
% tex version of sst.txt 
% 22/04/89 file sst.tex



\def\degree{$^\circ$}
\lessons



\centerline{ \bf ESTIMATES OF ABSOLUTE SEA SURFACE TEMPERATURES}
%\vskip 0.5cm

%\centerline{{\bf  Aim of Lesson}}
\aims

To list the physical processes which couple infrared scanner measurements to the temperatures of an imaged field: to demonstrate how data from an infrared scanner is stored and how it is used to create a thermal map of the ocean.

%\centerline{{Specific Objectives}}
\objectives

After completing this lesson students should have learned to:

1)  identify calibration data in the header fields of scanned images

2)  estimate: mean reference black body temperatures; mean digital outputs from reference black bodies; mean digital outputs from outer space signals

3)  construct a calibration curve for a detector

4)  estimate brightness temperatures from chosen pixels in a thermal infrared image

5)  correct brightness temperatures into estimates of sea surface temperature by making apppropriate atmospheric corrections.

\background

{\bf Details of the image files used in this lesson}

In this exercise you are provided with image data files from the NOAA-7 satellite.  They are taken from orbit number 14608, date 23 April 1984, time 0403 GMT and show the geographical areas detailed in Figure 1.  The images are referred to as:

$$\vbox{\tt\halign{\hfil#\cr
IMAGE41.DAT\cr    
IMAGE42.DAT\cr
IMAGE51.DAT\cr
IMAGE52.DAT\cr
   TB41.DAT\cr
   TB42.DAT\cr
   TB51.DAT\cr
   TB52.DAT\cr
   SST1.DAT\cr
   SST2.DAT\cr
}}$$

\eject
%*****************************************
% put table 1 in here even tho its not the best place!

\input table1

%***************************************

Each of these data files is 512 pixels by 256 lines and comes with its corresponding \file{.HDR} file.


Filenames are coded in ways which you may find helpful as you carry out the exercises of this lesson, thus:

1) the last number in the filename, 1 or 2, defines the geographical area, in Figure 1, to which the file belongs

2) the second-last number in the filename, 4 or 5, specifies the AVHRR channel number to which it applies

3) text in front of the numbers, \file{IMAGE}, \file{TB} or \file{SST}, specifies the origin of the information - raw data, brightness temperature data or sea surface temperature data respectively.


The raw image data originally comes in 10-bit form (i.e. values in the range 0--1023).  Since BILKO requires the input as 8-bit data, the IMAGE files are presented in a converted form.  An offset of 350 has been subtracted from the 10-bit data to make these IMAGE files: to return to the 10-bit data value, you add this offset to the 8-bit return given by the \menu{Cursor} option in BILKO.  The temperature files TB and SST are displayed as 0--25.5\degree C, in 0.1 degree steps.
 
\outline

{\bf 1. Introduction}

Images obtained from a thermal infrared scanner flown above the
surface of the Earth depict the intensity of thermal infrared
radiation received from an instantaneous field of view (IFOV) on the
surface of the Earth. The intensity of this radiation depends on (i)
the temperature of the surface of the Earth in the IFOV, (ii) the
emissivity of the material at the surface of the Earth in the IFOV and
(iii) the extent to which the radiation is attenuated or augmented
during its passage from the surface of the Earth to the 
aircraft or satellite that carries the scanner. 


Over the land surface, both the temperature and the emissivity are
unknown and so it is not possible to determine both these parameters
from a single intensity measurement from each IFOV. Over the sea,
however, the emissivity is quite close to being constant.  Moreover, fortuitously, it also happens
that the actual value is about 0.98 and
for many purposes may be taken as unity. Thus in looking at a
thermal infrared image of the sea one is looking, but for some reservations about atmospheric attenuation, at a
temperature map of the surface of the sea.

Satellite images are often printed using a greyscale. This means that
different shades of grey in an image correspond to different
temperatures and it is common to show the image so that higher
temperatures appear lighter and lower temperatures appear darker.  Because the graphics adapter used in this exercise gives a choice of only four greys, it is easier and more appropriate to use a
colour scale. However we can still use the convention that lighter
colours refer to higher temperatures.

