Mixed-layer heat advection and entrainment during the sea breeze

A model is developed to simulate the potential temperature and the height of the mixed layer under advection conditions. It includes analytic expressions for the effects of mixed-layer conditions upwind of the interface between two different surfaces on the development of the mixed layer downwind from the interface. Model performance is evaluated against tethersonde data obtained on two summer days during sea breeze flow in Vancouver, Canada. It is found that the mixed-layer height and temperature over the ocean has a small but noticeable effect on the development of the mixed layer observed 10 km inland from the coast. For these two clear days, the subsidence velocity at the inversion base capping the mixed layer is estimated to be about 30 mm s^–1 from late morning to late afternoon. When the effects of subsidence are included in the model, the mixed-layer height is considerably underpredicted, while the prediction for the mean potential temperature in the mixed layer is considerably improved. Good predictions for both height and temperature can be obtained when values for the heat entrainment ratio,c, 0.44 and 0.68 for these two days respectively for the period from 1000 to 1300 LAT, were used. These values are estimated using an equation including the additional effects on heat entrainment due to the mechanical mixing caused by wind shear at the top of the mixed layer and surface friction. The contribution of wind shear to entrainment was equal to, or greater than, that from buoyant convection resulting from the surface heat flux. Strong wind shear occurred near the top of the mixed layer between the lower level inland flow and the return flow aloft in the sea breeze circulation.Symbols c entrainment parameter for sensible heat - c _p specific heat of air at constant pressure, 1010 J kg^–1 K^–1 - d ₁ the thickness of velocity shear at the mixed-layer top, m - Q _H surface sensible heat flux, W m^–2 - u _m mean mixed-layer wind speed, m s^–1 - u _* friction velocity at the surface, m s^–1 - w subsidence velocity, m s^–1 - W subsidence warming,^oC s^–1 - w _e entrainment velocity, m s^–1 - w _* convection velocity in the mixed layer, m s^–1 - x downwind horizontal distance from the water-land interface, m - y dummy variable forx, m - Z height above the surface, m - Z _i height of capping inversion, m - Z _m mixed-layer depth, i.e.,Z _i–Z_s, m - Z _s height of the surface layer, m - lapse rate of potential temperature aboveZ _i, K m^–1 - potential temperature step atZ _i, K - u _h velocity step change at the mixed-layer top - _m mean mixed-layer potential temperature, K     

Lidar measurements of the atmospheric entrainment zone and the potential temperature jump across the top of the mixed layer

Lidar measurements of the thickness of the atmospheric entrainment zone are presented. The measurements were obtained in central Illinois during 6 days of clear-air convection.A new method was developed to monitor the potential temperature jump across the entrainment zone. A single early morning temperature sounding and continuous lidar measurements of the mixed-layer height provide potential temperature jump values which agree well with in situ observations.Lidar measurements of the thickness of the entrainment zone normalized by mixed-layer depth are presented as a function of a convective Richardson number; these values show reasonable agreement with published laboratory results. The lidar observations span a wider range of mixed-layer depths and contain higher values of the normalized entrainment rate (dh/dt)/w _* than those observed in tank studies. Both lidar and tank results show that simple parcel theory does not properly predict entrainment-zone thickness. During this experiment which examined mostly high entrainment conditions, the normalized entrainment-layer thickness was linearly dependent on entrainment rate.     

Nearly steady convection and the boundary-layer budgets of water vapor and sensible heat

The budgets of water vapor and sensible heat in the convective atmospheric boundary (mixed) layer are analyzed by means of a simple slab approach adapted to steady large-scale advective conditions with radiation and cloud activity. The entrainment flux for sensible heat is assumed to be a linear function of the surface flux. The flux of water vapor at the top of the mixed layer is parameterized by extending the first-order Betts-Deardorff approach, i.e., by adopting linear changes for both the specific humidity and the flux across the mixed layer and across the inversion layer of finite thickness. In this way the dissimilarity of sensible heat and water vapor transport in the mixed layer can be taken into account. The experimental data were obtained from the Air Mass Transformation Experiment (AMTEX). The entrainment constant for sensible heat at the top of the mixed layer was found to have values similar to those observed in other weakly convective situations, i.e., around 0.4 to 0.6. This appears to indicate that the effect of mechanical turbulence was not negligible; however, the inclusion of this effect in the formulation did not improve the correlation. In contrast to the first-order approach, the zero-order approach, i. e., the jump equation commonly used for the flux of a scalar at the inversion, (ovwc ) _h = w_e c (where w _e is the entrainment velocity and c the concentration jump across the inversion), was found to be invalid and incapable of describing the data.     

