## NOAA Polar Orbiter Data User's Guide## Section 3.3 |

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AVHRR thermal data values (Channels 3 and 4, and 5 when present)
may be converted to temperature values; and AVHRR visible data
values (Channels 1 and 2) may be converted to albedos, by the
calibration procedures described herein. For more detail on how
NESDIS calibrates the TIROS-N/NOAA-A through -J radiometers, refer
to NOAA Technical Memorandum NESS 107 which is entitled *Data
Extraction and Calibration of TIROS-N/NOAA Radiometers.*

The format and order of the calibration coefficients is
described in Sections
3.1.2.1 and 3.2.2.1 for
GAC and LAC/HRPT data, respectively. Once the calibration
coefficients have been extracted (see
Appendix B), they must be scaled. The slope values must be
divided by 2^{30} and the intercept values by
2^{22}. The scaled slopes and intercepts may now be used as
described below.

New calibration formulae and techniques for the NOAA-14 AVHRR may be examined in depth in a paper by NOAA/NESDIS/ORA's Dr. C.R. Nagaraja Rao which can be accessed on the Internet at URL: http://orbit-net.nesdis.noaa.gov/ora/text/nrao02.txt. As of November 1996, monthly AVHRR calibration coefficient updates for NOAA-14 Channels 1 and 2 have also been included at URL: http://orbit-net.nesdis.noaa.gov/ora/text/nrao01.txt, as well as incorporated into the Level 1b datasets. Another source of calibration information for the NOAA polar orbiters can be found on a NOAA/NESDIS home page located at URL: http://www.osdpd.noaa.gov/PSB/CALIB/home.html. This page contains calibration quality control monitoring for NOAA-14 and the NOAA KLM spacecraft.

The scaled thermal channel slope values are in units of
mW/(m^{2}-sr-cm^{-1}) per count and the intercept
is in mW/(m^{2}-sr-cm^{-1}).

The radiance measured by the sensor (Channel i) is computed as a linear function of the input data values as follows:

where E_{i} is the radiance value in
mW/(m^{2}-sr-cm^{-1}), C is the input data value
(ranging from 0 to 1023 counts), and S_{i} and
I_{i} are respectively the scaled slope and intercept
values. The conversion to brightness temperature from radiance is
performed using the inverse of Planck's radiation equation:

where T is the temperature (K) for the radiance value E, ν is
the central wave number of the channel (cm^{-1}), and
C_{1} and C_{2} are constants (C_{1} =
1.1910659 x 10^{-5} mW/(m^{2}-sr-cm^{-4})
and C_{2} = 1.438833 cm-K).

Note that the temperatures obtained by this procedure are not corrected for atmospheric attenuation, etc.

The central wave numbers (cm^{-1}) for Channels 3, 4,
and 5 as a function of temperature can be found for each satellite
in Section 1.4

The following example shows how the raw data values may be converted to temperature values. Let the slope and intercept values for Channels 3 and 4 have the following values:

S_{4}= -171966195

S_{3}= -1638538

I_{4}= 667267071

I_{3}= 6365951

Since these values are scaled they must be divided by the proper
scale factor. The slope values must be divided by 2^{30};
therefore,

Similarly, the intercept values must be divided by
2^{22}:

Now, the video data for Channels 3 and 4 must be extracted from the tape. Assume the data values for spot n are:

Channel 3 = 857

Channel 4 = 513

For spot n+1, assume the values are:

Channel 3 = 858

Channel 4 = 515

To convert these values into radiance values, the calibration coefficients must be applied to the data using Equation 3.3.1-1. Therefore, for Channel 4:

And for Channel 3:

These radiance values can be converted to temperatures by use of
Equation 3.3.1-2. Assuming ν= 2638.05 cm^{-1} for
Channel 3 and ν= 912.01 cm ^{-1} for Channel 4, the
radiance values correspond to 273.94 K and 274.84 K for Channels 3
and 4, respectively.