\eject

%**************************************************

%space for figure 2 here

\null
\vfill
\centerline{Figure 2.}
\eject

%*****************************************************

\Activity  Load and display \file{IMAGE41.DAT} on the screen.  Use the \menu{Modify LUT} and \menu{Modify Palette} commands to form an image which shows variations in sea surface temperature and follow the convention that lighter colours represent higher temperatures.

\endgroup

For some purposes qualitative pictures of this sort are perfectly adequate.  In studying the geographical location of shelf fronts it is not necessary to have an absolute calibration of the greyscale in terms of temperature.  But for some other purposes it is necessary to obtain actual temperatures of the water to the surface of the sea; one example would be the relationship between water surface temperature and fish population movements since it is absolute, and not relative, temperatures to which the fish will be sensitive.

The various exercises which follow exemplify procedures used to derive absolute temperatures from AVHRR data.  Such procedures differ in detail from satellite to satellite but derive from common physical principles.  Appendix 1 provides a brief comparison of AVHRR with other data sources.

Figure 2 traces, on the left, the physical processes by which infrared radiation from the sea is linked to the digital record of a scene.  On the right are shown the computational processes by which the record is converted to an estimate of sea surface temperature.

{\bf 2.  Data Interpretation Procedures}

To make estimates of sea surface temperature using AVHRR data calls for a knowledge of the available data and an understanding of the mathematical procedures used in its interpretation.  In the three sections which follow the procedures are treated in the sequence listed above, the relevant sources of data being introduced as required.

{\bf 2.1  Calibration points}

There are three infrared channels on the older version of the AVHRR
and four channels on the newer version. The first of these is a near-infrared channel and this receives almost exclusively reflected rather
than emitted radiation and is of no interest in the present context.
The remaining channels are one mid-infrared channel (with wavelength
of 3.5--3.9$\mu$m) and either one or two channels in the range 10.5--12.5$\mu$m; in daytime the radiation in the mid-infrared channel
consists of both reflected and emitted radiation and data from this
channel can usefully be used for sea-surface temperature
determination only at night.

AVHRR thermal infrared channels are monitored at each scan line by a two-point in-flight calibration using two sources of radiation from bodies at known temperatures.  The sources are  (i) an on-board black body target and  (ii) deep space.  Also incorporated in the record is a measurement of the temperature of the on-board black body.  The temperature of deep space is assumed to be known.

As the temperatures are known the black-body radiances for the two sources
can be determined; these radiances can then be used with the
corresponding digital outputs from the scanner
and a straight-line calibration curve constructed.  A non-linearity correction is commonly applied to this
straight line, but it is small. The
calibration\eject

%******************************************

\null
\vfill
\centerline{Figure 3. HRPT minor frame format}
\eject

%*********************************************


 curve can then be used to convert  digital values
output by the scanner  into satellite-received radiances.

Data is transmitted, and usually stored, in minor frames; each
minor frame contains a header followed by the data from one scan line
of the Earth's surface; the structure is shown in Figure 3. For present purposes certain words in the header are required.  Words 18, 19 and 20 of a minor frame are concerned with the
temperature of the on-board black body:


\hskip30pt word 18 = channel 3 black body temperature

\hskip30pt word 19 = channel 4 black body temperature

\hskip30pt word 20 = channel 5 black body temperature

The on-board black body is calibrated before launch and maintained at
approximately the operating temperature of the radiometer, namely
15\degc\  or 288K.  Its temperature is measured with four platinum
resistance thermometers and the readings they produce are fed back
into the data stream.  The data from one thermometer are fed into one minor frame
(corresponding to one scan line), the data from the the second
thermometer are fed into the next minor frame (corresponding to the
next scan line) and so on with the data from the third and fourth
thermometers; in the fifth minor frame a reference value 
much smaller than any likely thermometer reading is
inserted in each of the three words 18, 19 and 20. This reference provides way of telling which
of the four thermometer readings is which.  Thus we may find, for
example, in 5 successive minor frames:

