Dispersion in sheared Gaussian homogeneous turbulence

By integrating the Fokker-Planck equation corresponding to a Lagrangian stochastic trajectory model, which is consitent with the selection criterion of Thomson (1987), an analytical solution is given for the joint probability density functionp(x_i, u_i, t) for the position (x _i) and velocity (u _i) at timet of a neutral particle released into linearly-sheared, homogeneous turbulence. The solution is compared with dispersion experiments conforming to the restrictions of the model and with a shortrange experiment performed in highly inhomogeneous turbulence within and above a model crop canopy. When the turbulence intensity, wind shear and covariance are strong, the present solution is better than simpler solutions (Taylor, 1921; Durbin, 1983) and as good as any numerical Lagrangian stochastic model yet reported.     

A note on peak-to-mean concentration ratios

The peak-to-mean concentration ratio obtained from observations near a point source of pollution is a particular example of the ratio of any short-period concentration to the long-term mean. The value of this ratio may be obtained from the probability distribution function: $$F(C) = F(0) exp [ - F(0) C/M]$$ whereF(C) is the probability or frequency that the ratio of a short-period average concentration (C) to the long-term mean (M) exceeds the valueC/M, andF(0) is a parameter dependent on the length of the short period and the position of the sampler relative to the centre-line of the plume. From (1) the peak-to-mean concentration ratio is shown to be related to the two averaging times by the expression $$P/M = 1/F(0) [lnF(0) - lnt_M /t_P ]$$ wheret _M andt _P are, respectively, the averaging times of the long-term meanM and the short-term peakP. Using recently published experimental data, Equation (1) and hence also (2) are shown to be valid for averaging timest _P from 5 s to 24 h and oft _M from 6 min to 5 yr providedt _P ?t _M .     

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.     

The characteristics of turbulent velocity components in the surface layer under convective conditions

It is proposed that the ratios of the standard deviations of the horizontal velocity components to the friction velocity in the surface layer under convective conditions depend only onz _i /L wherez _i is the height of the lowest inversion andL is the Monin-Obukhov length. This hypothesis is tested by using observations from several data sets over uniform surfaces and appears to fit the data well. Empirical curves are fitted to the observations which have the property that at largez _i /-L, the standard deviations become proportional tow _*, the convective scaling velocity.Fluctuations of vertical velocity obtained from the same experiments scale withz/L, wherez is the height above the surface, in good agreement with Monin-Obukhov theory.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Linear response functions to project contributions to future sea level

We propose linear response functions to separately estimate the sea-level contributions of thermal expansion and solid ice discharge from Greenland and Antarctica. The response function formalism introduces a time-dependence which allows for future rates of sea-level rise to be influenced by past climate variations. We find that this time-dependence is of the same functional type, R(t) ～ t ^α, for each of the three subsystems considered here. The validity of the approach is assessed by comparing the sea-level estimates obtained via the response functions to projections from comprehensive models. The pure vertical diffusion case in one dimension, corresponding to α =  ?0.5, is a valid approximation for thermal expansion within the ocean up to the middle of the twenty first century for all Representative Concentration Pathways. The approximation is significantly improved for α =  ? 0.7. For the solid ice discharge from Greenland we find an optimal value of α =  ?0.7. Different from earlier studies we conclude that solid ice discharge from Greenland due to dynamic thinning is bounded by 0.42 m sea-level equivalent. Ice discharge induced by surface warming on Antarctica is best captured by a positive value of α = 0.1 which reflects the fact that ice loss increases with the cumulative amount of heat available for softening the ice in our model.     

Statistics of Scalar Fields in the Atmospheric Boundary Layer Based on Large-Eddy Simulations. Part II: Forced Convection

Forced convection in a quasi-steady atmospheric boundary layer is investigated based on a large-eddy simulation (LES) model. The performed simulations show that in the upper portion of the mixed layer the dimensionless (in terms of mixed layer scales) vertical gradients of temperature, humidity, and wind velocity depend on the dimensionless height z/z _i and the Reech number Rn. The peak values of variances and covariances at the top of the mixed layer, scaled in terms of the interfacial scales, are functions of the interfacial Richardson number Ri. As a result expressions for the entrainment rates, in the case when the interfacial layer has a finite depth, and a condition for the presence of moistening or drying regimes in the mixed layer, are derived. Profiles of dimensionless scalar moments in the mixed layer are proposed to be expressed in terms of two empirical similarity functions F _m and F _i , dependent on dimensionless height z/z _i , and the interfacial Richardson number Ri. The obtained similarity expressions adequately approximate the LES profiles of scalar statistics, and properly represent the impact of stability, shear, and entrainment. They are also consistent with the parameterization proposed for free convection in the first part of this paper.     

