## R

Figure 11.5 Summary of the POSSM model evaluation methodology (Lauer, 1979).

were evaluated and one model was selected as the standard against which to compare the other models. More than 10 different model versions were evaluated using an ocean environment described by a single sound-speed profile and a flat bottom (i.e. range-independent environment).

All subject models were executed at four frequencies ranging from 35 to 200 Hz. The resulting TL data were modestly smoothed and then compared with the standard model. These comparisons were conducted within variable range intervals specifically chosen to correspond to common sonar detection zones: direct path (DP); first and second bottom bounce (BB) regions; and first, second and third convergence zone (CZ). The means and standard deviations (a) of the differences in TL between the standard and the subject models were then calculated within each interval. A zero mean indicated that the standard model and the subject model produced TL values that were identical when averaged over the interval. The resulting means and standard deviations were appropriately weighted and averaged to obtain the cumulative accuracy measures (CAM). Mathematically, the CAMs for the mean and standard deviation were expressed as (Lauer and Sussman, 1979)

where i is the case index, j the range interval index, Nc the total number of cases, Nr. the total number of range intervals for the ith case, Wjj the weights in each case and range interval bin (AR)j to be applied to mean values of transmission loss (TL) differences, and Wj the weights applied to ij standard deviations of TL differences.

In the event that all values of Wj and Wj were chosen to be unity, CAMM became the "grand" mean taken over all cases and range intervals, and CAMff became the "grand" standard deviation taken over all cases and range intervals. The weighting functions (Wj, Wj) were functions of the acoustic frequency (f), source depth (Zs), receiver depth (Zr) and range interval (AR).

For the present discussions, only four specific versions of propagation models have been selected. These models represent four of the five different modeling approaches described earlier in Chapter 4. The only modeling approach not investigated by POSSM was the parabolic equation (PE) approach. At the time of POSSM's activities, PE models were not yet widely used. Moreover, fast-field program (FFP) models were considered to be the most accurate available and were commonly used as standards for comparison. The four approaches and corresponding models represented are:

Approach Model

Ray theory (with corrections) FACT

Multipath expansion (hybrid) RAYMODE

Normal mode NLNM

### Fast-field program FFP

In the comparisons described by Lauer and Sussman (1979), and by DiNapoli and Deavenport (1979), the FFP model was used as the standard. Table 11.1 summarizes the computer program sizes and execution times for each model in the context of the standard problem selected by POSSM. A quantitative comparison of model accuracies was reported by Lauer and Sussman (1979) based on the methodology summarized in Figure 11.5. Only the four particular models identified above will be discussed here. Representative results from one test case are summarized in Table 11.2. It must be

Model |
Program size |
Execution time (s) |

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