$$\vbox{\offinterlineskip\hrule
\halign{&\vrule#&\strut\quad\hfil#\quad\hfil\cr
height10pt&  & &\multispan5\hfil   Word \hfil   &\cr
   &\omit& &\multispan5\hrulefill&\cr
  &  &&18&&   19  && 20&\cr
&     &&  (chan 3 data) &&(chan 4 data)&& (chan 5 data)&\cr
\noalign{\hrule}
height10pt&  $n $&&   PRT3& &   PRT3& &   PRT3&\cr
  & $n + 1$&&         PRT4& &   PRT4&  &   PRT4&\cr
 &$ n + 2 $&&        REF& &     REF& &    REF&\cr
&$n + 3$& &          PRT1& &    PRT1& &      PRT1&\cr
depth5pt& $n + 4 $& &    PRT2&&      PRT2&&  PRT2&\cr}
\hrule}$$



The REF value can easily be identified by inspection.  In the data presented above we have, therefore, a temperature
measurement for each of the three infrared channels of the AVHRR and
from each of the four platinum resistance thermometers.


Rather than just use the data from one set of 5 scan lines it is
better to take an average over several sets of 5 scan lines. Suppose
that $X_i$ is the mean value of a set of readings from PRTi taken from a
set of minor frames $n$, $n + 5$, $n + 10$, $n + 15$, \dots  then a set of
calibration coefficients $a_{ij}$ are available from NOAA for the
conversion of the values in the data stream into temperatures. The
coefficients $a_{ij}$ are determined on the ground before launch, the
formula for the temperature of the black body being:
$$T_i = a_{i0} + a_{i1}(X_i) + a_{i2}(X_i)^2 + a_{i3}(X_i)^3 + a_{i4}(X_i)^4$$
\eject
%************************************************

\input table2

%***********************************************

It is important to note that the particular  $a_{ij}$ used in our example and given
in Table 1 are only valid for data coming from the particular AVHRR
onboard the NOAA-7 satellite; for any other satellite in the series other values obtain.  Finally, to estimate the temperature of the black
body it is necessary to take a weighted mean of the values $T_1$, $T_2$, $T_3$,
and $T_4$ by writing:
$$		\overline{T}=\sum_1^4 b_i T_i $$


where the values of the coefficients $b_i$ are also available from NOAA.
It is useful to remember that, for each of the AVHRRs on the satellites that have
been launched to date a simple average, with $b_i$ = 0.25, has been used.


\Question{1}  Table 2 contains the data in words 18, 19 and 20 from 60 scanlines in
\file{IMAGE41.DAT}. Using this data what are the channel 4 and
channel 5 blackbody temperatures.

\endgroup


Because the calibration data are
very stable with respect to time, it will be assumed that the
calibration carried out over these 60 scanlines will suffice for both
image areas examined in this lesson. Ideally though, every image should be calibrated
separately using calibration data over the entire image.

If we continue through the header data in any minor frame we find the
data corresponding to radiances received by the scanner from the
observation of the black body and of deep space.  The black body data is known as back scan data and the data arrangement is:
$$\vbox{\halign{#\hfil\quad&\quad#\quad\cr
                            & Words\cr
Back scan data (30 words)  & 23 -- 52\cr
Space data (50 words)     & 53 -- 102\cr
}}$$


The back scan data contains 10 values of the radiometer reading from
the black body, multiplexed as chan 3 (1st value), chan 4 (1st value),
chan 5 (1st value), chan 3 (2nd value), chan 4 (2nd value)
 \dots chan 3 (10th value), chan 4 (10th value), chan 5 (10th
value). The space data contains 10 values of the radiometer reading
from the observation of deep space  in a similar format, but for all
5 channels. ( i.e. chan 1 (1st value), chan 2 (1st value), chan 3 (1st
value), \dots chan 3 (10th value), chan 4 (10th value), chan 5 (10th
value) ). Notice that there is Earth-scan data in all 5 channels whereas
there is only data from observation of the black body for the
(thermal) infrared channels.

