THE UNSTABLE MODES OF NATURAL CONVECTION BOUNDARY LAYER

The instability of natural convection boundary layer around a vertical heated flat plate is analyzed theoretically in this paper. The results illustrate that the 'loop' in the neutral curve is not a real loop but a twist of the curve in the frequency-wave number-Grashof number space, and there is only one unstable mode at small Prandtl numbers. Specially, when the Prandtl number is large enough two unstable modes will be found in the 'loop' region. Along the amplifying surface intersection the two unstable modes have the same Grashof number, wave number and frequency but different amplifying rates. Their instability characteristics are analyzed and the criterion for determining the existence of the multi-unstable modes is also discussed.

Development of a Single-Column Model in RegCM4 and Its Preliminary Application for Evaluating PBL Schemes in Simulating the Dry Convection Boundary Layer

A single-column model(SCM)is developed in the regional climate model RegCM4.The evolution of a dry convection boundary layer(DCBL)is used to evaluate this SCM.Moreover,four planetary boundary layer(PBL)schemes,namely the Holtslag-Boville scheme(HB),Yonsei University scheme(YSU),and two University of Washington schemes(UW01,Grenier-Bretherton-Mc Caa scheme and UW09,Bretherton-Park scheme),are compared by using the SCM approach.A large-eddy simulation(LES)of the DCBL is performed as a benchmark to examine how well a PBL parameterization scheme reproduces the LES results,and several diagnostic outputs are compared to evaluate the schemes.The results show that the SCM is properly constructed.In general,with the DCBL case,the YSU scheme performs best for reproducing the LES results,which include well-mixed features and vertical sensible heat fluxes;the simulated wind speed,turbulent kinetic energy,entrainment flux,and height of the entrainment zone are all underestimated in the UW09;the UW01 has all those biases of the UW09 but larger,and the simulated potential temperature is not well mixed;the HB is the least skillful scheme,by which the PBL height,entrainment flux,height of the entrainment zone,and the vertical gradients within the mixed layer are all overestimated,and a inversion layer near the top of the surface layer is wrongly simulated.Although more cases and further testing are required,these simulations show encouraging results towards the use of this SCM framework for evaluating the simulated physical processes by the RegCM4.

Summer atmospheric boundary layer structure in the hinterland of Taklimakan Desert, China

Understanding the characteristics of the structure of desert atmospheric boundary layer and its land surface process is of great importance to the simulations of regional weather and climate. To investigate the atmospheric boundary layer structure and its forming mechanism of Taklimakan Desert, and to improve the accuracy and precision of regional weather and climate simulations, we carried out a GPS radiosonde observation experiment in the hinterland of Taklimakan Desert from 25 June to 3 July, 2015. Utilizing the densely observed sounding data, we analyzed the vertical structures of daytime convective boundary layer and nighttime stable boundary layer in summer over this region, and also discussed the impacts of sand-dust and precipitation events on the desert atmospheric boundary layer structure. In summer, the convective boundary layer in the hinterland of Taklimakan Desert developed profoundly and its maximum height could achieve 4,000 m; the stable boundary layer at nighttime was about 400-800-m thick and the residual mixing layer above it could achieve a thickness over 3,000 m. Sand-dust weather would damage the structures of nighttime stable boundary layer and daytime convective boundary layer, and the dust particle swarm can weak the solar radiation absorbed by the ground surface and further restrain the strong development of convective boundary layer in the daytime. Severe convective precipitation process can change the heat from the ground surface to the atmosphere in a very short time, and similarly can damage the structure of desert atmospheric boundary layer remarkably. Moreover, the height of atmospheric boundary layer was very low when raining. Our study verified the phenomenon that the atmospheric boundary layer with supernormal thickness exists over Taklimakan Desert in summer, which could provide a reference and scientific bases for the regional numerical models to better represent the desert atmospheric boundary layer structure.

