On the magnitude and apparent range of variation of the von Karman constant in the atmospheric surface layer

The half-century history of the experimental evaluation of the von Karman constant in the atmospheric surface layer is reviewed, an evidence indicating that this well-known scaling factor,k, is actually a weak variable that decreases with increasing Reynolds number is discussed. A combined average ofk=0.390 with a standard error of ±0.010 is found from two field studies, a result which indicates that there is only one chance in 40 that the true value of the scaling factor in the population from which the experimental sample was drawn could have been as large as the laboratory value of 0.40. Based on experimental and theoretical results given by others, it is suggested thatk varies from a maximum of 0.41 in light winds over open water and smooth land surfaces, to a minimum near 0.37 in stronger winds over forests and cities. This range is shown to imply that a working value ofk=0.39±1% is appropriate for flows over surfaces characterized by 0.7<z ₀<8.7 cm, a roughness subrange which corresponds to a wide variety of terrain types from sparsely vegetated level plains to mixed croplands with occasional hedges and trees.sponsored in part by the Global Change Post Doctoral Program, Office of Health and Environmental Research, U. S. Department of Energy.Work sponsored by the National Science Foundation under Grant No. ATM-9019682.     

A comparison between observed and predicted values for the entrainment coefficient in the planetary boundary layer

A new method is presented for determining experimentally the entrainment coefficient % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeyqaiabg2% da9iabgkHiTiaacIcadaqdaaqaaiabeI7aXjaacEcacaWG3bGaai4j% aaaacaGGPaGaamyAaiabg+caViaacIcadaqdaaqaaiabeI7aXjaacE% cacaWG3bGaai4jaaaacaGGPaWaaSbaaSqaaiaaicdaaeqaaaaa!4646!\[{\text{A}} = - (\overline {\theta 'w'} )i/(\overline {\theta 'w'} )_0 \] characteristic of a convective, planetary boundary layer. This method, which makes use of sodar records together with simultaneous meteorological observations, can be applied to morning convection situations (i.e. shallow mixed layer capped by a marked temperature inversion). Data from the Voves experiment (France, summer 1977) yield A values between 0 and 1, thus departing from the 0.2 ± 0.1 interval which is the range of commonly accepted values.A comparison between these results and theoretical predictions using models developed by Stull (1976) and Zeman and Tennekes (1977) indicates a fair amount of agreement; the importance of mechanically driven turbulence in the entrainment process, especially for the early morning hours, is therefore confirmed.

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Résumé Une méthode de détermination expérimentale du coefficient d'entraînement % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeyqaiabg2% da9iabgkHiTiaacIcadaqdaaqaaiabeI7aXjaacEcacaWG3bGaai4j% aaaacaGGPaGaamyAaiabg+caViaacIcadaqdaaqaaiabeI7aXjaacE% cacaWG3bGaai4jaaaacaGGPaWaaSbaaSqaaiaaicdaaeqaaaaa!4646!\[{\text{A}} = - (\overline {\theta 'w'} )i/(\overline {\theta 'w'} )_0 \] dans une couche limite planétaire convective est proposée. Cette méthode, qui combine les données enregistrées par un sodar à des mesures météorologiques in situ, s'applique aux cas de convection matinale (couche de mélange assez peu développée surmontée par une inversion de température marquée.) Dans le cas des observations recueillies lors de la campagne de Voves (1977) elle fournit des valeurs de A qui s'écartent parfois de 0.2 ± 0.1 (gamme des valeurs souvent adoptées) et couvrent la totalité de l'intervalle 0-1.La comparaison entre les valeurs de A déterminées par cette méthode et celles prédites à partir des modèles de Stull (1976) et Zeman (1977) conduit à un accord satisfaisant, ce qui confirme le rôle joué par la turbulence mécanique dans le processus d'entraînement durant les premières heures de la convection matinale.

     

The Kolmogorov constant for carbon dioxide in the atmospheric surface layer over a paddy field

From measurements in the atmospheric surface layer over a paddy field, the Kolmogorov constants for CO₂ and longitudinal wind velocity were obtained. In this study, the nondimensional dissipation rate _nc = (1–16 _v )^-1/2 for CO₂ variance and = (1–16 _v )^-1/4 – _v for turbulent energy were used, assuming the equality of the local production term and the local dissipation term, and neglecting the divergence flux term in the budget equation. The value of the constant for CO₂ was consistent with recent determinations for temperature and humidity. The constant for longitudinal wind velocity showed good agreement with other recent observations.     

