estimation of absolute surface temperature by … · from the advanced spaceborne thermal emission...

ESTIMATON OF ABSOLUTE SURFACE TEMPERATURE BY SATELLITE REMOTE SENSING.

INTERNATIONAL INSTITUTE FOR GEOINFORMATION SCIENCE AND EARTH OBSERVATION. I

ESTIMATION OF ABSOLUTE SURFACE TEMPERATURE

BY SATELLITE REMOTE SENSING.

Michael Tsehaye Wubet March 2003


INTERNATIONAL INSTITUTE FOR GEOINFORMATION SCIENCE AND EARTH OBSERVATION. II

ESTIMATION OF ABSOLUTE SURFACE TEMPERATURE BY SATELLITE REMOTE SENSING.

By

Michael Tsehaye Wubet

Thesis submitted to the International Institute for Geo-information Science and Earth Observation in partial fulfillment of the requirements for the degree of Master of Science in Water Resources and Environmental Management Specializing in Watershed Management, Conservation and River Basin Planning. Degree Assessment Board Prof. Dr. W.G.M. Bastiaanssen (Chairman)

ITC, Enschede.

Dr. Bob Su (External Examiner)

Netherlands Alterra-Wageningen University.

Dr. A.S.M. Gieske (First Supervisor)

ITC, Enschede.

Ir. Wim Timmermans (Second supervisor)

ITC, Enschede.

Ir. G.N. Parodi (Member)

ITC, Enschede.

INTERNATIONAL INSTITUTE FOR GEO-INFORMATION SCIENCE AND EARTH OBSERVATION

ENSCHEDE, THE NETHERLANDS


INTERNATIONAL INSTITUTE FOR GEOINFORMATION SCIENCE AND EARTH OBSERVATION. III

Disclaimer This document describes work undertaken as part of a programme of study at the International Institute for Geo-information Science and Earth Observation. All views and opinions expressed therein remain the sole responsibility of the author, and do not necessarily represent those of the institute.


INTERNATIONAL INSTITUTE FOR GEOINFORMATION SCIENCE AND EARTH OBSERVATION. IV

This thesis is dedicated to my wife Etsegenet and to all my families.


INTERNATIONAL INSTITUTE FOR GEOINFORMATION SCIENCE AND EARTH OBSERVATION. V

Acknowledgement

I would like to express my Sincere and heartfelt gratitude to the Netherlands Government

through the Netherlands Fellowship Program (NFP) for granting me the opportunity to

pursue this course of study without which I would not have realized my dream to further my

studies. I am grateful to my former employer, Commission for Sustainable Agriculture and

environmental Rehabilitation in Tigray (COSAERT) who through the Vice-commissioner Mr.

Leul Kashay complemented my efforts by supporting me to fulfil my wish.

My thanks go to all the staff of WREM for the support and guidance throughout the modules

and thesis preparation. Special thanks goes to my Supervisor Dr. A.S.M Gieske, for the

guidance and critical comments that made this research a success. My gratitude also goes to

my second supervisor, Ir. Wim Timmermans, for all his effort to furnish me all the necessary

data. I am particularly grateful for his help during the fieldwork in Okavango delta,

Botswana. I would also like to thank the University of Botswana Harry Oppenheimer

Okavango Research center (HOORC) and Max Planck Institute in Jena, Germany for

providing me their meteorological data. I am also grateful to my classmates in WREM 2001

with whom we shared jokes. Many thanks to Kenta Ogawa and Mekonnen G/Michael from

USA who gave me their unreserved material and advice.

My heartfelt gratitude goes to my wife Etsegenet G/hanna for your patience, support and

encouragement and, those special words especially through the hardest times gave me the

courage to continue. Special thanks go to all my dear parents who have been my mentors

always supportive and urging me on. Last but not least I would like to thank all my friends

specially Tsige G/wahide, the list is endless, for the e-mails and calls that always cheered me

up.


INTERNATIONAL INSTITUTE FOR GEOINFORMATION SCIENCE AND EARTH OBSERVATION. VI

Abstract

Land surface temperatures are important in global change studies, in estimating radiation budgets in heat balance studies and as a control for climate models. Land surface temperature is strongly influenced by the ability of the surface to emit radiation, i.e. surface emissivity. Therefore, knowledge of the surface emissivity is crucial for estimating the radiation balance at the earth surface. A new algorithm for estimating land surface temperature and emissivity spectra for multi spectral thermal

infrared ranging from 8 to 12 µm images has been developed recently by [1] and [2] for use with data

from the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) on the TERRA platform. Similar methods are also used with the MODIS sensor on the same platform.

The temperature emissivity separation (TES) algorithm is based on an empirical relationship between spectral contrast and minimum emissivity, determined from laboratory and field emissivity spectra. It is used to equalize the number of unknown parameters and the number of measurements so that the set of Planck’s equations for the measured thermal radiances can be inverted. Surface temperatures are independent of wavelength and can be recovered from even a single band of radiance data provided atmospheric characteristics can be specified and surface emissivity is known. However, emissivity of land surfaces is not known a priori (except for water bodies) but should be estimated along with the temperature. Moreover, emissivity values vary with wavelength.

In this study, the method developed by [3] was adopted to estimate the broadband emissivity from the narrow band emissivities of the five TIR channels of ASTER instrument in an area close to Maun (Botswana). MODTRAN 4 was used to calculate the necessary atmospheric corrections (for standard atmospheres). All programming was done using the ILWIS script language. The results were compared with field data, with a LANDSAT 7 image of the same day, and finally also with reported ASTER surface temperature and emissivities for the same image (High level ASTER product).

Results indicate that information on atmospheric conditions is crucial. The surface temperature is rather sensitive to atmospheric transmissivity. No relation was found between broadband emissivity and NDVI, contrary, to earlier findings by [4]. Using the TES method it becomes possible to obtain more reliable solutions to the energy balance and evapotranspiration problem, especially in semi-arid areas.


INTERNATIONAL INSTITUTE FOR GEOINFORMATION SCIENCE AND EARTH OBSERVATION. VII

TABLE OF CONTENTS

ACKNOWLEDGEMENT ...................................................................................................................... v ABSTRACT........................................................................................................................................... vi TABLE OF CONTENTS...................................................................................................................... vii LIST OF TABLES: ................................................................................................................................ ix LIST OF FIGURES:............................................................................................................................... ix LIST OF PLATES:................................................................................................................................. xi LIST OF PLATES:................................................................................................................................. xi LIST OF APPENDIXES:....................................................................................................................... xi 1 General Introduction ....................................................................................................................... 1

1.1. Introduction/back ground/setting: .......................................................................................... 1 1.2. Research objectives: .............................................................................................................. 2 1.3. Research questions:................................................................................................................ 2 1.4. Methods and Materials: ......................................................................................................... 2

1.4.2.1 Preliminary preparation................................................................................................. 2 1.4.2.2 Field work ..................................................................................................................... 3 1.4.2.3 Meteorological data....................................................................................................... 3 1.4.2.4 Field data collected during the satellite overpass time.................................................. 3 1.4.2.5 Data processing and analysis......................................................................................... 3 1.4.2.6 Materials and data used................................................................................................. 4

1.5 Thesis outline......................................................................................................................... 4 2 Theoretical Background ................................................................................................................ 10

2.1 Literature Review of Thermal Infrared Theory ................................................................... 10 2.1.1 Introduction ..................................................................................................................... 10 2.1.2 Introduction ..................................................................................................................... 11 2.1.2.1 The Planck’s law ......................................................................................................... 12 2.1.2.2 Wien Law.................................................................................................................... 12 2.1.2.3 Stefan Boltzman law ................................................................................................... 13 2.1.2.4 Energy emitted by grey and real bodies. ..................................................................... 13 2.1.3. Literature review on Temperature emissivity separation algorithm (TES) ..................... 14

3 Description of Study area.............................................................................................................. 15 3.1 Location ............................................................................................................................... 15 3.2 Climate................................................................................................................................. 17

3.2.1 Rainfall ............................................................................................................................ 17 3.2.2 Temperature..................................................................................................................... 18 3.2.3 Relative Humidity ........................................................................................................... 19 3.2.4 Wind speed ...................................................................................................................... 20 3.2.5 Net radiation .................................................................................................................... 20 3.2.6 Parameters Measured During Field Work....................................................................... 23

3.3 Vegetation............................................................................................................................ 25


INTERNATIONAL INSTITUTE FOR GEOINFORMATION SCIENCE AND EARTH OBSERVATION. VIII

3.3.1.1 Introduction ................................................................................................................. 25 3.3.1.2 Previous work (adapted and extracted from WRC report).......................................... 25 3.3.2 Vegetation........................................................................................................................ 29 3.3.2.1 Introduction ................................................................................................................. 29 3.3.2.2 False Colour Composite (FCC)................................................................................... 29 3.3.3 Land cover mapping using satellite imagery ................................................................... 31 3.3.3.1 Introduction ................................................................................................................. 31 3.3.3.2 Results and discussion................................................................................................. 31

3.4 Soils ..................................................................................................................................... 33 4 Estimation of Surface Temperature and Emissivity using TES algorithm.................................... 35

4.1 Introduction.......................................................................................................................... 35 4.2 The ASTER Imaging System............................................................................................... 36 4.3 Methods and Measurements ................................................................................................ 37 4.4 Estimation of Broadband Emissivity ................................................................................... 40

4.4.1 Introduction ..................................................................................................................... 40 4.4.2. Method............................................................................................................................. 40

5. Surface temperature and Emissivity estimation using Landsat 7 .................................................. 42 5.1. Introduction.......................................................................................................................... 42 5.2. Conversion of DN values to Radiance................................................................................. 42 5.3. Conversion of Radiance to Reflectance............................................................................... 43 5.4. Normalized Difference Vegetation Index, NDVI................................................................ 45 5.5. Thermal infrared surface emissivity, εo ............................................................................... 45 5.6. Estimation of surface temperature, To.................................................................................. 47

5.6.1. Computation of Brightness temperature from LANDSAT 7 ETM+ thermal band......... 47 5.6.2. Algorithm for atmospheric correction of brightness temperature ................................... 48 5.6.3. Determination of atmospheric temperature, Tat ............................................................... 51 5.6.4. Estimation of surface temperature................................................................................... 52

6. RESULTS AND DISCUSSION: .................................................................................................. 53 6.1. Broad band emissivity ......................................................................................................... 53 6.2. Surface temperature estimation............................................................................................ 56 6.3. Cross validating ASTER and LANDSAT 7 ........................................................................ 58 6.4. Sensitivity analysis .............................................................................................................. 61 6.5. High level ASTER product.................................................................................................. 62

6.5.1. Surface Emissivity (AST_05).......................................................................................... 62 6.5.2. Surface Kinetic Temperature (AST_08).......................................................................... 63

7. Conclusions and Recommendation. .............................................................................................. 65 7.1. Conclusion ........................................................................................................................... 65 7.2. Recommendation: ................................................................................................................ 67

References: ............................................................................................................................................ 68


INTERNATIONAL INSTITUTE FOR GEOINFORMATION SCIENCE AND EARTH OBSERVATION. IX

LIST OF TABLES:

Table 1 General Natural Vegetation Cover of Maun (WRC, 2001.).....................................................26 Table 2 Major species found in vegetation associations in Maun.........................................................27 Table 3 Definitions of Various Okavango Ecosystems (After MLGLH, 1989) ...................................28 Table 4 Description of Main Soils in Maun (From Soil Mapping and Advisory Services Project,

1990b). ...........................................................................................................................................33 Table 5 Spectral considerations of ASTER...........................................................................................36 Table 6 Calibrated Coefficients obtained using JHU/ASTER Library. ................................................41 Table 7 Spectral Considerations of LANDSAT 7 ETM+. ....................................................................42 Table 8 LANDSAT 7 ETM+ Spectral radiance range (Wm-2sr-1µm-1). ................................................43 Table 9. Solar Spectral Irradiance. ........................................................................................................44 Table 10 Emissivity and NDVI measurements for various natural surfaces.........................................46 Table 11 Thermal band calibration constants........................................................................................47 Table 12. Data used to estimate a6 and b6. ...........................................................................................50 Table 13 Summary results estimated from ASTER and LANDSAT 7 for February 20, 2002.............58 Table 14 Comparison of ASTER and LANDSAT 7 derived surface temperature for different land

cover. ..............................................................................................................................................60 Table 15Comparison of ASTER and LANDSAT 7 derived broadband emissivity for different land

cover. ..............................................................................................................................................60 Table 16 Basic data used to develop TES algorithm in spreadsheet. ....................................................61 Table 17 Summary of the sensitivity analysis of the parameters for changes in ±10% of MODTRAN 4

out puts for Planck tower. ..............................................................................................................61

LIST OF FIGURES:

Figure 1 General approaches and Methodology flow chart. ................................................................... 6 Figure 2 General approach and methodology used for developing TES algorithm using ILWIS script. 7 Figure 3 (continued) General approach and methodology used for developing TES algorithm using

ILWIS script.................................................................................................................................... 8 Figure 4 General approach and methodology used for estimating surface temperature and emissivity

using LANDSAT 7.......................................................................................................................... 9 Figure 5 Comparison of TES and LANDSAT 7 derived surface temperature and emissivity................ 9 Figure 6 The electromagnetic spectrum. ............................................................................................... 10 Figure 7 Spectral exitance distributions for blackbodies at 6000, 4000, 2000, and 1000 K. ................ 11


INTERNATIONAL INSTITUTE FOR GEOINFORMATION SCIENCE AND EARTH OBSERVATION. X

Figure 8 Location of the study area....................................................................................................... 16 Figure 9 Mean monthly rainfall of the period 1925 to 2001. ................................................................ 17 Figure 10 Annual mean rainfall of the study area for the period 1925 to 2001. ................................... 18 Figure 11 Monthly temperature of the study area, from 1998 to 2001. ................................................ 18 Figure 12 Air temperatures from the Planck tower dated on February 20, 2002. ................................. 19 Figure 13 Relative humidity measured at 10 minutes interval dated on February 20, 2002................. 19 Figure 14 Wind speed measured at 10 minutes interval dated on 20/02/2001...................................... 20 Figure 15 Radiation components from the Planck tower dated on 20/02/2001. ................................... 21 Figure 16 surface temperatures measured by thermal Infrared thermometer dated on September 16,

2002............................................................................................................................................... 23 Figure 17 Incoming and out going short wave radiations measured for bare soil-using Pyrnometer

dated on September 16, 2002. ....................................................................................................... 24 Figure 18 Incoming and out going short wave radiations measured for short bushes Pyrnometer dated

on September 16, 2002.................................................................................................................. 24 Figure 19 LANDSAT 7 FCC 742 of the study area dated on February 20, 2002 at 10:15 hours. ........ 30 Figure 20 ASTER FCC 321 of the study area dated on February 20, 2002 at 10:45 hours. ................. 30 Figure 21 Classified Images Showing the distributions of the Dominant land cover in Maun............. 32 Figure 22 Feature space used for making the land cover units. ............................................................ 32 Figure 23 Soil Map of the study area. ................................................................................................... 34 Figure 24 ASTER spectral bands (extracted from: http://asterweb.jpl.nasa.gov/instrument/band.htm)37 Figure 25 Shows the different components used to extract Surface temperature. ................................ 37 Figure 26 Plot of the mean emissivity versus the mean NDVI. ............................................................ 46 Figure 27 Determination of a6 and B6 coefficients................................................................................ 51 Figure 28 Broadband emissivity map and histogram derived using ASTER sensor............................. 53 Figure 29 Broadband emissivity map and histogram derived using LANDSAT 7 sensor.................... 54 Figure 30 Correlation result of broadband emissivity of LANDSAT 7 and ASTER for February 20,

2002............................................................................................................................................... 54 Figure 31 Correlation result of ASTER broadband emissivity and NDVI for February 20, 2002........ 55 Figure 32_1 ASTER broadband emissivity correlation graph derived using Ogwa, K. et al., 2002 and

Van Griend Owe methods. ............................................................................................................ 55 Figure 33 Correlation results of ASTER and LANDSAT 7 derived Surface temperature. .................. 56 Figure 34 Surface temperature map of Maun derived from ASTER and LANDSAT 7. ...................... 57 Figure 35 Histograms of Surface temperature for Maun derived from ASTER and LANDSAT 7...... 58 Figure 36 Map showing spatial variation of out going Long wave radiations derived from ASTER and

LANDSAT 7 [Wm-2]..................................................................................................................... 59 Figure 37. Broadband emissivity computed from the narrow band channels of AST_05 products for

February 20, 2002. ........................................................................................................................ 62 Figure 38 AST_08 Surface temperature product for February 20, 2002............................................... 63


INTERNATIONAL INSTITUTE FOR GEOINFORMATION SCIENCE AND EARTH OBSERVATION. XI

LIST OF PLATES:

Plate 1 Planck Tower meteorological flux station................................................................................. 22

LIST OF APPENDIXES:

APPENDIX A1 Maun and Shakawe Metrological data (In CD) APPENDIX B 1 Planck's Tower data and ground data measured during fieldwork. ............................71

APPENDIX C 1APPENDIX C1: ILWIS SCRIPT USED TO DEVELOP TES ALGORITHM. ........ 84

APPENDIX D 1: ILWIS SCRIPT USED TO ESTIMATE SURFACE TEMPERATURE USING LANDSAT 7. .............................................................................................................................. 102

APPENDIX E 1: ATMOSPHERIC CORRECTION USING MODTRAN 4..................................... 108

APPENDIX F 1 : APPENDIX F1: ASTER narrow band emissivity channel maps and histograms.. 114


INTERNATIONAL INSTITUTE FOR GEOINFORMATION SCIENCE AND EARTH OBSERVATION. 1

1 General Introduction

1.1. Introduction/back ground/setting:

In 1998, NASA launched EOS-AM1, the first of a series of the earth observation system

(EOS) satellites. An integrated view of the earth is needed to study the interchange of energy,

moisture and carbon between the lands, oceans, and atmosphere. The launch of this EOS-

AM1 marks a new phase of climate and global change research, which has been on going for

more than a century. It is now recognized that processes that vary very rapidly in time and

space, such as clouds, land use, sea and land surface temperature, and exchanges of energy

and moisture must be considered to adequately explain the temperature record and predict

future climate change. Frequent measurements with adequate resolution (temporal and

spatially), as only possible from spacecraft, are key tools in such an effort.

The versatile and highly accurate EOS-AM1 data, together with previous satellite records, as

well as ground-based networks are expected to revolutionize the way scientists look at climate

change. One of the sensors on board of the EOS-AM1 plat form is the Advanced Space Borne

Thermal Emission and Reflection Radiometer (ASTER), of which the primary science

objective is to improve the understanding of the local and regional scale processes occurring

on or near the earth’s surface and lower atmosphere, including surface atmosphere

interactions [5]. Among others the ASTER mission is designated to an accurate mapping of

land cover parameters such as surface reflection (albedo) and land surface temperature.

Land surface temperatures are important in global change studies, in estimating radiation

budgets, in heat balance studies, and as control for climate models. Thermal emitted radiance

from any surface depends on two factors:

��The surface temperature which is an indication of the thermodynamic state resulting

from the energy balance of the fluxes between the atmosphere, surface and the sub

surface soil.

��The surface emissivity, which is the efficiency of the surface for transmitting the

radiant energy generated in the soil in to the atmosphere. It depends on the



composition, surface roughness and physical parameters of the surface, for example

the moisture content.

Thus, to make a quantitative estimate of the surface temperature, one needs to separate the

effects of temperature and emissivity in the observed radiation as measured by satellites.

In this study, an approach as described by [1] and [2] will be explored, applied, tested and

validated on data collected in the Northern part of Botswana under the Kalahari Monitoring

project, as part of the SAFARI-2000 program by NASA.

1.2. Research objectives:

��The following objectives are to be met in the project:

��Geometric and radiative transfer correction of ASTER data,

��Transformation into compatible format for currently used RS/GIS systems, and

ultimately;

��Determination of surface emissivity and surface temperatures over different areas in

the northern part of Botswana, comprising several heterogeneous and characteristic

natural land covers, using ASTER and Land sat data for 20th February 2002.

1.3. Research questions:

The research will basically try to answer the following questions:

Can the estimation of surface temperature from space be improved by using data from the

ASTER sensor on board of the EOS-AM1 plat form?

Is there any relationship between broadband emissivity and NDVI derived using ASTER?

1.4. Methods and Materials:

In order to achieve the set objectives, the research was conducted in three phases: Pre-

fieldwork, fieldwork and post fieldwork.

1.4.2.1 Preliminary preparation

This was the initial step and included the following. Literature review of existing reports,

journals, and publications on temperature emissivity separation algorithm (TES) and their

assessment techniques.



In order to get acquitted to the study area, literature of topography, climate, geology

vegetation and soils in the study area was reviewed. By using satellite images, a

familiarization of the area was carried out. A database of the available data was organized,

screened and pre-processed. Field survey points were mapped out. Definition and

organization of the field work activities during this phase. Necessary equipment and sample

containers were prepared for the fieldwork.

