Non-stationary Generation of Weak Turbulence for Very Stable and Weak-Wind Conditions

Turbulence measurements for very stable conditions near the surface are contrasted among three sites: a high altitude basin during winter with grass or snow-covered grass, a broad valley with complex agricultural land use, and a more narrow valley that is influenced by a valley cold pool and cold air drainage. In contrast to previous studies, this investigation emphasizes the very weak turbulence with large bulk Richardson number occurring during extensive periods between brief mixing events. The relationship of the turbulence to the non-stationary wind and stratification is examined along with the impact of short-term flow accelerations, directional shear and downward diffusion of turbulence from higher levels. The failure of the turbulence for strong stratification to decrease with further increase of stratification is explored. Additional analyses are applied to weak-wind cases for the entire range of stratification, including weak stratification associated with cloudy conditions.     

Observations of Wind-Direction Variability in the Nocturnal Boundary Layer

Large sudden wind-direction shifts and submeso variability under nocturnal conditions are examined using a micrometeorological network of stations in north-western Victoria, Australia. The network was located in an area with mostly homogeneous and flat terrain. We have investigated the main characteristics of the horizontal propagation of events causing the wind-direction shift and not addressed in previous studies. The submeso motions at the study site exhibit behaviour typical of flat terrain, such as the lower relative mesovelocity scale and smaller cross-wind variances than that for complex terrain. The distribution of wind-direction shifts shows that there is a small but persistent preference for counter-clockwise rotation, occurring for 55% of the time. Large wind-direction shifts tend to be associated with a sharp decrease in air temperature (74% of the time), which is associated with rising motion of cold air, followed by an increase in turbulent mixing. The horizontal propagation of events was analyzed using the cross-correlation function method. There is no preferred mean wind direction associated with the events nor is there any relationship between the mean wind and propagation directions. The latter indicates that the events are most likely not local flow perturbations advected by the mean flow but are rather features of generally unknown origin. This needs to be taken into account when developing parametrizations of the stable boundary layer in numerical models.     

黄土高原复杂地形受中尺度运动影响的稳定边界层湍流特征

利用兰州大学半干旱气候与环境观测站(Semi-Arid Climate and Environment Observatory of Lanzhou University,简称SACOL)2008年12月观测资料,研究了稳定边界层湍流特征.使用涡动相关资料研究湍流通量时,定义湍流的平均时间τ内的中尺度运动是造成湍流统计量变化范围大的主要原因,稳定情形? τ取几十秒至几分钟.对梯度理查森数大于0.3的强稳定情形的湍流尺度分解(MRD)谱分析表明,感热通量在112.4～449.9 s存在谱隙,尺度大于谱隙的中尺度运动造成了通量观测资料离散性大,甚至有支配性影响.动量通量的谱隙在112.4～224.9 s之间.弱风时,中尺度运动的影响更大,垂直风速标准差以0.1的比率随中尺度风速变化;垂直风速标准差同广义风速表现出很好的相关性,并随着广义风速消失而消失.三维风速标准差与摩擦速度呈很好的线性关系,垂直、水平、横风风速的无量纲标准差分别为1.35、2.54、2.21.对湍流动能的研究发现,在梯度理查森数大于0.3的条件下,仍然存在连续的湍流.以湍动能为依据,分析了湍流的平稳时间长度,其长度随稳定度变化而变化,2008年12月7～11日从133.5 s变化到856.2 s,湍流平稳时间长度反映了中尺度运动的发生频率.     

The Near-Calm Stable Boundary Layer

For the near-calm stable boundary layer, nominally 2-m mean wind speed <0.5 ms⁻¹, the time-average turbulent flux is dominated by infrequent mixing events. These events are related to accelerations associated with wave-like motions and other more complex small-scale motions. In this regime, the relationship between the fluxes and the weak mean flow breaks down. Such near-calm conditions are common at some sites. For very weak winds and strong stratification, the characteristics of the fluctuating quantities change slowly with increasing scale and the separation between the turbulence and non-turbulent motions can become ambiguous. Therefore, a new analysis strategy is developed based on the scale dependence of selected flow characteristics, such as the ratio of the fluctuating potential energy to the kinetic energy. In contrast to more developed turbulence, correlations between fluctuating quantities are small, and a significant heat flux is sometimes carried by very weak vertical motions with large temperature fluctuations. The relation of the flux events to small-scale increases of wind speed is examined. Large remaining uncertainties are noted.     

