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This article presents a method for obtaining the mean structure of the temperature, specific volume anomaly, and velocity of an ocean current, using isopycnal float data combined with gravest empirical mode (GEM) fields calculated from historical hydrography. A GEM field is a projection on a geostrophic streamfunction space of hydrographic data, which captures most of the vertical structure associated with frontal regions. This study focuses on the North Atlantic Current–subpolar front (NAC–SPF) current system, but the float–GEM method has broad applicability to baroclinic ocean currents in general. The NAC–SPF current system is of climatic interest, being an important conduit of warm salty waters into the northern North Atlantic. It constitutes the upper limb of the thermohaline circulation of the Atlantic Ocean and plays a crucial role in the moderation of European climate, but uncertainties regarding its transport and corresponding heat fluxes remain, mainly because the structure of the system is not well known. This paper shows how isopycnal floats can be used to obtain such estimates. The performance of the float–GEM method is tested in two ways. First, two synoptic hydrographic sections (one across the NAC and the other across the SPF) are reconstructed from simulated isopycnal float pressure measurements. The baroclinic transports of volume and temperature (relative to 1000 dbar) across the sections are well reproduced by the method: the float–GEM transport estimates have an accuracy of ±20% and a precision of ±15% or less, which result in deviations of less than ±10% from the “real” values. In the second test, horizontal maps of pressure and temperature on the δ = −12.7 × 10−8 m3 kg−1 specific volume anomaly surface (σθ ≈ 27.5 kg m−3) are produced, using RAFOS float data from two experiments that sampled the region from 1993 to 2000. These maps compare well with similar maps constructed in previous studies and establish the consistency of the method. The good performance of the float–GEM method gives confidence in this novel way of using isopycnal floats to obtain information on the structure of the ocean. Combined with the velocity measured by the floats, it has the potential to estimate absolute transports and heat fluxes along the NAC–SPF system.