Examination of Schumann's method of judging the realizability of turbulence closure models

Schumann's (1977) method of judging the realizability of turbulence closure models is examined. The relation between model constants obtained by this method does not always ensure the realizability of double moments. Still, this relation shows the degree of realizability. It is likely that Schumann's method is effective to determine values of unknown constants in second-order closure models.     

On the gap in the spectra of surface-layer atmospheric turbulence

A large set of tower data was used to identify the gap that separates small-scale turbulence and mesoscale structures in the cospectra of surface fluxes. The cospectra were obtained using a multi-resolution decomposition algorithm. The gap time scale τ _g was found by fitting a fifth-order polynomial to the cospectra and identifying special points occurring after the peak at small scales. In unstable conditions (day) τ _g was found to fall as the mean wind speed increased, while no such dependence was observed in stable conditions (night). The gap scale was found to change very weakly with stability both in moderately stable and moderately unstable conditions, with a sharp drop from about 1100 to 250 s occurring in near-neutral conditions. The vertical fluxes computed at different averaging intervals were found to correlate exceptionally well with each other, the scatter being somewhat larger during the night. Although considerable discrepancy may occur for individual records, when averaged over 10 months, the difference in the flux estimated at 7 to 109 min intervals never exceeded 4%, which is comparable or less than the instrumental error.     

On the sensitivity of mesoscale models to surface-layer parameterization constants

The Colorado State University standard mesoscale model is used to evaluate the sensitivity of one-dimensional (1D) and two-dimensional (2D) fields to differences in surface-layer parameterization constants. Such differences reflect the range in the published values of the von Karman constant, Monin-Obukhov stability functions and the temperature roughness length at the surface. The sensitivity of 1D boundary-layer structure, and 2D sea-breeze intensity, is generally less than that found in published comparisons related to turbulence closure schemes generally.     

A generalization of the Kolmogorov-von Kármán relationship and some further implications on the values of the constants

A general relation between the Kolmogorov (₁) and von Kármán (k) constants appropriate to flows in the surface boundary layer is obtained by including stability and divergence dependent terms in the development. The result is used to show that the author's earlier inference of the valuek = 0.36 drawn from the observed value ,k ^4/3=0.141 cannot have been underestimated due to the neglect of stability or divergence effects. It is concluded that if k is to be 0.4, then ₁ must be 0.5.Work performed under the auspices of the U.S. Energy Research and Development Administration.     

Characterizing the severe turbulence environments associated with commercial aviation accidents. A real-time turbulence model (RTTM) designed for the operational prediction of hazardous aviation turbulence environments

Summary In this paper, we will focus on the real-time prediction of environments that are predisposed to producing moderate-severe (hazardous) aviation turbulence. We will describe the numerical model and its postprocessing system that is designed for said prediction of environments predisposed to severe aviation turbulence as well as presenting numerous examples of its utility. The purpose of this paper is to demonstrate that simple hydrostatic precursor circulations organize regions of preferred wave breaking and turbulence at the nonhydrostatic scales of motion. This will be demonstrated with a hydrostatic numerical modeling system, which can be run in real time on a very inexpensive university computer workstation employing simple forecast indices. The forecast system is designed to efficiently support forecasters who are directing research aircraft to measure the environment immediately surrounding turbulence. The numerical model is MASS version 5.13, which is integrated over three different grid matrices in real-time on a university workstation in support of NASA-Langley’s B-757 turbulence research flight missions. The model horizontal resolutions are 60, 30, and 15 km and the grids are centered over the region of operational NASA-Langley B-757 turbulence flight missions. The postprocessing system includes several turbulence-related products including four turbulence forecasting indices, winds, streamlines, turbulence kinetic energy, and Richardson numbers. Additionally there are convective products including precipitation, cloud height, cloud mass fluxes, lifted index, and K-index. Furthermore, soundings, sounding parameters, and Froude number plots are also provided. The horizontal cross section plot products are provided from 16,000–46,000 feet in 2,000 feet intervals. Products are available every three hours at the 60 and 30 km grid interval and every 1.5 hours at the 15 km grid interval. The model is initialized from the NWS ETA analyses and integrated two times a day.     