1.4.2.2 Field work

Fieldwork was carried out from the 9th to 25th September 2002 and consisted of the following

activities and described in the consecutive pages.

1.4.2.3 Meteorological data

This data was obtained from Maun meteorological station located close to the study area. See

Appendix A (see in CD)

1.4.2.4 Field data collected during the satellite overpass time

On the 16th of September 2002 starting from 7:30 AM to 2:30 PM of the Land sat overpass

time falls, various measurements were carried out.

��Instantaneous incoming short-wave radiation and Extraterrestrial radiation were

measured using a hand held pyranometer

��Surface temperature measured using a hand held thermal infrared radiometer.

��Ground control points for georeferencing and classifying the satellite image using the

GPS. Details of the land use and land cover were noted

��Meteorological data from Planck’s tower for that day will be downloaded

1.4.2.5 Data processing and analysis

This was the major phase of the research and consisted of data integration from the field,

analysis and interpretations using GIS, excel spreadsheets and development of temperature

emissivity separation (TES) script in ILWIS software. The results are the contents of this

thesis.



1.4.2.6 Materials and data used

For estimating the spatial and temporal variations of surface temperature and emissivity, the

basic inputs are the LANDSAT 7 AND ASTER images of February 20,2002. For comparison

of the estimate extra site measured input (Planck tower) is used.

In general the data used for analysis comprises the following combined Satellite images and

ground measured data: -

��LANDSAT 7 scene of all eight bands of February 20,2002

��ASTER scene of all fourteen bands of February 20,2002

��Land cover, land use and soil data type in the form of polygon map, which was

prepared by Ministry of Agriculture of Botswana.

��Data collected from Planck tower and field data collected during the field campaign

dated from 9th to 25th September of 2002.

1.5 Thesis outline

The general content of this thesis is divided in to two main parts. The first part of the thesis,

comprises three chapters, have a general content describing the introduction, theoretical

aspect from literature review, the study area description and field measurements. The second

part of the thesis deals with the methodology applied, the obtained result, the conclusion and

recommendation drawn from this thesis.

Chapter 2 deals with the theoretical aspect of thermal infrared theory and temperature

emissivity separation algorithm (TES) giving specific attention to the various factors that

governs surface temperature and techniques of its estimation. Chapter 3 deals with the

physical nature of the study area and the field measurements carried from 9th to 25th

September of 2002.

Chapter 4, the first part of the second part, deals with the remote sensing techniques of

temperature and emissivity estimation using ASTER (TES algorithm). Mainly focused on the

basic steps to be followed in developing TES algorithm for estimating the five emissivity

maps and one temperature map.



Chapter 5, also the first part of the second part, deals with the remote sensing techniques of

temperature and emissivity estimation using LANDSAT 7 (SEBAL algorithm). Mainly

focused on the basic steps to be followed in estimating surface temperature and emissivity

from NDVI.

Chapter 6 describes the discussion and result comparison based on the result derived from

ILWIS scripts of TES algorithm, LANDSAT 7 derived surface temperature and emissivity.

Eventually, chapter 7 ends up with the conclusion and recommendations drawn from the

study.



Figure 1 General approaches and Methodology flow chart.

INPUT DATA.

LANDSAT 7SATELLITE

IMAGES.

ASTER SATELLITE

IMAGES.

SUB MAP COMPUTATION.

GEOMETRIC AND ATMOSPHERIC CORRECTIONS.

GEOMETRIC AND ATMOSPHERIC CORRECTIONS.

SPECTRAL MAP INFORMATIONS.

SPECTRAL MAP INFORMATIONS.

COMPUTATIONS OF SURFACE

TEMPERATURE AND EMISSIVITY

DEVELOPMENT OF TES

ALGORITHM IN ILWIS SCRIPT.

ONE MAXIMUM SURFACE TEMPERATURE AND FIVE

EMISSIVITIES MAPS.

FIELD DATA MEASUREMENTS AND

LABORATORY RESULTS,

LITERATURE.

RESULT COMPARISON ,

DISCUSSION AND CONCLUSION.

GENERAL APPROACH AND METHODOLOGY FLOW CHART.



Figure 2 General approach and methodology used for developing TES algorithm using ILWIS script.

Aster standard products and calibration constants.Emissivity(initial)=0.98

Atmospheric and Geometric corrections.

Radiance at the surface(Lj)

Spectral radiance(LBB)

Maximum Temperature(Tmax)

Radiance using Tmax.

Emissivity.

Beta.

Recompute emissivity.

Real body radiance(emissivity*Lbb).

Re compute Beta

Re compute emissivity using the revised beta.

Flow charts showing the major steps for developing TES algorithm.



Figure 3 (continued) General approach and methodology used for developing TES algorithm using ILWIS script.



Figure 4 General approach and methodology used for estimating surface temperature and emissivity using LANDSAT 7.

Figure 5 Comparison of TES and LANDSAT 7 derived surface temperature and emissivity.



2 Theoretical Background

2.1 Literature Review of Thermal Infrared Theory

2.1.1 Introduction

The wavelength range for infrared region found approximately between 0.70 to 100 µm,

which is hundred times wider than the visible portion. Infrared is subdivided mainly in to two

parts based on its radiation properties: -

��Reflected infrared

��Emitted or Thermal infrared

Radiation in the reflected infrared region is used for remote sensing purposes in a way similar

to radiation in the visible portion and this covers from 0.70 to 3.0 µm where as the thermal

infrared region is different from the visible and reflected region, as this energy is essential to

the radiation that is emitted from the earth surfaces in the form of heat and this ranges covers

between 3.0 to 100µm.

Figure 6 The electromagnetic spectrum.



2.1.2 Introduction

Each energy/ radiation source or radiator emits a characteristic array of radiation curves. A

black body is useful concept, which is widely used by physicists in the study of radiation.

Thus from black body radiation can be defined as follows: -

��Sun and earth surfaces behave approximately as black bodies.

��An object, which is perfect emitter, and absorber of radiation.

��For a given temperature and wavelength no surface can emit more energy than a black

body.

Figure 7 Spectral exitance distributions for blackbodies at 6000, 4000, 2000, and 1000 K.

Thus, a series of laws were derived which relate to compare natural surfaces/radiators to those of black

body and explained below.



2.1.2.1 The Planck’s law

Planck’s law gives the emissive power of a black body at any wavelength and temperature.

For a radiation in to a vacuum or a medium of refractive index of unity, this law in a simple

form can be written as follows: -

[ ]1)/(51

2 −=

kTCb eCF λλ λ 2.1

Where Fbλ is the hemispherical spectral emissive power of a black body [Wm-2µm-1]

C1 is the first radiation constant [3.7427*108 Wm-2 µm4]

C2 is the second radiation constant [1.4388*104 µmK]

λ is the wavelength [µm]

Tk is the black body temperature [K]

In general, three basic three basic points can be extracted from figure 2.2 above: -

��The emissive power increases with temperature at each wavelength.

��Relatively more energy is emitted at shorter wavelengths (area under curves).

��The position of the maximum emissive power (maximum peaks) shifts towards

shorter wavelengths

2.1.2.2 Wien Law

Most objects emit radiation at many wavelengths. However there is one wavelength that a

given object can emits the highest amount of radiation. The Planck’s law can be put in a more

universal form dividing by ‘Tk5’ in equation 2.1 above.

]1[*)*( )/(51

5 2 −=kTC

kk

b

eTC

TF

λλ

λ 2.2

The above equation can be expressed ‘Fbλ/Tk

5’ in terms of a single variable ‘λ*Tk’.

Plotting this equation as a function of ‘λ*Tk’, then the result shows that a maximum peak

occurs at: - λmax*Tk =2897.8 µmK.



kTmKµλ 8.2897

max = 2.3

From figure 2-2 above and based on Weins displacement formula above, the earth and the sun

can emit the highest radiation at 9.7 µm and 0.48 µm wavelengths respectively.

2.1.2.3 Stefan Boltzman law

The total surface under the spectral radiant exitance curve shown in figure 2.2 above will

represent the total amount of radiant energy coming from the black body for the spectral band

of all wavelengths. The total surface under the spectral radiant exitance curve shown in figure

2.2 above will represent the total amount of radiant energy coming from the black body for

the spectral band of all wavelengths.

4

42

441

0 0

)*/2(51

*

*15/**

]1[/*

k

k

TCbb

T

CTC

eCdFF k

σπ

λλλ

λ

λ

λ

λλ

=

=

−== � �∞=

=

∞=

=

2.4

Where Fb is the total amount of energy at temperature, T [Wm-2]

λ is wavelength [m]

σ is Stefan boltzman constant [5.67*10-8 Wm-2K-4]

2.1.2.4 Energy emitted by grey and real bodies.

Real bodies resemble more to grey bodies. The allow some energy to be reflected back or pass

through them. Not all-incoming energy is used to raise their internal temperature. The kinetic

temperature of a real body is always less than the one of the black body of similar

characteristics that receives the same energy. Emissivity is the ratio of emittance of a given

object and a theoretical black body at the same temperature. The emissivity of a theoretical

black body is defined as one and a perfect reflector as zero.

The emissivity is always less than one and greater than zero. Since, a black body absorbs all

the energy that reaches it, it radiates a maximum heat flux compatible with its internal

temperature. A black body then is considered to have a radiant temperature equal to its

internal body temperature. The emissivity of a black body is one.



Real bodies at the same internal temperature radiates less than a black body. When aiming to

the real bodies with thermal radiometer they show a radiant temperature lower than its

internal or kinetic temperature.

kr TT *)( 25.0ε= 2.5 Thermal radiometer will allow us to determine the surface temperature of a terrestrial object if

the emissivity of the object is known.

2.1.3. Literature review on Temperature emissivity separation algorithm (TES)

Knowledge of the surface emisivity is important for knowing the energy balance at the earth

surface. The emissivity is relatively uniform for dense vegetated surfaces; while the

emissivity value for semi arid lands is highly variable this variability is resulted due to

heterogeneous nature of the area (exposed rocks and soils). But it is possible to estimate the

spectral emissivity variation for the heterogeneous areas of semi arid lands using multi

spectral thermal infrared (TIR) The temperature emissivity separation algorithm combines attractive features of two

Precursors and some new features It is most closely related to the mean minimum maximum

difference (MMD) method [6] it self based on the Alpha Derived Emissivity (ADE) technique

[7], [8] and [9]. Essentially, the Temperature Emissivity (TES) algorithm uses the Normalized

Emissivity Method (NEM) [10] to estimate T, from which emissivity ratios are computed

(Ratio algorithm). These”β” values are the NEM emissivities normalized by their average

value. [11] and [12] showed that emissivity band ratios were insensitive to errors in

temperature estimation and this is true for normalized β spectra also. The β spectrum

preserves the shape, but not the amplitude, of the actual emissivities. To recover the

amplitude, and hence a refined estimate of the temperature, the minimum maximum

difference (MMD) is computed and adopted to predict the minimum emissivity (εmin).

Temperature and emissivity separation (TES) operates on ASTER “land –leaving TIR

radiance “data that have already been corrected for atmospheric τ and S [13]. The same

standard ASTER product reports S↓ that cannot be removed with out knowledge of ε

(emissivity). Temperature and emissivity separation (TES) removes reflected S↓ iteratively,

before estimating the NEM [14]. Eventually, the TES algorithm is briefly discussed in detail

in chapter four.



3 Description of Study area

This chapter focuses on the description of the study area and the methods and materials used

in the preliminary data preparation, fieldwork activities that were undertaken

3.1 Location

Botswana is one of the semi arid African countries characterized by a low and erratic rainfall

pattern, which results in scarce surface water resource. Botswana is one of the largest worlds

exporter of gemstone diamonds as well as a large exporter of beef to the European

community. The study area is defined by the availability of Aster images. Thus, the study

area is found in Ngamiland district, which mainly focused around Maun town having a

geographical coordinates of latitude from 19.46o to 20.30o South and Longitude from 23.42o

to 24.21o East, having an altitude of 945 meter above sea level. The total study area

approximately covers one scene of Aster image of 3600 km2 and is shown in the next page.



Figure 8 Location of the study area.

Geographic Extent -19.460Lat, 23.510 Lon; -19.570 Lat, 24.210 Lon; -20.130 Lat, 24.130 Lon; -20.300 Lat, 23.420 Lon.



3.2 Climate

The study area is characterized by a semi arid climate with cool dry winters and hot moist

summers, which is influenced in its variability by the movement of the Inter Tropical

convergence zone (ITCZ). In common with Botswana, the climate of the study region is semi

arid climate with cool dry winters and hot moist summers. Maun, Shakawe and also Planck’s

tower station, which was supervised by the university of Botswana Okavango Research center

and Max Planck institute Jena, Germany, is used to describe the climate of the study area.

3.2.1 Rainfall

Botswana receives most of its rainfall from convection processes such as instability showers

and thunderstorms which is less in magnitude than the synoptic systems which control the air

masses supplying the moisture [15]. Most of semi arid African countries like Botswana have a

rainfall, which occurs only for short period of time, which is torrential by its nature. The

annual rainfall of the study area is around 455 mm, which is not evenly distributed through

out the year. Figure 9 below shows the mean monthly rainfall of the study area from 1925 to

2001 and the time series of the monthly rainfall from 1925 to 2001 is shown in appendix A

(see in CD).

Figure 9 Mean monthly rainfall of the period 1925 to 2001.



Figure 10 Annual mean rainfall of the study area for the period 1925 to 2001.

3.2.2 Temperature

The mean monthly maximum, minimum and average temperatures of the study area are

estimated from Maun and Shakawe meteorological stations. Like the rainfall pattern, the

temperature of the study area is highly variable. The warmest periods are in the months of

November/December having a mean maximum temperature of 35.6 oC while the coldest

periods extends from July to August having a minimum temperature of 7.5 oC. Tmax and Tmin

are the average maximum and minimum temperatures per month computed for the periods

from 1998 to 2001. Then, Tavg is computed by averaging the minimum and maximum

temperatures of each month.

Figure 11 Monthly temperature of the study area, from 1998 to 2001



The variation of air temperature of the LANDSAT 7 satellite overpass for February 20,2002, is shown below in Figure12

Figure 12 Air temperatures from the Planck tower dated on February 20, 2002.

3.2.3 Relative Humidity

Relative humidity is the ratio of water vapor in the air to the amount of water vapor the air

could hold at the same temperature. It is dimensionless and is expressed as a percentage.

Relative humidity measured in Planck’s tower at every 10 minutes interval and is shown

graphically below.

Figure 13 Relative humidity measured at 10 minutes interval dated on February 20, 2002



3.2.4 Wind speed

Wind speed is one of the meteorological parameters measured at Planck’s tower. It is

measured at 2 and 7 m to enable an accurate estimate of turbulence. Turbulence is the driving

force for removing water vapor from the evaporating surfaces. Note that the wind speed for

February 20, 2002 is not available but tower data for February 20, 2001 is attached just to

show the trends. The wind speed is measured at every 10 minutes interval and is shown

graphically below.

Figure 14 Wind speed measured at 10 minutes interval dated on 20/02/2001.

3.2.5 Net radiation

The net radiation and its components data for the satellite over pass dates were obtained from

the Planck’s tower station, which is operated HOORC (Harry Oppenheimer Botswana

University Okvango Research Centre) and the Max Planck Institute in Jena, Germany). The

geographical location of the tower is 19o54’59. 9’’S and 23o33’37. 4’’E.



Figure 15 (Note that the radiation component except Long wave out going radiation for

February 20, 2002 is not available but tower data for February 20, 2001 is attached just to

show the trends) shows that the incoming short wave radiation is greater than the outgoing

short wave radiation during the day time and reaches peak at about mid day and more over the

net radiation is positive, negative during the day and night respectively.

Figure 15 Radiation components from the Planck tower dated on 20/02/2001.



Plate 1 Planck Tower meteorological flux station.



3.2.6 Parameters Measured During Field Work

The fieldwork was conducted from Sep 9 to 25, 2002. During the fieldwork time the surface

temperature, incoming and out going short wave radiations were measured for selected areas,

which are more or less homogenous from 7:30 AM to 2:30 PM using the thermal infrared and

pyranometer respectively. Note that the emissivity is set to one while measuring the surface

temperature. More over a soil sample for emissivity test is taken from the different parts of the

study area. All the values measured during the fieldwork are attached and available in

appendix B. The incoming short wave radiation measured at fieldwork during the satellite

over pass is shown below.

Figure 16 surface temperatures measured by thermal Infrared thermometer dated on September 16, 2002.



Figure 17 Incoming and out going short wave radiations measured for bare soil-using Pyrnometer dated on September 16, 2002.

Figure 18 Incoming and out going short wave radiations measured for short bushes Pyrnometer dated on September 16, 2002.



3.3 Vegetation

3.3.1.1 Introduction

This section deals with identifying of the major vegetation types and land cover with in the

study area using Landsat 7 Enhanced Thematic Mapper (ETM+) images of February 20,2002

of the Wet season. Vegetation is essential in estimating the emissivity and temperature for

different land cover with in the study area of interest. The land cover and analysis is based on

previous studies, field observations, and satellite images analysis.

3.3.1.2 Previous work (adapted and extracted from WRC report)

The natural vegetation has been mapped by the Soil Mapping and Advisory Services Project [16]

at 1:2,000,000 over Botswana. In most areas, the vegetation is designated as tree/shrub savanna

with various wetland associations (See table 2). Much of the sandveld supports A3b and A3d

vegetation types, which are broad designations containing Terminalia sericea, Lonchocarpus

nelsii and/or Combretum spp. and Acacia erubescens. In the sandveld areas immediately

associated with the delta (and floodplains) the vegetation type H17e is dominant. This includes

such species as Colophospermun mophane, Terminalia sericea, Dichrostachys cinerea and

Lonchocarpus nelsii as dominant species. On the southern flanks of the delta area, F15a

comprises regular shrub savanna with Combretum imberbe, Acacia erioloba and C. mophane.

The wetter most central part of the delta comprises I21a with the main species being Cyperus

papyrus and Miscanthus junceus associations. Peripheral to the wetter central core of the delta

is the vegetation association I20b that has as its dominant species the Imperata and Setaria spp.

along with A.nigrescens and Lonchocarpus capassa.

Semi-detailed vegetation mapping has not been previously undertaken in this part of the

Okavango Delta area. Previous botanical analyses have identified around 1,200 woody and

herbaceous species in the entire Okavango Delta area (22,000 km2) that comprises a species/area

ratio of 0.0545 [17, 18]. This is a higher ratio than that encountered in all other parts of the sub-

continent, except in the fynbos area of the Cape Region, South Africa. Despite the foregoing,

indicates that the instability of the Okavango's hydrological regime has not encouraged much

diversity or speciation among the aquatic and wetland plants as shown by the almost complete

lack of regional endemics. The terminology of the Okavango system has evolved following

numerous studies. Definitions of various Okavango ecosystems are shown in Table 3 and, where

relevant, comparable terminology is used WRC study.



A major challenge of vegetation mapping in savanna ecosystems is the extreme spatial

variability of the cover. The Okavango Delta area, in particular, is characterised by

heterogeneity. Therefore, mapping of the cover, particularly down to the species level, involves

some generalisation based on the best available information. Both anthropogenic agencies and

the effects of wildlife have modified much of the natural vegetation cover. People have modified

the area by removing woodland species for agricultural, fuel wood and construction purposes.

Heavily grazed areas are also found in the vicinity of settlements and cattle posts with

concomitant halos of vegetation depletion. A further part natural and part anthropogenic effect is

the role of fire which, along with elephant impacts, has caused localised damage in the form of

felled trees or depleted areas. Hence, the density of vegetation cover depends on a number of

inter-related socio-economic and biophysical factors [19]. Beyond the immediate delta area, the

natural vegetation is typical of that forming the north-central Kalahari region (Table 1).

Location Unit

Natural Vegetation Description

Sandveld south of Boteti A3b Terminalia sericea, Lonchocarpus nelsii and Acacia erubescens

Sandveld north of Boteti A3d Terminalia sericea, Lonchocarpus nelsii, Combretum spp.

Sandveld associated with former delta floodplains etc.

H17e Colophospermum mophane, Terminalia sericea, Dichrostachys cinerea and Lonchocarpus nelsii

Sandveld associated with the southwest flank of delta

F15a

Combretum imberbe, Acacia erioloba and C. mophane

Wetlands associated with semi-permanent swamp

I21a Cyperus papyrus, Miscanthus junceus associations with Garcinia livingstonei, Phoenix reclinata, Hyphaene petersiana and Ficus verriculosa associations

Wetlands associated with seasonal swamp

I20b Imperata cylindrica, Setaria sphaeclata, Hyparrhenia rufa association along with A.nigrescens, Lonchocarpus carpassa, Phragmites australis and the Schoenplectus corymbosus and Cyperus artiluris associations.

