Sandra Castro, Gary Wick, Peter Minnett , Andrew Jessup & Bill Emery

1. The Impact of Measurement Uncertainty and Spatial Variability on the Accuracy of Regression-based SST Algorithms Sandra Castro, Gary Wick, Peter Minnett, Andrew Jessup & Bill Emery

3. The Issue… IR Radiom Buoys

4. Initial Question • Does direct regression of satellite infrared brightness temperatures to observed in situ skin temperatures result in SST-product accuracy improvements over traditional regression retrievals to the subsurface temperature?

5. Approach • We evaluated parallel skin and subsurface MCSST-type models using coincident in situ skin and SST-at-depth measurements from research-quality ship data. • RMS accuracy of skin and SST-at-depth regression equations directly compared

6. Data: 2003-2005 NOPP Skin SST Satellite IR: 2003-2005 AVHRR/N17 GAC and LAC NAVOCEANO BTs Royal Caribbean EXPLOrer of the seas Skin SST: M-AERI Interferometer (RSMAS) SST-at-depth: Sea-Bird thermometer (SBE-38) @ 2m NOAA R/V Ronald H. Brown Skin SST: CIRIms Radiometer (APL) Sst-at-depth: sea-bird thermometer (SBE-39) @ 2m

7. Satellite - In situ SST Matchups • Spatial windows: 25, 8, 4 km • Temporal windows: 4, 1 hrs Min Time Mean All

8. Results There is no improvement in accuracy for the skin-only SST products in spite of the more direct relationship between the satellite BTs and the in situ skin SST observations!

9. Results • Regression models fitted to the SST-at-depth almost always resulted in better accuracies (lower RMSE) than skin models regardless of: • Algorithm type (split vs. dual window) • Collocation criteria (window bounds/sampling) • Satellite spatial resolution (GAC vs. LAC) • Radiometric sensor (CIRIMS and M-AERI) • Time of day (day, night, day and night) • Time span (individual years vs. all years combined) • Geographical region

10. Next question • Can differences in measurement uncertainty and spatial variability explain the lack of accuracy improvement in the skin SST retrievals?

11. Approach • Explore the combination of the effects by adding increasing levels of noise to the SST-at-depth, such that: RMSE bulk SST = RMSE skin SST • Attempt to decompose the supplemental noise into individual contributions from the two effects using Variogram techniques.

12. Added discrete realizations of white noise processes to SST-at-depth: Build RMSE curve for noise-degraded SST-at-depth. Where the RMSE (skin) intercepts the curve, corresponds to the supplemental noise needed for equivalence in RMSE Note that, for equal number of observations: RMSE SST-at-depth < RMSE SST skin, but RMSE SST skin < RMSE SST emulated buoy

13. Estimates of Required Noise • The noise generally decreases with tighter collocation windows and finer satellite resolution • Required supplemental noise ranged between 0.17 and 0.14 K for the GAC cases in which all the data streams were combined and between 0.09 and 0.14 for the LAC

14. Instrument Measurement Error • From literature: M-AERI: 0.079°C and CIRIMS: 0.081°C • IR Radiometers: σ~O(0.08°K) • Thermometers: σ~O(0.01 K) • Added Noise: σ~O(0.08°K) Empirical distributions for the measurement uncertainty of M-AERI skin SST and coincident SST-at-depth support the required supplemental noise!!

15. Variogram Analysis M-AERI CIRIMS The variogram (Cressie, 1993, Kent et al., 1999) is a means by which it is possible to isolate the individual contributions from the 2 sources of variability, since the behavior at the origin yields an estimate of the measurement error variance, while the slope provides an indication of the changes in natural variability with separation distance.

16. Method We fitted a linear variogram model by weighted least squares to both skin SST and SST-at-depth with separation distances up to 200 km, and extrapolated to the origin to obtain the variance at zero lag. Measurement Uncertainty M-AERI Spatial Variability

17. SST Uncertainty Estimates On spatial scales of O(25 km): • Variogram estimates provide strong support to the notion that the combined role of differences in measurement uncertainty and spatial variability between the skin and SST-at-depth account for the range of required subsurface supplemental noise found graphically. • Measurement uncertainty estimates are consistent with the noise required to reconcile the accuracy differences between thermometers and IR radiometers (σ~O(0.08 K)).

18. Conclusions • Removal of the near-surface temperature profile effects through directly fitting the regression models to radiometric skin SSTs did not result in satellite SST estimates with better accuracy than regression models fit to coincident, research-grade ship-borne subsurface SSTs. • Lack of improvement was consistent with the expected impact of both measurement uncertainty and enhanced spatial variability of the skin observations. • The noise level required to ensure a subsurface SST product accuracy equivalent to that of the skin products ranged between 0.09 and 0.17 K for those cases in which all data streams were combined. • Variogram analysis suggested that differences in measurement uncertainty could account for 0.07 to 0.10 K of the required supplemental noise, while differences in spatial variability could account for up to an additional 0.07–0.10 K on scales of 25 km.

19. Implications • Even if technological advances allowed for IR radiometer accuracies of σ~O(0.01 K), we still have spatial variability to worry about… • The role of spatial variability in the uncertainty budget arises in part because inadequacies in point-to-pixel comparisons • Sparse radiometric sampling along a single track does not provide full coverage of the spatial variability within the satellite footprint. • The satellite measurement is a spatial average over the FOV. This spatial average might be smoothing out the enhanced variability of the skin, making the variability of the estimate more representative of the variability of point measurements of SST-at-depths • To better understand and quantify these effects, we require increased observations of sub-pixel satellite SST variability. In particular, direct observations of spatial variability as a function of measurement depth are needed. • Need for higher accuracy buoy sensors and improved atmospheric corrections.

20. Sum of two random variables