Distributions of electric fields in two-dimensional arrays of gold nanodisks on Si3N4 membranes are modeled by use of the discrete-dipole approximation as a function of nanodisk diameter (20 nm to 50 nm), height (10 nm to 100 nm), ratio of the array spacing to diameter (1.3 to 4.7), and angle of incident light. The primary focus is on fields in a plane near the circular gold/vacuum interface with light of 532 nm wavelength incident through the membrane, a configuration that is particularly relevant to potential applications in plasmon-mediated Brillouin light scattering, nanolithography, and photovoltaics. The height/diameter ratio for maximum intensities over this plane is between 0.7 and 1.5 and not strongly dependent on the spacing for a given angle. The average intensity increases with decreasing array spacing and incident angle relative to the substrate normal. This dependence is attributed primarily to a combination of fractional coverage area of the gold and increased excitation of a dipolar contribution to the fields. The incident light at 532 nm simultaneously excites dipolar and quadrupolar surface-plasmon modes. Because the quadrupolar mode has a peak close to 532 nm, its excited fields are approximately out of phase with the incident light.