On the vorticity and energy budgets of the cold vortex in Northeast China: a case study

This study examines the vorticity budgets, turbulent extended exergy and kinetic energy evolution equations to investigate the major dynamical and energy conversion processes contributing to the initiation and intensification of the cold vortex over Northeast China that occurred during June 19–22, 2009. The results show that the cyclonic vorticity was initiated in the lower troposphere due to the intense convergence of horizontal winds. The growth of cyclonic vorticity in the middle troposphere is mainly due to the vertical transportation of the vorticity, yet the increase of cyclonic vorticity in the upper troposphere primarily results from the horizontal advection of vorticity. Of special interest in this study is the evaluation of the role of thermal advections in the baroclinic development of the cold vortex. The results indicate that the rising of the air over relatively warm areas and the sinking of the air in relatively cold regions are favorable for releasing turbulent extended exergy $ \left( {e_{\text{t}} } \right) $ , which is later converted to turbulent kinetic energy $ \left( {k_{\text{t}} } \right) $ , and this process occurs during the initiation and intensification of the cold vortex. In addition, barotropic energy conversion is another important process that contributes to the growth of k _t, and it strengthens gradually after the initiation of the cold vortex. Other than frictional consumption, the flux of k _t in the vertical direction also depletes some of k _t. The fluxes of e _t, baroclinic energy conversions and diabatic generations are favorable factors for the growth of e _t, whereas it decreases with time as a result of a large amount of e _t that is released. Most of the energy conversion processes, including the baroclinic and the barotropic energy transformations and the energy conversions from e _t to k _t, as well as the fluxes of e _t, are stronger in the lower troposphere than the other areas during the formation of the cold vortex. This accounts for the initiation of the cyclonic vorticity in the lower troposphere. Finally, the fact that the turbulent extended exergy releases primarily in the middle troposphere through the vertical thermal circulation is consistent with our understanding based on the vorticity budget analyses.     

Measurements Of Thermal Updraft Intensity Over Complex Terrain Using American White Pelicans And A Simple Boundary-Layer Forecast Model

An examination of boundary-layer meteorological and avian aerodynamic theories suggests that soaring birds can be used to measure the magnitude of vertical air motions within the boundary layer. These theories are applied to obtain mixed-layer normalized thermal updraft intensity over both flat and complex terrain from the climb rates of soaring American white pelicans and from diagnostic boundary-layer model-produced estimates of the boundary-layer depth z_i and the convective velocity scale w_*. Comparison of the flatland data with the profiles of normalized updraft velocity obtained from previous studies reveals that the pelican-derived measurements of thermal updraft intensity are in close agreement with those obtained using traditional research aircraft and large eddy simulation (LES) in the height range of 0.2 to 0.8 z_i. Given the success of this method, the profiles of thermal vertical velocity over the flatland and the nearby mountains are compared. This comparison shows that these profiles are statistically indistinguishable over this height range, indicating that the profile for thermal updraft intensity varies little over this sample of complex terrain. These observations support the findings of a recent LES study that explored the turbulent structure of the boundary layer using a range of terrain specifications. For terrain similar in scale to that encountered in this study, results of the LES suggest that the terrain caused less than an 11% variation in the standard deviation of vertical velocity.     

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.     

