Extended Range(10–30 Days) Heavy Rain Forecasting Study Based on a Nonlinear Cross-Prediction Error Model

Extended range （10-30 d） heavy rain forecasting is difficult but performs an important function in disaster prevention and mitigation. In this paper, a nonlinear cross prediction error （NCPE） algorithm that combines nonlinear dynamics and statistical methods is proposed. The method is based on phase space reconstruction of chaotic single-variable time series of precipitable water and is tested in 100 global cases of heavy rain. First, nonlinear relative dynamic error for local attractor pairs is calculated at different stages of the heavy rain process, after which the local change characteristics of the attractors are analyzed. Second, the eigen-peak is defined as a prediction indicator based on an error threshold of about 1.5, and is then used to analyze the forecasting validity period. The results reveal that the prediction indicator features regarded as eigenpeaks for heavy rain extreme weather are all reflected consistently, without failure, based on the NCPE model; the prediction validity periods for 1-2 d, 3-9 d and 10-30 d are 4, 22 and 74 cases, respectively, without false alarm or omission. The NCPE model developed allows accurate forecasting of heavy rain over an extended range of 10-30 d and has the potential to be used to explore the mechanisms involved in the development of heavy rain according to a segmentation scale. This novel method provides new insights into extended range forecasting and atmospheric predictability, and also allows the creation of multi-variable chaotic extreme weather prediction models based on high spatiotemporal resolution data.

Analytical exploration of γ-function explicit method for pseudodynamic testing of nonlinear systems

It has been well studied that the γ-function explicit method can be effective in providing favorable numerical dissipation for linear elastic systems. However, its performance for nonlinear systems is unclear due to a lack of analytical evaluation techniques. Thus, a novel technique is proposed herein to evaluate its efficiency for application to nonlinear systems by introducing two parameters to describe the stiffness change. As a result, the numerical properties and error propagation characteristics of the γ-function explicit method for the pseudodynamic testing of a nonlinear system are analytically assessed. It is found that the upper stability limit decreases as the step degree of nonlinearity increases; and it increases as the current degree of nonlinearity increases. It is also shown that this integration method provides favorable numerical dissipation not only for linear elastic systems but also for nonlinear systems. Furthermore, error propagation analysis reveals that the numerical dissipation can effectively suppress the severe error propagation of high frequency modes while the low frequency responses are almost unaffected for both linear elastic and nonlinear systems.

Extensions of nonlinear error propagation analysis for explicit pseudodynamic testing

Two important extensions of a technique to perform a nonlinear error propagation analysis for an explicit pseudodynamic algorithm （Chang, 2003） are presented. One extends the stability study from a given time step to a complete step-by-step integration procedure. It is analytically proven that ensuring stability conditions in each time step leads to a stable computation of the entire step-by-step integration procedure. The other extension shows that the nonlinear error propagation results, which are derived for a nonlinear single degree of freedom （SDOF） system, can be applied to a nonlinear multiple degree of freedom （MDOF） system. This application is dependent upon the determination of the natural frequencies of the system in each time step, since all the numerical properties and error propagation properties in the time step are closely related to these frequencies. The results are derived from the step degree of nonlinearity. An instantaneous degree of nonlinearity is introduced to replace the step degree of nonlinearity and is shown to be easier to use in practice. The extensions can be also applied to the results derived from a SDOF system based on the instantaneous degree of nonlinearity, and hence a time step might be appropriately chosen to perform a pseudodynamic test prior to testing.

NONLINEAR WAVELET SMOOTHING OF ERROR DENSITY IN A SEMIPARAM ETRIC REGRESSION MODEL

In this paper,a sem iparam etric regression m odel in w hich errors are i.i.d random variables from an unknow n density f(·) is considered.Based on Hallet al.(1995),a nonlinear w avelet estim ation of f(·) withoutrestrictions ofcontinuity everyw here on f(·) is given,and the convergence rate ofthe estim ators in L2 is obtained.

