Stable boundary layers: observations,models and variability part II: Data analysis and averaging effects

As argued in Part I (Derbyshire, 1995), variability is a key issue in stable boundary layers, and differences in variability between observations and idealized models may imply sytematic biases. Here we discuss how data analysis can be geared to allow for variability and thus consistency with models. Instrumental errors, smoothing methods and vertical discretization are considered. We then show how statistical averaging broadly improves the agreement of heterogeneous results in Part I with the Brost-Wyngaard closure. Recommendations are made for the information needed to analyze apparent differences between homogeneous and heterogeneous stable boundary layers.Part of UK Meteorological Office Atmospheric Processes Research Division     

Inertial subrange correlation between temperature and humidity fluctuations in the unstable surface layer above vegetated terrains

Observations of the temperature-humidity cospectrum and correlation spectrum were made with a cold platinum wire and a Ly- hygrometer at 3.7 and 10 m above vegetated surfaces during unstable atmospheric conditions. It was found theoretically that a separation between the temperature and humidity sensors causes a drop-off of the correlation spectrum at wavenumbers > 0.3 ^–1. The observed drop-off follows the theoretical one reasonably well. Measurements made with the temperature sensor placed in the center of the Ly- gap reveal a % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaccaGae8NKby% kaaa!37B5!\[f\]^–5/3 dependence of the temperature-humidity cospectrum in the inertial subrange up to frequencies of 20 Hz. The drop-off at higher frequenties is thought to be caused by limitations inherent to the Ly- humidiometer.     

The influence of anisotropy on stress estimation by the indirect dissipation method

A comparison of observations by different authors reveals that systematic differences exist between momentum fluxes measured directly, and momentum fluxes determined indirectly by the dissipation method. This discrepancy is attributed to systematic errors due to the indirect determination of energy dissipation from the presumed inertial subrange spectrum of the horizontal wind component. The discrepancy increases with increasing degree of anisotropy, indicated by the ratio (vertical wind spectrum): (horizontal wind spectrum) deviating from % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaaiaais% daaeaacaaIZaaaaaaa!33E6!\[\frac{4}{3}\]The results support a value of 0.48 for Kolmogoroff's constant.     

Microwave vegetation optical depth and inverse modelling of soil emissivity using Nimbus/SMMR satellite observations

Summary A radiative transfer model has been used to determine the large scale effective 6.6 GHz and 37 GHz optical depths of the vegetation cover. Knowledge of the vegetation optical depth is important for satellite-based large scale soil moisture monitoring using microwave radiometry. The study is based on actual observed large scale surface soil moisture data and observed dual polarization 6.6 and 37 GHz Nimbus/SMMR brightness temperatures over a 3-year period. The derived optical depths have been compared with microwave polarization differences and polarization ratios in both frequencies and with Normalized Difference Vegetation Index (NDVI) values from NOAA/AVHRR. A synergistic approach to derive surface soil emissivity from satellite observed brightness temperatures by inverse modelling is described. This approach improves the relationship between satellite derived surface emissivity and large scale top soil moisture fromR ²=0.45 (no correction for vegetation) toR ²=0.72 (after correction for vegetation). This study also confirms the relationship between the microwave-based MPDI and NDVI earlier described and explained in the literature.List of Symbols f frequency [Hz] - f _i(p) fractional absorption at polarizationp - h surface roughness - h h cos² - H horizontal polarization - n _i complex index of refraction - p polarization (H orV) - R _s microwave surface reflectivity - T _B(p) brightness temperature at polarizationp - T ^* normalized brightness temperature - T polarization difference (T _v-T _H) - T _s temperature of soil surface - T _c temperature of canopy - T _max daily maximum air temperature - T _min daily minimum air temperature - V vertical polarization - soil moisture distribution factor; also used for the constant to partition the influence of bound and free water components to the dielectric constant of the mixture - empirical complex constant related to soil texture - microwave transmissivity of vegetation (=e ^–) - ^* effective transmissivity of vegetation (assuming =0) - microwave emissivity - _s emissivity of smooth soil surface - _rs emissivity of rough soil surface - _vs emissivity of vegetated surface - soil moisture content (% vol.) - K dielectric constant [F·m^–1] - K _fw dielectric constant of free water [F·m^–1] - K _ss dielectric constant of soil solids [F·m^–1] - K _m dielectric constant of mixture [F·m^–1] - K _o permittivity of free space [8.854·10^–12 F·m^–1] - high frequency limit ofK _wf [F·m^–1] - wavelength [m] - incidence angle [degrees from nadir] - polarization ratio (T _H/T _V) - b soil bulk density [gr·cm^–3] - s soil particle density [gr·cm^–3] - R surface reflectivity in red portion of spectrum - NIR surface reflectivity in near infrared portion of spectrum - _eff effective conductivity of soil extract [mS·cm^–1] - vegetation optical depth - _6.6 vegetation optical depth at 6.6 GHz - ₃₇ vegetation optical depth at 37 GHz - ^* effective vegetation optical depth (assuming =0) - single scattering albedo of vegetation With 12 Figures     