Pre-launch calibrations of the infrared and microwave channels are carried out in a thermal vacuum chamber to minimize absorption of radiation in the path between the source and the radiometer and to simulate conditions in space. The radiometer sequentially views the warm calibrated laboratory blackbody (in place of the earth "target"), a blackbody cooled to approximately 77 K (representing the cold space view), and its own internal blackbodies. Temperatures of all blackbodies are sensed with thermistors or platinum resistance thermometers (PRTs). Radiances for each channel can be computed from those temperatures by the methods described in Section 3.3.1. Data are collected as the laboratory blackbody is cycled through a sequence of temperature plateaus approximately 10 K apart between 175 K and 320 K, which spans the entire range of earth target temperatures. The entire procedure is carried out independently for several instrument operating temperatures (e.g., 10, 15 and 20C for the AVHRR) that bracket the range of operating temperatures encountered in orbit. The operating temperature is represented by the temperature of the instrument's baseplate, which is also approximately the same as the temperature of its internal warm blackbody.

The instrument manufacturers and NESDIS independently analyze the data from the pre-launch tests to determine operating characteristics of the instruments, such as their signal-to-noise ratios, stability, linearity of response, and gain (output in digital counts per unit incident radiance). However, these characteristics cannot be expected to remain the same in orbit as they were before launch. One reason is that the thermal environment varies with position in the orbit, causing gains to vary orbitally. Also, instrument components age in the several years that usually elapse between the time of the pre-launch test and launch, and the aging process continues during the two or more years the instrument typically operates in orbit. Therefore, the TIROS/NOAA radiometers have been designed to view cold space and one or more internal warm blackbodies as part of their normal scan sequences in orbit. This provides data in the microwave and infrared channels for determining signal-to-noise and radiometric slopes and intercepts. Unfortunately, there are no on-board calibration sources for the visible region. Therefore, the pre-launch calibration must be used for the visible channels.

There are other coefficients necessary for in-orbit calibration that must be derived from pre-launch test data. These include the coefficients to account for the non-linearity in the AVHRR's response, which will be described later in this section.

The pre-launch calibration relates the AVHRR's output, in digital counts, to the radiance of the scene. In pre-launch tests, the scene is represented by the laboratory blackbody. The calibration relationship is a function of channel and baseplate temperature. For channel 3, which uses an InSb detector, the calibration is highly linear. However, because channels 4 and 5 use HgCdTe detectors, their calibrations are slightly non-linear.

To characterize the calibration when the AVHRR is in orbit, the only data available are those acquired when the AVHRR views space and the internal blackbody. This gives two points on the calibration curve, sufficient to determine only a straight-line approximation to the calibration. The linear approximation is what is applied to determine scene radiances. Scene brightness temperatures are then derived via the temperature-to-radiance look-up tables described in each spacecraft's respective subsection of Section 1.4.

To account for non-linearities, NESDIS provides corrections in each spacecraft's respective subsection of Section 1.4 that are added to the scene brightness temperatures computed from the linear calibration. The corrections are tabulated against scene temperatures, and there is a separate table for each channel and each baseplate temperature. NESDIS derives the pre-launch test data as follows:

- A quadratic is fitted by least squares to the scene radiance vs. AVHRR output count data.
- The quadratic equation is applied to the AVHRR response, in counts, when it viewed its internal blackbody. This determines the radiance of the internal blackbody. In effect, the AVHRR itself is used to transfer the calibration of the laboratory blackbody to the internal blackbody. Note that no assumptions have been made about the emissivity of the internal blackbody.
- Using counts from the "view" of the cold target (whose radiance is assumed to be zero) and the internal target (whose radiance was determined in step b., the linear calibration equation is determined.
- The linear calibration is then applied to the AVHRR output, in counts, obtained when the AVHRR viewed the laboratory blackbody. This produces radiances, one for each of the temperature plateaus of the laboratory blackbody. The radiances are converted to brightness temperatures by the method described in NESS 107, Appendix A.
- The brightness temperatures are subtracted from the actual temperatures of the laboratory blackbody, determined from its PRTs. The differences are the correction terms.

It should be noted that the procedures outlined above were **
not** used for TIROS-N, NOAA-6, NOAA-7 and NOAA-8. For these
spacecraft, the variation in the non-linearity correction with
internal blackbody temperature was not allowed for, and a negative
radiance of space, N_{sp}, was introduced to minimize
temperature errors in the range of 225-310 K.

