Methodology and data analysis

Spaceborne SAR provides fine-resolution radar images over broad areas. The pixel size in the ERS images analyzed here is ~20 m over a swath of 100 km in width. The radar data comprise a grid of complex vectors, one for every pixel. The length of the vector is a measure for the backscatter intensity and yields information on the roughness of the imaged surface. Over water surfaces, the backscatter intensity is dominated by Bragg scattering. Contrasts in surface roughness, quantified in the normalized radar cross section ($\sigma ^0$), can be interpreted as differences in mainly wind speed and direction [Stoffelen(1998)]. Sea state or heavy rain are further atmospheric phenomena which may influence the intensity. SAR images can detail small scale structures over seas such as boundary layer rolls [Alpers and Brümmer(1994)]. Here we used a C-band model, CMOD4, to compute the wind speed from the normalized radar cross section and the incidence angle of the radar waves [Stoffelen(1998)]. This model correlates backscatter intensity with the wind at 10 m height ¹.

The phase of the vector is a superposition of three components; a path length component, depending on the geometric distance between the spacecraft and the resolution cell, a propagation velocity component, and a scattering component due to the unknown reflection characteristics of the many different scatterers within a resolution cell. The superposition of the three components prohibits unambiguous interpretation of the phase measurement.

In the repeat-pass interferometric configuration, two SAR images are acquired from nearly the same position in space at two epochs, resulting in two nearly identical images. Differences in the phase information in both images are caused by the differences in the imaging geometry (different path lengths) and the different distribution of propagation delay during the first and the second acquisition. The scattering components over land and ice surfaces can be similar for both acquisitions, especially for short intervals. This principle enables the formation of a coherent phase-difference image or interferogram, see, e.g., Bamler and Hartl [1998] and Massonnet and Feigl [1998]. Here we eliminate phase signal due to geometric path length differences using an elevation model [Massonnet et al.(1993)]. As the interferometric pairs are acquired with a time interval of only 24 hours, coherent phase information is obtained in which no surface deformation occurred. This methodology ensures that the interferometric phase is only due to atmospheric propagation delay.

The delay of the radar signal is caused by an integration over the refractive index of the propagation medium, along the line of sight. Horizontal and vertical heterogeneities in refractive index are influenced by the spatial distribution of water vapor, pressure, temperature, liquid water, and electron content. Yet, over distances less than ~50 km, the main signal in the interferogram is due to water vapor, albeit temperature and liquid water can add some additional mm's of delay [Hanssen et al.(1999)]. Using surface temperature observations, the integrated water vapor signal can be converted to precipitable water--its liquid equivalent, when assuming a fixed vertical temperature profile [Bevis et al.(1992)].

¹

Other models correlate to a so-called neutral equivalent wind, but in that case accurate ancillary information is needed on atmospheric stratification [Stoffelen(1998)]