Upon its completion the Herschel ATLAS (H-ATLAS) will be the largest submillimetre survey to date, detecting close to half-a-million sources. It will only be possible to measure spectroscopic redshifts for a small fraction of these sources. However, if the rest-frame spectral energy distribution (SED) of a typical H-ATLAS source is known, this SED and the observed Herschel fluxes can be used to estimate the redshifts of the H-ATLAS sources without spectroscopic redshifts. In this paper, we use a subset of 40 H-ATLAS sources with previously measured redshifts in the range 0.5<z<4.2 to derive a suitable average template for high redshift H-ATLAS sources. We find that a template with two dust components T_c = 23.9 K, T_h = 46.9 K and ratio of mass of cold dust to mass of warm dust of 30.1) provides a good fit to the rest-frame fluxes of the sources in our calibration sample. We use a jackknife technique to estimate the accuracy of the redshifts estimated with this template, finding a root mean square of Delta z/(1+z) = 0.26. For sources for which there is prior information that they lie at z > 1 we estimate that the rms of Delta z/(1+z) = 0.12. We have used this template to estimate the redshift distribution for the sources detected in the H-ATLAS equatorial fields, finding a bimodal distribution with a mean redshift of 1.2, 1.9 and 2.5 for 250, 350 and 500 um selected sources respectively. end{abstract}
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