The source area influencing a measurement in the Planetary Boundary Layer: The “footprint” and the “distribution of contact distance”

This paper considers the ground area which affects the properties of fluid parcels observed at a given spot in the Planetary Boundary Layer (PBL). We examine two source-area functions; the footprint, giving the source area for a measurement of vertical flux: and the distribution of contact distance, the distance since a particle observed aloft last made contact with the surface. We explain why the distribution of contact distance extends vastly farther upwind than the footprint, and suggest for the extent of the footprint the inequalities: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOabaeqabaGaamyvam% aalaaabaGaamiAaaqaaiabeo8aZnaaBaaaleaacaWGxbaabeaakiaa% cIcacaWGObGaaiykaaaacqGH8aapcaWG4bGaeyipaWJaamyvaKazaa% iadaGabaqaamaaDaaajqwaacqaaiaadIgacaGGVaGabmOEayaacaGa% aiilaiaabccacaGGVbGaaiiDaiaacIgacaGGLbGaaiOCaiaacEhaca% GGPbGaai4CaiaacwgaaeaacaWGubWaaSbaaKazcaiabaGaamitaaqa% baqcKfaGaiaacIcacaWGObGaaiykaiaabYcacaqGGaGaaeiAaiaabc% cacaGGHbGaaiOyaiaac+gacaGG2bGaaiyzaiaabccacaGGZbGaaiyD% aiaackhacaGGMbGaaiyyaiaacogacaGGLbGaeyOeI0IaaiiBaiaacg% gacaGG5bGaaiyzaiaackhaaaaajqgaacGaay5EaaaakeaaaeaacaGG% 8bGaamyEaiaacYhacqGH8aapcqaHdpWCdaWgaaWcbaGaamODaaqaba% GccaGGOaGaamiAaiaacMcadaWcaaqaaiaadIhaaeaacaWGvbaaaaaa% aa!7877!\[\begin{array}{l} U\frac{h}{{\sigma _W (h)}} < x < U\left\{ {_{h/\dot z,{\rm{ }}otherwise}^{T_L (h){\rm{, h }}above{\rm{ }}surface - layer} } \right. \\ \\ |y| < \sigma _v (h)\frac{x}{U} \\ \end{array}\] where U is the mean streamwise (x) velocity, h is the observation height, _L is the Lagrangian timescale, _v and _w are the standard deviations of the cross-stream horizontal (y) and vertical (z) velocity fluctuations, and is the Lagrangian Similarity prediction for the rate of rise of the centre of gravity of a puff released at ground.Simple analytical solutions for the contact-time and the footprint are derived, by treating the PBL as consisting of two sub-layers. The contact-time solutions agree very well with the predictions of a Lagrangian stochastic model, which we adopt in the absence of measurements as our best estimate of reality, but the footprint solution offers no improvement over the above inequality.     

