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Rod Frehlich and Robert Sharman

Abstract

The effective model resolution of three numerical weather prediction (NWP) models is determined from analyses of spatial structure functions and spatial spectra. In this paper, the effective resolution is defined as the dimensions of the rectangular spatial filter that describes the net effect of all of the NWP model’s numerical filtering and smoothing effects. These effects are determined by comparison of spatial statistics of the NWP model output with statistical climatologies derived from aircraft data for the upper troposphere and lower stratosphere. The comparisons are based on both spatial structure functions and spatial spectra. The structure function approach has fewer assumptions and fewer numerical artifacts. Accurate estimates of NWP effective model resolution require a robust climatology of the spatial statistics, which are a function of latitude and location, such as over mountainous regions. An artifact in the climatology of the velocity statistics resulting from mountain waves is identified from NWP model output and corroborated with research aircraft data, which has not been previously observed in global statistical climatologies.

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Rod Frehlich and Robert Sharman

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The climatology of the spatial structure functions of velocity and temperature for various altitudes (pressure levels) and latitude bands is constructed from the global rawinsonde network and from Aircraft Communications, Addressing, and Reporting System/Aircraft Meteorological Data Relay (ACARS/AMDAR) data for the tropics and Northern Hemisphere. The ACARS/AMDAR data provide very dense coverage of winds and temperature over common commercial aircraft flight tracks and allow computation of structure functions to scales approaching 1 km, while the inclusion of rawinsonde data provides information on larger scales approaching 10 000 km. When taken together these data extend coverage of the spatial statistics of the atmosphere from previous studies to include larger geographic regions, lower altitudes, and a wider range of spatial scales. Simple empirical fits are used to approximate the structure function behavior as a function of altitude and latitude in the Northern Hemisphere. Results produced for spatial scales less than ∼2000 km are consistent with previous studies using other data sources. Estimates of the vertical and global horizontal structure of turbulence in terms of eddy dissipation rate ϵ and thermal structure constant CT 2 are derived from the structure function levels at the smaller scales.

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Rod Frehlich and Robert Sharman

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Estimates of small-scale turbulence from numerical model output are produced from local estimates of the spatial structure functions of model variables such as the velocity and temperature. The key assumptions used are the existence of a universal statistical description of small-scale turbulence and a locally universal spatial filter for the model variables. Under these assumptions, spatial structure functions of the model variables can be related to the structure functions of the corresponding atmospheric variables. The shape of the model spatial filter is determined by comparisons with the spatial structure functions from aircraft data collected at cruising altitudes. This universal filter is used to estimate the magnitude of the small-scale turbulence, that is, scales smaller than the filter scale. A simple yet universal description of the basic statistics (such as the probability density function and the spatial correlation) of these small-scale turbulence levels in the upper troposphere and lower stratosphere is proposed. Various applications are presented including 1) predicting the statistics of turbulence experienced by aircraft at upper levels, 2) diagnosing and forecasting turbulence for aviation safety, and 3) estimating the total observation error for optimal data assimilation and for improving operational weather prediction models. It is determined that the total observation error for typical rawinsonde measurements of velocity are dominated by the sampling error or “error of representativeness” resulting from the effects of small-scale turbulence.

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Rod Frehlich and Robert Sharman

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The performance of pulsed coherent Doppler lidar in estimating aircraft trailing wake vortices by scanning across the aircraft flight track is evaluated using Monte Carlo lidar simulations of a simple vortex pair in both a nonturbulent and turbulent environment. The performance estimates are based on maximum likelihood estimates of aircraft wake vortex parameters and provide a measure of the ability of the lidar to detect and track wake vortices under the best possible conditions. Two aircraft types are considered: the Boeing 737 and the Boeing 747. Rigorous error analyses are produced by comparing the estimated parameters from numerical simulations of raw lidar data with the known input parameters of the simulation. It is shown that the probability density functions for the estimates are approximately Gaussian and the bias is very small. The main source of the bias was determined to be the movement of the vortex during the lidar scan. The estimation error is increased by the effects of a background turbulent velocity field. The trade-off between lidar pulse energy and pulse repetition frequency for the standard condition of constant laser power is also presented. It is shown that these maximum likelihood estimates provide accurate detection and tracking of the key vortex parameters for a simple vortex model, with and without background turbulence.