Planetary boundary layer and surface layer sensitivity to land surface parameters

The sensitivity of the development of the convective planetary boundary layer (PBL) and the surface layer are examined using a coupled surface parameterization and detailed PBL model. First, the coupling is verified against observations from the First ISLSCP (International Satellite Land Surface Climatology Project) Field Experiment (FIFE). Results of the sensitivity experiments indicate that the PBL is most sensitive to the amount of soil water content, and the proximity of the soil water content to critical soil texture values (field capacity and wilting point). While vegetation cover is not the most sensitive parameter at the surface, its influence on the surface energy and hydrologic balance is crucial. Model sensitivity to minimum stomatal resistance, type of soil parameterization and canopy height (surface roughness and displacement depth) is also discussed.     

利用行星边界层顶上方最邻近标准等压面的实测风推算地面风的方法及其比较

文中提出了一种在实际地形条件下,利用行星边界层顶上方最邻近标准等压面的实测风推算地面风的方法——修正的Taylor螺线法。试算表明,按这种方法和Taylor螺线法推算的地面风场的基本流型均与实测流场相似,但在风速模的均方根误差上,前者较之后者有显著改进.按文中方法推算得到的地面风场所求得的散度场的分布与天气区的配置也较合理,且散度值与实况比较接近.     

The atmospheric boundary layer over a wavy surface

The wavy area of north-west Bohemia (Czechoslovakia) is simulated by a cylindrical surface model. A curvilinear orthogonal system of coordinates along the model surface is introduced. The hydrodynamical equations of motion are transformed into this system of coordinates. By applying boundary-layer assumptions, the equations of motion for the atmospheric boundary layer (ABL) above the model are derived. The equations and boundary conditions show an equivalence of the ABL above the model with that above a flat surface with external pressure gradient.     

The role of surface heterogeneity in modelling the stable boundary layer

High-resolution numerical simulations are performed for three nights for each of two areas of the United Kingdom. Area-averaging techniques are then used to calculate effective stability functions for turbulence parametrizations in models using typical mesoscale and global spatial resolutions. Comparisons are made with parametrizations commonly used in numerical weather prediction models. The present results do not suggest that significant enhancement of the stability functions above 50 m is justified. Closer to the surface, more significant enhancement is observed in some regions. It is shown that the amount of enhancement is related to the variability of the orography.     

On the existence of a relation between the Kolmogoroff and von Kármán constants

A model is described, in which the mean vertical wind profile and turbulence spectra at different heights are calculated for a turbulent boundary layer without thermal stratification. The model makes use of Heisenberg's formula for the transfer of turbulent energy and is based on the assumption of a constant shearing stress in that boundary layer. As a result, a logarithmic wind profile follows with 0.39 as the value of von Kármán's constant, which is — in this model — strongly related to the inertial subrange of the turbulent energy spectra and therefore to the Kolmogoroff constant.This paper is based on studies done by the author during a one-year visit to CSIRO Division of Meteorological Physics, Aspendale, Australia, and was presented at the AGARD Specialists Meeting on The Aerodynamics of Atmospheric Shear Flows sponsored by the Fluid Dynamics Panel at Munich, Germany, during 15–17 Sept. 1969.     

Temperature oscillations observed in the stable boundary layer over four different underlying surfaces

夜间边界层内的温度时空特征决定了边界层的稳定性。由于稳定边界层的间歇性和复杂性,模式在夜间的参数化方案还不完善,研究夜间边界层的温度变化有助于改进模式在夜间的表现。本文利用四座在不同下垫面上的气象塔的数据,研究了夜间边界层中的温度波动。研究表明,无论是海边、草原还是沙漠下垫面,夜间形成的稳定边界层中,振幅大约2摄氏度,周期在数分钟的温度波动非常频繁地出现。而在北京,由于城市下垫面较大的热容量和人为热源使得稳定边界层不容易形成,温度波动也较弱。用布朗特维萨拉频率代表的静力稳定度是影响温度脉动强弱的重要因子。     

