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.     

A Mixed-Layer Model Of The Well-Mixed Stratocumulus-Topped Boundary Layer

Recently a range of sophisticated large-eddy simulations of thecloud-topped boundary layer have been intercompared and furthercompared with observations and single column models. Here we comparethese results with perhaps the simplest model of the cloud-toppedboundary layer, namely a mixed-layer model. Results from the model aredescribed with two aims in mind. Firstly, the good results act as areminder of the success of simple models, and, secondly, we suggestthat a simple mixed-layer model could be used as a baseline for futuremodel intercomparisons.The mixed-layer model is based on two assumptions that follow previousstudies. Firstly, the liquid-water potential temperature and the total waterspecific humidity are assumed to be constant with height in the boundarylayer. Secondly, turbulence entrains air across the inversion into the boundarylayer at a rate that is assumed to be proportional to the jump in radiative flux at the cloud top and inversely proportional to the jump in buoyancy at the inversion. The constant of proportionality is called the entrainment efficiency.Results from the model for the entrainment rate and height evolutionof the boundary layer are compared with the observations and modelsconsidered in a EUCREM intercomparison study. Thepresent mixed-layer model accurately predicts the observed heightevolution of the boundary layer, but over-estimates the entrainmentrate to a similar degree as the large-eddy simulations. We show that,if the subsidence rate is reduced to the value given by observationsrather than the value used in the EUCREM intercomparison study,then the model agrees well with observed value of the entrainment rateif the entrainment efficiency is taken to be 0.6. With this value, themodel also agrees well with a further case study byBechtold et al. An entrainment efficiency of 0.6 is a little higherthan suggested by large eddy simulations, but such simulations do notcurrently resolve the entrainment events explicitly. Hence this pointdeserves further study.     

Local advection of momentum,heat, and moisture in micrometeorology

The local advection of momentum, heat and moisture in micrometeorology due to a horizontal inhomogeneity in surface conditions is numerically investigated by a higher-order turbulence closure model which includes equations for the mean quantities, turbulent fluxes, and the viscous dissipation rate. The application of the two-dimensional model in this paper deals with the simulation of the flow from an extensive smooth dry area to a grassy wet terrain. The mean wind speed, temperature, and humidity distributions in the resulting internal boundary layer downstream of the surface discontinuity are determined such that the energy and moisture balances at the Earth's surface are satisfied.Numerical calculations of the mean temperature and humidity profiles are compared with available observed ones. The results include the advective effects on turbulent flux distributions, surface energy balance, evaporation rate, and Bowen ratio. The sensitivity of the predicted mean profiles and turbulent flux distributions to the surface relative humidity, thermal stratification, and the roughness change is discussed.NRC-NAS Resident Research Associate at AFCRL.     

Climate variability in the southern Indian Ocean as revealed by self-organizing maps

Using a non-linear statistical analysis called “self-organizing maps”, the interannual sea surface temperature (SST) variations in the southern Indian Ocean are investigated. The SST anomalies during austral summer from 1951 to 2006 are classified into nine types with differences in the position of positive and negative SST anomaly poles. To investigate the evolution of these SST anomaly poles, heat budget analysis of mixed-layer using outputs from an ocean general circulation model is conducted. The warming of the mixed-layer by the climatological shortwave radiation is enhanced (suppressed) as a result of negative (positive) mixed-layer thickness anomaly over the positive (negative) SST anomaly pole. This contribution from shortwave radiation is most dominant in the growth of SST anomalies. In contrast to the results reported so far, the contribution from latent heat flux anomaly is not so important. The discrepancy in the analysis is explained by the modulation in the contribution from the climatological heat flux by the interannual mixed-layer depth anomaly that was neglected in the past studies.     

HUBEX试验区近地面层的湍流输送

1998年淮河流域能量和水循环试验(HUBEX)期间曾进行了1个月的近地面层湍流观测.分析不稳定条件下湍流的统计特性和谱特征,并与Monin-Obukhov相似理论进行了比较.结果表明,不稳定的时候各湍流量的统计特征与相似理论的预期相符.虽然不稳定条件下温度和湿度涨落的相关系数很高,谱的式样也相近,但湿度谱的峰值频率高于温度谱.协谱曲线的形状显示感热通量的谱峰较宽,表现出w和T在较宽范围的强相关性,而水汽通量谱在高频段下降很快,说明水汽的输送更多地出现在低频部分.从谱相关系数可见,在近中性的时候,各尺度湍流涡的热量输送效率普遍较低,随着不稳定性增强而显著提高.分析还发现,不论不稳定性的程度如何,小尺度湍流的水汽输送效率都较低.水汽通量谱的相关系数随稳定度的变化不如热通量的谱相关系数大,表明近中性时除小尺度湍流外其他湍流涡的水汽输送效率高于热量输送.     

