Thursday, March 4, 2010

AMSU Limb Adjustment

This post looks at the Limb Adjustment done for the AMSU. We talk about what the Limb Adjustment is, how it is done, and some problems associated with it.

What Is The Limb Adjustment?
If you stand up, bend over at the waist and swing your arm in an arc under you, you'll notice your arm is closest to the floor when it's directly under you. And you'll notice your arm gets further from the floor as it continues through the arc in either the left or right direction.

The scanning of the AMSU on the Aqua satellite has a similar situation. When it scans directly below itself,  it gets data from closest to the surface, but the scans to the left and right of the satellite don't penetrate as deeply. Because of this, the temperatures read by the scans to the left and right need to be adjusted. This is called a Limb Adjustment. Publishing in the American Meteorological Society, Quanhua Liu and Fuzhong Weng (2006) had this to say about Limb Adjustment:
A remarkable effect of the cross-scan sensor is the variation of the brightness temperatures across the scan line, even though the scene temperature is homogeneous. The variation in the cross-track measurements due to the change of the scanning angle is called limb effect and can be as much as 30 K for the 23.8-GHz water vapor channel and 15 K for troposphere sounding channels (Goldberg et al. 2001). Because the limb effect is often stronger than the real variation of the signatures from scenes, the unadjusted measurements prevent the objective analysis of weather systems and may make the regression retrieval algorithm complicated. More important, averaging satellite brightness temperatures to a given grid map for climate study requires that the data be limb adjusted prior to averaging.
For microwave instruments, like the AMSU, a different form of adjustment needs to be done over land and water, due to surface emissivity. Again from Liu and Weng (2006):
It is a little complicated for the microwave channels. The surface emits either more or less than the atmosphere at the microwave range, with full dependence on the surface emissivity. The water surface may emit much less energy than the atmosphere in the microwave range. The weighting function of the microwave troposphere channel is broader than that of the infrared channel. Asymmetric behavior of AMSU-A channels on the two sides of the nadir is recognizable (Weng et al. 2003).Goldberg et al. (2001) have developed a limb-correction algorithm to overcome the difficulties for AMSU-A. They computed the limb adjustment from multiple-channel observations and the scan position–dependent coefficients. Their algorithm is routinely applied for National Oceanic and Atmospheric Administration (NOAA) operational products.
How Limb Adjustment Is Done
A collection of scans from the month of July, 1998 is used to provide a mean for each latitude for each footprint, within 2˚ latitude. These historical scans are combined with current scans from the channel being examined and its neighboring channels, and a set of  physical and statistical coefficients. Publishing in the American Meteorological Society, Mitchell D. Goldberg, David S. Crosby, and Lihang Zhou (2001) had this to say about Limb Adjustment:
 A global set of coefficients is used for channels 6–14. Separate sea and nonsea coefficients are used for channels affected by the surface—channels 1–5 and 15. The predictors are generally the channel itself plus the adjacent channel whose weighting functions peak below and above. In other words to limb adjust channel 6, we use unadjusted channels 5, 6, and 7 observations as predictors. The exceptions are channel 14 uses channels 12, 13, and 14; channel 3 uses channels 3, 4, and 5; channel 1 and 2 both use channels 1 and 2, and channel 15 uses channels 1 and 15.
So to adjust for, say, channel 5, the historical values for channel 5 at the satellites current location, the current scan values for channels 4, 5, and 6, and a set of physical and statistical coefficients are used.

Potential Problems With Limb Adjustment
From what I can see, there are two potential problems with Limb Adjustment. The first is when current scan values are outside the limits expected based on the historical scans. For example, the scan line shown at the beginning of this post has a value at foot print 1 that is 40% below the expected low limit, which is shown in the diagram at the start of this section.

The second potential problem is when a neighboring scan line used for the adjustments doesn't have any available data. For channel 5, the channel we've been looking at in this series of posts, the neighboring scan lines are 4 and 6. Channel 4 had no data at all in it for the entire month of January. A sample of this is shown in using HDFView in the image provided below.
Screen Shoot Showing No Data In Channel 4.
Click for larger image.

