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Sunshine duration is an important indicator of the amount of solar radiation received in a region and an important input parameter for the study of atmospheric energy balance, climate change, ecosystem evolution, and social sustainability. Currently, extrapolation and interpolation of data from meteorological stations are the most common methods used to calculate sunshine duration on a regional scale. However, it is difficult to obtain high precision sunshine duration in areas lacking ground observation or where sunshine duration is highly heterogeneous on the ground. In this paper, a new method is proposed to estimate sunshine duration with hourly total cloud amount (CTA) data from sunrise to sunset derived from the Fengyun-2G geostationary meteorological satellite (FY-2G). This method constructs a new index known as daytime mean total cloud coverage amount and provides quadratic equations relating daytime mean total cloud coverage amount to relative sunshine duration in different seasons. The method was validated with ground observation data for 2016 from 18 meteorological stations in the Three-River Headwaters Region of Qinghai Province, China. For individual stations, the coefficient of determination (R2) between estimated and measured sunshine was at least 0.894, the RMSE (root mean square error) was 0.977 h/day or less, the MAE (mean absolute error) was 0.824 h/day or less, the RE (relative error) was 0.150 or lower, and the value of d was 0.963 or greater, which validated that the proposed method can effectively predict daily sunshine duration. These equations can also provide higher precision estimates of regional-scale sunshine duration. This was demonstrated by comparing, for the entire study region, the spatial distribution of sunshine duration estimated from season-based equations with results from three different interpolation methods based on ground observations. Overall, the study confirms that total cloud amount measures from a geostationary satellite can be used to successfully estimate sunshine duration. [ABSTRACT FROM AUTHOR]