A Prediction System for Local Wind Variations in Mountainous Terrain

A three-level model system for the prediction of local flows in mountainous terrain is described. The system is based upon an operational weather prediction model with a horizontal grid spacing of about 10 km. The large-scale flow is transformed to a more detailed terrain, first by a mesoscale model with grid spacing of about 1 km, and then by a local-scale model with a grid spacing of about 0.2 km. The weather prediction model is hydrostatic, while the two other models are non-hydrostatic. As a case study the model system has been applied to estimate wind and turbulence over Várnes airport, Norway, where data on turbulent flight conditions were provided near the runway. The actual case was chosen due to previous experiences, which indicate that south-easterly winds may cause severe turbulence in a region close to the airport. Local terrain induced turbulence seems to be the main reason for these effects. The predicted local flow in the actual region is characterized by narrow secondary vortices along the flow, and large turbulent intensity associated with these vortices. A similar pattern is indicated by the sparse observations, although there seems to be a difference in mean wind direction between data and predictions. Due to fairly coarse data for sea surface temperature, errors could be induced in the turbulence damping via the Richardson number. An adjustment for this data problem improved the predictions.     

The influence of nonstationarity on the turbulent flux–gradient relationship for stable stratification

Extensive eddy-correlation datasets are analyzed to examine the influence of nonstationarity of the mean flow on the flux–gradient relationship near the surface. This nonstationarity is due to wavelike motions, meandering of the wind vector, and numerous unidentified small-scale mesoscale motions. While the data do not reveal an obvious critical gradient Richardson number, the maximum downward heat flux increases approximately linearly with increasing friction velocity for significant stability. The largest of our datasets is chosen to more closely examine the influence of stability, nonstationarity, distortion of the mean wind profile and self-correlation on the flux-gradient relationship. Stability is expressed in terms of z/L, the gradient Richardson number or the bulk Richardson number over the tower layer. The efficiency of the momentum transport systematically increases with increasing nonstationarity and attendant distortion of the mean wind profile. Enhancement of the turbulent momentum flux associated with nonstationarity is examined in terms of the nondimensional shear, Prandtl number and the eddy diffusivity.     

Stability Dependence of Canopy Flows over a Flat Larch Forest

The dependence on atmospheric stability of flow characteristics adjacent to a very rough surface was investigated in a larch forest in Japan. Micrometeorological measurements of three-dimensional wind velocity and air temperature were taken at two heights above the forest, namely 1.7 and 1.2 times the mean canopy height h. Under near-neutral and stable conditions, the observed turbulence statistics suggest that the flow was likely to be that of the atmospheric surface layer (ASL) at 1.7h, and of the roughness sublayer (RSL) at 1.2h. However, in turbulence spectra, canopy-induced large coherent motions appeared clearly at both heights. Even under strongly stable conditions, the large-scale motions were retained at 1.2h, whereas they were overwhelmed by small-scale motions at 1.7h. This phenomenon was probably due to the enhanced contribution of the ASL turbulence associated with nocturnal decay of the RSL depth, because the small-scale motions appeared at frequencies close to the peak frequencies of well-known ASL spectra. This result supports the relatively recent concept that canopy flow is a superimposition of coherent motions and the ASL turbulence. The large-scale motions were retained in temperature spectra over a wider region of stability compared to streamwise wind spectra, suggesting that a canopy effect extended higher up for temperature than wind. The streamwise spacing of dominant eddies according to the plane mixing-layer analogy was only valid in a narrow range at near neutral, and it was stabilised at nearly half its value under stable conditions.     

