Remote Sensing Applications Area, Space Applications (ISRO), Ahmedabad. Centre 380 015, India; e-mail: [email protected]. (Received 5 September ...
. . , 2003, . 24, . 11, 2207–2220
Regional thermal inertia mapping over the Indian subcontinent using INSAT-1D VHRR data and its possible geological applications T. J. MAJUMDAR Earth Sciences and Hydrology Division, Marine and Water Resources Group, Remote Sensing Applications Area, Space Applications (ISRO), Ahmedabad Centre 380 015, India; e-mail: tjmajumdar@rediffmail.com (Received 5 September 2001; in final form 30 January 2002) Abstract. Thermal inertia is a measure of the resistance power of a material to changes in temperature, and this property of a material is very important from the aspects of hydrological and geological studies. Generation of thermal inertia images and their possible geological application has been attempted over the Indian peninsula and its surroundings using INSAT-1D (Indian National Satellite) VHRR (Very High Resolution Radiometer) day-time and consecutive nighttime data. Using the concepts of energy balance computation and also using the procedures involved in albedo computation and the digital registration of day time and pre-dawn imagery, a thermal inertia map over the whole peninsula and its surroundings has been generated. An attempt has been made to correlate the thermal inertia anomalies with sub-surface structures. The analysis done over the subcontinent shows the possibility of delineation of subsurface structures by thermal inertia mapping.
1. Introduction The thermal inertia of a material is defined as P=(KrC)1/2 where K represents the thermal conductivity of the material, r its density and C its specific heat. This physical property is very important in geological and hydrological studies and is gaining further importance in remote sensing technology (Watson 1985). Thermal inertia is a volume property (using measurement by volume) and it determines the resistance of the material to changes in temperature. To date, almost all the physical parameters of studies in remote sensing technologies deal with the surficial property; however it is known that microwave energy can penetrate the Earth’s surface by a few centimetres. The change in temperature of the Earth’s surface actually depends on its thermal inertia (Kahle 1977, Reeves 1975). The thermal inertia of a surficial feature of interest cannot be directly measured. Therefore, modelling is required for its estimation. A model has been generated by Watson (1973, 1975) for geological applications. Pohn et al. (1974) have successfully used it for creating a thermal inertia contour map from Nimbus data. The model has been further modified by Kahle (1977) to include the latent and sensible heat transfer between the atmosphere and the ground, in addition to radiative heat International Journal of Remote Sensing ISSN 0143-1161 print/ISSN 1366-5901 online © 2003 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 10.1080/01431160210161724
2208
T . J. Majumdar
transfer. Gillespie and Kahle (1977) later used this model successfully to create the thermal inertia image of Pisgah Crater, California, USA. Studies using HCMM (Heat Capacity Mapping Mission) data have improved our ability to map subsurface features which were invisible to other similar systems (Short and Stuart 1982). For example, it has been shown that thermal inertia can be a useful tool for geological mapping and canopy temperature can be a good indicator of soil moisture conditions (Watson 1975, Gillespie and Kahle 1977, Pratt and Ellyett 1978, Sabins 1978, Jackson et al. 1981). Day-time HCMM thermal infrared data have been used to simulate night-time thermal infrared imagery and then thermal inertia imagery over a part of Europe (Majumdar and Bhattacharya 1990). Information on HCMR (Heat Capacity Mapping Radiometer) is available elsewhere (NASA 1980). Generation of regional thermal inertia image from INSAT-1D VHRR data has been taken up for the first time, probably because of the surface temperature modelling efforts which are essential prerequisites (Majumdar and Bhattacharya 1988, Sobrino and El Kharraz 1999). Currently, only NOAA and INSAT give a unique advantage of day and night-time data coverage with a comparatively high resolution and global coverage (NOAA 1990). Details of INSAT-1D data specifications and preprocessing have been discussed elsewhere (Joseph et al. 1994, Prakash and Bhandari 