Artificial neural network assisted Bayesian calibration of climate models

We demonstrate and validate a Bayesian approach to model calibration applicable to computationally expensive General Circulation Models (GCMs) that includes a posterior estimate of the intrinsic structural error of the model. Bayesian artificial neural networks (BANNs) are trained with output from a GCM and used as emulators of the full model to allow a computationally efficient Markov Chain Monte Carlo (MCMC) sampling of the posterior for the GCM parameters calibrated against seasonal climatologies of temperature, pressure, and humidity. We validate the methodology by calibrating to targets produced by a model run with added noise. We then demonstrate a calibration of five GCM parameters against an observational data set. The approach accounts for both parametric and structural uncertainties of the model as well as uncertainties associated with the observational calibration data. This enables the generation of statistically rigorous probabilistic forecasts for future climate states. All calibration experiments are performed with emulators trained using a maximum of one hundred model runs, in accord with typical resource restrictions imposed by computationally expensive models. We conclude by summarizing remaining issues to address in order to create a complete and validated operational methodology for objective calibration of computationally expensive models.     

A Bayesian statistical model for deriving the predictive distribution of hydroclimatic variables

Recent publications have provided evidence that hydrological processes exhibit a scaling behaviour, also known as the Hurst phenomenon. An appropriate way to model this behaviour is to use the Hurst-Kolmogorov stochastic process. The Hurst-Kolmogorov process entails high autocorrelations even for large lags, as well as high variability even at climatic scales. A problem that, thus, arises is how to incorporate the observed past hydroclimatic data in deriving the predictive distribution of hydroclimatic processes at climatic time scales. Here with the use of Bayesian techniques we create a framework to solve the aforementioned problem. We assume that there is no prior information for the parameters of the process and use a non-informative prior distribution. We apply this method with real-world data to derive the posterior distribution of the parameters and the posterior predictive distribution of various 30-year moving average climatic variables. The marginal distributions we examine are the normal and the truncated normal (for nonnegative variables). We also compare the results with two alternative models, one that assumes independence in time and one with Markovian dependence, and the results are dramatically different. The conclusion is that this framework is appropriate for the prediction of future hydroclimatic variables conditional on the observations.     

Modelling of concentration fluctuations in canopy turbulence

The knowledge of the concentration probability density function (pdf) is of importance in a number of practical applications, and a Lagrangian stochastic (LS) pdf model has been developed to predict statistics and concentration pdf generated by continuous releases of non-reactive and reactive substances in canopy generated turbulence. Turbulent dispersion is modelled using a LS model including the effects of wind shear and along-wind turbulence. The dissipation of concentration fluctuations associated with turbulence and molecular diffusivity is simulated by an Interaction by Exchange with the Conditional Mean (IECM) micromixing model. A general procedure to obtain the micromixing time scale needed in the IECM model useful in non-homogeneous conditions and for single and multiple scalar sources has been developed. An efficient algorithm based on a nested grid approach with particle splitting, merging techniques and time averaging has been used, thus allowing the calculation for cases of practical interest. The model has been tested against wind-tunnel experiments of single line and multiple line releases in a canopy layer. The approach accounted for chemical reactions in a straightforward manner with no closure assumptions, but here the validation is limited to non-reacting scalars.     

A new method for multi-point pollution source identification

对于污染源源项特征(数量,位置及排放强度)的快速且精确估计是污染事件应急响应的关键.与单点源估计相比,多点源的重建更具挑战性.本文提出了一种新的针对于多点源污染事件的两步反演算法,该算法通过结合大气化学模式与有限的浓度观测数据以实现对于未知数量的多点源的准确估计.在其计算过程中,无需任何未知量的先验信息,且可以自动识别污染源的数量,并确定每一个污染源的位置及强度.本文通过使用若干组理想试验验证了算法的适用性,试验结果表明,该算法可准确估计单点源,两点源和三点源的个数及位置,强度的估计误差可基本忽略.且该算法的估计精度和计算效率不会随着点源个数的增加而减弱.     

A nonlinear stochastic low-order energy balance climate model

The effects of stochastic forcing on a one-dimensional, energy balance climate model are considered. A linear, stochastic model is reviewed in analogy with the Brownian motion problem from classical statistical mechanics. An analogous nonlinear model is studied and shows different behavior from the linear model. The source of the nonlinearity is the dynamical heat transport. The role of nonlinearity in coupling different temporal and spatial scales of the atmosphere is examined. The Fokker-Planck equation from statistical mechanics is used to obtain a time evolution equation for the probability density function for the climate, and the climatic potential function is calculated. Analytical solutions to the steady-state Fokker-Planck equation are obtained, while the time-dependent solution is obtained numerically. The spread of the energy produced by a stochastic forcing element is found to be characterized by movement mainly from smaller to larger scales. Forced and free variations of climate are also explicitly considered.     

