Possible　sunshine　duration　(PSD)　determines　the　solar　energy　received　by　the　surface　of　Earth.　The　objective　of　this　research　is　to　explore　the　spatial　structure　of　PSD　which　is　closely　related　to　slope　and　PSD.　We　chose　40　sample　areas　representing　diversified　landforms　in　China　and　then　computed　the　PSD　by　using　the　digital　elevation　models　(DEMs)　with　a　resolution　of　30 m　for　the　sample　areas.　We　define　the　concept　of　the　spectrum　which　reveals　the　relation　between　the　PSD　and　slope　over　an　analysis　window　on　the　DEM,　and　propose　the　method　for　deriving　the　spectrum.　Using　this　method,　we　derive　the　corresponding　spectra　in　a　year　or　in　a　season　in　the　study　areas　when　the　analysis　window　is　larger　than　the　corresponding　value　of　area,　the　stable　area.　The　value　of　the　spectrum　generally　decreases　with　the　slope;　the　stable　area　is　positively　related　to　the　variation　in　the　slope　and　that　of　the　relief　degree.　The　spectrum　may　be　useful　for　computing　PSD　while　considering　the　shielding　effect　quickly;　the　stable　area　may　be　used　as　the　minimum　value　of　the　area　in　studies　on　the　spatial　structure　of　PSD;　this　method　might　be　a　quantitative　one　in　geography　for　revealing　the　spatial　structure　of　other　meteorological　factors.　©　2020,　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature.