NOAA KLM User's Guide

Section 7.2

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7.2 HIRS/3

For each internal target PRT, the averaged counts aretransformed to temperatures by a quartic relation. The four temperatures, or those that are deemed to be operating properly, are averaged.

For each thermal channel (1-19, or all telemetry channels except number 12) the blackbody radiance can be computed from the Planck relation,

r={c sub 1 times nu ^3}over [e^({c sub 2 times nu}over T^*)-1]

using central wavenumbers, ν, computed prior to the launch of the satellite, and an "apparent" temperature defined by,

T^*=b+c times T

where b and c are channel dependent coefficients (the so-called band-correction coefficients) computed before the launch of the satellite, and T is the averaged temperature of the internal target. The two constant terms in the Planck relation are c1 = 1.1910439 X 10-5 mW/(m2-sr-cm-4) and c2 = 1.4387686 cm-K.

During the calibration cycle, the counts for the space and internal target views are each averaged, using a 3σ throw out criterion, over the range of the 56 measurements deemed to be free from scan mirror movement and other unsatisfactory conditions. If any positions are systematically deleted from one, they will also be deleted from the other.

Assuming that radiance can be related to counts through the quadratic:

r=a sub 0 + a sub 1 times C sub v + a sub 2 times {C sub v} ^2

where r is radiance, Cv is the output in counts from the view, and a0, a1 and a2 are calibration coefficients. Before launch, a2 is computed (see below) and the assumption is made that this is an unchanging characteristic of the channel.

Now the coefficients a0 and a1 can be determined. Equation 7.2-3 is applied to the views of space and the internal target, yielding:

0 = a sub 0 + a sub 1 times C sub s + a sub 2 {C sub s}^2


r sub b=a sub 0 + a sub 1 C sub b + a sub 2 {C sub b} ^2

where Cs and Cb are the mean counts from the views of space and the internal target, respectively, and rb is the radiance of the internal target. Or, since a2 is known,

-a sub 2 {C sub s}^2=a sub 0 + a sub 1 C sub s
r sub b - a sub 2 {C sub b}^2=a sub 0 + a sub 1 C sub b

Then the slope and intercept become:

a sub 1=[r sub b - a sub 2 times ({C sub b}^2-{C sub s}^2)]over (C sub b - C sub s)
a sub 0=-a sub 2 {C sub s} ^2- a sub 1 C sub s

Nominally, the slope and the intercept can be determined from simultaneous views of space and the internal blackbody source. As discussed below, only the intercept varies appreciably throughout an orbit, the linear and quadratic terms being essentially constant.

The HIRS/3 instrument measures all radiation falling on the detector. That is, it is a total radiometer. To minimize false fluctuations in the signals, the instrument temperature is carefully controlled, so that most optical components experience temperature changes very slowly with respect to the times between calibration cycles (256 seconds). However, the baffle (identified as the secondary mirror) is a blackened light material which is subject to short-term temperature changes from emission or blackbody radiation and absorption of incident radiation from the internal blackbody source (about 280 K), space (2.73 K), and the variable earth views (about 200-275 K plus reflected sunlight). The result is that the contribution by the baffle affects all measurements on a time scale of seconds and this must be accounted for.

At every line, the secondary mirror temperature is linearly interpolated to the midpoint of the radiometric data (beam position 28.5) according to:

T sub {snn} prime = T sub {snn-01} + 0.4609 (T sub {snn} - T sub {snn-01})

where nn is the line number in the superswath (00 to 39), nn-01 is the previous line, and Ts is the measurement of the secondary mirror temperature. In the first line of an orbit the value

T sub {snn}prime=T sub {snn} - 0.5391 (T sub {snn+1} -T sub {snn})

is used. The interpolated values are preserved during the processing of a superswath (40 values plus the value from the last line of the previous superswath).

It is assumed that the slopes do not change appreciably over a 24-hour period, varying only about one part in 8000 throughout an orbit. During each 24 hours, the slopes are saved (about 19 times 350 values) and are averaged,

mean of {a sub 100} double prime= {1 over N} times {sum from i=1 to N of a sub {1i}}

where N is the number of slopes, i is an index, and a1 is a slope defined in Eq. 7.2-8. A 3σ throw-out criterion is used. After the average is computed, the accumulated slopes are purged. The averaged values are used during the next 24 hours, during which a new group of slopes is accumulated (a rotating file is undesirable).