With the launch of NOAA-13, NESDIS changed its derivation of the non-linearity correction in the calibration of AVHRR Channels 4 and 5. The linear calibration now uses a negative, non-zero value for the radiance of space, instead of the former value of zero. This method makes the dependence of the correction terms on the internal calibration target negligible.

NESDIS continues to supply tables of brightness temperature correction terms for the non-linearity. These correction terms are valid only when applied to "linear" brightness temperatures based on the negative radiance of space. Since the correction terms no longer vary with the internal calibration target temperature, the user does not need to interpolate on the internal calibration target temperature. Otherwise, the user applies the non-linearity corrections as before.

NESDIS also supplies an alternate method of handling
the-non-linearity which can be applied to radiances instead of
brightness temperatures. For each instrument and for each channel,
three coefficients (A, B, and D) of a quadratic equation are
supplied in Section 1.4 all
spacecraft from NOAA-13 on. The following quadratic equation can be
used to compute the corrected radiance, RAD from the "linear"
radiance, R_{lin}:

This new treatment of the non-linearity plot corrections should be an improvement over the previous method because 1) it is less sensitive to noise in the thermal/vacuum test data, 2) it gives the user a choice of correcting either the radiance or the brightness temperatures, and 3) it is being applied retrospectively in the NOAA/NASA Pathfinder program (see URL: http://daac.gsfc.nasa.gov/DATASET_DOCS/avhrr_dataset.html for more information) to generate a consistent time series of AVHRR radiances from 1981 to the present for use in studies of climate change. Making the same method operational at NESDIS will eliminate a source of inconsistency between the Pathfinder dataset and future observations.

The scaled visible channel slope values are in units of percent albedo/count for slope and in percent albedo for intercept.

The percent albedo measured by the sensor channel i is computed as a linear function of the input data value as follows:

where A_{i} is the percent albedo measured by channel i,
C is the input data value in counts, and S_{i} and
I_{i} are respectively, the scaled slope and intercept
values. The visible channels (1 and 2) are calibrated using
Equation 3.3.2-1 to obtain the percent albedo.

The calibration procedure is very similar to the linear calibration procedure described above for the thermal channels. The pre-launch slopes and intercepts for AVHRR Channels 1 and 2 are shown in Table 3.3.2-1.

Satellite | S_{1} |
I_{1} |
S_{2} |
I_{2} |
---|---|---|---|---|

TIROS-N | 0.1071 | -3.9 | 0.1051 | -3.5 |

NOAA-6 | 0.1071 | -4.1136 | 0.1058 | -3.4539 |

NOAA-7 | 0.1068 | -3.4400 | 0.1069 | -3.488 |

NOAA-8 | 0.1060 | -4.1619 | 0.1060 | -4.1492 |

NOAA-9 | 0.1063 | -3.8464 | 0.1075 | -3.8770 |

NOAA-10 | 0.1059 | -3.5279 | 0.1061 | -3.4766 |

NOAA-11 | 0.0906 | -3.730 | 0.0900 | -3.390 |

NOAA-12 | 0.1042 | -4.4491 | 0.1014 | -3.9925 |

NOAA-13 | 0.1076 | -3.9747 | 0.1035 | -3.8280 |

NOAA-14 | 0.1081 | -3.8648 | 0.1090 | -3.6749 |

Note: Beginning in November 1996, the slopes and intercepts for AVHRR Channels 1 and 2 were computed monthly, incorporated into the Level 1b datasets and posted on the NOAASIS home page (URL: http://psbsgi1.nesdis.noaa.gov:8080/EBB/ml/niccal.html). |

The two visible channels on the AVHRR instrument are calibrated prior to launch using the following procedure: the calibration source is a large-aperture integrating sphere equipped with 12 calibrated quartz-halogen lamps. These lamps were carefully selected to match each other as closely as possible in spectral output and operating current. The sphere is then calibrated with all 12 lamps on against a National Institute of Standards and Technology secondary standard of spectral irradiance. The ratio of the output of n lamps to that of 12 lamps is also determined. This yields the spectral output of the sphere when any number of lamps, n, is on. By varying the number of bulbs which are turned on, a calibration curve from dark level to a maximum of 12 lamps output can be obtained.

