Asymmetric geopotential height fluctuations from symmetric winds

As a characterization of the variability of observed geopotential height fluctuations, their probability density function (PDF) and its skewness are studied in the global domain for winter and summer. The PDF of the geopotential, [Phi], is skewed toward low anomalies at midlatitudes and toward high anomalies in polar and tropical regions. When [Phi] is filtered spatially by discarding planetary wavenumbers less than [approximately]8, the skewness is small in the Tropics and in polar regions and large and negative in zonal bands approximately centered on the latitudes of the climatological jets. Where the skewness is large and negative, the zonally averaged PDF of [Phi] has an approximately exponential tail for negative anomalies. From a diagnostic study based on computing [Phi] from the observed winds through the balance equation, the negative skewness bands can clearly be attributed to the rectification of near-symmetric velocity fluctuations by the advective nonlinearity. This mechanism implies that where winds are highly variable, large synoptic-scale negative [Phi] anomalies are more likely than large positive [Phi] anomalies. The maximum of the (negative) zonally averaged skewness in the summer hemisphere tends to be larger than that in the winter hemisphere, and in both hemispheres these maxima lie [approximately]150 mb below the velocity variance maxima. The fact that skewness extrema do not precisely match maxima in the nonlinearities is attributed to asymmetries in the winds themselves. Interactions of the velocity fluctuations with the mean flow have a small but observable effect in modulating the skewness. The subtle dependence of the skewness on key flow parameters is illustrated through an analytic model for idealized fluctuations on a beta plane. General expressions for the PDF, its asymptotic form, criteria for the presence of exponential tails, and the generic dependence of the skewness on a generalized Rossby number are derived. For the case of a [Delta]-function velocity spectrum, closed-form expressions for the PDF and skewness are obtained and compared to observations.