Table 1 General Natural Vegetation Cover of Maun (WRC, 2001.)



Association Species (Woody-Forb-Grasses)

Mixed mophane woodland C. mophane, Ximenia americana, X. caffra, Commiphora africana, *A.erioloba, L.nelsii, T.sericea, Grewia flava, G.flavescens, Boscia albitrunca, Combretum collinum, Digitaria eriantha, Enteropogon macrostacys, Aristidia spp.

Monospecific mophane C. mophane - +\- Boscia mossambicensis, A. erioloba, G. flava, C. hereroense often lacks herbaceous layer

Shrub mophane C. mophane, G. flavescens Catophractes alexandri, Bauhinia petersiana, A. tortilis, Dichrostachys cinerea

Calcrete - mophane T. sericea, A. leuderitzii, A. erioloba, Albizia harveyii, Boscia albitruna, G. monticolor, C. mophane, Croton gratissimus, C. alexandri, Digitaria eriantha, Enteropogon macrostachys, Aristidia spp.

A. erioloba woodland (Many dead trees)

A. erioloba, A. nigrescens, A.leuderitzii, Combretum imberbe, Maytenus senegalensis, Ziziphus mucronata, B. albitrunca, B. mossambicensis, A. ataxacantha, Rhus retinervis, C. mophane, Ficus sycamorus Asparagus spp., Pogonarthria squarrosa, Stripagrostes uniplumis, Aristidia spp.

A.tortillis woodland A. tortilis, Dichrostachys cinerea, A. mellifera, G. flava, C. collinum, A. erioloba, A. hebeclada, Rhigozum brevispinosum, Asparagus spp.

Terminalia sericea woodland T. sericea, C. molle, L. nelsii, Grewia flava, Combretum collinum, A.erubescens, C.hereroense, R. brevispinosum, Rhus tenuinervis

Mixed sandveld woodland T. sericea, Z. mucronata, Albizia anthelmintica, Burkea africana, Lonchocarpus nelsii, G. flava, A. hebeclada, A. erioloba, C. collinum, A.erubescens, C.hereroense, Rhigozum brevispinosum, Rhus tenuinervis, Adansonia digitata, Cadaba termitaria Asparagus spp., Pogonarthria squarrosa, Stripagrostes uniplumis, Aristidia spp.

Disturbed sandveld Woodland-shrubland (Includes bush encroached areas)

A. tortilis, A.erubescens, Combretum apiculatum, Albizia harveyii, A. fleckii, G. flavescens, A. leuderitzii, Cadaba termitaria, A. mellifera, Bauhinia petersiana, Dichrostachys cinerea, Tephrosia sericea

Acacia nigrescens marginal woodland A.nigrescens, Garcinia livingstonei, Loncocarpus capassa, Combretum imberbe, H. petersiana, C. mossambicensis, Croton mossambicensis, C. megalobotrys, Ficus thonningii, Berchemia discolor, Kigelia africana, Euclea divinorum, Setaria verticillata, Digitaria eriantha, Panicum maximum

Hyphaene petersiana marginal woodland (wetter islands)

H. petersiana, Berchema discolor, K. africana, Combretum hereroense L. capassa, A. nigrescens, Vernonia spp. Cynodon dactylon

Combretum imberbe marginal woodland

C. imberbe, Euclea divinorum, Diospryos lycioides, A. erioloba, L.capassa, Croton magalobotrys, Berchemia dicolor, A. tortilis, Z. muronata, A. nigrescens, G. flava, L.nelsii, Boscia foetida

Terminalia prunioides marginal woodland (Boteti)

T. prunioides, A. hebeclada, A. erioloba, G. bicolor, C. albopunctatum, A. erubescens, C. africanum, Z. mucronata, X. caffra, X. americana, C. gratissimus,G. retinervis, G. flava, Commiphora africana, B. albitrunca, Combretum albopunctatum, A. mellifera, A. leuderitzii, A. tortilis

Bare soil -floodplain Panicum maximum Forb/grass floodplain Vernonia spp., Panicum maximum Shrub floodplain A. fleckii, Cadaba termitaria, A. mellifera, A. erioloba, Vernonia spp. Permanent/seasonal vegetation in channels

Miscanthus junceus associations, Cyperus articulatus, Schoenoplectus corymobosus and Phragmites australis.

Table 2 Major species found in vegetation associations in Maun.

* Underlining represents those species assumed to be deep rooting



ECOSYSTEM DEFINITION MAIN SPECIES **Perennial Swamp Inundated with water

throughout year Cyperus papyrus Phragmites australis

Seasonal Swamp Sufficiently seasonally inundated to support aquatics

Schoenoplectus corymobosus Cyperus articulatus

* Periodically Flooded Grasslands

Intermittently flooded extensions of the seasonal swamps

Panicum spp.

* Rarely Flooded Grasslands

Infrequently flooded extensions of the seasonal swamps

Panicum spp. Vernonia spp.

**Island Beaches Infrequently flooded areas of higher salinity/alkalinity

Cyperus laevigatus Sporobolus spicatus

Rainwater Pans Nutrient rich areas of run-on Oryza breviligulata Aponogeton junceus

*Riverine Woodland Linear fringe bordering most islands/mainland - frequently up to 200m wide

Sclerocarya birrea ssp. caffra Kigelia africana Hyphaene petersiana

Dense mophane and mixed woodland

Monospecific close to wetland edges - mixed in drier situations

Colophosphernum mophane Acacia erioloba

Shrubby mophane woodland (gumane)

Stunted form of mophane on fine soils -?fire

Colophosphernum mophane

Acacia Woodland Sandier areas including former floodplains

Acacia erioloba Acacia tortilis Terminalia spp.

Forbs and Grasses Inner island depressions and elsewhere where tree/shrub growth surpressed

Aristida stipoides Chlorus virgata Sesbania spp. Vernonia spp. Tribulus terrestris

Grewia shrubland Shrubs developed on sandy soils

Grewia flava Grewia bicolor Grewia flavescens

Taller Shrubland On fossil levees among Mophane

Terminalia sericea Lonchocarpus nelsii Combretum collinum

* Areas not previously mapped or identified in map format. ** Areas too small (to be mapped) or not part of the Maun Project Area

Table 3 Definitions of Various Okavango Ecosystems (After MLGLH, 1989)



3.3.2 Vegetation


LANDSAT 7 ETM+ images taken dated on 20th February 2002 at 10:15 hour’s local time

were used to identify the different land covers found with in the study area of interest. The

GIS software, [20] Integrated Land and Water Information System (ILWIS) version 3.0

developed at International institute for Geoinformation Sciences and Earth observation (ITC)

was employed for the entire image processing such as georeferencing, to create sub map of

the study area, histogram and also for developing TES algorithm

Georeferencing were done using the ground control points taken during the fieldwork dated

from 9th to 25th September 2002. Principal Component Analysis was initially conducted to

assist in vegetation discrimination, as this technique separates out the main different savanna

vegetation types based on their major reflectance characteristics and this was done on all

bands except band 8. Then, based on the results of the Principal Component Analysis a false

colour composite (FCC742) was created.

Later on, Point maps of the different Land cover were created based on the way points

collected during the field work and overlaid on top of the FCC742 to obtain an overview of

the vegetation association’s and types. Eventually, sub maps of all bands were created based

on the corners of the minimum and maximum values of the area of interest. Creating sub

maps minimized the time and space taken to process the entire Land sat images of 183*170

Km.

3.3.2.2 False Colour Composite (FCC)

Leaves reflectance characteristics mainly depend on the properties of the leaves including

orientation, structure of canopy, leaf type, Pigmentation and amount of water in the leaf

tissues. A color composite is created by combining 3 raster images (bands/maps). Band 7,4

and 2 are selected to display in shades of red, blue and green respectively. The vegetation

cover could then be mapped as “stressed” and “non stressed” and this is generally geared with

the availability of moisture. However, the degree of vegetative stress is difficult to map in flat,

sandy dry land areas as much of the vegetation cover is adapted to the dry conditions and can

withstand stress for a long periods of time, [21]. Figure 19 below shows that the healthy,



green and actively growing vegetation is having green color, surface water is in black tone,

bare land vary from white to light blue, and while the dense vegetation in red color.

Figure 19 LANDSAT 7 FCC 742 of the study area dated on February 20, 2002 at 10:15 hours.

Figure 20 ASTER FCC 321 of the study area dated on February 20, 2002 at 10:45 hours.



3.3.3 Land cover mapping using satellite imagery


Multi spectral image classification is used to extract thematic information from satellite

images in a semi-automatic way in order to have good imprecation on the different land cover

classes found within the study area of interest. The supervised classification method is

employed with the ground truth data collected during the fieldwork phase, from the previous

reports and information obtained from the local residents. Prior to an image classification,

sample pixels or training pixels have to be selected in a sample set. To create a sample set,

first a map list (FCC 742) and a domain have to be specified. Then, with sampling, assign

class names to groups of pixels that are supposed to represent a known feature on the ground

and that have similar spectral values in the maps in the map. Therefore classification is based

on the spectral values of the pixels selected as training pixels in a sample. During sampling, a

feature space was created to show the separation of classes of sampled pixels. The following

major steps were involved in image classification:

��Selection and preparation of image data,

��Definition of clusters in the feature space

��Selection of classification algorithm

��Running the actual classification

��Validation of results

For this study, six classes were created; riverine forest, mophane, dense marginal and

darkened vegetation, savanna grassland, bareland and water. The classification was done on a

small area to focus on the study area of interest, which is equivalent to one full ASTER scene.

The classifier minimum distance was used and a majority filter was applied for spatial

enhancement.

3.3.3.2 Results and discussion

During the fieldwork, it was observed that the riverine forests are found extensive along the

river channels intermingled with dense Acacia species. But it was noted from the classified

ETM+ Imagery shown in Figure 21 below that the riverine forests are not restricted only

following the river courses. From the classified ETM+ imagery, it was observed that, there is

a transition from riverine forest to mophane through occasional Savanna grassland and back

riverine forest. The mophane woodland as observed during the fieldwork and from the



information of the local people was at different foliage growth and density and this resulted in

a varied spectral response. There are some overlaps between the feature spaces of grassland

and mophane (Figure 22). The mophane is the most occurring tree species due to its tolerance

to saline waters.

Figure 21 Classified Images Showing the distributions of the Dominant land cover in Maun.

Figure 22 Feature space used for making the land cover units.



3.4 Soils

General soils data were obtained from the Soil Mapping and Advisory Services (1990b) soil

map and accompanying soil description. This map, at a scale of 1:1,000,000, covers all of

Botswana so the detail over the Project Area is limited but sufficient for the study purposes.

A brief description of the soils found within the study area is given in Table 4 and their

distribution is shown on Figures 23.

Soil Type (FAO Classification) Soil Description Eutric Gleysol Very deep, poorly to imperfectly drained black to dark greyish

brown sandy clay loam to clay Ferralic Arenosol Deep to very deep, well to excessively drained, yellowish

brown to dark red coarse sands to loamy fine sands Gleysol/Arenosol Complex Deep to very deep, poorly to imperfectly drained dark grey to

greyish brown sand (general description) Haplic Arenosol Deep to very deep, well to excessively well drained, dark

greyish brown to light yellowish brown, fine and medium fine sands to loamy fine sand

Haplic Luvisol Deep to very deep, imperfectly to moderately well drained, dark greyish brown to black sandy loam

Luvic Arenosol Very deep, moderately well to well drained, very dark grayish brown to brown, fine sand to loamy fine sand

Luvic Calcisol Deep to very deep, imperfectly to moderately well drained, dark grayish brown to pale brown massive loamy sands to sandy loams

Petric Calcisol Moderately deep, moderately well to well drained, greyish brown to pale brown, fine sandy loam to silt loam

Table 4 Description of Main Soils in Maun (From Soil Mapping and Advisory Services Project, 1990b).



Figure 23 Soil Map of the study area.



4 Estimation of Surface Temperature and Emissivity using TES algorithm.

4.1 Introduction


budget, heat balance studies and as control for climate models. Knowledge of the surface

emissivity is crucial for estimating the radiation balance at the earth surface. For densely

vegetated surfaces there is a little problem as their emissivity is relatively uniform and close

to one. However, for arid areas like Maun (Botswana) having sparse vegetation the problem is

difficult since the emissivity of the exposed soils and rocks is highly variable.

A new algorithm for estimating land surface temperature and emissivity spectra for multi

spectral thermal infrared ranging from 8 to 12 µm images has been developed for use by [1]

and [2] with data from the Advanced Spaceborne Thermal Emission and Reflection

Radiometer (ASTER). The temperature and emissivity separation (TES) algorithm is based on

an empirical relationship between spectral contrast and minimum emissivity, determined from

laboratory and field emissivity spectra, so as used to equalize the number of unknown and

measurements so that the set of Planck’s equations for the measured thermal radiances can be

inverted. Thermal radiances vary with both temperature and emissivity, which therefore must

be recovered from the measurements.

Surface temperatures are independent of wavelength and can be recovered from even a single

band of radiance data provided atmospheric characteristics can be specified and surface

emissivity in known. However, emissivity of land surfaces is not known apriori (except for

water bodies) but should be estimated along with the temperature. The inversion for

temperature and emissivity is therefore underdetermined which means there is always n+1

unknowns for radiances measured in n spectral channels, n emissivities and the one unknown

surface temperature. In this study, five emissivity and one surface temperature maps were

produced using TES algorithm, which is developed in ILWIS software.



4.2 The ASTER Imaging System.

ASTER includes five channel multi spectral thermal infrared (TIR) scanner designed for

recovery of land surface kinetic temperatures and emissivities not only temperatures of

homogenous areas of known emissivity like water bodies. With a TIR (Thermal infrared)

spatial resolution of 90 meter and a VNIR (Visible near infrared) resolution of 15 meter and

SWIR (Short wave infrared) resolution of 30 meter. ASTER acts as a zoom lens for other

EOS (Earth observation system) imaging experiments.

ASTER is a high spatial resolution multi spectral imagery, which was launched in 1998 by

National Aeronautics and Space Administration (NASA). This instrument has 14 nadirs

viewing channels; five of these are in the thermal infrared (see table 5) [5].

Wavelength region

Band number

Spectral range (µm)

Spatial Resolution (meter)

Swath width (km)

Pointing Telescope (degree)

1 0.52-0.60 2 0.63-0.69

3N 0.78-0.86

VNIR 3b 0.78-0.86

15

±24

4 1.60-1.70 5 2.145-2.185 6 2.185-2.225 7 2.235-2.285 8 2.295-2.365

SWIR

9 2.360-2.430

30

±8.55

10 8.125-8.475 11 8.475-8.825 12 8.925-9.275 13 10.25-10.95

TIR

14 10.95-11.65

90

60

±8.55

Table 5 Spectral considerations of ASTER.



Figure 24 ASTER spectral bands (extracted from: http://asterweb.jpl.nasa.gov/instrument/band.htm)

4.3 Methods and Measurements

In this study, an approach as described by [1] and [2] was used to develop as a bases to write

the temperature emissivity separation (TES) algorithm using ILWIS software for maun,

Botswana. The intensity of the thermal radiation from an object is computed by Planck’s

equation and shown below:

[ ]1**2

),( )**/*(5

2

−=

TKchBB ech

TL λλλ 4.1

Where h Planck’s constant, 6.626*10-34 Js

C speed of light, 2.998*108 ms-1

K Boltzman constants, 1.381*10-23 JK-1

LBB spectral radiance, Wm-2sr-1m-1

Figure 25 Shows the different components used to extract Surface temperature.



The radiance at the sensor is given by: -

[ ] atmjj

skyjjj

BBjj LLTLLS +−+= τεε *)1()( 4.2

Where

εj= surface emissivity at wavelength j,

LjBB(T)=spectral radiance from a blackbody at surface temperature T,

Ljsky=spectral radiance incident upon the surface from the atmosphere, from

MODTRAN,

Ljatm=spectral radiance emitted by the atmosphere, from MODTRAN,

τj=spectral atmospheric transmission, from MODTRAN,

LSj=spectral radiance observed by the sensor.

The radiances at the sensor data were corrected for atmospheric effects to obtain the radiance

emitted by the surface (Lj) using the MODTRAN radiative transfer model (see in Appendix

E). After getting all the necessary data from the MODTRAN, the radiance from the surface is

given by:

[ ]

[ ]1)/exp(

)()1(/)

25

1

−=

=−−−=

TCC

Lj

TLLLLSL

jj

j

BBjj

skyjjj

atmjjj

λπλε

εετ 4.3

Where C1=first radiation constant=3.74151*10-16 [Wm-2] C2= second radiation constant=0.0143879 [mK]

λj=wavelength of channel j , [m] T=temperature, [K].



If the surface emissivity is known, it is possible to correct for the reflected sky radiation in

Eq. (4.2) and inverting Eq. (4.3) to get the surface temperature:

[ ]1/ln 51

2

+=

πλελ jjjjj LC

CT 4.4

Equation 4.3 above shows that for radiance measured in n spectral channels, there will be n+1

unknowns, n emissivities and one surface temperature. TES [1] and [2] the estimated kinetic

temperature T is taken to be the maximum T estimated from the radiance for the five ASTER

TIR spectral channels computed from equation 4.3 above using an assumed emissivity value

(typically 0.98), so that the surface type vegetation, water, soil and rock will be with ±0.03 of

the chosen values. The relative emissivities (βj) were computed by the following relations

shown below:

)/(*)),(/( jBBjBBjj LLTLL λβ = 4.5

Where

[ ].)()5/1()(

,1)/exp(

)(

,)5/1(

5

1

25

1

5

1

�

�

=

=

=

=

=

−=

=

j

j

BBj

BB

jj

BBj

j

jjj

TLTL

TCCTL

LL

λπλ 4.6

From laboratory measurement emissivities [22], the relation between minimum emissivity

(εmin) and maximum minimum difference (MMD) will be shown below:

757.0

min )(*687.0994.0 MMD−=ε 4.7 Where MMD= Maximum (βj)-Minimum (βj) There fore, the revised emissivity can be computed using beta (βj) spectrum and shown below

( ))min(/min jjj βεβε = 4.8



Beta (βj) is determined from the measured surface radiance Lj (surface); new emissivity (εj)

and surface temperature can be obtained. Eventually based on the above procedures, a detail

ILWIS script is prepared to produce the one surface temperature and five emissivity maps and

is shown in Appendix C.

4.4 Estimation of Broadband Emissivity

4.4.1 Introduction

Surface broadband emisivity is an important parameter for estimating long wave radiative

budget. In this study, the method developed by [3] was adopted to estimate the broadband

emissivity from the narrow band emissivities of the five channels on the Advanced Space

borne Thermal Emission and Reflection Radiometer (ASTER). Broadband emissivities (3 to

14 µm) were computed using two spectral libraries, John Hopkins University Spectral library

(JHU Library) and MODIS UCSB (University of California Santa Barbara) emissivity

Library.

ASTER is a sensor on board the earth observing system (EOS) terra satellite launched in

1999, and has five channels in the thermal infrared region (8 to 12 µm). Temperature-

emissivity separation (TES) algorithm is used to estimate spectral emissivity of the five

channels. In there study, they express the broadband emissivity as a linear combination of the

five-channel emissivity from ASTER/TIR data. Eventually, this was applied to ASTER

emissivities over 60*60 Km area in Northern Botswana, Maun.

4.4.2. Method

They found that Broadband emissivity (3 to 14 µm) could be expressed as a linear

combination of ASTER channel emissivities. Broadband emissivity is defined as:

�

�=

=

=

=− = 2

1

2

121

),(

),()(

λλ

λλ

λλ

λλλλ

λλ

λλλεε

dTB

dTB 4.9

Where ε(λ) is the spectral emissivity at the wavelength λ,

B is the Planck function,

T is surface temperature.



ASTER broadband emissivity is defined as:

cach

chchch += �

=

=−

14

100.143.3 εε 4.10

Where ach is calibrated coefficients obtained using JHU/ASTER spectral library (see table 6

Below)

εch is the narrow band ASTER emissivities computed using TES algorithm.

C is constant (see table below)

a10 a11 a12 a13 a14 C 0.035 0.072 0.118 0.000 0.381 0.380

Table 6 Calibrated Coefficients obtained using JHU/ASTER Library.

Note that, Table 6 shows the calibrated coefficients of computed from the stepwise regression.

The coefficient of 0.000 for channel 13 (a 13) means that the variable was dropped, because it

was not statistically significant. Eventually, equation 4.10 above is applied to narrow band

emissivities computed from the data obtained with ASTER/TIR for Maun to produce a map of

broadband emissivity for the study area of interest.



5. Surface temperature and Emissivity estimation using Landsat 7

5.1. Introduction

LANDSAT 7 was launched in April 15th, 1999 and captures images of large areas of the sunlit

Earth daily by revisiting the same areas at every 16 days. It has an ETM+ sensor, a multi

spectral scanning radiometer with eight bands and being capable of providing high-resolution

image information of the earth ‘s surface.

