Space weather forecasting using SARIMA

Solar fluxes and geomagnetic activity influence the temperature of the air, and consequently the density. These phenomena are hard to predict because of their highly nonlinear and stochastic nature. However, they have significant effects on LEO space missions and orbital decay time estimations, since air drag is one of the major perturbations in this region. Inaccurate density estimates can indeed result in substantial errors in SmallSat mission operations-related quantities, such as station-keeping delta-v budgets, and compliance with mission disposal requirements that are getting stricter due to the growing amount of space debris.

This study addresses the problem of forecasting future atmospheric conditions by focusing on the prediction of key space weather indicators. Historical time series of the F10.7 solar radio flux and the Ap geomagnetic index are analyzed using a Seasonal Autoregressive Moving Average (SARIMA) modeling approach. This technique is selected for its ability to represent both long-term trends and recurring seasonal patterns embedded in the data. The resulting forecasts are expressed as probabilistic ranges rather than single-point estimates, allowing uncertainty to be explicitly quantified.

The predicted indices are then used to derive corresponding atmospheric density values, which can be directly employed in preliminary mission design activities. The proposed methodology is demonstrated through representative LEO use cases, including the estimation of station-keeping delta-v requirements and the assessment of orbital decay times. Results are evaluated with respect to European Cooperation for Space Standardization (ECSS) guidelines, showing that the approach provides a practical and statistically sound tool for early-phase mission analysis under space weather uncertainty.