Two-Dimensional Scalar Spectra in the Deeper Layers of a Dense and Uniform Model Canopy

The turbulent flow inside dense canopies is characterized by wake production and short-circuiting of the energy cascade. How these processes affect passive scalar concentration variability in general and their spectral properties in particular remains a vexing problem. Progress on this problem is frustrated by the shortage of high resolution spatial concentration measurements, and by the lack of simplified analytical models that connect spectral modulations in the turbulent kinetic energy (TKE) cascade to scalar spectra. Here, we report the first planar two-dimensional scalar concentration spectra (ϕ _cc ) inside tall canopies derived from flow visualization experiments. These experiments were conducted within the deeper layers of a model canopy composed of densely arrayed cylinders welded to the bottom of a large recirculating water channel. We found that in the spectral region experiencing wake production, the ϕ _cc exhibits directional scaling power laws. In the longitudinal direction (x), or the direction experiencing the largest drag force, the ϕ _cc (k _x ) was steeper than and followed an approximate at wavenumbers larger than the injection scale of wake energy, where k _x is the longitudinal wavenumber. In the lateral direction (y), the spectra scaled as up to the injection scale, and then decayed at an approximate power law. This departure from the classical inertial subrange scaling (i.e., k ^−5/3) was reproduced using a newly proposed analytical solution to a simplified scalar spectral budget equation. Near the velocity viscous dissipation range, the scalar spectra appear to approach an approximate k ⁻³, a tantalizing result consistent with dimensional analysis used in the inertial-diffusive range. Implications to subgrid modelling for large-eddy simulations (LES) inside canopies are briefly discussed.     

Uptake of the NO <Subscript>3</Subscript> Radical on Aqueous Surfaces

Using a single drop experiment, the uptake of NO₃ radicals on aqueous solutions of the dye Alizarin Red S and NaCl was measured at 293 K. Uptake coefficients in the range (1.7–3.1) ⋅ 10^{− 3} were measured on Alizarin Red S solutions. The uptake coefficients measured on NaCl solutions were in the range of (1.1–2.0) ⋅ 10⁻³ depending on the salt concentration. Both experiments lead to a consistent result for the mass accommodation coefficient of α_NO3 = (4.2_{− 1.7}^+2.2)⋅ 10⁻³. The product H(D_l k_Cl−^II)^0.5 for the NO₃ radical was determined to be (1.9 ± 0.2) M atm^{− 1} cm s^−0.5 M^−0.5 s^−0.5 by fitting the uptake data for the NaCl solutions to the so-called resistance model. The yield of the chemical NO₃ radical source was characterized using UV-VIS and FT-IR spectroscopy. The amount of gas-phase NO₃ radicals measured at elevated humidities was less than expected. Instead, a rise of the gas-phase HNO₃ concentration was found indicating a conversion of gas-phase NO₃ radicals to gas-phase HNO₃ on the moist reactor walls.     

Spectral scaling in a high reynolds number laboratory boundary layer

Spectra and co-spectra of the streamwise (u) and normal or vertical (w) velocity fluctuations have been measured in the inner region of a large Reynolds number laboratory boundary layer over a rough wall. There is reasonable evidence of ak ₁ ^–1 range in theu spectrum (wherek ₁ is the streamwise wavenumber). Such a range results from an overlap between a spectral region dominated by largescale, inactive motion, which scales on the boundary-layer thickness, and a region dominated by smaller-scale, active motion which scales on the distance from the wall. Spectra ofw, anduw cospectra, scale in a manner consistent with the dominance by active motion. The present spectral data do not support local isotropy over the inertial subrange. A comparison between measuredw spectra and calculations based on isotropy indicates that the inertial subrange anisotropy is only slightly affected by the magnitude of the non-dimensional mean shear.     