Characteristics of Submeso Winds in the Stable Boundary Layer

The characteristics of submeso motions in the stable boundary layer are examined using observations from networks of sonic anemometers with network sizes ranging from a few hundred metres to 100 km. This study examines variations on time scales between 1 min and 1 h. The analysis focuses on the behaviour of the spectra of the horizontal kinetic energy, the ratios of the three velocity variances, their kurtosis, the dependence of horizontal variability on time scale, and the inter-relationship between vertical vorticity, horizontal divergence and deformation. Motions on larger time and space scales in the stable boundary layer are found to be nearly two-dimensional horizontal modes although the ratio of the vorticity to the divergence is generally on the order of one and independent of scale. One exception is a small network where stronger horizontal divergence is forced by a decrease in surface roughness. The horizontal variability, averaged over 1 h, appears to be strongly influenced by surface heterogeneity and increases with wind speed. In contrast, the time dependence of the horizontal structure on time scales less than one hour tends to be independent of wind speed for the present datasets. The spectra of the horizontal kinetic energy and the ratio of the crosswind velocity variance to the along-wind variance vary substantially between networks. This study was unable to isolate the cause of such differences. As a result, the basic behaviour of the submeso motions in the stable boundary layer cannot be generalized into a universal theory, at least not from existing data.     

The Influence of Transient Flow Distortion on Turbulence in Stable Weak-Wind Conditions

Transport by very weak turbulence near the surface, particularly with strong stratification, often violates existing similarity theory due partly to transient distortion of the wind profile by nonstationary mesoscale motions. This problem is examined with 4 months of flux data at seven levels on a 30-m tower. Difficulties with calculation of fluxes and shear with weak winds and weak turbulence are examined. The distortion of the wind profile assumes a wide variety of forms, but sometimes occurs with a transient wind maximum in the lowest 10 m. Though the vertical mixing of momentum is weak for weak-wind nonstationary conditions, it is often more efficient than predicted by existing similarity theory. In fact for weak-wind stable conditions, the flux-gradient relationship depends more on the curvature of the wind profile than the value of the stability parameter. This statistical study suggests a new direction for future work, but does not unravel the physics of the complex and varied structure for stratified weak-wind conditions.     

Helicopter-Borne Flux Measurements in the Nocturnal Boundary Layer Over Land – a Case Study

This case study introduces measurements of turbulent fluxes in a nocturnal boundary layer in North Germany with the new helicopter-borne turbulence measurement system HELIPOD, a detailed data analysis and examination in regard of systematic errors of the instrument, and some comparison with local similarity theory and experiments of the past, in order to confirm the occurrence of small vertical turbulent fluxes. The examined nocturnal boundary layer offered excellent conditions to analyse the quality of the measurement system. In this connection, a detailed look at a strong ground-based inversion disclosed small turbulent fluxes with a spectral maximum at ten metres wavelength or less, embedded in intermittent turbulence. For verification of these fluxes, the measurements were compared with well established results from past experiments. Local similarity theory was applied to calculate dimensionless variances of the turbulent quantities, which were found in good agreement with other observations. Since shear and stratification varied significantly on the horizontal flight legs due to global intermittency, a method was developed to determine vertical gradients on a horizontal flight pattern, by use of small fluctuations of the measurement height. With these locally determined gradients, gradient transport theory became applicable and the turbulent diffusivities for heat and momentum, the Richardson number, and the flux Richardson number were estimated within isolated strong turbulent outbursts. Within these outbursts the flux Richardson number was found between 0.1 and 0.2. The functional relationship between the gradient Richardson number and the turbulent Prandtl number agreed well with observations in past experiments and large eddy simulation. The impact of the stratification on the vertical turbulent exchange, as already described for the surface layer using Monin–Obukhov similarity, was analogously observed in the very stably stratified bulk flow when local scaling was applied.     

50 Years of the Monin–Obukhov Similarity Theory

In weak wind stable conditions, eddy-correlation fluxes calculated using conventional averaging times of 5 min or longer to define the perturbations are severely contaminated by poorly sampled mesoscale motions. A method is developed to identify the averaging time for each individual data record that captures the turbulence while excluding most of the mesoscale motions. The method is based on multiresolution decomposition of the heat flux, and provides an objective procedure for selecting the averaging time for calculating eddy-correlation fluxes. Eddy-correlation data collected in weak turbulence conditions over grass, snow, a pine forest and the ocean are used to demonstrate the approach.When the small-scale turbulence and mesoscale motions are clearly separated by a gap region in the heat flux cospectra, the variable window width reduces the influence of nonstationarity by more effectively filtering out mesoscale motions compared to traditional methods using constant averaging time. For records where turbulence and mesoscale motions overlap in scale, the method is not well posed, although such records occur infrequently for our datasets. These ambiguous cases correspond to significant nonstationarity at scales that overlap with turbulence scales. The improved turbulence fluxes calculated with the proposed method are the appropriate fluxes for evaluating flux-gradient relationships and Monin–Obukov similarity theory for developing improved model parameterizations of turbulence for weakly turbulent flows     