1996). The INSAT VHRR provides full disk images of the earth in the visible (0.55–0.75 mm) and thermal infrared bands (10.5–12.5 mm) with near nadir ground resolution of 2.75 and 11 km for the INSAT-1 series of satellites. The first satellite of this series, INSAT-1A, was launched in April 1981. Currently, INSAT-1D, launched in July 1990, is operational. The INSAT meteorological data collection and processing is done primarily by the Meteorological Data Utilization Centre (MDUC) of the India Meteorological Department (IMD) at New Delhi (Kelkar and Yadav 1991). Sobrino and El Kharraz (1999) have used four NOAA imagaries to develop a new algorithm, known as FTA (Four Temperatures Algorithm) for mapping of thermal inertia over the Iberian Peninsula (Europe). The main advantage of the methodology is to obtain phase difference information from satellite data only without the need to know the value surface emissivity and total water vapour of the atmosphere (Sobrino and El Kharraz 1999). Mitra and Majumdar (2001) used NOAA AVHRR data for regional thermal inertia mapping with day and consecutive night-time data in a regional scale over the Brahmaputra valley, Assam and then used the same for further interpretation with reference to delineation of petroliferous basins on both sides of the valley. 2. Data source and area of interest The INSAT-1D data at around 12:00 and 24:00 h Indian standard time (IST) over the Indian peninsula and its surroundings were chosen for the present study. The corresponding in situ surface temperature data were made available from IMD (India Meteorological Department) Weather Chart (1996). INSAT-1D data, with spatial resolutions of 2.75 km for visible and 11 km for thermal IR (infrared) at nadir, have been widely used for environmental research at regional and global scales. INSAT-1D VHRR was chosen for generating thermal inertia images over the Indian peninsula and the surroundings as this is one of the important/indigenous sources of day and night-time thermal IR data in addition to the visible/IR data in the day-time.
T hermal inertia mapping of Indian region for geological applications
2209
The different data inputs for this study are as follows (Mahadevan 1994, Raju 1968): (1) (2) (3) (4)
Survey of India topographic sheets; Generalized relief map; Generalized rock types and geology map over the subcontinent; and Generalized tectono-stratigraphic map over the Indian subcontinent.
3. Methodology 3.1. Geometric correction of V HRR data and superimposition with toposheet INSAT-1D data (day and consecutive night-time) over a cloud-free atmosphere were acquired for 26 January 1996 (day/night) from IMD, Delhi along with related imageries. Work was carried out on extraction of the area of interest, suitable calibration, conversion of 10-bit data to 8-bit data, generation of thermal IR data, and surface temperature modelling after atmospheric corrections. 3.2. Calibration of V HRR data INSAT VHRR thermal IR data may be converted to temperature-based data by using the look-up table given in the INSAT-1D data. Accordingly, thermal IR channel data were converted to temperatures using the calibration chart and linear fitting. 3.3. Atmospheric attenuation correction for retrieving surface temperature Terrestrial surface temperature measurements made by remote sensors are attenuated by the Earth’s atmosphere by either increasing or decreasing the observed brightness temperature as received by the sensor. The VHRR TIR channel is designed to exploit atmospheric windows in the thermal region of the electromagnetic spectrum, where attenuation is relatively small. This, however, introduces significant error in VHRR-sensed surface temperature. Several split-window atmospheric attenuation correction models have been developed by a number of investigators (McClain et al. 1983, Singh 1984, Price 1985, Cooper and Asrar 1989, Di and Rundquist 1994, Majumdar and Mohanty 1998). However, in the case of single channel INSAT VHRR thermal IR data, correction due to atmospheric water vapour may be attempted using the model of Price (1983) (Majumdar and Bhattacharya 1988). Since it has been observed that in the range of 10.5–12.5 mm spectral emissivity of the ground range varies between 0.95 and 0.99 (Taylor 1979), the estimated temperature on the surface can be obtained by using the simpler equation of the basic radiative transfer equation (Chandrashekar 1960): T =(3.5+e)/(4.5)(aT +b), g sat
(1)
