Forecasting the Daily 10.7 cm Solar Radio Flux Using an Autoregressive Model
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Forecasting the Daily 10.7 cm Solar Radio Flux Using an Autoregressive Model Zhanle Du1
Received: 22 February 2020 / Accepted: 14 August 2020 © Springer Nature B.V. 2020
Abstract As an important proxy of the solar extreme ultraviolet radiation from the upper chromosphere and lower corona, the 10.7 cm solar radio flux (F10.7) has a wide range of applications in models of the thermosphere and ionosphere. Forecasting F10.7 has already become a routine business in space weather services. In this study, we analyzed the predictive power of autoregressive (AR) models with orders p = 15 – 1005, a training sample length L = 22 years, and a running time window w = 50 days on the daily F10.7, during the last two solar cycles (Solar Cycles 23 and 24) at the forecast steps n = 1 – 81 days. The main conclusions are as follows. (i) The mean forecast error (δ) at the nth day or over N days is minimum at an optimal order po , which tends to increase as n or N increases. (ii) δ is positively related to both n and F10.7. The large error during the maximum period is the result of the large daily variation in F10.7, mainly due to the appearance and decay of active regions, especially the eruptions of solar flares. (iii) The solar cycle can be divided into six parts in the rising order of δ: (a) closing part of the declining phase, (b) initial rising phase, (c) middle declining phase, (iv) closing rising phase, (v) middle rising phase, and (f) initial declining phase. (iv) The AR model at po is not inferior to other techniques. (v) po is uncorrelated to the autocorrelation coefficient, and (vi) δ is minimum at a certain L. Keywords Radio emission · Autoregression model · Solar cycle · Flares · Active regions · Earth’s atmosphere
1. Introduction The 10.7 cm solar radio flux (F10.7) is a measurement of the total emission flux density from all sources on the solar disk at a wavelength of 10.7 cm (hourly-averaged over a 100 MHzwide band centered at 2800 MHz), originating in the upper chromosphere and lower corona (Tapping, 2013). It consists of three components: a fairly constant one (from the quiet-sun
B Z. Du
[email protected]
1
Key Laboratory of Solar Activity, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China
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Z. Du
background emission), a slowly varying component (S-component, originating primarily in active regions), and a highly variable one (from occasional radio burst emission, Belmont, Dartt, and Ulstad, 1966; Tapping, 2013; Tapping and Morgan, 2017). Being considered to be highly correlated with the solar magnetic activity (Tapping and Morgan, 2017), solar extreme ultraviolet radiation (Belmont, Dartt, and Ulstad, 1966), temperature and density of the thermopause (Nicolet, 1963), and X-ray emissions (Donnelly and Puga, 1990; Huang, Liu, and Wang, 2009), the F10.7 is widely applied in the fields of space weather including satellite, navigation, communications, and terrestrial climate (Huang, Liu, and Wang, 2009; Yaya et al., 2017, etc.). For example, as a proxy for so
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