An Extension of Multiquadric Method Based on Trend Analysis for Surface Construction

The representation of spatial discrete data is crucial for the data analysis of meteorology, agriculture, geological exploration, and other fields. Among various methods for scattered data interpolation, the multiquadric (MQ) method is the most favorable in the field of surface construction. However, the classical MQ method has accuracy concern on the boundary and is time consuming for large dataset. This study proposes an algorithm by integrating the MQ method with trend surface analysis. In which, the low-order polynomial trend surface equation is first used to model the overall trend. Then, the MQ equation is applied to fit the residual surface after removal the trend from the data. Our implementation can eliminate the distortion in data missing areas by the classical MQ method, and the modeling efficiency can be improved significantly since the local MQ method divide the residual surface into a group of subsurfaces. The accuracy and efficiency of the proposed algorithm are validated on a synthetic model. The performance of the developed algorithm is further examined on the elevation data collected in Tibet and the seabed of a strait in Norway. The results show that with an equivalent resolution, the developed algorithm can be much more efficient than the classical MQ method and well-developed Kriging method.

Automated summary

The representation of spatial discrete data is crucial in various fields such as meteorology, agriculture, and geological exploration. The multiquadric (MQ) method is widely used for scattered data interpolation, but it has accuracy and efficiency limitations. This study proposes an algorithm that integrates the MQ method with trend surface analysis to overcome these limitations, and it is validated on synthetic and real-world datasets, showing improved efficiency and comparable accuracy to other methods.