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We developed a method to compute the temperature and density structure alongthe line of sight by inversion of the differential emission measure (DEM),under the assumptions of stratification and hydrostatic equilibrium. We appliedthis method to the DEM obtained from AIA observations and used the results,together with potential extrapolations of the photosheric magnetic field, tocompute the microwave emission of three sunspots, which we compared withobservations from the RATAN-600 radio telescope and the NobeyamaRadioheliograph (NoRH). Our DEM based models reproduced very well theobservations of the moderate-size spot on October 2011 and within 25% the dataof a similar sized spot on March 2016, but predicted too low values for the bigspot of April 14, 2016. The latter was better fitted by a constant conductiveflux atmospheric model which, however, could not reproduce the peak brightnesstemperature of $4.7\times10^6$ K and the shape of the source at the NoRHfrequency. We propose that these deviations could be due to low intensitynon-thermal emission associated to a moving pore and to an opposite polaritylight bridge. We also found that the double structure of the big spot at highRATAN-600 frequencies could be interpreted in terms of the variation of theangle between the magnetic field and the line of sight along the sunspot.

Modeling of the sunspot-associated microwave emission using a new method of DEM inversion