This paper explores the use of a recently developed chaotic lidar sensor to perform impulse response measurements underwater. The sensor's measured system impulse response, which approximates a thumbtack function with a 1 ns peak width, is used with an ocean impulse response simulator to predict the chaotic lidar's expected performance underwater. A calibration routine is developed to compensate for the finite resolution and sidelobes in the sensor's system impulse response, improving the accuracy of the simulated chaotic lidar results. In an example application of water turbidity measurement, the extinction coefficient of water, c, is extracted from simulated chaotic lidar impulse responses with an average error of 0.03/m over a range of turbidities from c=0.1/m to c=0.3/m. Simulations are also presented to demonstrate that the chaotic lidar sensor impulse response can simultaneously detect multiple reflective elements and the volumetric backscatter response with a 1 ns temporal resolution. Laboratory water tank measurements are performed to validate the simulation approach, and the experimental chaotic lidar measurements are in reasonable agreement with the simulated results.