Evaluation of numerical earthquake forecasting models

Evaluation of numerical earthquake forecasting models needs to consider two issues of equal importance: the application scenario of the simulation, and the complexity of the model. Criterion of the evaluation-based model selection faces some interesting problems in need of discussion.     

Field line resonances in discretized magnetospheric models: an artifact study

For more than two decades numerical models of the Earths magnetosphere have been used success- fully to study magnetospheric dynamic features such as the excitation of ULF pulsations and the mechanism of field line resonance. However, numerical formulations simplify important properties of the real system. For instance the Alfveén continuum becomes discrete because of a finite grid size. This discretization can be a possible source of numerical artifacts. Therefore a careful interpretation of any observed features is required. Examples of such artifacts are presented using results from a three dimensional dipole model of the magne tosphere, including an inhomogeneous distribution of the Alfveé n velocity.     

Energy geodynamo parameters compatible with analytical,numerical, paleomagnetic models and observations

A hydromagnetic dynamo is only possible at a sufficiently powerful convection. In the Earth’s core, it is probably the nonthermal convection very much in excess of its critical level with the molecular transporr coefficients. However, in the case of medium- or large-scale fields, the critical energy level caused by the turbulent tranport coefficients is likely to be slightly below the actual level. This probably explains both the 22-year success of this type of simplified geodynamo models and the energy scaling laws for hydromagnetic fields, which generalize these models. Also the review of energy-dependent analytical and observational estimates of vortex fields, hydromagnetic scale sizes, and velocities in the core is presented. These typical parameters are partly in a new way linked to the observed and more ancient magnetic variations. New, albeit, simplified and self-evident, substantiation is given to the paleomagnetic hypothesis about the predominance of the axial dipole under a certain time averaging. In (Pozzo et al., 2012) and more recent works, it is shown that the adiabatic heat flow and electrical conductivity in the Earth’s core are severalfold higher than the generally accepted estimates. Here, the dynamo supporting Braginsky’s convection (Braginsky, 1963) (under the crystallization of the heavy fraction of a liquid onto the solid core) started less than 1 Ga ago, whereas the more ancient geodynamo was supported by the compositional convection of another type. The known mechanisms implementing this convection, which differ by the scenarios of magnetic evolution, are reviewed. This may help identify the sought mechanism through the most ancient paleomagnetic estimates of the field’s intensity and through the numerical models. The probable mechanisms of generation and their absence for the primordial and recent magnetic field of the studied terrestrial planets are discussed.     

Earthquake strong motion simulated by stress drop models

Shallow strike slip earthquakes on vertical faults are modelled as two-dimensional antiplane strain ruptures in a uniformly prestressed homogeneous halfspace. Behind the rupture front, which is specified, the stress drops to a lower value. The elastodynamic boundary value problem is solved with a finite difference method. Several cases are studied, which include symmetric and one-directional rupture propagation, surface faulting, multiple events, variable rupture velocity, sticking and rebreaking of the fault plane. The time function of displacement, velocity and acceleration are interpreted as signals generated by events in the focus, namely starting, stopping and breaking through the surface of the rupture. The model explains peak velocity and peak acceleration in the near field of M5.5–6 earthquakes; which are typically about 0.2 m/s and 5 m/s² at 10 km epicentral distance, if the rupture velocity is close to the shear wave velocity. Sticking of the fault does not alter the accelerograms significantly, but it increases the seismic moment in simple events and decreases it in multiple events.Contribution No. 226, Geophysical Institute, University of Karlsruhe.     

Improving stability of regional numerical ocean models

An operational limited-area ocean modelling system was developed to supply forecasts of ocean state out to 3 days. This system is designed to allow non-specialist users to locate the model domain anywhere within the Australasian region with minimum user input. The model is required to produce a stable simulation every time it is invoked. This paper outlines the methodology used to ensure the model remains stable over the wide range of circumstances it might encounter. Central to the model configuration is an alternative approach to implementing open boundary conditions in a one-way nesting environment. Approximately 170 simulations were performed on limited areas in the Australasian region to assess the model stability; of these, 130 ran successfully with a static model parameterisation allowing a statistical estimate of the model’s approach toward instability to be determined. Based on this, when the model was deemed to be approaching instability a strategy of adaptive intervention in the form of constraint on velocity and elevation was invoked to maintain stability.     

