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:
Noise
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

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