Intersection and point-to-line solutions for geodesics on the ellipsoid

The paper presents two algorithms for the computation of intersection of geodesics and minimum distance from a point to a geodesic on the ellipsoid, respectively. They are based on the iterative use of direct and inverse problems of geodesy by means of their implementations with machine-precision accuracy in GeographicLib. The algorithms yield the same results as those obtained by Karney’s approach based on the use of auxiliary ellipsoidal gnomonic projections, with the advantage on our side that the algorithms are not limited to distances below 10000 km. This results in our algorithm being the only general solution for the problem of minimum distance from a point to a geodesic on the ellipsoid.     

Air temperature feedback and its contribution to global warming

Air temperature feedback results from the thermal-radiative coupling between the atmosphere and the surface and plays an important role in surface energy balance. This paper reveals the contribution of air temperature feedback to the global warming from 1980 to 2000. The air temperature feedback kernel, evaluated using the ERA-Interim reanalysis data, is used to discuss the physical mechanism for air temperature feedback, the dependency of the strength of air temperature feedback on the climatological spatial distributions of air temperature, water vapor and cloud content, and the contributions of air temperature feedback to rapid global warming. The coupling between temperature feedback and each of the external forcings and individual feedback processes will amplify the anomaly of direct energy flux convergence at the surface induced by the external forcings and individual processes. The air temperature feedback amplifies the initial surface warming due to the increase in CO₂ concentration, ice and snow melting, increase in water vapor, and change in ocean heat storage. It also amplifies the surface warming due to the longwave radiaitve forcing associated with the increase in cloud cover, which acts to suppress the cooling of the shortwave effect of cloud forcing. Overall, temperature feedback plays an important role in the global warming from 1980 to 2000, as the net positive contribution to the perturbation of global mean energy flux at the surface from the air temperature feedback is larger than the net negative contribution from external forcing and all non-temperature feedbacks.