Analysis on observing optimization for the wind-driven circulation by an adjoint approach

The adjoint approach is a variational method which is often applied to data assimilation widely in meteorology and oceanography. It is used for analyses on observing optimization for the wind-driven Sverdrup circulation. The adjoint system developed by Thacker and Long (1992), which is based on the GFDL Byran-Cox model, includes three components, i. e. the forward model, the adjoint model and the optimal algorithm. The GFDL Byran-Cox model was integrated for a long time driven by a batch of ideal wind stresses whose meridional component is set to null and zonal component is a sine function of latitudes in a rectangle box with six vertical levels and 2 by 2 degree horizontal resolution. The results are regarded as a "real" representative of the wind-driven Sverdrup circulation, from which the four dimensional fields are allowed to be sampled in several ways, such as sampling at the different levels or along the different vertical sections. To set the different samples, the fields of temperature, salinity and velocities function as the observational limit in the adjoint system respectively where the same initial condition is chosen for 4D VAR data assimilation. By examining the distance functions which measure the misfit between the circulation field from the control experiment of the adjoint system with a complete observation and those from data assimilation of adjoint approach in these sensitivity experiments respectively, observing optimizations for the wind-driven Sverdrup circulation will be suggested under a fixed observational cost.     

Prediction of effective porosity from seismic attributes using locally linear model tree algorithm

In this study, a locally linear model tree algorithm was used to optimize a neuro‐fuzzy model for prediction of effective porosity from seismic attributes in one of Iranian oil fields located southwest of Iran. Valid identification of effective porosity distribution in fractured carbonate reservoirs is extremely essential for reservoir characterization. These high‐accuracy predictions facilitate efficient exploration and management of oil and gas resources. The multi‐attribute stepwise linear regression method was used to select five out of 26 seismic attributes one by one. These attributes introduced into the neuro‐fuzzy model to predict effective porosity. The neuro‐fuzzy model with seven locally linear models resulted in the lowest validation error. Moreover, a blind test was carried out at the location of two wells that were used neither in training nor validation. The results obtained from the validation and blind test of the model confirmed the ability of the proposed algorithm in predicting the effective porosity. In the end, the performance of this neuro‐fuzzy model was compared with two regular neural networks of a multi‐layer perceptron and a radial basis function, and the results show that a locally linear neuro‐fuzzy model trained by a locally linear model tree algorithm resulted in more accurate porosity prediction than standard neural networks, particularly in the case where irregularities increase in the data set. The production data have been also used to verify the reliability of the porosity model. The porosity sections through the two wells demonstrate that the porosity model conforms to the production rate of wells. Comparison of the locally linear neuro‐fuzzy model performance on different wells indicates that there is a distinct discrepancy in the performance of this model compared with the other techniques. This discrepancy in the performance is a function of the correlation between the model inputs and output. In the case where the strength of the relationship between seismic attributes and effective porosity decreases, the neuro‐fuzzy model results in more accurate prediction than regular neural networks, whereas the neuro‐fuzzy model has a close performance to neural networks if there is a strong relationship between seismic attributes and effective porosity. The effective porosity map, presented as the output of the method, shows a high‐porosity area in the centre of zone 2 of the Ilam reservoir. Furthermore, there is an extensive high‐porosity area in zone 4 of Sarvak that extends from the centre to the east of the reservoir.     

Field-aligned currents of zones 1 and 2 in the magnetosphere according to the experimental data

The discrepancy between the model and measured magnetic fields, which can be described by the contribution of field-aligned currents, has been determined. The division of the initial data array into the individual data sets with different IMF values makes it possible to estimate the dependence of field-aligned currents on IMF.     

Application of a Discrete-Continuum Model to Karst Aquifers in North China

A generalized discrete-continuum model is developed to simulate ground water flow in the karst aquifers of North China. The model is a hybrid numerical flow model, which takes into account both quick conduit flow and diffusive fissure flow. The conduit flow is represented by a discrete network model, and the fissure flow is modeled by a continuum approach. The developed model strongly emphasizes the function of the conduits in the flow fields. They control the general drainage pattern, as demonstrated in the simulation of a complex karst aquifer in North China. The model reproduces reasonably well the flow field in response to an unanticipated discharge of ground water from the karst aquifer into an underground mine based on the aquifer parameters that are manually calibrated from a multiple-well pumping test. Sensitivity of the model to the aquifer parameters was evaluated in the context of the case study.     