The spectral velocity tensor for homogeneous boundary-layer turbulence

We have postulated a simple model for the spectral tensor _ij (k) of an anisotropic, but homogeneous turbulent velocity field. It is a simple generalization of the spectral tensor _inf ^{ij piso}(k) for isotropic turbulence and we show how in the limit of isotropy, _ij (k) becomes equal to _inf ^{ij piso}(k). Whereas _inf ^{ij piso}(k) is determined entirely by one scalar function of k = ¦k¦, namely the energy spectrum, we need three independent scalar functions of k to specify _ij (k). We show how it is possible by means of the three stream-wise velocity component spectra to determine the three scalar functions in _ij (k) by solving two uncoupled, ordinary linear differential equations of first and second order. The analytic form of the component spectra each has a set of three parameters: the variance and the integral length scale of the velocity component and a dimensionless parameter, which governs the curvature of the spectrum in the transition domain from the inertial subrange towards lower wave numbers. When the three sets of parameters are the same, the three spectra correspond to isotropic turbulence and they are all interrelated and related to the energy spectrum. We show how it is possible to obtain these spectral forms in the neutral surface layer and in the convective boundary layer from data reported in the literature. The spectral tensor is used to predict the lateral coherences for all three velocity components and these predictions are compared with coherences obtained in two experiments, one using three masts at a horizontally homogeneous site in Denmark and one employing two aircraft flying in formation over eastern Colorado. Comparison shows reasonable agreement although with considerable experimental scatter.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Atmosphere–Surface Fluxes of CO<Subscript>2</Subscript> using Spectral Techniques

Different flux estimation techniques are compared here in order to evaluate air–sea exchange measurement methods used on moving platforms. Techniques using power spectra and cospectra to estimate fluxes are presented and applied to measurements of wind speed and sensible heat, latent heat and CO₂ fluxes. Momentum and scalar fluxes are calculated from the dissipation technique utilizing the inertial subrange of the power spectra and from estimation of the cospectral amplitude, and both flux estimates are compared to covariance derived fluxes. It is shown how even data having a poor signal-to-noise ratio can be used for flux estimations.     

Turbulence spectra in the near-neutral surface layer over the Loess Plateau in China

We present the power spectra of wind velocity and the cospectra of momentum and heat fluxes observed for different wind directions over flat terrain and a large valley on the Loess Plateau. The power spectra of longitudinal (u) and lateral (v) wind speeds satisfy the −5/3 power law in the inertial subrange, but do not vary as observed in previous studies within the low frequency range. The u spectrum measured at 32 m height for flow from the valley shows a power deficit at intermediate frequencies, while the v spectrum at 32 m downwind of the valley reaches another peak in the low frequency range at the same frequency as the u spectrum. The corresponding peak wavelength is consistent with the observed length scale of the convective outer layer at the site. The v spectrum for flat terrain shows a spectral gap at mid frequencies while obeying inner layer scaling in its inertial subrange, suggesting two sources of turbulence in the surface layer. All the spectra and cospectra from the valley direction show a height dependency over the three levels.     

Vertical Structure of Selected Turbulence Characteristics above an Urban Canopy

Summary In this paper the results of an urban measurement campaign are presented. The experiment took place from July 1995 to February 1996 in Basel, Switzerland. A total of more than 2000 undisturbed 30-minute runs of simultaneous measurements of the fluctuations of the wind vector u′, v′, w′ and the sonic temperature θ _s ′ at three different heights (z=36, 50 and 76 m a.g.l.) are analysed with respect to the integral statistics and their spectral behaviour. Estimates of the zero plane displacement height d calculated by the temperature variance method yield a value of 22 m for the two lower levels, which corresponds to 0.92 h (the mean height of the roughness elements). At all three measurement heights the dimensionless standard deviation σ _w /u _* is systematically smaller than the Monin-Obukhov similarity function for the inertial sublayer, however, deviations are smaller compared to other urban turbulence studies. The σ_θ/θ_* values follow the inertial sublayer prediction very close for the two lowest levels, while at the uppermost level significant deviations are observed. Profiles of normalized velocity and temperature variances show a clear dependence on stability. The profile of friction velocity u _* is similar to the profiles reported in other urban studies with a maximum around z/h=2.1. Spectral characteristics of the wind components in general show a clear dependence on stability and dimensionless measurement height z/h with a shift of the spectral peak to lower frequencies as thermal stability changes from stable to unstable conditions and as z/h decreases. Velocity spectra follow the −2/3 slope in the inertial subrange region and the ratios of spectral energy densities S _w (f)/S _u (f) approach the value of 4/3 required for local isotropy in the inertial subrange. Velocity spectra and spectral peaks fit best to the well established surface layer spectra from Kaimal et al. (1972) at the uppermost level at z/h=3.2. Received September 26, 1997 Revised February 15, 1998     

