Sensitivity analysis of two-dimensional steady-state aquifer flow equations. Implications for groundwater flow model calibration and validation

This paper presents the analytical properties of the sensitivity of the two-dimensional, steady-state groundwater flow equation to the flow parameters and to the boundary conditions, based on the perturbation approach. These analytical properties are used to provide guidelines for model design, model calibration and monitoring network design. The sensitivity patterns are shown to depend on the nature of both the perturbed parameter and the variable investigated. Indeed, the sensitivity of the hydraulic head to the hydraulic conductivity extends mainly in the flow direction, while the sensitivity to the recharge spreads radially. Besides, the sensitivity of the flow longitudinal velocity to the hydraulic conductivity propagates in both the longitudinal and transverse directions, whereas the sensitivity of the flow transverse velocity propagates in the diagonal directions to the flow. The analytical results are confirmed by application examples on idealized and real-world simulations. These analytical findings allow some general rules to be established for model design, model calibration and monitoring network design. In particular, the optimal location of measurement points depends on the nature of the variable of interest. Measurement network design thus proves to be problem-dependent. Moreover, adequate monitoring well network design may allow to discriminate between the possible sources of error.     

Comparison of Dirichlet–Neumann operator expansions for nonlinear surface gravity waves

The Dirichlet–Neumann operator for the water-wave problem was introduced and expanded by Craig and Sulem [Craig, W., Sulem, C., 1993. [CS] Numerical simulation of gravity waves. J. Comput. Phys. 108, 73–83] and in a slightly different form and for 3D waves by Bateman, Swan and Taylor [Bateman, W.J.D., Swan, C., Taylor, P.H., 2001. [BST] On the efficient numerical simulation of directionally spread surface water waves. J. Comput. Phys. 174, 277–305]. This approach is supposedly superior to techniques derived earlier by West et al. [West, B.J., Brueckner, K.A., Janda, R.S., Milder, D.M., Milton, R.L., 1987. [WW] A new numerical method for surface hydrodynamics. J. Geophys. Res. 92 (C11), 11803–11824] and Dommermuth and Yue [Dommermuth, D.G., Yue, D.K.P., 1987. [DY] A high-order spectral method for the study of nonlinear gravity waves. J. Fluid Mech. 184, 267–288] under seemingly more restrictive assumptions. This paper extracts the Dirichlet–Neumann operator expansions from West et al. and Dommermuth and Yue. Concerning the operator expansions alone it is found that Bateman et al. is identical to West et al. and Dommermuth and Yue while Craig and Sulem is slightly different due to minor differences in the operator definition. For application to the free-surface boundary conditions West et al. devised a consistent truncation at nonlinear order. This alters the equivalence of the different approaches when it comes to the evaluation of the temporal derivative of the free surface elevation, which is decisive for wave evolution. In this regard Craig and Sulem is found to be identical to West et al. while Bateman et al. is identical to Dommermuth and Yue. Pseudo code is provided for alternative computational schemes in Fourier-space and physical space, respectively, along with a discussion of efficiency and potential flexibility.     

Variable Coefficient KdV Equation for Amplitude of Nonlinear Solitary Rossby Waves in a Sort of Time-Dependent Zonal Flow

On the basis of the quasi-geostrophic vorticity equation, theoretical research has been down upon the evolution of the amplitude of solitary Rossby waves employing the perturbation method, and come to the conclusion that the evolution of the amplitude satisfies the variable coefficient Korteweg-de Vries (KdV) equation.     

Ensemble Forecast for Tropical Cyclone Based on CNOP-P Method: A Case Study of WRF Model and Two Typhoons

In this paper, we set out to study the ensemble forecast for tropical cyclones. The case study is based on the Conditional Nonlinear Optimal Perturbation related to Parameter (CNOP-P) method and the WRF model to improve the prediction accuracy for track and intensity, and two different typhoons are selected as cases for analysis. We first select perturbed parameters in the YSU and WSM6 schemes, and then solve CNOP-Ps with simulated annealing algorithm for single parameters as well as the combination of multiple parameters. Finally, perturbations are imposed on default parameter values to generate the ensemble members. The whole proposed procedures are referred to as the Perturbed Parameter Ensemble (PPE). We also conduct two experiments, which are control forecast and ensemble forecast, termed Ctrl and perturbed-physics ensemble (PPhyE) respectively, to demonstrate the performance for contrast. In the article, we compare the effects of three experiments on tropical cyclones in aspects of track and intensity, respectively. For track, the prediction errors of PPE are smaller. The ensemble mean of PPE filters the unpredictable situation and retains the reasonably predictable components of the ensemble members. As for intensity, ensemble mean values of the central minimum sea-level pressure and the central maximum wind speed are closer to CMA data during most of the simulation time. The predicted values of the PPE ensemble members included the intensity of CMA data when the typhoon made landfall. The PPE also shows uncertainty in the forecast. Moreover, we also analyze the track and intensity from physical variable fields of PPE. Experiment results show PPE outperforms the other two benchmarks in track and intensity prediction.     