Development of the Convective Boundary Layer Capping with a Thick Neutral Layer in Badanjilin:Observations and Simulations

In this study, the development of a convective boundary layer （CBL） in the Badaujilin region was investigated by comparing the observation data of two cases. A deep neutral layer capped a CBL that occurred on 30 August 2009. This case was divided into five sublayers from the surface to higher atmospheric elevations： surface layer, mixed layer, inversion layer, neutral layer, and sub-inversion layer. The development process of the CBL was divided into three stages： S1, S2, and S3. This case was quite different from the development of the three-layer CBL observed on 31 August 2009 because the mixed layer of the five-layer CBL （CBL5） eroded the neutral layer during S2. The specific initial structure of the CBL5 was correlated to the synoptic background of atmosphere during nighttime. The three-stage development process of the CBL5 was confirmed by six simulations using National Center for Atmospheric Research （USA） large-eddy simulation （NCAR-LES）, and some of its characteristics are presented in detail.

A Diagnostic Analysis on the Effect of the Residual Layer in Convective Boundary Layer Development near Mongolia Using 20th Century Reanalysis Data

Although the residual layer has already been noted in the classical diurnal cycle of the atmospheric boundary layer, its effect on the development of the convective boundary layer has not been well studied. In this study, based on 3-hourly 20th century reanalysis data, the residual layer is considered as a common layer capping the convective boundary layer. It is identified dally by investigating the development of the convective boundary layer. The region of interest is bounded by （30^-60~N, 80^-120~E）, where a residual layer deeper than 2000 m has been reported using radiosondes. The lapse rate and wind shear within the residual layer are compared with the surface sensible heat flux by investigating their climatological means, interannual variations and daily variations. The lapse rate of the residual layer and the convective boundary layer depth correspond well in their seasonal variations and climatological mean patterns. On the interannual scale, the correlation coefficient between their regional averaged （40°-50°N, 90°-110°E） variations is higher than that between the surface sensible heat flux and convective boundary layer depth. On the daily scale, the correlation between the lapse rate and the convective boundary layer depth in most months is still statistically significant during 1970-2012. Therefore, we suggest that the existence of a deep neutral residual layer is crucial to the formation of a deep convective boundary layer near the Mongolian regions.

A Laboratory Modeling of the Velocity Field in the Convective Boundary Layer with the Particle Image Velocimetry Technique

Based on the research of the convective boundary layer (CBL) temperature field in a convective tank, this paper studies the characteristics of the CBL velocity field in the convective tank. Aluminium powder (400 orders) is used as a tracer particle in the application of the particle image velocimetry (PIV) technique. The experiment demonstrates: the velocity distribution in the mixed layer clearly possesses the characteristics of CBL thermals; the velocity distribution in the top zone of the mixed layer shows entrainment layer characteristics; the vertical distribution of turbulent characteristic variables is reasonable, which is similar to field observations and other tank results; the error analysis demonstrates the validity of aluminium powder, which implies the reliability of the results.

Footprint Characteristics of Scalar Concentration in the Convective Boundary Layer

Footprint characteristics for passive scalar concentration in the convective boundary layer （CBL） are investigated. A backward Lagrangian stochastic （LS） dispersion model and a large eddy simulation （LES） model are used in the investigation. Typical characteristics of the CBL and their responses to the surface heterogeneity are resolved from the LES. Then the turbulence fields are used to drive the backward LS dispersion. To remedy the spoiled description of the turbulence near the surface, MoninObukhov similarity is applied to the lowest LES level and the surface for the modeling of the backward LS dispersion. Simulation results show that the footprint within approximately 1 km upwind predominates in the total contribution. But influence from farther distances also exists and is even slightly greater than that from closer locations. Surface heterogeneity may change the footprint pattern to a certain degree. A comparison to three analytical models provides a validation of the footprint simulations, which shows the possible influence of along-wind turbulence and the large eddies in the CBL, as well as the surface heterogeneity.