Investigation of droplet dynamics in a convective cloud using a Lagrangian cloud model

A precipitating convective cloud is simulated successfully using the Lagrangian cloud model, in which the flow field is simulated by large eddy simulation and the droplets are treated as Lagrangian particles, and the results are analyzed to investigate precipitation initiation and to examine the parameterization of cloud microphysics. It is found that raindrops appear initially near the cloud top, in which strong turbulence and broadened droplet spectrum are induced by the entrainment of dry air, but high liquid–water mixing ratio is maintained within cloud parts because of insufficient mixing. Statistical analysis of the downward vertical velocity of a droplet W reveals that the transition from cloud droplets to raindrops occurs in the range 20 μm < r < 100 μm, while the variation of W depends on turbulence as well as the droplet radius r. The general pattern of the raindrop size distribution is found to be consistent with the Marshall–Palmer distribution. The precipitation flux can be underestimated substantially, if the terminal velocity $w_{\text{s}}$ is used instead of W, but it is not sensitive to the choice of the critical droplet radius dividing cloud drops and raindrops. It is also found that precipitation starts earlier and becomes stronger if the effect of turbulence is included in the collection kernel.     

Vertical velocity field in the convective boundary layer as observed with an acoustic Doppler sodar

The morning development of the daytime convective boundary layer (CBL) during fine weather has been observed with an acoustic Doppler sodar of the C.R.P.E. In particular, the vertical profile of the vertical velocity third-order statistic W* ³ has been obtained. This quantity is a maximum near 0.3z _I where z _I, is the height of the CBL. The histogram of vertical velocity in the CBL shows a relationship between W ³ and the convective velocity W _* and is useful for convective plume determination.     

A comparison of ABL heights inferred routinely from lidar and radiosondes at noontime

The height of the atmospheric boundary layer (ABL) obtained with lidar and radiosondes is compared for a data set of 43 noon (12.00 GMT) cases in 1984. The data were selected to represent the synoptic circulation types appropriately. Lidar vertical profiles at 1064 nm were used to obtain three estimates for the ABL height (h _lid), based on the first gradient in the back-scatter profile, namely, at the beginning, middle and top of the gradient. The boundary-layer height obtained with the radiosondes (h _s) was determined with the dry-parcel-intersection method in unstable conditions. As a first guess for near-neutral and stable conditions, the height of the first significant level in the potential temperature profile was taken. Overall, the boundary-layer thickness estimates agree surprisingly well (regression lineh _lidb=h_s:cc.=0.93 and the standard error=121 m). However, in 10% of the cases, the lidar estimate was significantly lower (difference>400 m) than the routinely inferredh _s. These outliers are discussed separately. For stable conditions, an estimate of ABL height (h _N) is also made based on the friction velocity and the Brunt-Väisälä frequency. The agreement betweenh _Nandh _lidbis good. Discrepancies between the two methods are caused by:

1. rapid growth of the boundary layer arround the measurement time;
2. the presence of a deep entrainment layer leading to a large zone in which quantities are not well mixed;
3. a large systematic error of 100–200 m in the estimate of boundary-layer height obtained from the radiosonde due to the way that profiles are recorded, as a series of significant points.

     

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     

A Modelling Study of Flux Imbalance and the Influence of Entrainment in the Convective Boundary Layer

It is frequently observed in field experiments that the eddy covariance heat fluxes are systematically underestimated as compared to the available energy. The flux imbalance problem is investigated using the NCAR’s large-eddy simulation (LES) model imbedded with an online scheme to calculate Reynolds-averaged fluxes. A top–down and a bottom–up tracer are implemented into the LES model to quantify the influence of entrainment and bottom–up diffusion processes on flux imbalance. The results show that the flux imbalance follows a set of universal functions that capture the exponential decreasing dependence on u _*/w _*, where u _* and w _* are friction velocity and the convective velocity scale, respectively, and an elliptic relationship to z/z _i , where z _i is the mixing-layer height. The source location in the boundary layer is an important factor controlling the imbalance magnitude and its horizontal and vertical distributions. The flux imbalance of heat and the bottom–up tracer is tightly related to turbulent coherent structures, whereas for the top–down diffusion, such relations are weak to nonexistent. Our results are broadly consistent with previous studies on the flux imbalance problem, suggesting that the published results are robust and are not artefacts of numerical schemes.     

Parameterization of sheared entrainment in a well-developed CBL. Part I: Evaluation of the scheme through large-eddy simulations

The entrainment flux ratio A _e and the inversion layer (IL) thickness are two key parameters in a mixed layer model. A _e 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 A _e is derived from the TKE budget in the firstorder 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 A _e and IL thickness agree well with the LES outputs.     

