, respectively. Calibration
coefficients for the QWIP as determined for the Station 7 trench ROI had the values of -10,521.1 DN,
2,077.23 DN/radiance unit. This was a change of 13 .1% and 13.0% for N
0
and N
1
, respectively. We
should emphasize this difference in calibration coefficients is not likely due to instrumental drift
as QWIP TIR arrays are stable over long periods of time [20] . The apparent changes in calibration
coefficients are likely attributed to sensitivities in the uncertainties of atmospheric opacity and air
temperature along the line of sight. Refer to Table 5 for complete calibration coefficient and emissivity
results. Fig. 6 illustrates the comparison of the radiance derived from the camera DN values using
our estimated calibration coefficients to the estimated radiance derived from the ground surface
temperature data, our estimated emissivity and our atmospheric correction. The largest discrepancies
occur during the hottest, followed by the coldest, times of the day.
T.N. Titus, J.J. Wynne and M.D. Jhabvala et al. / MethodsX 9 (2022) 101644 13
Fig. 7. Estimated noise of the camera determined from comparing pixel DN to interpolated pixel DN. The blue region was used
to determine camera noise when the estimated observed radiance was less than 6 radiance Wm
2
sr
1
μm
1 and the region
used to determine camera noise when the estimated observed radiance was greater than 8 Wm
2
sr
1
μm
1
. The results are
shown in Tabl e 6 .
Tabl e 6
Estimated camera noise based on DN levels at the 11 characterized sites.
Radiance Range
(Wm
2
sr
1
μm
1
)
Average Signal
(Wm
2
sr
1
μm
1
)
Standard
Deviation
(Wm
2
sr
1
μm
1
)
SNR Brightness
Temperature
for average
signal ( °C)
NEDT ( °C)
< 6 5.155 0.00961654 536.037 -3.85754 0.0815735
> 8 8.76 0.0812977 107.784 21.5288 0.483917
Characterization of uncertainties and possible systematic errors
The QWIP camera’s SNR and NEDT can be characterized using the data collected for this study. An
upper limit for the noise can be determined by comparing the DN value to the linearly interpolated
DN value based on the previous and subsequent DN values. The difference from these two DN values
over a range of DN values was used to determine SNR and the NEDT, assuming the previously
calculated calibration coefficients. Fig. 7 shows the distribution of “noise” as a function of DN.
Radiance and equivalent temperature are also shown on the axis. Table 6 shows the results with an
NEDT of 0.08 °C and 0.48 °C for brightness temperatures near 0 °C and 20 °C, respectively.
The largest uncertainty in the calibration process described here is the atmospheric correction.
The sampling of the air temperature at only one meter above ground level (AGL) and the absence of
commercially available sunshades could allow for contamination of the air temperature measurements
from radiance from the surface. This effect would be most prevalent during the mid-day, resulting in
over-correcting for atmosphere effects. The potential for over-correction would reduce the estimated
amount of radiance observed by the QWIP camera. The minimization approach used to determine
both calibration coefficients and surface emissivity estimates could be affected. A systematic lowering
of surface emissivity is possible. Additionally, any variation in atmospheric properties within the
QWIP’s FOV would be mapped into the emissivity parameters as there are site specific and the
calibration parameters apply across the scene.
The next largest uncertainty may be the assumption that the surface temperature estimate is
representative of the observed radiance across the entire pixel throughout the diurnal cycle. While
we intentionally selected relatively large flat areas that were of uniform composition and texture,
there were still local variations, such as rocks, that may be completely representative of the thermal
14 T. N. Titus, J.J. Wynne and M.D. Jhabvala et al. / MethodsX 9 (2022) 101644
Fig. 8. Image DN vs modeled radiance. These plots show a comparison of the image DN values for our 11 in situ sites compared
to the modeled radiance using (a) the derived surface emissivity, a fixed emissivity of 0.85, and a fixed emissivity of 0.9. The
red line shows a linear best-fit function while the blue line shows a quadratic best-fit function. For case that used our best-fit
emissivity (panel a), the quadratic fit is nearly identical to the linear fit.
response of the surface as measured by our in situ probes. The effect would potentially be mapped
into both the thermal diffusivity estimate (through the effects on the estimated time lag between
image pixel response to changing surface radiance and the in situ temperature measured) and the
emissivity as the predicted radiance would slightly differ from the observed radiance. The issue
of surface heterogeneity and the effects on estimated thermal physical properties is a well-known
problem and has been a topic of entire papers (e.g., [ 1 , 3 , 7 ]) Further discussion of the uncertainty in
emissivity and diffusivity estimates are discussed below. Emissivity estimates between the best fit
using the entire dataset and the best fit using only B Cave ROI increased from 7 to 10%. Emissivity
estimates between the best fit using all the data and the best fit using only Station 7 trench
ROI increased by only 4%. For both ROIs, the estimated emissivity remained below the laboratory
measured value of 0.86 for oblique views of basalt [2] . The oblique views in study ranged between
7 °and 10 °, and therefore could have even lower emissivity than prev