  Rayleigh--B\'enard convection, which is the buoyancy-induced motion of a
fluid enclosed between two horizontal plates, is an idealised setup to study
thermal convection. We analyse the modes that transport the most heat between
the plates by computing the proper orthogonal decomposition (POD) of numerical
data. Instead of the usual POD ansatz of finding modes that describe the energy
best, we propose a method that is optimal in describing the heat transport.
Thereby, we can determine the modes with the major influence on the heat
transport and the coherent structures in the convection cell. We also show that
in lower-dimensional projections of numerical convection data, the newly
developed modes perform consistently better than the standard modes. We then
use this method to analyse the main modes of three-dimensional convection in a
cylindrical vessel as well as two-dimensional convection with varying Rayleigh
number and varying aspect ratio.
