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Uncertainty calculation for SST indices

• We have estimated the uncertainty at each point of the space and time grid by taking into account:

• the satellite bias (constant = 0.2°C)
• the spatial et temporal sampling error resulting from the objective analysis (Reynolds and Smith 1994, Reynolds et al. 2002):

[remove E=, change biais->bias],

where [sigmaFG] is the "first guess" error, and E the normalized standard deviation [check] that results from the analysis procedure.

In order to estimate the error in the index, we have to determine the number of degrees of freedom in the area that defines the index. This was done empirically, by estimating a decorrelation scale. The meridional and zonal lag-correlation coefficients were calculated

,

and the lag corresponding to the first zero crossing was considered the characteristic spatial scale of the field.

The most representative lag of the time series, in latitude and in longitude was retained.

The number of degrees of freedom is estimated by:

,

where N-S is the north-south extent, and E-W the east-west extent of the box defining the index.

The propagation of uncertainty in the calculation of the index therefore:

where [w_j] are the weights associated with the surface area represented by the grid point. The error in the index is therefore:

[traduction correlated]

where N is the number of grid points involved in the calculation, and [delta y] is an estimate of the error assuming the number of degrees of freedom is N:

[more details soon]