An examination of turbulence statistics in the surface boundary layer

Simulated data derived from random numbers are used to show that the process of relating % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacaWG3baabeaakiaac+cacaWG1bWaaSbaaSqaaiabgEHiQaqa% baaaaa!3D7C!\[\sigma _w /u_ * \]and similar properties to the stability parameter % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaadQhacaGGVa% Gaamitaaaa!3A42!\[z/L\]is highly susceptible to error. An alternative method, making use of Ri as a stability index, is not affected in this way and is used to re-examine the data obtained in the 1968 Kansas micrometeorological experiment. The relationship % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacaWG3baabeaakiaac+cacaWG1bWaaSbaaSqaaiabgEHiQaqa% baGccqWIdjYocaaIXaGaaiOlaiaaikdacaaI1aaaaa!419F!\[\sigma _w /u_ * \simeq 1.25\] % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaamaabmaabaGaaG% ymaiabgkHiTiaaikdacaWG6bGaai4laiaadYeaaiaawIcacaGLPaaa% daahaaWcbeqaaiaaigdacaGGVaGaaG4maaaaaaa!4087!\[\left( {1 - 2z/L} \right)^{1/3} \]is found to provide a good fit to the unstable data, but it is unclear as to whether a small peak observed in stable conditions is real (perhaps associated with gravity waves) or not (possibly a consequence of measurement errors).The properties % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacaWG1baabeaakiaac+cacaWG1bWaaSbaaSqaaiabgEHiQaqa% baaaaa!3D7A!\[\sigma _u /u_ * \]and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacaWG1baabeaakiaac+cacaWG1bWaaSbaaSqaaiabgEHiQaqa% baaaaa!3D7A!\[\sigma _u /u_ * \] are found to attain a relatively constant value ( 3) in conditions more unstable than about Ri = -0.4. The shape ratio % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacaWG1baabeaakiaac+cacqaHdpWCdaWgaaWcbaGaamODaaqa% baaaaa!3E4F!\[\sigma _u /\sigma _v \] is found to decrease to less than unity in very unstable conditions, possibly as a consequence of some undetected error in measurement of _u . In the case of temperature fluctuations, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacqaHepaDaeqaaOGaai4laiaadsfadaWgaaWcbaGaey4fIOca% beaakiabg2da9iaaicdacaGGUaGaaGyoaiaaiwdacaGGOaGaeyOeI0% IaamOEaiaac+cacaWGmbGaaiykamaaCaaaleqabaGaeyOeI0IaaGym% aiaac+cacaaIZaaaaaaa!4A30!\[\sigma _\tau /T_ * = 0.95( - z/L)^{ - 1/3} \] is found to provide an excellent fit in unstable conditions (Ri < -0.1), even though this form also agrees well with random behavior.Now With: Atmospheric Turbulence and Diffusion Laboratory, NOAA, P. O. Box E, Oak Ridge Tenn., 37830, U.S.A.     

Wind profile constants in a neutral atmospheric boundary layer over complex terrain

The roughness height z ₀ and the zero-plane displacement height d ₀ were determined for a region of complex terrain in the Pre-Alps of Switzerland. This region is characterized by hills of the order of 100 m above the valley elevations, and by distances between ridges of the order of 1 km; it lies about 20 to 30 km north from the Alps. The experimental data were obtained from radiosonde observations under near neutral conditions. The analysis was based on the assumption of a logarithmic profile for the mean horizontal wind existing over one half of the boundary layer. The resulting (z ₀/h) and (d ₀/h) (where h is the mean height of the obstacles) were found to be in reasonable agreement with available relationships in terms of placement density and shape factor of the obstacles, which were obtained in previous experiments with h-scales 2 to 4 orders of magnitude smaller than the present ones.     

The resistance law for the atmospheric boundary layer over a wavy surface

In analogy with two-dimensional turbulent layers, the surface layer (where wall similarity is fulfilled) and the region near the outer edge of the boundary layer (where the flow described by the velocity defect belongs to then-parameter family) may be postulated to exist for the atmospheric boundary layer over a wavy surface. The matching of the two regions yields a resistance law.     

Similarity theory of diffusion and the observed vertical spread in the diabatic surface layer

The extension of Lagrangian similarity theory of diffusion to stratified flow is examined, to improve its prediction of the vertical spread of a passive substance. In the basic equation, where is the average height of a cluster of particles,u _* is the friction velocity andL is Monin-Obukhov length. It is shown theoretically, under the assumption of an equivalence between the diffusivities of heat and matter, that the unspecified function is the reciprocal of a more familiar meteorological parameter _n , the dimensionless temperature gradient. The universal constantb is found to be approximately equal to von Karman's constant for various stability conditions. The predicted effect of stability on vertical spread shows excellent agreement with that of the published data from the O'Neill experiments.     

