Underlying Physics

The Hydrogen line and L-band radiations from Space that illuminates the Earth:

The hydrogen line, 21 centimeter line or HI line refers to the electromagnetic radiation spectral line that is created by a change in the energy state of neutral hydrogen atoms. This electromagnetic radiation is at the precise frequency of 1420.40575177 MHz, which is equivalent to the vacuum wavelength of 21.10611405413 cm in free space. This wavelength or frequency falls within the L-band microwave radio region of the electromagnetic spectrum, and it is observed frequently in radio astronomy.

Hydrogen being the principal constituent of sun and of most of the stars and planets, the Earth is constantly illuminated by  a field of L-band radiations coming from Space.

 Sea surface emission at L-band and basic measurement principle

As illustrated in the above schematic figure, the radiations downwelling from space  at 1.4 GHz and impinging the ocean surface are partly absorbed within a thin ~1 cm layer just beneath the ocean-atmosphere interface (the so-called skin-layer) and partly reflected back toward the sky. If this layer is considered at statistical equilibrium (which is a valid assumption for our purposes), the ocean surface re-emits the entire energy that it absorbed towards the upper hemisphere. The apparent brightness of the sea or 'brightness temperature' is how much energy is coming from the ocean surface per square meter per second in a given direction at such electromagnetic frequency. An instrument that can measure the apparent brightness generated by these radiations  is called a radiometer.
The underlying physics of salinity remote sensing from satellites is based on the sensitivity of the brightness temperature of sea water, Tb, to Sea Surface Salinity (SSS) and sea surface temperature (SST), Ts. At microwave frequencies. Tb is related to SSS and Ts by the relation Tb = e x Ts, where e is the emissivity of the sea surface, itself a function of SSS and Ts.
This sensitivity is strongest in the frequency range from 0.5 to 1.5 GHz; the protected frequency band at 1.4 GHz (L-band) has therefore been selected for SMOS and Aquarius missions.
For typical ranges of SSS and Ts over the open oceans, the Tb at L-band has a range of about 4-6K. The sensitivity of Tb to changes in SSS vs. Ts :is greatest in warm water (0.7K/psu at 30 °C) and least in cold (0.3K/psu at 0°C). Therefore, given measurements of the apparent brightness of a water body surface at L-band with a radiometer and an estimate of its surface température, the salinity at the surface can be deduced. 
Additional difficulties:
Measurement of salinity with this technique is complicated by several factors, the largest of which is the significant effect of sea surface roughness on microwave emission.  Sea surface roughness (surface wind waves, swells, foam generated by breaking waves,..) effects can produce a  change in the apparent brightness Tb of up to ~5K, for very a rough sea surface.
This effect dictates the need for an accurate means of measuring the sea surface roughness, which also must be accomplished simultaneously with the Tb  measurements, due to the short time scale of sea surface wind variability.

Other contributions to the measured Tb at L-band  for a space orbiting radiometer include galactic emissions (DTb of ~2-8K), atmospheric emissions (DTb ~2.4-2.8K), and emission from water vapor and cloud liquid water (both have a small effect on Tb). Additionally, the Faraday rotation of the polarized microwave emissions as the radiation passes through the ionosphere, needs to be corrected for. (Although there is no effect on (TbV+TbH), the individual TbV and TbH measurements can change by up to 5K.

Retrieval Algorithm

The retrieval algorithm for SSS consists of several parts; a) evaluation of Tb at the sea surface by correcting for ionosphere, atmosphere and extra-terrestrial radiations b) correction of roughness and sea surface temperature contributions and c) retrieval of SSS from Tb.

. Radiative transfer models allow correction for up- and down-welling emission from the atmosphere, atmospheric and ionospheric attenuation and Faraday rotation. Down-welling galactic emissions are also taken into account using accurate maps established by radio-astronomers. With these corrections, plus knowledge of the Ts and surface roughness, salinity can be calculated from Tb.

Residual  corrections to these data analysis algorithms will be carried out in a series of steps that have already begun with a series of aircraft test programs, plus laboratory and model developments. Finally, instrument calibration will include three major thrusts including deep space calibration maneuvers, detailed calibration corrections using highly accurate in-situ measurements of SSS, Ts, winds  and roughness from buoy networks, plus error reduction approaches that have been proven to be effective approaches to error reduction on other satellite data analysis systems.