Wavelength

region Band

number Spectral

range (µm) Spatial

Resolution (meter)

Swath width (km

1 0.45-0.52 2 0.53-0.61

Visible

3 0.63-0.69 NIR 4 0.78-0.90

5 1.55-1.75 SWIR 7 2.09-2.35

30

TIR 6 10.4-12.5 60 Panchromatic 8 0.52-0.90 15

183*170

Table 7 Spectral Considerations of LANDSAT 7 ETM+.

5.2. Conversion of DN values to Radiance

LANDSAT 7(ETM+) data are acquired as the 8 bit gray-scale imagery in Level 1G products.

The equation and constants (see in Table 8 below) for converting the 8 bits digital number of

the image data into the spectral radiance is as follows:

BiasDNLL

biasDNGainLi +��

��

� −=+= *

255* minmax 5.1

Where: Li is spectral radiance received by the sensor [Wm-2sr-1µm-1]

Lmax is maximum detected spectral radiance [Wm-2sr-1µm-1] for ETM+ bands.

Lmin is minimum detected spectral radiance [Wm-2sr-1µm-1] for ETM+ bands.

DN is digital number.



Before July 1,2000 After July 1,2000 Low gain High gain Low gain High gain

Band number

Lmin Lmax Lmin Lmax Lmin Lmax Lmin Lmax Band1 -6.2 297.5 -6.2 194.3 -6.2 293.7 -6.2 191.6 Band2 -6.0 303.4 -6.0 202.4 -6.4 300.9 -6.4 196.5 Band3 -4.5 235.5 -4.5 158.6 -5.0 234.4 -5.0 152.9 Band4 -4.5 235 -4.5 157.5 -5.1 241.1 -5.1 157.4 Band5 -1.0 47.7 -1.0 31.76 -1.0 47.57 -1.0 31.06 Band6 0.0 17.04 3.2 12.65 0.0 17.04 3.2 12.65 Band7 -0.35 16.60 -0.35 10.932 -0.35 16.54 -0.35 10.80 Band8 -5.0 244.00 -5.0 158.40 -4.7 243.1 -4.7 158.3

Table 8 LANDSAT 7 ETM+ Spectral radiance range (Wm-2sr-1µµµµm-1).

5.3. Conversion of Radiance to Reflectance

The radiance is converted to atmospheric reflectance using the following equation and shown below:

θπλ

λ

λ

COSESUNdL

r ip ***

)(2

= 5.2

Where rp (λi) is planetary reflectance Lλ spectral radiance at the sensor aperture D is earth sun distance in astronomical units, ESUN is mean solar exo atmospheric irradiance (see Table 9 below) COSθ is solar zenith angle.



Bands ESUN (Wm-2µm-1) Band1 1970.00 Band2 1843.00 Band3 1555.00 Band4 1047.00 Band5 227.10 Band7 80.53 Band8 1368.00

Table 9. Solar Spectral Irradiance.

��Broadband surface albedo The broadband albedo will be computed as follows:

��=

λ

λESUN

rESUNr ip

p

)(* 5.3

Where rp is broadband reflectance at the top of atmosphere.

There fore the broad band surface albedo is:

2

min )(

τprrp

ro−

= 5.4

Where ro is broadband surface albedo Rp min the albedo of non-reflectance body τ2 are two-way transmittance of the broadband short wave radiation.

But exoS

S ↓=τ

Where τ is one-way atmospheric transmittance S↓ Instantaneous incoming short wave radiation (from station or field measurement) Sexo is exoatmospheric short wave radiation.



5.4. Normalized Difference Vegetation Index, NDVI

There are numerous vegetation indices developed to estimate vegetation cover with the

remotely sensed imagery. A vegetation index is a number that is generated by some

combination of remote sensing bands. The most common spectral index used to evaluate

vegetation cover is the Normalized Difference Vegetation Index (NDVI). The basic algebraic

structure of a spectral index takes for form of a ratio between two spectral bands Red and near

infrared (NIR). This index is calculated by subtracting Red reflectance from NIR reflectance,

and dividing by the sum of the two. For instance, in vegetation areas, the NIR portion of the

spectrum is reflected by leaf tissue, and the sensor records the reflectance.

The chlorophyll present in the leaf tissue absorbs red light, thus reducing the reflectance of

red light detected at the sensor. This contrast of reflectance and absorption by vegetation

cover allow us to evaluate the amount of vegetation present on the surface. The Normalized

difference Vegetation Index is an index of vegetation which can be computed from

LANDSAT ETM data using the following equation and shown below:

( ) ( )3434 rrrrNDVI +−= 5.5

Where, r3 is reflectance of band 3 which can be computed from section 5.3 r4 is reflectance of band 4 which can be computed from section 5.3

5.5. Thermal infrared surface emissivity, εεεεo

Emissivity of an object is the ratio of the energy radiated by an object at a given temperature

to the energy radiated by a blackbody at the same temperature. The emissivity of natural

surfaces can vary significantly due to difference in soil structure, soil composition, organic

matter, moisture content and also as a result of difference in vegetation cover characteristics.

Surface with complete or near complete vegetation cover will normally have a thermal

emissivity of 0.97 to 0.98 [23]. The emissivity of water surface were found to range from 0.97

for natural lake water [24, 25] to 1.0 for pure fresh water [26].



[4] have derived an equation which relate NDVI and thermal infrared surface emissivity

using the following data sets and shown below in table 10

Table 10 Emissivity and NDVI measurements for various natural surfaces.

Figure 26 Plot of the mean emissivity versus the mean NDVI.

Therefore, in SEBAL, surface emissivity is estimated using NDVI and an empirical method

derived above and shown below:

( ))(*047.00094.1 NDVILno +=ε 5.6

But the above formula works only for NDVI values ranges from 0.16 to 0.74. Hence, slightly

amendment should be made before arriving to the final emissivity map by adding the

following restrictions to equation (5.6):

))92.0,,16.0(,1,1.0(_ oNDVIIFFNDVIIFFfinalo εε >−<= 5.7



5.6. Estimation of surface temperature, To

5.6.1. Computation of Brightness temperature from LANDSAT 7 ETM+ thermal band.

The mono window algorithm is based on the premise that the brightness temperature at the

satellite level can be retrieved from the thermal band data of LANDSAT 7 ETM+. National

Aeronautics and space Administration (NASA) [27] has developed the following equation to

compute the spectral radiance from DN value of ETM+ data:

BiasDNLL

biasDNGainLi +��

��

� −=+= *

255* minmax 5.8

Where: Li is spectral radiance received by the sensor [Wm-2sr-1µm-1]

Lmax is maximum detected spectral radiance =17.04 [Wm-2sr-1µm-1] for ETM+ B6 low gain.

Lmin is minimum detected spectral radiance = 0.00 [Wm-2sr-1µm-1] for ETM+ B6 low gain.

DN is digital number.

Bias = Lmin =0.00

Thus, the brightness temperature, T6, can be computed by inverting the Planck’s function or

using the pre-launched calibration constants [28] and is shown below:

��

�� +

=1)( 1

2

λLKLn

KTrad 5.9

Where Trad effective satellite temperature [K]

K2 is calibration constant

K1 is also calibration constant

Lλ is spectral radiance in Wm-2sr-1µm-1

Band K1 (Wm-2sr-1µm-1)

K2 (K)

Band six 666.09 1282.71

Table 11 Thermal band calibration constants.



5.6.2. Algorithm for atmospheric correction of brightness temperature

(Adopted and Extracted from [29] ) The atmospheric correction mainly depends on the following three parameters:

��Ground emissivity, εo

��Temperature of the atmosphere, Tat

��Atmospheric transmittance, τ6

In this thesis the broadband emissivity is adopted from ASTER. According to black body

theory, the monochromatic thermal emittance from black body can be computed as follows:

( )1))/exp*()(

25

1

−=

TCC

TBλλλ 5.10

Where;

Bλ(T) is spectral radiance of the black body, generally in [Wm-2sr-1µm-1]

C1 is spectral constant 1.19104356*10-16 [Wm-2]

C2 is spectral constant 1.4387685*104 [µmK]

Black body is a theoretical concept. Most of the natural surfaces are in fact not blackbodies.

Thus, emissivity has to be considered for constructing the radiance transfer equation. In the

process of transferring radiances, the ground emittance is attenuated by the atmosphere

absorption. On the other hand, the atmosphere also contributes the emittance that reaches the

sensor either directly or indirectly. Combining all these components and effects, the sensor-

observed radiance for LANDSAT 7 band 6 can be defined as:

↑+−+= 66666666 ]*)1()([*)( IITBTB oαεετ 5.11

Where:

To is land surface temperature [K]

T6 is brightness temperature of band 6 of LANDSAT 7

τ6 is atmospheric transmittance.

ε6 is ground emissivity in band 6

B6Ts is ground radiance



I6↑ is up welling atmospheric radiance =(1-τ6)*B6 (Ta) [30]

I6∝ is down welling atmospheric radiance = (1-τ6)*B6 (Ta

∝) [31]

Ta is effective mean atmospheric temperature

Ta∝ is down ward effective mean atmospheric temperature.

In equation 5.11 above, the ε6B6 (To) represents the emission from the target, and (1-ε6)*I6∝,

the reflection from down welling radiation. Substituting in equation 5.11 above:

)()1()()1)(1()()( 66666666666 aao TBTBTBTB ττεττε α −+−−+= 5.12

In order to simplify the derivation of the algorithm, the authors analyzed the possibility to

equal the atmospheric radiance B6(Ta) with the down ward atmospheric radiance B6(Ta∝), for

different values of transmittance and difference between Ta and Ta∝ of 2,3,5 oC. Then, they

conclude that the approximation of these two radiances has insignificant effect on the

estimation of To. Then equation 5.12 can be written as:

)()]1(1)[1()()( 666666666 ao TBTBTB ετττε −+−+= 5.13

In order to solve Ts from equation 5.13 above, the Planck’s radiance function is linearized

using series of Taylor. Which means, the expression of radiance B6(Tj) (j=s,a or 6), in terms

of B6(T) , at a fixed temperature T. The parameter L6 is id defined as:

TTBTB

L∂

∂=

)()(

6

6

6 5.14

This can be applied to the three different radiances involved, that is B6(T6), B6(Ts) and B6(Ta).

Substituting in equation 5.13 above, the following equation is derived and is shown below:

)]()1(1)[1()( 6666666666 TTLTTLL ao −+−+−+−+= τεττε 5.15

For simplification, two new parameters are introduced:

C6=ε6τ6 5.16



D6=(1-τ6)[1+(1-ε6)τ6] 5.17 Then, equation 5.15 above can be re written as:

)()( 6666666 TTLDTTLCL ao −++−+= 5.18 For LANDSAT band 6, they found that L6 has a relation with temperature close to linearity

(see figure 27) and can be shown as follows:

6666 TbaL += 5.19 To prove this, for this thesis, the same function is analyzed. As can be seen in figure 27 for

arrange of temperature between 0 and 70oC, and central wavelength equal to 11.25µm, the

coefficients a6 and b6 were found to be –67.434 and 0.4568 respectively.

T6 Bλ(T) δB6(T)/δT L6 [K]

271 5.95 273 6.16 0.11 58.33 275 6.38 0.11 59.16 277 6.60 0.11 59.99 279 6.82 0.11 60.83 281 7.05 0.11 61.67 283 7.28 0.12 62.52 285 7.52 0.12 63.37 287 7.76 0.12 64.23 289 8.01 0.12 65.10 291 8.26 0.13 65.96 293 8.51 0.13 66.84 295 8.77 0.13 67.72 297 9.04 0.13 68.60 299 9.30 0.13 69.49 301 9.58 0.14 70.39 303 9.85 0.14 71.29 305 10.13 0.14 72.19 307 10.42 0.14 73.10 309 10.71 0.14 74.01 311 11.00 0.15 74.93 313 11.30 0.15 75.86 315 11.60 0.15 76.79 317 11.91 0.15 77.72 319 12.22 0.16 78.66 321 12.53 0.16 79.60 323 12.85 0.16 80.55 325 13.17 0.16 81.50 327 13.50 0.16 82.46 329 13.83 0.17 83.42 331 14.17 0.17 84.39 333 14.51 0.17 85.36 335 14.85 0.17 86.34 337 15.20 0.17 87.32 339 15.55 0.18 88.30 341 15.91 0.18 89.29 343 16.27 307

Table 12. Data used to estimate a6 and b6.



Figure 27 Determination of a6 and B6 coefficients.

Eventually, equation can be re written as follows:

666 Tba + = )()( 666666 TTLDTTLC ao −++−+ 5.20 Therefore, the surface temperature can be computed as follows:

66666666666 ]))1(()1([ CTDTDCDCbDCaT ato ÷−++−−+−−= 5.21

5.6.3. Determination of atmospheric temperature, Tat

The estimation of the local mean atmospheric temperature during the satellite over pass time can only

be done based on the distribution of the different atmosphere quantities. With the availability of

standard atmospheres provided by MODTRAN 4 from real atmospheric data, and following the

method of [32] , the authors show that the local meteorological data combined with these standard

atmospheric distributions can be utilized to the estimation of atmospheric temperature. In this study,

Tat is estimated using the following equation:

aat TT 91715.09769.17 += 5.22

For Maun, Botswana, a value of Tat =293 K is found for mean Ta =300 K, retrieved from

tower station. Eventually, the atmospheric transmittance is adopted by taking the average

value of ASTER band13 and 14 atmospheric transmittance, which is computed, from

MODTRAN 4.



5.6.4. Estimation of surface temperature

It is possible to estimate the surface temperature, once all the parameters are obtained in the

above sections. Therefore, the surface temperature is computed as follows:

66666666666 ]))1(()1([ CTDTDCDCbDCaT ato ÷−++−−+−−= 5.23

Where:

To is surface temperature [K]

T6 is brightness temperature, K from LANDSAT 7 band 6, using equation 5.9 above.

Tat is temperature of the atmosphere, K, from air temperature measurements in equation 5.22

above

a6= -67.434 from figure 28 above

b6= 0.4568 from figure 28 above

C6 is obtained using equation 5.16

D6 is obtained using equation 5.17

ε6 emissivity obtained from ASTER sensor.

τ6 is obtained by averaging ASTER atmospheric transmittance of band14 and 13.

Eventually based on the above procedures, a detail ILWIS script is prepared to produce a

surface temperature map using LANDSAT 7 and is shown in Appendix D.



6. RESULTS AND DISCUSSION:

6.1. Broad band emissivity

The calibrated coefficients computed using JHU Library is finally applied to the narrow band

emissivities computed from ASTER/TIR data acquired over Maun, (Botswana). The result is

shown in figure 28. The histogram of extracted emissivity is shown is figure 28. The

broadband emissivity computed ranges from 0.93 to 0.96 with the average 0.95, while the

broadband emissivity for LANDSAT 7 is estimated using Van griend and Owe method from

Normalized difference in vegetation index (NDVI). The result is shown in figure 29. The

broadband emissivity computed for LANDSAT 7 ranges from 0.94 to 0.98 with the average

0.96. For both cases, the highest broadband emissivity is shown in areas where there is dense

vegetation, which is red in color while the lowest is for bareland, which is blue in color.

Figure 28 Broadband emissivity map and histogram derived using ASTER sensor.



Figure 29 Broadband emissivity map and histogram derived using LANDSAT 7 sensor.

In this study, poor correlation (R2 0.02) is observed between broadband emissivity derived by

ASTER and LANDSAT 7 and the same holds true the correlation between ASTER derived

broadband emissivity and Normalized difference in vegetation index (NDVI). The results for

both correlations are shown in figure 30 and 31 respectively.

Figure 30 Correlation result of broadband emissivity of LANDSAT 7 and ASTER for February 20, 2002.



Figure 31 Correlation result of ASTER broadband emissivity and NDVI for February 20, 2002.

Figure 32_1 ASTER broadband emissivity correlation graph derived using Ogwa, K. et al., 2002 and Van Griend Owe methods.



6.2. Surface temperature estimation.

Fair and reasonable surface temperature result is obtained using the Temperature Emissivity

Separation (TES) algorithm, which is quite closer and comparable to the surface temperature

obtained from the tower station and also show good correlation with the surface temperature

derived from LANDSAT 7 (R2 0.59 as seen in figure 33). However good correlation doesn’t

necessary imply good accuracy, rather it signifies the association and interrelation between

the methods in keeping the same trend.

Figure 33 Correlation results of ASTER and LANDSAT 7 derived Surface temperature.

There is expected to be some relationship between ASTER and LANDSAT 7(as shown in

figure 33 above). But how the temperatures or emissivity values are computed, or how

atmospheric correction is done are different for each of the two sensor systems. So one could

expect a temperature difference of several K because of the following reasons:

��The over flight times are different which means that ASTER and LANDSAT 7 ETM+

can observe the same areas about 30 minutes apart in time. Since ASTER follows

LANDSAT 7, on the day side a surface will have some time to heat, so ASTER



derived surface kinetic temperatures should be some what higher than those measured

from LANDSAT 7.

��Wind at the scene causes several K difference locally and over small time intervals.

��The two images are processed independently and not exactly the same steps are

followed to estimate the final surface kinetic temperature, broadband emissivity and

outgoing long wave radiation.

Figure 34 below shows that both sensors have highest surface temperature for bareland,

which is red in color while the lowest is for open water (swampy area), which is blue in color.

Figure 34 Surface temperature map of Maun derived from ASTER and LANDSAT 7.



Figure 35 Histograms of Surface temperature for Maun derived from ASTER and LANDSAT 7.

6.3. Cross validating ASTER and LANDSAT 7

The computed ASTER and LANDSAT 7 out going long wave radiation needs to be tested by

the data generated from the Planck tower and summary of the result is shown in Table 13

below.

Satellite Estimation. Tower Data Difference with tower data

(%) Parameter Unit

LANDSAT 7 ASTER LANDSAT7 ASTER LANDSAT7 ASTER Surface temperature. K 315.386 332.77 336.931 342.546 6.39 2.85 Surface emissivity. - 0.938 0.938 1.00 1.00 Long wave outgoing radiation.

Wm-2 526.206 652.157 696.62 732.25 23.49 10.93

Table 13 Summary results estimated from ASTER and LANDSAT 7 for February 20, 2002.

In the above table, the out going instantaneous long wave radiation values of the two sensors

are obtained by using the following equation:

↓−+↑= LTsL *)1(4** εσε 6.1

Where L↑ is instantaneous long wave out going radiation Wm-2

L↓ is instantaneous long wave incoming radiation Wm-2

σ is Stefan Bolzman constant 5.67*10-8[Wm-2K-4]

ε is broadband emissivity.



When these values are compared with the long wave out going radiation computed from the

Planck tower, the following point can be drawn:

��The long wave out going radiation computed using ASTER sensor is closer to the

Planck tower data as compared to the result obtained from LANDSAT 7. This is

resulted due to better estimation in input data like surface temperature for computing

the out going long wave radiation. Figure 36 below shows that both sensors have

highest out going long wave radiation for bareland, which is red in color while the

lowest is for open water (swampy area), which is blue in color.

Figure 36 Map showing spatial variation of out going Long wave radiations derived from ASTER and LANDSAT 7 [Wm-2].



An alternative assessment of ASTER and LANDSAT 7 are made in Table 14 and 15 below

based on a classified vegetation map of the study area. Six units are identified and several

parameters like out going long wave radiation, broadband emissivity and surface temperature

are evaluated for each unit and the results are shown below.

LANDSAT 7 ASTER To [K] To [K]

Land cover. *NPIX

Min Max Avg σ *NPIX

Min Max Avg σ

Bare land 8198 308.87 327.63 318.77 2.83 8198 324.69 340.48 333.33 3.84

Dense marginal and darkened vegetation.

759259 306.89 329.18 317.62 3.29 759259 320.78 342.12 332.94 4.56

Mophane. 1359328 305.42 325.22 315.59 3.71 1359328 322.64 340.64 331.41 4.70

Riverine forest. 7398 303.91 316.27 308.08 1.89 7398 322.14 334.74 326.78 2.63

Savanna grassland. 1438720 303.59 327.62 312.65 3.58 1438720 320.77 341.51 330.33 4.74

Open water. 901 302.65 318.37 309.19 3.19 901 319.47 332.13 324.61 2.71

Table 14 Comparison of ASTER and LANDSAT 7 derived surface temperature for different land cover.

LANDSAT 7 ASTER

Surface emissivity Surface emissivity Land cover.

*NPIX Min Max Avg

σ *NPIX Min Max Avg

σ

Bare land 8198 0.920 0.981 0.946 0.02 8198 0.919 0.95 0.935 0.009

Dense marginal and darkened vegetation.

