Temperature Structure Function Parameter Research Articles

A Study of Intermittent Turbulence in Stable Arctic Boundary Layers

Polar boundary layers are difficult to model due to the existence of intermittent turbulence within stable layers. Here we present a case study evaluation of coherent structures in a stable boundary layer observed during a series of flights with an uncrewed aircraft system (DataHawk2) on 19 October 2016 at Oliktok Point, Alaska as part of the ERASMUS (Evaluation of Routine Atmospheric Sounding Measurements using Unmanned Systems) field campaign. During a sequence of five flights over a nine-hour period, 57 profiles of atmospheric properties (0–400 m a.g.l) were collected. Turbulence was identified using derived Richardson Number, temperature structure function parameter, and turbulence kinetic energy dissipation. Throughout all flights on this strongly stable day, intermittent turbulence was observed. These turbulent layers showed well-mixed potential temperature profiles embedded within otherwise stable potential temperature profiles; often resulting in a characteristic staircase pattern. Turbulent layers ranged from 1 to 30 m deep, with most individual layers being 1–2 m deep. Vertical propagation velocities of layers in the lower atmosphere were on the order of a few cm s−1, typical of non-convective environments. In different regions of the profile, turbulence was driven by a different balance of buoyancy and shear forces, with turbulence in the near surface environment driven by strong shear forces overcoming strong resistance to buoyancy, while turbulence in elevated layers characterized by weaker shear forces overcoming weaker resistance to buoyancy. We discuss the potential of such datasets for improving subgrid parameterizations of small-scale turbulence embedded within stable boundary layers.

On the Relationship between the TKE Dissipation Rate and the Temperature Structure Function Parameter in the Convective Boundary Layer

Abstract Under stably stratified conditions, the dissipation rate ε of turbulence kinetic energy (TKE) is related to the structure function parameter for temperature , through the buoyancy frequency and the so-called mixing efficiency. A similar relationship does not exist for convective turbulence. In this paper, we propose an analytical expression relating ε and in the convective boundary layer (CBL), by taking into account the effects of nonlocal heat transport under convective conditions using the Deardorff countergradient model. Measurements using unmanned aerial vehicles (UAVs) equipped with high-frequency response sensors to measure velocity and temperature fluctuations obtained during the two field campaigns conducted at Shigaraki MU observatory in June 2016 and 2017 are used to test this relationship between ε and in the CBL. The selection of CBL cases for analysis was aided by auxiliary measurements from additional sensors (mainly radars), and these are described. Comparison with earlier results in the literature suggests that the proposed relationship works, if the countergradient term γ D in the Deardorff model, which is proportional to the ratio of the variances of potential temperature θ and vertical velocity w, is evaluated from in situ (airplane and UAV) observational data, but fails if evaluated from large-eddy simulation (LES) results. This appears to be caused by the tendency of the variance of θ in the upper part of the CBL and at the bottom of the entrainment zone to be underestimated by LES relative to in situ measurements from UAVs and aircraft. We discuss this anomaly and explore reasons for it.

Measuring the turbulence profile in the lower atmospheric boundary layer.

Optical turbulence can have a severe effect on the propagation of laser beams through the atmosphere. In free space optics and directed energy applications, these laser beams quite often propagate along a slant or vertical path. In these cases, the refractive index structure function parameter cannot be assumed constant, since it varies with height. How it varies with height, especially in the first few meters above the ground, is not well behaved. Turbulence height profiles have been measured since the 1970s, mainly for astronomical observations. These profiles are usually measured for the atmospheric boundary layer (the layer of air from the ground up to approx. 1km during day and 100m during night) and some kilometers above it. We have measured the temperature fluctuations in the first few meters above ground level using a system containing eight resistance thermometer devices, mounted in a row at different spacings. Measurements were made flying this system under a tethered balloon or mounted on a telescoping mast. The temperature structure function parameter, CT2, can be estimated from the temperature fluctuations measured by the 28 different probe pairs and the unique distances between the two probes. Finally, Cn2 is estimated from this temperature structure function parameter and compared to values predicted by a turbulence profile model.

Estimation of Turbulence Parameters in the Lower Troposphere from ShUREX (2016–2017) UAV Data

Turbulence parameters in the lower troposphere (up to ~4.5 km) are estimated from measurements of high-resolution and fast-response cold-wire temperature and Pitot tube velocity from sensors onboard DataHawk Unmanned Aerial Vehicles (UAVs) operated at the Shigaraki Middle and Upper atmosphere (MU) Observatory during two ShUREX (Shigaraki UAV Radar Experiment) campaigns in 2016 and 2017. The practical processing methods used for estimating turbulence kinetic energy dissipation rate ε and temperature structure function parameter C T 2 from one-dimensional wind and temperature frequency spectra are first described in detail. Both are based on the identification of inertial (−5/3) subranges in respective spectra. Using a formulation relating ε and C T 2 valid for Kolmogorov turbulence in steady state, the flux Richardson number R f and the mixing efficiency χ m are then estimated. The statistical analysis confirms the variability of R f and χ m around ~ 0.13 − 0.14 and ~ 0.16 − 0.17 , respectively, values close to the canonical values found from some earlier experimental and theoretical studies of both the atmosphere and the oceans. The relevance of the interpretation of the inertial subranges in terms of Kolmogorov turbulence is confirmed by assessing the consistency of additional parameters, the Ozmidov length scale L O , the buoyancy Reynolds number R e b , and the gradient Richardson number Ri. Finally, a case study is presented showing altitude differences between the peaks of N 2 , C T 2 and ε , suggesting turbulent stirring at the margin of a stable temperature gradient sheet. The possible contribution of this sheet and layer structure on clear air radar backscattering mechanisms is examined.

