An application of the E-ε turbulence model for studying coupled air-sea boundary-layer structure

An E- turbulence model is used to study air-sea interaction characteristics and turbulence structure using a coupled model for air-sea boundary layers. The E- turbulence model consists of equations for the turbulent kinetic energy, the energy-dissipation, and for the turbulent exchange coefficient expressed in terms of turbulent kinetic energy and energy-dissipation. The energy-dissipation equations for the air-sea interface are solved analytically to obtain boundary conditions for energy-dissipation at the interface. The air-sea interaction and turbulence characteristics of the E- model are compared with those of the mixing-length model and with available observations.The simulations demonstrate that the air-sea interaction parameters obtained by the E- model agree well with observations. The numerical studies also show that the E- turbulence model with appropriate constants can give good results in modeling coupled air-sea boundary-layer flows.     

Reactions of alkoxy radicals under atmospheric conditions: The relative importance of decomposition versus reaction with O2

The reactions of alkoxy radicals determine to a large extent the products formed during the atmospheric degradations of emitted organic compounds. Experimental data concerning the decompositions, 1,5-H shift isomerizations and reactions with O₂ of several classes of alkoxy radicals are inconsistent with literature estimations of their absolute or relative rate constants. An alternative, although empirical, method for assessing the relative importance under atmospheric conditions of the reactions of alkoxy radicals with O₂ versus decomposition was derived. This estimation method utilizes the differences in the heats of reaction, (H)=(H_{decomposition}–H_{O 2 reaction}), between these two reactions pathways. For (H)[22–0.5(H_{O 2 reaction})], alkoxy radical decomposition dominates over the reaction with O₂ at room temperature and atmospheric pressure of air, while for (H)[25-0.5(H_{O 2 reaction})], the O₂ reaction dominates over decomposition (where the units of H are in kcal mol^–1). The utility and shortcomings of this approach are discussed. It is concluded that further studies concerning the reactions of alkoxy radicals are needed.     

Triggering of atmospheric circulations by moisture inhomogeneities of the earth's surface

A two-dimensional mesoscale soil-atmosphere model is used to simulate the triggering of atmospheric convection by horizontally varying soil water content. The variation is periodic with a wavelength between 4 and 40 km, which is considered a realistic scale for the variation of land surface characteristics. Three stages of convection can be clearly discerned: a short initial stage when convection sets in and where the size of the conective cells is determined by , a mature stage with well developed cells whose size is still determined by , and a decay/transformation stage, characterized by the formation of narrow regions of strong updrafts and wide regions of moderate downdrafts, independent of . Parameters relevant for the transition are given, and the importance of the feedback between soil and atmosphere is demonstrated. The dependence of convective parameters, e.g., height of the convective layer, vertical velocity and fluxes of heat and moisture on is investigated. The calculations of the mature stage are compared with the predictions of a linear model.     

The effect of synoptic-scale advection on the performance of the Priestley-Taylor evaporation formula

Measurements of the appropriate parameters for the calculation of the latent heat flux over a black spruce forest in northern Quebec were carried out in August, 1980. Values of the Priestley-Taylor parameter, , were derived by exploiting the Bowen-ratio-energy-balance (BREB) technique. Derived values of are then related to synoptic-scale warm air advection, derived from surface synoptic charts and tephigrams of the planetary boundary layer. It is found that when warm air advection is present, > 1.26, especially when the surface is wet. When advection enhancement is removed, however, values of approach unity. A new approach to calculating the latent heat flux, when warm air advection is present, is therefore proposed.     

Stability Analysis of the Climate-Vegetation System in the Northern High Latitudes

