[1] This paper describes the estimation of propagation loss and its statistical properties on the basis of observations of radar sea clutter data. This problem is solved by first finding an ensemble of relevant refractivity model parameters, and each refractivity model is weighted according to its data likelihood function. A parabolic equation propagation model is used both in mapping from environmental model to radar clutter data and also when mapping to propagation loss. Two different methods are then used for mapping from a statistical description of refractivity parameters to a statistical description of propagation loss. In the first approach, all of the sampled models explored in the inversion are used to give a statistical description of propagation loss. Alternatively, the environmental model is sampled from the probability for the refractivity model parameters and then mapped into propagation loss. This can be done efficiently if we are using the one-dimensional marginal distributions instead of the full distribution for the environmental parameters.

[1] The generation of a posteriori distribution of a statistic of propagation loss conditioned on observed radar sea clutter is described. The statistic u is the 20th percentile level of the two-way propagation loss at a 5-m height over the 10-60 km range interval. A discrete implementation of the Bayesian paradigm is employed. The forward mapping from the space of environmental parameters into the space of radar clutter incorporates a random process model such that many realizations of modeled clutter are generated for each environmental refractivity parameter combination. The algorithm is adjusted such that over a series of simulated inversion runs, it is seen that for intervals between percentile levels (e.g., between the 20th and 80th percentile levels), a posteriori distributions of u contain the ground truth values of u the correct percentage of the time (60% for the used interval). For real data cases, it is observed that the a posteriori distributions are too narrow. The inversion algorithm is used to examine the behavior of the a posteriori distribution as the noise floor is raised. An abrupt reduction in the information obtained from the clutter (indicated by a widening of the a posteriori distribution) occurs when peak clutter levels over the ranges of 25-50 km drop below about 15 dB for both simulated and real data cases.Citation: Rogers, L. T., M. Jablecki, and P. Gerstoft (2005), Posterior distributions of a statistic of propagation loss inferred from radar sea clutter, Radio Sci., 40, RS6005,