Shigaraki UAV-Radar Experiment (ShUREX): overview of the campaign with some preliminary results

The Shigaraki unmanned aerial vehicle (UAV)-Radar Experiment (ShUREX) is an international (USA-Japan-France) observational campaign, whose overarching goal is to demonstrate the utility of small, lightweight, inexpensive, autonomous UAVs in probing and monitoring the lower troposphere and to promote synergistic use of UAVs and very high frequency (VHF) radars. The 2-week campaign lasting from June 1 to June 14, 2015, was carried out at the Middle and Upper Atmosphere (MU) Observatory in Shigaraki, Japan. During the campaign, the DataHawk UAV, developed at the University of Colorado, Boulder, and equipped with high-frequency response cold wire and pitot tube sensors (as well as an iMET radiosonde), was flown near and over the VHF-band MU radar. Measurements in the atmospheric column in the immediate vicinity of the radar were obtained. Simultaneous and continuous operation of the radar in range imaging mode enabled fine-scale structures in the atmosphere to be visualized by the radar. It also permitted the UAV to be commanded to sample interesting structures, guided in near real time by the radar images. This overview provides a description of the ShUREX campaign and some interesting but preliminary results of the very first simultaneous and intensive probing of turbulent structures by UAVs and the MU radar. The campaign demonstrated the validity and utility of the radar range imaging technique in obtaining very high vertical resolution (~20 m) images of echo power in the atmospheric column, which display evolving fine-scale atmospheric structures in unprecedented detail. The campaign also permitted for the very first time the evaluation of the consistency of turbulent kinetic energy dissipation rates in turbulent structures inferred from the spectral broadening of the backscattered radar signal and direct, in situ measurements by the high-frequency response velocity sensor on the UAV. The data also enabled other turbulence parameters such as the temperature structure function parameter {C}_T^2 and refractive index structure function parameter {C}_n^2 to be measured by sensors on the UAV, along with radar-inferred refractive index structure function parameter {C}_{n,mathrm{radar}}^2 . The comprehensive dataset collected during the campaign (from the radar, the UAV, the boundary layer lidar, the ceilometer, and radiosondes) is expected to help obtain a better understanding of turbulent atmospheric structures, as well as arrive at a better interpretation of the radar data.

Comparison of Direct and Spectral Methods for Evaluation of the Temperature Structure Parameter in Numerically Simulated Convective Boundary Layer Flows

Abstract In many engineering and meteorological applications, atmospheric turbulence within the planetary boundary layer is described in terms of its representative parameters. One such parameter is the structure-function (or structure) parameter that is used to characterize the intensity of turbulent fluctuations of atmospheric flow variables. Structure parameters are derivatives of structure functions, but are used more frequently than the latter ones for practical needs as they do not explicitly include dependence on the separation distance. The structure parameter of potential temperature, which is the subject of this study, describes the spatial variability of the temperature fluctuations. It is broadly represented in theories and models of electromagnetic and acoustic wave propagation in the atmosphere, and forms the basis for the scintillometer measurement concept. The authors consider three methods to compute the potential temperature structure function and structure parameter: the direct method, the true spectral method, and the conventional spectral method. Each method is tested on high-resolution potential temperature datasets generated from large-eddy simulations of a variety of convective boundary layer flow cases reproduced by two representative numerical codes. Results indicate that the popular conventional spectral method routinely exaggerates the potential temperature structure-function parameter, likely due to the unrealistic assumptions underlying the method. The direct method and true spectral method are recommended as the more suitable approaches.

섬광계를 이용한 비균질 도시 지표에서의 현열속 산정

A large aperture scintillometer (LAS) was deployed with an optical path length of 2.1 km to estimate turbulent sensible heat flux (<TEX>${\mathcal{Q}}_H$</TEX>) over a highly heterogeneous urban area. Scintillation measurements were conducted during cold season in November and December 2013, and the daytime data of 14 days were used in the analysis after quality control processes. The LAS-derived <TEX>${\mathcal{Q}}_H$</TEX> show reasonable temporal variation ranging <TEX>$20{\sim}160W\;m^{-2}$</TEX> in unstable atmospheric conditions, and well compare with the measured net radiation. The LAS footprint analysis suggests that <TEX>${\mathcal{Q}}_H$</TEX> can be relatively high when the newly built-up urban area has high source contribution of the turbulent flux in the study area ('northwesterly winds'). Sensitivity tests show that the LAS-derived <TEX>${\mathcal{Q}}_H$</TEX> are highly sensitive to non-dimensional similarity function for temperature structure function parameter, but relatively less sensitive to surface aerodynamic parameters and meteorological variables (temperature and wind speed). A lower Bowen ratio also has a significant influence on the flux estimation. Overall uncertainty of the estimated daytime <TEX>${\mathcal{Q}}_H$</TEX> is expected within about 20% at an upper limit for the analysis data. It is also found that stable atmospheric conditions can be poorly determined when the scintillometry technique is applied over the highly heterogeneous urban area.