Free convection frequency spectra of atmospheric turbulence over the sea

Frequency spectra of atmospheric turbulenceS (f) in the inertial subrange are considered in the free convection regime over the sea surface in a case of motionless instrument measurements (Eulerian frequency spectra). The frequency spectra formulaef _* S (f)/ ² =c (f _*/f)^5/3 for wind velocity (=1–3), temperature (=t) and humidity (=e) fluctuations are derived on the basis of similarity theory and the –5/3 law. These relations also can be derived from a consideration of convective large-scale advection of small eddies. The frequency scalef _* = (N ^{1 2}/)^1/2 (H/z ²)^1/3 is the lower bound of the inertial subrange and it is of order 10^–2 Hz.The spectra formulae are compared with direct measurements of atmospheric turbulence from the fixed research tower in the coastal zone of the Black Sea in calm weather. It is shown that these formulae are realized at least over two to three decades of the frequency range (approximately from 10^–2 to 10 Hz) and values of the numerical coefficients are found. The derived formulae can be used for calculations of sensible and latent heat fluxes by measuring the high-frequency range of spectra at a fixed point at low wind speeds when the conventional inertial dissipation method is not applicable.     

Turbulent Kinetic Energy Dissipation in the Surface Layer

We estimated the turbulent kinetic energy (TKE) dissipation rate for thirty-two 1-h intervals of unstable stratification covering the stability range 0.12 ≤ −z/L ≤ 43 (z/L is the ratio of instrument height to the Obukhov length), by fitting Kolmogorov’s inertial subrange spectrum to streamwise spectra observed over a desert flat. Estimated values are compatible with the existence of local equilibrium, in that the TKE dissipation rate approximately equalled the sum of shear and buoyant production rates. Only in the neutral limit was the turbulent transport term in the TKE budget measured to be small.     

A Study of the Reaction of OH Radicals with N-Methyl Pyrrolidinone,N-Methyl Succinimide and N-Formyl Pyrrolidinone

A study of the oxidation mechanism of N-methyl pyrrolidinone (C₅H₉NO, NMP) initiated by hydroxyl radicals was made at EUPHORE at atmospheric pressure (1000 ± 10) mbar of air and ambient temperature (T = 300 ± 5 K). The main products were N-methyl succinimide (NMS) (52 ± 4)% and N-formyl pyrrolidinone (FP) (23 ± 9)%. The relative rate technique was used to determine the rate constants of OH with NMP, NMS and FP, the measured values were (in units of cm³ molecule ^{− 1} s^{− 1}): k_NMP = (2.2 ± 0.4) × 10^{− 11}, k_NMS = (1.4 ± 0.3) × 10^{− 12} and k_FP = (6 ± 1) × 10^{− 12}. The results are presented and discussed in terms of the atmospheric impact.     

Spectral Characteristics and Correction of Long-Term Eddy-Covariance Measurements Over Two Mixed Hardwood Forests in Non-Flat Terrain

