The uncertainty bounds for geoacoustic inversion results due to sound speed variability in the water column perturbed by internal waves are assessed. Our previous work showed that if the sound speed variations are not taken account into the water column model, they will affect the accuracy of geoacoustic inversions. In this paper, we seek to quantify how well the error bounds could be given under certain knowledge of the sound speed variations. In doing so, the equivalent transform method derived from the linear perturbation theory plays a role in error transferral from water column to bottom. The water column variability is decomposed into ocean dynamic modes or as empirical orthogonal function (EOF) modes. Obtaining the ocean dynamic modes requires having the buoyancy frequency profile, whereas obtaining the EOF modes requires having vertical time series data. In general, it is difficult to assemble full statistics of the sound speed variations, so we examine the uncertainty bounds of the inversion results in the case where only partial statistics can be observed.