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Domingo Muñoz-Esparza and Robert Sharman

Abstract

A low-level turbulence (LLT) forecasting algorithm is proposed and implemented within the Graphical Turbulence Guidance (GTG) turbulence forecasting system. The LLT algorithm provides predictions of energy dissipation rate (EDR; turbulence dissipation to the one-third power), which is the standard turbulence metric used by the aviation community. The algorithm is based upon the use of distinct log-Weibull and lognormal probability distributions in a statistical remapping technique to represent accurately the behavior of turbulence in the atmospheric boundary layer for daytime and nighttime conditions, respectively, thus accounting for atmospheric stability. A 1-yr-long GTG LLT calibration was performed using the High-Resolution Rapid Refresh operational model, and optimum GTG ensembles of turbulence indices for clear-air and mountain-wave turbulence that minimize the mean absolute percentage error (MAPE) were determined. Evaluation of the proposed algorithm with in situ EDR data from the Boulder Atmospheric Observatory tower covering a range of altitudes up to 300 m above the surface demonstrates a reduction in the error by a factor of approximately 2.0 (MAPE = 55%) relative to the current operational GTG system (version 3). In addition, the probability of detection of typical small and large EDR values at low levels is increased by approximately 15%–20%. The improved LLT algorithm is expected to benefit several nonconventional turbulence-prediction sectors such as unmanned aerial systems and wind energy.

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Todd P. Lane and Robert D. Sharman

Abstract

Deep moist convection generates turbulence in the clear air above and around developing clouds, penetrating convective updrafts and mature thunderstorms. This turbulence can be due to shearing instabilities caused by strong flow deformations near the cloud top, and also to breaking gravity waves generated by cloud–environment interactions. Turbulence above and around deep convection is an important safety issue for aviation, and improved understanding of the conditions that lead to out-of-cloud turbulence formation may result in better turbulence avoidance guidelines or forecasting capabilities. In this study, a series of high-resolution two- and three-dimensional model simulations of a severe thunderstorm are conducted to examine the sensitivity of above-cloud turbulence to a variety of background flow conditions—in particular, the above-cloud wind shear and static stability. Shortly after the initial convective overshoot, the above-cloud turbulence and mixing are caused by local instabilities in the vicinity of the cloud interfacial boundary. At later times, when the convection is more mature, gravity wave breaking farther aloft dominates the turbulence generation. This wave breaking is caused by critical-level interactions, where the height of the critical level is controlled by the above-cloud wind shear. The strength of the above-cloud wind shear has a strong influence on the occurrence and intensity of above-cloud turbulence, with intermediate shears generating more extensive regions of turbulence, and strong shear conditions producing the most intense turbulence. Also, more stable above-cloud environments are less prone to turbulence than less stable situations. Among other things, these results highlight deficiencies in current turbulence avoidance guidelines in use by the aviation industry.

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Stanley B. Trier and Robert D. Sharman

Abstract

Geostationary Operational Environmental Satellite-14 (GOES-14) 1-km visible satellite data with 1-min frequency revealed horizontally propagating internal gravity waves emanating from tropopause-penetrating deep convection on 3–4 June 2015 during the Plains Elevated Convection at Night (PECAN) field experiment. These waves had horizontal wavelengths of ~6–8 km and approximate ground-relative phase speeds of 35 m s−1. PECAN radiosonde data are used to document the environment supporting the horizontally propagating gravity waves within the 200-km-long downstream thunderstorm anvil. Comparisons among soundings within the anvil core, at the downstream anvil edge, and outside of the anvil, together with supporting high-resolution numerical simulations, establish the importance of the storm-induced upper-tropospheric/lower-stratospheric (UTLS) outflow in providing conditions allowing vertical trapping of internal gravity waves over large horizontal distances within the mesoscale anvil. Turbulence was reported by commercial aviation in proximity to the gravity waves near the downstream anvil edge. The simulations suggest that the strongest turbulence was consistent with a mesoscale destabilization of the outer portion of the downstream anvil at elevations immediately below the outflow jet, where differential temperature advection owing to the strong associated vertical shear reduces static stability. The simulated gravity waves are trapped at this elevation and extend for several kilometers below. Local minima of moist gradient Richardson number occur immediately above the simulated warm gravity wave temperature perturbations at anvil base, suggesting a possible role these waves could play in establishing precise locations for the onset of turbulence.