Consistency of the spatial autocorrelation method with seismic interferometry and its consequence

We have cross‐checked the conventional theory of the spatial autocorrelation method and the consequence of seismic interferometry: the retrieval of the elastodynamic Green's function. Their mutual consistency is almost complete. The basic formulas of the conventional spatial autocorrelation theory can be derived by an alternative approach based on the retrieval of the elastodynamic Green's function. The only discrepancy is found with the average of the complex coherence function over azimuth in a wavefield dependent on azimuth. It is hypothesized, in discussion, that this discrepancy is due to the way of representing the wavefield in the background theory of seismic interferometry that can produce only wavefields moderately dependent on azimuth and that the mentioned consequence of seismic interferometry can also only make sense in a wavefield moderately dependent on azimuth. Our field experiment with a wavefield dependent on azimuth showed that the consequence of seismic interferometry in the logical framework of the conventional spatial autocorrelation theory is appropriate under such degrees of approximation as the measure proposed in this study, i.e., the deviation of the total dispersion curves is between about 10 and 16 per cent at the maximum from those averaged over azimuth. The acceptance of the retrieval of Green's function gives a proper physical meaning to the complex coherence function: the real part of the elastodynamic Green's function normalized by its zero‐offset version. This makes it possible to take a deterministic approach rather than the statistical one on which the conventional spatial autocorrelation method is based and gives fruitful new aspects and perspectives. For example, the formula for the multi‐mode case is given and the possibility of exploration of two or three dimensional velocity structures is suggested.     

Simultaneous identification of the pollutant release history and the source location in groundwater by means of a geostatistical approach

This paper describes an innovative procedure that is able to simultaneously identify the release history and the source location of a pollutant injection in a groundwater aquifer (simultaneous release function and source location identification, SRSI). The methodology follows a geostatistical approach: it develops starting from a data set and a reliable numerical flow and transport model of the aquifer. Observations can be concentration data detected at a given time in multiple locations or a time series of concentration measurements collected at multiple locations. The methodology requires a preliminary delineation of a probably source area and results in the identification of both the sub-area where the pollutant injection has most likely originated, and in the contaminant release history. Some weak hypotheses have to be defined about the statistical structure of the unknown release function such as the probability density function and correlation structure. Three case studies are discussed concerning two-dimensional, confined aquifers with strongly non-uniform flow fields. A transfer function approach has been adopted for the numerical definition of the sensitivity matrix and the recent step input function procedure has been successfully applied.     

水平层状介质中双侧向测井资料的迭代Tikhonov正则化反演

根据非线性反演理论与Morozov偏差原理研究建立从双侧向测井(DLL)资料中同时重构地层原状电阻率、侵入带电阻率、侵入半径、层界面位置以及井眼泥浆电阻率的迭代正则化算法.首先利用Tikhonov正则化反演理论将双侧向测井资料的反演问题转化为含有稳定泛函的非线性目标函数的极小化问题,并利用Gauss-Newton算法确定极小化解.为得到稳定的反演结果并有效实现测井资料的最佳拟合,在迭代过程中将Morozov偏差原理和Cholesky分解技术相结合,建立了一套后验选择正则化因子的方法.最后通过理论模型和大庆油田实际测井资料的处理结果,验证了该算法能够取得更为满意的反演效果.     

Estimation of tropical cyclone parameters and wind fields from SAR images

The traditional method of Synthetic Aperture Radar(SAR)wind field retrieval is based on an empirical relation between the near surface winds and the normalized radar backscatter cross section to estimate wind speeds,where this relation is called the geophysical model function(GMF).However,the accuracy rapidly decreases due to the impact of rainfall on the measurement of SAR and the saturation of backscattered intensity under the condition of tropical cyclone.Because of no available instrument synchronously monitoring rain rate on the satellite platform of SAR,we have to derive the precipitation of the SAR observation time from non-simultaneous passive microwave observations of rain in combination with geostationary IR images,and then use the model of rain correction to remove the impact of rain on SAR wind field measurements.For the saturation of radar backscatter cross section in high wind speed conditions,we develop an approach to estimate tropical cyclone parameters and wind fields based on the improved Holland model and the SAR image features of tropical cyclone.To retrieve the low-to-moderate wind speed,the wind direction of tropical cyclone is estimated from the SAR image using wavelet analysis.And then the maximum wind speed and the central pressure of tropical cyclone are calculated by a least square minimization of the difference between the improved Holland model and the low-to-moderate wind speed retrieved from SAR.In addition,wind fields are estimated from the improved Holland model using the above-mentioned parameters of tropical cyclone as input.To evaluate the accuracy of our approach,the SAR images of typhoon Aere,typhoon Khanun,and hurricane Ophelia are used to estimate tropical cyclone parameters and wind fields,which are compared with the best track data and reanalyzed wind fields of the Joint Typhoon Warning Center(JTWC)and the Hurricane Research Division(HRD).The results indicate that the tropical cyclone center,maximum wind speed,and central pressure are generally consistent with the best track data,and wind fields agree well with reanalyzed data from HRD.     

