Assimilating atmospheric infrasound data to constrain atmospheric winds in a two-dimensional grid

Infrasound waves travelling through atmospheric channels are affected by the conditions the encounter in their path. The shift in the backazimuth angle of a wave front detected at the reception site depends on the cross-wind it encountered. Estimating the original field from this integrated measurement is an (ill-posed) inverse problem. By using a prior, this can be converted into a Bayesian estimation problem. In this work we use the (ensemble) Kalman filter to tackle this problem. In particular, we provide an illustration of the setup and solution of the problem in a two-dimensional grid, depending on both across-track distance and height, which has not been done in previous works. We use a synthetic setup to discuss the details of the method. We show that one of the effects of along-track averaging (something done in previous studies to simplify the problem) is to overestimate the magnitudes of the analysed values, and propose that this should a source of model error. We also illustrate the process with real data corresponding to nine controlled ammunition explosions that took place in the summer of 2018. In these cases, the real infrasound waves we study seldom reach higher than 40 km in height. However, the use of covariance-based methods (e.g. the EnKF) allows for updates in higher regions where the wave did not travel, and where traditional observations are sparse. In fact, the larger impacts from observations in these cases are in the region of 40 to 60 km, agreeing with previous works. This study contributes in paving the way towards the ultimate goal of assimilating information derived from infrasound waves into operational numerical weather forecasting. More studies in quality control of the observations and proper validation of the results are urgently needed.