where e is the emissivity, T is the brightness temperature observed at the satellite sat point and a and b are two constants. Values of those parameters are: emissivity (e) around 0.97, a=1.23 and b=−77.3. The calibration information for TIR data is available from INSAT calibration chart with the following linear relationship (Majumdar and Bhattacharya 1988): Brightness Temperature=−0.499 (grey level)+329.4
(2)
2210
T . J. Majumdar
3.4. Basic approach for thermal inertia The thermal inertia model is based on two important relationships; namely, the one-dimensional heat flow equation and another known as the energy balance equation (Kahle 1977). The one-dimensional heat flow equation is given by ∂T ∂2T =K9 ∂t ∂Z2
(3)
where T=temperature, t=time, Z=depth beneath the surface, and K 9 =K/rC, the thermal diffusivity. The boundary condition across the Earth’s surface gives the heat balance equation: S+R+H+L +G=0,
(4)
where S=the net solar radiation, R=the net thermal radiation, H=the sensible heat flux between the atmosphere and the ground, L =the latent heat flux between the atmosphere and the ground, and G=the heat flux in the soil. For the lower boundary condition, it is assumed that the temperature at a depth of 50 cm (T ) is constant. It is pertinent to mention that the diurnal variation of the 50 surface temperature in the soil is confined to within one metre from the Earth’s surface. The basic approach for generation of thermal inertia images is shown in figure 1. A look-up table can be made for DT as a function of albedo, slope, slope-azimuth and thermal inertia (Kahle 1977). This look-up table is used to compute the thermal inertia of the materials. Pratt and Ellyett (1978) simplified the problem further by presenting a look-up table for three variables, namely thermal inertia, albedo and DT , by the plots as shown in figure 2. For planar terrain in the Indian region (excepting Himalayan terrain), the slope and slope-azimuth variations contribute relatively less to thermal inertia values; therefore these simplifications are justified. Figure 3 shows the generalized relief map of India. 3.5. Construction of albedo imagery The albedo imagery is constructed from the digital multispectral data, with the help of the following simple relationship: A =S W DN (5) i i,n n (i,n) where A =the albedo value of the ith pixel, DN =the digital number (reflectance i (i,n) value) of the ith pixel in the spectral channel ‘n’, and W =the weighting factor for n channel ‘n’. The day-time data is used for the construction of the albedo imagery. 3.6. Registration of day-time and night-time imagery As estimation of thermal inertia values for different surface materials requires computation of surface temperature variations, registration of day-time and nighttime data is an important step in the construction of the thermal inertia imagery. A procedure making use of ground control points has been developed for this purpose. Using a minimum of six ground control points, which are easily recognizable in both the day-time and night-time data, a second degree polynomial fit is established between the two sets of data. Together with knowledge of the polynomial coefficients, the reference between the two sets of data can be established. The rms error for the
T hermal inertia mapping of Indian region for geological applications
2211
Figure 1. Basic procedure for thermal inertia image generation.
registered data is found to be around 2.5 pixels. The difference between night-time and the corresponding day-time temperature images is shown in figure 4. A good number of features appear in the land portion, whereas very little temperature difference could be observed in the Himalayan belt. As expected, night-time temperatures of sea water are mostly high. Similarly, high day-time temperatures and low night-time temperatures have been reported elsewhere for different rock types, e.g. sandstone, siltstone, etc. (Sabins 1978). Traditional geometric correction of remotely sensed data involves relating the pixel coordinates (row and column) of ground control points (GCPs) with their corresponding map coordinates (latitude/longitude position). A GCP is a point on the surface of the Earth that can be identified on both an image (in rows and columns) and a map (latitude/longitude). The geometric relationship between input
2212
T . J. Majumdar
Figure 2. Look-up table for albedo, DT and thermal inertia (after Pratt and Ellyett 1978).