Determination of similarity functions of the resistance laws for the planetary boundary layer using surface-layer similarity functions

Functional forms of the universal similarity functions A, B (for wind components parallel and normal to the surface stress), and C (for potential temperature difference) are determined based on the generalized theory of the resistance laws for the Planetary Boundary Layer (PBL). The similarity-profile functions for the surface layer are matched with the velocity and temperature-defect profiles that are assumed to have shapes modified by certain powers of nondimensional height z/h, where h is the PBL height. The powers of the outer-layer profile functions are determined, so that the functions become negligible in the surface layer. To close the temperature defect law, an assumption that the temperature gradient across the top of the PBL is continuous with the stratification of the overlying atmosphere is used. The result of this assumption is that nondimensional momentum and temperature profiles in the PBL can be described in terms of four basic ratios: (1) roughness ratio = /h (2) scale-height ratio =|f|h/u_*, (3) ambient stratification parameter =h/_*, and (4) stability parameter =h/L, where L is the Monin-Obukhov length, z₀ is the surface roughness, is the upper-air stratification, u _* is the friction velocity, and _* is the temperature scale at the surface. For stable conditions, the scale-height ratio can be related to the atmospheric stability and the upperair stratification, and the generalized similarity and Rossby number similarity theories become identical. Under appropriate boundary conditions, function A is explicitly dependent on the stability parameter , while B is a function of scale-height ratio , which in turn depends on the stability. Function C is shown to be dependent on the stability and the upper-air stratification, due to the closure assumption used for the temperature profile.The suggested functional forms are compared with other empirical approximations by several authors. The general framework used to determine the functional forms needs to be tested against good boundary-layer measurements.     

Parameterization of the surface-layer exchange coefficients for atmospheric models

A new surface-flux parameterization is presented and its impact on climate simulations with the Canadian Centre for Climate Modelling and Analysis (CCCMA) general circulation model (GCM) is discussed. The parameterization is based on the Monin-Obukhov similarity theory using well established flux-profile relationships for the unstable conditions. However, recently proposed new relationships are used in stable conditions. The new formulation allows different roughness lengths for heat and momentum, and gives transfer coefficients that are in agreement with Monin-Obukhov similarity theory. It also includes a parameterization for the free-convective boundary layer, which often occurs over warm surfaces within light winds. In circumstances where the surface layer is not neutrally stratified the proposed flux parameterization yields surface transfer coefficients that are different from those resulting from the standard surface flux formulation used in the GCM. The most marked effects of implementing the new formulation in the GCM are found over land and adjacent oceanic regions in winter where significant differences are found in the surface heat and moisture fluxes and surface temperatures.     

一种条件概率预报方法

本文提出一种计算较简便的非线性的概率预报方法——条件概率法。本方法在单站长期天气预报中使用了66次,结果相当于将预报量的观测资料分为五级时,其平均绝对误差接近于一级。     

A skillful method for precipitation prediction over eastern China

降水作为全球水循环的重要组成,与人们的生产生活密切相关.有效的降水预测对于防灾减灾,以及经济的可持续发展至关重要.然而,由于影响降水过程的复杂性,当前降水预测还存在诸多挑战.针对我国东部夏季降水,我们提出年际增量结合经验正交分解的新统计预测方法.首先计算降水年际增量的主模态,然后针对主模态时间序列构建预测模型,用预测的...     

Rate constants for reactions of OH radicals with some Br-containing haloalkanes

Rate constants have been measured for the gas-phase reactions of hydroxyl radical with two halons and three of their proposed substitutes and also with CHClBr-CF₃ using the discharge-flow-EPR technique over the temperature range 298–460 K. The following Arrhenius expressions have been derived (units are 10^–13 cm³ molecule^–1 s^–1): (9.3 _–0.9 ^+1.0 ) exp{–(1326±33)/T} for CHF₂Br; (7.2 _–0.6 ^+0.7 ) exp{–(1111±32)/T} for CHFBrCF₃; (8.5 _–0.8 ^+0.9 ) exp{–(1113±35)/T} for CH₂BrCF₃; (12.8 _–1.2 ^+1.5 ) exp{–(995±38)/T} for CHClBrCF₃. The rate constants at 298 K have been estimated to be <2×10^–17 cm³ molecule^–1 s^–1 for CF₃Br and CF₂Br—CF₂Br. The atmospheric lifetimes due to hydroxyl attack have been estimated to be 5.5, 3.3, 2.8, and 1.2 years for CHF₂Br, CHFBr—CF₃, CH₂Br—CF₃ and CHClBr—CF₃, respectively.     

A Note on Some Methods Suitable for Verifying and Correcting the Prediction of Climatic Anomaly

The weighted correlation coefficient of the predicted and observed anomalies and the ratio of the weighted norm of predicted anomaly to the observed one, both together, are suggested to be suitable for the estimating of the correctness of climate prediction. The former shows the similarity of the two patterns, and the later indicates the correctness of the predicted intensity of the anomaly. The weighting function can be different for different emphasis, for example, a constant weight means that the correlation coefficient is the conventional one, but same non-uniform weight leads to the ratio of correct sign of the anomaly, the stepwise weight leads lo the formulation of correctness of prediction represented by grades of the anomaly, and so on.Three methods for making correction to the prediction are given in this paper. After subtracting lie mean error of the prediction, one method is developed for maximizing the similarity between the predicted and observed patterns, based on the transformation of the spatial coordinates. Another method is to minimize the mean difference between the two fields. This method can also be simplified as similar to the “optimum interpolation” in the objective analysis of weather chart. The third method is based on the expansion of the anomaly into series or EOF, where the coefficients are the predicted but the EOFs are taken as the “observed” calculated from historical samples.     