An Investigation into Ridge-Top Turbulence Characteristics During Neutral and Weakly Stable Conditions: Velocity Spectra and Isotropy

An investigation into high Reynolds number turbulent flow over a ridge top in New Zealand is described based on high-resolution in-situ measurements, using ultrasonic anemometers for two separate locations on the same ridge with differing upwind terrain complexity. Twelve 5-h periods during neutrally stratified and weakly stable atmospheric conditions with strong wind speeds were sampled at 20 Hz. Large (and small) turbulent length scales were recorded for both vertical and longitudinal velocity components in the range of 7–23 m (0.7–3.3 m) for the vertical direction and 628–1111 m (10.5–14.5 m) for the longitudinal direction. Large-scale eddy sizes scaled to the WRF (Weather Research and Forecasting) numerical model simulated boundary-layer thickness for both sites, while small-scale turbulent features were a function of the complexity of the upwind terrain. Evidence of a multi-scale turbulent structure was obtained at the more complex terrain site, while an assessment of the three-dimensional isotropy assumption in the inertial subrange of the spectrum showed anisotropic turbulence at the less complex site and evidence of isotropic turbulence at the more complex site, with a spectral ratio convergence deviating from the 4/3 or unity values suggested by previous theory and practice. Existing neutral spectral models can represent locations along the ridge top with simple upwind complexity, especially for the vertical wind spectra, but sites with more orographic complexity and strong vertical wind speeds are often poorly represented using these models. Measured spectra for the two sites exhibited no significant diurnal variation and very similar large-scale and small-scale turbulent length scales for each site, but the turbulence energy measured by the variances revealed a strong diurnal difference.     

Stable Boundary-Layer Scaling Regimes: The Sheba Data

Turbulent and mean meteorological data collected at five levels on a 20-m tower over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are analyzed to examine different regimes of the stable boundary layer (SBL). Eleven months of measurements during SHEBA cover a wide range of stability conditions, from the weakly unstable regime to very stable stratification. Scaling arguments and our analysis show that the SBL can be classified into four major regimes: (i) surface-layer scaling regime (weakly stable case), (ii) transition regime, (iii) turbulent Ekman layer, and (iv) intermittently turbulent Ekman layer (supercritical stable regime). These four regimes may be considered as the basic states of the traditional SBL. Sometimes these regimes, especially the last two, can be markedly perturbed by gravity waves, detached elevated turbulence (‘upside down SBL’), and inertial oscillations. Traditional Monin–Obukhov similarity theory works well in the weakly stable regime. In the transition regime, Businger–Dyer formulations work if scaling variables are re-defined in terms of local fluxes, although stability function estimates expressed in these terms include more scatter compared to the surface-layer scaling. As stability increases, the near-surface turbulence is affected by the turning effects of the Coriolis force (the turbulent Ekman layer). In this regime, the surface layer, where the turbulence is continuous, may be very shallow (< 5 m). Turbulent transfer near the critical Richardson number is characterized by small but still significant heat flux and negligible stress. The supercritical stable regime, where the Richardson number exceeds a critical value, is associated with collapsed turbulence and the strong influence of the earth’s rotation even near the surface. In the limit of very strong stability, the stress is no longer a primary scaling parameter.     

Energy- and Flux-Budget Turbulence Closure Model for Stably Stratified Flows. Part II: The Role of Internal Gravity Waves