Previous Posts In This Series:
Proof That Temperature Area Determines Temperature Anomaly
Trying To Find The UAH January Anomaly In The Raw Data, Part 1 Of 2
Overview Of The Aqua Satellite Project, Update 1 Features
Aqua Satellite Project, Update 1 Released
Spot Checking The Spot Check
NASA, UAH Notified Of QA Spot Check Findings
About The Aqua Satellite Project
UAH January Raw Data Spot Check
So, About That January UAH Anomaly
A Note On UAH's High January Temperature

Uses of NOAA-16 and -18 Satellite Measurements for Verifying the Limb-Correction Algorithm
The Limb Adjustment of AMSU-A Observations: Methodology and Validation


  1. So lets see if i understand this correctly:

    1) Goldberg et al. (2001) developed a limb-correction algorithm to overcome the difficulties for AMSU-A.... and the Nasa website says Aqua was launched on May 4, 2002... So I wonder a) if anyone has managed to validate the pre-launch algorithm with any post-launch verification and b) if this algorithm is still robust after the sensors have been operational for seven years....

    2) A collection of scans from the month of July 1998 are used to provide a mean for each latitude for each footprint... So I wonder c) why would anyone would choose an extreme El NiƱo outlier month as a valid mean for each latitude and d) is it valid to combine July 1998 scans with current scans from the Aqua satellite that was launched May 4, 2002..

    3) More important, averaging satellite brightness temperatures to a given grid map for climate study requires that the data be limb adjusted prior to averaging... So I wonder e) if these limb adjustments are really robust and f) how grid maps are populated with data when there is sparse/missing data for a particular grid box...

  2. Would be very interested to know if you have discovered any statements regarding the accuracy / tolerances associated with the Limb Adjustments... it seems that channel 15 is likely to be the most accurate reading... but no doubt channel 15 has an associated error of range of plus or minus X degrees... does the error range grow as the Limb Adjustments are applied.... to plus or minus 2X degrees for channels 7 and 24.... and 3X degrees for channels 1 and 30... and what does this do to your overall error range if you aggregate channels 0 through 30...

    I suppose I am really trying to understand published statements, such as, "Monthly Global SST anomalies have dropped 0.014 deg C since January". Is this bogus accuracy / precision? Is this figure only accurate to, say, plus (or minus) 2 degrees?

  3. a) Yes, it's been validated. The Goldberg paper has a section on that. The error bars of the limb adjustment are considered to be smaller than the error bars of the noise of the instrument.

    b) The limb adjust described by Goldberg absolutely positively cannot function correctly on the Aqua AMSU for channel 5. Because you need the surrounding channels (4, 6) to do the adjustment and channel 4 isn't working, channel 5 is either invalid or using some other (unpublished) algorithm. I haven't posted it here yet, but going through the data, it looks like channel 4 has been broken for _at least_ 1 full year.

    c) I was wonder why they'd use an El Nino as a base year myself.

    d) This is the question that I'm trying to answer. Does this AMSU give us anything better than a rough guess what the temperatures are. I haven't seen anything so far to indicate it does. But I'm really only getting started with looking at the data.

    e) They've put a lot of thought into how the limb adjustments are done, details like using an El Nino year aside, I don't know what I'd have done differently. The tested the algorithm in various ways and it seemed to give decent results, see Goldberg for that. But the tests were done nearly a decade ago, and I don't know if they still hold up, even if channel 4 was working.

    f) I don't know how they fill missing areas. I can speculate that it's done using other satellite data. UAH is a blend of data from different satellites.

    For your second post, the Goldberg paper has the answers. The accuracy of the Limb Adjustments is considered to be below the noise of the instruments.

    UAH data has an accuracy of +/- 2 degrees C, if memory serves.

  4. Typo-ed that last part. I meant +/- 1 degree C, but even that's wrong. I just looked it up. The UAH error range is +/- 0.5 degrees.

  5. The choice of 1998 might have been picked based on the assumption that a lot of warming was coming in the future and the 1998 peak would be somewhere near the mean during the lifetime of the satellite. In 2001 no one except a few sceptics looking at the PDO predicted the trend that we have seen.

  6. Could be, Raven.

    They may have also swapped out the 1998 base with something less extreme. The software to process raw data is not in the satellite, but in computers at NASA and JAXA. It's probably noting more than a text lookup file.

    But I haven't seen anything published that says they have made such a swap.

  7. Have you gotten any response from Chritie on the QA failures?

  8. Not yet. I usually wait 2 weeks. But the truth is if they haven't responded in 1 week, they're probably not going to respond.