三维热导方程求解的波数域方法（MWN3D）及模型实验研究

给出了三维热导方程波数域的基本解和算法（MWN3D）,并通过数值模型的方式验证、讨论了这一方法的可靠性和适应能力. 模型实验表明这一方法具有计算速度快,处理问题灵活的特点. 模拟实验还显示,只有在横向较为均匀的三维构造条件下才能用一维模型替代三维模型. 事实上,由于在地壳和上地幔中物质的横向变化不可忽略,通过本方法构建一个真三维的热结构模型是必要的.     

Ensemble rainfall forecasting with numerical weather prediction and radar‐based nowcasting models

The overall objective of this study is to improve the forecasting accuracy of the precipitation in the Singapore region by means of both rainfall forecasting and nowcasting. Numerical Weather Predication (NWP) and radar‐based rainfall nowcasting are two important sources for quantitative precipitation forecast. In this paper, an attempt to combine rainfall prediction from a high‐resolution mesoscale weather model and a radar‐based rainfall model was performed. Two rainfall forecasting methods were selected and examined: (i) the weather research and forecasting model (WRF); and (ii) a translation model (TM). The WRF model, at a high spatial resolution, was run over the domain of interest using the Global Forecast System data as initializing fields. Some heavy rainfall events were selected from data record and used to test the forecast capability of WRF and TM. Results obtained from TM and WRF were then combined together to form an ensemble rainfall forecasting model, by assigning weights of 0.7 and 0.3 weights to TM and WRF, respectively. This paper presented results from WRF and TM, and the resulting ensemble rainfall forecasting; comparisons with station data were conducted as well. It was shown that results from WRF are very useful as advisory of anticipated heavy rainfall events, whereas those from TM, which used information of rain cells already appearing on the radar screen, were more accurate for rainfall nowcasting as expected. The ensemble rainfall forecasting compares reasonably well with the station observation data. Copyright © 2012 John Wiley & Sons, Ltd.     

A methodology for validating numerical ground water models

Ground water validation is one of the most challenging issues facing modelers and hydrogeologists. Increased complexity in ground water models has created a gap between model predictions and the ability to validate or build confidence in predictions. Specific procedures and tests that can be easily adapted and applied to determine the validity of site-specific ground water models do not exist. This is true for both deterministic and stochastic models, with stochastic models posing the more difficult validation problem. The objective of this paper is to propose a general validation approach that addresses important issues recognized in previous validation studies, conferences, and symposia. The proposed method links the processes for building, calibrating, evaluating, and validating models in an iterative loop. The approach focuses on using collected validation data to reduce uncertainty in the model and narrow the range of possible outcomes. This method is designed for stochastic numerical models utilizing Monte Carlo simulation approaches, but it can be easily adapted for deterministic models. The proposed methodology relies on the premise that absolute validity is not theoretically possible, nor is it a regulatory requirement. Rather, the proposed methodology highlights the importance of testing various aspects of the model and using diverse statistical tools for rigorous checking and confidence building in the model and its predictions. It is this confidence that will encourage regulators and the public to accept decisions based on the model predictions. This validation approach will be applied to a model, described in this paper, dealing with an underground nuclear test site in rural Nevada.     

Induction in laterally non-uniform conductors: Theory and numerical models

The study of electromagnetic induction in laterally non-uniform conductors is briefly reviewed. The two-dimensional perturbation problem is considered and the two polarization cases which arise from Maxwell's equations are discussed. Techniques for the solution of the equations for laterally non-uniform conductors are discussed with emphasis on numerical methods.     