An observational study of the structure of the nocturnal urban boundary layer

The formation mechanism of the nocturnal urban boundary layer (UBL), especially in the winter nighttime, was investigated based on the extensive field observations conducted during November 1984 in Sapporo, Japan. A strong, elevated inversion formed over the Sapporo urban area and the inversion base height was approximately twice the average building height. Velocity fluctuations _u, _w and Reynolds stress % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% WG1bWaaWbaaSqabeaacaaIXaaaaGGaaOGae8hiaaIaam4DamaaCaaa% leqabaGaaGymaaaaaaaaaa!3A9C!\[\overline {u^1 w^1 } \] had nearly uniform profiles within the nocturnal UBL and decreased with height above the UBL. On the other hand, temperature fluctuations _t , and heat fluxes % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% WG1bWaaWbaaSqabeaacaaIXaaaaGGaaOGae8hiaaIaeqiUde3aaWba% aSqabeaacaaIXaaaaaaaaaa!3B56!\[\overline {u^1 \theta ^1 } \] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% WG3bWaaWbaaSqabeaacaaIXaaaaGGaaOGae8hiaaIaeqiUde3aaWba% aSqabeaacaaIXaaaaaaaaaa!3B58!\[\overline {w^1 \theta ^1 } \] had peaks at the inversion base and small values within the nocturnal UBL. The turbulent kinetic energy budget showed that the turbulent transport term and shear generation from urban canopy elements are important in the nocturnal UBL development; the role of the buoyancy term is small. The turbulence data analysis and application of a simple advective model showed that the mechanism of UBL formation may be controlled by the downward transport of sensible heat from the elevated inversion caused by mechanically-generated turbulence.Nomenclature g accelaration due to gravity, m s^-2 - k turbulent kinetic energy, m² s^-1 - K _m eddy viscosity, m² s^-1 - L Monin-Obukhov lenght, m - p pressure, Kg m^-2 - U, V, W mean wind speed in the downwind, crosswind, and vertical directions, respectively, m s^-1 - u ¹, w ¹ wind speed fluctuation in the downwind and vertical direction, respectively, m s^-1 - u ₁ friction velocity, m s^-1 - % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% WG1bWaaWbaaSqabeaacaaIXaaaaGGaaOGae8hiaaIaam4DamaaCaaa% leqabaGaaGymaaaaaaaaaa!3A9C!\[\overline {u^1 w^1 } \] momentum flux, m²s^-2 - % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% WG1bWaaWbaaSqabeaacaaIXaaaaGGaaOGae8hiaaIaam4DamaaCaaa% leqabaGaaGymaaaaaaaaaa!3A9C!\[\overline {u^1 \theta^1 } \] sensible heat flux, m²s^-1°C - WD wind direction, deg - WS wind speed, m s^-1 - z altitude, m - Z _h inversion base height, m - Z _j wind maximum height, m - Z _t inversion top height, m - T _u-r heat island intensity, °C - temperature lapse rate at rural site, °C m^-1 - energy dissipation rate, m²s^-3 - ¹ Potential temperature fluctuation, °C - _* scaling temperature, (=-% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% WG1bWaaWbaaSqabeaacaaIXaaaaGGaaOGae8hiaaIaeqiUde3aaWba% aSqabeaacaaIXaaaaaaaaaa!3B56!\[\overline {u^1 \theta ^1 } \]/u_*) °C - mean potential temperature fluctuation, K - density of air, Kgm^-3 - K von Kármán constant (=0.4) - _u, _v, _w standard deviation of wind speed in the downwind, crosswind, and vertical directions, respectively, m s^-1 - standard diviation of temperature, °C     