759259 0.920 0.980 0.950 0.02 759259 0.929 0.951 0.940 0.007

Mophane. 1359328 0.920 0.993 0.960 0.02 1359328 0.923 0.951 0.937 0.009

Riverine forest. 7398 0.971 0.999 0.987 0.01 7398 0.937 0.951 0.944 0.004

Savanna grassland. 1438720 0.92 0.9933 0.9648 0.02 1438720 0.932 0.951 0.942 0.006

Open water. 901 0.920 1.000 0.950 0.02 901 0.94 0.95 0.945 0.003

Table 15Comparison of ASTER and LANDSAT 7 derived broadband emissivity for different land cover.



6.4. Sensitivity analysis

Sensitivity is a measure of change in the dependent variable due to a change in one of the

independent variables keeping all the rest input parameters constant. The relative importance

of each independent variable on surface temperature, broadband and out going long wave

radiation estimation will be shown. From this analysis, the sensitivity of surface temperature,

broadband emissivity and out going long wave radiation is investigated by developing TES

algorithm in spreadsheet for a single pixel.

Constants INCL (mWm-2sr-1µm)

Lamdabar (m)

Ldn (mWm-2sr-1µm)

Lup (mWm-2sr-1µm)

tau DN value of the tower

Band 10 0.006882 8.29 3497 1956 0.472 1284 Band 11 0.006780 8.63 2454 1477 0.599 1413 Band 12 0.006590 9.09 1833 1141 0.578 1501 Band 13 0.005693 10.66 1554 1275 0.663 1828 Band 14 0.005225 11.29 1638 1457 0.604 1881

Table 16 Basic data used to develop TES algorithm in spreadsheet.

εmax 0.98 (-) Initial emissivity 1.00 blackbody emissivity C1 3.74E+08 Wm-2 C2 1.44E+04 mm K By putting the above input values in to the spreadsheet the following results are obtained and

the summary of the result is shown in Table 18 below.

*tau *Ldn *Lup Parameters Unit

-10% +10% -10% +10% -10% +10% Surface temperature. K 341.75 324.50 332.52 332.42 333.95 330.99

Out going long wave radiation.

Wm-2 720.80 593.24 650.46 649.19 660.77 638.94

Broadband emissivity. 0.93 0.94 0.94 0.94 0.94 0.94

Table 17 Summary of the sensitivity analysis of the parameters for changes in ±±±±10% of MODTRAN 4 out puts for Planck tower.

Note:

*tau is atmospheric transmission obtained from MODTRAN 4.

*Ldn is down welling radiance obtained from MODTRAN 4.

*Lup is up welling radiation obtained from MODTRAN 4.



From the above table (Table 17), it is possible to conclude that up welling and down welling

radiances has no stronger influence on the magnitude of surface temperature and out going

long wave radiation. But, out of the MODTRAN 4 out puts involved in the estimation of

surface temperature and long wave out going radiation, the atmospheric transmittance (τ) is

found to be the most sensitive. Any error in its estimation will lead to devastating error in the

final estimation of surface temperature and out going long wave radiation which means a 10%

error in the atmospheric transmittance (τ) induces a 10% change in the out going long wave

radiation.

6.5. High level ASTER product

6.5.1. Surface Emissivity (AST_05)

The Level-2 land surface emissivity product contains surface emissivity at 90-m resolution

generated only over the land from ASTER five thermal infrared channels. Surface emissivity

is required to derive land surface temperature (AST_08) data, also at a resolution of 90

meters. The emissivity product is critical for deriving accurate land surface temperatures. It is

therefore important in studies of surface energy and water balance. The emissivity product is

also useful for mapping geologic and land-cover features. In this study, the method developed

by Ogawa et al., (2002) was adopted to estimate the broadband emissivity from the narrow

band emissivities of the five TIR channels of ASTER sensor. The result of broadband

emissivity computed from five ASTER TIR AST_05 products is shown below in Figure 37.

Figure 37. Broadband emissivity computed from the narrow band channels of AST_05 products for February 20, 2002.



6.5.2. Surface Kinetic Temperature (AST_08)

The Level-2 land surface kinetic temperature product contains surface temperatures at 90-m

resolution generated only over the land from ASTER five thermal infrared channels. Land

surface temperatures are determined from Planck's Law, using the emissivities from AST05 to

scale the measured radiances after correction for atmospheric effects. The result of AST_08 is

shown below in Figure 38.

Figure 38 AST_08 Surface temperature product for February 20, 2002.

The results were compared with tower data, with LANDSAT 7 image of the same day, and

finally with reported AST_05 and AST_08. The surface temperature estimated by AST_08 is

not closer to the Planck tower data; the possible reasons for this may be the use the Mid-

Latitude Summer (45o North Latitude). Similar results to AST_08 product are obtained when

Mid-Latitude Summer option is introduced in this thesis.

The closer result to the tower data is obtained when the atmospheric model is shifted from

Mid-Latitude Summer (45o North Latitude) to Tropical Atmosphere (15o North Latitude) and

this results in lowering the atmospheric transmittance value, which is the most sensitive part

in estimating the surface temperature. Results indicate that information on atmospheric

conditions is crucial. Eventually, the histograms of the surface temperature, broadband



emissivities derived from ASTER and LANDSAT 7 for the six land covers, the narrow band

emissivities of ASTER are attached in Appendix F.



7. Conclusions and Recommendation.

7.1. Conclusion


budgets in heat balance studies and as a control for climate models. Land surface temperature

is strongly influenced by the ability of the surface to emit radiation, i.e. surface emissivity.

Therefore, knowledge of the surface emissivity is crucial for estimating the radiation balance

at the earth surface. A new algorithm for estimating land surface temperature and emissivity

spectra for multi spectral thermal infrared ranging from 8 to 12µm images has been developed

recently by [1] and [2] for use with data from the Advanced Spaceborne Thermal Emission

and Reflection Radiometer (ASTER) on the TERRA platform. Similar methods are also used

with the MODIS sensor on the same platform.

The temperature emissivity separation (TES) algorithm is based on an empirical relationship

between spectral contrast and minimum emissivity, determined from laboratory and field

emissivity spectra. It is used to equalize the number of unknown parameters and the number

of measurements so that the set of Planck’s equations for the measured thermal radiances can

be inverted. Surface temperatures are independent of wavelength and can be recovered from

even a single band of radiance data provided atmospheric characteristics can be specified and

surface emissivity is known. However, emissivity of land surfaces is not known a priori

(except for water bodies) but should be estimated along with the temperature. Moreover,

emissivity values vary with wavelength.

In this study, the method developed by [3] was adopted to estimate the broadband emissivity

from the narrow band emissivities of the five TIR channels of ASTER instrument in an area

close to Maun (Botswana). MODTRAN 4 was used to calculate the necessary atmospheric

corrections (for standard atmospheres). The results were compared with tower data, with a

LANDSAT 7 image of the same day, and finally also with reported ASTER surface

temperature and emissivities for the same image (High level ASTER product) and this results

shows that, the surface temperature estimated by TES method is much more closer to the

tower data than the temperature estimated with LANDSAT 7.



There is expected to be some relationship between ASTER and LANDSAT 7 (as shown in

figure 33 above). But how the temperatures or emissivity values are computed, or how

atmospheric correction is done are different for each of the two sensor systems. So one could

expect a temperature difference of several K because of the following reasons:

��The over flight times are different which means that ASTER and LANDSAT 7 ETM+

can observe the same areas about 30 minutes apart in time. Since ASTER follows

LANDSAT 7, on the day side a surface will have some time to heat, so ASTER

derived surface kinetic temperatures should be some what higher than those measured

from LANDSAT 7.

��Wind at the scene causes several K difference locally and over small time intervals.

��The two images are processed independently and not exactly the same steps are

followed to estimate the final surface kinetic temperature, broadband emissivity and

outgoing long wave radiation.

Results indicate that information on atmospheric conditions is crucial. The surface

temperature is rather sensitive to atmospheric transmissivity. This study likes to draw the

attention of hydrologists to the use of [4] method for estimation of emissivity. Probably this

method is the most cited and widely used in estimating emissivity, but results of this study

shows that the formula does not hold true always. This is an important finding because it

could affect the result and conclusion of studies, which implemented this method at some

point. This study is not the first to show the breakdown of this method, it has also been

reported in research done in Jornada, New Mexico, USA (Kenta Ogawa, personal

communication).

Obviously the soils and vegetation species there can have wide range of broadband

emissivity value. It mainly depends on their chemical contents and vegetation species. But in

areas with single type of soil with somewhat homogenous vegetation cover, there would be a

possibility to get good correlation. Using the TES method it becomes possible to obtain more

reliable solutions to the energy balance and evapotranspiration problem, especially in semi-

arid areas.



7.2. Recommendation:

This study has used the TES algorithm for estimating surface temperature from ASTER/TIR

channels using iteratively mathematical approaches. As stated in section 4, the TES method

makes it possible to estimate surface temperature from remote sensing. However, since this

result has been validated/compared with long wave out going radiation under a particular set

of environmental conditions, further field work and surface temperature measurements are

required to further extend this approach to a broader set of environmental conditions.



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APPENDIX A1 : Maun and Shakawe Meteorological Station (In CD)

APPENDIX B 1 Planck's Tower data and ground data measured during fieldwork.

Table B 1 Planck’s Tower data used for computing Long wave radiations for comparing LANDSAT 7 and ASTER image of February 20,2002. ...................................................................................... 72

Table B 2 Incoming Short, Long Wave radiation and Surface temperature measured at the field. ..... 79 Table B 3 Ground data collected during the fieldwork used for geocoding and image processing. ..... 82



Table B 1 Planck’s Tower data used for computing Long wave radiations for comparing LANDSAT 7 and ASTER image of February 20,2002.

Parameter P T Tpot Tdew Rh Vpmax Vpact VPdef Unit mbar degC K degC % Mbar Mbar mbar Parameter Sh H2OC Rho Rain Typr TDR TUR SWDR Unit g/Kg mmol/mol g/m3 mm degC W/m2 W/m2 W/m2 Parameter SWUR Albedo LWDR LWUR TRAD PAR Rn Unit W/m2 W/m2 W/m2 degC Umol/sm2 W/m2



Table B 1 continued…



Table B 2 Incoming Short, Long Wave radiation and Surface temperature measured at the field.

Land cover % ageStudy area Maun, Botswana Bare soil 80Date sep16,2002 Bush 20Emissivity is set to 1Surface type bushInstrument used Pyronmeter and Thermal radiometerCollected by Samantha and Michael

Time Temperature ISWR OSWR ISWR OSWR(hrs) (oC)

(mvolts) (mvolts) (Wm-2) (Wm-2)7:56 16.500 3.070 1.010 338.479 111.3568:00 17.000 3.050 1.160 336.273 127.8948:07 16.500 3.270 1.000 360.529 110.2548:12 18.500 4.180 1.000 460.860 110.2548:15 17.500 4.400 1.120 485.116 123.4848:20 19.500 3.960 1.460 436.604 160.9708:23 19.500 4.930 1.350 543.550 148.8428:29 18.500 4.210 1.410 464.168 155.4588:30 18.500 4.440 1.210 489.526 133.4078:34 20.000 4.330 1.350 477.398 148.8428:37 19.500 4.800 1.260 529.217 138.9208:43 20.500 4.700 1.160 518.192 127.8948:50 22.000 4.730 1.250 521.499 137.8178:53 23.000 5.360 1.210 590.959 133.4079:00 23.000 5.360 1.500 590.959 165.3809:05 22.000 5.350 1.520 589.857 167.5859:10 24.500 6.000 1.300 661.521 143.3309:13 25.000 5.180 1.420 571.114 156.5609:18 27.000 6.350 1.270 700.110 140.0229:21 27.500 6.100 1.470 672.547 162.0739:25 26.500 6.360 1.410 701.213 155.4589:34 27.500 6.330 1.380 697.905 152.1509:40 25.500 7.300 1.250 804.851 137.8179:44 25.000 7.060 1.360 778.390 149.9459:51 25.000 7.000 1.580 771.775 174.2019:55 26.000 7.810 1.400 861.080 154.355

10:00 23.500 7.760 1.650 855.568 181.91810:04 26.000 7.550 1.610 832.415 177.50810:08 29.000 7.590 1.310 836.825 144.43210:15 25.500 7.970 1.670 878.721 184.12310:20 25.000 7.890 1.540 869.901 169.79110:24 29.500 7.890 1.460 869.901 160.97010:28 27.000 8.420 1.800 928.335 198.45610:31 31.000 8.300 1.410 915.105 155.45810:45 26.500 9.080 1.620 1001.103 178.61110:59 28.000 8.730 1.630 962.514 179.71311:01 30.500 9.460 1.460 1042.999 160.97011:07 27.500 9.450 1.400 1041.896 154.35511:10 29.900 9.280 1.440 1023.153 158.76511:13 29.500 9.260 1.650 1020.948 181.91811:19 30.500 9.460 1.830 1042.999 201.76411:22 28.000 9.380 1.650 1034.179 181.91811:26 29.000 9.120 1.550 1005.513 170.89311:49 27.500 9.390 1.650 1035.281 181.91811:56 32.500 9.530 1.660 1050.717 183.02112:00 30.000 9.450 1.760 1041.896 194.04612:15 28.000 9.390 1.430 1035.281 157.66312:22 28.000 9.360 1.440 1031.974 158.765

max 32.5min 16.5




Land cover % ageStudy area Maun, Botswana Bare soil 80Date sep16,2002 Bush 20Emissivity Set 1Surface type bushInstrument used Pyronmeter and Thermal radiometerCollected by Samantha and Michael

Time Temperature Incoming short wave Out going short wave Incoming short wave Out going short wave(hrs) (oC) radiation radiation radiation radiation

(mvolts) (mvolts) (Wm-2) (Wm-2)7:56 16.500 3.070 1.010 338.479 111.3568:00 17.000 3.050 1.160 336.273 127.8948:07 16.500 3.270 1.000 360.529 110.2548:12 18.500 4.180 1.000 460.860 110.2548:15 17.500 4.400 1.120 485.116 123.4848:20 19.500 3.960 1.460 436.604 160.9708:23 19.500 4.930 1.350 543.550 148.8428:29 18.500 4.210 1.410 464.168 155.4588:30 18.500 4.440 1.210 489.526 133.4078:34 20.000 4.330 1.350 477.398 148.8428:37 19.500 4.800 1.260 529.217 138.9208:43 20.500 4.700 1.160 518.192 127.8948:50 22.000 4.730 1.250 521.499 137.8178:53 23.000 5.360 1.210 590.959 133.4079:00 23.000 5.360 1.500 590.959 165.3809:05 22.000 5.350 1.520 589.857 167.5859:10 24.500 6.000 1.300 661.521 143.3309:13 25.000 5.180 1.420 571.114 156.5609:18 27.000 6.350 1.270 700.110 140.0229:21 27.500 6.100 1.470 672.547 162.0739:25 26.500 6.360 1.410 701.213 155.4589:34 27.500 6.330 1.380 697.905 152.1509:40 25.500 7.300 1.250 804.851 137.8179:44 25.000 7.060 1.360 778.390 149.9459:51 25.000 7.000 1.580 771.775 174.2019:55 26.000 7.810 1.400 861.080 154.355

10:00 23.500 7.760 1.650 855.568 181.91810:04 26.000 7.550 1.610 832.415 177.50810:08 29.000 7.590 1.310 836.825 144.43210:15 25.500 7.970 1.670 878.721 184.12310:20 25.000 7.890 1.540 869.901 169.79110:24 29.500 7.890 1.460 869.901 160.97010:28 27.000 8.420 1.800 928.335 198.45610:31 31.000 8.300 1.410 915.105 155.45810:45 26.500 9.080 1.620 1001.103 178.61110:59 28.000 8.730 1.630 962.514 179.71311:01 30.500 9.460 1.460 1042.999 160.97011:07 27.500 9.450 1.400 1041.896 154.35511:10 29.900 9.280 1.440 1023.153 158.76511:13 29.500 9.260 1.650 1020.948 181.91811:19 30.500 9.460 1.830 1042.999 201.76411:22 28.000 9.380 1.650 1034.179 181.91811:26 29.000 9.120 1.550 1005.513 170.89311:49 27.500 9.390 1.650 1035.281 181.91811:56 32.500 9.530 1.660 1050.717 183.02112:00 30.000 9.450 1.760 1041.896 194.04612:15 28.000 9.390 1.430 1035.281 157.66312:22 28.000 9.360 1.440 1031.974 158.765

max 32.5min 16.5



Table B 3 Ground data collected during the fieldwork used for geocoding and image processing.

Number LATITUDE LONGITUDE Description of way points.

1 -19.89933 23.53688 HOORC Center.2 -19.91660 23.56032 turnoff road at old Francistown road.3 -20.03115 23.38503 Crossing Maun Sehitwa road shshe bridge.4 -19.99984 23.40398 Turnoff from dirty road to tar road.5 -19.94159 23.49541 Bridge over Thamalakane.6 -19.87527 23.57528 Turnoff from the main road.7 -19.86574 23.56685 Track crosses Thamalakane before entering river.8 -19.88517 23.54299 Thamalakane river.9 -19.88678 23.54154 Opposite old bridge western bank of Thamalakane river.

10 -19.89310 23.54840 Trurnoff from the main road to old bridge.11 -19.91697 23.51553 Boro junction.12 -19.96111 23.45996 Alfa lodge.13 -20.00335 23.38357 Foot ball field bare soil.14 -20.00171 23.37921 Mixed savanna with woodland.15 -19.99599 23.37222 Dense riverine forest.16 -19.99164 23.36629 Major crossing roads in Shashe area.17 -19.99406 23.36081 Short height mophane to the left.18 -19.98852 23.34969 Short height mophane to the left.19 -19.97650 23.34401 Dense mophane with some Acacia which are big in size.20 -19.95634 23.33012 Green dense Acacia to the left.21 -19.94801 23.32861 Dry riverine forest.22 -19.94724 23.32880 Dry yellow grasses and bushes in the Shashe River valley.23 -19.94381 23.32957 Dense vegetation to the right.24 -19.93907 23.32582 Open areas to left and right of road.25 -19.93557 23.31117 Open woodland.26 -19.93350 23.30923 Open areas dominated by yellow grass.27 -19.92179 23.29108 Inside dense mixed forest.28 -19.87325 23.22184 Short dry Mophane to both sides of the road.29 -19.97026 23.34896 Road crossing the Shashe.30 -19.98490 23.37903 Bare soil excvation area near the town.31 -20.00598 23.43269 Maun Francistown road T-junction to old bridge.32 -20.08421 23.53076 T-junction francistown road to Samedupi.33 -20.11243 23.52693 Boteti River bridge(Samedupi).34 -20.06322 23.34200 Toteng road abrupt change from open savanna to dense green Acacia.35 -20.35679 22.95351 T-junction Toteng.36 -20.35955 22.94596 Toteng road near to Kunyere River bridge.37 -20.13951 23.37326 Thamalakane Boteti Nhabe junction.38 -20.08936 23.32922 Crossing track main Toteng road.39 -19.91660 23.56029 Planck tower.40 -19.92093 23.56186 Old Francistown road which is oppostie to the guard hut.



APPENDIX C 1 APPENDIX C1: ILWIS SCRIPT USED TO DEVELOP TES ALGORITHM.