We present turbulence spectra and cospectra derived from long-term eddy-covariancemeasurements (nearly 40,000 hourly data over three to four years) and the transferfunctions of closed-path infrared gas analyzers over two mixed hardwood forests inthe mid-western U.S.A. The measurement heights ranged from 1.3 to 2.1 times themean tree height, and peak vegetation area index (VAI) was 3.5 to 4.7; the topographyat both sites deviates from ideal flat terrain. The analysis follows the approach ofKaimal et al. (Quart. J. Roy. Meteorol. Soc. 98, 563–589, 1972) whose results were based upon 15 hours of measurements atthree heights in the Kansas experiment over flatter and smoother terrain. Both thespectral and cospectral constants and stability functions for normalizing and collapsingspectra and cospectra in the inertial subrange were found to be different from those ofKaimal et al. In unstable conditions, we found that an appropriate stabilityfunction for the non-dimensional dissipation of turbulent kinetic energy is of the form ₍₎ = (1 - b^-)^-1/4 - c^-, where representsthe non-dimensional stability parameter. In stable conditions, a non-linear functionG_xy() = 1 + b_xy^c _xy (c_xy < 1) was found to benecessary to collapse cospectra in the inertial subrange. The empirical cospectralmodels of Kaimal et al. were modified to fit the somewhat more (neutraland unstable) or less (stable) sharply peaked scalar cospectra observed over forestsusing the appropriate cospectral constants and non-linear stability functions. Theempirical coefficients in the stability functions and in the cospectral models varywith measurement height and seasonal changes in VAI. The seasonal differencesare generally larger at the Morgan Monroe State Forest site (greater peak VAI) andcloser to the canopy.The characteristics of transfer functions of the closed-path infrared gas analysersthrough long-tubes for CO₂ and water vapour fluxes were studied empirically. This was done by fitting the ratio between normalized cospectra of CO₂ or watervapour fluxes and those of sensible heat to the transfer function of a first-order sensor.The characteristic time constant for CO₂ is much smaller than that for water vapour. The time constant for water vapour increases greatly with aging tubes. Three methods were used to estimate the flux attenuations and corrections; from June through August, the attenuations of CO₂ fluxes are about 3–4% during the daytime and 6–10% at night on average. For the daytime latent heat flux (Q_E), the attenuations are foundto vary from less than 10% for newer tubes to over 20% for aged tubes. Correctionsto Q_E led to increases in the ratio (Q_H + Q_E)/(Q^* - Q_G) by about 0.05 to0.19 (Q_H is sensible heat flux, Q^* is net radiation and Q_G is soil heat flux),and thus are expected to have an important impact on the assessment of energy balanceclosure.     

Turbulence decay in stratified and homogeneous marine layers

A spectral approach is applied to shear-induced turbulence in stratified layers. A system of spectral equations for stationary balance of turbulent energy and temperature variances was deduced in the vicinity of the local shear scale L_U = (ε/U_Z³)^1/2. At wavenumbers between the inertial-convective (k^−5/3) and wak turbulence (k⁻³) subranges, additional narrow spectral intervals—‘production’ subranges—may appear (E k⁻¹, E_T k⁻²). The upper boundary of these subranges is determined as L_U, and the lower boundaries as L_R (ε/U_ZN²)^1/2(χ/T_Z²). It is shown that the scale L_U is a unique spectral scale that is uniform up to a constant value for every hydrophysical field. It appears that the spectral scale L_U is equivalent to the Thorpe scale L_Th for the active turbulence model. Therefore, if turbulent patches are generated in a background of permanent mean shear, a linear relation between temperature and mass diffusivities exists. In spectral terms, the fossil turbulence model corresponds to the regime of the Boldgiano-Obukhov buoyancy subrange (E k^−11/5, E_T k^−7/5). During decay the buoyancy subrange is expanded to lower and higher wavenumbers. At lower wavenumbers the buoyancy subrange is bounded by L_** = 3(χ^1/2/N^1/2T_Z), which is equivalent to the Thorpe scale L_Th. In such a transition regime only, when the viscous dissipation rate is removed from the set of main turbulence parameters, the Thorpe scale does not correlate with the buoyancy scale L_N ε^1/2/N^3/2 and fossil turbulence is realized. Oceanic turbulence measurements in the equatorial Pacific near Baker Island confirm the main ideas of the active and fossil turbulence models.     

Measurements of the humidity structure function parameters,C q 2and C Tq,over the ocean

Atmospheric turbulence measurements, including temperature and humidity fluctuations, were made from the R/V Acania off the coast of California in June, 1979. The purpose of the experiment was to investigate the scaling properties of the humidity structure function parameter (C _q ²) and temperaturehumidity cospectrum structure parameter (C _Tq) in the marine surface layer. The bulk parameterization method was used to obtain Monin-Obukhov Similarity (MOS) scaling parameters u _*, T _*, q _*and L. Assuming a neutral stability humidity drag coefficient c _qn = 1.3 × 10^-3the dimensionless humidity structure function parameter C _q ²Z^2/3/q_* ²was found to be 18% lower than the corresponding temperature function obtained by Wyngaard et al. (1971). Furthermore, the measurements indicate that the temperature-humidity fluctuations are highly coherent well into the inertial subrange. The results have direct application to turbulent scattering of waves propagating in the atmosphere (particularly microwaves) and methods of estimating air-sea surface fluxes.     

