Estimating Lava Tube Roof Thickness with

1
Estimating Lava Tube Roof Thickness with NASA
TIMS Data and Thermal Modeling
Ronald G. Resmini v 703-735-3899 ronald.g.resmini
_at_boeing.com
December 8, 2004
2
Outline

• Introduction
• TIMS Data
• Data Processing and Analysis
• Results
• Thermal Modeling
• Analysis and Discussion Issues
• Summary and Conclusions
• Future Directions

3
Introduction (1 of 2)

• Use RS data to determine lava tube roof thickness
• Analyze NASA TIMS of Kilauea Volcano, Hawaii
• Six band TIR MSI from 8 to 12 mm
• Archived data from 1988
• Use analytical and numerical solutions to the
  heatequation in conjunction with RS data
• Determine surface temperature over lava tube
• Use modeling to match surface temperature
  anddetermine roof thickness
• Many parameters to consider e.g., h, heat
  transfercoefficient for Newtons law of cooling
  boundarycondition (thermal modeling)

4
A Lava Tube With A Partially Collapsed Roof At
Kilauea In Hawaii
From http//wrgis.wr.usgs.gov/docs/parks/sunset/s
unsetft6.html
5
Introduction (2 of 2)

• Monitor lava tube roof thickness over time
• Establish a baseline
• Utilize archived data resources
• A very rich source of information
• Apply new data analysis techniques
• E.g., ISAC
• Its a relevant volcanological application
• Curriculum development
• TIMS similar to current NASA systems
• Interested in modeling physical process observed
  in remotely sensed data

6
The NASA TIMS Data

• Thermal Infrared Multispectral Scanner - TIMS
• Six bands, TIR MSI from 8 to 12 mm
• On-board calibration sources
• Airborne sensor system C-130B
• Archived data from 1988
• More parameters given on next slide...
• Lots of info. available on TIMS in the lit.
  andon line

7
CCSD3ZF0000100000001NJPL3IF0PDS20000000001
SFDU_LABEL RECORD_TYPE
FIXED_LENGTH RECORD_BYTES
698 FILE_RECORDS 6263 / Pointers to
objects / IMAGE
("kil48t1.imq") / Image description
/ DATA_SET_ID 'C130-E-TIMS-0-EDR-COMPR
-V1.0' PRODUCT_ID KIL48T1 DATA_TYPE
DIGITAL_IMAGE INSTRUMENT_NAME
'THERMAL INFRARED MULTISPECTRAL
SCANNER' PLATFORM_NAME
'C-130B' TARGET_NAME
EARTH FEATURE_NAME KILAUEA ACQUISITION_D
ATE '1988-10-01T145412' START_LATITUDE
19.273333 STOP_LATITUDE
19.398333 START_LONGITUDE
-154.990010 STOP_LONGITUDE
-155.068330 SITE_NUMBER
217 FLIGHT_LINE_NUMBER 3 FLIGHT_RUN_NUMBER
2 AGL_ALTITUDE 2286.0
ltMETERSgt NADIR_PIXEL_SIZE 5.7
ltMETERS/PIXELgt SCAN_RATE
25.0 GAIN_SETTING 2.0 MIN_BLACKBODY_TEMP
15.0 MAX_BLACKBODY_TEMP 32.0 BAND_NUMBER
1 / Description of objects / OBJECT
IMAGE LINES
6263 LINE_SAMPLES 638
LINE_PREFIX_BYTES 60 SAMPLE_TYPE
UNSIGNED_INTEGER SAMPLE_BITS 8
ENCODING_TYPE COMPRESS END_OBJECT
IMAGE END
A TIMS Data Header Record
8
TIMS Spectral Channels
______________________________________
Channel Wavelength
______________________________________
1 8.2 mm - 8.6 mm
2 8.6 mm -
9.0 mm 3
9.0 mm - 9.4 mm 4
9.4 mm - 10.2 mm 5
10.3 mm - 11.1 mm
6 11.3 mm - 11.7 mm
______________________________________
Radiance units mW / m2.sr.mm
9
The TIMS Data (continued)

• TIMS data shipped with utilities for
  decompression, calibration
• The data utilized here were extracted from the
  bundled package
• Kilauea Compiled Volcanolongy Data, Set I
• Glaze et al., (1992)
• JPL, Pasadena, CA
• A six CD collection of data and information
• These data published on by Realmuto et al., (1992)

10
From Glaze et al., (1992)
11
Data Processing and Analysis

• TIMS data utilities
• ENVI
• ISAC
• NEM
• FlexPDE
• Finite element modelingpackage (2D numerical
  solutions to theheat equation)
• 1D and 2D solutions to the heat equation
• Pencil n paper (analytical solutions)

12
Results
Ocean
Steam, et al.
Hot Water
Lava Tube System
TIMS Band 1 (8.2 mm - 8.6 mm) Grayscale Image
13
TIMS Band 3 (9.0 mm - 9.4 mm) Grayscale
Image (further upslope)
14
Inspected the Data...
Calibrated, at aperture radiance
15
Results Atmospheric Correction
Transmissivity Term
Upwelling Term
Applied ENVIs Thermal Atm Correction its
ISAC (Young, et al., 2002). (This was an
iterative process.)
16
ROI Used for Atmospheric Compensation (ISAC)

• Water is a good blackbody
• The T varies due to the lava
• ROI addresses assumptionsof ISAC

