A Cumulative Distribution Function Method for Normalizing Variable-Angle Microwave Observations

Microwave remote sensing has been widely acknowledged as the most promising technique to measure the spatial distribution of near-surface soil moisture. However, due to a strong incidence angle dependence in microwave radiometer and radar data, airborne observations typically have an across-track variation in incidence angle that needs to be normalized to a fixed angle for the purposes of data visualization and aggregation to spatial resolutions that mimic spaceborne data. There are two normalization methods commonly used, often resulting in a noticeable stripe pattern along the flight direction. This paper develops a 2-D cumulative distribution function (CDF)-based normalization method, which normalizes the variable-angle observations to a reference angle by matching the CDF of observations for each nonreference angle, using the information content from multiple partially overlapped swaths. The performance of this method is tested using an airborne microwave radiometer and radar observations collected during three Australian field experiments. The normalization results show that the stripe pattern problem over heterogeneous land surfaces when not any prior knowledge of land surface types is primarily attributed to the linearity of the commonly used normalization methods, and that the nonlinear 2-D CDF-based method produced the least noticeable stripe pattern and the highest normalization accuracy when compared with independent data. Compared with the two linear methods, a root-mean-squared error improvement of up to 2 K was obtained using 1-km radiometer data, and a correlation coefficient improvement of 0.2 and RMSE improvement of ~0.2 dB were achieved for the 7-m resolution radar data.