pixel location (row and column) and the associated map coordinates (x, y ) can be determined by a group of GCPs. The typical projection equations relating map coordinates and image coordinates are polynomials: x∞=a +a x+a y +a x2+a xy +a y 2+... 0 1 2 3 4 5 y ∞=b +b x+b y +b x2+b xy+b y 2+... (6) 0 1 2 3 4 5 where x and y are the positions in the rectified image or map and x∞ and y ∞ represents the corresponding positions in the original input image (Di and Rundquist 1994). 3.7. Construction of thermal inertia imagery The thermal inertia imagery is constructed with the help of the albedo imagery generated from the day-time data and with the knowledge of the surface temperature change between the day-time and night-time data (figure 4). The thermal inertia values are computed for all pixels common to both day and night (Majumdar et al. 1982). Figure 5 shows the thermal inertia imagery generated for the study area. 3.8. T he apparent thermal inertia model The thermal inertia of a surface cannot be measured directly, so a model is required for its estimation. Such a model was generated by Watson (1975) for geological applications. This was further modified by Kahle (1977) to include the latent and sensible heat transfer. Recently, a new term, ‘apparent thermal inertia’ has been defined which has many of the attributes of true thermal inertia (Sabins 1978, Price 1985, Majumdar and Bhattacharya 1990, Xue and Cracknell 1995). The
T hermal inertia mapping of Indian region for geological applications
2213
Figure 3. Generalized relief map of India.
thermal inertia model (SoA-TI model) developed by Xue and Cracknell (1995) is an intermediate approach between simple models that can give apparent thermal inertia, and complex models which need more in situ measurements along with satellite data. The apparent thermal inertia (ATI) is defined as: ATI=NC (1−a)/(DT ), (7) 1 where N is the scaling factor, C =sinH sinW (1−tan2H tan2W)+cosH cosW arc cos 1 (−tanH tanW), where H=latitude and W=solar declination, a=apparent albedo, and DT =temperature difference as produced by differencing the radiometric temperatures during the night and the day passes (no atmospheric correction). In the present case, thermal inertia imagery was generated by the model of Pratt and Ellyett (1978).
2214
T . J. Majumdar
Figure 4. Difference of temperature image over Indian subcontinent.
4. Results and discussion In this study, albedo image generation, registration of day–night thermal imageries for generation of temperature image differences, and modelling for thermal inertia image generation have been carried out, as discussed. The thermal inertia values computed for water are high, nearing the expected range of TIUs (thermal inertia units), where the thermal inertia values reported for water and clouds are 5000 TIUs (Sobrino and El Kharraz 1999). However, the model developed using equation (3) is for solid materials only and may not be applicable to a large water body. Similar high thermal inertia values for water have also been reported elsewhere (Reeves 1975, Sabins 1978). The value computed in the final thermal inertia imagery matched reasonably well with the reported values available in the literature (table 1). Among other features which are discernible in the thermal inertia image are snow and ice
T hermal inertia mapping of Indian region for geological applications
2215
Figure 5. Generated thermal inertia image over Indian subcontinent.
in the Himalayan terrain, forest, agricultural land, arid zones with dry sand in the Rajasthan areas, etc., though one has to keep in mind that the thermal inertia concept may not be applicable to day-time snow and ice as long as melting is involved; both day–night imageries have to be used. In addition, thermal inertia values over the arid region do not match well with the dry sand and sandy soil values as given in the standard chart (table 1) of Sobrino and El Kharraz (1999). They have also compared the final thermal inertia map with the existing geological maps over the area of interest, with a reasonable matching of most of the features. A similar attempt has been made here—the existing geological map over the subcontinent has been compared with the final thermal inertia map obtained from INSAT-1D imagery (figures 5 and 6). The major rock types discernible in the thermal inertia image generated are the Deccan Flood Basalts in the Western region
T . J. Majumdar
2216
Table 1. TIU values for different materials (after Sobrino and El Kharraz 1999). Material Water and clouds Ice Snow Dry sand Wet sand Dry clay Wet clay Shale Granite Bush Grass Corn Alfalfa Oats Woodland
P(TIU) 5000 2000 150 590 2500 550 2200 1900 2200 2000 2100 2700 2900 2500 4200
Reference Vieillefose and Favard (1979) Vieillefose and Favard (1979) Vieillefose and Favard (1979) Price (1982) Price (1982) Price (1982) Price (1982) Miller and Watson (1977) Miller and Watson (1977) Bernier et al. (1980) Bernier et al. (1980) Bernier et al. (1980) Bernier et al. (1980) Bernier et al. (1980) Bernier et al. (1980)
TIU=1 W s−D m−2 K−1.