Impact of observational MJO forcing on ENSO predictability in the Zebiak-Cane model: PartⅠ.Effect on the maximum prediction error

With the observational wind data and the Zebiak-Cane model, the impact of Madden-Iulian Oscillation （MJO） as external forcing on El Nino-Southern Oscillation （ENSO） predictability is studied. The observational data are analyzed with Continuous Wavelet Transform （CWT） and then used to extract MJO signals, which are added into the model to get a new model. After the Conditional Nonlinear Optimal Perturbation （CNOP） method has been used, the initial errors which can evolve into maximum prediction error, model errors and their join errors are gained and then the Nifio 3 indices and spatial structures of three kinds of errors are investigated. The results mainly show that the observational MJO has little impact on the maximum prediction error of ENSO events and the initial error affects much greater than model error caused by MJO forcing. These demonstrate that the initial error might be the main error source that produces uncertainty in ENSO prediction, which could provide a theoretical foundation for the adaptive data assimilation of the ENSO forecast and contribute to the ENSO target observation.

Selection of time step for pseudodynamic testing

Although the step degree of nonlinearity has been introduced to conduct basic analysis and error propagation analysis for the pseudodynamic testing of nonlinear systems, it cannot be reliably used to select an appropriate time step before performing a pseudodynamic test. Therefore, a novel parameter of instantaneous degree of nonlinearity is introduced to monitor the stiffness change at the end of a time step, and can thus be used to evaluate numerical and error propagation properties for nonlinear systems. Based on these properties, it is possible to select an appropriate time step to conduct a pseudodynamic test in advance. This possibility is very important in pseudodynamic testing, since the use of an arbitrary time step might lead to unreliable results or even destroy the test specimen. In this paper, guidelines are proposed for choosing an appropriate time step for accurate integration of nonlinear systems. These guidelines require estimation of the maximum instantaneous degree of nonlinearity and the solution of the initial natural frequency. The Newmark explicit method is chosen for this study. All the analytical results and the guidelines proposed are thoroughly confirmed with numerical examples.

Angle measurement technology based on magnetization vector for narrow space applications

With the wide application of laser in the field of skin plastic surgery, micro laser galvanometer scanner has made great progress in this field with its portability. However, the measurement method used to measure the deflection angle of laser galvanometer in the narrow space of scanner with high precision remains to be studied. In this paper, an angle measurement method based on magnetic field is proposed, and the effect of the shapes of permanent magnets(PMs) on the measurement is studied by theoretical and experimental study under the condition that the maximum available space for the PMs is a 10 mm side cube. An angle measuring experimental device is set up, and the contrast experiment is carried out with different PMs which are the same as simulation. The experimental results show that cylindrical PM is more suitable than other PMs, which is consistent with the simulation results, and the maximum nonlinearity error is 0.562%. This method has the advantages of small volume,non-contact measurement, small moment of inertia, good dynamic response and no external excitation for the PMs, so it has a broad application prospect in micro laser galvanometer scanner.

Adsorption Isotherm, Kinetic and Thermodynamic Modelling of <i>Bacillus subtilis</i>ATCC13952 Mediated Adsorption of Arsenic in Groundwaters of Selected Gold Mining Communities in the Wassa West Municipality of the Western Region of Ghana

This study investigated Bacillus subtilis ATCC13952 as an adsorbent for arsenic in groundwater. Batch experiments were used to determine the effect of contact time, adsorbent dose, arsenic (III) concentration, pH, and temperature on the process. The percentage of arsenic (III) removed was high at a contact time of four days, 3.0 mL of Bacillus subtilis ATCC13952, pH 8 and temperature of 35°C. The kinetics of the process showed the Elovich kinetics model as the best fit for the process. This indicates that arsenic removal was by chemisorption. The analysis of the nonlinear equilibrium isotherms and the error functions showed the Langmuir isotherm as best fit for the process. Mechanistic study of the process indicated bulk diffusion to be the rate-determining step. Thermodynamically, the process was favourable, spontaneous and feasible. When the community water samples were treated with the Bacillus subtilis ATCC13952 at the optimum contact time, adsorbent dose, pH and temperature, 99.96% - 99.97% of arsenic was removed across all sampling points within the studied communities. Hence, the results show that Bacillus subtilis ATCC13952 is an efficient adsorbent for arsenic in aqueous systems and the organism appears to hold the key to purging the environment of arsenic contamination.