The stability of the climate-vegetation system in the northern high latitudesis analysed with three climate system models of different complexity: A comprehensive 3-dimensional model of the climate system, GENESIS-IBIS, and two Earth system models of intermediate complexity (EMICs), CLIMBER-2 andMoBidiC. The biogeophysical feedback in the latitudinal belt 60–70° N, although positive, is not strong enough to support multiple steady states: A unique equilibriumin the climate-vegetation system is simulated by all the models on a zonal scale for present-day climate and doubled CO₂ climate.EMIC simulations with decreased insolation also reveal a unique steady state. However, the climate sensitivity to tree cover, T_F, exhibits non-linear behaviour within the models. For GENESIS-IBIS and CLIMBER-2, T_F islower for doubled CO₂ climate than for present-day climate due to a shorter snow season and increased relative significance ofthe hydrological effect of forest cover. For the EMICs, T_F is higher for low tree fraction than for high treefraction, mainly due to a time shift in spring snow melt in response to changes in tree cover. The climate sensitivity to tree coveris reduced when thermohaline circulation feedbacks are accounted for in the EMIC simulations. Simpler parameterizations of oceanic processes have opposite effects on T_F: T_F is lower in simulations with fixed SSTs and higher in simulations with mixed layer oceans. Experiments with transient CO₂ forcing show climate and vegetation not in equilibrium in the northern high latitudes at the end of the 20thcentury. The delayed response of vegetation and accelerated global warming lead to rather abrupt changes in northern vegetation cover in the first halfof the 21st century, when vegetation cover changes at double the present day rate.     

An observational study of heat fluxes and their relationships with net radiation

Experimental evidence indicates that the diurnal behaviour of the fluxes of heat into the ground and into the atmosphere versus the net flux of radiation can be modelled by closed curves, the hourly values folowing one another in either a clockwise or counter clockfashion. A general formulation to express the different heat fluxes as a function of net radiation is proposed. This relationship between the different heat fluxes and can be expressed as a sum of three terms: the first indicates a direct proportionality to , the second gives the deviation from linearity and depends on /t, and the third gives the value of the flux when = 0. The formulae are then expressed as a function of time and the ratios between the heat fluxes and are evaluated. A comparison with the approximations generally used shows that the latter may be considered as particular cases of the more general equations proposed here.     

Numerical modeling of the nocturnal urban boundary layer

A numerical case study with a second-order turbulence closure model is proposed to study the role of urban canopy layer (UCL) for the formation of the nocturnal urban boundary layer (UBL). The turbulent diffusion coefficient was determined from an algebraic stress model. The concept of urban building surface area density is proposed to represent the UCL. Calculated results were also compared with field observation data. The height of the elevated inversion above an urban center was simulated and found to be approximately twice the average building height. The turbulent kinetic energy k, energy dissipation rate , and turbulence intensities u ² and w ² increase rapidly at the upwind edge of the urban area. The Reynolds stress uw displayed a nearly uniform profile inside the UBL, and the vertical sensible heat flux w had a negative value at the inversion base height. This indicates that the downward transport of sensible heat from the inversion base may play an important role in the formation of the nocturnal UBL.     

Some observations of turbulence and turbulent transport within and above plant canopies

Observations have been made of the structure of turbulence and turbulent exchange within plant canopy layers. A new three-dimensional anemometer was used to measure the eddy fluxes of heat and momentum, and the related cospectra, within and above a corn crop and above a red pine forest. Measured values of momentum and heat fluxes, at each height within the corn canopy, were relatively constant proportions of the flux above the canopy, for the period of a day's observation. Extensive regions obeying a –5/3 power relation were found. Isotropy was found above the forest at high frequencies while above and within the corn crop, the ratios of the lateral and vertical spectral densities to the longitudinal component were less than the expected value in the – 5/3 region. In all situations, the vertical velocity spectra were more peaked than a universal curve, particularly a vertical velocity spectrum from above the forest. It is suggested that the additional variance results from the mixing caused by the individual roughness elements. As expected, the spectra could not be normalized using the height above the soil surface to calculate a non-dimensional frequency, but scaling heights were estimated by matching the frequencies of the peak of each curve with that of the universal curve. Cospectra of uw and wT within the corn canopy were of similar shape and frequency regime, and were basically similar in shape to cospectra above the crop. All of the cospectra were more sharply peaked than universal cospectral curves.     

On the inner-layer scale height of boundary-layer flow over low hills

Jackson and Hunt's (1975) equation for the depth of the inner layer of flows over low hills does not depend on any closure assumption as contrarily supposed in literature. This equation contains a constant which can arbitrarily be specified. It is suggested that this inner-layer constant should be determined from experimental data. A preliminary check with some data from the Askervein experiment suggests that Jackson and Hunt's equation fits these data almost as well as Jensen's equation provided that fitted inner-layer constants are used.     

