Ensemble prediction experiments using conditional nonlinear optimal perturbation

Two methods for initialization of ensemble forecasts are compared, namely, singular vector (SV) and conditional nonlinear optimal perturbation (CNOP). The comparison is done for forecast lengths of up to 10 days with a three-level quasi-geostrophic (QG) atmospheric model in a perfect model scenario. Ten cases are randomly selected from 1982/1983 winter to 1993/1994 winter (from December to the following February). Anomaly correlation coefficient (ACC) is adopted as a tool to measure the quality of the predicted ensembles on the Northern Hemisphere 500 hPa geopotential height. The results show that the forecast quality of ensemble samples in which the first SV is replaced by CNOP is higher than that of samples composed of only SVs in the medium range, based on the occurrence of weather regime transitions in Northern Hemisphere after about four days. Besides, the reliability of ensemble forecasts is evaluated by the Rank Histograms. The above conclusions confirm and extend those reached earlier by the authors, which stated that the introduction of CNOP improves the forecast skill under the condition that the analysis error belongs to a kind of fast-growing error by using a barotropic QG model. Supported by Knowledge Innovation Project of the Chinese Academy of Sciences (Grant No. KZCX3-SW-230), National Natural Science Foundation of China (Grant Nos. 40675030, 40633016)     

A SVD-based ensemble projection algorithm for calculating the conditional nonlinear optimal perturbation

Conditional nonlinear optimal perturbation(CNOP) is an extension of the linear singular vector technique in the nonlinear regime.It represents the initial perturbation that is subjected to a given physical constraint,and results in the largest nonlinear evolution at the prediction time.CNOP-type errors play an important role in the predictability of weather and climate.Generally,when calculating CNOP in a complicated numerical model,we need the gradient of the objective function with respect to the initial perturbations to provide the descent direction for searching the phase space.The adjoint technique is widely used to calculate the gradient of the objective function.However,it is difficult and cumbersome to construct the adjoint model of a complicated numerical model,which imposes a limitation on the application of CNOP.Based on previous research,this study proposes a new ensemble projection algorithm based on singular vector decomposition(SVD).The new algorithm avoids the localization procedure of previous ensemble projection algorithms,and overcomes the uncertainty caused by choosing the localization radius empirically.The new algorithm is applied to calculate the CNOP in an intermediate forecasting model.The results show that the CNOP obtained by the new ensemble-based algorithm can effectively approximate that calculated by the adjoint algorithm,and retains the general spatial characteristics of the latter.Hence,the new SVD-based ensemble projection algorithm proposed in this study is an effective method of approximating the CNOP.     

The application of the orthogonal conditional nonlinear optimal perturbations method to typhoon track ensemble forecasts

The orthogonal conditional nonlinear optimal perturbations (CNOPs) method, orthogonal singular vectors (SVs)method and CNOP+SVs method, which is similar to the orthogonal SVs method but replaces the leading SV (LSV) with the first CNOP, are adopted in both the Lorenz-96 model and Pennsylvania State University/National Center for Atmospheric Research (PSU/NCAR) Fifth-Generation Mesoscale Model (MM5) for ensemble forecasts. Using the MM5, typhoon track ensemble forecasting experiments are conducted for strong Typhoon Matsa in 2005. The results of the Lorenz-96 model show that the CNOP+SVs method has a higher ensemble forecast skill than the orthogonal SVs method, but ensemble forecasts using the orthogonal CNOPs method have the highest forecast skill. The results from the MM5 show that orthogonal CNOPs have a wider horizontal distribution and better describe the forecast uncertainties compared with SVs. When generating the ensemble mean forecast, equally averaging the ensemble members in addition to the anomalously perturbed forecast members may contribute to a higher forecast skill than equally averaging all of the ensemble members. Furthermore, for given initial perturbation amplitudes, the CNOP+SVs method may not have an ensemble forecast skill greater than that of the orthogonal SVs method, but the orthogonal CNOPs method is likely to have the highest forecast skill. Compared with SVs, orthogonal CNOPs fully consider the influence of nonlinear physical processes on the forecast results; therefore, considering the influence of nonlinearity may be important when generating fast-growing initial ensemble perturbations. All of the results show that the orthogonal CNOP method may be a potential new approach for ensemble forecasting.     

