Low-frequency variations of the large-scale ocean circulation in the Atlantic are reconstructed from NODC pentadal anomalies of temperature and salinity from 1955 to 1998 based on hydrographic data, in addition to atmospheric reanalysis surface forcing. Diagnostic ocean circulations are estimated from simple methods using dynamical model integrations: namely diagnostic, robust diagnostic, and short prognostic. Mean transports of heat and mass are sensitive to the method and model configuration, but their decadal variability is much more coherent and does not depend explicitly on the variations of the surface forcing, its influence being imprinted in the thermohaline structure. Multidecadal variations are of the order of 20%, with large transports in the subpolar gyre in the early 1960's and mid 1990's, and low values in the mid 1970's. By reducing the influence of subgrid-scale parameterizations and surface forcings, these methods offer alternatives to exhaustive GCM simulations.