An Analysis of the Lifetimes of Large Elliptical Orbits of Space Debris

The lunisolar perturbation is the principal factor that causes variation in the orbit of a GTO (geosychronous transfer orbit) space debris. In the present article the analytical expression of the long-periodic term of the altitude of the GTO orbital perigee caused by the lunisolar perturbation is derived, and the basic characteristics of the variation of the perigee caused by the lunisolar perturbation are analyzed. A method of selecting a launch window that will help to improve the space debris situation is given, and its correctness is tested and verified through simulation calculation.     

Wavefield dependency on virtual shifts in the source location

The wavefield dependence on a virtual shift in the source location can provide information helpful in velocity estimation and interpolation. However, the second‐order partial differential equation (PDE) that relates changes in the wavefield form (or shape) to lateral perturbations in the source location depends explicitly on lateral derivatives of the velocity field. For velocity models that include lateral velocity discontinuities this is problematic as such derivatives in their classical definition do not exist. As a result, I derive perturbation partial differential wave equations that are independent of direct velocity derivatives and thus, provide possibilities for wavefield shape extrapolation in complex media. These PDEs have the same structure as the wave equation with a source function that depends on the background (original source) wavefield. The solutions of the perturbation equations provide the coefficients of a Taylor's series type expansion for the wavefield. The new formulas introduce changes to the background wavefield only in the presence of lateral velocity variation or in general terms velocity variations in the perturbation direction. The accuracy of the representation, as demonstrated on the Marmousi model, is generally good.     

热带气旋的内、外区结构──Ⅰ.正压模式

将热带气旋分为内外两区，两区的空间、时间及物理量有不同的尺度，应用尺度分析和摄动法到热带气旋的两个区域，分别在正压模式和斜压模式中求得了这两个区域的控制方程，在两个模式中，还解析地求得了两个区域的流场和气压场，得到的结构与实际热带气旋的结构较为接近。研究表明，热带气旋内区和外区有不同的控制方程，内区受旋转风和一个演化方程制约，而外区受梯度风和另一个演化方程制约。     

热带气旋的内、外区结构──Ⅱ.斜压模式

将热带气旋分为内外两区，两区的空间、时间及物理量有不同的尺度。应用尺度分析和摄动法到热带气旋的两个区域，分别在正压模式和斜压模式中求得了这两个区域的控制方程。在两个模式中，还解析地求得了两个区域的流场和气压场，得到的结果与实际热带气旋的结构较为接近。研究表明：热带气旋内区和外区有不同的控制方程，内区受旋转风和一个演化方程制约，而外区受梯度风和另一个演化方程制约。     

Lorenz 96模式中三种目标观测方法的有效性比较

目标观测是有效提升观测效能和观测质量的一种观测策略,其核心部分是敏感区的识别。本文在Lorenz-96模式上比较了奇异向量法(SVs)、集合变换卡尔曼滤波法(ETKF)和条件非线性最优扰动法(CNOP)识别敏感区的优劣,并尝试揭示ETKF方法性能不稳定的原因与机制。试验结果表明:在312h内的不同预报时刻,CNOP方法识别的敏感区范围较小且对预报效果的提升率最高;SVs方法识别的敏感区对72h内的预报有较好的改进,但72h后改进程度急剧下降,到120h后基本失效;ETKF方法识别的敏感区在72h内不如其他方法的效果好。此外,在ETKF方法识别的敏感区与随机选取的敏感区对比中发现,由于ETKF方法操作时采用顺序观测资料处理方案搜寻敏感区,本质上忽略了观测资料间的相关性,导致ETKF方法识别出的敏感区并不一定是全局信号方差最大的区域,对预报效果的改善有限,这也说明了如何优化敏感区搜寻方案是提高ETKF方法效能的关键。