1. Noise in ASCAT ocean backscatter measurements
Craig Anderson, Hans Bonekamp, Colin Duff, Julia Figa & Julian Wilson.

2. Contents Introduction Rough estimates of ASCAT Kp ASCAT Kp algorithm
ASCAT Kp requirements & verification
Other issues
incidence angle dependence
Kp over sea ice
Summary

3. Introduction
ASCAT measurements are averaged on board in range and azimuth and then transmitted to the ground station.
Ground processing spatially averages these at defined grid points to produce to produce two level 1b products, SZO & SZR, which differ in the grid spacing and size of the spatial averaging window.
An estimate of the error in mean backscatter is also calculated and Kp = error_estimate/mean_backscatter values are also provided in the products.

4. Rough Estimates of ASCAT Kp
For N independent values, error in mean = sdev/sqrt(N) For a one look backscatter distribution, sdev = mean and hence we have Kp = 1/sqrt(N) For ASCAT, number of samples = samples in along track averaging  samples in range averaging  samples in spatial averaging  8  5  100  Hence Kp  (1.6%) But the onboard range and azimuth averaging produces correlated data so the samples are not independent. Reducing N to 2000 gives a more realistic result for Kp of about 2.2%

5. ASCAT Kp algorithm
Suppose x1 x2 ... xn are n identically distributed correlated variables with variance 2 and correlation(xi,xj) = ij Sample mean and variance are m=xi/n and s2 = (xi-m)2 /n Then (A) Variance in mean = var(xi/n) =  cov(xi,xj)/n2 = 2/n2 ij (B) Sample variance can be expressed as (xi-xj)2/(2n(n-1)) and taking the expectation leads to 2(n2 – ij)/(n(n-1))

6. ASCAT Kp algorithm
Hence basic algorithm used to calculate Kp is 1. for the n samples that will be spatially averaged, calculate ij using knowledge of onboard range and azimuth processing 2. calculate sample mean and variance, m & s2 3. estimate  from B, var(m) from A, then Kp = var(m)/m Actual algorithm is modified to take into account the Hamming weights used in the spatial averaging.

7. ASCAT Kp requirements
For a given error in wind speed, simulation using backscatter model and retrieval algorithm leads to a maximum error in backscatter and hence to a maximum value for Kp The requirements for Kp in the ASCAT mid beams are:
SZO
SZR
Near range, low crosswind
< 3 %
< 4.8 %
Near range, high upwind
< 6 %
Far range, low crosswind
< 7.9 %
< 13.8 %
Far range, high upwind

8. ASCAT Kp verification
To verify Kp using only ASCAT data - extract backscatter, incidence angle and Kp over ocean - split data into upwind and crosswind cases - calculate an approximate wind speed - examine Kp as function of the wind speed

9. Upwind and crosswind data sets
Transform backscatter triplets into x = (fore + aft)/sqrt(2) y = (fore - aft)/sqrt(2) z = mid Plotting x against z for any given incidence angle shows the characteristic ocean cone shape:

10. Upwind and crosswind data sets
Taking a slice through the cone by considering only data where |y| < 0.2 dB shows the upwind/downwind and crosswind cases, which can readily be separated.

11. Approximate wind speed
Fore and aft beams have look directions approximately 90 apart and over the ocean (fore + aft)/2 is relatively insensitive to wind direction CMOD5 ocean backscatter model shows a monotonic relationship between wind speed and (fore + aft)/2 Hence from (fore + aft)/2 we can readily obtain an estimate of the wind speed.

12. Example results
Typical results using this approach for SZO data: Red symbols show maximum density of data points.

13. Results
From plots of the different cases we obtain Hence the ASCAT Kp requirements are satisfied (except possibly for very low crosswinds in near range).
Required SZO Kp
Measured SZO Kp
Required SZR Kp
Measured SZR Kp
Near range, low crosswind
< 3%
3.1 %
< 4.8 %
5.1 %
Near range, high upwind
< 3 %
2.3 %
< 6 %
4.3 %
Far range, low crosswind
< 7.9 %
2.1 %
< 13.8 %
4.5 %
Far range, high upwind
1.5 %
3.3 %

14. Other issues - Kp versus incidence angle
The spacing of the full resolution data and the size of the Hamming window vary across the swath. This leads to a small increase in Kp at low incidence angles, which is more obvious in the mid beams.

15. Other issues - Kp over sea ice
Kp over regions of sea is not uniform but shows a number of spatial features:
ASCAT SZR 0 over Arctic ASCAT SZR Kp over Arctic

16. Other issues - Kp over sea ice
Features in sea ice Kp appear to be more obvious than features in backscatter and may be useful for tracking movement of sea ice, e.g. t = 0 t = 3.5 t = 7 days
Sequence of
0 images
Kp images

17. Summary
The ASCAT Kp algorithm takes into account correlations between samples and the weighting of the samples to give an estimate of the error in the mean backscatter. Examination of upwind/downwind and crosswind cases as a function of approximate wind speed shows that the Kp values in SZO and SZR data satisfy their requirements. Kp values over land/sea ice may be useful for applications such as sea ice tracking or classification.