17
Inspected the Atmos. Comp. Results...
Ground-leaving radiance (GLR)
18
Temperature/Emissivity Separation (TES)
The Normalized Emissivity Method (NEM)

• On a pixel-by-pixel basis
• Find the maximum radiance value
• Assume e 0.97 (or some such value)
• Find T by inverting the Planck function
• Divide original GLR spectrum but thePlanck
  function just calculated

Applied ENVIs Emissivity Normalization. (Attemp
ted various TES routines in ENVI.)
19
Inspected the TES Results...
Emissivity Spectrum
20
Temperature Image Following TES with NEM
21
Inspected the Temperatures...
22
min 308 K max 320 K mean 312 K
Build an ROI
Thresholded Temperatures
23
Now have temperatures must interpret them...
24
Thermal Modeling Analytical Solutions to the 1D
Heat Equation
25
On the following
Y 0
Y D
solidus temperature
kT thermal conductivity, W/m.K h heat
transfer coefficient, W/m2.K
26
The Solution
D Lava tube roof thickness
27
Use equation on previous slide with
ROI-derived temperatures from the TIMS data...
min 308 K max 320 K mean 312 K
min 35 C max 47 C mean 39 C
28
Build a Nomogram...
Surface Temperature vs. Lava Tube Roof Thickness
47 C
35 C
Tenviron 0º C TLava 1200º C
29
Alternative 1D Solution...
Analytical solution to
On the following
(Tenviron 0º C)
Y 0
Radiative boundary condition added
Y D
solidus temperature
s Stefan-Boltzmann constant
30
The Solution
and
D Lava tube roof thickness
Solve with a root-finding algorithm
31
Thermal Modeling Solutions to the 2D Heat
Equation See Backup Slides
32
Analysis and Discussion

• With Tenviron 0º C and TLava 1200º C 0.5
  meters to 3.75 meters
• From Keszthelyi (1994) roofs can range from 0
  meters (skylights) to 31 meters in this area
• TIMS-derived roof thickness is realistic
• Solidus temperature is a bit high

33
Issues

• Constraining/measuring the value of h
• Modeling with varying lava tube diameter
• Determining if the lava tube is subpixel in the
  TIMS data
• Distinguishing sky lights from unbroken tube roof
• Widely ranging surface temperatures in the data
• Validity of B.C.s used in modeling
• Radiative upper B.C.?
• Mapping/contouring roof thickness throughoutthe
  entire TIMS Kilauea scene
• Thermal history of natural environment and B.C.s
• Need to double-check my math (always)!
• Other...

34
Summary and Conclusions

• Used RS data to determine lava tube roof
  thickness
• Analyzed NASA TIMS of Kilauea Volcano, Hawaii
• Determined surface temperature over lava tube
• Used an analytical solution to the heat equation
  in conjunction with RS temperature data
• Used modeling to match surface temperature
  anddetermine roof thickness
• With Tenviron 0º C and TLava 1200º C 0.5
  meters to 3.75 meters
• TIMS-derived roof thickness is realistic
• Lava tubes in this area can range from 0 to 31
  meters

35
Future Directions

• Still lots of analysis to do
• Incorporate other 1D solutions (e.g., radiative
  B.C.)
• Utilize 2D solutions
• Obtain lab-measurements of h (if they exist)
• Incorporate met data, if available
• Incorporate diurnal thermal history
• Apply other methods for estimating T (e.g., RT
  modeling)
• Analyze TIMS data of the other 1988 flight lines
• Analyze data collected since 1988 (if available)
• Other...

36
References Cited
Glaze, L.S., G.N. Karas, S.I. Chernobieff, M.W.
Thomas, E.D. Paylor,and D.C. Pieri, (1992).
Kilauea Compiled Volcanology Data, Set I.Jet
Propulsion Laboratory (JPL), California Institute
of Technology,Pasadena, CA. Keszthelyi, L.,
(1994). The Thermal Budget of the 1990-1992
Waha'ula LavaTube. Hawaii Center for
Volcanology Newsletter, v. 2, no. 1,
December. Realmuto, V. J., K. Hon, A. B. Kahle,
E. A. Abbott, and D.C. Pieri (1992).Multispectral
Thermal Infrared Mapping of the 1 October 1988
Kupaianahaflow field, Kilauea Volcano, Hawaii.
Bulletin of Volcanology, v. 55, pp.
33-44. Young, S.J., Johnson, R.B., and Hackwell,
J.A., (2002). An in-scene method for
atmospheric compensation of thermal hyperspectral
data. Journal of Geophysical Research, v.
107, no. D24, 4774, doi10.1029/2001JD001266,
20 p.
37
Backup Slides
38
Thermal Modeling Numerical Solutions to the 2D
Heat Equation
39
On the following
40
On the following
41
Numerical 2D Modeling with FlexPDE
42
(No Transcript)
43
Thermal Modeling An Analytical Solution to
the 2D Heat Equation
44
On the following
X 0
X L
Y 0
Y D
Defining f(x)...see next slides...
45
(No Transcript)
46
X0
XL
Y0

YD
X0
XL
Y0
Y0

YD
YD
47
The Solution
Technique Principle of superposition and
separation of variables
Evaluate the boundary condition at y D
Evaluate the coefficients
48
(No Transcript)
49
The B.C. at Y D
At y D