A Laboratory Study of the Turbulent Velocity Characteristics in the Convective Boundary Layer

Based on the measurement of the velocity field in the convective boundary layer （CBL） in a convection water tank with the particle image velocimetry （PIV） technique, this paper studies the characteristics of the CBL turbulent velocity in a modified convection tank. The experiment results show that the velocity distribution in the mixed layer clearly possesses the characteristics of the CBL thermals, and the turbulent eddies can be seen obviously. The comparison of the vertical distribution of the turbulent velocity variables indicates that the modeling in the new tank is better than in the old one. The experiment data show that the thermal＇s motion in the entrainment zone sometimes fluctuates obviously due to the intermittence of turbulence. Analyses show that this fluctuation can influence the agreement of the measurement data with the parameterization scheme, in which the convective Richardson number is used to characterize the entrainment zone depth. The normalized square velocity wi^2/w＊^2. at the top of the mixed layer seems to be time-dependent, and has a decreasing trend during the experiments. This implies that the vertical turbulent velocity at the top of the mixed layer may not be proportional to the convective velocity （w＊）.

Secondary flows in statistically unstable turbulent boundary layers with spanwise heterogeneous roughness

Large-scale secondary motions are known to occur in turbulent flows over surfaces with spanwise roughness heterogeneity.Numerical studies often use adjacent high-and low-roughness longitudinal strips to investigate these secondary rolls in boundary layers without any thermal stratification.In the present study,the effect of unstable thermal stratification on secondary rolls in a very high-Reynolds-number turbulent flow with spanwise-heterogeneous roughness is investigated by means of large-eddy simulation.The strength of the unstable stratification is systematically changed from L/h=−20 to L/h=−1,where L and h are Monin-Obukhov length and boundary-layer height,respectively.This range covers the transition from neutral stratification to unstable stratification.The results show that the positive buoyancy associated with the unstable thermal stratification acts against the roughness-induced secondary rolls.In the case of unstable stratification,secondary rolls are completely canceled out by buoyancy and replaced by new stronger convection-induced rolls rotating in opposite directions.

On similarity profiles predicted in the convective marine boundary layer

On the basis of the ideal of local scale similarity theory, the profile equations of wind, temperature and humidity for the eonvective marine boundary layer have been obtained. The marine boundary layer measurements were made over the western Pacific Ocean as past of the Tropical Ocean and Global Atmosphere (TOGA) Programme during Nov. 1986-Feb. 1987. The similarity profiles predicledfor wind. temperature and humidity in the MBL are in good agreement with the observational data.

Convective Boundary Layer in the Region of the Monsoon Trough-A Case Study

A case study of the convectively driven monsoon boundary layer has been carried out using the aerological observations at four stations in the region of monsoon trough during Monsoon Trough Boundary Layer Experiment (MONTBLEX) 1988. The Convective Boundary Layer (CBL) in the region of monsoon trough did not show double mixing line structure. A single mixing line representing the CBL with different stabilities with respect to the convective activities was observed.

Analysis of Pressure Forcings for the Vertical Turbulent Fluxes in the Convective Boundary Layer at Gray Zone Resolutions

At kilometer and sub-kilometer resolutions,known as the numerical gray zone for boundary layer turbulence,the atmospheric boundary layer turbulence becomes partially resolved and partially subgrid-scale(SGS) in a numerical model,thus requiring scale-adaptive turbulence schemes.Such schemes are often built by modifying the existing parameterizations,either the planetary boundary layer(PBL) schemes or the large-eddy simulation(LES) closures,to produce the right SGS turbulent fluxes at gray zone resolutions.However,the underlying forcings responsible for the changes in the vertical turbulent fluxes are largely ignored in these approaches.This study follows the original approach of Wyngaard(2004) and analyzes the turbulent buoyancy and momentum flux budgets,to gain a better understanding of the variations of flux forcings at gray zone resolutions.The investigation focuses on the pressure covariance term,which is one of the most dominant terms in the budget equations.By using the coarse-grained LES of a dry convective boundary layer(CBL) case as reference,two widely-used pressure covariance models are evaluated and optimized across the gray zone resolution range.The optimized linear model is further evaluated a priori against another dry CBL case with a different bulk stability,and a shallow-cumulus-topped boundary layer case.The model applies well to both cases,and notably shows good performance for the cloud layer.Based on the analysis of the flux forcings and the optimized pressure model,a scale-adaptive turbulence model for the gray zone is derived from the steady-state flux budgets.