One could, of course, take the values
from just one minor frame  to give the radiometer outputs for the
calibration points. However, it is better to use the average of the
values from a number of adjacent minor frames. Such averages will here be denoted:

\hskip30pt $N_{\overline{{\rm  T}}} $ = digital output from black body target

and

\hskip30pt $N_{sp}$ = digital output from space.

%**********************************************************

\input table3

%*********************************************************


In Table 3 is shown backscan and space data from one of the scanlines in \file{IMAGE41.DAT} corresponding the calibration data in Table 1.  The back scan and space data for 5 minor frames before, and 5 minor frames after, that particular scanline are also shown.  For the purposes of this exercise only these data will be averaged, but it is genrally advisable  to average back scan and space data over at least 50 minor frames.


\Question{2}  From the data in Table 3 calculate the average digital outputs $N_{\rm \overline{T} }$ and $N_{sp}$ for each of the two channels 4 and 5.

\endgroup

We now have the mean digital outputs, $ N_{sp}$ and $ N_{\rm \overline{T} }$, from deep space and the reference black body and the corresponding temperatures.  These data can  be used to provide estimates of brightness temperature, and that is the next step in this lesson.

{\bf 2.2  Determination of the calibration curve}

A detector responds to radiance, that is to the quantity of radiation falling on it.  In establishing calibration points, however, detector output was related to black body temperature and the relationship between brightness temperature and scanner output is not linear.

Calibration curves are based on the supposition that the output of a detector is a linear function of the radiation falling on it.  Denote the radiance incident on the instrument in channel $i$ 
by $L_i$ and the digital output (\lq counts\rq\  ) in channel $i$ 
by $N_i$, then the calibration curve for the channel takes the form:

$$L_i = G_i N_i + I_i           \eqno(1)$$



where $G_i$ is the slope and $I_i$ is the intercept.

Now the radiance $L_i$ is the integral over the range of $\nu$ , the frequency, (or
of $k$, the wavenumber) of the product of $E(\nu )d\nu$ , the radiation falling
on the detector in the range $d\nu$ , and the response function of the
detector at this frequency. Expressed in terms of wavenumbers instead
of frequencies and expressed as a summation over wavenumbers rather
than as an integral it is given by:

$$L_i =   \sum_{j=1}^n B(k_j,T_{bi}) \hat\phi(k_j) k_j  \eqno(2)$$


where $B(k_j,T_{bi})$ comes from the Planck distribution function,   $\hat\phi(k_j)$ is
the normalised spectral response function of the detector (Lauritson
{\it et al.}  1979) at the wavenumber $k_j$, $n$ is the number of steps over
which the range of wavenumber has been divided for the purpose of the
summation, and $k_j$ is the width of the step corresponding to wavenumber
$k_j$. For the purposes of the calibration it is  necessary to
calculate radiances for the  deep space and for the black body from the
temperatures $T_{sp}$ and $\overline{T}$  obtained above.

\Question{3} Using the following expression for $ B(k_j,T)$

\eject
%*****************************************************

\input table4

%*****************************************************

$$ B(k_j,T) ={ 2\pi  hc^2 x^3 \over   \exp(hcx /kT) - 1}$$

\item{}and the values of the detector response function given in Table 4
find the values of $L_i$ for the two calibration temperatures that
you used in Question 3.  Do this for each of channels 4 and 5.

\endgroup


\Question{4} Estimate the slope $G_i$ and the intercept $I_i$  defined in equation (1) from the
data for the two calibration points for each of the three thermal
infrared channels of the AVHRR.

\endgroup

{\bf  2.3  Calculation of brightness temperatures}


The slopes and intercepts that you have just calculated can now be
used to determine the radiances corresponding to a selection of pixels
in your image.

\Question{5}  Using the  \menu{Cursor}   option, select a number of pixels in \file{IMAGE41.DAT}.
Record their positions and pixel values. Now load in \file{IMAGE51.DAT} and
record the corresponding channel 5 pixel values. Remember to add the
offset of 350 to the values recorded to give the original 10-bit
values.  Use equation (1) with the slope and
intercept you have calculated for this channel and determine the
satellite-received radiances, $L_i$ for these pixels.