Figure 6. (a) Map showing Deccan Trap region (after SubbaRao 1988); (b) Major tectonostratigraphic divisions in India (after Mahadevan 1994).
T hermal inertia mapping of Indian region for geological applications
2217
(figure 6(a), SubbaRao 1988); also the arid zone of Rajasthan, may be due to high diurnal variations in the day–night period. The Deccan Traps are relatively thin—about 100 m—in the north-eastern area and gradually thicken towards the west coast, reaching a thickness of 1.5 km. The same thickness is reached in the southern and western coasts of Saurastra and its northern region. The west coast of India, from Surat to Bombay, was a region of Moho unwarp during the Late Cretaceous period, representing a transition type crust, and acted as a major source of Deccan Trap flows. Through this source area basaltic magma erupted by rifting and spread over long distances to the east, west and north (Kaila 1988). Figure 6(b) shows the major tectono-stratigraphic divisions in India (Mahadevan 1994). Viewed in the light of these broad aspects of geological evolution, the Indian
2218
T . J. Majumdar
subcontinent may be divided into nine groups relating to the deep interior of the Indian crust (Mahadevan 1994): (i)
(ii) (iii) (iv) (v) and (vi)
(vii) and (viii) (ix)
The Precambrian shield comprising both the Archean cratonic regions and the associated Archean to Proterozoic high-grade mobile belts. The Proterozoic platformal sedimentary basins. The horst-graben belts of dominant Gondowana sedimentation. The regions of Deccan and Rajmahal-Sylhet volcanism. The Phanerozoic platformal sedimentary belts and basins, largely along the fringes of the shields and the Indo-GangeticBrahmaputra alluvial plains and the Bengal basin along or close to the Himalayan front. The Himalaya and the Andaman-Nicobar Island arc. The submerged continental margins and the Island clusters in the Arabian Sea and the Bay of Bengal.
A good matching could be observed between different thermal inertia zones and various tectono-stratigraphic units, broadly in areas other than sea (figures 5 and 6). Among other important features, the Himalayan terrain has appeared as a separately identifiable zone in both the imageries of difference of temperatures as well as thermal inertia imageries. In addition, the Bengal Basin with its planer terrains could also be specifically identified in these imageries. However, thermal inertia image generation over the higher elevation zones, e.g. the Himalayan Terrain, requires further corrections due to the terrain heights (Kahle et al. 1981). High values of thermal inertia computed for mountain regions indicate better ventilation and not different soil types. Also, bathymetric near-shore and deep sea contours are traceable in the final thermal inertia imagery, which needs further study (figure 5). 5. Conclusions A procedure for generating thermal inertia imagery has been described and tested over the Indian subcontinent. The evaluation for a typical feature, such as a water body, with high thermal inertia, indicates the efficacy of the procedure. The analysis performed over the Indian subcontinent and its surroundings shows the possibility of delineation of regional sub-surface structures by thermal inertia mapping. Acknowledgments The author wishes to thank two anonymous referees for their suggestions and critical comments for improving the manuscript. The author would also like to thank Dr A. K. S. Gopalan, Director, SAC, and Dr S. R. Nayak, Group Director, MWRG/RESA/SAC for their keen interest in this study. Thanks are also due to Dr Pranav S. Desai, Chief Scientist, Remote Sensing Applications for his help in acquiring the INSAT-1D data and to Shri K. K. Mohanty, ESHD/MWRG for help during INSAT data processing. INSAT-1D imageries have been obtained courtesy of IMD, New Delhi. References B, M., B, R., and B, E., 1980, Cartographie de l’inertie thermique de certains secteurs du Quebec a´ partir de donnes aeriennes et du satellite H. C. M. M. Paper presented at V I Canadian Symposium on Remote Sensing, Halifax, Nova Scotia, 21–23 May 1980, edited by T. T. Alfoldi, pp. 473–482.
