Identifying the scale-dependent motifs in atmospheric surface layer by ordinal pattern analysis

Ramp-like structures in various atmospheric surface layer time series have been long studied, but the presence of motifs with the finer scale embedded within larger scale ramp-like structures has largely been overlooked in the reported literature. Here a novel, objective and well-adapted methodology, the ordinal pattern analysis, is adopted to study the finer-scaled motifs in atmospheric boundary-layer (ABL) time series. The studies show that the motifs represented by different ordinal patterns take clustering properties and 6 dominated motifs out of the whole 24 motifs account for about 45% of the time series under particular scales, which indicates the higher contribution of motifs with the finer scale to the series. Further studies indicate that motif statistics are similar for both stable conditions and unstable conditions at larger scales, but large discrepancies are found at smaller scales, and the frequencies of motifs “1234” and/or “4321” are a bit higher under stable conditions than unstable conditions. Under stable conditions, there are great changes for the occurrence frequencies of motifs “1234” and “4321”, where the occurrence frequencies of motif “1234” decrease from nearly 24% to 4.5% with the scale factor increasing, and the occurrence frequencies of motif “4321” change nonlinearly with the scale increasing. These great differences of dominated motifs change with scale can be taken as an indicator to quantify the flow structure changes under different stability conditions, and motif entropy can be defined just by only 6 dominated motifs to quantify this time-scale independent property of the motifs. All these results suggest that the defined scale of motifs with the finer scale should be carefully taken into consideration in the interpretation of turbulence coherent structures.