\endgroup


The determination of the brightness temperature for each pixel
involves inverting equation (2) to find $T_{bi}$ from a given value of $L_i$.
 For a given pixel we know everything on the right-hand side
of equation (2) and we know the value of $L_i$:  we need a means of calculating  $T_{bi}$. Unfortunately, we cannot calculate $T_{bi}$  directly. It is
necessary to take a number of values of $T_{bi}$, calculate the
corresponding values of $L_i$ and so  construct a calibration curve that can
then be used to determine the required blackbody temperatures from the
given pixel radiances. This is tedious and in practice it
has been found that, over a restricted range of temperature, one can
represent the relationship between $T_{bi}$ and $L_i$, for each channel $i$, in
the form

$$\ln(L_i) =  \alpha   +{\beta\over T_{bi} } \eqno(3)$$

which can be rearranged to give
$$T_{bi} =    {\beta\over \ln(L_i) -  \alpha } \eqno(4)$$



Values of the coefficients and for NOAA-7 AVHRR channels 3, 4 and 5,
have been determined to be

$$\vbox{\offinterlineskip\hrule
\halign{&\vrule#&\strut\quad\hfil#\hfil\quad\cr
height10pt&  $i$  &&  3 &&    4 &&         5&\cr
\noalign{\hrule}
height10pt& $\alpha$ &&  12.2554&&  9.2058 &&    8.9373&\cr
depth5pt  & $\beta$  &&  3821.046&& 1344.832 && 1226.189&\cr
}\hrule}$$




\Question{6} Use equation (4) to convert the radiances you calculated in Question 4
into brightness temperatures. Results will be in degrees~K.

\endgroup

{\bf 2.4  Atmospheric corrections}

The correction of the brightness temperatures to enable one to recover
the sea surface temperatures is, in itself, a topic deserving of a
complete separate lesson and we shall not go into great detail here.
We simply note (i) that the actual correction is quite small, usually  a fraction of a degree K and  very
unlikely to exceed 5\degree K, (ii) to a first approximation the effect of
the atmospheric correction will be to offset all the calculated
brightness temperatures by a fixed amount, and (iii) more refined
corrections are quite complicated and there are several factors to be
taken into account and several ways of making the corrections.

For this lesson we use a straightforward  atmospheric correction.  This is a multichannel, or
multispectral, approach and  is applied in an empirical fashion. (See, 
for example,  Singh 1984, Browers {\it et al.} 1982, Llewellyn-Jones {\it et al.} 1984).  The method involves calculating the brightness temperatures $T_3$, $T_4$ and $T_5$
separately from the data in channels 3, 4 and 5 respectively of the
AVHRR data in the manner indicated earlier. We
then assume that the sea surface temperature may be derived from the
brightness temperatures using a formula whose coefficients have been found by fitting the formula to in-situ
data obtained from ships or buoys. Remember that channel 3 can only
be used for night-time data  so we have different formula for daytime and
nighttime. The following formula are due to NOAA where the
coefficients have been determined by fitting with data from buoys.

Daytime:
	$$T = 1.0351 T_4 + 3.046(T_4 - T_5) - 283.93$$

Night-time:
$$T = 1.0239 T_4 + 0.9936(T_3 - T_5) - 278.46$$

Tests of the formulae have indicated that they are capable of yielding
results with an absolute accuracy of better than 1\degree C.


\Question{7}  Choose the appropriate  multi-channel formula to convert the
brightness temperatures you calculated in Question 6 into sea surface
temperatures.
 Although the images presented are taken from night
time/early morning satellite passes,  the daytime algorithm
has been  used to produce \file{SST1.DAT} and \file{SST2.DAT}.
 Load and display
\file{SST1.DAT}. Examine  the pixels  for which you calculated the sea-surface
temperature . Are they similar?

\item{} Also presented are the corresponding brightness temperature files for
channel 4, called \file{TB41.DAT} and \file{TB42.DAT}. The digital values 0--255
correspond to temperatures of 0--25.5\degree  C. Is the increment of 0.1\degree  C justified. What is the instrument sensitivity? You can determine
this approximately by calculating the brightness
temperatures for two consecutive digital numbers in one of the
channels. What do you get?