Short timescale air-sea coupling in the tropical deep convective regime

Summary The relationship between surface rainfall rate and sea-surface temperature (SST) over tropical cloudy areas is revisited, and associated air-sea interaction processes are investigated based on hourly grid simulation data over cloudy areas from a two-dimensional coupled ocean-cloud resolving atmosphere model. A cloud-weighted data analysis shows that surface evaporation flux decreases with increasing SST and is one order of magnitude smaller than the residual between moisture convergence and condensation, playing a negligible role in moisture budget. Moisture convergence determines the surface rainfall rate by determining vapor condensation and deposition rates. Ocean mixed-layer thermal budget shows that the atmospheric surface flux is a major process responsible for SST variation while thermal advection and thermal entrainment play a secondary role. The results indicate that atmospheric impacts on the ocean are important whereas oceanic impacts on the atmosphere are not, in the tropical air-sea system, on short timescales. Thus, the relationship between surface rainfall rate and SST over tropical cloudy areas is not physically important. Further estimates indicate that the surface evaporation flux and residual between moisture convergence and condensation could have the same order of magnitude in daily-mean moisture budget.     

A bulk mass flux convection scheme for climate model: description and moisture sensitivity

A convection scheme for climate model is developed based on Tiedtke’s (Mon Weather Rev 117:1779–1800, 1989) bulk mass flux framework and is evaluated with observational data and cloud resolving model simulation data. The main differences between the present parameterization and Tiedtke’s parameterization are the convection trigger, fractional entrainment and detrainment rate formulations, and closure method. Convection is triggered if the vertical velocity of a rising parcel is positive at the level at which the parcel is saturated. The fractional entrainment rate depends on the vertical velocity and buoyancy of the parcel as well as the environmental relative humidity. For the fractional detrainment rate, a linear decrease in the updraft mass flux above maximum buoyancy level is assumed. In the closure method, the cloud base mass flux is determined by considering both cloud layer instability and subcloud layer turbulent kinetic energy as controlling factors in the strength of the convection. The convection scheme is examined in a single column framework as well as using a general circulation model. The present bulk mass flux (BMF) scheme is compared with a simplified Relaxed Arakawa-Schubert (RAS) scheme. In contrast to the RAS, which specifies the cloud top, cloud top height in BMF depends on environmental properties, by considering the conditions of both the parcel and its environment in a fractional entrainment and detrainment rate formulations. As a result, BMF shows improved sensitivity in depth and strength of convection on environmental humidity compared to RAS, by strengthening coupling between cloud and environment. When the mid to lower troposphere is dry, the cloud resolving model and BMF produce cloud top around the dry layer and moisten the layer. In the framework of general circulation model, enhanced coupling between convection and environmental humidity in BMF results in improved representation of eastward propagating intraseasonal variability in the tropics—the Madden-Julian oscillation.     

Analysis of aircraft measurements of momentum flux in the subcloud layer over the tropical atlantic ocean during gate

The momentum flux data obtained by the gust probe aboard the NOAA DC-6 aircraft during GATE are analyzed. Vertical profiles are obtained for Phases I and III and correlated with vertical wind velocity profiles using the geostrophic departure method. Reasonable agreement is obtained using the horizontal equations of motion with negligible advective acceleration. The vertical profiles of momentum flux and wind speed variance compare well with the numerical model results of Deardorff (1972) and Wyngaard et al. (1974). Vertical distributions of power spectra for vertical eddy motion and cospectra corresponding to the momentum flux components are obtained along with the height variation of the dominant length scales of vertical eddy motion and the dissipation rate of turbulence kinetic energy. When normalized by mixed-layer similarity, these results agree well with previous determinations in the boundary layer over tropical oceans and over land.     

