Consider a fixed point in the Milankovich cycle and the solar cycle, a fixed Earth-Sun distance, and a fixed horizontal location on Earth, and assume that the Sun is at the zenith for that location. Wikipedia says that on a clear day, the global horizontal irradiance at the Earth's surface (i.e. including both direct normal irradiance directly from the Sun and diffuse horizontal irradiance from atmospheric scattering) is about 1120 W/m$^2$ at sea level, although of course the exact value will depend on all of the quantities assumed fixed above.
By about what fraction is the solar irradiance at the Earth's surface (more precisely, the global horizontal irradiance) reduced on a cloudy day? I assume that the answer will depend significantly on the types and thickness of the clouds, and (much less strongly) on all of the variables assumed fixed above, but what is a reasonable range of values? Do clouds reduce the solar irradiance at the Earth's surface by 50%? 90%? 99.999%?
I assume that clouds block the large majority of the irradiance - at least in the visible range of the EM spectrum - because clouds have an easily visible effect on the Sun's brightness, but our eyes perceive brightness on a logarithmic scale, so if the clouds didn't reduce the irradiance by a significant factor than we'd barely be able to see the difference. But clouds might be more (or less) transparent to other frequencies of sunlight (although most of the Sun's luminosity is in the visible range, so maybe that doesn't matter too much).