This paper presents a convergent weighted-averaging interpolation scheme for obtaining detailed atmospheric data analysis. The method is based on the assumption that the two-dimensional distribution of an atmospheric variable can be represented by the summation of an infinite number of independent waves, i.e., a Fourier integral representation. The scheme uses a weight factor that is explicitly related to the density of observations, which determines the ultimate resolution of the analysis. The weight factor is defined as a function of the distance from the grid point and the parameter k, which determines the shape of the weight factor. The scheme has been tested on 500-mb height data over the United States and sea level pressure data, producing results comparable to manual analysis. The scheme is also applicable to mesoscale wavelengths. The interpolation scheme involves a series of iterations to regain lost details in the analysis. The process starts with an initial guess, then subtracts the initial guess from the data points to obtain a difference field. This difference field is then interpolated using the same weight factor, and the result is added to the initial guess to produce a second-guess analysis. This process is repeated until the differences are minimized. The number of iterations required depends on the data accuracy and the desired level of detail. The scheme has been tested on various data sets, including 500-mb height data, sea level pressure data, and regional surface analyses. The results show that the scheme can produce detailed analyses with accuracy comparable to manual analysis. The scheme is computationally simple and efficient, making it suitable for practical applications. However, the scheme is limited by the data density and accuracy, and the number of iterations required depends on the data quality. The scheme is most effective when applied to reasonably uniform data distributions. The paper concludes that the convergent weighted-averaging interpolation scheme is a valuable tool for obtaining detailed atmospheric data analysis.This paper presents a convergent weighted-averaging interpolation scheme for obtaining detailed atmospheric data analysis. The method is based on the assumption that the two-dimensional distribution of an atmospheric variable can be represented by the summation of an infinite number of independent waves, i.e., a Fourier integral representation. The scheme uses a weight factor that is explicitly related to the density of observations, which determines the ultimate resolution of the analysis. The weight factor is defined as a function of the distance from the grid point and the parameter k, which determines the shape of the weight factor. The scheme has been tested on 500-mb height data over the United States and sea level pressure data, producing results comparable to manual analysis. The scheme is also applicable to mesoscale wavelengths. The interpolation scheme involves a series of iterations to regain lost details in the analysis. The process starts with an initial guess, then subtracts the initial guess from the data points to obtain a difference field. This difference field is then interpolated using the same weight factor, and the result is added to the initial guess to produce a second-guess analysis. This process is repeated until the differences are minimized. The number of iterations required depends on the data accuracy and the desired level of detail. The scheme has been tested on various data sets, including 500-mb height data, sea level pressure data, and regional surface analyses. The results show that the scheme can produce detailed analyses with accuracy comparable to manual analysis. The scheme is computationally simple and efficient, making it suitable for practical applications. However, the scheme is limited by the data density and accuracy, and the number of iterations required depends on the data quality. The scheme is most effective when applied to reasonably uniform data distributions. The paper concludes that the convergent weighted-averaging interpolation scheme is a valuable tool for obtaining detailed atmospheric data analysis.