Application of a Bivariate Gamma Distribution for a Chemically Reacting Plume in the Atmosphere

The joint concentration probability density function of two reactive chemical species is modelled using a bivariate Gamma distribution coupled with a three-dimensional fluctuating plume model able to simulate the diffusion and mixing of turbulent plumes. A wind-tunnel experiment (Brown and Bilger, J Fluid Mech 312:373–407, 1996), carried out in homogeneous unbounded turbulence, in which nitrogen oxide is released from a point source in an ozone doped background and the chemical reactions take place in non-equilibrium conditions, is considered as a test case. The model is based on a stochastic Langevin equation reproducing the barycentre position distribution through a proper low-pass filter for the turbulence length scales. While the meandering large-scale motion of the plume is directly simulated, the internal mixing relative to the centroid is reproduced using a bivariate Gamma density function. The effect of turbulence on the chemical reaction (segregation), which in this case has not yet attained equilibrium, is directly evaluated through the covariance of the tracer concentration fields. The computed mean concentrations and the O₃–NO concentration covariance are also compared with those obtained by the Alessandrini and Ferrero Lagrangian single particle model (Alessandrini and Ferrero, Physica A 388:1375–1387, 2009) that entails an ad hoc parametrization for the segregation coefficient.     

Forward-in-time and Backward-in-time Dispersion in the Convective Boundary Layer: the Concentration Footprint

The turbulence field obtained using a large-eddy simulation model is used to simulate particle dispersion in the convective boundary layer with both forward-in-time and backward-in-time modes. A Lagrangian stochastic model is used to treat subgrid-scale turbulence. Results of forward dispersion match both laboratory experiments and previous numerical studies for different release heights in the convective boundary layer. Results obtained from backward dispersion show obvious asymmetry when directly compared to results from forward dispersion. However, a direct comparison of forward and backward dispersion has no apparent physical meaning and might be misleading. Results of backward dispersion can be interpreted as three-dimensional or generalized concentration footprints, which indicate that sources in the entire boundary layer, not only sources at the surface, may influence a concentration measurement at a point. Footprints at four source heights in the convective boundary layer corresponding to four receptors are derived using forward and backward dispersion methods. The agreement among footprints derived with forward and backward methods illustrates the equivalence between both approaches. The paper shows explicitly that Lagrangian simulations can yield identical footprints using forward and backward methods in horizontally homogeneous turbulence.     

Dispersion of a Passive Scalar Fluctuating Plume in a Turbulent Boundary Layer. Part III: Stochastic Modelling

We analyze the reliability of the Lagrangian stochastic micromixing method in predicting higher-order statistics of the passive scalar concentration induced by an elevated source (of varying diameter) placed in a turbulent boundary layer. To that purpose we analyze two different modelling approaches by testing their results against the wind-tunnel measurements discussed in Part I (Nironi et al., Boundary-Layer Meteorology, 2015, Vol. 156, 415–446). The first is a probability density function (PDF) micromixing model that simulates the effects of the molecular diffusivity on the concentration fluctuations by taking into account the background particles. The second is a new model, named VP\(\varGamma \), conceived in order to minimize the computational costs. This is based on the volumetric particle approach providing estimates of the first two concentration moments with no need for the simulation of the background particles. In this second approach, higher-order moments are computed based on the estimates of these two moments and under the assumption that the concentration PDF is a Gamma distribution. The comparisons concern the spatial distribution of the first four moments of the concentration and the evolution of the PDF along the plume centreline. The novelty of this work is twofold: (i) we perform a systematic comparison of the results of micro-mixing Lagrangian models against experiments providing profiles of the first four moments of the concentration within an inhomogeneous and anisotropic turbulent flow, and (ii) we show the reliability of the VP\(\varGamma \) model as an operational tool for the prediction of the PDF of the concentration.     

