## NOAA KLM User's Guide## Section 7.1 |

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The Advanced Very High Resolution Radiometer, Version 3 (AVHRR/3), scheduled to be flown on the NOAA KLM spacecraft, differs from AVHRR Versions 1 and 2 that have been used operationally to date. The AVHRR/3 is a six channel instrument, with three of the channels located in the visible and near-infrared regions of the spectrum, having effective wavelengths around 0.63 micrometers (channel 1), 0.86 micrometers (channel 2), and 1.6 micrometers (channel 3A), while the remaining three are located in the atmospheric window regions in the infrared with effective wavelengths centered around 3.7 micrometers (channel 3B), 10.8 micrometers (channel 4), and 11.5 micrometers (channel 5). Since quantitative radiometric applications of the AVHRR radiance measurements are becoming increasingly important both in research and operational environments, it becomes necessary to calibrate the sensors accurately in order that the AVHRR radiance measurements meet the stringent performance requirements necessitated by the accuracy requirements of the products derived from these radiances. For example, accuracies on the order of 1 to 2% are desired in the AVHRR radiances measured in channels 1, 2 and 3A. These radiances are used for improving the accuracy of atmospheric aerosol retrievals over the oceans in order that they may be used with confidence in atmospheric energy balance studies. Similarly, the well established need that sea surface temperatures determined using the brightness temperatures measured in channels 3B, 4 and 5 should be accurate to a few tenths of a degree K for use in climate and global change necessitates development of user friendly correction procedures for the non-linearities associated with the AVHRR thermal infrared channels, and also imposes stringent requirements on the allowable noise-equivalent temperatures associated with the same.

Against this background, the procedures for the pre- and post-launch calibration of the different AVHRR channels are described. This description is based on the work performed at the NOAA/NESDIS Office of Research and Applications and on material furnished by ITT Aerospace/Communications Division, Fort Wayne, Indiana (the instrument manufacturer).

The visible and near-infrared channels of the AVHRR/3 are calibrated prior to launch at the facilities of ITT, following a protocol which has evolved over the past two decades. A 102 cm (40 in) diameter integrating sphere is used as the source of illumination. The integrating sphere is equipped with seventeen 45-W lamps, and three 150-W lamps mounted in a ring pattern. The radiance emerging from the integrating sphere port which has a diameter of 35.6 cm (14 in), can be varied over three orders of magnitude by illuminating the sphere with a suitable combination of the various lamps. A separate 11.4 cm (4.5 in) diameter integrating sphere, equipped with a 45-W lamp and an aperture wheel, is used as the source when lower levels of illumination are desired. The level of illumination is varied in twenty-five steps for channel 1; sixteen steps for channel 2; and eleven steps for channel 3A. At each level of illumination of the integrating sphere, 3600 measurements of the signal issuing from the AVHRR when it views the sphere and the space clamp target are made, and the mean and standard deviation recorded, and converted to digital counts on a 10-bit scale. Generally, the AVHRR signals when it views the integrating sphere with all of the lamps turned off, and when it views the space clamp target (essentially a blackbody) are very close to each other.

The integrating sphere is periodically calibrated for its spectral output and linearity with an Optronic Laboratories Model OL750S Automated Spectroradiometer System and an Optronics Laboratories Model OL410 Integrating Sphere Standard; the Integrating Sphere Standard is traceable to radiance standards maintained at the NIST. The uncertainty in the calibration of the 102 cm (40 in) integrating sphere source is estimated to be of the order of 5%.

It should be noted that the AVHRRs will be calibrated periodically, at intervals not to exceed one year, until they are launched. The last calibration will be performed as close to launch as is practicable. Greater details of the pre-launch calibration of the AVHRR are found in Rao (1987).

It is the usual practice in NOAA to give the pre-launch calibration results in the form of a simple linear regression
relationship between the measured AVHRR signal, C_{10}, expressed in ten-bit counts, and the albedo, A, of the integrating
sphere source at different levels of illumination. Thus,

where S is the slope (percent albedo/count) and I is the intercept (percent albedo) listed in the Level 1b data under the
heading "pre-launch." **It should therefore be noted that the use of these slope and intercept values with the measured AVHRR
signal will yield the albedo in percent under the assumption that the pre-launch calibration is valid in orbit.**

