The ellipsoidal corrections for boundary value problems of deflection of the vertical with ellipsoid boundary

The boundary value problem of deflections of vertical with ellipsoid boundary is studied in the paper. Based on spherical harmonic series, the ellipsoidal corrections for the boundary value problem are derived so that it can be well solved. In addition, an imitation arithmetic is given for examining the accuracies of solutions for the boundary value problem as well as its spherical approximation problem, and the computational results illustrate that the boundary value problem has higher accuracy than its spherical approximation problem if deflection of the vertical are measured on geoid.

Response to climate warming of winter wheat varieties bred across different eras in the North China Plain

By the 2000s,the winter wheat regions in the North China Plain had undergone six major variety renewals.It is crucial to know how the winter wheat varieties bred across different eras respond to climate change,especially climate warming.From 2017 to 2022,we conducted a two-factor,two-level field experiment at Gucheng and Raoyang,with a temperature difference of 1℃existing between the two sites.The experiment used ten winter wheat varieties bred from the 1960s to the 2000s and included both fertilization and no fertilization treatments.The experiment aimed to separate the effects of warming and fertilization on the growth and development of the winter wheat varieties,thereby revealing the differences in their responses to warming.All the winter wheat varieties across different eras had higher yields in warmer environments.By separating the effects of warming and fertilization,the rate of yield increase decreased with the breeding eras of varieties due to the impact of warming alone.However,it still increased with the eras due to the combined effects of warming and fertilization.For varieties from the 1980s and 2000s,there is a strong correlation between higher fertility and warmer climate adaptability.Warming has a yield gain effect,significantly amplifying the yield increase under fertilization for the middle and late varieties.Therefore,the average yield increase for varieties from the 2000s reached 67%in warmer environments.Warming has increased the average daily minimum temperature during the winter wheat growing season.It has significantly reduced the number of days below zero degrees Celsius,shortening the overwintering stage and thereby shortening the growth period of winter wheat.However,the effective developmental days(>0℃days)maintained a consistent level.Warming promotes the development of large tillers,increases leaf area and dry matter accumulation,and reduces the ratio of sterile spikelets.The varieties from the 2000s had the lowest ratio of sterile spikelets and the highest harvest index(HI)in warmer environments,resulting in a significant increase in yield.This study reveals the differential responses to the warming of winter wheat varieties across different eras,which have a specific reference for winter wheat breeding to cope with climate change.