Extended Kalman filter for material parameter estimation in nonlinear structural finite element models using direct differentiation method

This paper presents a novel nonlinear finite element (FE) model updating framework, in which advanced nonlinear structural FE modeling and analysis techniques are used jointly with the extended Kalman filter (EKF) to estimate time‐invariant parameters associated to the nonlinear material constitutive models used in the FE model of the structural system of interest. The EKF as a parameter estimation tool requires the computation of structural FE response sensitivities (total partial derivatives) with respect to the material parameters to be estimated. Employing the direct differentiation method, which is a well‐established procedure for FE response sensitivity analysis, facilitates the application of the EKF in the parameter estimation problem. To verify the proposed nonlinear FE model updating framework, two proof‐of‐concept examples are presented. For each example, the FE‐simulated response of a realistic prototype structure to a set of earthquake ground motions of varying intensity is polluted with artificial measurement noise and used as structural response measurement to estimate the assumed unknown material parameters using the proposed nonlinear FE model updating framework. The first example consists of a cantilever steel bridge column with three unknown material parameters, while a three‐story three‐bay moment resisting steel frame with six unknown material parameters is used as second example. Both examples demonstrate the excellent performance of the proposed parameter estimation framework even in the presence of high measurement noise. Copyright © 2015 John Wiley & Sons, Ltd.     

Experimental study on soil CO2 emission in the alpine grassland ecosystem on Tibetan Plateau

The Tibetan Plateau, the Roof of the World, is the highest plateau with a mean elevation of 4000 m. It is characterized by high levels of solar radiation, low air temperature and low air pressure compared to other regions around the world. The alpine grassland, a typical ecosystem in the Tibetan Plateau, is distributed across regions over the elevation of 4500 m. Few studies for carbon flux in alpine grassland on the Tibetan Plateau were conducted due to rigorous natural conditions. A study of soil respiration under alpine grassland ecosystem on the Tibetan Plateau from October 1999 to October 2001 was conducted at Pangkog County, Tibetan Plateau (31.23°N, 90.01°E, elevation 4800 m). The measurements were taken using a static closed chamber technique, usually every two weeks during the summer and at other times at monthly intervals. The obvious diurnal variation of CO2 emissions from soil with higher emission during daytime and lower emission during nighttime was discovered. Diurnal CO2 flux fluctuated from minimum at 05:00 to maximum at 14:00 in local time. Seasonal CO2 fluxes increased in summer and decreased in winter, representing a great variation of seasonal soil respiration. The mean soil CO2 fluxes in the alpine grassland ecosystem were 21.39 mgCO2 · m-2 · h-1, with an average annual amount of soil respiration of 187.46 gCO2 · m-2 · a-1. Net ecosystem productivity is also estimated, which indicated that the alpine grassland ecosystem is a carbon sink.     

大地电磁三维交错网格有限差分数值模拟的并行计算研究

为了更有效的提高大地电磁三维正演的计算速度,引入了并行处理技术.大地电磁三维交错网格有限差分数值模拟是按照不同频率来计算的,各频率之间求取电磁场值的过程是相互独立的.根据这一特点,可以将多个频率的计算任务平均划分为一个或者几个频率的计算子任务,分配到各个计算节点去并行执行,计算完成后将结果汇总.本文通过采用主从并行模式、分频并行计算的方案,在曙光TC5000A高性能并行平台上实现了基于MPI的大地电磁三维正演的并行计算.通过两个理论模型对实现的大地电磁三维正演并行算法进行试算,对比分析了多个节点机下程序的执行效率.测试结果表明,所实现的三维正演并行算法是正确的、高效的,为进一步的大地电磁三维反演并行算法研究奠定了重要基础.     