The albedo A (or the reflectance factor or scaled radiance) of the Earth scene is given by:

and

where τ_{λ} is the normalized response of the instrument at the wavelength λ, I_{λ} is the
radiance (W m^{-2} sr^{-1} μm ^{-1}) and F_{0}_{λ}is the extraterrestrial solar
irradiance (W m^{-2} μm^{-1}) at the wavelength λ; where, λ_{1} and λ_{2}, are
the lower and upper cut-off wavelengths of the channel. Other quantities of interest are the equivalent width ω (μm) and
the effective wavelength λ_{e} given by:

and

It should be noted that the albedo calculated using Equation 7.1.1.1-2 shows a small but finite variation with the
extraterrestrial solar irradiance spectra used in the calculation of F. It is thus preferable to work with the in-band radiance I or
the radiance I_{λ}; however, these quantities are not included in the Level 1b data stream

A salient feature of the AVHRR/3 is the use of dual gain detection circuitry in the visible and near-infrared channels to enhance radiometric resolution at the lower end of the dynamic range of the albedo; this results in minor losses in resolution at the higher values of albedo. The dual gain settings for channels 1, 2, and 3A are given in Table 7.1.1.1-1 below.

Channel | Albedo range (percent) | Counts |
---|---|---|

1 and 2 | 1 - 25 | 0 - 500 |

26 - 100 | 501 - 1000 | |

3A | 1 - 12.5 | 0 - 500 |

12.6 - 100 | 501 - 1000 |

The dual gain feature necessitates the use of two sets of slopeand intercept values for channels 1, 2, and 3A to
accommodate the two gain ranges. Thus, the Level 1b data stream will have, in addition to the pre-launch calibration
coefficients, two sets of slope and intercept values for each of the three channels based on post-launch calibration
(see next section). These are listed under the heading "operational" in the Level 1b data stream as and when
the post-launch calibration updates are available. As mentioned earlier, since these slope and intercept values are
in the albedo (or reflectance factor or scaled radiance) representation, use of the same with the AVHRR Earth scene
signal will yield the albedo (in percent). The dual gain cross-over point is defined as the count value at which both
the high and low range regression equations for the albedo A will yield the same value of the albedo. The cross-over
point is determined using the integrating sphere (pre-launch) and the electronic calibration ramp. The user will be
furnished with the slopes and intercepts, and with the values of F, ω, and λ_{e} in
Appendix D.

The visible and near-infrared channels of the TIROS-N series AVHRRs are known to degrade in orbit; it is expected similar degradations will occur in Channels 1 and 2 of the NOAA KLM AVHRR/3. The in-orbit behavior of channel 3A is unknown since there is no prior experience to draw upon.

The absence of on board calibration devices for these channels necessitates the development of vicarious techniques for post-launch calibration. Accordingly, vicarious calibration techniques that have been developed (e.g., Rao and Chen 1995) to characterize the post-launch performance of Channels 1 and 2 of the TIROS-N series AVHRRs will be adapted to the AVHRR/3; these techniques use radiometrically stable terrestrial calibration target sites, and congruent path aircraft/satellite measurements to monitor the calibration of the instrument as a function of time. These techniques will be suitably modified to account for the split-gain feature of the instrument.

Pre-launch calibration of the infrared channels is carried out in a thermal vacuum chamber to simulate conditions in space. The radiometer sequentially views three blackbody targets; a cold target (95K) representing cold space, an external laboratory blackbody representing "Earth", and its own warm blackbody, the internal calibration target (ICT). The sequence is the same as shown in Figure 7.1.2.2-1. All blackbody sources have calibrations traceable to NIST. The internal and external blackbody temperatures are measured by Platinum Resistance Thermometers (PRTs). From these temperatures, AVHRR radiances for each thermal channel are computed. The AVHRR outputs 10-bit count values, integers in the 0-1023 range. The detection circuits for these channels are such that count output increases when incoming radiance decreases.

The entire pre-launch calibration test cycle is repeated on either three, four, or five separate days. Each day, the instrument operating temperature (measured by the PRTs) is fixed at a different value in the 10, 15, 20, 25, and 30C range for the entire cycle. This range brackets the range of operating temperatures encountered in orbit. For each calibration run, temperature (radiance) and count data are collected as the laboratory blackbody is cycled through 15-17 temperature plateaus between 180K and 335K, which spans the entire range of Earth target temperatures.

During each in-orbit scan line, the AVHRR views three different types of targets, as shown in Figure 7.1.2.2-1. It first outputs 10 counts when it views cold space, then a single count for each of the 2,048 Earth targets (pixels), and finally 10 counts when it views its own internal blackbody target. (Only the AVHRR scan mirror actually rotates.) The cold space and internal blackbody target views are used to calibrate the AVHRR, because a radiance value can be independently assigned to each target.