Mixed-layer characteristics as related to the monsoon climate of New Delhi,India

Annual variations of mixed-layer characteristics at New Delhi, India have been studied for a weak monsoon (1987) and a strong monsoon (1988) year. In the weak monsoon year (1987), the maximum mixing depthh _max was found to have a value of around 3000 m during the pre-monsoon, less than 2000 m during the summer monsoon, around 2000 m during the post-monsoon, and less than 1000 m in the winter season. For the strong monsoon year (1988),h _max values were less than 1987 values for comparable periods throughout the year. The seasonal and yearly differences ofh _max were explained by the surface energy balance and potential temperature gradient at a time close to sunrise. According to the spatial patterns of obtained by an objective analysis of the 850 to 700 hPa layers. mixed-layer characteristics obtained at New Delhi are representative of the north and central regions of India.     

Impacts of Aerosol Shortwave Radiation Absorption on the Dynamics of an Idealized Convective Atmospheric Boundary Layer

We investigated the impact of aerosol heat absorption on convective atmospheric boundary-layer (CBL) dynamics. Numerical experiments using a large-eddy simulation model enabled us to study the changes in the structure of a dry and shearless CBL in depth-equilibrium for different vertical profiles of aerosol heating rates. Our results indicated that aerosol heat absorption decreased the depth of the CBL due to a combination of factors: (i) surface shadowing, reducing the sensible heat flux at the surface and, (ii) the development of a deeper inversion layer, stabilizing the upper CBL depending on the vertical aerosol distribution. Steady-state analytical solutions for CBL depth and potential temperature jump, derived using zero-order mixed-layer theory, agreed well with the large-eddy simulations. An analysis of the entrainment zone heat budget showed that, although the entrainment flux was controlled by the reduction in surface flux, the entrainment zone became deeper and less stably stratified. Therefore, the vertical profile of the aerosol heating rate promoted changes in both the structure and evolution of the CBL. More specifically, when absorbing aerosols were present only at the top of the CBL, we found that stratification at lower levels was the mechanism responsible for a reduction in the vertical velocity and a steeper decay of the turbulent kinetic energy throughout the CBL. The increase in the depth of the inversion layer also modified the potential temperature variance. When aerosols were present we observed that the potential temperature variance became significant already around $0.7z_i$ (where $z_i$ is the CBL height) but less intense at the entrainment zone due to the smoother potential temperature vertical gradient.     

Time Scales in the Unstable Atmospheric Surface Layer

Calculation of eddy covariances in the atmospheric surface layer (ASL) requires separating the instantaneous signal into mean and fluctuating components. Since the ASL is not statistically stationary, an inherent ambiguity exists in defining the mean quantities. The present study compares four methods of calculating physically relevant time scales in the unstable ASL that may be used to remove the unsteady mean components of instantaneous time signals, in order to yield local turbulent fluxes that appear to be statistically stationary. The four mean-removal time scales are: (t _c ) based on the location of the maximum in the ogive of the heat flux cospectra, () the location of the zero crossing in the multiresolution decomposition of the heat flux, (t ^*) the ratio of the mixed-layer depth over the convective velocity, and () the convergence time of the vertical velocity and temperature variances. The four time scales are evaluated using high quality, three-dimensional sonic anemometry data acquired at the Surface Layer Turbulence and Environmental Science Test (SLTEST) facility located on the salt flats of Utah’s western desert. Results indicate that and , with t _c achieving values about 2–3 times greater than t ^*. The sensitivity of the eddy covariances to the mean-removal time scale (given a fixed 4-h averaging period during midday) is also demonstrated.     