Application of a “Big-Tree” model to regional climate modeling: a sensitivity study

Summary ¶In order to better understand land-atmosphere interactions and increase the predictability of climate models, it is important to investigate the role of forest representation in climate modeling. Corresponding to the big-leaf model commonly employed in land surface schemes to represent the effects of a forest, a so called big-tree model, which uses multi-layer vegetation to represent the vertical canopy heterogeneity, was introduced and incorporated into the National Center for Atmospheric Research (NCAR) regional climate model RegCM2, to make the vegetation model more physically based. Using this augmented RegCM2 and station data for China during 1991 Meiyu season, we performed 10 experiments to investigate the effects of the application of the big-tree model on the summer monsoon climate.With the big-tree model incorporated into the regional climate model, some climate characteristics, e.g. the 3-month-mean surface temperature, circulation, and precipitation, are significantly and systematically changed over the model domain, and the change of the characteristics differs depending on the area. Due to the better representation of the shading effect in the big-tree model, the temperature of the lower layer atmosphere above the plant canopy is increased, which further influences the 850hPa temperature. In addition, there are significant decreases in the mean latent heat fluxes (within 20–30W/m²) in the three areas of the model domain.The application of the big-tree model influences not only the simulated climate of the forested area, but also that of the whole model domain, and its impact is greater on the lower atmosphere than on the upper atmosphere. The simulated rainfall and surface temperature deviate from the originally simulated result and are (or seem to be) closer to the observations, which implies that an appropriate representation of the big-tree model may improve the simulation of the summer monsoon climate.We also find that the simulated climate is sensitive to some big-tree parameter values and schemes, such as the shape, height, zero-plane displacement height and mixing-length scheme. The simulated local/grid differences may be very large although the simulated areal-average differences may be much lower. The area-average differences in the monthly-mean surface temperature and heat fluxes can amount to 0.5°C and 4W/m², respectively, which correspond to maximum local/grid differences of 3.0°C and 40W/m² respectively. It seems that the simulated climate is most sensitive to the parameter of the zero-plane displacement among the parameters studied.     

Effect of finite sampling on atmospheric spectra

The effect of a finite averaging time on variances is well known, but its effect on power spectra is less clearly understood. We present numerical solutions for the spectral distortion arising from sampling over a finite time interval T and show that the commonly used filter function (1 – sinc²f T), valid for variances, is a reasonable approximation for power spectra only when T 10 _m , where f is the cyclic frequency, and _m is the dominant time scale of the process. Our results exhibit an increasingly steeper low-frequency roll-off as T decreases relative to _m , indicating that the measured spectrum is subject to a greater suppression of the lower frequencies (f > 1/T) than predicted by (1 – sinc²f T). This suppression is, in a sense, compensated by an overestimation of spectral estimates in the frequency range f 1/T.     

A study of the seasonal migration of ITCZ and the quasi-periodic oscillations in a simple monsoon system using an energy balance model

