We present a comprehensive solar flare forecast model with a probability and a statistically significant range of daily peak X-ray flux. For this, we consider μ-corrected total unsigned radial magnetic fluxes from the SOHO/MDI and SDO/HMI, and flare lists from GOES from 1996 to 2021. Our model predicts two types of forecast results when a magnetic flux of an active region (AR) is given. First, using a relationship between magnetic fluxes and flaring rates, a probability of C1.0 or greater flares and a probability of M1.0 or greater flares within a day are predicted respectively. Second, a mean (μ) and standard deviation (σ) of daily peak X-ray fluxes are given from a historical distribution between magnetic fluxes and daily peak X-ray fluxes. Using the mean and standard deviation, we provide the statistical range of possible flare sizes. We verify two forecast results by using various performance metrics and investigate the performance depending on the climatology event rate. Based on the metric values, our model can give a better performance than the climatology forecast. Solar flares are considered to be caused by specific triggers and physical mechanisms that have not yet been precisely identified. In addition, there is another perspective that the size of the flare that will occur due to a trigger is close to random because the flaring loop is in a self-organized critical state. Our model can give the simplest forecasting results considering these two perspectives.

We develop forecast models of daily probabilities of major flares (M- and X-class) based on empirical relationships between photospheric magnetic parameters and daily flaring rates from May 2010 to April 2018. In this study, we consider ten magnetic parameters characterizing size, distribution, and non-potentiality of vector magnetic fields from Solar Dynamics Observatory (SDO)/Helioseismic and Magnetic Imager (HMI) and Geostationary Operational Environmental Satellites (GOES) X-ray flare data. The magnetic parameters are classified into three types: the total unsigned parameters, the total signed parameters, and the mean parameters. We divide the data into two sets chronologically: 70% for training and 30% for testing. The empirical relationships between the parameters and flaring rates are used to predict flare occurrence probabilities for a given magnetic parameter value. Major results of this study are as follows. First, major flare occurrence rates are well correlated with ten parameters having correlation coefficients above 0.85. Second, logarithmic values of flaring rates are well approximated by linear equations. Third, using total unsigned and signed parameters achieved better performance for predicting flares than the mean parameters in terms of verification measures of probabilistic and converted binary forecasts. We conclude that the total quantity of non-potentiality of magnetic fields is crucial for flare forecasting among the magnetic parameters considered in this study. When this model is applied for operational use, it can be used using the data of 21:00 TAI with a slight underestimation of 2–6.3%.