ON THE AMOUNT OF INFORMATION CONTENT IN MICROWAVE RADIOMETRY FOR WET DELAY ESTIMATION J. Gual and A. Camps Remote Sensing Lab, Dept. of Signal Theory and Communications Universitat Politècnica de Catalunya-Barcelona Tech and IEEC/CTE-UPC UPC Campus Nord, building D4, 08034 Barcelona, Spain, e-mail: jmgualcovas@gmail.com, camps@tsc.upc.edu Abstract—This work aims at determining the set of optimum frequencies to be used in the companion microwave radiometers in future synthetic aperture radar altimeters, to provide higher spatial resolution of the atmospheric water vapor state so as to improve the wet delay correction in coastal regions. The channel selection is based on the study of the frequencies that provide the largest amount of information, as defined by the largest information entropy change from a prior knowledge state. It is found that four frequencies, one close to the 22 GHz peak, and three other ones around 175.188 GHz provide a near optimum compromise between the amount of information measured, and the instrument’s complexity. Index Terms—wet delay, atmospheric water vapor, microwave radiometer, radar altimeter, weighting functions, entropy, information content. I. INTRODUCTION Satellite altimetry plays an important role among the Earth observation techniques, and it is very useful for ocean missions. Coastal Altimetry (approximately 0-50 km away from the coast), allows to study storm surge’s by measuring the Total Water Level Envelope (TWLE), and it is also very useful in wave models. However, coastal altimetry data is inaccurate and difficult to interpret due to the variation of the waveforms’ shape (shape of the radar returns), when the antenna footprint of the instrument enters in the land, and because of the rapid variations of the wet tropospheric delay. The application of SAR techniques to radar altimetry, such as in ESA’s CryoSat-2 mission has allowed to significantly improve the along-track resolution, providing much better results than in pulse-limited altimeters. Nevertheless for these high-resolution altimeters, an optimized delay correction is needed to solve the rapid tropospheric wet delay variability [1]. In this study a methodology is presented to identify from the measured brightness temperature of the atmosphere, a set of frequency channels that provide the most significant and uncorrelated information on the water vapor content in the atmosphere. Previous works [2] have provided a water vapor content analysis based on the number of degrees of freedom for a ground-based zenith-viewing model, assuming clear skies, and different seasons. A similar brightness temperature model, based on space-based observations is presented in this study. However, unlike in [2], in this work, the water vapor entropy is used to define the optimum channels, for three different climates and types of surfaces. First of all a Mathematical model is defined to describe the Physics of the atmosphere, and from this model the contribution of the water vapor into the brightness temperatures as measured by a nadir-looking microwave radiometer are derived. Then, a Mathematical model using inversion methods to select frequency channels providing the largest amount of data (i.e. uncorrelated data) is defined. Finally, results for three “standard” climates (tropical, temperate, and polar) are presented. Synthetic atmospheric pressure, temperature, and water vapor profiles are used, and different surface emissivities are also considered in the computation of the down-looking brightness temperatures for the three atmosphere models. II. METHODOLOGY A. Forward Model In this study three different atmosphere models are considered for the three different climates: tropical, temperate, and polar, and for the three different types of surfaces: ice, sea, and coastal regions. The three standard atmosphere models are generated using as input parameters the water vapor, temperature, and pressure from 0 km (sea surface height), up to 64 km height (mesosphere). The atmospheric temperature, pressure, and water vapor profiles (T(z), P(z), and ρ v (z)) for the three different climates are described in [3, pp. 339-373] (Fig. 1), and they are used to compute the gas absorption (κ α (f, z)) as a function of the frequency and height, the atmospheric optical thickness (τ(z, ∞)), the upwelling temperature (T UP ), and down-welling temperature (T DN ) as a function of the frequency (f). Finally, three different surface emissivities are used to calculate the surface brightness temperature (T b ), and the downwelling temperature reflected back to the atmosphere (T sc ). The emissivity values are 1.00, 0.50 and 0.75, which correspond approximately to those of the ice, ocean, and coastal regions, respectively. Finally, the brightness temperature reaching the radiometer antenna (T B , Eqn. 1) is then computed for the nine possible combinations of the three different climates and the three different surfaces: a)