The internal blackbody temperature T_{BB } is measured by four Platinum Resistance Thermometers (PRTs) embedded in the AVHRR instrument.
The radiance N_{BB} received by the AVHRR from the internal blackbody in each thermal channel is computed from T_{BB } and the
spectral response (filter) function of the channel. The radiance of space value N_{S}, designed to accurately account for pre-launch
information, is computed from pre-launch data. These radiances, together with the average space count C_{S} and the average blackbody
count C_{BB} provide two points (C_{BB}, N_{BB}) and (C_{S}, N_{S}) on the radiance versus count graph.
A straight line drawn between the two points generates the linear radiance versus count estimate. The AVHRR count output C_{E} from
viewing an Earth target is substituted into the linear equation and produces linear radiance N_{LIN}. Pre-launch measurements indicate
that the actual radiance versus count graph is quadratic so N_{LIN} is input into a quadratic equation, defined by pre-launch measurements,
to give the nonlinear radiance correction N_{COR}. The incoming radiance N_{E} from the Earth target that causes AVHRR output count
value C_{E} is found by adding N_{COR} to N_{LIN}. An equivalent blackbody temperature T_{E} can be computed from
Earth radiance value N_{E}.

Starting with the NOAA-15 satellite, NESDIS now incorporates the nonlinear radiance corrections for AVHRR thermal channels 4 and 5 into the
new Level 1b data stream. The corrections are in the GAC and LAC datasets, and also in the HRPT datasets produced operationally by NESDIS.
Users compute the Earth scene radiance N_{E} in units of mW/(m^{2}-sr-cm^{-1}) from the 10-bit Earth scene count C_{E}
by the formula:

There is a set of coefficients for each thermal channel 3B, 4, and 5 in the NOAA KLM Level 1b dataset. The channel 3B detector responds linearly
to incoming radiance so for channel 3B the coefficient a_{2} will always be 0. Section 8 contains format
information about how the Level 1b data are stored. The coefficient a_{0} for AVHRR channel 4 is specified as "IR Operational
Cal Ch4 Coefficient 1"; etc.

As a numerical example, when C_{E} = 410 counts for channel 4, and a_{0} = 155.58, a_{1} = -0.1668, and a_{2} = 0.000010,
then,

N_{E} = 155.58 - 0.1668 x 410 + 0.000010 x (410)^{2 }= 88.9 mW/(m^{2}-sr-cm^{-1})

To convert the computed Earth scene radiance value N_{E} into an equivalent blackbody temperature value T_{E}, use the two-step process defined by
Equations 7.1.2.4-8 and 7.1.2.4-9 in Section 7.1.2.4

The constants for converting radiance to blackbody temperature are also found in the Level 1b LAC and GAC Header Records, but in a slightly different form. In
Tables 8.3.1.3.2-1 and 8.3.1.4.2-1 (for LAC and GAC data, respectively),
under the heading Radiance Conversion (octets 281-328), channels 3B, 4, and 5 each have three sets of constants; these constants are called central wavenumber,
constant1, and constant2. The central wavenumber value ν_{c} is used in Equation 7.1.2.4-8 to calculate T_{E}*, and the blackbody temperature
T_{E} is computed by the formula:

**Step 1.** The temperature of the internal blackbody target is measured by four PRTs. In each scanline, data words 18, 19, and 20 in the HRPT minor frame
format contain three readings from one of the four PRTs. (See Section 4.1.3.) A different PRT is sampled each scanline;
every fifth scanline all three PRT count values are set equal to 0 to indicate that a set of four PRTs has just been sampled.

The count value C_{PRT} of
each PRT is converted to temperature T_{PRT} by the formula

The coefficients d_{0}, d_{1}, d_{2}, d_{3}, and d_{4} vary slightly for each PRT. Values for the coefficients
are found in Appendix D, in Table D.1-8 for NOAA-15 (coefficients d_{3} and d_{4} are 0 for NOAA-15), <
a href="../d/app-d2.htm#td2-9">Table D.2-9 for NOAA-16, Table D.3-3 for NOAA-17, and
Table D.4-3 for NOAA-18.

To calculate the internal blackbody temperature T_{BB}, NESDIS uses the simple average

**Step 2.** The radiance N_{BB} sensed in each thermal AVHRR channel from the internal blackbody at temperature T_{BB} is the
weighted mean of the Planck function over the spectral response of the channel. The spectral response function for each channel is measured in
approximately 200 wavelength intervals and provided to NESDIS by the instrument manufacturer. In practice, a look-up table relating radiance to
temperature is generated for each channel. Each table specifies the radiance at every tenth of a degree (K) between 180 and 340K. The tables are
referred to as "Energy Tables". It has been found that the following two-step equation accurately reproduces Energy Table equivalent blackbody
temperatures to within ± 0.01K in the 180 to 340K range. Each thermal channel has one equation, which uses a centroid wavenumber ν_{C}
and an "effective" blackbody temperature T_{BB}*. The two steps are:

where the first and second radiation constants are:

c_{1} = 1.1910427 x 10^{-5} mW/(m^{2}-sr-cm^{-4})

c_{2} = 1.4387752 cm-K .