Laboratory measurements of the <Superscript>12</Superscript>C/<Superscript>13</Superscript>C kinetic isotope effects in the gas-phase reactions of unsaturated hydrocarbons with Cl atoms at 298 ± 3 K

The carbon kinetic isotope effects (KIEs) in the reactions of several unsaturated hydrocarbons with chlorine atoms were measured at room temperature and ambient pressure using gas chromatography combustion isotope ratio mass spectrometry (GCC-IRMS). All measured KIEs, defined as the ratio of the rate constants for the unlabeled and labeled hydrocarbon reaction k ₁₂/k ₁₃, are greater than unity or normal KIEs. The KIEs, reported in per mil according to ^Cl ɛ = (k ₁₂/k ₁₃−1) × 1000‰ with the number of experimental determinations in parenthesis, are as follows: ethene, 5.65 ± 0.34 (1); propene, 5.56 ± 0.18 (2); 1-butene, 5.93 ± 1.16 (1); 1-pentene, 4.86 ± 0.63 (1); cyclopentene, 3.75 ± 0.14 (1); toluene, 2.89 ± 0.31 (2); ethylbenzene, 2.17 ± 0.17 (2); o-xylene, 1.85 ± 0.54 (2). To our knowledge, these are the first reported KIE measurements for reactions of unsaturated NMHC with Cl atoms. Relative rate constants were determined concurrently to the KIE measurements. For the reactions of cyclopentene and ethylbenzene with Cl atoms, no rate constant has been reported in refereed literature. Our measured rate constants are: cyclopentene (7.32 ± 0.88) relative to propene (2.68 ± 0.32); ethylbenzene (1.15 ± 0.04) relative to o-xylene (1.35 ± 0.21), all × 10⁻¹⁰ cm³ molecule⁻¹ s⁻¹. The KIEs in reactions of aromatic hydrocarbons with Cl atoms are similar to previously reported KIEs in Cl-reactions of alkanes with the same numbers of carbon atoms. Unlike the KIEs for previously studied gas-phase hydrocarbon reactions, the KIEs for alkene–Cl reactions do not exhibit a simple inverse dependence on carbon number. This can be explained by competing contributions of normal and inverse isotope effects of individual steps in the reaction mechanism. Implications for the symmetries of the transition state structures in these reactions and the potential relevance of Cl-atom reactions on stable carbon isotope ratios of atmospheric NMHC are discussed.     

Drag coefficients and turbulence spectra within three boreal forest canopies

Atmospheric turbulence was measured within a black spruce forest, a jack pine forest, and a trembling aspen forest, located in southeastern Manitoba, Canada. Drag coefficients (C _d ) varied little with height within the pine and aspen canopies, but showed some height dependence within the dense spruce canopy. A constant C _d of 0.15, with the measured momentum flux and velocity profiles, gave good estimates of leaf-area-index (LAI) profiles for the pine and aspen canopies, but underestimated LAI for the spruce canopy.Velocity spectra were scaled using the Eulerian integral time scales and showed a substantial inertial subrange above the canopies. In the bottom part of the canopies, the streamwise and cross-stream spectra showed rapid energy loss whereas the vertical spectra showed an apparent energy gain, in the region where the inertial subrange is expected. The temperature spectra showed an inertial subrange with the expected -2/3 slope at all heights. Cospectra of momentum and heat flux had slopes of about -1 in much of the inertial subrange. Possible mechanisms to explain some of the spectral features are discussed.     

Measurement and investigation of chamber radical sources in the European Photoreactor (EUPHORE)

It is essential to quantify the background reactivity of smog-chambers, since this might be the major limitation of experiments carried out at low pollutant concentrations typical of the polluted atmosphere. Detailed investigation of three chamber experiments at zero-NO _x in the European Photoreactor (EUPHORE) were carried out by means of rate-of-production analysis and two uncertainty analysis tools: local uncertainty analysis and Monte Carlo simulations with Latin hypercube sampling. The chemical mechanism employed was that for methane plus the inorganic subset of the Master Chemical Mechanism (MCMv3.1). Newly installed instruments in EUPHORE allowed the measurement of nitrous acid and formaldehyde at sub-ppb concentrations with high sensitivity. The presence of HONO and HCHO during the experiments could be explained only by processes taking place on the FEP Teflon walls. The HONO production rate can be described by the empirical equation W(HONO)_EUPHORE ^dry = a × j _{NO 2}× exp (− T ₀/T) in the low relative humidity region (RH < 2%, a = 7.3×10²¹ cm⁻³, T ₀ = 8945K), and by the equation W(HONO)_EUPHORE ^humid = W(HONO)_EUPHORE ^dry+ j _{NO 2}× b × RH ^q in the higher relative humidity region (2% < RH < 15%, b = 5.8×10⁸ cm⁻³ and q = 0.36, and RH is the relative humidity in percentages). For HCHO the expression W(HCHO)_EUPHORE = c × j _{NO 2}exp (− T′₀/T) is applicable (c = 3.1×10¹⁷ cm⁻³ and T′₀ = 5686 K). In the 0–15% relative humidity range OH production from HONO generated at the wall is about a factor of two higher than that from the photolysis of 100 ppb ozone. Effect of added NO₂ was found to be consistent with the dark HONO formation rate coefficient of MCMv3.1.     

