Examining constants in the Paulus-Jeske evaporation duct model

The propagation of electromagnetic waves in the environment can be subjected to anomalies due to the structure of the index of refraction in the atmosphere. In the marine environment, one of the most common anomalies results from evaporation ducts, which are due to moisture gradients in the surface layer that extend a few tens of meters above the air-sea interface. The Paulus-Jeske evaporation duct model (PJ) (Paulus, 1990] is frequently used for representing evaporation ducts in propagation simulations. This logarithmic model is considered a single parameter model, where the free parameter is the duct height, which is determined from bulk measurements of atmospheric and oceanic conditions near the sea surface and utilizes Monin-Obukhov similarity theory. While much work has been performed over the years evaluating and improving estimates of the duct height from atmospheric measurements (e.g., Babin et al. 1997; Fairall et al. 1996, Pasricha et al., 2002, Ivanov et al. 2007], discrepancies between measured and predicted propagation remain (e.g., Gunashekar et al. 2007). To address these shortcomings, recent efforts have begun utilizing inverse problem approaches to invert for the refractivity profile based on measured sea clutter and forward propagation models (Gerstoft et al. 2003; Karimain et. al 2011; Xiaofeng and Sixun 2012). Many of these “refractivity-from-clutter” studies also use the PJ model to invert for parameters that will adequately describe the refractivity profile for evaporation ducts. These implementations also consider the PJ model as a one-parameter model. In addition to the duct height, two constant values (fixed parameters] appear in the PJ model formulation, which represent the aerodynamic roughness (Z₀ = 1.5×10^-4 m] and the critical potential refractivity gradient (c₀=-0.125 M-units/m) (Paulus, 1990). A number of assumptions go into fixing these constants, and although atmospheric and o- eanic conditions often do not adhere to these assumptions, the PJ model is frequently used to represent evaporation ducts in all types of conditions.