Summary A zonally averaged global energy balance model with feedback mechanisms was constructed to simulate (i) the poleward limits of ITCZ over the continent and over the ocean and (ii) a simple monsoon system as a result of differential heating between the continent and the ocean. Three numerical experiments were performed with lower boundary as (1) global continent, (2) global ocean and (3) continent-ocean, with freezing latitudes near the poles. Over the continent, midlatitude deserts were found and the ITCZ migrates 25° north and south with seasons. Over a global swamp ocean results do not show migration of ITCZ with time but once the ocean currents are introduced the ITCZ migrates 5° north and south with seasons. It was found that the seasonal migration of ITCZ strongly depends on the meridional distribution of the surface temperature. It was also found that continent influences the location of the oceanic ITCZ. In the tropics northward progression of quasi-periodic oscillations called events are found during the pre- and post-monsoon periods with a period of 8 to 15 days. This result is consistent with the observed quasi-periodic oscillations in the tropical region. Northward propagation of the surface temperature perturbation appears to cause changes in the sensible heat flux which in turn causes perturbations in vertical velocity and latent heat flux fields.List of Symbols vertical average - ₀ zonal average - vertical mean of the zonal average - _0s zonal average at the surface - _0a zonal average at 500 mb level - latitude We now define the various symbols used in the model rate of atmospheric heating due to convective cloud formation (K/sec) - dp/dt (N/m²/sec) - density - potential temperature (K) - rate of rotation of the earth (rad/sec) - empirical constant - humidity mixing ratio - ^* saturated humidity mixing ratio - opacity of the atmosphere - ₁,₂ factors for downward and upward effective black body long wave radiation from the atmosphere - Stefan-Boltzmann constant - emissivity of the surface - _D subsurface temperature (K) - a specific volume - _0xs ,_0ys eastward and northward components of surface frictional stress - ^* vertical velocity at the top of the boundary layer (N/m²/sec) - P Thickness of the boundary layer (mb) - nondimensional function of pressure - P pressure - P _a pressure of the model atmosphere (N/m²) - P _s pressure at the surface (N/m²) - t time (sec) - U eastward wind speed (m/sec) - V northward wind speed (m/sec) - surface water availability - T absolute temperature (K) - heat addition due to water phase changes - g acceleration due to gravity (m²/sec) - a radius of the earth (m) - R gas constant for dry air (J/Kg/K) - C _p specific heat of air at constant pressure (J/Kg/K) - k R/C _p - L latent heat of condensation (J/Kg) - f coriolis parameter (rad/sec) - H _s H _0s ⁽¹⁾ +H _0s ⁽²⁾ +H _0s ⁽³⁾ +H _0s ⁽⁴⁾ +H _0s ⁽⁵⁾ (J/m²/Sec)=sum of the rates of vertical heat fluxes per unit surface area, directed toward the surface - H _a H _0a ⁽¹⁾ +H _0a ⁽²⁾ +H _0a ⁽³⁾ +H _0a ⁽⁴⁾ (J/m²/Sec)=sum of the rates of heat additions to the atmospheric column per unit horizontal area by all processes - H _0s ⁽¹⁾ ,H _0a ⁽¹⁾ heat flux due to short wave radiation - H _0s ⁽²⁾ ,H _0a ⁽²⁾ heat flux due to long wave radiation - H _0s ⁽³⁾ ,H _0a ⁽³⁾ heat flux due to small scale convection - H _0s ⁽⁴⁾ heat flux due to evaporation - H _0a ⁽⁴⁾ heat flux due to condensation - H _0s ⁽⁵⁾ heat flux due to subsurface conduction and convection - e ^* saturation vapor pressure - R solar constant (W/m²) - r _a albedo of the atmosphere - r _s albedo of the surface - b ₂ empirical constant (J/m²/sec) - c ₂ empirical constant (J/m²/sec) - e ₂ nondimensional empirical constant - f ₂ empirical constant (J/m₂/sec) - factor proportional to the conductive capacity of the surface medium - a _s constant used in Sellers model - b _s positive constant of proportionality used in the Sellers model (kg m²/J/sec²) - K _HT coefficient for eddy diffusivity of heat (m²/sec) - K _HE exchange coefficient for water vapor (m²/sec) - h depth of the water column (m) - z height (m) - V _0ws meridional component of surface current (m/sec) - n cloud amount - G _0,n long wave radiation form the atmosphere for cloud amount n (W/m²) - B ₀ long wave radiation from the surface (W/m²) - S _0,n short wave radiation from the atmosphere for cloud amount n (W/m²) - A _n albedo factor for a cloud amount n - R _f1 large scale rainfall (mm/day) - R _f2 small scale rainfall (mm/day) With 22 Figures     

