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(The following is provided to assist NOAA-14 AVHRR users to properly calibrate the visible channels data)

Revised post-launch calibration of channels 1 and 2 of the Advanced Very High Resolution Radiometer on board the NOAA-14 spacecraft

C.R. Nagaraja Rao and Jianhua Chen Washington, D.C. 20233

1. Background

Starting in November 1996, the NOAA/NESDIS Office of Satellite Data Processing and Distribution has been updating the calibration coefficients of AVHRR channels 1(0.58 - 0.68um) and 2 (0.72 - 1.1um) on the NOAA-14 spacecraft given in the 1b tapes at monthly intervals, generally on the second Tuesday of the month. These updates are the values of the slope S and intercept I for each channel calculated using the calibration prediction formulae given in Rao and Chen (1996). The AVHRR albedo(in per cent) in either channel is calculated by multiplying the AVHRR signal, C10 , in 10-bit counts, by the slope S, and adding to the result the intercept I, a negative quantity; the AVHRR signal should be corrected for the seasonal variations in the solar radiation incident at the top of the atmosphere. Thus,

equation for albedo in percent

where psi is the Earth-Sun distance expressed in astronomical units; the quantity generally referred to as the Earth-Sun distance correction factor, accounts for the seasonal variations in the solar irradiation at the top of the atmosphere; simple formulae for the calculation of psior psi squared are found in standard textbooks on astronomy or atmospheric radiation (e.g., Paltridge and Platt 1976). We have used here the formula

earth sun distance correction equation

with (in degrees) being given by 0.9863*n where n is the day of the year; n is set equal to 0 on January 1, and equal to 364 on December 31.

An analysis of the time series of the NOAA-14 AVHRR albedo in the two channels over selected sites around the globe for the period 1995-97 has revealed that the calibration prediction formulae given in Rao and Chen 1996 on which the calibration updates given in the 1b tapes were based might lead to slight overestimates of the albedo, and consequently to a small, but finite, greening in the Normalized Difference Vegetation Index (NDVI) records. We have therefore revised the calibration prediction formulae to remove, or minimize, these anomalies. Details of the procedure used to revise the calibration formulae will be published in the open literature shortly.

2. Revised calibration

As was done in Rao and Chen (1996), we give below the revised calibration as a function of elapsed time in orbit, expressed in days 'd' after launch. In the AVHRR albedo representation, the calibration equations are:

Channel 1: S1 = 0.0000135 d + 0.111 (3)

Channel 2: S2 = 0.0000133 d + 0.134 (4)

where Si is the slope for the ith channel, expressed in units of (per cent albedo/count. Si is thus the albedo of the Earth scene-- essentially a measure of energy-- required to generate unit response from the AVHRR in the ithchannel. Accordingly, the albedo Ai of an Earth scene generating a response C10 is:

albedo of an earth scene equation

where C0 is the dark or offset signal, expressed in 10-bit counts. Please note that Equation (5)

can also be written as:

alternate albedo of an earth scene equation

Thus, the intercept Ii, listed in the 1b tape, is the negative of the product of the slope and the dark counts, (Si C0). For the AVHRR on the NOAA-14 spacecraft, C0 is set equal to 41 counts in both channels. It is apparent that as the instrument degrades in orbit, the amount of energy required to generate unit response from the instrument, Si , increases. We shall now illustrate the use of Equation 5.

Let us say that the AVHRR on NOAA-14, while looking at a bright Earth scene, generated a signal, C10 , of 370 counts in channel 1 on March 20, 1996. Since the spacecraft was launched on December 30, 1994, the elapsed time in orbit, expressed in days, d, after launch is 444 days. Substituting this value of d in Equation 3, we find that S1 is 0.117. We get for psi squared the value 0.992 from Equation 2, since n is equal to 79. Substituting the values of S1, C0, and psi squared in Equation 5, we find the albedo of the Earth scene to be 38.19 per cent.

However, in the 1b tape, the user finds the values of Si and the intercept Ii. As mentioned earlier, the intercept Ii is the quantity ( - C0 * Si ); thus, the value of I1 listed in the 1b tape for March 20, 1996, would be: I1 = - 41*0.117 = - 4.797, if the revised calibrations are used. Using the values of S1 and I1 listed in the 1b tape for March 20, 1996, in Equation 6, we find the albedo of the Earth scene in the above example to be 38.19 per cent. Equations 5 and 6 thus yield the same values of the albedo for the Earth scene.

There are several applications where the radiance Li measured in the two AVHRR channels, expressed in units of (W/m2 um sr), is required. The AVHRR radiance Li and albedo Ai are related as follows:

alternate equation for albedo

where omega sub i: effective width of the ith channel, expressed in micrometers,

F0i : extra-terrestrial solar irradiance (Wm-2) within the pass band of the ith channel; and

theta sub zero solar zenith angle.

F0i has values of 207.1 Wm-2 and 251.01 Wm-2 for channels 1 and 2 of the AVHRR on NOAA-14; omega sub i for channel 1 is 0.129 um, and for channel 2, 0.244 um. Using Equations 3, 4, and 7, and the numerical values of the effective channel width, and the extra-terrestrial solar irradiance, we get for the calibration equations in the radiance representation:

Channel 1: S1 = 0.0000690 d + 0.566 (8)

and Channel 2: S2 = 0.0000435 d + 0.440 (9)

where the slope Si is expressed in units of (W/m2 um sr count).

3. Implementation of the revised calibration in the 1b tape

We will implement the revised calibration coefficients-- slopes and intercepts in the AVHRR albedo representation-- based on Equations 3 and 4 in the 1b tapes starting December 8, 1998. This would lead to discontinuities in the time series of AVHRR-derived products based on measurements in channels 1 and 2 which have been generated to date using either the formulae given in Rao and Chen (1996), or the slopes and intercepts given in the 1b tape since November 1996. Those of the users who have access to the raw AVHRR radiometric data (counts) can reprocess their data, using Equations 3 and 4 in the albedo representation, and Equations 8 and 9 in the radiance representation. For the convenience of those of the users who do not have access to the raw AVHRR radiometric data (counts), and who have to reprocess the albedo and/or radiance time series, we give below the correction factors for the two channels, as a function of days after launch, d. The correct albedo/radiance values are obtained by multiplying the albedo/radiance values calculated using the formulae given in Rao and Chen (1996), or the calibration coefficients given in the 1b tape since November 1996 by the correction factors given below. The correction factors for the two channels are:

Channel 1: CF1 = (1.015 - 8.8*10-5 d + 1.3*10-8 d2 ) (10)

Channel 2: CF2 = (1.037 - 1.8*10-4 d + 3.2*10-8 d2 ) (11)

Please note that the correction factors should not be used after December 8, 1998 when the revised calibration coefficients will be incorporated into the 1b tapes.

References:

Rao, C.R.N., and J. Chen, 1996: Post-launch calibration of the visible and near-infrared channels of the Advanced Very High Resolution Radiometer on the NOAA-14 spacecraft. International Journal of Remote Sensing, 17, 2743-2747.

Paltridge, G.W., and C.M.R. Platt, 1976: Radiative Processes in Meteorology and Climatology (Elsevier Scientific Publishing company, New York), ppXVII + 318.

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