A Velocity–Dissipation Lagrangian Stochastic Model for Turbulent Dispersion in Atmospheric Boundary-Layer and Canopy Flows

An extended Lagrangian stochastic dispersion model that includes time variations of the turbulent kinetic energy dissipation rate is proposed. The instantaneous dissipation rate is described by a log-normal distribution to account for rare and intense bursts of dissipation occurring over short durations. This behaviour of the instantaneous dissipation rate is consistent with field measurements inside a pine forest and with published dissipation rate measurements in the atmospheric surface layer. The extended model is also shown to satisfy the well-mixed condition even for the highly inhomogeneous case of canopy flow. Application of this model to atmospheric boundary-layer and canopy flows reveals two types of motion that cannot be predicted by conventional dispersion models: a strong sweeping motion of particles towards the ground, and strong intermittent ejections of particles from the surface or canopy layer, which allows these particles to escape low-velocity regions to a high-velocity zone in the free air above. This ejective phenomenon increases the probability of marked fluid particles to reach far regions, creating a heavy tail in the mean concentration far from the scalar source.     

Analysis of wind tunnel dispersion data over two-dimensional obstacles

An analysis of wind tunnel data of dispersion from elevated point sources over a flat floor and gently sloping, 2-D hills is performed. (The data were obtained by Khurshudyan et al., 1981.) Formulas for the mixing lengths and the Lagrangian time scales are tested, suitable for use in various dispersion models. Some expressions for the vertical first moments of the plume concentration distribution suitable for shear flow (Hunt, 1985) are also tested.Then, a normalization is suggested, based on the source mean flow and turbulence parameters, for the ground-level concentration maximum value and position along the plume centerline. Using this normalization, the maximum position is almost constant, regardless of source height variation and of whether the hill is present or not, at least for source positions upstream or over the top.The maximum values allow the determination of normalized terrain amplification factors TAF_N, which are shown to be in most cases closer to one than the corresponding TAF obtained without normalization.     

The Transport Time pdf for a Simple Turbulent Flow

In a turbulent fluid, the time a particle needs to travel from a point source to the observation point, can be considered as a random variable. It is shown that the probability density function (pdf) for this random variable is determined by the Lagrangian particle position pdf. The characteristics of the transport time pdf are discussed for the simple case of a turbulent fluid moving with a constant mean velocity.     

基于贝叶斯模型的器测、古气候重建与气候模拟数据的融合试验

气象部门馆藏的西部最早的器测气象资料始于20世纪30年代,不能满足建立20世纪以来中国气候变化序列的需求,而古气候重建或气候模拟资料则可以延伸到器测时代以前。为了探讨长序列多源气候资料序列融合方法,采用贝叶斯方法对中国北疆地区8条树轮气温重建资料、器测资料与国际耦合模式比较计划第5阶段（CMIP5）模式模拟资料进行了融合试验。首先利用器测资料对气温代用资料进行校验与网格重建,并以此作为贝叶斯模型的先验分布,然后,用泰勒图选出了该区域气候模拟效果最佳的几个模式;最后将网格重建和气候模拟序列用贝叶斯模型进行了融合试验。结果表明,贝叶斯融合模型能有效提取各种数据来源的有用信息进行融合,融合结果的长期变化（线性）趋势更接近器测气候序列,并在一定程度上提高了序列的精度,减小了结果的不确定性;并且,融合结果能够纠正先验分布及气候模拟数据的明显偏差,为长年代气候序列重建提供了一个可行的思路。      

An Advanced Puff Model Based On A Mixed Eulerian/Lagrangian Approach For Turbulent Dispersion In The Convective Boundary Layer

An advanced model aimed at describing the problem of dispersion in theconvective boundary layer is proposed. The pollutant particles are groupedin clusters and modelled as Gaussian puffs. The expansion of each puff ismodelled according to the concept of relative dispersion and expressed interms of the spectral properties of the energy containing eddies of the turbulent field. The centre of mass of each puff is moved along a stochastic trajectory, obtained using a Lagrangian stochastic model and filtering the velocity with a recursive Kalman filter. At any instant, a filtering procedure, depending both on travel time and on puff size, acts to select spectral components involved in the expansion and in the meandering of the puff. Such an approach requires only a moderate number of puff releases, so that the proposed model is faster to run than a standard Lagrangian model. On the other hand, unlike the traditional puff model, it allows us to simulate both expansion and meandering of the puff. Therefore, it is well suited to simulate dispersion when the turbulent structures are larger thanthe plume dimensions, as for example in convective conditions. Being based onspectral formulations in both Eulerian and Lagrangian parts, the model is consistent in all the turbulent parameterizations utilised. Comparisons with a standard Lagrangian particle model as well as with a classical convective experimental dataset show good performance of the proposed model.     

粒子群优化算法在随机分布控制中的应用

将粒子群优化算法应用到随机分布系统中,其随机系统控制目标不局限于传统的均值和方差,而是估算某些变量的概率密度函数.该方法能减少基于泛函算子模型的随机分布控制算法在仿真过程中的计算量,避免计算中间变量的概率密度函数,且对模型的要求不高,从而使控制结果更加精确高效.     

