Revisting the limits of atmospheric temperature retrieval from cosmic-ray measurements

A priori, cosmic-ray measurements offer a unique capability to determine the vertical profile of atmospheric temperatures directly from ground. However, despite the increased understanding of the impact of the atmosphere on cosmic-ray rates, attempts to explore the technological potential of the latter for atmospheric physics remain very limited. In this paper we examine the intrinsic limits of the process of cosmic-ray data inversion for atmospheric temperature retrieval, by combining a detection station at ground with another one placed at an optimal depth, and making full use of the angular information. With that aim, the temperature-induced variations in c. r. rates have been simulated resorting to the theoretical temperature coefficients $W_T(h, \theta, E_{th})$ and the temperature profiles obtained from the ERA5 atmospheric reanalysis. Muon absorption and Poisson statistics have been included to increase realism. The resulting c.r. sample has been used as input for the inverse problem and the obtained temperatures compared to the input temperature data. Relative to early simulation works, performed without using angular information and relying on underground temperature coefficients from a sub-optimal depth, our analysis shows a strong improvement in temperature predictability for all atmospheric layers up to 50 hPa, nearing a factor 2 error reduction. Furthermore, the temperature predictability on 6 h-intervals stays well within the range 0.8-2.2 K. Most remarkably, we show that it can be achieved with small-area m$^2$-scale muon hodoscopes, amenable nowadays to a large variety of technologies. For mid-latitude locations, the optimal depth of the underground station is around 20 m.