An efficient PBL model for global circulation models-design and validation

An efficient, pianetary boundary layer (PBL) model is developed and validated with empirical data for applications in general circulation models (GCMs). The purpose of this PBL model is to establish the turbulent surface fluxes as a function of the principal external PBL parameters in a numerically efficient way. It consists of a surface layer and a mixed layer matched together with the conditions of constant momentum and heat flux at the interface. An algebraic solution to the mean momentum equations describes the mixed-layer velocity profile and thus determines the surface wind vector. The velocity profile is globally valid by incorporating the effect of variable Coriolis force without becoming singular at the equator. Turbulent diffusion depends on atmospheric stability and is modeled in the surface layer by a drag law and with first-order closure in the mixed layer. Radiative cooling in the stably stratified PBL is considered in a simple manner. The coupled system is solved by an iterative method. In order to preserve the computational efficiency of the large-scale model, the PBL model is implemented into the GISS GCM by means of look-up tables with the bulk PBL Richardson number, PBL depth, neutral drag coefficient, and latitude as independent variables.A validation of the PBL model with observed data in the form of Rossby number similarity theory shows that the internal feedback mechanisms are represented correctly. The model, however, underpredicted the sensible heat-flux. A subsequent correction in the turbulence parameterization yields better agreement with the empirical data. The behavior of the principal internal PBL quantities is presented for a range of thermal stabilities and latitudes.     

Impact of moisture flux convergence and soil moisture on precipitation: a case study for the southern United States with implications for the globe

Interactions between soil moisture, evapotranspiration (ET), atmospheric moisture fluxes and precipitation are complex. It is difficult to attribute the variations of one variable to another. In this study, we investigate the influence of atmospheric moisture fluxes and land surface soil moisture on local precipitation, with a focus on the southern United States (U.S.), a region with a strong humidity gradient and intense moisture fluxes. Experiments with the Weather Research and Forecasting model show that the variation of moisture flux convergence (MFC) is more important than that of soil moisture for precipitation variation over the southern U.S. Further analyses decompose the precipitation change into several contributing factors and show that MFC affects precipitation both directly through changing moisture inflow (wet areas) and indirectly by changing the precipitation efficiency (transitional zones). Soil moisture affects precipitation mainly by changing the precipitation efficiency, and secondly through direct surface ET contribution. The greatest soil moisture effects are over transitional zones. MFC is more important for the probability of heavier rainfall; soil moisture has much weaker impact on rainfall probability and its roles are similar for the probability of intermediate-to-heavy rainfall (>10 mm day^?1). Although MFC is more important than soil moisture for precipitation over most regions, the impact of soil moisture could be large over certain transitional regions. At the submonthly time scale, the African Sahel appears to be the only major region where soil moisture has a greater impact than MFC on precipitation. This study provides guidance to understanding and further investigation of the roles of local land surface processes and large-scale circulations on precipitation.     

Influence of Coriolis Parameter Variation on Langmuir Turbulence in the Ocean Upper Mixed Layer with Large Eddy Simulation

Langmuir turbulence is a complex turbulent process in the ocean upper mixed layer. The Coriolis parameter has an important effect on Langmuir turbulence through the Coriolis–Stokes force and Ekman effect, however, this effect on Langmuir turbulence has not been systematically investigated. Here, the impact of the Coriolis parameter on Langmuir turbulence with a change of latitude (LAT) from 20°N to 80°N is studied using a non-hydrostatic large eddy simulation model under an ideal condition. The results show that the ratio of the upper mixed layer depth to Ekman depth scale (RME) RME = 0.266 (LAT = 50°N) is a key value (latitude) for the modulation effect of the Coriolis parameter on the mean and turbulent statistics of Langmuir turbulence. It is found that the rate of change of the sea surface temperature, upper mixed layer depth, entrainment flux, crosswind velocity, downwind vertical momentum flux, and turbulent kinetic energy budget terms associated with Langmuir turbulence are more evident at RME ≤ 0.266 (LAT ≤ 50°N) than at RME ≥ 0.266 (LAT ≥ 50°N). However, the rate of change of the depth-averaged crosswind vertical momentum flux does not have a clear variation between RME ≤ 0.266 and RME ≥ 0.266. The complex changes of both Langmuir turbulence characteristics and influence of Langmuir turbulence on the upper mixed layer with latitude presented here may provide more information for further improving Langmuir turbulence parameterization.     