The following computations must be made in order to present the
calibration in terms of percent albedo vs. radiometer output.
First, the spectral output of the sphere is integrated with the
spectral response function of the AVHRR channel to yield an
effective radiance for the spectral band for 12 lamps operating.
This is then multiplied by the appropriate K_{n}factor to
convert to n lamps. This is described by equation 3.3.2-2:

where,

N_{L}=effective radiance as seen by the channel in the appropriate spectral band,

K_{n}= the factor to convert to radiance for n lamps,

C(λ)=calibrated spectral radiance of the sphere with 12 lamps on,

λ=wavelength, in the spectral region λ_{1}to λ_{2},

φ(λ)=the measured spectral response of the channel being calibrated.

Similarly, if one takes the solar irradiance at the top of the atmosphere and performs a similar calculation, the results are shown in Equation 3.3.2-3.

where,

N_{s}=effective radiance of the radiometer viewing reflected sunlight,

S(λ)=spectral irradiance viewed at the top of the atmosphere,

φ(λ)=spectral response function of the channel.

The resultant N_{s} represents what would be "seen" from
space with a 100% reflecting, diffuse surface when the Solar Zenith
Angle is zero.

Thus, the percent albedo A is calculated using Equation 3.3.2-4:

To convert from percent albedo A to spectral radiance R (in
W/(m^{2}-micrometer-sr)), the following equation must be
used:

where:

F = integrated solar spectral irradiance, weighted by the spectral response function of the channel W/mTable 3.3.2-2 contains the values of W and F derived from^{2}.W = equivalent width of the spectral response function μ.

Satellite | W_{1} |
F_{1} |
W_{2} |
F_{2} |
---|---|---|---|---|

TIROS-N | 0.325 | 443.3 | 0.303 | 313.5 |

NOAA-6 | 0.109 | 179.0 | 0.223 | 233.7 |

NOAA-7 | 0.108 | 177.5 | 0.249 | 261.9 |

NOAA-8 | 0.113 | 183.4 | 0.230 | 242.8 |

NOAA-9 | 0.117 | 191.3 | 0.239 | 251.8 |

NOAA-10 | 0.108 | 178.8 | 0.222 | 231.5 |

NOAA-11 | 0.113 | 184.1 | 0.229 | 241.1 |

NOAA-12 | 0.124 | 200.1 | 0.219 | 229.9 |

NOAA-13 | 0.121 | 194.09 | 0.243 | 249.42 |

NOAA-14 | 0.136 | 221.42 | 0.245 | 252.29 |

Although the pre-launch calibration procedures are quite extensive, it is not sufficient to rely on these calibration data alone to achieve the desired accuracy from AVHRR data. The instrument characteristics cannot be expected to remain the same in orbit as they were before launch. This situation occurs primarily because the thermal environment varies with the satellite's position in orbit, causing the output in digital counts to vary. Initially, Channels 1 and 2 are observed to degrade in orbit because of the outgassing and launch associated contamination (Rao and Chen, 1994). Continued exposure to the harsh space environment (Brest and Rossow, 1992) is also a contributing factor. In addition, the instrument's components age in the years that elapse between the pre-launch tests and actual launch. Furthermore, this aging process continues during the two or more years that the instrument is typically operational.

Unfortunately, there are no onboard calibration sources for the visible channels and the pre-launch calibration must be used or the user must rely on ground-based experimental techniques for deriving the calibration equations. NOAA and the National Aeronautics and Space Administration (NASA) recognized the inherent problems with the AVHRR data and collaborated to form the NOAA/NASA AVHRR Pathfinder program. The main objective of the Pathfinder program is to reprocess and rehabilitate the long term records of AVHRR and AVHRR-derived geophysical products from 1981 to the present. As part of this program, the AVHRR Pathfinder Calibration activity has determined the in-orbit degradation of the AVHRR visible and near-infrared channels (Rao et al., 1993a). After applying the appropriate formulae to account for in-orbit degradation, most (if not all) spurious trends are removed from the long term records of AVHRR and AVHRR-derived geophysical products. Currently, these formulae exist for the AVHRRs flown on NOAA-7, NOAA-9, NOAA-11and NOAA-14 spacecraft.

Post-launch calibration information for NOAA-7, NOAA-9 and NOAA-11 can be accessed on the NOAASIS website at http://www.osdpd.noaa.gov/EBB/noaasis.html or see Appendix G for more information.

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