This is the official ECHAM documentation as foung on the MPI website.
http://www.mpimet.mpg.de/en/science/models/echam.html

ECHAM5:

ECHAM5 Part1

ECHAM5 Part2

ECHAM4:

MPI-Report_218

Model description:
http://www-pcmdi.llnl.gov/projects/modeldoc/amip1/26mpi_ToC_b.html

ECHAM3:

ECHAM3_DKRZ

Model description:
http://www-pcmdi.llnl.gov/projects/modeldoc/amip1/26mpi_ToC.html