Reconstruction of the Total Solar Irradiance during the last Millenium

Solar irradiance variations across various timescales, from minutes to centuries, represents a potential natural driver of past regional and global climate cold phases. To accurately assess the Sun's effect on climate, particularly during periods of exceptionally low solar activity known as grand minima, an accurate reconstruction of solar forcing is essential. While direct measurements of Total Solar Irradiance (TSI) only began in the late 1970s with the advent of space radiometers, indirect evidence from various historical proxies suggests that the Sun's magnetic activity has undergone possible significant fluctuations over much longer timescales. Employing diverse and independent methods for TSI reconstruction is essential to gaining a comprehensive understanding of this issue. This study employs a semi-empirical model to reconstruct TSI over the past millennium. Our approach uses an estimated open solar magnetic field ($F_{o}$), derived from cosmogenic isotope data, as a proxy for solar activity. We reconstruct the cyclic variations of TSI, due to the solar surface magnetic features, by correlating $F_{o}$ with the parameter of active region functional form. Instead, we obtain the long-term TSI trend by applying the Empirical Mode Decomposition (EMD) algorithm to the reconstructed $F_{o}$ to filter out the 11-year and 22-year solar variability. We prepare a reconstructed TSI record, spanning 971 to 2020 CE. The estimated departure from modern TSI values occurred during the Sp\"{o}rer Minimum (around 1400 CE), with a decrease of approximately 2.3 $W m^{-2}$. A slightly smaller decline of 2.2 $W m^{-2}$ is reported during the Maunder Minimum, between 1645 and 1715 CE.