A heuristic model of three-dimensional spectra of temperature inhomogeneities in the stably stratified atmosphere

Many measurements have shown that the random temperature fields in the stably stratified atmosphere are not locally isotropic (LI). The local axial symmetry (LAS) hypothesis looks more appropriate under these conditions. The object of this paper consists in the development of a flexible tool for spectral studies of LAS scalar fields independently of their origin in stably stratified geophysical flows. A heuristic model of a 3D spatial spectrum is proposed in order to describe and study statistical properties of LAS temperature inhomogeneities from LI structures up to quasi-layered ones. To simplify the solution of this problem, a main assumption was accepted: the consideration is restricted to 3D spectra which may be given on a one-parametric family of surfaces of rotation. Such 3D spectra may be represented by a single function of one variable which is the parameter of the family. This approach allows one to introduce the generalized energy spectrum which describes an energy distribution according to inhomogeneity sizes. The family of surfaces determines the shape of inhomogeneities. The family of ellipsoids of rotation and power-law generalized energy spectrum is used as the simplest example of the model application in order to study the general properties of LAS-structure spectra. The behavior of vertical, horizontal, and oblique 1D spectra and coherency spectra is studied. The relationship between the suggested model and some existing models of temperature spectra is considered. The application of the model for the analysis of experimental data is shown for two sets of measurements. It is shown that the suggested model may quantitatively describe experimental 1D spectra and coherency spectra from a unique point of view. It is noted that the model may be used for both the planning of measurements and data processing. Possible generalizations of the model are considered for random fields with more degenerate symmetry and for space-temporal spectra.     

Evolution of Vertical Moist Thermodynamic Structure Associated with the Indian Summer Monsoon 2010 in a Regional Climate Model

The 2010 boreal summer marked a worldwide abnormal climate. An unprecedented heat wave struck East Asia in July and August 2010. In addition to this, the tropical Indian Ocean was abnormally warm during the summer of 2010. Several heavy rainfall events and associated floods were also reported in the Indian monsoon region. During the season, the monsoon trough (an east–west elongated area of low pressure) was mostly located south of its normal position and monsoon low pressure systems moved south of their normal tracks. This resulted in an uneven spatial distribution with above-normal rainfall over peninsular and Northwest India, and deficient rainfall over central and northeastern parts of India, thus prediction (and simulation) of such anomalous climatic summer season is important. In this context, evolution of vertical moist thermodynamic structure associated with Indian summer monsoon 2010 is studied using regional climate model, reanalysis and satellite observations. This synergised approach is the first of its kind to the best of our knowledge. The model-simulated fields (pressure, temperature, winds and precipitation) are comparable with the respective in situ and reanalysis fields, both in intensity and geographical distribution. The correlation coefficient between model and observed precipitation is 0.5 and the root-mean-square error (RMSE) is 4.8 mm day^?1. Inter-comparison of model-simulated fields with satellite observations reveals that the midtropospheric temperature [Water vapour mixing ratio (WVMR)] has RMSE of 0.5 K (1.6 g kg^?1), whereas the surface temperature (WVMR) has RMSE of 3.4 K (2.2 g kg^?1). Similarly, temporal evolution of vertical structure of temperature with rainfall over central Indian region reveals that the baroclinic nature of monsoon is simulated by the model. The midtropospheric warming associated with rainfall is captured by the model, whereas the model failed to capture the surface response to high and low rainfall events. The model has strong water vapour loading in the whole troposphere, but weaker coherent response with rainfall compared to observations. Thus, strong water vapour loading and overestimation of rainfall are reported in the model. This study put forward that the discrepancy in the model-simulated structure may be reduced by assimilation of satellite observations.     

Truncated multiGaussian fields and effective conductance of binary media

Truncated Gaussian fields provide a flexible model for defining binary media with dispersed (as opposed to layered) inclusions. General properties of excursion sets on these truncated fields are coupled with a distance-based upscaling algorithm and approximations of point process theory to develop an estimation approach for effective conductivity in two-dimensions. Estimation of effective conductivity is derived directly from knowledge of the kernel size used to create the multiGaussian field, defined as the full-width at half maximum (FWHM), the truncation threshold and conductance values of the two modes. Therefore, instantiation of the multiGaussian field is not necessary for estimation of the effective conductance. The critical component of the effective medium approximation developed here is the mean distance between high conductivity inclusions. This mean distance is characterized as a function of the FWHM, the truncation threshold and the ratio of the two modal conductivities. Sensitivity of the resulting effective conductivity to this mean distance is examined for two levels of contrast in the modal conductances and different FWHM sizes. Results demonstrate that the FWHM is a robust measure of mean travel distance in the background medium. The resulting effective conductivities are accurate when compared to numerical results and results obtained from effective media theory, distance-based upscaling and numerical simulation.     