Estimation of the Monin-Obukhov similarity functions from a spectral model

From measured one-dimensional spectra of velocity and temperature variance, the universal functions of the Monin-Obukhov similarity theory are calculated for the range –2 z/L + 2. The calculations show good agreement with observations with the exception of a range –1 z/L 0 in which the function _m , i.e., the nondimensional mean shear, is overestimated. This overestimation is shown to be caused by neglecting the spectral divergence of a vertical transport of turbulent kinetic energy. The integral of the spectral divergence over the entire wave number space is suggested to be negligibly small in comparison with production and dissipation of turbulent kinetic energy.Notation a,b,c contants (see Equations (–4)) - C_i constants i=u, v, w, (see Equation (5) - k_me,k_mT peak wave numbers of 3-d moel spectra of turbulent kinetic energy and of temperature variance, respectively - k_mi peak wave numbers of 1-d spectra of velocity components i=u, v, w and of temperature fluctuations i= - k_sb, k_c characteristics wave numbers of energy-feeding by mechanical effects being modified by mean buoyancy, and of convective energy feeding, respectively - L Monin-Obukhov length - % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Gabeivayaaraaaaa!3C5B!\[{\rm{\bar T}}\] difference of mean temperature and mean potential temperature - T* Monin-Obukhov temperature scale - velocity of mean flow in positive x-direction - u* friction velocity - u, v, w components of velocity fluctuations - z height above ground - von Kármanán constant - temperature fluctuation - _m nondimensional mean shear - _H nondimensional mean temperature gradient - nondimensional rate of lolecular dissipation of turbulent kinetic energy - _D nondimensional divergence of vertical transports of turbulent linetic energy     

Evidence of recent climatic anomalies at Trieste (Italy)

A recent noticeable climatic anomaly in some meteomarine quantities is analysed based on observations during the period March 1, 1971-February 28, 1993 taken in Trieste (Italy). Marked deviations from the normal values of the coupled quantities atmospheric pressure-solar irradiance and atmospheric pressure-sea level elevation, during the last 22 years, are analysed. The procedures used bring out a clear and persistent configuration of high pressure, high irradiance and low sea level from 1989 on, previously unmatched.     

On Modelling the One-Dimensional Atmospheric Boundary Layer

Several commonly used turbulence closure schemes forthe atmospheric boundarylayer (ABL) are applied to simulate neutral, nocturnal and diurnal cyclesituations in a one-dimensional ABL. Results obtained with the differentschemes, E-, E- and its modified versions, and twoversions ofthe q ² Level 2.5, are compared and discussed.     

A framework for evaluating air quality models

This paper describes a framework to evaluate air quality model predictions against observations. We propose the following relationship between observations and predictions from an adequate model% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabm4qayaaja% WaaSbaaSqaaiaaicdaaeqaamXvP5wqonvsaeHbfv3ySLgzaGqbaOGa% e8hkaGIaamiEamaaBaaaleaacaaIXaaabeaakiaacYcacaWG4bWaaS% baaSqaaiaaikdaaeqaaOGae8xkaKIaeyypa0Jabm4qayaajaWaaSba% aSqaaiaadchaaeqaaOGae8hkaGIaamiEamaaBaaaleaacaaIXaaabe% aakiab-LcaPiab-TcaRiabew7aLjab-HcaOiaadIhadaWgaaWcbaGa% aGOmaaqabaGccqWFPaqkaaa!4F93!\[\hat C_0 (x_1 ,x_2 ) = \hat C_p (x_1 ) + \varepsilon (x_2 )\],where x ₁ refers to the inputs used in the model prediction C _p(x ₁), and x ₂denotes unknown variables which affect the observed concentration C ₀. The hats associated with C _pand C ₀denote transformations to convert the residual to a white noise sequence which is normally distributed. In this paper we assume % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabm4qayaaja% GaeyyyIORaciiBaiaac6gacaWGdbaaaa!3B39!\[\hat C \equiv \ln C\].The standard deviation of determines the expected deviation between model prediction and observation. The purpose of model improvement is to make this deviation as small as possible.The formalism we have proposed is applied to the evaluation of two models developed by this author. We show how careful analysis of residuals can lead to improvements in the model. We have also estimated for each of the models.In the last part of the part of the paper we show how the statistics of can be used to interpret model predictions.     

