An approach to estimating and extrapolating model error based on inverse problem methods:towards accurate numerical weather prediction

Model error is one of the key factors restricting the accuracy of numerical weather prediction （NWP）. Considering the continuous evolution of the atmosphere, the observed data （ignoring the measurement error） can be viewed as a series of solutions of an accurate model governing the actual atmosphere. Model error is represented as an unknown term in the accurate model, thus NWP can be considered as an inverse problem to uncover the unknown error term. The inverse problem models can absorb long periods of observed data to generate model error correction procedures. They thus resolve the deficiency and faultiness of the NWP schemes employing only the initial-time data. In this study we construct two inverse problem models to estimate and extrapolate the time-varying and spatial-varying model errors in both the historical and forecast periods by using recent observations and analogue phenomena of the atmosphere. Numerical experiment on Burgers＇ equation has illustrated the substantial forecast improvement using inverse problem algorithms. The proposed inverse problem methods of suppressing NWP errors will be useful in future high accuracy applications of NWP.

The ‘Two oceans and one sea' extended range numerical prediction system with an ultra-high resolution atmosphere-ocean-land regional coupled model

The‘Two Oceans and One Sea’area(West Pacific,Indian Ocean,and South China Sea;15°S–60°N,39°–178°E)is a core strategic area for the‘21st Century Maritime Silk Road’project,as well as national defense.With the increasing demand for disaster prevention and mitigation,the importance of 10–30-day extended range prediction,between the conventional short-term(around seven days)and the climate scale(longer than one month),is apparent.However,marine extended range prediction is still a‘blank point’in China,making the early warning of marine disasters almost impossible.Here,the authors introduce a recently launched Chinese national project on a numerical forecasting system for extended range prediction in the‘Two Oceans and One Sea’area based on a regional ultra-high resolution multi-layer coupled model,including the scientific aims,technical scheme,innovation,and expected achievements.The completion of this prediction system is of considerable significance for the economic development and national security of China.

A study on the numerical prediction method for the vertical thermal structure in the Bohai Sea and the Huanghai Sea-I.One-dimensional numerical prediction model

In this paper, on the basis of the heat conduction equation without consideration of the advection and turbulence effects, one-dimensional model for describing surface sea temperature ( T1), bottom sea temperature ( Tt ) and the thickness of the upper homogeneous layer ( h ) is developed in terms of the dimensionless temperature θT and depth η and self-simulation function θT - f(η) of vertical temperature profile by means of historical temperature data.The results of trial prediction with our one-dimensional model on T, Th, h , the thickness and gradient of thermocline are satisfactory to some extent.

AN AIR POLLUTION PREDICTION TECHNIQUE FOR URBAN DISTRICTS BASED ON MESO-SCALE NUMERICAL MODEL

Taking Shenzhen city as an example, the statistical and physical relationship between the density of pollutants and various atmospheric parameters are analyzed in detail, and a space-partitioned city air pollution potential prediction scheme is established based on it. The scheme considers quantitatively more than ten factors at the surface and planetary boundary layer (PBL), especially the effects of anisotropy of geographical environment, and treats wind direction as an independent impact factor. While the scheme treats the prediction equation respectively for different pollutants according to their differences in dilute properties, it considers as well the possible differences in dilute properties at different districts of the city under the same atmospheric condition, treating predictions respectively for different districts. Finally, the temporally and spatially high resolution predictions for the atmospheric factors are made with a high resolution numerical model, and further the space-partitioned and time-variational city pollution potential predictions are made. The scheme is objective and quantitative, and with clear physical meaning, so it is suitable to use in making high resolution air pollution predictions.

Hydrological Evaluation with SWAT Model and Numerical Weather Prediction for Flash Flood Warning System in Thailand

Flash floods are a natural disaster that occurs annually, especially in the mountainous terrain and steep slopes of northern Thailand. The current flood forecasting systems and tools are available but have low accuracy and efficiency. The numbers of rainfall and runoff stations are less, because the access to the station area is difficult. Additionally, the operation and maintenance costs are high. Hydrological modeling of a SWAT （Soil and Water Assessment Tool） was used in this study with the application of three days weather forecast from the NWP （numerical weather prediction）, which provided temperature, relative humidity, rainfall, sunshine and wind speed. The data from NWP and SWAT were used to simulate the runoff from the Nan River in the last 10 years （2000-2010）. It was found that the simulated flow rate for the main streams using data from NWP were higher than the observations. At the N64 and Nl stations, the ratios of the maximum simulated flow rate to the observations were equal to 108% and 118%, respectively. However, for the tributaries, it was found that the simulated flow rate using NWP data was lower than the observations, but, it was still within the acceptable range of not greater than 20%,6. At N65, D090201 and D090203 stations, the ratio of the maximum simulated flow rate were 90.0%, 83.0% and 86.0%, respectively. This was due to the rainfall from the NWP model being greater than the measured rainfall. The NWP rainfall was distributed all over the area while the rainfall data from the measurements were obtained from specific points. Therefore, the rain from the NWP model is very useful especially for the watershed areas without rain gauge stations. In summary, the data from the NWP can be used with the SWAT model and provides relatively sound results despite the value for the main river being slightly higher than the observed data. Consequently, the output can be used to create a flood map for flash flood warning in the area.