位场向下延拓的改进迭代维纳滤波法

根据维纳滤波理论导出的位场向下延拓滤波器为最佳下延滤波器,但因其实现需要已知待求位场和噪声的功率谱而在实际应用中受到限制.针对该问题,本文首先提出一种基于位场径向平均功率谱的位场噪声水平估计方法,进而利用偏差准则求取正则化参数,实现位场正则化向下延拓;然后将位场正则化下延结果的功率谱作为待求位场功率谱的估计初值,采用带修正项的迭代维纳滤波方法来更新对待求位场功率谱的估计,最后提出本文的位场向下延拓改进迭代维纳滤波方法.基于理论重力模型数据及航磁实测数据进行了向下延拓对比试验,结果表明,改进迭代法具有较好的收敛性,且下延精度优于Tikhonov正则化法和递增型维纳滤波法.     

Impact of simulation model solver performance on ground water management problems

Ground water management models require the repeated solution of a simulation model to identify an optimal solution to the management problem. Limited precision in simulation model calculations can cause optimization algorithms to produce erroneous solutions. Experiments are conducted on a transient field application with a streamflow depletion control management formulation solved with a response matrix approach. The experiment consists of solving the management model with different levels of simulation model solution precision and comparing the differences in optimal solutions obtained. The precision of simulation model solutions is controlled by choice of solver and convergence parameter and is monitored by observing reported budget discrepancy. The difference in management model solutions results from errors in computation of response coefficients. Error in the largest response coefficients is found to have the most significant impact on the optimal solution. Methods for diagnosing the adequacy of precision when simulation models are used in a management model framework are proposed.     

Comparison between two approaches to the implementation of the optimization method for reconstructing a nonlinear force-free field

A comparative testing of two methods for reconstructing a nonlinear force-free field in a bounded spatial domain has mainly been studied based on the optimization method, using (1) fixed boundary values and weighting function and (2) purposefully varied boundary values. The quantitative and qualitative characteristics, reflecting the degree of correspondence between the calculated and known model fields, are presented. It is indicated that the second approach to the implementation of the optimization method gives the best approximation to the required solution, corresponding to the finite solution in an unbounded domain, and the quality of this solution remains unchanged up to the reconstruction domain boundaries.     

Simplified methods for real-time prediction of storm surge uncertainty: The city of Venice case study

Providing reliable and accurate storm surge forecasts is important for a wide range of problems related to coastal environments. In order to adequately support decision-making processes, it also become increasingly important to be able to estimate the uncertainty associated with the storm surge forecast. The procedure commonly adopted to do this uses the results of a hydrodynamic model forced by a set of different meteorological forecasts; however, this approach requires a considerable, if not prohibitive, computational cost for real-time application. In the present paper we present two simplified methods for estimating the uncertainty affecting storm surge prediction with moderate computational effort. In the first approach we use a computationally fast, statistical tidal model instead of a hydrodynamic numerical model to estimate storm surge uncertainty. The second approach is based on the observation that the uncertainty in the sea level forecast mainly stems from the uncertainty affecting the meteorological fields; this has led to the idea to estimate forecast uncertainty via a linear combination of suitable meteorological variances, directly extracted from the meteorological fields. The proposed methods were applied to estimate the uncertainty in the storm surge forecast in the Venice Lagoon. The results clearly show that the uncertainty estimated through a linear combination of suitable meteorological variances nicely matches the one obtained using the deterministic approach and overcomes some intrinsic limitations in the use of a statistical tidal model.     

Soil moisture estimation using tomographic ground penetrating radar in a MCMC–Bayesian framework