A forecast error correction method in numerical weather prediction by using recent multiple-time evolution data

The initial value error and the imperfect numerical model are usually considered as error sources of numerical weather prediction (NWP). By using past multi-time observations and model output, this study proposes a method to estimate imperfect numerical model error. This method can be inversely estimated through expressing the model error as a Lagrange interpolation polynomial, while the coefficients of polynomial are determined by past model performance. However, for practical application in the full NWP model, it is necessary to determine the following criteria: (1) the length of past data sufficient for estimation of the model errors, (2) a proper method of estimating the term "model integration with the exact solution" when solving the inverse problem, and (3) the extent to which this scheme is sensitive to the observational errors. In this study, such issues are resolved using a simple linear model, and an advection-diffusion model is applied to discuss the sensitivity of the method to an artificial error source. The results indicate that the forecast errors can be largely reduced using the proposed method if the proper length of past data is chosen. To address the three problems, it is determined that (1) a few data limited by the order of the corrector can be used, (2) trapezoidal approximation can be employed to estimate the "term" in this study; however, a more accurate method should be explored for an operational NWP model, and (3) the correction is sensitive to observational error.     

集合预报多尺度奇异向量初值扰动方法研究

目前国际上采用的奇异向量集合预报初值扰动法对于初值不确定性的描述存在一定的不足,为了更有效地反映初始误差的时空多尺度特性,基于GRAPES全球奇异向量计算技术,计算了不同空间分辨率及不同最优时间间隔的多个尺度的奇异向量,并采用基于高斯分布的线性组合法来构造多尺度奇异向量的扰动初值,以代表在相空间中增长最快的多尺度初值误差模态。通过2019年1月19日的初值扰动集合预报试验,对比分析了单一尺度奇异向量初值扰动法与多尺度初值扰动法的扰动特征及集合预报效果。结果表明,多尺度奇异向量初值扰动法为区域集合预报提供的初始扰动场是合理的,扰动的大小随时间增长,且在空间分布上较好地反映了当前大气的斜压不稳定特征。此外,多尺度奇异向量扰动可以描述一定的大尺度以及中小尺度运动误差特征,较单一尺度奇异向量扰动能反映出更多初始场的不确定性信息。检验分析表明,GRAPES多尺度奇异向量集合预报在集合一致性、连续等级概率评分、离群值等方面有一定的优势,相比于单一尺度奇异向量法有较好的预报技巧。因此,基于GRAPES的多尺度奇异向量初值扰动法对于集合预报的预报效果有一定的提高,能为构建一套完善的GRAPES区域奇异向量集合预报系统提供一定的科学依据和应用基础。      

A three-dimensional model for calculating the concentration distribution in inhomogeneous turbulence

A new approach for calculating the concentration distribution in inhomogeneous turbulence is suggested. The model is a 3-D model, constrained to describe incompressible flow. The model requires a knowledge of the covariance matrix of the Eulerian velocities and the two-point third moments. The model is applied for three types of turbulent field: homogeneous isotropic turbulence, constant flux neutral boundary layer and free convective turbulence. The required Eulerian moments are calculated using the eddy model of the turbulent field. Concentration moments are calculated and results are compared to experimental data. Other model predictions which have no experimental support can be compared to measurements when available.     

Determination of rate constants for reactions of some hydrohaloalkanes with OH radicals and their atmospheric lifetimes

Rate constants have been measured for the gas-phase reactions of hydroxyl radical with partly halogenated alkanes using the discharge-flow-EPR technique over the temperature range 298–460 K. The following Arrhenius expressions have been derived (units 10^–13 cm³ molecule^–1 s^–1): (8.1 _–1.2 ^+1.5 ) exp{–(1516±53)/T} for CHF₂Cl (HCFC-22); (10.3 _–1.5 ^+1.8 ) exp{–(1588±52)/T} for CH₂FCF₃ (HFC-134a); (11.3 _–1.6 ^+2.1 ) exp{–(918±52)/T} for CHCl₂CF₂Cl (HCFC-122); (9.2 _–2.0 ^+2.5 ) exp{–(1281±85)/T} for CHFClCF₂Cl (HCFC-123a).The atmospheric lifetimes for the substances have been estimated to be 12.6, 12.9, 1.05, and 4.8 years, respectively, and the accuracy of the estimates is discussed.     

一种初始方程中应用实测风进行风场初值化的方法

本文提出一种利用实测风场、高度场、温度场和地面三小时气压变化资料,考虑风场和质量场之间基本满足准地转平衡关系,大气具有准无辐散性,但又保留一部分与地面气压变化相应散度的地转偏差,将以实测的等压面风场插到σ坐标的风场进行订正的初值化方法,并用一个单时资料进行初步试验.文中还对风场初值化问题进行了讨论.