Precise calculations of the total Rayleigh-scattering optical depth have been performed at 88 wavelengths ranging from 0.20 to 4.00 microm for the six well-known standard atmosphere models by integrating the volume Rayleigh-scattering coefficient along the vertical atmospheric path from sea level to a 120-km height. The coefficient was determined by use of an improved algorithm based on the Ciddor algorithm [Appl. Opt. 35, 1566 (1996)], extended by us over the 0.20-0.23-microm wavelength range to evaluate the moist air refractive index as a function of wavelength, air pressure, temperature, water-vapor partial pressure, and CO2 volume concentration. The King depolarization factor was also defined taking into account the moisture conditions of air. The results indicate that the influence of water vapor on Rayleigh scattering cannot be neglected at tropospheric altitudes: for standard atmospheric conditions represented in terms of the U.S. Standard Atmosphere (1976) model, the relative variations produced by water vapor in the Rayleigh scattering parameters at a 0.50-microm wavelength turn out to be equal to -0.10% in the moist air refractivity at sea level (where the water-vapor partial pressure is equal to approximately 7.8 hPa), -0.04% in the sea-level King factor, -0.24% in the sea-level Rayleigh-scattering cross section, and -0.06% in the Rayleigh-scattering optical depth.