干湿地表的湍流特征及其对深对流影响的大涡模拟

利用大涡模式模拟了对流边界层结构演变以及深对流触发过程.通过改变鲍恩比的敏感性试验研究不同大气初始状况下湿润和干旱下垫面湍流特征及其对深对流触发过程的影响.结果表明:干旱下垫面的混合层干而暖,厚度较大;湿润下垫面相反.由于地表感热通量对热力湍流形成的作用更大,干旱下垫面上湍流混合和夹卷作用更强,使得水汽和相当位温在边界...     

Surface-level moisture transport over the Indian Ocean during southwest monsoon months using NOAA/HIRS data

Surface-level moisture transport over the Indian Ocean has been computed using NOAA/HIRS data for the years 1980, 1981 and 1984. The global relation between monthly mean surface-level humidity and precipitable water (Liu, 1986) has been applied for the computation of surface-level humidity using monthly mean satellite-derived water vapour. The monthly mean surface wind fields over the Indian ocean provided by Florida State University have been used for the surface-level moisture flux computations. Our analysis indicates net positive surface-level moisture flux divergence over the Arabian Sea and negative moisture flux divergence over the Bay of Bengal. It has also been found that evaporation over the Arabian Sea is a variable quantity and forms a significant part of the net moisture budget over the Arabian Sea. The relative contribution of cross-equatorial flux and evaporation from the Arabian Sea has been studied for all three years.     

Further results from a laboratory model of the convective planetary boundary layer

The turbulence in a laboratory convective mixed layer is probed more extensively than in the preliminary study of Willis and Deardorff (1974), and results presented. Turbulence intensities, spectra and probability distributions using mixed-layer scaling compare favorably with similarly scaled field measurements not available or plentiful in 1974. However, the velocity spectra in the convection tank exhibit only a short inertial subrange due to the close proximity of the dissipation subrange to the energy-containing range.The turbulence budget suggests that the convergence of the vertical transport of pressure fluctuations is a rather important term.Results on the entrainment rate are also presented, using both mixed-layer scaling and local interfacial scaling.     

Sensitivity analysis of the equations for a convective mixed layer

Jump or slab models are frequently used to calculate the depth of the convectively mixed layer and its potential temperature during the course of a clear day. Much attention has been paid theoretically to the parameterization of the budget for turbulent kinetic energy that is required in these models. However, for practical applications the sensitivity of the solutions of the model equations to variations in the entrainment formulation and in the initial and boundary conditions is also very important. We analyzed this sensitivity on the basis of an analytical solution for the model which uses the well-known constant heat flux ratio. The initial conditions for the mixed-layer height (h) and potential temperature ( _m ) quickly lose their influence. Only the initial temperature deficit is important. The mixed-layer temperature at noon on convective days is insensitive to the entrainment coefficient c. It is governed by the integral of the heat input and by the stable lapse rate. A change in c from 0.2 to 0.5 leads to a variation of 20% in h. This is not very much considering the accuracy in the determination of h from actual observations.     

A Simple Parametrization for the Concentration Variance Dissipation in a Lagrangian Single-Particle Model

A new quasi-analytical mixed-layer model is formulated describing the evolution of the convective atmospheric boundary layer (ABL) during cold-air outbreaks (CAO) over polar oceans downstream of the marginal sea-ice zones. The new model is superior to previous ones since it predicts not only temperature and mixed-layer height but also the height-averaged horizontal wind components. Results of the mixed-layer model are compared with dropsonde and aircraft observations carried out during several CAOs over the Fram Strait and also with results of a 3D non-hydrostatic (NH3D) model. It is shown that the mixed-layer model reproduces well the observed ABL height, temperature, low-level baroclinicity and its influence on the ABL wind speed. The mixed-layer model underestimates the observed ABL temperature only by about 10 %, most likely due to the neglect of condensation and subsidence. The comparison of the mixed-layer and NH3D model results shows good agreement with respect to wind speed including the formation of wind-speed maxima close to the ice edge. It is concluded that baroclinicity within the ABL governs the structure of the wind field while the baroclinicity above the ABL is important in reproducing the wind speed. It is shown that the baroclinicity in the ABL is strongest close to the ice edge and slowly decays further downwind. Analytical solutions demonstrate that the \(\mathrm{e}\)-folding distance of this decay is the same as for the decay of the difference between the surface temperature of open water and of the mixed-layer temperature. This distance characterizing cold-air mass transformation ranges from 450 to 850 km for high-latitude CAOs.     

