We analyze the statistical channel properties of short to very shortrange shallow water communication environments based on real channel measurements taken in a water-tank, a swimming pool, very shallow and shallow lakes. More specifically, we estimate the channel impulse response (CIR), the probability density function (PDF) of channel fading and fit to Rayleigh, Nakagami, Weibull, Rician and Beta distributions. We compare the 'goodness-of-fit' of these distributions based on the Kullback-Leibler (KL) divergence criteria. From our experimental results, we confirm that the shallow water acoustic channel is highly time-varying and does not necessarily follow a Rayleigh distribution. Instead, we observe that in very-shallow water lake environments the channel fading exhibits close-to Weibull or Rician distribution. On the other hand, in shallow water lake the channel fading behavior is better captured by a Beta distribution.