Abstract: Objectives: In solving the Earth's surface boundary value problem through terrain adjustment and downward analytical continuation of gravity data, the process ultimately reduces to the computation of a global integral model for the disturbance potential functional in the external space of the Earth, which contains a kernel function with geocentric radius factor. When the computation point approaches infinitely close to the spherical grid nodes, singularities occur in the integral kernel functions of such computational models, leading to failure in calculation results. Methods: To address this issue, two distinct solutions were proposed to eliminate the singularities in the integral kernel functions: one is called central grid data block separation method, and another called computation point grid data remove-restore technique. Concurrently, a practical modification scheme was developed for converting global integral models into localized numerical integration models, resolving the challenge of precise calculation of ultra-low-altitude height anomalies in the Earth's external space. The influence characteristics and equilibrium relationships between observational data errors and height anomaly computation results were systematically analyzed, identifying the primary interference sources affecting the accuracy of external height anomaly calculations. Results: The Mount Everest region was selected as a test area, where the singularity elimination solutions and model modification schemes were numerically validated using the ultrahigh-degree geopotential model EGM2008. The results confirmed the feasibility and effectiveness of the proposed methodologies. Even in the Mount Everest region where gravity field variations are extremely intense, the refined rigorous computational model can achieve an internal consistency accuracy better than 1 cm. Conclusions: It is showed that reducing systematic bias in data observation and implementing kernel truncation modification measures are key to improving the accuracy of external height anomaly calculations. And using the modification model recommended in this paper for calculating external height anomalies can meet the requirements of constructing high-accuracy and high-resolution numerical models of height anomalies today.