Sampling Results Summary CLARREO Science Team Meeting May 12, 2009 Dan Kirk-Davidoff

1. Sampling Results Summary CLARREO Science Team Meeting May 12, 2009 Dan Kirk-Davidoff Ben Katsuo Johnson University of Maryland Acknowledgements: David Young, David Doelling, LARC Hank Revercomb, David Tobin, Robert Knuteson, Jerry Robodaik, U. Wisconsin-Madison.

2. Review of results to date: • CLARREO errors calculated for virtual orbiters in sun-synchronous and three precessing orbits, as well as for pairs of orbiters, using LARC’s one-degree hourly data set • CLARREO errors found to depend in predictable ways on random (weather noise) errors, diurnal sampling errors, and spatial autocorrelation • For precessing orbiters, 3-s errors of 0.1 K are marginally attainable for zonal mean observations with a single satellite. • With two precessing orbiters, 3-s errors of 0.1 K are attainable at a grid resolution of 30 degrees (or for regional averages, e.g. over the U.S.) • 4km GOES data shows that dependence on footprint is weak, due to high autocorrelation: e.g. for 10s sampling, errors for 100 km footprint are about 25% smaller than for 25 km footprint.

3. We consider the following orbits: • Sun-synchronous 98° orbit • Precessing 90° orbit • Precessing 82° orbit • Precessing 74° orbit

4. Single Orbiter (errors in K)

5. Two Orbiters (errors in K)

6. Three Orbiters (errors in K)

7. Averages of grid point errors Single satellite errors Two satellite errors Three satellite errors Broadband Channel

8. Averages of grid point errors Single satellite errors Two satellite errors Three satellite errors Window Channel

9. Averages of zonal mean errors Single satellite errors Two satellite errors Three satellite errors At 15 degree width: 74: <0.02 K 82: <0.02 K 90: <0.02 K 98: = 0.02 K Broadband Channel

10. Averages of zonal mean errors Single satellite errors Two satellite errors Three satellite errors At 15 degree width: 74: 0.02 K 82: 0.02 K 90: 0.02 K 98: 0.03 K Window Channel

11. Errors for 3 month average, two satellites Zonal mean errors Mean Gridpoint errors

12. Errors for 3 month average, two satellites

13. Previously, we showed predictions of errors derived by scaling the grid point standard deviation by the number of point, and the decorrelation length scale. Here we show prediction by the formula: where e is the grid point error, s is the standard deviation of observations in the grid point, n is the number of observations in each grid point, r1 is the average lag-one temporal autocorrelation along the scan track for each overpass of the grid square, and r2 is the lag-one autocorrelation of the time series of grid square averages for each overpass. The first fraction adjusts n for the independence of the data, while the second adjusts s for the lack of randomness of seasonally varying radiances.

14. Here are results for four pairs of orbiters. Note the underprediction of error for the sunsynchronous orbiters, due to diurnal sampling bias.

15. A check on random errors Do our proxy data accurately reflect the real variability that a CLARREO orbiter would see? We select six representative 15° x 15° regions within which to test the sensitivity of CLARREO sampling errors to the frequency and footprint of observations. Sector 5 Sector 6 Sector 3 Sector 2 Sector 1 Sector 4

16. Footprint dependence of Sampling Errors

17. Sampling Frequency Dependence of Sampling Error (Error shown for a single 90° precessing satellite)

18. Ground track errors Sampling bias can be caused by ground track repeat cycles and their interaction with the diurnal and seasonal cycles. Figure a shows the standard deviation of observation numbers among 15 degree grid squares as a function of orbit altitude. For each altitude, the orbit inclination is adjusted so that the orbit precesses twice per year (approximately 82°). In Figure b the standard deviation of the mean hour of the half-day over all 15° grid squares is shown in blue. That is, for each satellite observation, the local time in hours, modulo 12 is noted. All observations are averaged over each grid square; due to correlations between the orbit ground track repeat cycle and the diurnal cycle, this number is not the same in each grid square. The same phenomenon occurs for the seasonal cycle; shown in red is the standard deviation over all 15° grid squares of the mean day of the year of observations, modulo 182.5. a b