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Stanley B. Trier and Robert D. Sharman

Abstract

Mechanisms supporting a cold-season aviation turbulence outbreak over the northwest Atlantic Ocean and adjacent coastal regions of North America are investigated using high-resolution numerical simulations. Two distinct episodes of moderate-or-greater turbulence in the upper troposphere are observed, and the simulations suggest the turbulence is linked to eastward-translating mesoscale perturbations of negative potential vorticity (PV) emanating from upstream organized deep convection along the anticyclonic shear side of an upper-level jet. Within the exit region of the jet where the turbulence episodes occur, thermodynamic and kinematic fields in the vicinity of the PV perturbations exhibit structural characteristics of mesoscale inertia–gravity waves. These wavelike perturbations are shown to facilitate turbulence by influencing the vertical shear and static stability, which promotes mesoscale regions of banded cirrus clouds, near or within which the observed turbulence occurs.

The simulations also suggest that the turbulence arises from fundamentally different mechanisms in the two episodes. In the first and most severe turbulence episode, mesoscale wave-related vertical shear enhancements lead to Kelvin–Helmholtz instability (KHI) near aircraft cruising altitudes (~8.9–11.2 km MSL). Simulated KHI is most prevalent near relatively isolated areas of shallow, moist convection, where smaller-scale internal gravity waves originating in the middle troposphere in response to the shallow convection may play a role in excitation of the KHI located above. The second turbulence episode is consistent with simulated thermal-shear instability related to wave-induced mesoscale reductions in upper-tropospheric static stability. However, unlike for the earlier episode of enhanced turbulence, cloud-radiative feedbacks are necessary for the instability and mesoscale regions of banded cirrus to develop.

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Stanley B. Trier and Robert D. Sharman

Abstract

Widespread moderate turbulence was recorded on three specially equipped commercial airline flights over northern Kansas near the northern edge of the extensive cirrus anvil of a nocturnal mesoscale convective system (MCS) on 17 June 2005. A noteworthy aspect of the turbulence was its location several hundred kilometers from the active deep convection (i.e., large reflectivity) regions of the MCS. Herein, the MCS life cycle and the turbulence environment in its upper-level outflow are studied using Rapid Update Cycle (RUC) analyses and cloud-permitting simulations with the Weather Research and Forecast Model (WRF). It is demonstrated that strong vertical shear beneath the MCS outflow jet is critical to providing an environment that could support dynamic (e.g., shearing type) instabilities conducive to turbulence. Comparison of a control simulation to one in which the temperature tendency due to latent heating was eliminated indicates that strong vertical shear and corresponding reductions in the local Richardson number (Ri) to ∼0.25 at the northern edge of the anvil were almost entirely a consequence of the MCS-induced westerly outflow jet. The large vertical shear is found to decrease Ri both directly, and by contributing to reductions in static stability near the northern anvil edge through differential advection of (equivalent) potential temperature gradients, which are in turn influenced by adiabatic cooling associated with the mesoscale updraft located upstream within the anvil. On the south side of the MCS, the vertical shear associated with easterly outflow was significantly offset by environmental westerly shear, which resulted in larger Ri and less widespread model turbulent kinetic energy (TKE) than at the northern anvil edge.

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Rod Frehlich, Larry Cornman, and Robert Sharman

Abstract

New algorithms for the simulation of three-dimensional homogeneous turbulent velocity fields are compared with standard spectral domain algorithms. Results are presented for a von Kármán model of the covariance tensor. For typical atmospheric conditions, it is impossible to produce a simulated velocity field that simultaneously satisfies a given spatial correlation and the corresponding spatial spectrum, because of spectral aliasing. The goal of the new algorithms is to produce a turbulent velocity field that has accurate spatial correlations. The algorithms are a modification of the standard spectral domain method that attempts to produce a given spatial spectrum.

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