\item{}Using the Multi-Image option in BILKO create a file containing the
atmospheric corrections applied to the image. This may be simply done
by subtracting one of the SST files from the corresponding TB files.
Notice the variation over the image.

\endgroup

\vfill
\eject

{\bf References}

Browers D.G., Crook P.J.E., and Simpson J.H., 1982, An evaluation of
sea-surface temperature estimates from the AVHRR, Proceedings of the
Annual Technical Conference, Liverpool December 1982 (Reading: Remote
Sensing Society), pp. 143--154.

Lauritson L., Nelson G.J., and Porto F.W., 1979, Data extraction and
calibration of TIROS-N/AVHRR Radiometers. NOAA Technical memorandum
NESS 107, US Department of Commerce, Washington DC.

LLewellyn-Jones D.T., Minnet P.J., Saunders R.W., and Zavody A.M.,
1984, Satellite multichannel infrared measurements of sea surface
temperature of the N.E. Atlantic Ocean using AVHRR/2. Quarterly J.
Roy. Met. Soc., {\bf 110}, 613

Singh S.M., 1984 Removal of atmospheric effects on a pixel by pixel
basis from the thermal infrared data from measurements on satellites.
The Advanced Very High Resolution Radiometer (AVHRR). Int. J. Remote
Sensing, {\bf 5}, 161.

\vskip1cm
\hrule
\byline{ R. D. Callison and A. C. Cracknell}

\vfill
\eject

{\bf Appendix I: AVHRR data}

It is useful to compare AVHRR data with that from other scanners and to justify its use for this particular study.


The advantages of the AVHRR include the following:

1)  The AVHRR thermal infrared data is much less noisy than, for example,  that from other satellite-flown scanners such as the Coastal Zone Colour Scanner flown on NIMBUS-7.

2) The AVHRR is equipped with proper in-flight calibration which is not to be found on a number of other satellites, such as METEOSAT for example.

3)  The spatial resolution (about 1km at the surface of the Earth at nadir) is substantially better than that of any of the geostationary meteorological satellites (about  5km at nadir for METEOSAT).

4)  The system is operational: there is a considerable data archive  since the launch of TIROS-N in 1978 and the system is guaranteed to continue into the mid 1990s.

There are, of course, disadvantages of the AVHRR as well.  These include the fact that it generates data for any given area of the surface of the Earth less frequently than do  the geostationary meteorological satellites; however, in polar regions this disadvantage no longer applies since the polar-orbiting NOAA satellites cross the polar regions frequently but they are below the horizon for a goestationary satellite.  Secondly, the spatial resolution of about 1km may not be good enough for studying very small-scale effects such as thermal plumes in coastal waters.  In this situation the LANDSAT Thematic Mapper with its resolution of 120m in the thermal infrared channel provides much better spatial resolution; however this satellite revisits any given area of the surface of the Earth much less frequently than  do the NOAA satellites.
 
\vfill
\eject

\centerline{ \bf Answers to Questions --- Section 3}

{ \bf Question 1}

\indent{\obeylines\parskip= 0pt
T    =  292.4K
T    =  292.5K
T    =  293.1K
T    =  291.3K
T    =  292.3K
}

Channels 4 and 5 give the same values.



{\bf Question 2}

$N    =  341$  (both channels 4 and 5)

$N    =  992$ (channel 4),  991 (channel 5)


{\bf Question 3}

For radiance 992,  $L_i =  -1.176$

For radiance 341, $L_i =  99.58$


{\bf Question 4}

\indent\halign{\hfil#&$#$\hfil\cr
Channel 4 \quad  $G$   &=  -0.1548\cr
           $I$   &=  152.4\cr
                        \cr
Channel 5  \quad $G$   &=  -0.178\cr
          $I$   &=  175.1\cr}


\par

{\bf Question 5}

Student provides numbers.


{\bf Question 6}

Student provides numbers.


{\bf Question 7}

i.  The values should be similar

ii. Instrument sensitivity is about 0.12K so the increment of 0.1\degc\  is justified.





\vfill
\eject

