A mode-based technique for estimating uncertainty in range-averaged transmission loss results from underwater acoustic calculations

Abstract

The equivalence of range and frequency averaging of acoustic propagation model results, based on the similarity of their analytic forms in mode calculations, was shown by Harrison [J. Acoust. Soc. Am. 97, 1314–1317 (1995)]. Here it is shown how oceanographic measurement errors and receiver bandwidth can be mapped into uncertainty in the number of modes being propagated. This can be mapped into range boundaries for averaging calculations, thereby giving upper and lower confidence boundaries for frequency-averaged transmission loss calculations. Examples of the application of this technique to synthetic data, where the measurement uncertainties are known and deliberately included, are shown.

Representative environments for reduced estimation time of wide area acoustic performance

“…A method for mapping these values into overall uncertainty in sound TL levels has been developed by Zingarelli (2008) and is known as the uncertainty band, or UBAND algorithm. UBAND is used here to translate uncertainty in the ocean waveguide, as described by the spread of the environmental cost functions, into TL and system performance uncertainty.…”

“…The UBAND algorithm (Zingarelli, 2008) is based on Harrison and Harrison (1995), who noted that a range average of TL is very similar to a frequency average over the system band width, due to the mathematical similarity of the two techniques using sums over normal modes.…”

“…By examining how the cost function spread relates to the TL spread, the uncertainty of the performance of each province is characterized. This is done using the uncertainty band algorithm (UBAND) developed by Zingarelli (2008). UBAND takes the rms difference of various acoustic model inputs and translates that to upper and lower bands on the TL curve.…”

“…The pdf need not be normal, have a mean of zero, or uni-modal. " *http://www.spatial.maine.edu/~worboys/SIE565/papers/pang%20viz%20uncert.pdf http://www.onr.navy.mil/sci_tech/chief/cuwg/index.html uncertainty band (UBAND) -an algorithm developed by Zingarelli (2008), based on Harrison and Harrison (1995), who noted that a range average of TL is very similar to a frequency average over the system band width, due to the mathematical similarity of the two techniques using sums over normal modes. Zingarelli (2008) extended that range averaging technique to calculate upper and lower boundaries on a TL prediction by estimating an uncertainty in the number of modes used in the mode sum, based on the uncertainty in the environmental inputs.…”

“…The acoustic model is then run for each representative and substituted for those that it represents to generate a sensor coverage (PAC) or related performance map. In order to capture the variation within the provinces, the UBAND algorithm (Zingarelli, 2008) has been applied to obtain upper and lower bounds on the TL that can be converted to error bars on the performance predictions.…”