Correction of Interferometric High-Order Nonlinearity Error in Metrological Atomic Force Microscopy

Metrological atomic force microscopes(Met.AFMs)with built-in interferometers are one of the main workhorses for versatile dimensional nanometrology.The interferometric nonlinearity error,particularly the high-order(i.e.,3rd-and 4th-order)nonlinearity errors,is a dominant error source for further improving their metrology performance,which cannot be corrected using the conventional Heydemann correction method.To solve this problem,two new methods were developed.One uses a capacitive sensor embedded in the Met.AFM,and the other applies an external physical artifact with a flat surface.Both methods can be applied very conveniently and can effectively reduce the nonlinearity error.In this paper,the propagation of the(residual)nonlinearity error in step height calibrations is examined.Finally,the performance of the improved tool is verified in the calibration of a highly demanding industrial sample.For the measurements performed at 25 different positions and repeated six times,the standard deviation of the total 150 measured values is 0.08 nm,which includes the contributions from the reproducibility of the metrology tool and sample inhomogeneity.This research has significantly improved our dimensional nanometrology service.For instance,the extended measurement uncertainty(k=2)is reduced from 1.0 to 0.3 nm for the step height or etching depth calibrations.

TWO-GRID CHARACTERISTIC FINITE VOLUME METHODS FOR NONLINEAR PARABOLIC PROBLEMS＊

In this work, two-grid characteristic finite volume schemes for the nonlinear parabolic problem are considered. In our algorithms, the diffusion term is discretized by the finite volume method, while the temporal differentiation and advection terms are treated by the characteristic scheme. Under some conditions about the coefficients and exact solution, optimal error estimates for the numerical solution are obtained. Furthermore, the two- grid characteristic finite volume methods involve solving a nonlinear equation on coarse mesh with mesh size H, a large linear problem for the Oseen two-grid characteristic finite volume method on a fine mesh with mesh size h = O（H2） or a large linear problem for the Newton two-grid characteristic finite volume method on a fine mesh with mesh size h = 0（I log hll/2H3）. These methods we studied provide the same convergence rate as that of the characteristic finite volume method, which involves solving one large nonlinear problem on a fine mesh with mesh size h. Some numerical results are presented to demonstrate the efficiency of the proposed methods.

ASYMPTOTIC ERROR EXPANSION FOR THE NYSTROM METHOD OF NONLINEAR VOLTERRA INTEGRAL EQUATION OF THE SECOND KIND

While the numerical solution of one-dimensional Volterra integral equations of the second kind with regular kernels is well understood, there exist no systematic studies of asymptotic error expansion for the approximate solution. In this paper,we analyse the Nystrom solution of one-dimensional nonlinear Volterra integral equation of the second kind and show that approkimate solution admits an asymptotic error expansion in even powers of the step-size h, beginning with a term in h2. So that the Richardson's extrapolation can be done. This will increase the accuracy of numerical solution greatly.

A novel pressure sensor calibration system based on a neural network

According to the specific input-output characteristics of a pressure sensor, a novel calibration algorithm is presented and a calibration system is developed to correct the nonlinear error caused by temperature. In contrast to the routine BP and RBF, curve fitting based on RBF is first used to get the slope and intercept, and then the voltage-pressure curve is described. Test results show that the algorithm features fast convergence speed, strong robustness and minimum SSE （sum of squares for error）. It is proven by practical applications that this calibration system works well and the measurement precision is better than the design demands. Furthermore, this calibration system has a good real-time capability.