沙尘天气过程起沙特征的观测试验和参数化研究进展

沙尘天气过程研究中,起沙过程是沙尘传输和沉降的基础,沙尘模式中的起沙参数化方案决定了能否准确模拟和预报沙尘天气。试验观测和数值模拟是研究起沙过程的重要途径。基于风蚀起沙的物理机制,总结了起沙机制和起沙特征的研究成果,介绍了风蚀起沙的主要影响因子,回顾了起沙关键参数（临界起沙摩擦速度（u*t ）或临界起沙风速（Ut ）、水平跃移沙尘通量（Q）和起沙通量（F））的试验观测及其沙尘模式应用中的参数化方案,并讨论了不同起沙参数化方案的应用与校验。同时,针对目前研究中存在的问题和今后可能的研究方向提出建议。     

不同生育期水分胁迫对玉米光合特性的影响

利用遮雨棚以夏玉米为对象进行水分胁迫大田试验,通过分析玉米叶片光合测量数据,研究不同生育期水分胁迫对玉米光合特性的影响,为定量分析不同水分胁迫程度对玉米生育的可能机理提供数据和初步的理论支持.结果表明:土壤水分下降会使玉米叶片的光合速率(Pn)、气孔导度(Gs)、蒸腾速率(Tr)降低,而胞间CO2浓度(Ci)和水分利用效率(WUE)会增加;Pn随着光照强度的增加而增加,且随着水分胁迫强度增强,Pn增加速率降低;干旱胁迫会改变Pn、Tr日变化规律,并且对拔节期光合作用的抑制小于成熟期;WUE与Pn存在极显著的正相关关系,与Tr、Ci及Gs存在显著的负相关关系.     

Parameterization of Sheared Entrainment in a Well-developed CBL.Part Ⅱ: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 (A _e). This leads to a simple expression of the entrainment rate, in which A _e needs to be parameterized. According to the results in Liu et al. (2016), A _e 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.     

内蒙古科尔沁沙地临界起沙阈值的范围确定

临界起沙阈值可表征地表土壤的可蚀性,是风蚀起沙研究中非常重要的物理量之一。基于微气象学方法,将沙尘浓度和垂直沙尘通量均开始增加且至少持续0.5 h所对应的摩擦速度(或风速)确定为临界起沙摩擦速度u_*t(或临界起沙风速U_t)。利用内蒙古科尔沁沙地地区2010-2013年春季大气环境综合观测资料,分析了不同沙尘天气过程(扬沙、沙尘暴和强沙尘暴)起沙阶段沙尘浓度和垂直沙尘通量随摩擦速度的演变特征,精细确定了该地区临界起沙摩擦速度(u_*t)和临界起沙风速(U_t)的范围分别为0.45±0.20和6.5±3.0 m/s,同时讨论了不同起沙判据对确定临界起沙阈值产生的影响。相比而言,采用的起沙判据尽可能地排除了沙尘输送和沉降过程的影响,适用于不同的沙尘天气类型,使沙尘粒子进入大气的起沙结果更趋于合理,其结果可为建立统一、合理的起沙判据提供参考。     

Atmospheric circulation epochs and climate changes

The atmospheric circulation studies allow climate changes to be diagnosed and forecasted. Variations in occurrence frequencies of the atmospheric circulation forms W, E, and C (by the Vangengeim classification) and Z, M ₁, and M ₂ (by the Girs classification), which characterize climatic conditions in most of the Northern Hemisphere, are analyzed over a period of more than 100 years. It is shown that the occurrence frequency of the forms W, C, and M ₁ continually decreased, while that of the forms E and Z increased, which indicates a significant change in atmospheric circulation in the Northern Hemisphere during the last century. The occurrence frequency of the forms C and Z demonstrates specific features at inter-decade time scales. Correlations are found between accumulated sums of anomalies of occurrence frequencies of the atmospheric circulation forms C, (W + E), Z, and (M ₁ + M ₂) and inter-decade variations of the Earth’s rotation. The causes of these relationships are discussed along with possibilities of their use for diagnosis of climatic variations in the Northern Hemisphere.