海啸传播模型与数值模拟研究进展

海啸在浅水大陆架的传播问题由于其非线性作用和浅水效应而变得十分复杂,然而目前成熟的海啸传播理论及数值模拟结果在这方面与实际并不一致.本文比较分析了可用来模拟大陆架海啸传播的浅水波模型和数值方法,并提出对我国东海陆架边缘可能发生的近海海啸需要开展数值试验研究.     

Resolution issues in numerical models of oceanic and coastal circulation

The baroclinic and barotropic properties of ocean processes vary on many scales. These scales are determined by various factors such as the variations in coastline and bottom topography, the forcing meteorology, the latitudinal dependence of the Coriolis force, and the Rossby radius of deformation among others. In this paper we attempt to qualify and quantify scales of these processes, with particular attention to the horizontal resolution necessary to accurately reproduce physical processes in numerical ocean models. We also discuss approaches taken in nesting or down-scaling from global/basin-scale models to regional-scale or shelf-scale models. Finally we offer comments on how vertical resolution affects the representation of stratification in these numerical models.     

Physical and numerical models of the magnetization self-reversal in rocks

The paper addresses the physical mechanism of the magnetization self-reversal in rocks. The self-reversal is the phenomenon of magnetization of a rock in the direction antiparallel to the magnetizing field. Experimental data on the self-reversal of thermal and thermoremanent magnetizations in natural analogues of hemoilmenites and synthetic hemoilmenites are presented. It is shown that the most probable mechanism of self-reversal is the single-phase Néel mechanism of the N-type. The N-type mechanism underlies the physical mechanism and numerical model of self-reversal developed in the paper. The numerical modeling results are compared with experimental data.     

Secular variation in numerical geodynamo models with lateral variations of boundary heat flow

We study magnetic field variations in numerical models of the geodynamo, with convection driven by nonuniform heat flow imposed at the outer boundary. We concentrate on cases with a boundary heat flow pattern derived from seismic anomalies in the lower mantle. At a Rayleigh number of about 100 times critical with respect to the onset of convection, the magnetic field is dominated by the axial dipole component and has a similar spectral distribution as Earth’s historical magnetic field on the core-mantle boundary (CMB). The time scales of variation of the low-order Gauss coefficients in the model agree within a factor of two with observed values. We have determined the averaging time interval needed to delineate deviations from the axial dipole field caused by the boundary heterogeneity. An average over 2000 years (the archeomagnetic time scale) is barely sufficient to reveal the long-term nondipole field. The model shows reduced scatter in virtual geomagnetic pole positions (VGPs) in the central Pacific, consistent with the weak secular variation observed in the historical field. Longitudinal drift of magnetic field structures is episodic and differs between regions. Westward magnetic drift is most pronounced beneath the Atlantic in our model. Although frozen flux advection by the large-scale flow is generally insufficient to explain the magnetic drift rates, there are some exceptions. In particular, equatorial flux spot pairs produced by expulsion of toroidal magnetic field are rapidly advected westward in localized equatorial jets which we interpret as thermal winds.     

How processing digital elevation models can affect simulated water budgets

For regional models, the shallow water table surface is often used as a source/sink boundary condition, as model grid scale precludes simulation of the water table aquifer. This approach is appropriate when the water table surface is relatively stationary. Since water table surface maps are not readily available, the elevation of the water table used in model cells is estimated via a two-step process. First, a regression equation is developed using existing land and water table elevations from wells in the area. This equation is then used to predict the water table surface for each model cell using land surface elevation available from digital elevation models (DEM). Two methods of processing DEM for estimating the land surface for each cell are commonly used (value nearest the cell centroid or mean value in the cell). This article demonstrates how these two methods of DEM processing can affect the simulated water budget. For the example presented, approximately 20% more total flow through the aquifer system is simulated if the centroid value rather than the mean value is used. This is due to the one-third greater average ground water gradients associated with the centroid value than the mean value. The results will vary depending on the particular model area topography and cell size. The use of the mean DEM value in each model cell will result in a more conservative water budget and is more appropriate because the model cell water table value should be representative of the entire cell area, not the centroid of the model cell.     