Measurements of solar radiation and estimation of optical depth in the high Andes of Peru

Summary During an expedition to the high Andes of Southern Peru in June–July 1977, measurements of direct solar radiation in four spectral bands (0.270–0.530–0.630–0.695–2.900 ) were conducted at six sites in elevations ranging from sea level to 5645 m. These measurements were evaluated in Langley plots to determine total optical depths () and irradiances at the top of the atmosphere. In addition, water vapor optical depths (_wv) were calculated from the mean radiosounding over Lima during the expedition, and Rayleigh (_ray) and ozone (_oz) optical depths were obtained from published tabulations. Subtracting _ray, _oz, and _wv from yielded estimates of aerosol optical depth _aer. The components _ray and _oz decrease from the shorter towards the longer wavelength bands and from the lower towards the higher elevation sites; _aer also decreases towards the higher elevations. Particularly pronounced is the decrease of _aer and from the lowlands of the Pacific coast to the highlands of the interior, reflecting the effect of a persistent lower-tropospheric inversion and the contrast from the marine boundary layer to the clear atmosphere of the high Andes.With 4 Figures     

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.     

Stability functions correct at the free convection limit and consistent for for both the surface and Ekman layers

For the thermal stability function _h used to calculate heat and moisture fluxes in the surface layer, we choose a formulation which has the theoretically correct free convection limit % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeikaiabgk% HiTGqaciaa-PhacaqGVaGaamitaiaabMcadaahaaWcbeqaaiabgkHi% TiaaigdacaGGVaGaaG4maaaaaaa!3DFE!\[{\rm{(}} - z{\rm{/}}L{\rm{)}}^{ - 1/3} \]. We then use the experimental result that z/L Ri to deduce a formulation with an exponent -1/6 for the momentum stability function _m. This formulation also resolves the matching problem at the interface between the surface and Ekman layers. The proposed functions are found to remain reasonably close to another formulation that is well supported by observations and has exponents -1/2 for _h and -1/4 for _m. The intent of the proposals is mainly to clarify and simplify the parameterization of the convective boundary layer in present day atmospheric models, without significantly altering the results.     

Occurrence of roll circulations in a shallow boundary layer

Meteorological measurements taken at the Näsudden wind turbine site during slightly unstable conditions have been analyzed. The height of the convective boundary layer (CBL) was rather low, varying between 60 and 300 m. Turbulence statistics near the ground followed Monin-Obukhov similarity, whereas the remaining part of the boundary layer can be regarded as a near neutral upper layer. In 55% of the runs, horizontal roll vortices were found. Those were the most unstable runs, with -z _i/L > 5. Spectra and co-spectra are used to identify the structures. Three roll indicators were identified: (i) a low frequency peak in the spectrum of the lateral component at low level; (ii) a corresponding increase in the vertical component at mid-CBL; (iii) a positive covariance {ovvw} together with positive wind shear in the lateral direction (V/z) in the CBL. By applying these indicators, it is possible to show that horizontal roll circulations are likely to be a common phenomenon over the Baltic during late summer and early winter.     

A numerical study of the Chicago lake breeze

A two-dimensional numerical model is presented for the study of the Chicago area lake breeze. The hydrostatic approximation used by previous workers in this field is not employed. Instead, the complete z-momentum equation is solved and the equation of continuity is retained in its original form. The numerical model employs a staggered mesh, and Alternating Direction Implicit methods are used for the integration of the equations. Computational stability is achieved without external filters, upstream space differencing, or artificial horizontal diffusion terms.The results obtained for realistic initial conditions but simplified boundary conditions compare reasonably well with observations obtained by Lyons in his 1967 observational study of the Chicago lake breeze. Limiting forms of the lower boundary condition bracket the observed wind speeds and other kinematic features of the breeze. Among the various eddy diffusivity models, that with constant eddy diffusivity with height produces the most realistic results. The models with a decrease of eddy diffusivity with height show unrealistic flow patterns in the upper layers. The stability of the atmosphere at the onset of the breeze is shown to have a pronounced effect on the intensity of the circulation, but not on the thickness of the inflow layer, which appears quite insensitive to large changes in the parameters involved.     