Parameterization of Sheared Entrainment in a Well-Developed CBL.Part I:Evaluation of the Scheme through Large-Eddy Simulations

The entrainment flux ratio Ae and the inversion layer （IL） thickness are two key parameters in a mixed layer model. Ae is defined as the ratio of the entrainment heat flux at the mixed layer top to the surface heat flux. The IL is the layer between the mixed layer and the free atmosphere. In this study, a parameterization of Ae is derived from the TKE budget in the first- order model for a well-developed CBL under the condition of linearly sheared geostrophic velocity with a zero value at the surface. It is also appropriate for a CBL under the condition of geostrophic velocity remaining constant with height. LESs are conducted under the above two conditions to determine the coefficients in the parameterization scheme. Results suggest that about 43% of the shear-produced TKE in the IL is available for entrainment, while the shear-produced TKE in the mixed layer and surface layer have little effect on entrainment. Based on this scheme, a new scale of convective turbulence velocity is proposed and applied to parameterize the IL thickness, The LES outputs for the CBLs under the condition of linearly sheared geostrophic velocity with a non-zero surface value are used to verify the performance of the parameterization scheme. It is found that the parameterized Ae and IL thickness agree well with the LES outputs.

Performance of WRF Large Eddy Simulations in Modeling the Convective Boundary Layer over the Taklimakan Desert, China

The maximum height of the convective boundary layer(CBL)over the Taklimakan Desert can exceed 5000 m during summer and plays a crucial role in the regional circulation and weather.We combined the Weather Research and Forecasting Large Eddy Simulation(WRF-LES)with data from Global Positioning System(GPS)radiosondes and from eddy covariance stations to evaluate the performance of the WRF-LES in simulating the characteristics of the deep CBL over the central Taklimakan Desert.The model reproduced the evolution of the CBL processes reasonably well,but the simulations generated warmer and moister conditions than the observation as a result of the over-prediction of surface fluxes and large-scale advection.Further simulations were performed with multiple configurations and sensitivity tests.The sensitivity tests for the lateral boundary conditions(LBCs)showed that the model results are sensitive to changes in the time resolution and domain size of the specified LBCs.A larger domain size varies the distance of the area of interest from the LBCs and reduces the influence of large forecast errors near the LBCs.Comparing the model results using the original parameterization of sensible heat flux with the Noah land surface scheme and those of the sensitivity experiments showed that the desert CBL is sensitive to the sensible heat flux produced by the land surface scheme during daytime in summer.A reduction in the sensible heat flux can correct overestimates of the potential temperature profile.However,increasing the sensible heat flux significantly reduces the total time needed to increase the CBL to a relatively low altitude(<3 km)in the middle and initial stages of the development of the CBL rather than producing a higher CBL in the later stages.

Characteristics of Secondary Circulations in the Convective Boundary Layer over Two-Dimensional Heterogeneous Surfaces

Large-eddy simulations are conducted to investigate the impacts of the scale of chessboard-like heteroge- neous surface heating and the background wind on secondary circulations （SCs） in the convective boundary layer （CBL）. When the wind blows along the diagonal of the chessboard pattern, the cases with different heterogeneity length scales （λ = 1.2, 2.4, and 4.8 km） and weak background wind （U = 2.5 m s-1） suggest that there exists a threshold for the roll-like SCs, which is satisfied when the heterogeneity length scale is 1.6 times the boundary layer height （λ = 1.6zi）. During the CBL development, the SC intensity increases before this threshold is met, whereas it decreases thereafter. The cases with different background wind speeds （U = 2.5, 5.0, and 10.0 m s-1） and relatively large heterogeneity length scale （λ = 4.8 km） show that the SCs are strengthened by larger wind speeds when the heterogeneity length scale is so large that the threshold cannot be met during the CBL development. Another case with wind direction along neither the diagonal nor the side of the chessboard pattern shows that the roll-like SCs can still be triggered, but the roll axes are orientated along the diagonal of the chessboard pattern rather than along the wind direction.