We advance our prior energy- and flux-budget (EFB) turbulence closure model for stably stratified atmospheric flow and extend it to account for an additional vertical flux of momentum and additional productions of turbulent kinetic energy (TKE), turbulent potential energy (TPE) and turbulent flux of potential temperature due to large-scale internal gravity waves (IGW). For the stationary, homogeneous regime, the first version of the EFB model disregarding large-scale IGW yielded universal dependencies of the flux Richardson number, turbulent Prandtl number, energy ratios, and normalised vertical fluxes of momentum and heat on the gradient Richardson number, Ri. Due to the large-scale IGW, these dependencies lose their universality. The maximal value of the flux Richardson number (universal constant ≈0.2–0.25 in the no-IGW regime) becomes strongly variable. In the vertically homogeneous stratification, it increases with increasing wave energy and can even exceed 1. For heterogeneous stratification, when internal gravity waves propagate towards stronger stratification, the maximal flux Richardson number decreases with increasing wave energy, reaches zero and then becomes negative. In other words, the vertical flux of potential temperature becomes counter-gradient. Internal gravity waves also reduce the anisotropy of turbulence: in contrast to the mean wind shear, which generates only horizontal TKE, internal gravity waves generate both horizontal and vertical TKE. Internal gravity waves also increase the share of TPE in the turbulent total energy (TTE = TKE + TPE). A well-known effect of internal gravity waves is their direct contribution to the vertical transport of momentum. Depending on the direction (downward or upward), internal gravity waves either strengthen or weaken the total vertical flux of momentum. Predictions from the proposed model are consistent with available data from atmospheric and laboratory experiments, direct numerical simulations and large-eddy simulations.     

TURBULENCE STRUCTURE IN A STRATIFIED BOUNDARY LAYER UNDER STABLE CONDITIONS

Turbulence structure in stably stratified boundary layers isexperimentally investigated by using a thermally stratified wind tunnel. Astably stratified flow is created by heating the wind tunnel airflow to atemperature of about 50 °C and by cooling the test-section floor to asurface temperature of about 3 °C. In order to study the effect ofbuoyancy on turbulent boundary layers for a wide range of stability, thevelocity and temperature fluctuations are measured simultaneously at adownwind position of 23.5 m from the tunnel entrance, where the boundarylayer is fully developed. The Reynolds number, Re, ranges from 3.14× 104 to 1.27 × 105, and the bulk Richardson number, Ri,ranges from 0 to 1.33. Stable stratification rapidly suppresses thefluctuations of streamwise velocity and temperature as well as the verticalvelocity fluctuation. Momentum and heat fluxes are also significantlydecreased with increasing stability and become nearly zero in the lowest partof the boundary layer with strong stability. The vertical profiles ofturbulence quantities exhibit different behaviour in three distinct stabilityregimes, the neutral flows, the stratified flows with weak stability(Ri = 0.12, 0.20) and those with strong stability (Ri= 0.39,0.47, 1.33). Of these, the two regimes of stratified flows clearly showdifferent vertical profiles of the local gradient Richardson number Ri,separated by the critical Richardson number Ri cr of about 0.25. Moreover,turbulence quantities in stable conditions are well correlated with Ri.     

Turbulent characteristics and bulk transfer coefficients over the desert in the HEIFE area

Observations of surface-layer turbulence and turbulent fluxes were made over a desert in northwestern China as a part of HEIFE (HEIhe river Field Experiment). These show that the normalized variations of the vertical wind component and of the air temperature obey Monin-Obukhov similarity well, especially in free convective conditions. However, the variations of specific humidity do not obey Monin-Obukhov similarity.Mean bulk transfer coefficients of sensible heat and momentum flux are obtained as functions of stability over a wide stability range from the observed data of turbulent fluxes and mast profiles. However, the bulk transfer coefficient for water vapor could not be obtained because of the large scatter of the data. In free convective conditions, the sensible heat flux was found to be approximately proportional to the 1.4 power of temperature difference between the surface and 20m. The bulk transfer coefficient of sensible heat is also obtained as a function of the bulk Richardson number for practical convenience.     

Turbulence intensity and turbulent kinetic energy parameters over a heterogeneous terrain of Loess Plateau

A deep understanding of turbulence structure is important for investigating the characteristics of the atmospheric boundary layer, especially over heterogeneous terrain. In the present study, turbulence intensity and turbulent kinetic energy (TKE) parameters are analyzed for different conditions with respect to stability, wind direction and wind speed over a valley region of the Loess Plateau of China during December 2003 and January 2004. The purpose of the study is to examine whether the observed turbulence intensity and TKE parameters satisfy Monin-Obukhov similarity theory (MOST), and analyze the wind shear effect on, and thermal buoyancy function of, the TKE, despite the terrain heterogeneity. The results demonstrate that the normalized intensity of turbulence follows MOST for all stability in the horizontal and vertical directions, as well as the normalized TKE in the horizontal direction. The shear effect of the wind speed in the Loess Plateau region is strong in winter and could enhance turbulence for all stability conditions. During daytime, the buoyancy and shear effect together constitute the generation of TKE under unstable conditions. At night, the contribution of buoyancy to TKE is relatively small, and mechanical shearing is the main production form of turbulence.     

