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%.

In this study, instead of economic estimation of forecast value, we evaluated the value score(VS) of the user satisfaction using the concept of satisfaction/dissatisfaction. We compared the collective Value Scores (cVS) based on outputs of probabilistic forecasts of precipitation seasonally in Seoul and Busan during the period of 2004 to 2013 and ÿnally found the optimum threshold that can improve cVS of both cities. When using 30% threshold, the users can expect a higher cVS compared with those using other thresholds. When using the seasonal optimum threshold in Seoul, the cVS is additionally higher by 9%. These results show the level of satisfaction of the forecast that can be improved when the meteorological communities inform the users the correct threshold of the rainfall probabilistic forecast.