To account for variations in the temperature of the telescope baffle, the intercepts at the time of the calibration are related to the baffle temperature through the relation:

a sub {000}=b sub 0 + b sub 1 T sub {s00} prime

where Ts00' is the interpolated secondary mirror (baffle) temperature in line 00 (space view). The constants b0 and b1 are evaluated when this equation is solved by least squares from intercepts and interpolated secondary mirror temperature accumulated during 24 hours (about 350 values of each), using a 3σ throw-out criterion. Only the term b1 is used hereafter. It is applied during the following 24 hours.

At each calibration cycle, intercepts are recomputed from the mean space counts and the averaged slopes,

a sub {000} double prime = - mean {a sub 100 double prime} times C sub {s00} - a sub 2 {C sub {s00}}^2

where the value a000'' is used at the time of the space view, mean of a sub 100 double prime is the mean slope, and Cs00 is the mean of the space counts in line 00.

Only the averaged slopes are applied to the earth-viewing data. The intercepts must be interpolated between calibration cycles by using the secondary mirror temperature:

a sub {0nn}double prime=a sub {000} double prime + nn {(a sub {040} double prime - a sub {000}double prime)}
 over 40 + b sub 1 times [(T sub {snn}prime - T sub {s00}prime)-nn{(T sub {s40}prime - T sub {s00}prime) over 40]

where nn is a scan line number in a superswath numbered 00-39; nn = 40 refers to nn = 00 of the next superswath.

For partial superswaths at the start and end of an orbit the intercepts are computed according to

a sub {0nn} double prime=a sub {0xx}double prime + b sub 1 (T sub {snn}prime - T sub {sxx}prime)

where the subscript xx refers to the nearest calibration cycle (xx = 40 or 00, respectively).

The initial values of b1 immediately after launch will be derived from current data from another satellite or will be zeroes (optional). The initial values of the mean slopes immediately after launch will be from another satellite or from data for a single orbit (optional). Data in the Level 1b files derived from use of these initial data will be excluded from the archive; that is, they will be excluded for at least 24 hours after processing begins.

The HgCdTe detector used in the HIRS/3 instrument operates in the photoconductive mode and is slightly non-linear in its response to radiative flux. Adjustments for non-linear response are made in Eqs. 7.2-8, 7.2-9, and 7.2-14. The coefficients a2 are computed from test data taken by the fabricator of the instrument, and will not change throughout the lifetime of the instrument. The combined coefficients will be saved in the Level 1b data and will be applied to earth measurements.

In summary, for the thermal channels:

a. During an orbit, accumulate

(1) The Channel 1-19 radiances for the blackbody temperatures at the time of the internal target views,
(2) The means and standard deviations of the space counts and the blackbody counts (in scan lines 00 and 01) for each channel, and
(3) The interpolated secondary mirror temperatures (Eqs. 7.2-10 and 7.2-11).

b. Compute the slopes and intercepts from the radiances and counts according to Eqs. 7.2-8 and 7.2-9. Save both coefficients in temporary 24-hour files, along with the interpolated secondary mirror temperatures.

c. Once per day, compute the relation between intercepts and secondary mirror temperatures from a least-squares solution to Eq. 7.2-13, using a 3σ throw-out criterion.

d. Once per day, compute the average slopes over the previous 24-hour period, using a 3σ throw-out criterion. These are the slopes to be used during the subsequent 24 hours. After steps c. and d., the accumulated slopes will be purged.

e. Recompute the intercepts according to Eq. 7.2-14 at the time of the space views, n = 00.

f. Return to the start of the orbit or superswath and interpolate (which requires the recomputed intercept at the next space view) or extrapolate the intercepts for the times of the earth views (lines 02-39) according to Eqs. 7.2-15 or 7.2-16. Note that the starting point for all coefficients is line 00; for an incomplete superswath at the start of an orbit the reference is line 40 (line 00 of the second superswath).

g. Compute earth-viewed radiances according to Eq. 7.2-3.

The calibration coefficients for Channel 20 (telemetry Channel 12) will be furnished by the fabricator of the instrument and will not change during the lifetime of the satellite.

The mean slopes, the interpolated intercepts, and the quadratic term will be the calibration coefficients appended to scan lines 02-39 of the Level 1b data; the 00 line will have zeroes; and line 01 will have the slope and intercept computed at the time of the calibration, a000'' (Eq. 7.2-14). Data encompassing a flagged calibration cycle (the preceding and current superswaths) are considered to be unusable, the calibration coefficients in lines 02-39 will be set to zero, and the Level 1b data will be properly flagged as unusable.

Logical records of Level 1b data will contain an even number of 8-bit bytes, and all logical records in the archive, regardless of purpose, will be the same length.

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