Carbon dioxide and the δ18O record of late-Quaternary climatic change: a global model

A dynamical model for the late-Quaternary global variations of ¹⁸O, mean ocean surface tempeature , ice mass I, deep ocean temperature , and atmospheric carbon dioxide concentration , is constructed. This model consists of two diagnostic equations (for ¹⁸O and ), and three prognostic equations (for I, , and ) of a form studied extensively in previous articles. The carbon dioxide equation includes forcing by a representation of the Milankovitch earth-orbital radiation effects, and contains a basic instability that drives a free oscillation of period near 100,000 years. The system is constrained to conserve mass and energy, contain physically plausible feedbacks including a system time constant no greater than 10.000 years, and be robust (i. e., structurally stable in the presence of expected noise levels and uncertainties in values of coefficients). Within the limits of these constraints, coefficients are chosen such that (i) the solution gives a good fit to the observed SPECMAP ¹⁸O variations, and (ii) the ice mass variations are qualitatively similar to the ¹⁸O variations. The predicted long term variations of sea surface temperature and atmospheric carbon dioxide are in reasonably good agreement with the limited observational evidence available for these quantities, while the predicted variations of deep ocean temperature remain to be verified when paleoclimatic estimates of this quantity become available. The relative contributions of ice mass changes and surface water temperature changes to the variations of ¹⁸O at any time are given by the model.     

On the representation of frequency spectra in meteorology

The common representation of frequency spectra in meteorology and climatology is discussed. It is pointed out that this representation is misleading since spectral peaks and spectral gaps are obtained even when the spectrum density is monotonously decreasing in the whole frequency range. A plea is made for using the spectrum distribution function, F() which gives an unambiguous picture of the distribution of variance with frequency.     

A study of the sensitivity of bare soil evaporation schemes to soil surface wetness,using the coupled soil moisture and surface temperature prediction model,BARESOIL

Summary The performance of evaporation schemes with and approach and their combination within resistance representation of evaporation from bare soil surface is discussed. For this purpose nine schemes, based on different functions of or , on the ratio of the volumetric soil moisture content and its saturated value are used.The quality of the chosen schemes has been evaluated using the results of time integration by the coupled soil moisture and surface temperature prediction model, BARESOIL, using in situ data. A sensitivity analysis was made using two sets of data derived from the volumetric soil moisture content of the top soil layer. One with values below the wilting point (0.17 m³m^–3) and the second with values above 0.20m³m^–3. Data sets were obtained at the experimental site Rimski anevi, Yugoslavia, from the bare surface of a chernozem soil.With 4 Figures     

SODAR-based estimation of TKE and momentum flux profiles in the atmospheric boundary layer: Test of a parameterization model

Summary A simple parameterization for the estimation of turbulent kinetic energy (TKE) and momentum flux profiles under near-neutral stratification based on sodar measurements of the vertical velocity variance has been tested using data from the LINEX-2000 experiment. Measurements included operation of a phased-array Doppler sodar DSDPA.90 and of a sonic anemometer USA-1 mounted at a meteorological tower at a height of 90m. Good agreement has been found between the TKE and momentum flux values derived from the sonic and sodar data (with correlation coefficients r>0.90 and a slope of the regression lines of about 1.01.1) suggesting the possible use of sodar measurements of _w ² to derive turbulence parameter profiles above the tower range.     

Stable boundary layers: Observations,models and variability part I: Modelling and measurements

Selected field measurements of evening stable boundary layers are presented in detail comparable with published Large Eddy Simulation results. Such models appear to match idealized theories more closely than do some boundary-layer observations. Any attempt to compare detailed observations with idealized models therefore highlights the variability of the real boundary layer.Here direct turbulence measurements across the stable boundary layer from a heterogeneous and an ideal site are contrasted. Recommendations are made for the information needed to distinguish heterogeneous and ideal cases.The companion paper (Part II) discusses further the issues of data, analysis in the presence of variability, and the effects of averaging over heterogeneous terrain.Part of UK Meteorological Office Atmospheric Process Research Division.