The Predictability Problems in Numerical Weather and Climate Prediction

The uncertainties caused by the errors of the initial states and the parameters in the numerical model are investigated. Three problems of predictability in numerical weather and climate prediction are proposed, which are related to the maximum predictable time, the maximum prediction error, and the maximum admissible errors of the initial values and the parameters in the model respectively. The three problems are then formulated into nonlinear optimization problems. Effective approaches to deal with these nonlinear optimization problems are provided. The Lorenz’ model is employed to demonstrate how to use these ideas in dealing with these three problems.

Analogue correction method of errors and its application to numerical weather prediction

In this paper, an analogue correction method of errors （ACE） based on a complicated atmospheric model is further developed and applied to numerical weather prediction （NWP）. The analysis shows that the ACE can effectively reduce model errors by combining the statistical analogue method with the dynamical model together in order that the information of plenty of historical data is utilized in the current complicated NWP model, Furthermore, in the ACE, the differences of the similarities between different historical analogues and the current initial state are considered as the weights for estimating model errors. The results of daily, decad and monthly prediction experiments on a complicated T63 atmospheric model show that the performance of the ACE by correcting model errors based on the estimation of the errors of 4 historical analogue predictions is not only better than that of the scheme of only introducing the correction of the errors of every single analogue prediction, but is also better than that of the T63 model.

Prediction of Precipitation during Summer Monsoon with Self-memorial Model

In view of the fact that the atmospheric motion is an irreversible process, a memory function which can recall the observation data in the past is introduced, moreover, a special concept of self-memorization of the atmospheric motion is proposed, and a so-called self-memorization equation of the atmospheric motion has been derived. Based on the self-memorization principle, a numerical model for decadal forecast is established by means of the thermodynamic equation and the precipitation equation. The verification scores of the hindcasts of the model in the period from 1 to 12 years are much higher than that of monthly weather forecasts at present.

Evaluation of numerical wave model for typhoon wave simulation in South China Sea

The simulating waves nearshore(SWAN) model has typically been designed for wave simulations in near-shore regions. In this study, the model's applicability to the simulation of typhoon waves in the South China Sea(SCS) was evaluated. A blended wind field, consisting of an interior domain based on Fujita's model and an exterior domain based on Takahashi's model, was used as the driving wind field. The waves driven by Typhoon Kai-tak over the SCS that occurred in 2012 were selected for the numerical simulation research. Sensitivity analyses of time step, grid resolution, and angle resolution were performed in order to obtain optimal model settings. Through sensitivity analyses, it can be found that the time step has a large influence on the results, while grid resolution and angle resolution have a little effect on the results.

A Simplified Numerical Approach for the Prediction of Rainfall-Induced Retrogressive Landslides

Retrogressive landslides are common geological phenomena in mountainous areas and on onshore and offshore slopes. The impact of retrogressive landslides is different from that of other landslide types due to the phenomenon of retrogression. The hazards caused by retrogressive landslides may be increased because retrogressive landslides usually affect housing, facilities, and infrastructure located far from the original slopes. Additionally, substantial geomorphic evidence shows that the abundant supply of loose sediment in the source area of a debris flow is usually provided by retrogressive landslides that are triggered by the undercutting of water. Moreover, according to historic case studies, some large landslides are the evolution result of retrogressive landslides. Hence the ability to understand and predict the evolution of retrogressive landslides is crucial for the purpose of hazard mitigation. This paper discusses the phenomenon of a retrogressive landslide by using a model experiment and suggests a reasonably simplified numerical approach for the prediction of rainfall-induced retrogressive landslides. The simplified numerical approach, which combines the finite element method for seepage analysis, the shear strength reduction finite element method, and the analysis criterion for the retrogression and accumulation effect, is presented and used to predict the characteristics of a retrogressive landslide. The results show that this numerical approach is capable of reasonably predicting the characteristics of retrogressive landslides under rainfall infiltration, particularly the magnitude of each landslide, the position of the slip surface, and the development processes of the retrogressive landslide. Therefore, this approach is expected to be a practical method for the mitigation of damage caused by rainfall-induced retrogressive landslides.

