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The recent increase in spatial resolution for satellite instruments has  made it feasible to study distributions of trace gas column  densities on a regional scale. For this application a new gridding  algorithm was developed to map measurements from the instrument's  frame of reference (level 2) onto a longitude–latitude grid (level 3). The algorithm is designed for the Ozone Monitoring Instrument  (OMI) and can easily be employed for similar instruments – for  example, the upcoming TROPOspheric Monitoring Instrument (TROPOMI).  Trace gas distributions are reconstructed by a continuous parabolic  spline surface. The algorithm explicitly considers the spatially  varying sensitivity of the sensor resulting from the instrument  function. At the swath edge, the inverse problem of computing the  spline coefficients is very sensitive to measurement errors and is  regularised by a second-order difference matrix. Since this  regularisation corresponds to the penalty term for smoothing  splines, it similarly attenuates the effect of measurement noise  over the entire swath width. Monte Carlo simulations are conducted  to study the performance of the algorithm for different  distributions of trace gas column densities. The optimal weight of  the penalty term is found to be proportional to the measurement  uncertainty and the width of the instrument function. A comparison  with an established gridding algorithm shows improved performance  for small to moderate measurement errors due to better  parametrisation of the distribution. The resulting maps are smoother  and extreme values are more accurately reconstructed. The  performance improvement is further illustrated with high-resolution  distributions obtained from a regional chemistry model. The new  algorithm is applied to tropospheric NO<sub>2</sub> column densities  measured by OMI. Examples of regional NO<sub>2</sub> maps are shown for  densely populated areas in China, Europe and the United States of  America. This work demonstrates that the newly developed gridding  algorithm improves regional trace gas maps; its application could be  very helpful for the study of satellite-derived trace gas  distributions

A novel gridding algorithm to create regional trace gas maps from satellite observations