  The increased amount of information provided by ongoing missions such as the
Solar Dynamics Observatory (SDO) represents a great challenge for the
understanding of basic questions such as the internal structure of sunspots and
how they evolve with time. Here, we contribute with the exploitation of new
data, to provide a better understanding of the separate growth and decay of
sunspots, umbra and penumbra. Using fuzzy sets to compute separately the areas
of sunspot umbra and penumbra, the growth and decay rates for active regions
NOAA 11117, NOAA 11428, NOAA 11429, and NOAA 11430 are computed, from the
analysis of intensitygrams obtained by the Helioseismic and Magnetic Imager
onboard SDO. A simplified numerical model is proposed for the decay phase,
whereby an empirical irrotational and uniformly convergent horizontal velocity
field interacting with an axially symmetric and height invariant magnetic
field, reproduces the large-scale features of the much more complex convection
observed inside sunspots.