Convective plumes in the atmospheric boundary layer as observed with an acoustic Doppler sodar

The vertical velocity field and the convective plumes in the atmospheric boundary layer have been observed during morning hours with the acoustic Doppler sounder of the C.R.P.E. A method for plume determination using acoustic soundings in the well-mixed layer is presented. Using Telford's 1970 and Manton's 1975 models, a comparison is made between the predictions of the models and the plume properties as observed by the Doppler sodar. The mean plume velocity is found to be parabolic. It is shown, restricting Monin and Obukhov similarity to conditions inside plumes and using only vertical velocity within plumes, that the observed convective plumes carry nearly sixty percent of the sensible heat flux at the top of the surface layer.     

Diurnal variations of the planetary boundary layer observed with anL-band clear-air doppler radar

Based on continuous observations of the planetary boundary layer (PBL) with anL-band (1357.5 MHz) boundary-layer radar (BLR) at a hilly location in Japan, we have discovered that on clear days, a thin enhanced echo layer corresponding to the top of the PBL (or mixed layer) appeared at about 500 m height in the morning and ascended to about 1500 m in the afternoon. Strong upward velocities were observed below the echo layer (or inside the PBL), reaching 1500 m in the afternoon.     

Minimum friction velocity and heat transfer in the rough surface layer of a convective boundary layer

A simple model is deduced for the surface layer of a convective boundary layer for zero mean wind velocity over homogeneous rough ground. The model assumes large-scale convective circulation driven by surface heat flux with a flow pattern as it would be obtained by conditional ensemble averages. The surface layer is defined here such that in this layer horizontal motions dominate relative to vertical components. The model is derived from momentum and heat balances for the surface layer together with closures based on the Monin-Obukhov theory. The motion in the surface layer is driven by horizontal gradients of hydrostatic pressure. The balances account for turbulent fluxes at the surface and fluxes by convective motions to the mixed layer. The latter are the dominant ones. The model contains effectively two empirical coefficients which are determined such that the model's predictions agree with previous experimental results for the horizontal turbulent velocity fluctuations and the temperature fluctuations. The model quantitatively predicts the decrease of the minimum friction velocity and the increase of the temperature difference between the mixed layer and the ground with increasing values of the boundary layer/roughness height ratio. The heat transfer relationship can be expressed in terms of the common Nusselt and Rayleigh numbers, Nu and Ra, as Nu ~ Ra^{% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSGbaeaaca% aIXaaabaGaaGOmaaaaaaa!3779!\[{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}\]}. Previous results of the form Nu ~ Ra^{% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSGbaeaaca% aIXaaabaGaaG4maaaaaaa!377A!\[{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}\]} are shown to be restricted to Rayleigh-numbers less than a certain value which depends on the boundary layer/roughness height ratio.     

Conditional concentration statistics for surface plumes in the atmospheric boundary layer

A set of concentration time series from ground-level plumes in the atmosphere has been used to generate conditionally sampled (zeros ignored) plume concentration statistics. These have been compared and contrasted with corresponding unconditionally sampled statistics. It is found that conditional statistics are much less sensitive to the location of the receptor (relative to the mean plume) and to averaging time. Indeed, most of the variation apparent in unconditionally sampled statistics (both explained and unexplained) resides in the intermittency, the fraction of non-zero readings.The data are used to test three commonly used models for the concentration frequency distribution. At the simplest level of modelling, it is assumed that conditional statistics are invariant; then the data are best represented by a clipped-normal distribution. However, an exponential distribution is only slightly conservative and has the advantage of simplicity. A log-normal distribution is clearly not supported by the data. With this simple approach the intermittency remains unspecified and this is a serious deficiency.More advanced modelling must account for the residual variation in conditional statistics, which implies a relationship between these statistics and the intermittency. Although there is evidence for such a relationship in the data, it is not adequately represented by any of the distribution models considered.     

Atmospheric waves observed in the planetary boundary layer using an acoustic sounder and a microbarograph array

Acoustic sounder and microbarograph records of atmospheric waves propagating in the planetary boundary layer over Table Mountain, Colorado, are presented and compared. The two observing techniques are complementary in that the array provides wave amplitude, horizontal phase speed, direction, and wavelength, while the sounder provides a detailed picture of temporal changes in the structure of the lowermost kilometer or so of the Earth's atmosphere.