The values for ν_{C} and the coefficients A and B for channels 3B, 4, and 5 are unique for each spacecraft
and are found in Appendix D; Table D.1-11 for NOAA-15,
Table D.2-12 for NOAA-16,
Table D.3-7 for NOAA-17,
and Table D.4-7 for NOAA-18. The single centroid wavenumber for each channel replaces the method for previous AVHRRs,
which used a different central wavenumber in each of four temperature ranges. In the previous version of this documentation, the A coefficients in
Tables D.1-11 and D.2-12 were minus numbers and the B coefficients were slightly greater than one. They were used to convert radiance into equivalent
blackbody temperature, and converted "effective" temperature T_{BB}* into T_{BB}, instead of the reverse way as shown in Equation 7.1.2.4-3.

**Step 3.** Output from the two in-orbit calibration targets is used to compute a linear estimate of the Earth scene radiance N_{E}. Each
scanline, the AVHRR views the internal blackbody target and outputs 10 count values for each of the three thermal channel detectors; these are found in
words 23 to 52 in the HRPT datastream. When the AVHRR views cold space, 10 counts from each of the five channel sensors are output and placed into words
53 to102. (Table 4.1.3-1 describes how these data are multiplexed.) Count values for each channel are averaged together
to smooth out random noise; often counts from five consecutive scanlines are averaged because it takes five lines to obtain a set of all four PRT measurements.
The average blackbody count C_{BB} and average space count C_{S}, together with blackbody radiance N_{BB} and space radiance N_{S},
explained in the next paragraph, are used to compute the linear radiance estimate N_{LIN},

where C_{E} is the AVHRR count output when it views one of the 2,048 Earth targets.

The detector in thermal channel 3B has a linear response to incoming radiance so the linear radiance computed from Equation 7.1.2.4-5 is the correct value
for channel 3B. For this channel, the radiance of space value N_{S} is actually = 0; no nonlinear corrections need to be made.

The Mercury-Cadmium-Telluride detectors used for channels 4 and 5 have a nonlinear response to incoming radiance. Prelaunch laboratory measurements show that:

- scene radiance is a slightly nonlinear (quadratic) function of AVHRR output count,
- the nonlinearity depends on the AVHRR operating temperature.

It is assumed that the nonlinear response will persist in orbit. For the NOAA KLM series of satellites, NESDIS uses a radiance-based nonlinear correction method.
In this method, the linear radiance estimate is first computed using a non-zero radiance of space, the N_{S} term in Equation 7.1.2.4-5. Then, the linear
radiance value is input into a quadratic equation to generate the nonlinear radiance correction, N_{COR}:

Finally, the Earth scene radiance is obtained by adding N_{COR} to N_{LIN},

Introducing the non-zero radiance of space value is a mathematical device which has two primary advantages. First, only one quadratic correction
equation per channel is necessary; the quadratic coefficients are independent of AVHRR operating temperature. Second, the method reproduces prelaunch measurements
very well; RMS differences between the fitted data and the measured data are approximately 0.1K for both channels 4 and 5. Values for N_{S }and the quadratic
coefficients b_{0}, b_{1}, and b_{2} are found in Appendix D, Table D.1-14 for NOAA-15,
Table D.2-15 for NOAA-16,
Table D.3-2 for NOAA-17,
and Table D.4-2 for NOAA-18.

**Step 4.** Datausers often convert the computed Earth scene radiance value N_{E} into an equivalent blackbody temperature value T_{E}.
This temperature is defined by simply inverting the steps used to calculate the radiance N_{E} sensed by an AVHRR channel from an emitting blackbody
at temperature T_{E}. The two-step process is:

The values for ν_{C} and the coefficients A and B are again found in Appendix D;
Table D.1-11 for NOAA-15,
Table D.2-12 for NOAA-16,
Table D.3-7 for NOAA-17,
and Table D.4-7 for NOAA-18.

Compute the blackbody temperature:

Compute the blackbody radiance:

Compute the Earth view radiance using the nonlinearity correction:

Convert Earth view radiance to equivalent blackbody temperature:

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