Parameterization of Sheared Entrainment in a Well-developed CBL.PartⅡ:A Simple Model for Predicting the Growth Rate of the CBL

Following the parameterization of sheared entrainment obtained in the companion paper, Liu et al. （2016）, the present study aims to further investigate the characteristics of entrainment, and develop a simple model for predicting the growth rate of a well-developed and sheared CBL. The relative stratification, defined as the ratio of the stratification in the free atmosphere to that in the entrainment zone, is found to be a function of entrainment flux ratio （Ae）. This leads to a simple expression of the entrainment rate, in which Ae needs to be parameterized. According to the results in Liu et al. （2016）, Ae can be simply expressed as the ratio of the convective velocity scale in the sheared CBL to that in the shear-free CBL. The parameterization of the convective velocity scale in the sheared CBL is obtained by analytically solving the bulk model with several assumptions and approximations. Results indicate that the entrainment process is influenced by the dynamic effect, the interaction between mean shear and environmental stratification, and one other term that includes the Coriolis effect. These three parameterizations constitute a simple model for predicting the growth rate of a well-developed and sheared CBL. This model is validated by outputs of LESs, and the results show that it performs satisfactorily. Compared with bulk models, this model does not need to solve a set of equations for the CBL. It is more convenient to apply in numerical models.

Modified Adomian decomposition method for solving the problem of boundary layer convective heat transfer

In this paper,we apply a new modification of the Adomian decomposition method for solving the problem of boundary layer convective heat transfer with viscous dissipation and low pressure gradient over a at plate.The technique is based on the standard Adomian decomposition method and the Chebyshev pseudospectral method.Comparisons are made between the pro-posed technique,the standard Adomian decomposition method,and the numerical solutions to demonstrate the applicability,validity,and high accuracy of the present approach.The results demonstrate that the new modification is more efficient and converges faster than the Adomian decomposition method.

BOUNDARY LAYER GROWTH AND LAPSE RATE CHANGES DETERMINED BY LIDAR AND SURFACE HEAT FLUX IN SOFIA

In this study the results from a boundary layer experiment,conducted in autumn 1991 over a flat,build-up urban area in Southeast Sofia,together with some models for mixed layer growth rates are used to investigate the layered struc- ture of the vertical atmospheric stability distribution in the Sofia Valley.Lidar measurements of aerosol layer heights and morning boundary layer development are combined with surface eddy correlation measurements of kinematic heat and moisture fluxes,profiles of temperature and humidity,wind speed and wind direction.A diagnostic method is pres- ented for determining vertical lapse rates using surface meteorological measurements and lidar returns observed during the transition from nighttime stable stratification to daytime convective boundary layer after the sunrise.

ON THE PDF MODELS FOR ATMOSPHERIC DIFFUSION IN BOUNDARY LAYER

In this paper, taking its turbulent exchange coefficient as a function of the Lagrangian time scale and standard variance of the turbulence in atmosphere, the atmospheric dispersion PDF models are obtained on the basis of atmospheric diffusion K-theory. In the model the statistics of wind speed are directly used as its parameters instead of classic dispersion parameters. The bi- Gaussian PDF is derived in convective boundary layer (CBL), from the statistics of vertical velocity in both of the downdraft and updraft regions that are investigated theoretically in the other part of this paper. Giving the driven parameters of the CBL (including the convective velocity scale w* and the mixing depth h_i) and the time-averaged wind speed at release level, the PDF model is able to simulate the distribution of concentration released at any levels in the CBL. The PDF's simulations are fairly consistent with the measurements in CONDORS experiment or the results brought out by some numerical simulations.