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why would we calculate using the DALR ... instead of the standard ELR
Because we are talking about different things.
DALR/SALR relate to what happens for a parcel of air (dry/wet and reasonably presumed not to have any energy changes associated with heat transfer to/from the surroundings) subject to a varying external pressure as it moves vertically. In this case, we refer to the energy processes as being "adiabatic changes" - eg
The emphasis is on what happens to a parcel of air under those two conditions and, for the atmosphere, involves movement of the air (usually vertically). As the pressure varies (up or down), that takes energy to effect expansion or compression. If the energy can't be had from (or transferred to) external sources, it has to come from changes in the internal thermal energy of the moving air parcel and that results in the parcel's temperature varying. The difference between dry and wet relates to the energy considerations associated with evaporation and condensation ("latent heat" eg
ELR is a representation of what the temperature variation happens to be if we take a series of measurements vertically through a section of atmospheric air. The emphasis here is on conduction/radiation processes in the atmosphere associated with solar heating and so on.