The linear relationship between attenuation and average rainfall rate for terrestrial links

Attenuation measured on terrestrial links can be used to estimate surface rainfall rates along a link path. There is current interest in the use of inverse methods to estimate rainfall over areas inferred from terrestrial links. A power-law relationship can be used to estimate rainfall rate from attenuation measured by a terrestrial link. However, the inverse method is simplified with a linear relationship between attenuation and rainfall rate when determining path averaged rainfall rates. This paper investigates power-law and linear relationships between rainfall rate and attenuation. It examines their goodness of fit for a range of frequencies and rainfall rates. Six years of disdrometer data from Chilbolton in the U.K. has been used to study both linear and power-law fits to attenuation and quantify the associated errors.