T hermal inertia mapping of Indian region for geological applications
2219
C, S., 1960, Radiative T ransfer (New York: Dover). C, D. I., and A, G., 1989, Evaluating atmospheric correction models for retrieving surface temperatures from the AVHRR over a tallgrass Prairie. Remote Sensing of Environment, 27, 93–102. D, L., and R, D. C., 1994, A one-step algorithm for correction and calibration of AVHRR Level 1b data. Photogrammetric Engineering and Remote Sensing, 60, 165–171. G, A. R., and K, A. B., 1977, Construction and interpretation of digital thermal inertia image. Photogrammetric Engineering and Remote Sensing, 43, 983–1000. J, R. D., I, S. B., R, J., and P, J, P. J., 1981, Canopy temperature as a crop water stress indicator. Water Resources Research, 17, 1133–1138. J, G., I, V. S., N, K., K K, A. S., A, B. V., K, V. N., D, R. K., and N, C. M., 1994, Very high resolution radiometers for INSAT-2. Current Science, 66, 42–56. K, A. B., 1977, A simple thermal model of the earth’s surface for geologic mapping by remote sensing. Journal of Geophysical Research, 82, 1673–1680. K, A. B., S, J. P., A, M. J., A, R. E., and L, C. J., 1981, Geological application of thermal inertia imaging using HCMM data. JPL Publication 81-55, Jet Propulsion Laboratory Quarterly Technical Review, JPL, Pasadena, CA, USA. K, K. L., 1988, Mapping the thickness of Deccan Trap flows in India from DSS studies and inferences about a hidden Mesozoic basin in the Narmada-Tapti region. In Deccan Flood Basalts, edited by K. V. SubbaRao, Memoir 10 (Bangalore: Geological Society of India), pp. 91–116. K, R. R., and Y, B. R., 1991, A basic guide for use of INSAT imagery. Meteorological Monograph, India Meteorological Department, New Delhi, 30 pp. MC, E. P., P, W. G., W, C. C., A, Z., and S, J., 1983, Multichannel improvements to satellite-derived global sea surface temperatures. Advances in Space Research, 2, 43–47. M, T. M., 1994, Deep Continental Structure of India: A review (Bangalore: Geological Society of India). M, T. J., S, V. L., K, D. S., M, D. S., and V, K., 1982, Remote sensing and thermal inertia mapping and likely applications to geological exploration. 12th International Symposium on Remote Sensing of Environment (2nd T hematic Conference), T exas, USA, 6–10 December 1982 (Ann Arbor, MI: ERIM), pp. 591–598. M, T. J., and B, B. B., 1988, Derivation of surface temperatures on land after correction due to atmospheric water vapor—a case study with INSAT VHRR data. Remote Sensing of Environment, 26, 185–191. M, T. J., and B, B. B., 1990, Simulation of thermal inertia imagery with daytime HCMM data. International Journal of Remote Sensing, 11, 139–147. M, T. J., and M, K. K., 1998, Derivation of land surface temperatures from MOS-1 VTIR data using split-window channel computation technique. International Journal of Remote Sensing, 19, 287–294. M, S. H., and W, K., 1977, Evaluation of algorithms for geological thermal inertia mapping. Proceedings of the 11th International Symposium on Remote Sensing of Environment, Ann Arbor, Michigan, April 1977 (Ann Arbor, MI: ERIM), pp. 1147–1160. M, D. S., and M, T. J., 2001, Thermal inertia mapping over known fields in India using NOAA-AVHRR data. Joint ISRO-ONGC Report (Unpublished), May 2001, 25 pp. NASA, 1980, HCMM Data Users’ Handbook (Greenbelt, Maryland: NASA/Goddard Space Flight Center). NOAA, 1990, NOAA Polar Orbiter Data Users’ Guide. US Department of Commerce. NOAA, NESDIS, NCDC, and the Satellite Data Service Division, Washington, DC. P, H. A., O, T. W., and W, K., 1974, Thermal inertia mapping from satellite discrimination of geologic units in Oman. Journal of Research: US Geological Survey, 2, 147–158. P, W. J., and B, S. M., 1996, An algorithm to overlay continental boundaries and latitude-longitude grids over INSAT-VHRR images. Computers and Geosciences, 22, 433–440.
