Fig. 3

The prediction performance of maize yield from 2016 to 2021 simulated by the yield_NPP&EP method (a), the yield_\({{\rm{APAR}}}_{{\varepsilon }_{g}}\)& \(a\) method (b) and the yield_\({{\rm{APAR}}}_{{\varepsilon }_{g}}\)& \(a\) method (c) without outliers; the prediction performance of rice yield from 2016 to 2021 simulated by the yield_NPP&EP method (d), the yield_\({{\rm{APAR}}}_{{\varepsilon }_{g}}\)& \(a\) method (e) and the yield_\({{\rm{APAR}}}_{{\varepsilon }_{g}}\)& \(a\) method (f) without outliers; the prediction performance of soybean yield from 2016 to 2021 simulated by the yield_NPP&EP method (g), the yield_\({{\rm{APAR}}}_{{\varepsilon }_{g}}\)& \(a\) method (h) and the yield_\({{\rm{APAR}}}_{{\varepsilon }_{g}}\)& \(a\) method (i) without outliers.