1.Nanjing University of Information Science & Technology;2.NOAA/OAR/National Severe Storms Laboratory
Stream function and velocity potential are useful for representing the vorticity and divergence of flow fields, and thus been widely used in studies of global and regional atmospheric and oceanic circulation, pollutant diffusion and data assimilations for a long time. In recent years, it has been noted that the accuracy decreases sharply when commonly used algorithms are applied to complex flows driven by mesoscale and storm-scale weather systems especially in boundary layers over complex terrains and/or heterogeneous underlying surfaces. This paper presents a comprehensive review of the algorithms developed since the 1950s in five categories, emphasizing on their strengths and weakness from the perspective of mathematical principles and physical meanings, followed by summarizing their scopes of applications. The previously developed harmonic-cosine series expansion spectral approach is revisited and corrected for its ill-positioned solvability conditions in order to improve its suitability and accuracy in solving complex flow fields. Numerical experiments based on both idealized and real flow fields are performed to illustrate/highlight and summarize the applicability and accuracy of the algorithms in each category for different types of datasets with different spatial resolutions. The objective of this paper is to provide a solid scientific basis for the correct and efficient applications of stream function, velocity potential and their derived variables in the diagnostic analysis and numerical prediction of extreme weather and climate events.