The depth of the daytime mixed layer at two coastal sites: A model and its validation

A mathematical model of mixed-layer depth based on the thermodynamic analysis of Tennekes (1973) is generalized to include advection and subsidence. The effects of advection on mixed-layer depth have been modelled by setting the model equations in a Lagrangian frame, performing an approximate first integral in order to derive the spatial dependence of the model variables, and using these spatial forms to give a set of Eulerian equations. The effects of subsidence have been modelled by imposing a subsidence velocity on the top of the mixed layer as well as allowing subsidence-induced warming above that layer.The model thus derived consists of a system of non-linear differential equations which may be numerically solved to elucidate the temporal behaviour of mixed-layer depth. The boundary conditions necessary for such a solution are drawn from field studies at two coastal sites: one with a relatively simple coastline and essentially flat land under agricultural use, the other with a considerably more complex coastline, rolling relief and mixed land use (agricultural, parkland and urban). In both cases the modelled evolution of mixed-layer depth is in good agreement with the measured depth.The sensitivity of the model to all the input variables is investigated by examining the dependence of the maximum mixed-layer depth on each of these variables in an artificial set.     

Surface Temperature and Surface-Layer Turbulence in a Convective Boundary Layer

Previous laboratory and atmospheric experiments have shown that turbulence influences the surface temperature in a convective boundary layer. The main objective of this study is to examine land-atmosphere coupled heat transport mechanism for different stability conditions. High frequency infrared imagery and sonic anemometer measurements were obtained during the boundary layer late afternoon and sunset turbulence (BLLAST) experimental campaign. Temporal turbulence data in the surface-layer are then analyzed jointly with spatial surface-temperature imagery. The surface-temperature structures (identified using surface-temperature fluctuations) are strongly linked to atmospheric turbulence as manifested in several findings. The surface-temperature coherent structures move at an advection speed similar to the upper surface-layer or mixed-layer wind speed, with a decreasing trend with increase in stability. Also, with increasing instability the streamwise surface-temperature structure size decreases and the structures become more circular. The sequencing of surface- and air-temperature patterns is further examined through conditional averaging. Surface heating causes the initiation of warm ejection events followed by cold sweep events that result in surface cooling. The ejection events occur about 25 % of the time, but account for 60–70 % of the total sensible heat flux and cause fluctuations of up to 30 % in the ground heat flux. Cross-correlation analysis between air and surface temperature confirms the validity of a scalar footprint model.     

山丘地形的陆面过程及边界层特征的模拟

将模式NP-89的陆面过程参数化方法应用到北京大学的三维复杂地形中尺度数值模式中, 得到了一个较理想的三维陆面过程及边界层模式, 利用这个改进的三维模式对20 km×20 km范围的山丘地形的陆面过程及边界层特征进行了数值模拟。模拟结果表明, 由于地形阻挡所造成山后的湍流较山前强, 进而造成近地面温度梯度和感热支出小, 最终造成山后的温度比山前的温度明显偏高; 而且随着山高的增加, 这种现象更加明显, 即该模式对山丘地形条件下的陆面过程和大气边界层特征具有较强的模拟能力; 模拟结果合理, 对研究过山气流形成机制、起伏地形大气边界层物理特征和污染物的扩散具有理论和应用价值。     

Regional Fluxes Of Momentum And Sensible Heat Over A Sub-Arctic Landscape During Late Winter

Based on measurements at Sodankylä Meteorological Observatory the regional (aggregated) momentum and sensible heat fluxes are estimated for two days over a site in Finnish Lapland during late winter. The forest covers 49% of the area. The study shows that the forest dominates and controls the regional fluxes of momentum and sensible heat in different ways. The regional momentum flux is found to be 10–20% smaller than the measured momentum flux over the forest, and the regional sensible heat flux is estimated to be 30–50% of the values measured over a coniferous forest.The regional momentum flux is determined in two ways, both based on blending height theory. One is a parameterised method, the other represents a numerical solution of an aggregation model. The regional sensible heat flux is determined from the theory of mixed-layer growth. At near neutral conditions the regional momentum flux can be determined independently of the regional sensible heat flux. At unstable conditions the two models become coupled.The information that is needed by the parameterised blending height method and by the mixed-layer evolution method in order to derive the regional fluxes of momentum and sensible heat can be obtained from radiosonde profiles of wind speed and temperature.