台风莫拉克 (0908) 影响期间近地层风特性

通过对台风莫拉克 (0908) 影响范围内的33座测风塔观测资料的分析可知:台风莫拉克越靠近陆地,风场的非对称性越明显,其行进方向的左侧测风塔风向呈逆时针旋转,右侧测风塔风向顺时针旋转。在远离台风莫拉克的地方风向稳定,湍流强度变化较平稳;在台风莫拉克登陆点附近,风向、风速和湍流强度均会出现突变。台风莫拉克影响期间,湍流强度与风速的关系未出现IEC标准曲线那样随风速增大稳定减小,其I₁₅达B级和A级及以上的平均湍流强度会在风速7~17 m·s-1形成一个峰值;无论南风或北风,风速越大,各层湍流强度差异趋于减小,同等风速、高度的湍流强度偏南大风均大于偏北大风。位于台风莫拉克登陆点北侧测风塔湍流强度随风速的增加先减小后增大,最终各高度全部超过IEC标准A级曲线,而位于南侧测风塔湍流强度随风速的变化比北侧小,并随风速增大趋于标准A级曲线;另外北侧测风塔湍流强度大于南侧,且各高度偏北大风湍流强度之间的差异比南侧相应风向明显,表明北侧垂直方向的扰动更强。台风莫拉克阵风系数为1.2~1.7,其随高度变化与地形有关,一般情况下随高度升高而减小,在复杂地形条件下不符合随高度升高减小的规律。     

Daily and annual cycle of CO2 concentration near the surface depending on boundary layer structure at a rural site in Spain

CO₂ in the rural atmosphere is related to respiration–photosynthesis processes, although the evolution of the low atmosphere is also a determinant factor. CO₂ concentrations were measured at surface and meteorological variables obtained from a radio acoustic sounding system sodar at a flat rural site during a 3-year campaign. Yearly and daily cycles of CO₂ were described. Maxima were observed in spring and autumn during the night. Wind speed and thermal structure of the lower atmosphere were analysed. Low level jets were observed during the night, their core proving lower in summer. Surface inversions observed with low winds reached up to 100 m. The turbulence layer which developed during the day extended up to 300–400 m and was capped by a stable layer. Median vertical wind speed reached 1 m s^?1 in super-adiabatic conditions in summer. Determination of decoupled low level jets proved difficult with the device used and corresponding concentrations were slightly higher than medians calculated with all the observations. The bulk Richardson number was calculated in the lower atmosphere and four intervals were considered: drainage, transitional, shear flows and unstable conditions. Median CO₂ concentrations were split according to these intervals. Higher values corresponded to drainage flow, which was associated to more stable conditions being less frequent and lower values to shear flow and unstable conditions, revealing a satisfactory link between the bulk Richardson number as a turbulence indicator in the low atmosphere and CO₂ surface concentrations.     

Terrain-influenced local wind forecasting for the Sasebo typhoon haven: Improved empirical techniques

Although the Sasebo, Japan harbor is usually a “typhoon haven” from tropical cyclone (TC) winds due to terrain-blocking effects, in rare cases damaging winds occur that may be attributed to terrain channeling. An empirical parametric model technique is developed and tested that includes consideration of the TC wind structure, land frictional effects, and terrain influences affecting the maximum wind speeds in the harbor when TCs pass within 200 nautical miles of Sasebo. The terrain influence is represented by two sets of wind direction-dependent acceleration factors. The first set, which is directly from the ratio of the local wind to the adjusted parametric wind for TCs passages during 2003–2010, provides mean values that represent the terrain blocking and channeling effects, but the variability with wind direction may be suspect. The second set derived from a large sample of reanalysis winds not limited to TCs has better variability properties, but is not easily related to just the TC passages. A new nomogram modified to include TC wind structure has higher estimates of Sasebo sustained winds for some TC tracks that may be related to terrain influences, but is limited due to the number of TC structure estimates in the developmental sample. These empirical models have the advantage of ease and low cost for future use in also estimating the combined uncertainty in the local winds in Sasebo harbor due to TCs.