Assessment of a stochastic downscaling methodology in generating an ensemble of hourly future climate time series

This study extends a stochastic downscaling methodology to generation of an ensemble of hourly time series of meteorological variables that express possible future climate conditions at a point-scale. The stochastic downscaling uses general circulation model (GCM) realizations and an hourly weather generator, the Advanced WEather GENerator (AWE-GEN). Marginal distributions of factors of change are computed for several climate statistics using a Bayesian methodology that can weight GCM realizations based on the model relative performance with respect to a historical climate and a degree of disagreement in projecting future conditions. A Monte Carlo technique is used to sample the factors of change from their respective marginal distributions. As a comparison with traditional approaches, factors of change are also estimated by averaging GCM realizations. With either approach, the derived factors of change are applied to the climate statistics inferred from historical observations to re-evaluate parameters of the weather generator. The re-parameterized generator yields hourly time series of meteorological variables that can be considered to be representative of future climate conditions. In this study, the time series are generated in an ensemble mode to fully reflect the uncertainty of GCM projections, climate stochasticity, as well as uncertainties of the downscaling procedure. Applications of the methodology in reproducing future climate conditions for the periods of 2000–2009, 2046–2065 and 2081–2100, using the period of 1962–1992 as the historical baseline are discussed for the location of Firenze (Italy). The inferences of the methodology for the period of 2000–2009 are tested against observations to assess reliability of the stochastic downscaling procedure in reproducing statistics of meteorological variables at different time scales.     

基于模式先验信息的贝叶斯集合降水概率预报试验

为了更好地利用降水预报历史先验概率分布函数信息修订集合概率预报效果,基于贝叶斯原理和贝叶斯降水概率预报模型,分别使用1952—2007年历史观测资料和2009—2011年6月24~120 h中国T213全球集合预报历史资料作为先验信息,对中国不同气候区代表站（广州、南京、武汉和成都）建立贝叶斯降水概率预报模型,对比不同先验信息下集合成员与集成贝叶斯降水概率预报拟合结果差异,分析先验信息对贝叶斯降水概率预报模型的影响,在此基础上,采用模式先验信息的贝叶斯降水概率预报模型,进行2008年6月降水概率预报试验。试验结果表明,由T213集合预报产生的先验信息较历史观测资料产生的先验信息更优,当先验信息的降水概率分布函数曲率最大处偏向降水大值区时,贝叶斯模型的降水预报结果也偏向降水大值区,反之亦然。结果还显示,先验信息对贝叶斯降水概率预报模型有重要影响,若先验信息偏向更多更大降水量时,贝叶斯降水概率预报对有降水的预报更优,若降水先验信息偏向更少更小降水量时,对无雨或微量降水预报效果越好。     

A Wind Tunnel and Numerical Investigation of Turbulent Dispersion in Coastal Atmospheric Boundary Layers

Thermal internal boundary layers in onshore air flows have a significant influence on pollutant diffusion in coastal areas. Although several models for this diffusion problem exist, measurements for model verification are scarce. In this paper, we present a set of wind tunnel observations and examine the performance of a Lagrangian stochastic model. The good agreement between the model simulation and the tunnel measurements confirms the usefulness of the Lagrangian stochastic model for practical purposes. Sensitivity tests of the model to turbulence statistics show that uncertainty in velocity skewness to the extent of observational scatter does not seem to have a significant influence on pollutant dispersion, while uncertainties in turbulence intensity (variance) significantly influence the dispersion pattern.     

热带海洋对大气进行非绝热加热的随机效应的进一步研究

本文考虑了热带海洋对大气进行非绝热加热过程中海温起伏的随机效应,建立了朗之万方程形式的描写大气热量变化的发展方程。由该随机微分方程的定态解,给出了加热势函数和概率密度函数。在确定的热力学参数下,利用实际海温起伏方差值,计算求得了加热势函数的分布及概率密度分布曲线。文中还进一步计算了概率密度流,得到了在两种稳定状态之间穿透势垒的弛豫时间。计算结果表明,海温异常的随机效应是一个长周期过程,时间尺度约为140天,可以用实际测得的拖曳系数C_D和海温起伏方差q2值对它进行预测。      

一个具有统计意义的参量

长期以来,在实际工作中我们一直用频率(k/n)这个统计学参量来估计概率,对小样本容量的事件,求概率已成为问题,给统计气象学带来很多不便。本文结合评价预报能力推导一个新的统计学参量,以期弥补频率在统计学中所呈现的缺陷。而且讨论了这个新参量在气象学中的应用。