# Presentation: 928208

## Random errors: Sampling density for Infrared Spectra

- Robert Knuteson (oral), Steve Dutcher (poster)Hank Revercomb, Dave TobinUniversity of Wisconsin-Madison
- 22 October 2008    CLARREO Workshop

*[Simulating CLARREO footprints from satellite observations.]*

## Presentation Outline

-  Sampling dimensions: latitude, longitude, time, wavenumber (vertical) AND field of view size.
-  Use of radiance observations to estimate observed atmospheric random errors from inter-annual variability. Compare global, zonal, regional variability.
-  Investigation of the field of view dependence on the inter-annual variability.
-  Implications for mission requirements.
-  Preliminary examples from synthetic CLARREO dataset derived from AIRS data.
-  Workshop questions.

## Random Error Assessment Method

- Define random sampling error to be the RMS deviation from a linear fit on annual mean spectra. (This is the atmospheric random noise over that time period.)
- Inspect histograms of selected channels for various regions of the globe. (The PDF contains information beyond that contained in the distribution mean.)

**Random Error Assessment Method**

## Implications for Mission Requirements

-  The inter-annual variability can be used to estimate the number of years required to detect a signal trend which is relevant to mission lifetime. This is a function of wavelength since both the atmospheric variability and the expected signals vary by spectral channel.
-  Inter-annual variability provides only a coarse upper bound on the CLARREO absolute accuracy requirement. The CLARREO absolute accuracy should be much less than the atmospheric variability or else it will be impossible to beat down the random component of the signal by collecting more data.
-  To what extent is the inter-annual variability dependent on CLARREO field of view size? The answer should be quantitatively answered with relevant observations.

## Example of Annual Ensemblesof AIRS radiances

- For 10x15 deg grid boxes
- Produced from
- A) contiguous nadir 13.5 km footprints, every 2.667 seconds
- B) contiguous nadir 100 km footprints (created from the native resolution FOVs), every ~16 seconds
- Example of a 910 cm-1, a LW window channel
- About 2 million samples in the global annual dataset.
- C_omments_:
- Little difference in means, stds, and distributions between 13.5 and 100 km FOVs
- Radiance distributions can be highly non-gaussian  in shape although an estimate of the mean of the distribution is gaussian according to the central limit theorem.

## 910 cm-1 Regional (10°x15°) Annual Mean AIRS Radiances

**Produced from 100 km FOVs every 16 sec**

**Produced from 13.5 km FOVs every 2.667 sec**

**910 cm****-1**** Regional (10°x15°) Annual Mean AIRS Radiances**

**100 km**

**13.5 km**

## UW Synthetic CLARREO Dataset

- The UW-Madison has created a “user-friendly” condensed AIRS product of monthly spectral means and variances on a 5x5 lat/lon grid . (See Steve Dutcher poster for  product details.)
- Produced from AIRS radiances at two spatial resolutions;
- A) contiguous nadir 13.5 km footprints, every 2.667 seconds
- B) contiguous nadir 100 km footprints (created from the native resolution 6x6 AIRS FOVs), every ~16 seconds
- For each 5x5 grid box product contains, Number of points, sum, sum of squares for every AIRS channel. Will show results from January 2003 to December 2007 (5 year period).
- _Comments_:
- This dataset can be made available for use by the CLARREO study teams. (< 16 GBytes)
- Preliminary results of global and zonal averages are included in this presentation (not a complete analysis).

- WARNING:  ONLY A 5+ YEAR RECORD!!!

##  100 km FOV

** ****100 km FOV**

**CO2**

**O3**

**--- window ----**

**- window -**

**CO2**

**----------- H2O ---------------**

**CH4**

**GLOBAL AIRS**

## 13.5 km FOV

**13.5 km FOV**

**GLOBAL AIRS**

##  100 km FOV

** ****100 km FOV**

**GLOBAL AIRS**

## GLOBAL ANNUAL AIRS

-  The observed trends are interesting but not long enough to be significant..

**GLOBAL ANNUAL AIRS**

** ****100 km FOV**

## GLOBAL ANNUAL AIRS

-  Five years is not long enough to remove a trend. Use std. deviation instead.

**GLOBAL ANNUAL AIRS**

** ****100 km FOV**

## GLOBAL AIRS

**13.5 km FOV**
** ****100 km FOV**
** ****500 km FOV**

**GLOBAL AIRS**

## ZONAL AIRS

**100 km FOV**

**ZONAL AIRS**

**NOTE**
**SCALE**
**CHANGE**

## STRATOSPHERE (15 m)

**STRATOSPHERE** **(15 ********m)**

## STRATOSPHERE (15 m)

**STRATOSPHERE (15 ********m)**

## TROPOPAUSE (15 m)

**TROPOPAUSE** **(15 ********m)**

## TROPOPAUSE (15 m)

**TROPOPAUSE** **(15 ********m)**

## LW IR Window (11 m)

**LW IR Window (11 ********m)**

## LW IR Window (11 m)

**LW IR Window (11 ********m)**

## LW IR Window (3.9 m)

**LW IR Window (3.9 ********m)**

## LW IR Window (3.9 m)

**LW IR Window (3.9 ********m)**

## Mid-Trop. H2O (6.3 m)

**Mid-Trop. H2O (6.3 ********m)**

## Mid-Trop. H2O (6.3 m)

**Mid-Trop. H2O (6.3 ********m)**

## Upper Trop. H2O (6.3 m)

**Upper Trop. H2O (6.3 ********m)**

## Upper Trop. H2O (6.3 m)

**Upper Trop. H2O (6.3 ********m)**

## Questions for this Workshop:

- What metric of CLARREO science value should be used in the field of view trade?  Some useful metrics are the following;
- Mean radiance trends.  Are the trends independent of FOV size? What spatial grid averaging scales are relevant?
- Inter-annual variability in the radiances.  Is the inter-annual variability independent of FOV size? Global, zonal, regional?
- Shape of the radiance population distribution within averaging grid boxes.  Is the shape of the probability distribution independent of FOV size? What are the proper metrics for the characterization of radiance distributions beyond simple means and standard deviations?

## Notes Regarding UW Synthetic CLARREO Dataset

- 	5.7 years	choice of daytime or nighttime	choice of FOV size	number observations, sum, sum of squares
- Each data set in this case is 8 GBFYI, those images of BT mean by Latitude are a good example of using the 8GB data set. We started from 5.7 years of AIRS data, Jan 1, 2003 through Sept 15, 2008.   From that we generated this many of each FOV size:    100 km (6x6 AIRS)         10,823,852     13.5km (1 AIRS pixel)         66,419,103 In theory there should be 1/6th the number of 100km as there are 13.5km since its 6x6 or 1x1.  However if there is a single bad radiance in the 6x6 AIRS FOV then I throw that one out.  They are still pretty close though.  I would just say that we simulated:     66 million 13.5 km footprints over 5.7 years   and     11 million 100km footprints over 5.7 years Info about the data set the user started from:     5x5 degree gridded data set     Each grid cell consists of 3 arrays of 2378 points         - number of observations         - sum of observations         - sum of observations squared     The data set is broken up by months
- In this usage case the user wanted to look at years instead of months and 5 degree latitude stripes rather than grid boxes.  So, the user read in all the arrays for 1 year for each Latitude, sum those arrays up and then calculate the mean BT.  This was repeated for every year and every 5 degrees of Latitude. The whole calculation took about 20 minutes on a standard Desktop

**Notes Regarding UW Synthetic CLARREO Dataset**