In this study, we focus on a hydrogeological inverse problem specifically targeting monitoring soil moisture variations using tomographic ground penetrating radar (GPR) travel time data. Technical challenges exist in the inversion of GPR tomographic data for handling non-uniqueness, nonlinearity and high-dimensionality of unknowns. We have developed a new method for estimating soil moisture fields from crosshole GPR data. It uses a pilot-point method to provide a low-dimensional representation of the relative dielectric permittivity field of the soil, which is the primary object of inference: the field can be converted to soil moisture using a petrophysical model. We integrate a multi-chain Markov chain Monte Carlo (MCMC)–Bayesian inversion framework with the pilot point concept, a curved-ray GPR travel time model, and a sequential Gaussian simulation algorithm, for estimating the dielectric permittivity at pilot point locations distributed within the tomogram, as well as the corresponding geostatistical parameters (i.e., spatial correlation range). We infer the dielectric permittivity as a probability density function, thus capturing the uncertainty in the inference. The multi-chain MCMC enables addressing high-dimensional inverse problems as required in the inversion setup. The method is scalable in terms of number of chains and processors, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. The proposed inversion approach can successfully approximate the posterior density distributions of the pilot points, and capture the true values. The computational efficiency, accuracy, and convergence behaviors of the inversion approach were also systematically evaluated, by comparing the inversion results obtained with different levels of noises in the observations, increased observational data, as well as increased number of pilot points.     

有限长圆柱体磁异常场全空间正演方法

在经典位场理论中,许多简单形体位场异常难以通过积分得到全空间的解析式.圆柱体是一类很重要的理论模型体,常用于模拟圆柱状地质体或非地质体(如管线),但目前还不能用解析公式正演有限长圆柱体在三维空间里的磁异常,而多是采用近似简化为有限长磁偶极子或线模型代替.对于有限长圆柱体,特别是半径相对于上顶埋深较大时,这种近似的误差不可忽略.本文利用共轭复数变量替换法,推导出有限长圆柱体在全空间的引力位一阶、二阶导数,利用Poisson关系得到磁异常正演公式,进而利用有限长圆柱体磁异常正演公式求解管状体的磁异常,得到不同磁化方向、不同大小的管线产生的磁场的特征,并将其推广到截面为椭圆的情况.最后通过模拟计算定量给出了将圆柱体近似为线模型的条件.     

Gravity and magnetic field interpretation based on transformations of horizontal gradients in the VECTOR system

A method of potential field processing based on the transformation of vectors of the total horizontal gradient in windows of various sizes is considered. The gradients are calculated at the centers of triangles, whose vertices are points of observations, as a rule, of gravity and magnetic fields. Averaging of horizontal gradients of the field rather than initial values of the field is the main distinction of this approach from the known methods. This procedure, referred to in this paper as vector scanning of the field, makes it possible to obtain layer distributions of field sources in a 3-D diagram that is a quasi-density model of the study medium within the framework of certain model concepts. The paper presents a model example demonstrating the possibility of separating the fields produced by two sources located on a vertical line and an example illustrating the application of this method to the interpretation of the gravity field in the zone of the geodynamic influence of the Urals.     

Modeling ground water flow in alluvial mountainous catchments on a watershed scale

In large mountainous catchments, shallow unconfined alluvial aquifers play an important role in conveying subsurface runoff to the foreland. Their relatively small extent poses a serious problem for ground water flow models on the river basin scale. River basin scale models describing the entire water cycle are necessary in integrated water resources management and to study the impact of global climate change on ground water resources. Integrated regional-scale models must use a coarse, fixed discretization to keep computational demands low and to facilitate model coupling. This can lead to discrepancies between model discretization and the geometrical properties of natural systems. Here, an approach to overcome this discrepancy is discussed using the example of the German-Austrian Upper Danube catchment, where a coarse ground water flow model was developed using MODFLOW. The method developed uses a modified concept from a hydrological catchment drainage analysis in order to adapt the aquifer geometry such that it respects the numerical requirements of the chosen discretization, that is, the width and the thickness of cells as well as gradients and connectivity of the catchment. In order to show the efficiency of the developed method, it was tested and compared to a finely discretized ground water model of the Ammer subcatchment. The results of the analysis prove the applicability of the new approach and contribute to the idea of using physically based ground water models in large catchments.     

利用微分进化法确定海洋磁场向下延拓中的最优参数

位场的解析延拓是实现不同高度海洋地磁场相互转换的主要途径,是构建海洋三维磁空间背景场模型的关键技术.针对位场向下延拓迭代法中最优正则化参数及最佳迭代次数难以确定问题,尝试引入微分进化法,以正则化参数及迭代次数为种群变量,以延拓结果的熵值为目标函数,以目标函数最小化为搜索准则,实现两种参数的并行全局寻优.采用实测数据对微分进化法在几种常用的迭代法中最优正则化参数及最佳迭代次数的确定进行了分析,与传统L-曲线准则确定的最优正则化参数及多次试验确定的最佳迭代次数进行对比,结果表明：微分进化法确定的最优参数能使三种迭代法取得最佳迭代效果,延拓结果与真实地磁场最为接近,并且该法计算稳定、自适应强,建议在海洋磁场数据向下延拓中应用.