Bayesian flood frequency analysis in the light of model and parameter uncertainties

The specific objective of the paper is to propose a new flood frequency analysis method considering uncertainty of both probability distribution selection (model uncertainty) and uncertainty of parameter estimation (parameter uncertainty). Based on Bayesian theory sampling distribution of quantiles or design floods coupling these two kinds of uncertainties is derived, not only point estimator but also confidence interval of the quantiles can be provided. Markov Chain Monte Carlo is adopted in order to overcome difficulties to compute the integrals in estimating the sampling distribution. As an example, the proposed method is applied for flood frequency analysis at a gauge in Huai River, China. It has been shown that the approach considering only model uncertainty or parameter uncertainty could not fully account for uncertainties in quantile estimations, instead, method coupling these two uncertainties should be employed. Furthermore, the proposed Bayesian-based method provides not only various quantile estimators, but also quantitative assessment on uncertainties of flood frequency analysis.     

A comparative study of nonlinear Markov chain models for conditional simulation of multinomial classes from regular samples

Simulating fields of categorical geospatial variables from samples is crucial for many purposes, such as spatial uncertainty assessment of natural resources distributions. However, effectively simulating complex categorical variables (i.e., multinomial classes) is difficult because of their nonlinearity and complex interclass relationships. The existing pure Markov chain approach for simulating multinomial classes has an apparent deficiency—underestimation of small classes, which largely impacts the usefulness of the approach. The Markov chain random field (MCRF) theory recently proposed supports theoretically sound multi-dimensional Markov chain models. This paper conducts a comparative study between a MCRF model and the previous Markov chain model for simulating multinomial classes to demonstrate that the MCRF model effectively solves the small-class underestimation problem. Simulated results show that the MCRF model fairly produces all classes, generates simulated patterns imitative of the original, and effectively reproduces input transiograms in realizations. Occurrence probability maps are estimated to visualize the spatial uncertainty associated with each class and the optimal prediction map. It is concluded that the MCRF model provides a practically efficient estimator for simulating multinomial classes from grid samples.     

基于平均导数优化方法的VTI介质频率空间域正演

本文提出了一种新的基于平均导数优化方法(average-derivative optimal method,简称ADM)的二维VTI介质qP波波动方程频率空间域二阶9点格式,这种新算法将二维VTI介质qP波波动方程中中心空间导数项的差分近似表示为正交方向上3个网格点的加权平均形式.通过最小二乘优化方法求取空间导数项和加速度项的加权优化系数从而使数值频散达到极小化,每个波长所需要的网格点数在1%的误差范围内仅为3.57个网格点数,而VTI介质常规9点差分格式在相同的误差范围内则需要约12个网格点数,新方法的计算精度明显提高.复杂BP2007 2D VTI海洋标准模型数值模拟结果也验证了本文VTI介质9点ADM算法的有效性和准确性.     

Modeling gross primary production of a temperate grassland ecosystem in Inner Mongolia,China, using MODIS imagery and climate data

