We present new high resolution spectroscopic observations of the Herbig-Haro object HH 32 from System Verification observations made with the GMOS IFU at Gemini North Observatory. The 3D spectral data covers a 8.7 x 5.85 spatial field and 4820 - 7040 Angstrom spectral region centered on the HH~32 A knot complex. We show the position-dependent line profiles and radial velocity channel maps of the Halpha line, as well as line ratio velocity channel maps of [OIII]5007/Halpha, [OI]6300/Halpha, [NII]6583/Halpha, [SII](6716+6730)/Halpha and [SII]6716/6730. We find that the line emission and the line ratios vary significantly on spatial scales of ~1 and over velocities of ~50 km/s. A ``3/2-D bow shock model is qualitatively successful at reproducing the general features of the radial velocity channel maps, but it does not show the same complexity as the data and it fails to reproduce the line ratios in our high spatial resolution maps. The observations of HH 32 A show two or three superimposed bow shocks with separations of ~3, which we interpret as evidence of a line of sight superposition of two or three working surfaces located along the redshifted body of the HH 32 outflow.
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