Correlated humidity and temperature measurements in the urban atmospheric boundary layer

Summary To investigate the effect of atmospheric turbulence on microwave communication links, temperature and water vapor pressure have been measured and radio refractivity has been computed, during different meteorological conditions, in the atmospheric boundary layer of an urban site. The cospectra between temperature (T) and water vapor pressure (e) have been found to be either negative over the whole range of frequencies, or the low-frequency end of the cospectrum is of opposite sign relative to higher frequency end. In both cases cospectra follow a–5/3 law in the inertial subrange, in agreement with the theoretical predictions. The coherence spectra clearly show that the temperature and humidity fluctuations are highly coherent within the inertial subrange under both convective and stable conditions. The relative contribution ofC _T ² ,C _eT andC _e ² to the real refractive index structure parameterC _n ² is examined and discussed.With 4 Figures     

Relationship between Net Radiation and Broadband Solar Radiation in the Tibetan Plateau

The characteristics of net radiation (R_n)(0.3--10 μm) in Lhasa and Haibei in the Tibetan Plateau were analyzed based on long-term in-situ measurements of surface radiation data. The monthly average of daily R_n reached a minimum during the winter period followed by an increase until May and then a decline until January. This variation is consistent with solar activity. The annual mean daily total R_n values were 0.92 MJ m^-2 d^-1 and 0.66 MJ m^-2d^-1 in Lhasa and Haibei, respectively. A relationship between R_n and broadband solar radiation (R_s) was demonstrated by a good linear correlation at the two sites. R_n can be an accurate estimate from R_s. The estimated R_n values were similar to the observed values, and the relative deviations between the estimates and measurements of R_n were 2.8% and 3.8% in Lhasa and Haibei, respectively. The application of the R_n estimating model to other locations showed that it could provide acceptable estimated R_n values from the R_s data. Furthermore, we analyzed the influence of clouds on R_n by different clear index (K_s), defined as the ratio of R_s to the extraterrestrial solar irradiance on a horizontal surface. The results indicate that more accurate results are associated with increased cloudy conditions. The influence of the albedo was also considered, but its inclusion in the model resulted in only a slight improvement. Because surface albedo is not usually measured, an expression based solely on global solar radiation could be of more extensive use.     

Fractal aspects of integrated concentration fluctuations

Time series of vertically integrated concentrations (VIC) across neutrally buoyant plumes are used to study the fractal and multifractal characteristics of passive scalar fluctuations in turbulent flow fields. Here, the multifractal analysis is based on a novel definition of the singularity spectrum-F() of the time records. Approximations for quantities such as the fractal dimension and the spectral exponent are derived as functions ofF() and are compared with the experimental results. Among other things, we show that VIC records are characterized by two typical subdomains. One domain, which is related to integrated concentration fluctuations, is a subfractal process; whereas the second one, which is directly related to the concentration fluctuations, is a fractal process.     

Spectra of temperature derivatives in the atmospheric surface layer

Measured spectra ofθ _x,θ _y,θ _z, the derivatives of temperature in streamwise, lateral and vertical directions, respectively, indicate that the spectral densities ofθ _z andθ _y are nearly similar but significantly different from the spectral density ofθ _x. The high-frequency parts of the three spectra satisfy, in a qualitative sense, local isotropy requirements. In the high-frequency end of the inertial subrange, the relative behaviour of spectra ofθ _x,θ _y andθ _z is also consistent with local isotropy.