Carbon fluxes in temperate grassland ecosystems are characterized by large inter-annual variations due to fluctuations in precipitation and land water availability. Since an eddy flux tower has been in operation in the Xilin Gol grassland, which belongs to typical temperate grassland in North China, in this study, observed eddy covariance flux data were used to critically evaluate the biophysical per- formance of different remote sensing vegetation indices in relation to carbon fluxes. Furthermore, vegetation photosynthesis model (VPM) was introduced to estimate gross primary production (GPP) of the grassland ecosystem for assessing its dependability. As defined by the input variables of VPM, Moderate Resolution Imaging Spectroradimeter (MODIS) and standard data product MOD09A1 were downloaded for calculating enhanced vegetation index (EVI) and land surface water index (LSWI). Measured air temperature (Ta) and photosynthetically active radiation (PAR) data were also included for model simulating. Field CO2 flux data, during the period from May, 2003 to September, 2005, were used to estimate the "observed" GPP (GPPobs) for validation. The seasonal dynamics of GPP predicted from VPM (GPPVPM) was compared quite well (R2=0.903, N=111, p<0.0001) with the observed GPP. The ag- gregate GPPVPM for the study period was 641.5 g C·m?2, representing a ~6% over-estimation, compared with GPPobs. Additionally, GPP predicted from other two typical production efficiency model (PEM) represents either higher overestimation or lower underestimation to GPPobs. Results of this study demonstrate that VPM has potential for estimating site-level or regional grassland GPP, and might be an effective tool for scaling-up carbon fluxes.     

基于高斯束与高斯波包的Gabor框架散射波模拟方法

在给出真实模型和相应光滑背景模型的情况下,如何计算扰动模型(散射体)产生的散射波场是一个有实际意义的正演问题.在Gabor变换域描述散射体,且入射波场为短时宽带信号时,散射波场可以在频率域用高斯束或时间域用高斯波包描述.相对于波动方程方法,高斯束和高斯波包的计算效率更高;背景模型光滑时,高斯束和高斯波包方法的精度也接近波动方程方法.文中导出了声波假设下应用高斯束和高斯波包计算散射波的方法.测试分析了高斯波包的计算精度.给出了一般散射体的散射波模拟策略.同时针对一个理论模型完成了本文方法计算散射波的实验,实验结果表明高斯波包散射波计算方法是有效可行的.     

Analysis of the influence of parameter and scale uncertainties on a local multi-criteria land use evaluation model

Land use evaluation involves careful consideration of several environmental factors and their relative importance quantified by factor weights. Local multi-criteria evaluation provides a mechanism for computing factor (criteria) weights within local neighborhoods that capture spatial heterogeneity and contribute to more accurate evaluation results. The accuracy of results, however, is tempered by the potential uncertainty of criteria weights. The paper presents a spatially explicit approach to uncertainty and sensitivity analysis of local criteria weights and modeling scale on the variability of model output. The efficacy of the approach is presented on the example of Environmental Benefit Index (EBI) model used by the U.S. Department of Agriculture Conservation Reserve Program (CRP) to select environmentally sensitive agricultural areas for conservation. The uncertainty analysis resulted in identifying robust areas for CRP selection characterized by high suitability and low uncertainty. The sensitivity analysis focused on the next-best group of candidates characterized by high suitability and high uncertainty. The results show that there is a relationship between spatial heterogeneity, data representation scale, and the level of uncertainty in the results of EBI model. The sensitivity of model output can be attributed to both the uncertainty of criteria weights and the modeling scale. A potential practical value of this approach is the improved analytical support for land suitability evaluation requiring a consideration of sub-optimal land units (high suitability/high uncertainty). Also, this approach can guide modelling effort by allowing the analyst to visualize spatial distribution and patterns of model output uncertainty and focus data collection on influential model input factors.     