Experiments on scalar dispersion within a model plant canopy part II: An elevated plane source

This paper describes a wind-tunnel experiment on the dispersion of trace heat from an effectively planar source within a model plant canopy, the source height being h _s = 0.80 h _c , where h _c is the canopy height. A sensor assembly consisting of three coplanar hot wires and one cold wire was used to make simultaneous measurements of the temperature and the streamwise and vertical velocity components. It was found that:

1. The thermal layer consisted of two parts with different length scales, an inner sublayer (scaling with h _s and h _c ) which quickly reached streamwise equilibrium downstream of the leading edge of the source, and an outer sublayer which was self-preserving with a length scale proportional to the depth of the thermal layer.
2. Below 2h _c , the vertical eddy diffusivity for heat from the plane source (K _HP ) was substantially less than the far-field limit of the corresponding diffusivity for heat from a lateral line source at the same height as the plane source. This shows that dispersion from plane or other distributed sources in canopies is influenced, near the canopy, by turbulence ‘memory’ and must be considered as a superposition of both near-field and far-field processes. Hence, one-dimensional models for scalar transport from distributed sources in canopies are wrong in principle, irrespective of the order of closure.
3. In the budgets for temperature variance, and for the vertical and streamwise components of the turbulent heat flux, turbulent transport was a major loss between h _s and h _c and a principal gain mechanism below h _s , as also observed in the budgets for turbulent energy and shear stress.
4. Quadrant analysis of the vertical heat flux showed that sweeps and ejections contributed about equal amounts to the heat flux between h _s and h _c , though among the more intense events, sweeps were dominant. Below h _s , almost all the heat was transported by sweeps.

     

Flux-gradient profiles for momentum and heat over an urban surface

Summary In this paper, we evaluate the applicability of flux-gradient relationships for momentum and heat for urban boundary layers within the Monin-Obukhov similarity (MOS) theory framework. Although the theory is widely used for smooth wall boundary layers, it is not known how well the theory works for urban layers. To address this problem, we measured the vertical profiles of wind velocity, air temperature, and fluxes of heat and momentum over a residential area and compared the results to theory. The measurements were done above an urban canopy whose mean height z_h is 7.3 m. 3-D sonic anemometers and fine wire thermocouples were installed at 4 heights in the region 1.5z_h < z < 4z_h. We found the following: (1) The non-dimensional horizontal wind speed has good agreement with the stratified logarithmic profile predicted using the semi-empirical Monin-Obukov similarity (MOS) function, when it was scaled by the surface friction velocity that is derived from the shear stress extrapolated to the roof-top level. (2) The scaled gradient of horizontal wind speed followed a conventional semi-empirical function for a flat surface at a level (z/z_h = 2.9), whereas, in the vicinity of the canopy height was larger than the commonly-used empirical relationship. (3) The potential temperature profile above the canopy shows dependency on the atmospheric stability and the scaled gradient of temperature is in good agreement with a conventional shear function for heat. In the case of heat, the dependency on height was not found. (4) The flux-gradient relationship for momentum and heat in the region 1.5z_h < z < 4z_h was rather similar to that for flat surfaces than that for vegetated canopies.     

The role of molecular diffusion in the deepening of the mixed layer

Turbulent mixing across heat-stratified density interfaces was studied in the laboratory using oscillating-grid generated turbulence. The aim was to study the transition between the entrainment regimes dominated by interfacial wave-breaking and molecular diffusion, and to study the characteristics of the latter. It was observed that, above a critical Richardson number Ri_c, which depends on the Peclet number Pe, the mixing due to wave breaking disappears and that Ri_c Pe⁻ⁿ, where the mean value of the exponent n is approximately . Above Ri_c, the entrainment is molecular-diffusion dominated and takes place through a sequence of events: the buoyancy gradient of the initially sharp density interface is weakened by molecular diffusion until the mixed-layer eddies can engulf a portion of the interfacial layer wherefore the interface sharpens again. Thus, the entrainment events are recurrent with a rate-controlling diffusion stage between them. An entrainment law of the form E Ri⁻²Pe⁻², where E is the entrainment coefficient and Ri is the Richardson number, is suggested for the diffusion-dominated entrainment regime.     