A Forecast Error Correction Method in Numerical Weather Prediction by Using Recent Multiple-time Evolution Data

The initial value error and the imperfect numerical model are usually considered as error sources of numerical weather prediction （NWP）. By using past multi-time observations and model output, this study proposes a method to estimate imperfect numerical model error. This method can be inversely estimated through expressing the model error as a Lagrange interpolation polynomial, while the coefficients of polyno- mial are determined by past model performance. However, for practical application in the full NWP model, it is necessary to determine the following criteria： （1） the length of past data sufficient for estimation of the model errors, （2） a proper method of estimating the term ＂model integration with the exact solution＂ when solving the inverse problem, and （3） the extent to which this scheme is sensitive to the observational errors. In this study, such issues are resolved using a simple linear model, and an advection diffusion model is applied to discuss the sensitivity of the method to an artificial error source. The results indicate that the forecast errors can be largely reduced using the proposed method if the proper length of past data is chosen. To address the three problems, it is determined that （1） a few data limited by the order of the corrector can be used, （2） trapezoidal approximation can be employed to estimate the ＂term＂ in this study; however, a more accurate method should be explored for an operational NWP model, and （3） the correction is sensitive to observational error.

An evaporation duct prediction model coupled with the MM5

Evaporation duct is an abnormal refractive phenomenon in the marine atmosphere boundary layer. It has been generally accepted that the evaporation duct prominently affects the performance of the electronic equipment over the sea because of its wide distribution and frequent occurrence. It has become a research focus of the navies all over the world. At present, the diagnostic models of the evaporation duct are all based on the Monin-Obukhov similarity theory, with only differences in the flux and character scale calculations in the surface layer. These models are applicable to the stationary and uniform open sea areas without considering the alongshore effect. This paper introduces the nonlinear factor a and the gust wind item wg into the Babin model, and thus extends the evaporation duct diagnostic model to the offshore area under extremely low wind speed. In addition, an evaporation duct prediction model is designed and coupled with the fifth generation mesoscale model （MMS）. The tower observational data and radar data at the Pingtan island of Fujian Province on May 25-26, 2002 were used to validate the forecast results. The outputs of the prediction model agree with the observations from 0 to 48 h. The relative error of the predicted evaporation duct height is 19.3% and the prediction results are consistent with the radar detection.

Numerical microstructure prediction for an aluminium casting and its experimental validation

Virtual manufacturing based on through-process modelling becomes an evolving research area which aims at integrating diverse simulation tools to realize computer-aided design, analysis, prototyping and manufacturing. Numerical prediction of the as-cast microstructure is an initial and critical step in the whole through- process modelling chain for engineering components. A commercial software package with the capability of calculating important microstructure features for aluminium alloys is used to simulate a G-AISi7MgCu0.5 laboratory casting. The simulated microstructure, namely grain size, secondary dendrite arm spacing and diverse phase fractions are verified experimentally. Correspondence and discrepancies are reported and discussed.

Real-time 3-D space numerical shake prediction for earthquake early warning

In earthquake early warning systems, real-time shake prediction through wave propagation simulation is a promising approach. Compared with traditional methods, it does not suffer from the inaccurate estimation of source parameters. For computation efficiency, wave direction is assumed to propagate on the 2-D surface of the earth in these methods. In fact, since the seismic wave propagates in the 3-D sphere of the earth, the 2-D space modeling of wave direction results in inaccurate wave estimation. In this paper, we propose a 3-D space numerical shake pre- diction method, which simulates the wave propagation in 3-D space using radiative transfer theory, and incorporate data assimilation technique to estimate the distribution of wave energy. 2011 Tohoku earthquake is studied as an example to show the validity of the proposed model. 2-D space model and 3-D space model are compared in this article, and the prediction results show that numerical shake prediction based on 3-D space model can estimate the real-time ground motion precisely, and overprediction is alleviated when using 3-D space model.

Rapid prediction models for 3D geometry of landslide dam considering the damming process

The geometry of a landslide dam plays a critical role in its stability and failure mode,and is influenced by the damming process.However,there is a lack of understanding of the factors that affect the 3D geometry of a landslide dam.To address this gap,we conducted a study using the smoothed particle hydrodynamics numerical method to investigate the evolution of landslide dams.Our study included 17 numerical simulations to examine the effects of several factors on the geometry of landslide dams,including valley inclination,sliding angle,landslide velocity,and landslide mass repose angle.Based on this,three rapid prediction models were established for calculating the maximum height,the minimum height,and the maximum width of a landslide dam.The results show that the downstream width of a landslide dam remarkably increases with the valley inclination.The position of the maximum dam height along the valley direction is independent of external factors and is always located in the middle of the landslide width area.In contrast,that position of the maximum dam height across the valley direction is significantly influenced by the sliding angle and landslide velocity.To validate our models,we applied them to three typical landslide dams and found that the calculated values of the landslide dam geometry were in good agreement with the actual values.The findings of the current study provide a better understanding of the evolution and geometry of landslide dams,giving crucial guidance for the prediction and early warning of landslide dam disasters.