A numerical study of rotating annulus flows using a modified Galerkin method

Summary Physical phenomena fundamental to rotating, baroclinically driven flows are studied with reference to results of numerical simulation of rotating annulus flows, using a modified Galerkin Model. Both local and global effects of sources, sinks, and transports of heat and momentum are discussed. A convenient energy exchange diagram reveals detailed information that is used to analyze nonlinear equilibration and amplitude vacillation of quasi-geostrophic baroclinic eddies. Transient inertial oscillations, sidewall boundary layers, and internal boundary layers are also discussed.A detailed study of symmetric flows is made, eleven of which are tested numerically for stability with respect to three-dimensional disturbances of a given zonal wave number. Two of the four unstable cases are integrated to a numerical steady state with finite-amplitude, quasi-geostrophic baroclinic waves. With the rigid-lid geometry assumed, the average zonal velocity is zero, resulting in zero phase velocity of the waves. The structure of the thermal wave is nearly coherent in the vertical. These numerical results are consistent with laboratory observations.The eddy flow is quasi-geostrophic except in horizontal boundary layers, where the flow is driven toward low pressure. A small cross-isotherm advection is sufficient to maintain the temperature wave against diffusion and vertical advection. The eddy flow adjusts spontaneously toward the form of the fastest growing or slowest decaying disturbance representable by the truncated space resolution. The eddy flow feeds energy into the mean zonal flow in barotropic-type interactions reflected mainly by the familiar tilted trough. During equilibration, the eddy flow alters the mean zonal flow in such a way that eddy energy sources are reduced relative to energy sinks. However, this adjustment is small compared to the change of total flow, which reflects a relatively large change of eddy amplitude. This suggests that small errors in the mean zonal flow representation can lead to relatively large errors in total flow representation.In most flows studied the kinetic energy dissipation is concentrated in thin boundary layers. In spite of this thinness, the basically laminar character of these dissipative boundary layers allows accurate and economical numerical simulation through the use of characteristic functions, which is a natural refinernent of the basic Galerkin method used. (In this prototype study, only moderately characteristic functions are used, thus sacrificing numerical economy while simplifying the programming.) Similarly, the generation of potential energy, which is transformed into the kinetic energy of the flow, is accurately simulated. In most cases studied, this generation is also concentrated in thin boundary layers where thermal energy is extracted from cold fluid and added to warm fluid.Contribution number 76 of the Geophysical Fluid Dynamics Institute, Florida State University, USA.     

最优系数有限单元法色散介质GPR频率域正演模拟

工程实际勘探对象如土壤、岩石等多为色散介质,雷达波在其中传播时易发生衰减与畸变,应用常规有限单元法（Finite Element Method,FEM）方法进行数值模拟时,存在数值频散现象.为此,作者以色散介质为研究对象,开展最优系数有限单元法探地雷达（Ground Penetrating Radar,GPR）频率域正演.首先,分析了有限元质量、刚度矩阵的约束条件对有限元求解精度的影响,基于归一化相速度与1的误差最小策略,利用最小二乘法,仅需三个优化参数求取最优的有限元刚度矩阵与质量矩阵.四种不同方法的频散曲线分析及精度对比实验结果表明,优化矩阵在单位波长仅需4.8个网格点下便可达到误差小于0.2%的精度;而一致、集中和折衷矩阵不仅需要更多的网格点,且误差较大.然后,将精确完全匹配层（Exact Perfectly Matched Layer,EPML）吸收边界条件引入最优系数频域有限单元（Finite Element Frequency Domain,FEFD）算法中,简化了吸收参数优化过程,取5层即可达到常规完全匹配层（Perfectly Matched Layer,PML）的10层的吸收效果,能够有效提升正演效率.并将基于EPML的最优系数有限单元法算法引入到城市道路病害模型正演中,实验表明：本文算法能有效压制频散并实现实际色散介质高精度模拟,模拟结果更接近波在地下介质中的实际传播特性.

     

Acoustic reflection well logging modeling using the frequency-domain finite-element method with a hybrid PML

In this paper, we propose a hybrid PML (H-PML) combining the normal absorption factor of convolutional PML (C-PML) with tangential absorption factor of Mutiaxial PML (M-PML). The H-PML boundary conditions can better suppress the numerical instability in some extreme models. and the computational speed of finite-element method and the dynamic range are greatly increased using this HPML. We use the finiteelement method with a hybrid PML to model the acoustic reflection of the interface when wireline and well logging while drilling (LWD), in a formation with a reflector outside the borehole. The simulation results suggests that the PS- and SP- reflected waves arrive at the same time when the inclination between the well and the outer interface is zero, and the difference in arrival times increases with increasing dip angle. When there are fractures outside the well, the reflection signal is clearer in the subsequent reflection waves and may be used to identify the fractured zone. The difference between the dominant wavelength and the model scale shows that LWD reflection logging data are of higher resolution and quality than wireline acoustic reflection logging.     