Estimation of turbulent sensible heat and momentum fluxes over a heterogeneous urban area using a large aperture scintillometer

The accurate determination of surface-layer turbulent fluxes over urban areas is critical to understanding urban boundary layer (UBL) evolution. In this study, a remote-sensing technique using a large aperture scintillometer (LAS) was investigated to estimate surface-layer turbulent fluxes over a highly heterogeneous urban area. The LAS system, with an optical path length of 2.1 km, was deployed in an urban area characterized by a complicated land-use mix (residential houses, water body, bare ground, etc.). The turbulent sensible heat (Q H) and momentum fluxes (τ) were estimated from the scintillation measurements obtained from the LAS system during the cold season. Three-dimensional LAS footprint modeling was introduced to identify the source areas (“footprint”) of the estimated turbulent fluxes. The analysis results showed that the LAS-derived turbulent fluxes for the highly heterogeneous urban area revealed reasonable temporal variation during daytime on clear days, in comparison to the land-surface process-resolving numerical modeling. A series of sensitivity tests indicated that the overall uncertainty in the LAS-derived daytime Q H was within 20%–30% in terms of the influence of input parameters and the nondimensional similarity function for the temperature structure function parameter, while the estimation errors in τ were less sensitive to the factors of influence, except aerodynamic roughness length. The 3D LAS footprint modeling characterized the source areas of the LAS-derived turbulent fluxes in the heterogeneous urban area, revealing that the representative spatial scales of the LAS system deployed with the 2.1 km optical path distance ranged from 0.2 to 2 km2 (a “micro-a scale”), depending on local meteorological conditions.

A comparison of new and existing equations for estimating sensible heat flux using surface renewal and similarity concepts

This paper describes two approaches for estimating sensible heat flux, using surface renewal and similarity concepts. One approach depends on a temperature structure function parameter and is valid in the inertial sublayer. The other approach depends on the temperature standard deviation and operates when measurements are made above the canopy top, either in the roughness or inertial sublayer. The approaches were tested over grass, rangeland grass, wheat, grape vineyard, and nectarine and olive orchards. It is shown that the free convection limit expression for the standard deviation method holds for slightly unstable conditions. When surface homogeneity and fetch requirements are not fully met in the field, the results show that the equations based on surface renewal principles are more robust and accurate than equations exclusively based on similarity backgrounds. It is likely that the two methods are less sensitive to site‐specific adjustment of the similarity relationships unless the canopy is rather heterogeneous. Under unstable conditions, the free convection limit equation, which depends on the temperature standard deviation, can provide online sensible heat flux estimates using affordable battery‐powered data logger with temperature data as the only input. The approach performed well when measuring above the canopy in the roughness and inertial sublayers, thus suggesting that the method is useful for long‐term monitoring over growing vegetation.

An aircraft study of turbulence dissipation rate and temperature structure function in the unstable marine atmospheric boundary layer

The dissipation rate of turbulent kinetic energy, e, and the temperature structure function parameter, C T 2, have been measured over water from the near surface (Z = 3 m) to the top of the boundary layer. The near surface values of e and C T 2 were used to calculate the velocity and temperature Monin-Obukhov scaling parameters u * and T *. The data collected during unstable lapse rates were used to evaluate the feasibility of extrapolating the values of e and C T 2 as a function of height with empirical scaling formulae. The dissipation rate scaling formula of Wyngaard et al. (l971 a) gave a good fit to an average of the e data for Z < 0.8 Z i. In the surface layer the scaling formula of Wyngaard et al. (1971b) disagreed with the C T 2 values by as much as 50%. This disagreement is due to an unexpected reduction in the measured values of C T 2 forZ < 30 m. At this point it is not clear if the discrepancy is a unique property of the marine boundary layer or if it is simply some unknown instrumental or analytical problem. The mixed layer scaling results were similar to the overland results of Kaimal et al. (1976).

Observation of the temperature structure function parameter, C T 2, over the ocean

Shipboard measurements of temperature fluctuations, mean wind, temperature, and humidity permit comparisons to be made of experimental and empirical estimates of ct2, the temperature structure function parameter. Surface flux estimates are obtained from bulk aerodynamic formulae. Temperature fluctuation data are selected to minimize a salt-contamination effect which causes increases in temperature variance. Predictions for CT2 based on surface flux scaling agree within 20%, except for near neutral and large unstable conditions where disagreement can be attributed to measurement problems.