Highlights • Empirical model using radiosonde (52 yrs), M-100 rocket (17 yrs), SABER (22 yrs) over Indian region. • SAO, TAO, AO, QBO variability is incorporated to the temperature to obtain the empirical model. • Model compares well with observations below (RMSE < 1 K) and differences above 20 km (RMSE ∼ 4–6 K). • First study to use ground and space-based measurements for a long period to develop empirical model.

Abstract An empirical model of temperature is developed using long-term observations of radiosonde (52 years), M-100 Rocket (17 years), and Sounding of the Atmosphere by Broadband Emission Radiometry (SABER) (22 years) data. The dominant oscillations such as Annual Oscillation (AO), Semi-Annual Oscillation (SAO), Terr-Annual oscillation (TAO), and Quasi-Biennial Oscillation (QBO) variability has been incorporated into the temperature to obtain the empirical atmosphere. The monthly mean of temperature obtained from radiosonde from 0 to 25 km, M-100 rocket from 26 to 80 km and SABER from 26 to 109 km has been subjected to the Fast Fourier Transform technique to retrieve the amplitudes and phases of AO, SAO, TAO, and QBO. The amplitudes and phases obtained are put in an empirical formula along with the temperature obtained from the observations to retrieve the empirical temperature. The empirical model is developed for two epochs (1971–1990, and 2002–2023). The amplitude is similar in both epochs for the TAO, and it is high in the first compared to the second epoch for SAO, AO, and QBO. The peak in the amplitude (3–4 K) is obtained between 80 and 90 km for TAO, and between 70 and 80 km (2–3 K) for SAO. The amplitude is less than 1 K for AO in both the epochs. The peaks in the QBO are observed between 20 and 30 km (2–3 K), another between 60 and 70 km (3–4 K) in the first epoch and above 80 km (2–3 K). Downward phase propagation is dominant for all the oscillations observed below 50 km, and upward propagation above. The empirical temperature obtained compares well with the observations below 20 km (RMSE <1 K) and shows differences above it (RMSE ∼ 4–6 K). This is due to the fact, that the amplitude of the oscillation is more in the stratosphere and mesosphere which results in perturbation of the background temperature.