Small-Scale Variability in the Coastal Atmospheric Boundary Layer

The influence of the main large-scale wind directions on thermally driven mesoscale circulations at the Baltic southwest coast, southeast of Sweden, is examined. The aim of the study is to highlight small-scale alterations in the coastal atmospheric boundary layer. A numerical three-dimensional mesoscale model is used in this study, which is focused on an overall behaviour of the coastal jets, drainage flows, sea breezes, and a low-level eddy-type flow in particular. It is shown that synoptic conditions, together with the moderate terrain of the southeast of Sweden (max. height h₀ 206 m), governs the coastal mesoscale dynamics triggered by the land-sea temperature difference T. The subtle nature of coastal low-level jets and sea breezes is revealed; their patterns are dictated by the interplay between synoptic airflow, coastline orientation, and T.The simulations show that coastal jets typically occur during nighttime and vary in height, intensity and position with respect to the coast; they interact with downslope flows and the background wind. For the assigned land surface temperature (varying ±8 K from the sea temperature) and the opposing constant geostrophic wind 8 m s^-1, the drainage flow is more robust to the opposing ambient flow than the sea breeze later on. Depending on the part of the coast under consideration, and the prevailing ambient wind, the sea breeze can be suppressed or enhanced, stationary at the coast or rapidly penetrating inland, locked up in phase with another dynamic system or almost independently self-evolving. A low-level eddy structure is analyzed. It is governed by tilting, divergence and horizontal advection terms. The horizontal extent of the coastal effects agrees roughly with the Rossby radius of deformation.     

Averaging Intervals For Spectral Analysis Of Nonstationary Turbulence

We formulate a method for determining the smallest time interval Tover which a turbulence time series can be averaged to decompose it intoinstantaneous mean and random components. From the random part the method defines the optimal interval (or averaging window) AW over which this part should be averaged to obtain the instantaneous spectrum. Both T and AW vary randomly with time and depend on physical properties of the turbulence. T also depends on the accuracy of the measurements and is thus independent of AW. Interesting features of the method are its real-time capability and the non-equality between AW and T.     

Diurnal variation of horizontal wind direction fluctuations in complex terrain at Geysers,Cal.

Horizontal diffusion in the surface layer is dependent on the standard deviation of wind direction fluctuations . Diurnal variation of this parameter in complex terrain was studied for the July 1979 Geysers, Cal., experiment using data from a network of 11 short meteorological towers in the 25 km² Anderson Creek watershed Valley side slopes are roughly 20 ° and maximum terrain difference is about 1 km.Values of for wind directions sampled for one hour at a height of 10 m are about 35 ° during the daytime. They slowly decrease to about 20 ° by 8 to 10 p.m. as stability increases but wind speeds are still relatively high. After 10 p.m. the drainage flow sets in at most stations, with speeds of 1 to 2 m s^-1, and average increases to about 30° during the period 11 p.m. to 6 a.m. In general, highest values of at night are associated with lowest values of wind speed and greatest static stability. This enhancement of by the terrain suggests that horizontal diffusion at night always conforms to that expected during nearly neutral stabilities. That is, Pasquill class D diffusion applies to the horizontal component all night in complex terrain.     

A simple model of neutrally stratified boundary-layer flow over real terrain incorporating wavenumber-dependent scaling

Our experience in applying earlier versions of a model of boundary-layer flow over low hills to real terrain (see Walmsley et al., 1982) has led to the development of a new version which we designate MS3DJH/3. The main improvements are the use of terrain-dependent length and velocity scales and the blending of inner and outer layer results into a single universally valid solution for the velocity perturbation field. MS3DJH/3 was carefully calibrated against alternative computations of flow over idealized two-dimensional terrain features using more detailed models prior to its application to real, three-dimensional terrain. It still provides high spatial resolution with low computing cost and is applicable to flow over terrain features with horizontal scales from 10 m to 10 km.Contractor: 24 Heslop Drive, Toronto.     

Spectral distribution of solar radiation in Athens

Summary A 25-year (1966–1990) record of measurements of the broadband direct solar irradiances performed in Athens, has been utilized to determine the radiant energy distribution in several spectral bands. Using these data the year-to-year trend of the time sequences of the mean values of the irradiation ratios in the various spectral intervals, viz. blue, green/orange, red, and photosynthetically active radiation (PAR) and the total direct irradiance for the whole spectrum, are evaluated.From this trend the following can be concluded: the blue spectral band (0.380–0.525 m) decreased from the beginning of the examined period until the mid-seventies and then increased gradually; the red band (0.630–0.710 m) shows similar trend but opposite in sense. The PAR band (0.380–0.710 m) decreased slightly until 1985 and then increases. In the green/orange band (0.525–0.630 m) the trend can be considered as nearly constant throughout the examined period. This trend of the irradiation ratios is related to the aerosol and gaseous pollutant content of the atmosphere, which probably reflects the urbanization, industrialization and heavy traffic conditions of the Athens area, during the last three decades.With 2 Figures     

