Quarterly Journal of the Royal Meteorological Society Q. J. R. Meteorol. Soc. 141: 3268 – 3284, October 2015 B DOI:10.1002/qj.2608 Information content on temperature and water vapour from a hyper-spectral microwave sensor J.-F. Mahfouf, a * C. Birman, a F. Aires, b,c C. Prigent, c E. Orlandi d and M. Milz e a CNRM–GAME, M´ et´ eo-France and CNRS, France b Estellus, Paris, France c LERMA, Observatoire de Paris, Paris, France d University of Cologne, Cologne, Germany e LTU, Lulea, Sweden *Correspondence to: J.-F. Mahfouf, M´ et´ eo-France, CNRM/GMAP/OBS, 42 Avenue G. Coriolis, 31057 Toulouse, France. E-mail: jean-francois.mahfouf@meteo.fr This study examines the information content on atmospheric temperature and humidity profiles that could be provided by a future spaceborne microwave sensor with a few hundred radiances in the millimetre and submillimetre spectral domains (ranging from 7 – 800 GHz). A channel selection method based on optimal estimation theory is undertaken, using a database of profiles with associated errors from the European Centre for Medium-Range Weather Forecasts (ECMWF) numerical weather prediction model and the radiative transfer model Atmospheric Radiative Transfer Simulator (ARTS) under clear-sky conditions. The main results indicate that, by increasing the number of channels within the oxygen absorption band around 60 GHz and within the water-vapour absorption band at 183 GHz, the accuracy of temperature and humidity retrievals in the troposphere and stratosphere (for temperature) would be noticeably improved compared with present and planned microwave radiometers. The channels located in the absorption lines at 118 GHz and above 200 GHz do not bring significant additional information regarding atmospheric profiles under clear-sky conditions, partly due to greater radiometric noise. With a set of 137 selected channels that contribute to 90% of the total information content (measured by the degree of freedom for signal), it is possible to achieve almost the same performance in terms of variance error reduction as with 276 candidate channels. Sensitivity studies of various prescribed quantities defining the channel selection have been undertaken, in order to check the robustness of the conclusions. They show that none of the choices modifies the above findings. Key Words: microwave radiometer; information content; hyperspectral sounders Received 30 September 2014; Revised 7 June 2015; Accepted 12 June 2015; Published online in Wiley Online Library 08 September 2015 1. Introduction During the last two decades, there have been quite significant improvements in the skill of numerical weather prediction (NWP) models, particularly in the Southern Hemisphere, thanks to the increased usage of satellite observations in data assimilation systems, as presented for example in Simmons and Hollingsworth (2002). Recent Observing System Experiments (OSEs) and Forecast Sensitivity to Observations (FSO) experiments have revealed that the major contributors to the reduction of forecast errors are the Advanced Microwave Sounding Unit-A (AMSU- A) for temperature soundings on board several platforms and the Infrared Atmospheric Sounding Interferometer (IASI) hyperspectral instrument on board Meteorological Operational (MetOp) satellites (Zhou and Gelaro, 2008; Cardinali, 2009; Collard and McNally, 2009; Radnoti et al., 2010; McNally, 2012; McNally et al., 2013; English et al., 2013; Lorenc and Marriott, 2014). The AMSU-A instrument has a very low radiometric noise and is rather insensitive to non-precipitating clouds, but is limited to 10 sounding channels around the oxygen band at 60 GHz to retrieve atmospheric temperature profiles. On the other hand, the IASI instrument has 8461 channels in the infrared spectrum (from 4–15 μm), but cloudy pixels have to be precisely identified in order to avoid any contamination when retrieving temperature information. Moreover, among the whole set of available channels only about 100 are currently assimilated in NWP models, for both practical and scientific reasons (Hilton et al., 2012). The selected channels have been chosen in order to be the most informative about temperature and water vapour (Fourri´ e and Rabier, 2004; Collard et al., 2007). When considering water vapour, recent progress in surface emissivity retrievals over continents and sea ice (Aires c  2015 Royal Meteorological Society