Prediction of Weld Joint Shape and Dimensions in Laser Welding Using a 3D Modeling and Experimental Validation

This paper presents an experimentally validated weld joint shape and dimensions predictive 3D modeling for low carbon galvanized steel in butt-joint configurations. The proposed modelling approach is based on metallurgical transformations using temperature dependent material properties and the enthalpy method. Conduction and keyhole modes welding are investigated using surface and volumetric heat sources, respectively. Transition between the heat sources is carried out according to the power density and interaction time. Simulations are carried out using 3D finite element model on commercial software. The simulation results of the weld shape and dimensions are validated using a structured experimental investigation based on Taguchi method. Experimental validation conducted on a 3 kW Nd: YAG laser source reveals that the modelling approach can provide not only a consistent and accurate prediction of the weld characteristics under variable welding parameters and conditions but also a comprehensive and quantitative analysis of process parameters effects. The results show great concordance between predicted and measured values for the weld joint shape and dimensions.

NUMERICAL GEODYNAMIC MODELLING OF COUPLED MECHANO-THERMO-HYDROLOGICAL PROCESSES AND ITS APPLICATION IN PREDICTIVE EXPLORATION IN THE FENGHUANGSHAN ORE FIELD, TONGLING

Mineralisation is the result of the coupled multi-geodynamic processes in the crust. The coupled mechano-thermo-hydrological （MTH） processes are the basic physical processes that govern the location of the hydrothermal mineralization, which can be simulated in the computer by using of the numerical codes, such as FLAC. The numerical modeling results can be used not only to explain the features of existing ore deposits, but also to predict the fhvorable mineralization locations. This paper has summarized the basic equations describing coupled MHT processes in the water-saturated porous rocks, the principles of FLAC, and its application to the MHT processes related to copper mineralization in the Fenghuangshan ore field. We used the FLAC to simulate the syn-deformation cooling and fluid flowing evolution after the intrusion was emplaced and solidified. The modeling results suggest a most prospective exploration area where the subsequent exploration supported the prediction and the test bore hole disclosed the high quality copper ore bodies in the target, demonstrating a positive role of the numerical MTH modeling in facilitating predictive ore discovery.

A Simplified Model for the Prediction of the Erosion of a Metal Screen for Sand Control

In oil drilling processes,sand production in the oil layer is a common issue,generally mitigated by means of sand control screens.To prevent or reduce the risk of damage of these screens and to improve the related service life,it is necessary to investigate the related erosion dynamics.In this study,a screen mesh model based on the flow field similarity theory is proposed to overcome the otherwise too complex geometric structure of this type of equipment.Such model is optimized using experimental data.The predicted results are in good agreement with the measured values,and the error is less than 15%.The results also show that the simplified geometric screen model and the optimized Zhang et al.erosion model have high reliability;therefore,they could effective be used to select underground screen meshes and improve the design of production process.

Numerical modeling of global seismic phases and its application in seismic phase identification

Earthquake data include informative seismic phases that require identification for imaging the Earth's structural interior.In order to identify the phases,we created a numerical method to calculate the traveltimes and raypaths by a shooting technique based upon the IASP91 Earth model,and it can calculate the traveltimes and raypaths for not only the seismic phases in the traditional traveltime tables such as IASP91,AK135,but also some phases such as pPcP,pPKIKP,and PPPPP.It is not necessary for this method to mesh the Earth model,and the results from the numerical modeling and its application show that the absolute differences between the calculated and theoretical traveltimes from the ISAP91 tables are less than 0.1 s.Thus,it is simple in manipulation and fast in computation,and can provide a reliable theoretical prediction for the identification of a seismic phase within the acquired earthquake data.

Real-time numerical shake prediction and updating for earthquake early warning

Ground motion prediction is important for earthquake early warning systems, because the region＇s peak ground motion indicates the potential disaster. In order to predict the peak ground motion quickly and pre- cisely with limited station wave records, we propose a real- time numerical shake prediction and updating method. Our method first predicts the ground motion based on the ground motion prediction equation after P waves detection of several stations, denoted as the initial prediction. In order to correct the prediction error of the initial prediction, an updating scheme based on real-time simulation of wave propagation is designed. Data assimilation technique is incorporated to predict the distribution of seismic wave energy precisely. Radiative transfer theory and Monte Carlo simulation are used for modeling wave propagation in 2-D space, and the peak ground motion is calculated as quickly as possible. Our method has potential to predict shakemap, making the potential disaster be predicted before the real disaster happens. 2008 Ms8.0 Wenchuan earthquake is studied as an example to show the validity of the proposed method.