From the link, what appears to be the crux of the issue:
> Figure 1 shows plots of [solar] energy irradiance as functions of both wavelength and frequency. The red line is the solar irradiance at the top of the atmosphere. The green curve in the left panel is the corresponding blackbody irradiance for a temperature of 5782 K, reduced by the distance of the Earth from the Sun
> The peak of the blackbody irradiance spectrum is at 501 nm for a temperature of 5782 K. This corresponds to a frequency of ν = c/λ = 5.98 ⋅ 10¹⁴ Hz.
> The right panel of the plot shows the same solar data plotted as a function of frequency, along with the corresponding blackbody spectrum
> Note that when plotted as a function of frequency, the solar and blackbody spectra have their maxima near 3.40 ⋅ 10¹⁴ Hz, which is not the frequency corresponding to the maximum when plotted as a function of wavelength in the left panel. Indeed, 3.40 ⋅ 10¹⁴ Hz corresponds to a wavelength of λ = c/ν = 880 nm.
> In other words, when plotted as a function of wavelength, the solar irradiance is a maximum near 500 nm, in the visible, whereas the maximum is at 880 nm, in the near infrared, when the spectrum is plotted as a function of frequency.
[emphasis original]
> This occurs because the relationship between wavelength and frequency is not linear, so that a unit wavelength interval corresponds to a different size of frequency interval for each wavelength: ∣dν∣ = ∣c / λ² dλ∣.
However, it continues:
> Figure 2 shows the solar photon irradiance [number of photons per second, as opposed to number of joules delivered per second] and the corresponding blackbody spectra
> Now the maximum is at 635 nm when plotted as a function of wavelength and at 1563 nm, in the short-wave infrared, when plotted as a function of frequency. The maxima are at still different locations if the spectra are plotted as a function of wavenumber.
This time the emphasis is mine. This contradicts the explanation given above, that the curve peaks in different places along different scales because those scales are nonlinearly related. The relationship between wavenumber and frequency is linear. Why does that lead to a different plotted peak?
Are we measuring wavenumber somewhere within the atmosphere (where?), rather than in a vacuum? That would mean that different frequencies of light had different velocities, complicating the relationship between frequency and wavenumber. But it would also be a strangely artifactual way to represent solar irradiance. What's so special about wherever it is that we standardized wavenumber measurements?