Interpolation of Scattered Data on the Sphere by Multinode Shepard Operators

In this paper, we introduce a multinode Shepard operator for interpolating scattered data on the sphere. This method combines local polynomial interpolants with multinode Shepard functions based on geodesic distances. We analyze the operator’s approximation properties and convergence behavior, providing error bounds for smooth target functions. Numerical experiments confirm the accuracy and efficiency of the method in various test scenarios. Additionally, we apply it to real-world data, demonstrating its effectiveness in predicting monthly mean temperatures. The proposed approach offers a reliable tool for applications requiring spherical data interpolation.