Patterns in the Occurrences of Richardson Numbers Less Than Unity in the Lower Atmosphere

Abstract

It is assumed that the presence of turbulence in the atmosphere is strongly correlated with low values of the gradient Richardson number (Ri ≤ 1.0). The critical Richardson number, Ric = 1.0, is an indicator of the onset of turbulence. Values of the gradient Richardson number are calculated using rawinsonde measurements of wind and temperature obtained from 144 rawinsonde stations from 1971 to 1975. Computer algorithms are developed for a statistical analysis of the critical Richardson number based on years, latitude, longitude, altitude and season. Twice-daily sets of rawinsonde height measurements of wind and temperature are fit using a Hermite interpolation algorithm. Richardson numbers calculated from these profiles are analyzed to determine the number and percent of occurrences of Ri ≤ Ric on a seasonal basis. Summary (seasonal) statistics on this critical Richardson number, or turbulence indicator, as well as all variables used, are computed for 1 km altitude bins from 2 to 25 km, a range determined to provide good statistical accuracy and precision. Particular features in the height profiles of percent occurrences of Ri ≤ Ric appear with remarkable consistency and are dependent on season and latitude. A characteristic peak layer in the percent occurrence of Ri ≤ 1.0 near 10 km is found in data obtained from sites located from low to midlatitudes. The range in occurrence for this layer is from 40% in winter to 5% in summer. Multiple regression analyses are applied using data from 21 of the stations covering a region from latitude 25 to 48°N and longitude 69 to 123°W. The data are sectioned for separate analysis into four altitude regions: 2?7, 8?13, 14?19 and 20?25 km. The analyses demonstrate that the patterns of turbulence based on a critical Richardson number of 1 have a substantial component which is stable and reproducible from year to year. The regressions relate percent occurrences of Ri ≤ Ric to location (latitude, longitude), altitude and season; the coefficients of multiple correlation, for altitudes below 20 km, range from 0.62 to 0.78 (i.e., up to 60% variation in percent occurrences explained). Yearly variations increase the square of the multiple correlation coefficients only by a maximum of 0.003 (i.e., at most 0.3% variation explained).