Abstract
Abstract. A new Clifford algebra-based vector field filtering method, which combines amplitude similarity and direction difference synchronously, is proposed. Firstly, a modified correlation product is defined by combining the amplitude similarity and direction difference. Then, a structure filtering algorithm is constructed based on the modified correlation product. With custom template and thresholds applied to the modulus and directional fields independently, our approach can reveal not only the modulus similarities but also the classification of the angular distribution. Experiments on exploring the tempo-spatial evolution of the 2002–2003 El Niño from the global wind data field are used to test the algorithm. The results suggest that both the modulus similarity and directional information given by our approach can reveal the different stages and dominate factors of the process of the El Niño evolution. Additional information such as the directional stability of the El Niño can also be extracted. All the above suggest our method can provide a new powerful and applicable tool for geophysical vector field analysis.
Highlights
We can apply a certain threshold on the Normalized Cross Correlation (NCC) similarity NCC(x) and the angle θ ∗(x) to extract the features according to the relations between the original and template data
The 0.5◦ Grided Global Average QuikSCAT Surface Wind Velocity Field data during May 2002 to March 2003 are used as the original data, and the Nino 3.4 region of the composite El Nino Modoki spatial pattern (Wang and Xin, 2013), which averages the NCEP-NCAR reanalysis wind velocity vector data during the seven El Nino Modoki events, are used as the template
The boundaries between the eastward and westward regions in central and east Pacific have very similar structure to that of the weak El Nino composed by sea surface temperatures (SSTs) anomalies (Wang and Fiedler, 2006)
Summary
The most commonly used 2-D vector field expression is founded on Euclidean space with Cartesian coordinates. The Clifford algebra provides the coordinate-free expression and computation of vectors. The hybrid expression and unified computation of different dimensional subspace provide ultimate power of the Clifford algebra. All the four parts can construct multivector functions in Cl2,0 space with a general form of A = a0 + a1e1 + a2e2 + a3e12. Different from the complex or tensorial approaches, the Clifford algebra approach encodes geometric objects of all dimensions (including all subspace dimensions) as algebraic objects and allows measurements of length, areas and volumes, and of dihedral angles across all dimensions (Hestenes and Sobcyk, 1984; De Bie et al, 2011). Clifford algebra allows coordinate free formulations and computation (Hestenes and Sobcyk, 1984)
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