用正演数值计算方法开展双侧向测井对裂缝的响应研究

采用有限元分析软件ANSYS对裂缝的双侧向测井视电阻率与裂缝孔隙度、泥浆电阻率、裂缝倾角和基岩电阻率的关系进行了计算. 在大量正演数据的基础上得出双侧向测井响应反演公式和裂缝孔隙度计算公式,提出更为精细的裂缝倾角的弹性划分模型,用双侧向视电阻率值近似估算裂缝倾角的方法,提高了利用双侧向测井求裂缝产状与裂缝孔隙度（裂缝宽度）的精度.     

Earthquake site effect modeling in the Granada basin using a 3-D indirect boundary element method

In this work, we develop the indirect boundary element method (IBEM) to simulate the seismic site response in a realistic, large-scale 3-D sedimentary basin. Most previous applications of boundary element method have used full-space Green’s functions for wave propagation between element points. We use half-space Green’s functions, which include the seismic wavefield interactions at the free surface and require only the boundary elements of the basin interface. In this way, the size of the matrix equation for solution in the IBEM can be reduced to approximately a quarter of that using full-space Green’s functions. The site response modeling of the Granada basin in southern Spain using the IBEM shows that the basin-induced scattering waves were identified as propagating back and forth inside the basin. The scattered waves also generate surface waves that are weakly propagated outside of the basin. The wave propagation inside and outside of the basin shows different patterns. We observe that the scattered wave is locally amplified, and its propagation direction deviates from that of the incident waves propagation direction. Therefore, the computed seismic response in the basin could provide us with good estimates of the seismic motion.     

旋转网格和常规网格混合的时空域声波有限差分正演

压制数值频散,提高正演模拟精度,一直是有限差分正演模拟研究的重要内容.基于时空域频散关系的有限差分法,比基于空间域频散关系的传统有限差分法,模拟精度更高.时空域声波方程数值模拟,普遍采用常规十字交叉型高阶有限差分格式.而在频率-空间域,普遍采用旋转网格和常规网格混合的有限差分格式,有效提高了模拟精度和计算效率.本文将频率-空间域混合网格有限差分的思想引入到时空域,提出了时空域混合网格2M+N型声波方程有限差分方法.首先推导出基于时空域频散关系的混合网格差分系数计算方法,然后进行频散分析、稳定性分析,并和传统高阶、时空域高阶有限差分法对比,结果表明：计算量相同时,新方法能有效压制数值频散,显著提高模拟精度;新方法相比传统2M阶有限差分法,稳定性增强,与时空域2M阶有限差分法稳定性基本相当.最后利用新方法进行均匀介质、层状介质、盐丘模型的数值模拟和盐丘模型的逆时偏移,模拟效果和成像质量进一步证实了该方法的有效性和普遍适用性.     

页岩气地震勘探中页岩各向异性的地震模拟研究

页岩的强各向异性特征挑战地震波传播数值模拟方法的精度极限, 特别是易引起频散的高频波(>100 Hz)传播的数值模拟.鉴于目前我国页岩气地震勘探主要以常规地震声波资料为主,本文首先介绍了一种VTI介质声波方程的任意偶数阶有限差分数值模拟方法,并讨论其稳定性条件和吸收边界条件.任意偶数阶的差分解可有效提高计算精度,压制数值频散噪声.针对页岩较强的各向异性特征,本文比较了不同模型的声波方程和VTI介质声波方程计算得到的地震响应.数值结果表明,各向异性对地震波的运动学(相位)和动力学(振幅)特性影响作用明显.因此,在页岩气地震勘探资料处理的各个环节必须充分考虑各向异性的影响,采取有别于常规油气勘探的处理流程和技术.