Method : to assume a Faraday rotation angle, then select bias or noise on this angle, then simulate a regression procedure using the Klein-Swift formulation.

In the Faraday angle case, since if there is an error it is likely to be the same for every data over a single satellite path, it is more adequate to speak of a bias than of a noise. When considering a bias, in order to estimate accurately the resulting bias on SSS, the measurement noise is set equal to zero. Otherwise (first 2 lines), the noise is taken to be 1 K over the TB. (In such cases, the "bias" figure on SSS simply expresses the consequences of injecting random noise on the TB)

The following table shows the main issues.(see columns A,B,C,D,E,K;L).

 A B C D E F K L Comments SST (0.01 K) Npol Faraday angle FA (°) Bias (D°) Bias SSS (0.01) Std SSS (0.01) Incidence angle range :16 angles from 20°, step 1.4 ° No rotation 27300 2 0.0 0.0 0.0 0 0 0 0 -96 73 (1 polar) 27300 1 0.0 0.0 0.0 0 0 0 0 -15 105 1 ° rotation 27300 2 1.0 0.0 0.0 0 0 0 0 0 0 + bias 1° 27300 2 1.0 1.0 0.0 0 0 0 0 38 0 1 polar 27300 1 1.0 1.0 0.0 0 0 0 0 848 0 10° rotation 27300 2 10.0 1.0 0.0 0 0 0 0 38 0 (1 polar) 27300 1 10.0 1.0 0.0 0 0 0 0 625 0 T=293 29300 2 10.0 1.0 0.0 0 0 0 0 15 0 T=293 29300 1 10.0 1.0 0.0 0 0 0 0 264 0

Results :

• The effect of a bias on Faraday angle FA does not depend much on the angle itself in the 0° - 10 ° range ;
• With single polarisation data a bias on FA has catastrophic consequences ;
• With dual polarisation the SSS bias is considerably reduced (by a factor 20 to 30); in order to be within 0.1 PSU the FA bias then has to be smaller than 0.25°.
• For the ionospheric error to be small with respect to the total 0.1 PSU bracket, one should aim at estimation errors on the Faraday angle better than 0.1 °. For weak ionosphere (morning orbit), this means about 10% on the TEC estimate ; for strong ionosphere, more like 1%.