ILWIS SCRIPT 1 Short Summary of the codes, map names etc. used in the ILWIS scripts used to develop ASTER/TES ALGORITHM:

Short Summary of the codes, map names etc. used in the ILWIS scripts used to develop ASTER/TES ALGORITHM: GEOGRAPHY ILWIS SCRIPT Step I: Pre-processing Parameters: %1 Local Standard time 10.75 %2 Julian day no. 51 %3 Standard Meridian 30 Latitude and Longitude maps in degree decimal: “lati” = Map of Latitude in degree decimal “long” = Map of Longitude in degree decimal The hour angle θ, and the cosine of the solar zenith angle cos (θz): “DA_map” = day angle map DA = function to calculate day angle [radian] = 0.01721420632*(a-1) Where, a = Julian day no. “Delta” = map of solar declination of the day in [radian] DE = function to calculate solar declination [radian] = (0.006918-0.399912*cos(a)+0.070257*sin(a)-0.006758*cos(2*a)+0.000907*sin(2*a)-0.002697*cos(3*a)+0.00148*sin(3*a)) Where, a = DA “Lc” = Map of longitude correction in minutes “LAT” = Map of local apparent time in hours ET = function to calculate equation of time [minutes] = (0.000075+0.001868*cos(a)-0.032077*sin(a)-0.014615*cos(2*a)-0.04089*sin(2*a))*229.18 Where, a = DA “w” = Map of hour angel in degree “COS_Zen” = Map of COS of solar zenith angle The exo-atmospheric irradiance for the time of satellite overpass: “Kexo” = Map of Instantaneous exo-atmospheric incoming irradiance (Wm-2) Solar constant = 1367 Wm-2 EO = function to calculate eccentricity correction factor for the day =1.00011+0.034221*cos(a)+0.00128*sin(a)+0.000719*cos(2*a)+0.000077*sin(2*a) Where, a = DA



Radiances per band: is already converted when we import it using ASTER level 1A/1B The broadband albedo: Reflectances per band “ds” = Map of Sun Earth distance in astronomical unit Solar spectral irradiance (Esun) for ASTER (Wm-2sr-1µm-1) at: Band 1 = 1846 Band 2 = 1555 Band 3n = 1120 Band 4 = 231 Band 5= 79 Band 6 = 74.4 Band 7 = 70.5 Band 8= 59.6 Band 9= 56.3 “Spectralref_B1” = Planetary reflectance at band 1 “PRefB Spectralref_B2” = Planetary reflectance at band 2 “Spectralref_B3n” = Planetary reflectance at band 3n “Spectralref_B4” = Planetary reflectance at band 4 “Spectralref_B5” = Planetary reflectance at band 5 “Spectralref_B6” = Planetary reflectance at band 6 “Spectralref_B7” = Planetary reflectance at band 7 “Spectralref_B8” = Planetary reflectance at band 8 “Spectralref_B9” = Planetary reflectance at band 9 Broad band planetary albedo “BBreflectance” = broad band planetary albedo (weighted average of the Planetary reflectance’s per band)



Vegetation Indixes: a. NDVI map “NDVI” = NDVI map (were computed using band 3n and 2) b. SAVI and LAI for savannah land-cover “SAVI_temp” = temporary map of SAVI calculated using correction factor 0.5 “SAVI” = Adjusted SAVI map (i.e. setting negative values to 0.00001 to avoid problems with logarithms and divisions by 0) “LAI_temp” = Map of calculated LAI by the empirical relation LAI = (SAVI-C1)/C2 The constants C1 = 0.13 and C2 = 0.47 are adopted from the AHAS manual page 9. (Sahelian agroecological landscape of Niger) “LAI” = Adjusted LAI map (i.e. setting negative values to 0.00001 to avoid problems with logarithms and divisions by 0) The surface temperature (one map) and emissivity(five maps) were basically computed using the following inputs : Parameters: %1 ASTER/TIR_Band10 %2 ASTER/TIR_Band11 %3 ASTER/TIR_Band12 %4 ASTER/TIR_Band13 %5 ASTER/TIR_Band14 Bands INCL

(Wm-2sr-1mm-1)

Lamdabar,centeral wave length. ( m)

**Ldn (mWm-2sr-1mm-1)

**Lup (mWm-2sr-1mm-1)

** tau

Band_10 0.006882 8.29 3497 1956 0.472 Band_10 0.006780 8.63 2454 1477 0.599 Band_10 0.006590 9.09 1833 1141 0.578 Band_10 0.005693 10.66 1554 1275 0.663 Band_10 0.005225 11.29 1638 1457 0.604

εmax 0.98 (-) Initial emissivity ε 1.00 blackbody emissivity C1 3.74E+08 Wm-2 C2 1.44E+04 µm K **Ldn,Lup and tau were obtained from MODTRAN 4 Software



TEMPERATURE-EMISSIVITY SEPARATION (PREPROCESSING)

STEP_1, Conversion of the digital number of each ASTER thermal images to the radiances, Wm-2sr-1µµµµm-1 L_10.mpr{dom=Value.dom;vr=-50.00:15000.00:0.001} :=(0.006882*(%1-1))*1000 L_11.mpr{dom=Value.dom;vr=-50.00:15000.00:0.001} :=(0.006780*(%2-1))*1000 L_12.mpr{dom=Value.dom;vr=-50.00:15000.00:0.001} :=(0.006590*(%3-1))*1000 L_13.mpr{dom=Value.dom;vr=-50.00:15000.00:0.001} :=(0.005693*(%4-1))*1000 L_14.mpr{dom=Value.dom;vr=-50.00:15000.00:0.001} :=(0.005225*(%5-1))*1000

STEP_2 Computation of total radiances at the ground surface excluding the atmospheric effect of the reflected sky brightness,Wm-2sr-1µµµµm-1 LSFC_10.mpr{dom=Value.dom;vr=-50.00:20000.00:0.001}:=(L_10-%1)/%5 LSFC_11.mpr{dom=Value.dom;vr=-50.00:20000.00:0.001}:=(L_11-%2)/%6 LSFC_12.mpr{dom=Value.dom;vr=-50.00:20000.00:0.001}:=(L_12-%3)/%7 LSFC_13.mpr{dom=Value.dom;vr=-50.00:20000.00:0.001}:=(L_13-%4)/%8 LSFC_14.mpr{dom=Value.dom;vr=-50.00:20000.00:0.001}:=(L_14-%1)/%2

Parameters: %1 Lup_Band10 %2 Lup_Band11 %3 Lup_Band12 %4 Lup_Band13 %5 tau_Band10 %6 tau_Band11 %7 tau_Band12 %8 tau_Band13

STEP_3 LSFCRED is the computation of spectral radiance from a black body at surface temperature T,Wm-2sr-1µµµµm-1 Parameters: %1 Lup_Band14 %2 tau_Band14 %3 Ldn_Band10 %4 Ldn_Band11 %5 Ldn_Band12 %6 Ldn_Band13 %7 Ldn_Band14



LSFCRED_10.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_10-(1-0.98)*%3)/0.98 LSFCRED_11.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_11-(1-0.98)*%4)/0.98 LSFCRED_12.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_12-(1-0.98)*%5)/0.98 LSFCRED_13.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_13-(1-0.98)*%6)/0.98 LSFCRED_14.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_14-(1-0.98)*%7)/0.98

STEP_4 Computation of Surface temperature of each band,K T_10.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(8.29*LN(((3.74E+08*1)/(LSFCRED_10*PI*(8.29^5)*0.001))+1)) T_11.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(8.63*LN(((3.74E+08*1)/(LSFCRED_11*PI*(8.63^5)*0.001))+1)) T_12.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(9.09*LN(((3.74E+08*1)/(LSFCRED_12*PI*(9.09^5)*0.001))+1)) T_13.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(10.66*LN(((3.74E+08*1)/(LSFCRED_13*PI*(10.66^5)*0.001))+1)) T_14.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(11.29*LN(((3.74E+08*1)/(LSFCRED_14*PI*(11.29^5)*0.001))+1))

STEP_5 Computation of maximum Surface temperature from STEP_4 above, K TEMP_1.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=MAX(T_10,T_11,T_12) TEMP_2.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=MAX(T_13,T_14) TEMP_MAX.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=MAX(TEMP_1,TEMP_2)

STEP_6 Computation of spectral radiance of black body of each ASTER thermal bands using the maximum temperature computed in STEP_5 above RAD_TMAX_10.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((8.29)^5*PI*(EXP(1.44E+04/(8.29*TEMP_MAX))-1))) RAD_TMAX_11.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((8.63)^5*PI*(EXP(1.44E+04/(8.63*TEMP_MAX))-1))) RAD_TMAX_12.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((9.09)^5*PI*(EXP(1.44E+04/(9.09*TEMP_MAX))-1))) RAD_TMAX_13.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((10.66)^5*PI*(EXP(1.44E+04/(10.66*TEMP_MAX))-1))) RAD_TMAX_14.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((11.29)^5*PI*(EXP(1.44E+04/(11.29*TEMP_MAX))-1)))

STEP_7 Computation of tentative emissivities of each ASTER thermal bands EMISSIVITYTENT_10.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=LSFC_10/RAD_TMAX_10 EMISSIVITYTENT_11.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=LSFC_11/RAD_TMAX_11 EMISSIVITYTENT_12.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=LSFC_12/RAD_TMAX_12 EMISSIVITYTENT_13.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=LSFC_13/RAD_TMAX_13 EMISSIVITYTENT_14.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=LSFC_14/RAD_TMAX_14

STEP_8 Computation of realitive emissivities of each ASTER thermal bands BETA_IMAGE10.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=%3/RAD_TMAX_10 BETA_IMAGE11.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=%4/RAD_TMAX_11 BETA_IMAGE12.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=%5/RAD_TMAX_12 BETA_IMAGE13.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=%6/RAD_TMAX_13 BETA_IMAGE14.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=%7/RAD_TMAX_14



STEP_9 Computation of emissivities for each ASTER thermal bands using STEP_7 & STEP_8 above EMISSIVITY_10.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=(EMISSIVITYTENT_10-BETA_IMAGE10)/(1-BETA_IMAGE10) EMISSIVITY_11.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=(EMISSIVITYTENT_11-BETA_IMAGE11)/(1-BETA_IMAGE11) EMISSIVITY_12.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=(EMISSIVITYTENT_12-BETA_IMAGE12)/(1-BETA_IMAGE12) EMISSIVITY_13.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=(EMISSIVITYTENT_13-BETA_IMAGE13)/(1-BETA_IMAGE13) EMISSIVITY_14.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=(EMISSIVITYTENT_14-BETA_IMAGE14)/(1-BETA_IMAGE14)

STEP_10 Computation of radiances from the ground surface after correction for atmospheric effects including the reflected sky brightness LEM_10.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_10-(1-EMISSIVITY_10)*%3 LEM_11.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_11-(1-EMISSIVITY_11)*%4 LEM_12.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_12-(1-EMISSIVITY_12)*%5 LEM_13.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_13-(1-EMISSIVITY_13)*%6 LEM_14.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_14-(1-EMISSIVITY_14)*%7

STEP_11 Computations of the average radiances from the ground surfaces and the average spectral radiance of black body using STEP_10 &STEP_6 respectively AVG_LEM.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=(LEM_10+LEM_11+LEM_12+LEM_13+LEM_14)/5 AVGRAD_TMAX.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=(RAD_TMAX_10+RAD_TMAX_11+RAD_TMAX_12+RAD_TMAX_13+RAD_TMAX_14)/5

STEP_12 Computations of relative emissivities of each ASTER thermal band using STEP_10,STEP_11 & STEP_6 BETA_10.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEM_10/AVG_LEM)*(AVGRAD_TMAX/RAD_TMAX_10) BETA_11.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEM_11/AVG_LEM)*(AVGRAD_TMAX/RAD_TMAX_11) BETA_12.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEM_12/AVG_LEM)*(AVGRAD_TMAX/RAD_TMAX_12) BETA_13.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEM_13/AVG_LEM)*(AVGRAD_TMAX/RAD_TMAX_13) BETA_14.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEM_14/AVG_LEM)*(AVGRAD_TMAX/RAD_TMAX_14)

STEP_13 Computations of maximum and minimum relative emissivities using STEP_12 BETA_MAX1.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MAX(BETA_10,BETA_11,BETA_12) BETA_MAX2.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MAX(BETA_13,BETA_14) BETA_MAX.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MAX(BETA_MAX1,BETA_MAX2) BETA_MIN1.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MIN(BETA_10,BETA_11,BETA_12) BETA_MIN2.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MIN(BETA_13,BETA_14) BETA_MIN.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MIN(BETA_MIN1,BETA_MIN2)

STEP_14 Computation of maximum-minimum differences using STEP_13 MMD.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=BETA_MAX-BETA_MIN

STEP_15 Computation of minimum emissivity using STEP_14 EMISSIVITY_MIN.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=0.994-0.687*(MMD)^0.737



STEP_16 revised emissivities of each ASTER theraml bands using STEP_12, STEP_15 &STEP_13 EMISSIVITYREV_10.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETA_10*(EMISSIVITY_MIN/BETA_MIN) EMISSIVITYREV_11.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETA_11*(EMISSIVITY_MIN/BETA_MIN) EMISSIVITYREV_12.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETA_12*(EMISSIVITY_MIN/BETA_MIN) EMISSIVITYREV_13.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETA_13*(EMISSIVITY_MIN/BETA_MIN) EMISSIVITYREV_14.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETA_14*(EMISSIVITY_MIN/BETA_MIN)

STEP_17 Computation of maximum emissivity from STEP_16 EMISSIVITY_MAX1.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=MAX(EMISSIVITYREV_10,EMISSIVITYREV_11,EMISSIVITYREV_12) EMISSIVITY_MAX2.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=MAX(EMISSIVITYREV_13,EMISSIVITYREV_14) EMISSIVITYREV_MAX.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=MAX(EMISSIVITY_MAX1,EMISSIVITY_MAX2) del LSFCRED_*.* -force del T_*.* -force del TEMP_*.* -force del RAD_TMAX_*.* -force del EMISSIVITYTENT_*.* -force del BETA_*.* -force del EMISSIVITY_*.* -force del LEM_*.* -force del AVG_*.* -force del AVGRAD_*.* -force del MMD.* -force

TEMPERATURE-EMISSIVITY SEPARATION ALGORITHM ITERATION Parameters: %1 Ldn_Band10 %2 Ldn_Band11 %3 Ldn_Band12 %4 Ldn_Band13 %5 Ldn_Band14 TES ALGORITHM ITERATION ONE

STEP_18 Computation of revised_one radiances from the ground surface after correction for atmospheric effects including the reflected sky brightness using STEP_16 LEMREV1_10.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_10-(1-EMISSIVITYREV_10)*%1 LEMREV1_11.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_11-(1-EMISSIVITYREV_11)*%2 LEMREV1_12.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_12-(1-EMISSIVITYREV_12)*%3 LEMREV1_13.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_13-(1-EMISSIVITYREV_13)*%4 LEMREV1_14.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_14-(1-EMISSIVITYREV_14)*%5



STEP_19 Computaion of revised_one spectral radiance from a black body at surfacd temperature T,Wm-2sr-1mm-1 using STEP_3 and STEP_17 LSFCREDREV1_10.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_10-(1-MISSIVITYREV_MAX)*%1)/MISSIVITYREV_MAX LSFCREDREV1_11.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_11-(1-MISSIVITYREV_MAX)*%2)/MISSIVITYREV_MAX LSFCREDREV1_12.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_12-(1-MISSIVITYREV_MAX)*%3)/MISSIVITYREV_MAX LSFCREDREV1_13.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_13-(1-MISSIVITYREV_MAX)*%4)/MISSIVITYREV_MAX LSFCREDREV1_14.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_14-(1-MISSIVITYREV_MAX)*%5)/MISSIVITYREV_MAX

STEP_20 Computation of revised_one surface temperature of each ASTER thermal bands using STEP_19 TREV1_10.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(8.29*LN(((3.74E+08*1)/(LSFCREDREV1_10*PI*(8.29^5)*0.001))+1)) TREV1_11.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(8.63*LN(((3.74E+08*1)/(LSFCREDREV1_11*PI*(8.63^5)*0.001))+1)) TREV1_12.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(9.09*LN(((3.74E+08*1)/(LSFCREDREV1_12*PI*(9.09^5)*0.001))+1)) TREV1_13.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(10.66*LN(((3.74E+08*1)/(LSFCREDREV1_13*PI*(10.66^5)*0.001))+1)) TREV1_14.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(11.29*LN(((3.74E+08*1)/(LSFCREDREV1_14*PI*(11.29^5)*0.001))+1))

STEP_21 Computation of revised_one maximum surface temperature using STEP_20 TEMPREV1_1.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=MAX(TREV1_10,TREV1_11,TREV1_12) TEMPREV1_2.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=MAX(TREV1_13,TREV1_14) TEMPREV1_MAX.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=MAX(TEMPREV1_1,TEMPREV1_2)

STEP_22 Computation of revised_one spectral radiance of black body of each ASTER thermal bands using the maximum temperature computed in STEP_21 above RADREV1_TMAX_10.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((8.29)^5*PI*(EXP(1.44E+04/(8.29*TEMPREV1_MAX))-1))) RADREV1_TMAX_11.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((8.63)^5*PI*(EXP(1.44E+04/(8.63*TEMPREV1_MAX))-1))) RADREV1_TMAX_12.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((9.09)^5*PI*(EXP(1.44E+04/(9.09*TEMPREV1_MAX))-1))) RADREV1_TMAX_13.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((10.66)^5*PI*(EXP(1.44E+04/(10.66*TEMPREV1_MAX))-1))) RADREV1_TMAX_14.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((11.29)^5*PI*(EXP(1.44E+04/(11.29*TEMPREV1_MAX))-1)))



STEP_23 Computations of the revised _one average radiances from the ground surfaces and the average spectral radiance of black body using STEP_18 &STEP_22 respectively AVG1_LEM.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=(LEMREV1_10+LEMREV1_11+LEMREV1_12+LEMREV1_13+LEMREV1_14)/5 AVGRAD1_TMAX.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=(RADREV1_TMAX_10+RADREV1_TMAX_11+RADREV1_TMAX_12+RADREV1_TMAX_13+RADREV1_TMAX_14)/5

STEP_24 Computations of relative revised_one emissivities of each ASTER thermal band using STEP_18,STEP_23 & STEP_22 BETAREV1_10.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV1_10/AVG1_LEM)*(AVGRAD1_TMAX/RADREV1_TMAX_10) BETAREV1_11.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV1_11/AVG1_LEM)*(AVGRAD1_TMAX/RADREV1_TMAX_11) BETAREV1_12.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV1_12/AVG1_LEM)*(AVGRAD1_TMAX/RADREV1_TMAX_12) BETAREV1_13.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV1_13/AVG1_LEM)*(AVGRAD1_TMAX/RADREV1_TMAX_13) BETAREV1_14.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV1_14/AVG1_LEM)*(AVGRAD1_TMAX/RADREV1_TMAX_14)

STEP_25 Computations of revised_one maximum and minimum relative emissivities using STEP_24 BETAREV1_MAX1.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MAX(BETAREV1_10,BETAREV1_11,BETAREV1_12) BETAREV1_MAX2.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MAX(BETAREV1_13,BETAREV1_14) BETAREV1_MAX.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MAX(BETAREV1_MAX1,BETAREV1_MAX2) BETAREV1_MIN1.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MIN(BETAREV1_10,BETAREV1_11,BETAREV1_12) BETAREV1_MIN2.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MIN(BETAREV1_13,BETAREV1_14) BETAREV1_MIN.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MIN(BETAREV1_MIN1,BETAREV1_MIN1)

STEP_26 Computation of revised_one maximum-minimum differences using STEP_25 MMDREV1.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=BETAREV1_MAX-BETAREV1_MIN

STEP_27 Computation of revised_one minimum emissivity using STEP_26 EMISSIVITYREV1_MIN.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=0.994-0.687*(MMDREV1)^0.737

STEP_28 revised_one emissivities of each ASTER thermal bands using STEP_24, STEP_27 &STEP_25 EMISSIVITYREV1_10.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV1_10*(EMISSIVITYREV1_MIN/BETAREV1_MIN) EMISSIVITYREV1_11.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV1_11*(EMISSIVITYREV1_MIN/BETAREV1_MIN) EMISSIVITYREV1_12.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV1_12*(EMISSIVITYREV1_MIN/BETAREV1_MIN) EMISSIVITYREV1_13.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV1_13*(EMISSIVITYREV1_MIN/BETAREV1_MIN) EMISSIVITYREV1_14.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV1_14*(EMISSIVITYREV1_MIN/BETAREV1_MIN)



STEP_29 Computation of revised_one maximum emissivity from STEP_28 EMISSIVITYREV1_MAX1.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=MAX(EMISSIVITYREV1_10,EMISSIVITYREV1_11,EMISSIVITYREV1_12) EMISSIVITYREV1_MAX2.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=MAX(EMISSIVITYREV1_13,EMISSIVITYREV1_14) EMISSIVITYREV1_MAX.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=MAX(EMISSIVITYREV1_MAX1,EMISSIVITYREV1_MAX2) del LEMREV1_*.* -force del LSFCREDREV1_*.* -force del TREV1_*.* -force del TEMPREV1_*.* -force del RADREV1_TMAX_*.* -force del AVG1_LEM.* -force del AVGRAD1_TMAX*.* -force del BETAREV1_*.* -force del MMDREV1.* -force del EMISSIVITYREV1_MIN.* -force

TES ALGORITHM ITERATION TWO LEMREV2_10.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_10-(1-EMISSIVITYREV1_10)*%1 LEMREV2_11.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_11-(1-EMISSIVITYREV1_11)*%2 LEMREV2_12.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_12-(1-EMISSIVITYREV1_12)*%3 LEMREV2_13.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_13-(1-EMISSIVITYREV1_13)*%4 LEMREV2_14.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_14-(1-EMISSIVITYREV1_14)*%5 LSFCREDREV2_10.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_10-(1-EMISSIVITYREV1_MAX)*%1)/EMISSIVITYREV1_MAX LSFCREDREV2_11.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_11-(1-EMISSIVITYREV1_MAX)*%2)/EMISSIVITYREV1_MAX LSFCREDREV2_12.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_12-(1-EMISSIVITYREV1_MAX)*%3)/EMISSIVITYREV1_MAX LSFCREDREV2_13.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_13-(1-EMISSIVITYREV1_MAX)*%4)/EMISSIVITYREV1_MAX LSFCREDREV2_14.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_14-(1-EMISSIVITYREV1_MAX)*%5)/EMISSIVITYREV1_MAX TREV2_10.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(8.29*LN(((3.74E+08*1)/(LSFCREDREV2_10*PI*(8.29^5)*0.001))+1)) TREV2_11.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(8.63*LN(((3.74E+08*1)/(LSFCREDREV2_11*PI*(8.63^5)*0.001))+1)) TREV2_12.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(9.09*LN(((3.74E+08*1)/(LSFCREDREV2_12*PI*(9.09^5)*0.001))+1)) TREV2_13.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(10.66*LN(((3.74E+08*1)/(LSFCREDREV2_13*PI*(10.66^5)*0.001))+1)) TREV2_14.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(11.29*LN(((3.74E+08*1)/(LSFCREDREV2_14*PI*(11.29^5)*0.001))+1))