An applied model for the height of the daytime mixed layer and the entrainment zone

A model is presented for the height of the mixed layer and the depth of the entrainment zone under near-neutral and unstable atmospheric conditions. It is based on the zero-order mixed-layer height model of Batchvarova and Gryning (1991) and the parameterization of the entrainment zone depth proposed by Gryning and Batchvarova (1994). However, most zero-order slab type models of mixed-layer height may be applied. The use of the model requires only information on those meteorological parameters that are needed in operational applications of ordinary zero-order slab type models of mixed-layer height: friction velocity, kinematic heat flux near the ground and potential temperature gradient in the free atmosphere above the entrainment zone. When information is available on the horizontal divergence of the large-scale flow field, the model also takes into account the effect of subsidence, although this is usually neglected in operational models of mixed-layer height owing to lack of data. Model performance is tested using data from the CIRCE experiment.     

Experimental investigations into variations of ground-based inversions and comparisons with results of simple boundary-layer models

Meteorological data obtained from sensors mounted on a 300-m antenna mast, including wind components and temperature fluctuations together with high resolution profile measurements, were used to calculate quantities which describe the most important processes during the development and decay of ground-based inversions. The vertical distribution of air temperature during the developing phase of radiation inversions has been measured continuously and compared with an existing simple prognostic model. Free and forced convection conditions have been investigated for the inversion lifting phase by measuring the heat fluxes at the surface (H _s) and at the inversion base (H _i), the heating rate of the mixed layer (/z) _m , the friction velocity (u _*) and the entrainment rate (dh/dt). Comparisons between the directly measured entrainment rates and those calculated by models show good agreement. For nearly free convection conditions, the entrainment parameter (k = -H _i/H_s) has been determined to be about 0.25.     

北京地区大气混合层的探测与预测模式的检验

本文使用1986年7月和12月北京地区低空探空和湍流感热通量的实测资料,并对照室内水槽模拟实验的结果,对于大气混合层的零阶和一阶预测模式进行了检验。文中着重探讨了混合层顶卷夹层的卷夹系数与混合层发展之间的关系。     

A mixed-layer model for regional evaporation

A simple mixed-layer model is developed to describe evaporation into a convective planetary boundary layer (PBL). The model comprises volume budget equations for temperature and humidity, equations to describe transport through the surface layer which is treated as part of the lower boundary, and equations to describe entrainment at the top of the PBL. The ground surface is modelled as a canopy resistance. The model was integrated with canopy resistance, surface-layer resistance and available energy, (R _n – G), input as given functions of time, and the simulated PBL was allowed to grow into an atmosphere with known temperature and humidity profiles.Two variants of the mixed-layer model were tested using data from the KNMI tower site at Cabauw in the Netherlands. These variants differed only in the formulation of entrainment: one used a formulation developed by Driedonks (1982) while the other was a simpler formulation. Simulated evaporation agreed very well with observations irrespective of which entrainment formulation was used, despite discrepancies between simulated and observed PBL height growth which were sometimes quite large for the simpler formulation. Sensitivity analysis of the model confirms that good PBL height-growth predictions are not always a prerequisite for good evaporation predictions.     

Fluctuations of the horizontal wind under unstable conditions

The similarity relations for _u/u_* proposed by Panofskyet al. (1977) and Højstrup (1982) have been verified using eddy-correlation data collected during the EFEDA-experiment, conducted over the extensive plain of La Mancha (Spain), where vine plants form a primary crop. Also, the standard Monin-Obukhov relation is considered. It is found that the expressions by Panofskyet al. and Højstrup both yield almost identical results, and are better than the Monin-Obukhov expression. Also, _u measured with a cup anemometer obeys the similarity expressions well, provided that the effect of the variation of wind direction on propellor wind speed is accounted for. The relationship of Panofskyet al. works rather well even when the boundary-layer height scaleh is replaced by a fixed height,h _c. Best results were obtained forh _c=1800 m. This height scale is possibly associated with the horizontal variability in the surface sensible heat flux pattern.     

