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Uncertainty calculation for SST indices
Following Reynolds and Smith (1994) and Reynolds et al. (2002,) the expected uncertainty of the SSTA-based indices is determined by estimating two components; the satellite bias and the analysis error. Here, the satellite bias at each analysis grid point is estimated to be 0.2 degrees C (see Reynolds and Smith 1994,) and the representative analysis error is taken as the spatial average of product of the "First Guess Error," which ranges from about 0.2 to 0.8 degrees C depending on location and accounts for the expected error in the case that no new observations are available to constrain the analysis, and the normalized error variance over the index averaging region, a product of the analysis, which ranges from 0 (perfect constraint from observations) to 1 (no constraint from observations.) These values are averaged over the index region assuming that the satellite bias has zonal and meridional spatial scales of 850km and 616km, respectively, and the spatial scale for the analyis error is the first-baroclinic Rossby radius of deformation (see Chelton et al. 1997.) The estimated satellite and analysis errors are then added in quadrature to determine the expected uncertainty of the given SSTA-based index.
Because the estimated spatial scales associated with the satellite bias are larger than those of the analyis error, the satellite component is generally the domininant source of error for the surface SSTA-based indices. This type of error is prone to occur following major volcanic acitivity (Reynolds and Smith 1994,) though resulting errors are still expected to be small compared to the variability of the surface indices.
Chelton, D. B., R. A. deSzoeke, M. G. Schlax, K. El Naggar and N. Siwertz (1998) Geographical variability of the first-baroclinic Rossby radius of deformation. J. Phys. Oceanogr., 28, 433-460.
Reynolds, R.W. and T.M. Smith (1994) Improved global sea surface temperature analyses using optimum interpolation. J. Climate, 7, 929-948.
Reynolds, R.W., N.A. Rayner, T.M. Smith, D.C. Stokes and W. Wang (2002) An improved in situ satellite SST analysis for climate. J. Climate, 15, 1609-1625.