2220
T hermal inertia mapping of Indian region for geological applications
P, D. A., and E, C. D., 1978, Image registration for thermal inertia mapping and its potential use for mapping of soil moisture and geology in Australia. 12th International Symposium on Remote Sensing of Environment, Ann Arbor, MI, April 1978 (Ann Arbor, MI: ERIM), pp. 1207–1217. P, J. C., 1982, On the use of satellite data to infer surface fluxes at meteorological scales. Journal of Applied Meteorology, 21, 1111–1122. P, J. C., 1983, Estimating surface temperatures from satellite thermal infrared data—a simple formulation for the atmospheric effect. Remote Sensing of Environment, 13, 353–361. P, J. C., 1985, On the analysis of thermal infrared imagery: the limited utility of apparent thermal inertia. Remote Sensing of Environment, 18, 59–73. R, A. T. R., 1968, Geological evolution of Assam and Cambay Tertiary Basins of India. American Association of Petroleum Geologists Bulletin (AAPG), 52, 1136–1150. R, R. G., (editor), 1975, Manual of Remote Sensing (Volume I) (Falls Church, Virginia: American Society of Photogrammetry). S, F. F., 1978, Remote Sensing—Principles and Interpretation (San Francisco: W. H. Freeman). S, N. M., and S, L. M., J, 1982, T he Heat Capacity Mapping Mission (HCMM) Anthology (NASA SP-565) (Washington, D.C.: US Government Printing Office). S, S. M., 1984, Removal of atmospheric effects on a pixel by pixel basis from the thermal infrared data from instruments on satellites. The advanced very high resolution radiometer (AVHRR). International Journal of Remote Sensing, 5, 161–183. S, J. A., and E K, M. H., 1999, Combining afternoon and morning NOAA satellites for thermal inertia estimation 2. Methodology and application. Journal of Geophysical Research, 104, 9455–9465. SR, K. V., (editor), 1988, Deccan Flood Basalts. Memoir 10 (Bangalore: Geological Society of India). T, S. E., 1979, Measured emissivity of soils in the southeast United States. Remote Sensing of Environment, 8, 359–364. V, M., and F, J. C., 1979, Mesure des Variations Horaires des T emperatures et de l’Albedo T errestre par Satellite: Application a la T e´le´de´tection des Resources en Eau. T e´le´de´tection et Gestion des Resources, edited by F. Bonn (Ste-Foy: Association Quebecoise de Te´le´de´tection), pp. 119–128. W, K., 1973, Periodic heating of a layer over semi-infinite soilid. Journal of Geophysical Research, 78, 5904–5910. W, K., 1975, Geological applications of thermal infrared images. Proceedings of the IEEE, 63, 128–137. W, K., 1985, Remote sensing—a geophysical perspective. Geophysics, 50, 2595–2610. W C, 1996, India Meteorogical Department, New Delhi, January, 1996. X, Y., and C, A. P., 1995, Advanced thermal inertia modelling. International Journal of Remote Sensing, 16, 431–446.
