Resumen: We propose a physically-based, multispectral simulation to render underwater scenarios in real time, which also takes into account the RGB response curves of arbitrary sensors. Our approach can simulate the two main phenomena of underwater illumination. First, there is multiple scattering, light scattered several times between particles before reaching the sensor. This phenomenon is therefore very low frequency and can be modeled as a function of depth and wavelength. We propose a physically-based approximation to this complex phenomenon based on the measurable coefficient of diffuse downwelling attenuation. The second key component of underwater appearance is single scattering, light refracted on the surface that is scattered once before reaching the eye. Single scattering is responsible for the volumetric shadows and light rays visible underwater, and its simulation is key for real-time visualizations. We leverage a combination of volumetric lighting and caustics projection real-time techniques to provide a plausible approximation. We have implemented our proposed mixed method in Unity, and we show how our method is able to react to a variety of physical conditions, such as the water type or the underwater depth. We use measured data from oceanography, and show the ability of our method to approximate the appearance under different scattering, absorption and downwelling coefficients, as measured in the well known Jerlov water types from oceanography. We compare our approximation to a path traced simulation, showing great accuracy at a fraction of the computational cost. We also compare our method to another state-of-the-art method for underwater rendering, and show how our proposed model is more physically-based and controllable.