TEMPREV2_1.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=MAX(TREV2_10,TREV2_11,TREV2_12) TEMPREV2_2.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=MAX(TREV2_13,TREV2_14) TEMPREV2_MAX.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=MAX(TEMPREV2_1,TEMPREV2_2) RADREV2_TMAX_10.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((8.29)^5*PI*(EXP(1.44E+04/(8.29*TEMPREV2_MAX))-1))) RADREV2_TMAX_11.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((8.63)^5*PI*(EXP(1.44E+04/(8.63*TEMPREV2_MAX))-1))) RADREV2_TMAX_12.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((9.09)^5*PI*(EXP(1.44E+04/(9.09*TEMPREV2_MAX))-1))) RADREV2_TMAX_13.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((10.66)^5*PI*(EXP(1.44E+04/(10.66*TEMPREV2_MAX))-1))) RADREV2_TMAX_14.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((11.29)^5*PI*(EXP(1.44E+04/(11.29*TEMPREV2_MAX))-1))) AVG2_LEM.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=(LEMREV2_10+LEMREV2_11+LEMREV2_12+LEMREV2_13+LEMREV2_14)/5 AVGRAD2_TMAX.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=(RADREV2_TMAX_10+RADREV2_TMAX_11+RADREV2_TMAX_12+RADREV2_TMAX_13+RADREV2_TMAX_14)/5 BETAREV2_10.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV2_10/AVG2_LEM)*(AVGRAD2_TMAX/RADREV2_TMAX_10) BETAREV2_11.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV2_11/AVG2_LEM)*(AVGRAD2_TMAX/RADREV2_TMAX_11) BETAREV2_12.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV2_12/AVG2_LEM)*(AVGRAD2_TMAX/RADREV2_TMAX_12) BETAREV2_13.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV2_13/AVG2_LEM)*(AVGRAD2_TMAX/RADREV2_TMAX_13) BETAREV2_14.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV2_14/AVG2_LEM)*(AVGRAD2_TMAX/RADREV2_TMAX_14) BETAREV2_MAX1.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MAX(BETAREV2_10,BETAREV2_11,BETAREV2_12) BETAREV2_MAX2.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MAX(BETAREV2_13,BETAREV2_14) BETAREV2_MAX.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MAX(BETAREV2_MAX1,BETAREV2_MAX2) BETAREV2_MIN1.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MIN(BETAREV2_10,BETAREV2_11,BETAREV2_12) BETAREV2_MIN2.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MIN(BETAREV2_13,BETAREV2_14) BETAREV2_MIN.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MIN(BETAREV2_MIN1,BETAREV2_MIN1) MMDREV2.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=BETAREV2_MAX-BETAREV2_MIN EMISSIVITYREV2_MIN.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=0.994-0.687*(MMDREV2)^0.737 EMISSIVITYREV2_10.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV2_10*(EMISSIVITYREV2_MIN/BETAREV2_MIN) EMISSIVITYREV2_11.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV2_11*(EMISSIVITYREV2_MIN/BETAREV2_MIN) EMISSIVITYREV2_12.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV2_12*(EMISSIVITYREV2_MIN/BETAREV2_MIN) EMISSIVITYREV2_13.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV2_13*(EMISSIVITYREV2_MIN/BETAREV2_MIN) EMISSIVITYREV2_14.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV2_14*(EMISSIVITYREV2_MIN/BETAREV2_MIN) EMISSIVITYREV2_MAX1.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=MAX(EMISSIVITYREV2_10,EMISSIVITYREV2_11,EMISSIVITYREV2_12) EMISSIVITYREV2_MAX2.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=MAX(EMISSIVITYREV2_13,EMISSIVITYREV2_14) EMISSIVITYREV2_MAX.mpr{dom=Value.dom;vr=-1.00:1:0.001}:=MAX(EMISSIVITYREV2_MAX1,EMISSIVITYREV2_MAX2)



del LEMREV2_*.* -force del LSFCREDREV2_*.* -force del TREV2_*.* -force del TEMPREV2_*.* -force del RADREV2_TMAX_*.* -force del AVG1_LEM.* -force del AVGRAD2_TMAX*.* -force del BETAREV2_*.* -force del MMDREV2.* -force del EMISSIVITYREV2_MIN.* -force

TES ALGORITHM ITERATION THREE. LEMREV3_10.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_10-(1-EMISSIVITYREV2_10)*%1 LEMREV3_11.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_11-(1-EMISSIVITYREV2_11)*%2 LEMREV3_12.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_12-(1-EMISSIVITYREV2_12)*%3 LEMREV3_13.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_13-(1-EMISSIVITYREV2_13)*%4 LEMREV3_14.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_14-(1-EMISSIVITYREV2_14)*%5 LSFCREDREV3_10.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_10-(1-EMISSIVITYREV2_MAX)*%1)/EMISSIVITYREV2_MAX LSFCREDREV3_11.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_11-(1-EMISSIVITYREV2_MAX)*%2)/EMISSIVITYREV2_MAX LSFCREDREV3_12.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_12-(1-EMISSIVITYREV2_MAX)*%3)/EMISSIVITYREV2_MAX LSFCREDREV3_13.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_13-(1-EMISSIVITYREV2_MAX)*%4)/EMISSIVITYREV2_MAX LSFCREDREV3_14.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_14-(1-EMISSIVITYREV2_MAX)*%5)/EMISSIVITYREV2_MAX TREV3_10.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(8.29*LN(((3.74E+08*1)/(LSFCREDREV3_10*PI*(8.29^5)*0.001))+1)) TREV3_11.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(8.63*LN(((3.74E+08*1)/(LSFCREDREV3_11*PI*(8.63^5)*0.001))+1)) TREV3_12.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(9.09*LN(((3.74E+08*1)/(LSFCREDREV3_12*PI*(9.09^5)*0.001))+1)) TREV3_13.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(10.66*LN(((3.74E+08*1)/(LSFCREDREV3_13*PI*(10.66^5)*0.001))+1)) TREV3_14.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(11.29*LN(((3.74E+08*1)/(LSFCREDREV3_14*PI*(11.29^5)*0.001))+1)) TEMPREV3_1.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=MAX(TREV3_10,TREV3_11,TREV3_12) TEMPREV3_2.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=MAX(TREV3_13,TREV3_14) TEMPREV3_MAX.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=MAX(TEMPREV3_1,TEMPREV3_2) RADREV3_TMAX_10.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((8.29)^5*PI*(EXP(1.44E+04/(8.29*TEMPREV3_MAX))-1))) RADREV3_TMAX_11.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((8.63)^5*PI*(EXP(1.44E+04/(8.63*TEMPREV3_MAX))-1))) RADREV3_TMAX_12.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((9.09)^5*PI*(EXP(1.44E+04/(9.09*TEMPREV3_MAX))-1))) RADREV3_TMAX_13.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((10.66)^5*PI*(EXP(1.44E+04/(10.66*TEMPREV3_MAX))-1))) RADREV3_TMAX_14.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((11.29)^5*PI*(EXP(1.44E+04/(11.29*TEMPREV3_MAX))-1))) AVG3_LEM.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=(LEMREV3_10+LEMREV3_11+LEMREV3_12+LEMREV3_13+LEMREV3_14)/5 AVGRAD3_TMAX.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=(RADREV3_TMAX_10+RADREV3_TMAX_11+RADREV3_TMAX_12+RADREV3_TMAX_13+RADREV3_TMAX_14)/5 BETAREV3_10.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV3_10/AVG3_LEM)*(AVGRAD3_TMAX/RADREV3_TMAX_10) BETAREV3_11.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV3_11/AVG3_LEM)*(AVGRAD3_TMAX/RADREV3_TMAX_11) BETAREV3_12.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV3_12/AVG3_LEM)*(AVGRAD3_TMAX/RADREV3_TMAX_12) BETAREV3_13.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV3_13/AVG3_LEM)*(AVGRAD3_TMAX/RADREV3_TMAX_13) BETAREV3_14.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV3_14/AVG3_LEM)*(AVGRAD3_TMAX/RADREV3_TMAX_14)



BETAREV3_MAX1.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MAX(BETAREV3_10,BETAREV3_11,BETAREV3_12) BETAREV3_MAX2.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MAX(BETAREV3_13,BETAREV3_14) BETAREV3_MAX.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MAX(BETAREV3_MAX1,BETAREV3_MAX2) BETAREV3_MIN1.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MIN(BETAREV3_10,BETAREV3_11,BETAREV3_12) BETAREV3_MIN2.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MIN(BETAREV3_13,BETAREV3_14) BETAREV3_MIN.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MIN(BETAREV3_MIN1,BETAREV3_MIN1) MMDREV3.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=BETAREV3_MAX-BETAREV3_MIN EMISSIVITYREV3_MIN.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=0.994-0.687*(MMDREV3)^0.737 EMISSIVITYREV3_10.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV3_10*(EMISSIVITYREV3_MIN/BETAREV3_MIN) EMISSIVITYREV3_11.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV3_11*(EMISSIVITYREV3_MIN/BETAREV3_MIN) EMISSIVITYREV3_12.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV3_12*(EMISSIVITYREV3_MIN/BETAREV3_MIN) EMISSIVITYREV3_13.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV3_13*(EMISSIVITYREV3_MIN/BETAREV3_MIN) EMISSIVITYREV3_14.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV3_14*(EMISSIVITYREV3_MIN/BETAREV3_MIN) EMISSIVITYREV3_MAX1.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=MAX(EMISSIVITYREV3_10,EMISSIVITYREV3_11,EMISSIVITYREV3_12) EMISSIVITYREV3_MAX2.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=MAX(EMISSIVITYREV3_13,EMISSIVITYREV3_14) EMISSIVITYREV3_MAX.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=MAX(EMISSIVITYREV3_MAX1,EMISSIVITYREV3_MAX2) del LEMREV3_*.* -force del LSFCREDREV3_*.* -force del TREV3_*.* -force del TEMPREV3_*.* -force del RADREV3_TMAX_*.* -force del AVG3_LEM.* -force del AVGRAD3_TMAX*.* -force del BETAREV3_*.* -force del MMDREV3.* -force del EMISSIVITYREV3_MIN.* -force

TES ALGORITHM ITERATION FOUR. LEMREV4_10.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_10-(1-EMISSIVITYREV3_10)*%1 LEMREV4_11.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_11-(1-EMISSIVITYREV3_11)*%2 LEMREV4_12.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_12-(1-EMISSIVITYREV3_12)*%3 LEMREV4_13.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_13-(1-EMISSIVITYREV3_13)*%4 LEMREV4_14.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_14-(1-EMISSIVITYREV3_14)*%5 LSFCREDREV4_10.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_10-(1-EMISSIVITYREV3_MAX)*%1)/EMISSIVITYREV3_MAX LSFCREDREV4_11.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_11-(1-EMISSIVITYREV3_MAX)*%2)/EMISSIVITYREV3_MAX LSFCREDREV4_12.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_12-(1-EMISSIVITYREV3_MAX)*%3)/EMISSIVITYREV3_MAX LSFCREDREV4_13.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_13-(1-EMISSIVITYREV3_MAX)*%4)/EMISSIVITYREV3_MAX LSFCREDREV4_14.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_14-(1-EMISSIVITYREV3_MAX)*%5)/EMISSIVITYREV3_MAX TREV4_10.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(8.29*LN(((3.74E+08*1)/(LSFCREDREV4_10*PI*(8.29^5)*0.001))+1)) TREV4_11.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(8.63*LN(((3.74E+08*1)/(LSFCREDREV4_11*PI*(8.63^5)*0.001))+1)) TREV4_12.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(9.09*LN(((3.74E+08*1)/(LSFCREDREV4_12*PI*(9.09^5)*0.001))+1)) TREV4_13.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(10.66*LN(((3.74E+08*1)/(LSFCREDREV4_13*PI*(10.66^5)*0.001))+1))



TREV4_14.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(11.29*LN(((3.74E+08*1)/(LSFCREDREV4_14*PI*(11.29^5)*0.001))+1)) TEMPREV4_1.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=MAX(TREV4_10,TREV4_11,TREV4_12) TEMPREV4_2.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=MAX(TREV4_13,TREV4_14) TEMPREV4_MAX.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=MAX(TEMPREV4_1,TEMPREV4_2) RADREV4_TMAX_10.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((8.29)^5*PI*(EXP(1.44E+04/(8.29*TEMPREV4_MAX))-1))) RADREV4_TMAX_11.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((8.63)^5*PI*(EXP(1.44E+04/(8.63*TEMPREV4_MAX))-1))) RADREV4_TMAX_12.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((9.09)^5*PI*(EXP(1.44E+04/(9.09*TEMPREV4_MAX))-1))) RADREV4_TMAX_13.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((10.66)^5*PI*(EXP(1.44E+04/(10.66*TEMPREV4_MAX))-1))) RADREV4_TMAX_14.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((11.29)^5*PI*(EXP(1.44E+04/(11.29*TEMPREV4_MAX))-1))) AVG4_LEM.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=(LEMREV4_10+LEMREV4_11+LEMREV4_12+LEMREV4_13+LEMREV4_14)/5 AVGRAD4_TMAX.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=(RADREV4_TMAX_10+RADREV4_TMAX_11+RADREV4_TMAX_12+RADREV4_TMAX_13+RADREV4_TMAX_14)/5



BETAREV4_10.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV4_10/AVG4_LEM)*(AVGRAD4_TMAX/RADREV4_TMAX_10) BETAREV4_11.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV4_11/AVG4_LEM)*(AVGRAD4_TMAX/RADREV4_TMAX_11) BETAREV4_12.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV4_12/AVG4_LEM)*(AVGRAD4_TMAX/RADREV4_TMAX_12) BETAREV4_13.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV4_13/AVG4_LEM)*(AVGRAD4_TMAX/RADREV4_TMAX_13) BETAREV4_14.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV4_14/AVG4_LEM)*(AVGRAD4_TMAX/RADREV4_TMAX_14) BETAREV4_MAX1.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MAX(BETAREV4_10,BETAREV4_11,BETAREV4_12) BETAREV4_MAX2.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MAX(BETAREV4_13,BETAREV4_14) BETAREV4_MAX.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MAX(BETAREV4_MAX1,BETAREV4_MAX2) BETAREV4_MIN1.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MIN(BETAREV4_10,BETAREV4_11,BETAREV4_12) BETAREV4_MIN2.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MIN(BETAREV4_13,BETAREV4_14) BETAREV4_MIN.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MIN(BETAREV4_MIN1,BETAREV4_MIN1) MMDREV4.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=BETAREV4_MAX-BETAREV4_MIN EMISSIVITYREV4_MIN.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=0.994-0.687*(MMDREV4)^0.737 EMISSIVITYREV4_10.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV4_10*(EMISSIVITYREV4_MIN/BETAREV4_MIN) EMISSIVITYREV4_11.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV4_11*(EMISSIVITYREV4_MIN/BETAREV4_MIN) EMISSIVITYREV4_12.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV4_12*(EMISSIVITYREV4_MIN/BETAREV4_MIN) EMISSIVITYREV4_13.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV4_13*(EMISSIVITYREV4_MIN/BETAREV4_MIN) EMISSIVITYREV4_14.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV4_14*(EMISSIVITYREV4_MIN/BETAREV4_MIN) EMISSIVITYREV4_MAX1.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=MAX(EMISSIVITYREV4_10,EMISSIVITYREV4_11,EMISSIVITYREV4_12) EMISSIVITYREV4_MAX2.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=MAX(EMISSIVITYREV4_13,EMISSIVITYREV4_14) EMISSIVITYREV4_MAX.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=MAX(EMISSIVITYREV4_MAX1,EMISSIVITYREV4_MAX2) del LEMREV4_*.* -force del LSFCREDREV4_*.* -force del TREV4_*.* -force del RADREV4_TMAX_*.* -force del AVG4_LEM.* -force del AVGRAD4_TMAX*.* -force



TES ALGORITHM ITERATION FIVE. LEMREV5_10.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_10-(1-EMISSIVITYREV4_10)*%1 LEMREV5_11.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_11-(1-EMISSIVITYREV4_11)*%2 LEMREV5_12.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_12-(1-EMISSIVITYREV4_12)*%3 LEMREV5_13.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_13-(1-EMISSIVITYREV4_13)*%4 LEMREV5_14.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=LSFC_14-(1-EMISSIVITYREV4_14)*%5 LSFCREDREV5_10.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_10-(1-EMISSIVITYREV4_MAX)*%1)/EMISSIVITYREV4_MAX LSFCREDREV5_11.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_11-(1-EMISSIVITYREV4_MAX)*%2)/EMISSIVITYREV4_MAX LSFCREDREV5_12.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_12-(1-EMISSIVITYREV4_MAX)*%3)/EMISSIVITYREV4_MAX LSFCREDREV5_13.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_13-(1-EMISSIVITYREV4_MAX)*%4)/EMISSIVITYREV4_MAX LSFCREDREV5_14.mpr{dom=Value.dom;vr=-100.00:20000.00:0.001}:=(LSFC_14-(1-EMISSIVITYREV4_MAX)*%5)/EMISSIVITYREV4_MAX TREV5_10.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(8.29*LN(((3.74E+08*1)/(LSFCREDREV5_10*PI*(8.29^5)*0.001))+1)) TREV5_11.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(8.63*LN(((3.74E+08*1)/(LSFCREDREV5_11*PI*(8.63^5)*0.001))+1)) TREV5_12.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(9.09*LN(((3.74E+08*1)/(LSFCREDREV5_12*PI*(9.09^5)*0.001))+1)) TREV5_13.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(10.66*LN(((3.74E+08*1)/(LSFCREDREV5_13*PI*(10.66^5)*0.001))+1)) TREV5_14.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=1.44E+04/(11.29*LN(((3.74E+08*1)/(LSFCREDREV5_14*PI*(11.29^5)*0.001))+1)) TEMPREV5_1.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=MAX(TREV5_10,TREV5_11,TREV5_12) TEMPREV5_2.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=MAX(TREV5_13,TREV5_14) TEMPREV5_MAX.mpr{dom=Value.dom;vr=-100.00:1000.00:0.001}:=MAX(TEMPREV5_1,TEMPREV5_2) RADREV5_TMAX_10.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((8.29)^5*PI*(EXP(1.44E+04/(8.29*TEMPREV5_MAX))-1))) RADREV5_TMAX_11.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((8.63)^5*PI*(EXP(1.44E+04/(8.63*TEMPREV5_MAX))-1))) RADREV5_TMAX_12.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((9.09)^5*PI*(EXP(1.44E+04/(9.09*TEMPREV5_MAX))-1))) RADREV5_TMAX_13.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((10.66)^5*PI*(EXP(1.44E+04/(10.66*TEMPREV5_MAX))-1))) RADREV5_TMAX_14.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=1000*((3.74E+08*1)/((11.29)^5*PI*(EXP(1.44E+04/(11.29*TEMPREV5_MAX))-1))) AVG5_LEM.mpr{dom=Value.dom;vr=-5000.00:30000.00:0.001}:=(LEMREV5_10+LEMREV5_11+LEMREV5_12+LEMREV5_13+LEMREV5_14)/5 AVGRAD5_TMAX.mpr{dom=Value.dom;vr=-100.00:30000.00:0.001}:=(RADREV5_TMAX_10+RADREV5_TMAX_11+RADREV5_TMAX_12+RADREV5_TMAX_13+RADREV5_TMAX_14)/5



BETAREV5_10.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV5_10/AVG5_LEM)*(AVGRAD5_TMAX/RADREV5_TMAX_10) BETAREV5_11.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV5_11/AVG5_LEM)*(AVGRAD5_TMAX/RADREV5_TMAX_11) BETAREV5_12.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV5_12/AVG5_LEM)*(AVGRAD5_TMAX/RADREV5_TMAX_12) BETAREV5_13.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV5_13/AVG5_LEM)*(AVGRAD5_TMAX/RADREV5_TMAX_13) BETAREV5_14.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=(LEMREV5_14/AVG5_LEM)*(AVGRAD5_TMAX/RADREV5_TMAX_14) BETAREV5_MAX1.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MAX(BETAREV5_10,BETAREV5_11,BETAREV5_12) BETAREV5_MAX2.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MAX(BETAREV5_13,BETAREV5_14) BETAREV5_MAX.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MAX(BETAREV5_MAX1,BETAREV5_MAX2) BETAREV5_MIN1.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MIN(BETAREV5_10,BETAREV5_11,BETAREV5_12) BETAREV5_MIN2.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MIN(BETAREV5_13,BETAREV5_14) BETAREV5_MIN.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=MIN(BETAREV5_MIN1,BETAREV5_MIN1) MMDREV5.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=BETAREV5_MAX-BETAREV5_MIN EMISSIVITYREV5_MIN.mpr{dom=Value.dom;vr=-1.00:10.00:0.001}:=0.994-0.687*(MMDREV5)^0.737 EMISSIVITYREV5_10.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV5_10*(EMISSIVITYREV5_MIN/BETAREV5_MIN) EMISSIVITYREV5_11.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV5_11*(EMISSIVITYREV5_MIN/BETAREV5_MIN) EMISSIVITYREV5_12.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV5_12*(EMISSIVITYREV5_MIN/BETAREV5_MIN) EMISSIVITYREV5_13.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV5_13*(EMISSIVITYREV5_MIN/BETAREV5_MIN) EMISSIVITYREV5_14.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=BETAREV5_14*(EMISSIVITYREV5_MIN/BETAREV5_MIN) EMISSIVITYREV5_MAX1.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=MAX(EMISSIVITYREV5_10,EMISSIVITYREV5_11,EMISSIVITYREV5_12) EMISSIVITYREV5_MAX2.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=MAX(EMISSIVITYREV5_13,EMISSIVITYREV5_14) EMISSIVITYREV5_MAX.mpr{dom=Value.dom;vr=-1.00:1.00:0.001}:=MAX(EMISSIVITYREV5_MAX1,EMISSIVITYREV5_MAX2) del LEMREV5_*.* -force del LSFCREDREV5_*.* -force del TREV5_*.* -force del RADREV5_TMAX_*.* -force del AVG5_LEM.* -force del AVGRAD5_TMAX*.* -force



APPENDIX D 1: ILWIS SCRIPT USED TO ESTIMATE SURFACE TEMPERATURE USING LANDSAT 7.