Analytical and numerical models to explain steady rates of spring flow

Flow from some springs in former glacial lakebeds of the Upper Midwest is extremely steady throughout the year and does not increase significantly after precipitation events or seasonal recharge. Analytical and simplified numerical models of spring systems were used to determine whether preferential ground water flow through high-permeability features in shallow sandstone aquifers could produce typical values of spring discharge and the unusually steady rates of spring flow. The analytical model is based on a one-dimensional solution for periodic ground water flow. Solutions to this model suggest that it is unlikely that a periodic forcing due to seasonal variations in areal recharge would propagate to springs in a setting where high-permeability features exist. The analytical model shows that the effective length of the aquifer, or the length of flowpaths to a spring, and the total transmissivity of the aquifer have the greatest potential to impact the nature of spring flow in this setting. The numerical models show that high-permeability features can influence the magnitude of spring flow and the results demonstrate that the lengths of ground water flowpaths increase when high-permeability features are explicitly modeled, thus decreasing the likelihood for temporal variations in spring flow.     

A critical discussion of numerical models for multiaquifer systems

Leaky aquifers constitute complicated hydrological structures, whose inclusion in numerical models of hydrological systems is difficult, because of their three-dimensional nature. Methods for treating such systems can be classified as fully three-dimensional and quasi-three-dimensional. The latter have clear numerical advantages when applicable. In this paper a critical discussion of existing quasi-three-dimensional models is presented.     

Comparative analyses of current three-dimensional numerical solar wind models

We present a comparative study of the most advanced three-dimensional time-dependent numerical simulation models of solar wind. These models can be classified into two categories:(I) theoretical, empirical and numerically based models and(II) self-consistent multi-dimensional numerical magnetohydrodynamic(MHD) models. The models of Category I are used to separately describe the solar wind solution in two plasma flows regions: transonic/trans-Alfvénic and supersonic/super-Alfvénic, respectively. Models of Category II construct a complete, single, numerical solar wind solution through subsonic/sub-Alfvénic region into supersonic/super-Alfvénic region. The Wang-Sheeley-Arge(WSA)/ENLIL in CISM is the most successful space weather model that belongs to Category I, and the Block-Adaptive-Tree-Solarwind-Roe-Upwind-Scheme(BATS-R-US) code in SWMF(Space Weather Modeling Framework) and the solar-interplanetary conservative element solution element MHD(SIP-CESE MHD) model in SWIM(Space Weather Integrated Model) are the most commonly-used models that belong to Category II. We review the structures of their frameworks, the main results for solar wind background studies that are essential for solar transient event studies, and discuss the common features and differences between these two categories of solar wind models. Finally, we conclude that the transition of these two categories of models to operational use depends on the availability of computational resources at reasonable cost and point out that the models' prediction capabilities may be improved by employing finer computational grids, incorporating more observational data and by adding more physical constraints to the models.     

Nocturnal temperature changes over tropics during CAWSES-III campaign: Comparison with numerical models and satellite data

In the frame of the third CAWSES tidal campaign in June–August 2007, lidar and satellite data were collected and compared with numerical models. Continuous nocturnal middle atmospheric temperature measurements performed with a Rayleigh lidar located at La Reunion Island (20.8°S–55.5°E) were obtained for three subsequent nights. The results clearly show the presence of tidal components with a downward phase propagation. Comparisons with SABER satellite data show good agreement on tidal amplitude; however, some differences on the structures are reported probably due to the zonal nature of the retrieval provided by the SABER data. The observed tidal components are compared with two different numerical models such as the 2D global scale wave model and the 3D-GCM LMDz-REPROBUS. Both models reveal good agreement with temperature lidar patterns, while simulated tidal amplitudes are smaller by a factor of around 2–2.5 K.