It is determined how long a time series must be to estimate covariances and moments up to fourth order with a specified statistical significance. For a given averaging time T there is a systematic difference between the true flux or moment and the ensemble average of the time means of the same quantities. This difference, referred to here as the systematic error, is a decreasing function of T tending to zero for T→∞. The variance of the time mean of the flux or moment, the so-called error variance, represents the random scatter of individual realizations, which, when T is much larger than the integral time scale T of the time series, is also a decreasing function of T. This makes it possible to assess the minimum value of T necessary to obtain systematic and random errors smaller than specified values. Assuming that the time series are either Gaussian processes with exponential correlation functions or a skewed process derived from a Gaussian, we obtain expressions for the systematic and random e... Abstract It is determined how long a time series must be to estimate covariances and moments up to fourth order with a specified statistical significance. For a given averaging time T there is a systematic difference between the true flux or moment and the ensemble average of the time means of the same quantities. This difference, referred to here as the systematic error, is a decreasing function of T tending to zero for T→∞. The variance of the time mean of the flux or moment, the so-called error variance, represents the random scatter of individual realizations, which, when T is much larger than the integral time scale T of the time series, is also a decreasing function of T. This makes it possible to assess the minimum value of T necessary to obtain systematic and random errors smaller than specified values. Assuming that the time series are either Gaussian processes with exponential correlation functions or a skewed process derived from a Gaussian, we obtain expressions for the systematic and random e...

Shallow, maritime cumuli are ubiquitous over much of the tropical oceans, and characterizing their properties is important to understanding weather and climate. The Rain in Cumulus over the Ocean (RICO) field campaign, which took place during November 2004–January 2005 in the trades over the western Atlantic, emphasized measurements of processes related to the formation of rain in shallow cumuli, and how rain subsequently modifies the structure and ensemble statistics of trade wind clouds. Eight weeks of nearly continuous S-band polarimetric radar sampling, 57 flights from three heavily instrumented research aircraft, and a suite of ground- and ship-based instrumentation provided data on trade wind clouds with unprecedented resolution. Observational strategies employed during RICO capitalized on the advances in remote sensing and other instrumentation to provide insight into processes that span a range of scales and that lie at the heart of questions relating to the cause and effects of rain from shallow maritime cumuli.

The authors use large-eddy simulation (LES) to investigate entrainment and structure of the inversion layer of a clear convectively driven planetary boundary layer (PBL) over a range of bulk Richardson numbers, Ri. The LES code uses a nested grid technique to achieve fine resolution in all three directions in the inversion layer. Extensive flow visualization is used to examine the structure of the inversion layer and to illustrate the temporal and spatial interaction of a thermal plume and the overlying inversion. It is found that coherent structures in the convective PBL, that is, thermal plumes, are primary instigators of entrainment in the Ri range 13.6 ⩽ Ri ⩽ 43.8. At Ri = 13.6, strong horizontal and downward velocities are generated near the inversion layer because of the plume–interface interaction. This leads to folding of the interface and hence entrainment of warm inversion air at the plume’s edge. At Ri = 34.5, the inversion’s strong stability prevents folding of the interface but stron... Abstract The authors use large-eddy simulation (LES) to investigate entrainment and structure of the inversion layer of a clear convectively driven planetary boundary layer (PBL) over a range of bulk Richardson numbers, Ri. The LES code uses a nested grid technique to achieve fine resolution in all three directions in the inversion layer. Extensive flow visualization is used to examine the structure of the inversion layer and to illustrate the temporal and spatial interaction of a thermal plume and the overlying inversion. It is found that coherent structures in the convective PBL, that is, thermal plumes, are primary instigators of entrainment in the Ri range 13.6 ⩽ Ri ⩽ 43.8. At Ri = 13.6, strong horizontal and downward velocities are generated near the inversion layer because of the plume–interface interaction. This leads to folding of the interface and hence entrainment of warm inversion air at the plume’s edge. At Ri = 34.5, the inversion’s strong stability prevents folding of the interface but stron...

Large-scale use of wind power can alter local and global climate by extracting kinetic energy and altering turbulent transport in the atmospheric boundary layer. We report climate-model simulations that address the possible climatic impacts of wind power at regional to global scales by using two general circulation models and several parameterizations of the interaction of wind turbines with the boundary layer. We find that very large amounts of wind power can produce nonnegligible climatic change at continental scales. Although large-scale effects are observed, wind power has a negligible effect on global-mean surface temperature, and it would deliver enormous global benefits by reducing emissions of CO ₂ and air pollutants. Our results may enable a comparison between the climate impacts due to wind power and the reduction in climatic impacts achieved by the substitution of wind for fossil fuels.

We calculated integral scales for horizontal and vertical velocity components, temperature, humidity and ozone concentration, as well as for their variances and covariances from aircraft measurements in the convective atmospheric boundary layer over both ocean and land surfaces. We found that the integral scales of the second-order moment quantities are 0.67± 0.09 that of the variables themselves. Consequently, only the second-order moment integral scales are presented here. These results are used to calculate the averaging lengths necessary to measure second-order moment quantities to a given accuracy. We found that a measurement length of 10 to 100 times the boundary-layer height is required to measure variances to 10% accuracy, while scalar fluxes require a measurement length of 102 to 104 and stress a measurement length of 103 to 105 times the boundary layer height. We also show that the ratio of the wavelength of the spectral peak to the integral scale can be used to estimate the sharpness o... Abstract We calculated integral scales for horizontal and vertical velocity components, temperature, humidity and ozone concentration, as well as for their variances and covariances from aircraft measurements in the convective atmospheric boundary layer over both ocean and land surfaces. We found that the integral scales of the second-order moment quantities are 0.67± 0.09 that of the variables themselves. Consequently, only the second-order moment integral scales are presented here. These results are used to calculate the averaging lengths necessary to measure second-order moment quantities to a given accuracy. We found that a measurement length of 10 to 100 times the boundary-layer height is required to measure variances to 10% accuracy, while scalar fluxes require a measurement length of 102 to 104 and stress a measurement length of 103 to 105 times the boundary layer height. We also show that the ratio of the wavelength of the spectral peak to the integral scale can be used to estimate the sharpness o...