ILWIS SCRIPT 2 Short Summary of the codes; map names etc. used in the ILWIS scripts USING LANDSAT 7:

Step I: Pre-processing Parameters: %1 Local Standard time 10.25 %2 Julian day no. 51 %3 Standard Meridian 30 Latitude and Longitude maps in degree decimal: “lati” = Map of Latitude in degree decimal “long” = Map of Longitude in degree decimal The hour angle θ, and the cosine of the solar zenith angle cos (θz): “DA_map” = day angle map DA = function to calculate day angle [radian] = 0.01721420632*(a-1) Where, a = Julian day no. “Delta” = map of solar declination of the day in [radian] DE = function to calculate solar declination [radian] = (0.006918-0.399912*cos(a)+0.070257*sin(a)-0.006758*cos(2*a)+0.000907*sin(2*a)-0.002697*cos(3*a)+0.00148*sin(3*a)) Where, a = DA “Lc” = Map of longitude correction in minutes “LAT” = Map of local apparent time in hours ET = function to calculate equation of time [minutes] = (0.000075+0.001868*cos(a)-0.032077*sin(a)-0.014615*cos(2*a)-0.04089*sin(2*a))*229.18 Where, a = DA “w” = Map of hour angel in degree “COS_Zen” = Map of COS of solar zenith angle The exo-atmospheric irradiance for the time of satellite overpass: “Kexo” = Map of Instantaneous exo-atmospheric incoming irradiance (Wm-2) Solar constant = 1367 Wm-2 EO = function to calculate eccentricity correction factor for the day =1.00011+0.034221*cos(a)+0.00128*sin(a)+0.000719*cos(2*a)+0.000077*sin(2*a) Where, a = DA



The broadband albedo: Radiances per band Coefficients used for calibration: Spectral radiances (Wm-2sr-1µm-1) – After July 1, 2000 Bands Gain Lmin Lmax (Lmax - Lmin)/254 Remarks 1 High -6.2 191.6 0.77874 Used high gain 2 High -6.4 196.5 0.79882 Used high gain 3 High -5 152.9 0.62165 Used high gain 4 Low -5.1 241.1 0.96929 Low gain 5 High -1 31.06 0.12622 Used high gain 6 High 3.2 12.65 0.03720 Used low gain 7 High -0.35 10.8 0.04390 Used high gain “Spectral rad_B1” = Spectral radiances (Wm-2sr-1µm-1) in Band1 “Spectral rad_B2” = Spectral radiances (Wm-2sr-1µm-1) in Band2 “Spectral rad_B3” = Spectral radiances (Wm-2sr-1µm-1) in Band3 “Spectral rad_B4” = Spectral radiances (Wm-2sr-1µm-1) in Band4 “Spectral rad_B5” = Spectral radiances (Wm-2sr-1µm-1) in Band5 “Spectral rad_B_LG” = Spectral radiances (Wm-2sr-1µm-1) in Band6 Reflectances per band “ds” = Map of Sun Earth distance in astronomical unit Solar spectral irradiance (Esun) for Landsat 7 (Wm-2sr-1µm-1) at: Band 1 = 1970 Band 2 = 1843 Band 3 = 1555 Band 4 = 1047 Band 5= 227.1 Band 7 = 80.53 “Spectralref_B1” = Planetary reflectance at band 1 “PRefB Spectralref_B2” = Planetary reflectance at band 2 “Spectralref_B3” = Planetary reflectance at band 3 “Spectralref_B4” = Planetary reflectance at band 4 “Spectralref_B5” = Planetary reflectance at band 5 “Spectralref_B7” = Planetary reflectance at band 7 Broadband planetary albedo “BBreflectance” = broad band planetary albedo (weighted average of the Planetary reflectance’s per band)



Vegetation Indixes: a. NDVI map “NDVI” = NDVI map (were computed using band 4 and 3) b. SAVI and LAI for savannah land-cover “SAVI_temp” = temporary map of SAVI calculated using correction factor 0.5 “SAVI” = Adjusted SAVI map (i.e. setting negative values to 0.00001 to avoid problems with logarithms and divisions by 0) “LAI_temp” = Map of calculated LAI by the empirical relation LAI = (SAVI-C1)/C2 The constants C1 = 0.13 and C2 = 0.47 are adopted from the AHAS manual page 9. (Sahelian agroecological landscape of Niger) “LAI” = Adjusted LAI map (i.e. setting negative values to 0.00001 to avoid problems with logarithms and divisions by 0) The surface temperature: Radiance in band 6: “Trad_B6” = Spectral radiances (Wm-2sr-1µm-1) in Band6 Brightness temperature at the top of the atmosphere in Kelvin: “Trad_B6” = K2/(ln(K1/SRadB6+1)), is the brightness temperature at the top of the atmosphere (Kelvin). For Land sat 7 the constants are K2 = 1282.71 [K] and K1 = 669.09 [Wm-2sr-1µm-1] Calculate surface emissivity: “Tempemi” = Map of surface emissivity The relation is only valid for NDVI values over 0.16. Therefore, for NDVI values below 0.16 (usually bare soils) an exception was to be made and the emissivity is set to 0.92, a second exception was made for NDVI values below –0.1 (usually water), in this case it is set to 1. Surface temperature in Kelvin: “Tsur_temp” = Map of Surface temperature in Kelvin



Detail ILWIS scripts used to compute Surface temperature and Emissivity USING LANDSAT 7. GEOGRAPHY ILWIS SCRIPT: lati{dom=VALUE.dom;vr=-180.00000:180.00000:0.00001}:=iff(b1%2,crdy(transform(mapcrd(b1%2),latlon)),0) long{dom=VALUE.dom;vr=-180.00000:180.00000:0.00001}:=iff(b1%2,crdx(transform(mapcrd(b1%2),latlon)),0) LAT.mpr{dom=Value.dom;vr=-100.0000:100.0000:0.0001} :=%1-0.067*(%3-Long)+0.017*ET(da(%2)) Omega.mpr{dom=Value.dom;vr=-1000.0000:1000.0000:0.0001} :=15*(12-LAT) coszenith.mpr{dom=Value.dom;vr=-1.0000:1.0000:0.0001} :=sin(lati*0.017)*sin(DE(da(%2))*0.017)+cos(DE(da(%2))*0.017)*cos(lati*0.017)*cos(omega*0.017) K_ins.mpr{dom=Value.dom;vr=-10000000.0000:10000000.0000:0.0001} :=1367*EO(da(51))*coszenith tau_ins.mpr{dom=Value.dom;vr=0.0000:1.0000:0.0001} :=797/K_ins Extraterrestral component: Ws.mpr{dom=value.dom;vr=0:10:0.0}:=ACOS(-TAN(lati*3.14/180)*TAN(%1)) K_exoday.mpr{dom=value.dom;vr=0:1000000000:0.001}:=24/3.14*(1367*0.0036*%3)*COS(%2*3.14/180)*COS(%1)*(SIN(Ws)-Ws*COS(Ws))*11.57 Reflectance and Vegetation Indices.

��CONVERSION FROM DIGITAL NUMBERS (DN) TO SPECTRAL RADIANCE AT THE TOP OF THE ATMOSPHERE.

spectralrad_B1.mpr{dom=Value.dom;vr=0.0000:1000.0000:0.0001} := -6.2+((191.6-(-6.2))/254)*(B1-1) spectralrad_B2.mpr{dom=Value.dom;vr=0.0000:1000.0000:0.0001} := -6.4+((196.5-(-6.4))/254)*(B2-1) spectralrad_B3.mpr{dom=Value.dom;vr=0.0000:1000.0000:0.0001} := -5.0+((152.9-(-5.0))/254)*(B3-1) spectralrad_B4.mpr{dom=Value.dom;vr=0.0000:1000.0000:0.0001} := -5.1+((241.1-(-5.1))/254)*(B4-1) spectralrad_B5.mpr{dom=Value.dom;vr=0.0000:1000.0000:0.0001} := -1.0+((31.06-(-1.0))/254)*(B5-1) spectralrad_B7.mpr{dom=Value.dom;vr=0.0000:1000.0000:0.0001} := -0.35+((10.80-(-0.35))/254)*(B7-1)

��CALCULATION OF BAND WISE SPECRAL REFLECTANCE AT THE TOP OF THE ATMOSPHERE.

spectralref_B1.mpr{dom=Value.dom;vr=0.0000:1000.0000:0.0001} := (3.14159*spectralrad_B1*0.9889*0.9889)/(1970*coszenith) spectralref_B2.mpr{dom=Value.dom;vr=0.0000:1000.0000:0.0001} := (3.14159*spectralrad_B2*0.9889*0.9889)/(1843*coszenith) spectralref_B3.mpr{dom=Value.dom;vr=0.0000:1000.0000:0.0001} := (3.14159*spectralrad_B3*0.9889*0.9889)/(1555*coszenith) spectralref_B4.mpr{dom=Value.dom;vr=0.0000:1000.0000:0.0001} := (3.14159*spectralrad_B4*0.9889*0.9889)/(1047*coszenith) spectralref_B5.mpr{dom=Value.dom;vr=0.0000:1000.0000:0.0001} := (3.14159*spectralrad_B5*0.9889*0.9889)/(227.1*coszenith) spectralref_B7.mpr{dom=Value.dom;vr=0.0000:1000.0000:0.0001} := (3.14159*spectralrad_B7*0.9889*0.9889)/(80.53*coszenith)



��CALCULATION OF BROAD BAND REFLECTANCE AT THE TOP OF THE ATMOSPHERE

BBreflectance.mpr{dom=Value.dom;vr=0.0000:1.0000:0.0001}:=((spectralref_B1*1970)+(spectralref_B2*1843)+(spectralref_B3*1555)+(spectralref_B4*1047)+(spectralref_B5*227.1)+(spectralref_B7*80.53))/6722.63

��CALCULATION OF VEGETATION INDICES AND SURFACE EMISSIVITY

AT THE TOP OF THE ATMOSPHERE NDVI.mpr{dom=Value.dom;vr=-1.0000:1.0000:0.0001}:=(spectralref_B4-spectralref_B3)/(spectralref_B4+spectralref_B3) SAVI_temp.mpr{dom=Value.dom;vr=-1.0000:1.0000:0.000 1}:=(1+0.5)*(spectralref_B4-spectralref_B3)/(spectralref_B4+spectralref_B3+0.5) SAVI.mpr{dom=Value.dom;vr=0.00001:1.0000:0.0000001}:=iff(SAVI_temp<=0, 0.00001, SAVI_temp) Tempemi.mpr{dom=Value.dom;vr=-1.0000:1.0000:0.0001}:=IFF(NDVI<0,1,1.009+0.047*Ln(NDVI)) LAI_temp.mpr{dom=Value.dom;vr=-15.0000:15.0000:0.00001}:=(savi-0.13)/0.47 LAI.mpr{dom=Value.dom;vr=0.0000:15.0000:0.00001}:=iff(LAI_temp<=0,0.00001,LAI_temp) Finalemissivitymap.mpr{dom=Value.dom;vr=0.0000:1.0000:0.0001}:=iff(Tempemi<0.92,0.92,Tempemi) DEL SPEC*.* -FORCE

��CALCULATION OF SURFACE TEMPERATURE Parameters:

%1 Band6_Low gain. %2 Band6_High gain. %3 Final emissivity map. spectralrad_B6.mpr{dom=Value.dom;vr=0.0000:1000.0000:0.0001} := 0+0.067*%1 Trad_B6_L.mpr{dom=Value.dom;vr=0.0000:1000.0000:0.0001}:=1282.71/(LN((669.09/spectralrad_B6)+1)) Tsur_temp_Revisied_Low.mpr{dom=Value.dom;vr=0.0000:1000.0000:0.0001}:=Trad_B6_L*(%3)^-0.25 spectralrad_B61.mpr{dom=Value.dom;vr=0.0000:1000.0000:0.0001} := 3.2+0.037*%2 Trad_B6_H.mpr{dom=Value.dom;vr=0.0000:1000.0000:0.0001}:=1282.71/(LN((669.09/spectralrad_B61)+1))

Parameters: %1 surface emissivity %2 Trad_low gain C6.mpr{dom=Value.dom;vr=0.0000:1000.0000:0.0001}:=0.604*%1 D6.mpr{dom=Value.dom;vr=0.0000:1000.0000:0.0001}:=0.396*(1+(1-%1)*0.604) LS7_To_Rev.mpr{dom=Value.dom;vr=0.0000:1000.0000:0.0001}:=(-67.437*(1-c6-d6)+(0.4568*(1-c6-d6)+c6+d6)*%2-d6*293)/c6



APPENDIX E 1: ATMOSPHERIC CORRECTION USING MODTRAN 4



ATMOSPHERIC CORRECTION USING MODTRAN 4

The up welling atmosphere, or path radiance (Lup) augments the ground radiance. The ground

radiance together with the portion of down welling atmospheric radiance (Ldn) reflected (1-ε)

from the surface is attenuated by the transmittance of the atmosphere (τ) enroute to the sensor.

The spectral resolution of ASTER TIR is coarse to allow a separation of the atmosphere and

ground conditions to the measured radiance. Thus, Lup, Ldn and τ are estimated by the use of

Radiative transfer coders (MODTRAN 4) together with standard atmospheres.

In this study, the radiative transfer code developed by the US Air Force Geophysics

Laboratory is used to determine upwelling, down welling and atmospheric transmittance for

the ASTER TIR data. The radiance (up welling and down welling) is computed using

atmospheric conditions and Sun-Satellite geometry. Basically, the following atmospheric

parameters are essential to process Ldn and Lup during the satellite over pass period:

��The aerosol amount

��The temperature and water vapor profile

��The amount of ozone, or other gases

But, it is hard to get this data during the satellite overpass period. Hence, standard

atmospheric data’s were used in the absence of this data. A single input file, tape5 or

rootname.tp5 controls MODTRAN, which consists of a sequence of six or more CARDS

(inputs lines). In this study 8 cards were used as an input to run the MODTRAN 4 program

and listed below:

��CARD 1: deals with main radiation transfer driver and the following major parameters

were used for card1: -

��Band model: -MODRAN band model (M)

��Atmospheric profile: - Tropical atmosphere (15o North)

��Path altitude: - two altitude



��CARD 1A: deals with main radiation transfer driver (continued) and the following

major parameters were used for card1A:

��Use DISORT: - No use ISAAC’S two stream method

��Co2 mixing ratio: - 330 ppmv (default)

��Water vapor: - left blank

��Ozone gas: - left blank

��CARD2: deals with main aerosol and cloud options and the following major

parameters were used for card2: -

��Aerosol extinction: - Rural extinction, 5 km visibility

��Season dependent tropo and stratospheric aerosols: - coupled to model profile

��Air mass character: - 3

��Clouds and rain: - No clouds or rains (obtained from the satellite meta data)

��Surface altitude: - 1 km above sea level

��CARD3: deals with line of sight geometry and the following major parameters were

used for card3:

��Sensor altitude: - 100 km

��Target altitude: - 1 km and with curved line of sight.

��No of layers: - 36

Figure Rough Sketch of Line of Sight Geometry.

Where: H1 is observer on the edge of atmosphere. H2 is surface.

H1 H2

Sun



��CARD 3A1: deals with solar/linear scattering geometry and the following major

parameters were used in card 3A1: -

��Scattering Geometry: - Azimuth difference target sun + Solar zenith from sensor.

��Aerosol Scattering: - Mie generated interval data base of MODTRAN models

��CARD3A2: deals with solar/linear scattering geometry.

��CARD 4: deals with spectral range and resolution and the following major parameters

were used in card 4: -

��Spectral unit: - microns

��Silt function: - rectangular

��Start frequency or wavelength at: 8

��End frequency or wavelength at: - 12

��CARD 5: deals with repeat run option.

For detail, please see input data (tape 5) below



Figure 1 Basic step used to get atmospheric inputs using MODTRAN 4 for TES algorithm. Then, the weighted up welling, down welling and atmospheric transmittance are computed as

follows:

�

�=

=

=

== 12

8

12

8

)(

)(*)(_ λ

λ

λ

λ

λ

λλ

i

upi

r

LraverageLup

Where: Lup_average is weighted upwelling radiance for each ASTER TIR bands.

ri (λ) is ASTER TIR sensor response.

Lup(λ) is the up welling radiance at each wavelength from tape6.

λi in steps of 0.01 µm

MODTRAN 4 basic input preparation.

(tape 5)

MODTRAN 4(Fortran,

4V2R1.exe)

tape6.Solar flux.

Pltout(*.plt) tape7. tape8.

Multiplied with ASTER TIR sensor response.

Weighted Upwelling radiance for each ASTER TIR bands.

Weighted down welling radiance for each ASTER

TIR bands.

Weighted atmospheric transmittance for each

ASTER TIR bands.



�

�=

=

=

== 12

8

12

8

)(

)(*)(_ λ

λ

λ

λ

λ

λλ

i

dni

r

LraverageLdn

Where: Ldn_average is weighted down welling radiance for each ASTER TIR bands.

ri (λ) is ASTER TIR sensor response.)

Ldn(λ) is the down welling radiance at each wavelength from solar flux.


�

�=

=

=

== 12

8

12

8

)(

)(*)(_ λ

λ

λ

λ

λ

λτλτ

i

i

r

raverage

Where: τ_average is weighted atmospheric transmittance for each ASTER TIR bands.

ri (λ) is ASTER TIR sensor response.

τ (λ) is the atmospheric transmittance at each wavelength from pltout(*.plt).


The following results were used to run the TES algorithm together with other parameters and

the summary of the MODTRAN output is shown below in tabular form.

Constants INCL (mWm-2sr-1µm)

Lamdabar (m)

Ldn (mWm-2sr-1µm)

Lup (mWm-2sr-1µm)

tau

Band 10 0.006882 8.29 3497 1956 0.472 Band 11 0.006780 8.63 2454 1477 0.599 Band 12 0.006590 9.09 1833 1141 0.578 Band 13 0.005693 10.66 1554 1275 0.663 Band 14 0.005225 11.29 1638 1457 0.604

Eventually, please get in below the web site for ASTER TIR spectral response below: http://asterweb.jpl.nasa.gov/instrument/archive/tir.txt



APPENDIX F 1: APPENDIX F1: ASTER narrow band emissivity channel maps and histograms.



FIGURE F 1 ASTER narrow band emissivity channel maps.



FIGURE F1 2 Histograms of the narrow band channels ASTER emissivity



FIGURE F1 3 Figure C 3 Surface temperature histograms derived using ASTER and LANDSAT 7 for six land



FIGURE F1 4 Broad band emissivities derived by ASTER and LANDSAT 7 for six land cover units.

estimation of absolute surface temperature by … · from the advanced spaceborne thermal emission...

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