On the role of roughness lengths in flux parameterizations of boundary-layer models

Flux-profile relationships based on surface-layer similarity theory are used to derive relationships between the Monin-Obukhov stability parameter = z/L and the bulk Richardson number Ri _b . In contrast to previous studies, the roughness length for heat, z _0h ,is assumed unequal to the roughness length for momentum, z _0m .For the stable case, an analytic expression of in terms of Ri _b can be derived and in the unstable case, the solution is obtained through a simple iterative process.Errors introduced from the simplification of z _0h = z _0m are evaluated and are shown to be very significant in most cases. Thus, this error in many practical applications may invalidate the intended solution.     

Modelling evaporation from wetland tundra

Evapotranspiration is a major component of both the energy and water balances of wetland tundra environments during the thaw season. Reliable estimates of evapotranspiration are required in the analysis of climatological and hydrological processes occurring within a wetland and in interfacing the surface climate with atmospheric processes. Where direct measurements are unavailable, models designed to accurately predict evapotranspiration for a particular wetland are used.This paper evaluates the performance, sensitivity and limitations of three physically-based, one-dimensional models in the simulation of evaporation from a wetland sedge tundra in the Hudson Bay Lowland near Churchill, Manitoba. The surface of the study site consists of near-saturated peat soil with a sparse sedge canopy and a constantly varying coverage of standing water. Measured evaporation used the Bowen ratio energy balance approach, to which the model results were compared. The comparisons were conducted with hourly and daily simulations.The three models are the Penman-Monteith model, the Shuttleworth-Wallace sparse canopy model and a modified Penman-Monteith model which is weighted for surface area of the evaporation sources.Results from the study suggest that the weighted Penman-Monteith model has the highest potential for use as a predictive tool. In all three cases, the importance of accurately measuring the surface area of each evaporation source is recognized. The difficulty in determining a representative surface resistance for each source and the associated problems in modelling without it are discussed.

List of Symbols

Models BREB Bowen ratio energy balance - P-M Penman-Monteith combination - S-W Shuttleworth-Wallace combination - W-P-M Weighted Penman-Monteith combination Other AE Available energy-all surfaces - AE _c Available energy-canopy (S-W, W-P-M) - AE _s Available energy-bare soil (S-W, W-P-M) - AE _w Available energy-open water (W-P-M) - C _p Specific heat of air - D Vapor pressure deficit - DAI Dead area index - FAI Foliage area index - LAI Leaf area index - Q ^* Net radiation - Q _e Latent heat flux-total - Q _ec Latent heat flux-canopy (S-W, W-P-M) - Q _es Latent heat flux-bare soil (S-W, W-P-M) - Q _ew Latent heat flux-open water (W-P-M) - Q _g ground heat flux - Q _h Sensible heat flux - S Proportion of area in bare soil - W Proportion of surface in open water - r _a Aerodynamic resistance (P-M, W-P-M) - r _c Canopy resistance - r _s Generalized optimized surface resistance - r _st Stomatal resistance - r _c ^a Bulk boundary layer resistance (S-W) - r _s ^a Aerodynamic resistance below mean canopy level (S-W) - r _s ^s Soil surface resistance (S-W, W-P-M) Greek Bowen ratio - Psychrometer constant - Air density - Slope of saturation vapour pressure vs temperature curve     

Estimation of Scalar Source/Sink Distributions in Plant Canopies Using Lagrangian Dispersion Analysis: Corrections for Atmospheric Stability and Comparison with a Multilayer Canopy Model

