Variance-ranked sound speed bases misclassify the surface duct: limits of profile RMSE as a proxy for acoustic prediction skill in the Bay of Bengal

Derin George 

Sound speed profile (SSP) estimation from surface observables is operationally mature and is evaluated almost universally by profile root-mean-square error. Using 19,934 Argo profiles from the Bay of Bengal (2005–2020), season-stratified empirical orthogonal function (EOF) bases, and BELLHOP transmission loss (TL) at 500 Hz, 1500 Hz and 3500 Hz over 24 held-out locations, we show that this metric can be decoupled from, and even inverted relative to, acoustic prediction skill. The mechanism is a property of the basis. A variance-ranked EOF expansion places its leading modes at the depth of maximum variance, near 100 m, whereas surface-duct trapping is decided in the upper 60 m. Supplied with exact coefficients, a four-mode reconstruction attains an RMS error of 0.906 m/s - 4.4 times smaller than climatology - yet classifies duct trapping correctly in only 75.3% of held-out profiles, below climatology's 76.3%. Twelve modes reach 91.6%. The additional modes carry 4.4% of the variance and are recovered from perfect surface observables at mean R² = 0.10, leaving a 13.3 percentage-point observability gap. A pre-registered intervention, re-weighting the training objective toward the duct, reduced profile RMSE further but did not improve acoustic error: the criterion required 1.5 dB and the outcome was −3.97 dB with a 95% upper bound of +0.86 dB. Replacing idealised dynamic height with DUACS altimetry degrades RMSE from 2.124 to 2.923 m/s while changing duct classification by 0.9 points. We conclude that SSP products intended for acoustic use should be evaluated acoustically, and that in this basin the accuracy the acoustics requires is not attainable from the surface.