Hailstorms in Northern Greece: synoptic patterns and thermodynamic environment

Summary ¶Two cyclonic vortices close to each other, a binary cyclone or binary system, tend to rotate cyclonically relative to one another and to merge, i.e. the Fujiwhara effect. The point vortex model that represents barotropic binary cyclones predicts their rotation features as follows. The rotation rate is proportional linearly to the sum of the cyclones intensities and inversely to the square of their separation distance while the more intense cyclone rotates slower. Our earlier observational analysis of 1423 mid-latitude binary cyclones (Ziv and Alpert, 1995) showed a reasonable fit to theory, except for the absence of a correlation between individual speeds and intensities within the binary systems, and a reversal of the inverse rotation-separation relationship at the range of 1400–1800km.This study is the first attempt to describe the mid-latitude binary systems using potential vorticity concepts (PV thinking), which implies that a binary interaction takes place between the 3-D flow patterns induced by upper-PV or surface-thermal anomalies rather than by the surface cyclones alone. It is argued that the upper-anomalies dominate the rotation process, and hence the rotational speeds of the interacting surface cyclones are more closely correlated with the relative intensities of their corresponding upper-level anomalies rather than with their own intensities, as reflected in weather charts. Data analysis indicates that mid-latitude binary cyclones are normally associated with at least one upper-PV anomaly. This explains the absence of a correlation between the rotation speed and the intensity of the surface cyclones there.A unique type of a mid-latitude binary system is identified, in which one cyclone coincides with an upper major PV-anomaly and the other moves along the periphery of the former. Such a binary system is entitled here the Contact Binary System (CBS), in contrast with remote interacting systems implied by the point vortex theory.Analytical considerations yield an increase in the rotation rate with separation for CBSs of separation smaller than 1000–1500km, in contrast to the normal decrease with R ². The contribution of CBSs is suggested here to explain the abnormal increase in rotation rate at 1400–1900km range.     

Analytical solutions for the Ekman layer

The PBL equation that governs the transition from the constant-stress surface layer to the geostrophic wind in a neutrally stratified atmosphere for which the eddy viscosityK(z) is assumed to vary smoothly from the surface-layer value U _*z (0.4,U _*=friction velocity,z=elevation) to the geostrophic asymptoteK _GU _*d forzd is solved through an expansion in fd/U _*1 (f=Coriolis parameter). The resulting solution is separated into Ekman's constant-K solution an inner component that reduces to the classical logarithmic form forzd and isO() relative to the Ekman component forzd. The approximationKU _*d is supported by the solution of Nee and Kovasznay's phenomenological transport equation forK(z), which yieldsK–U _*d exp(–z/d), where is an empirical constant for which observation implies, 1. The parametersA andB in Kazanskii and Monin's similarity relation forG/U _* (G=geostrophic velocity) are determined as functions of . The predicted values ofG/U _* and the turning angle are in agreement with the observed values for the Leipzig wind profile. The predicted value ofB based on the assumption of asymptotically constantK is 4.5, while that based on the Nee-Kovasznay model is 5.1; these compare with the observed value of 4.7 for the Leipzig profile. A thermal wind correction, an asymptotic solution for arbitraryK(z) and 1, and an exact (unrestricted ) solution forK(z)=U _*d[1–exp(–z/d)] are developed in appendices.     

Turbulence Reynolds number and the turbulent kinetic energy balance in the atmospheric surface layer

The relation between the turbulence Reynolds numberR and a Reynolds numberz* based on the friction velocity and height from the ground is established using direct measurements of the r.m.s. longitudinal velocity and turbulent energy dissipation in the atmospheric surface layer. Measurements of the relative magnitude of components of the turbulent kinetic energy budget in the stability range 0 >z/L 0.4 indicate that local balance between production and dissipation is maintained. Approximate expressions, in terms of readily measured micrometeorological quantities, are proposed for the Taylor microscale and the Kolmogorov length scale .