Source/sink distributions of heat, water vapour andCO₂ within a rice canopy were inferred using aninverse Lagrangian dispersion analysis and measuredmean profiles of temperature, specific humidity andCO₂ mixing ratio. Monin–Obukhov similarity theorywas used to account for the effects of atmosphericstability on _w(z), the standard deviation ofvertical velocity and _L(z), the Lagrangian timescale of the turbulence. Classical surface layer scaling was applied in the inertial sublayer (z > z_ruf)using the similarity parameter = (z - d)/L, where z is height above ground, d is the zero plane displacementheight for momentum, L is the Obukhov length,and z_ruf 2.3h_c, where h_c iscanopy height. A single length scale h_c, was usedfor the stability parameter 3 = h_c/L in the height range 0.25 < z/h_c < 2.5. This choice is justified by mixing layer theory, which shows that within the roughness sublayer there is one dominant turbulence length scaledetermined by the degree of inflection in the windprofile at the canopy top. In the absence of theoretical or experimental evidence for guidance,standard Monin–Obukhov similarity functions, with = h_c/L, were used to calculate the stabilitydependence of _w(z) and _L(z) in the roughness sublayer. For z/h_c < 0.25 the turbulence length and time scales are influenced by the presence of the lowersurface, and stability effects are minimal. With theseassumptions there was excellent agreement between eddycovariance flux measurements and deductions from theinverse Lagrangian analysis. Stability correctionswere particularly necessary for night time fluxes whenthe atmosphere was stably stratified.The inverse Lagrangian analysis provides a useful toolfor testing and refining multilayer canopy models usedto predict radiation absorption, energy partitioningand CO₂ exchanges within the canopy and at thesoil surface. Comparison of model predictions withsource strengths deduced from the inverse analysisgave good results. Observed discrepancies may be dueto incorrect specification of the turbulent timescales and vertical velocity fluctuations close to theground. Further investigation of turbulencecharacteristics within plant canopies is required toresolve these issues.     

A numerical study of daily transitions in the convective boundary layer

We examine daily (morning–afternoon) transitions in the atmospheric boundary layer based on large-eddy simulations. Under consideration are the effects of the stratification at the top of the mixed layer and of the wind shear. The results describe the transitory behaviour of temperature and wind velocity, their second moments, the boundary-layer height Z _m (defined by the maximum of the potential temperature gradient) and its standard deviation σ _m , the mixed-layer height z _i (defined by the minimum of the potential temperature flux), entrainment velocity W _e, and the entrainment flux H _i . The entrainment flux and the entrainment velocity are found to lag slightly in time with respect to the surface temperature flux. The simulations imply that the atmospheric values of velocity variances, measured at various instants during the daytime, and normalized in terms of the actual convective scale w_*, are not expected to collapse to a single curve, but to produce a significant scatter of observational points. The measured values of the temperature variance, normalized in terms of the actual convective scale Θ_*, are expected to form a single curve in the mixed layer, and to exhibit a considerable scatter in the interfacial layer.     

Flux determination over a smooth surface under strongly unstable conditions

Careful micrometeorological measurements on an empty parking lot allowed determination of the surface fluxes of sensible heatH and of momentum by applying profile equations derived from Monin-Obukhov similarity theory with two sets of the stability correction function for momentum _m and sensible heat _h . These fluxes were compared with reference values ofH independently determined by means of an eddy correlation technique. In general, better agreement was found betweenH values derived from profiles with the stability functions of Brutsaert (1992) and referenceH values, than when the Businger-Dyer functions were used to deriveH. The disagreement in the latter comparison was especially serious under strongly unstable conditions, with the value ofy=–z/L (wherez is the height andL is the Obukhov length) larger than 10. A closer look at the procedure for calculatingH from the profiles revealed that the large differences between theH values derived with these two different versions of the stability correction functions were caused by the small differences of the _h values, and not by the larger differences of the _m values. This result stems from the strong sensitivity of the resultingH values on the choice of _h .     

Bulk characteristics of heat transfer in the unstable,baroclinic atmospheric boundary layer

Field data for the unstable, baroclinic, atmospheric boundary layer over land and over the sea are considered in the context of a general similarity theory of vertical heat transfer. The dependence of δθ/θ_* upon logarithmic functions of h _c z _T and stability (through the similarity function C) is clearly demonstrated in the data. The combined data support the conventional formulation for the heat transfer coefficient δθ/θ_* when,

1. the surface scaling length is z _T (« z ₀), the height at which the surface temperature over land is obtained by extrapolation of the temperature profile
2. the height scale is taken as the depth of convective mixing h _c
3. the temperature profile equivalent of the von Karman constant is taken as 0.41
4. areal average, rather than single point, values of δθ are employed in strongly baroclinic conditions. No significant effect of baroclinity or the height scale ratio as proposed in the general theory is found. Variations in C about a linear regression relation against stability are most probably due to uncertainties in the areal surface temperature and to experimental errors in general temperature measurements.