Numerical Variational Analysis Research Articles

Numerical analysis of variation among accessions of West African okra Abelmoschuscaillei (a. chev) stevel)

Numerical analysis of variation among accessions of West African okra Abelmoschuscaillei (a. chev) stevel)

Numerical analysis of variation among accessions of West African okra Abelmoschuscaillei (a. chev) stevel)

Nineteen quantitative characters were observed on 14 accessions of West African Okra. Principal Component Analysis (PCA) and Complete Linkage Cluster Analysis (CLCA) were employed to analyses the variation pattern in these accessions. The first three principal components accounted for 68.47% of the total variation. Using character variation, complete linkage cluster analysis summarized the position of accessions into a dendrogram at interval of 5% level of similarity, while the accessions were sorted into five distinct groups.

A numerical model of blood oxygenation during veno-venous ECMO: analysis of the interplay between blood oxygenation and its delivery parameters.

Veno-venous extracorporeal membrane oxygenation (VV-ECMO) is an important tool in the management of most severe forms of acute respiratory failure. The determinants and management of oxygen delivery in patients treated with VV-ECMO is a complex topic. The physiological principles of oxygenation on VV-ECMO are reviewed in many textbooks. However a numerical model is an additional instrument to be used in understanding and exploring this intricate subject matter. We present a numerical model of blood oxygenation during VV-ECMO. Using this model we examined the role and impact of each determinant on blood oxygenation. The numerical analysis of variation and interplay between each oxygenation determinants during VV-ECMO is presented in graphical form. These results corroborate all the findings of previous studies. The proposed numerical model facilitates understanding of oxygenation physiology during VV-ECMO; it can be used for a medical simulation system and for teaching the principles of oxygenation during VV-ECMO.

Application of Sasaki's numerical variational technique to the analysis of height and wind fields over Indian region

An objective analysis method based on Sasaki's numerical variational analysis technique has been taken up for the analysis of geopotential height and wind over the Indian region. The univariate optimum interpolation (UOI) method is used to generate the initial or input fields. These fields are then adjusted by the variational method.
 A study of this method over Indian and adjoining region for 850, 700, 500, 300 and 200 hPa levels is made from 4 to 8 July 1979 and the analyses obtained using this method are compared with the FGGE analyses.

Development and Testing of Statistical Tropical Cyclone Forecasting Techniques for the Southern Hemisphere

The Fleet Numerical Oceanography Center (FNOC) Numerical Variational Analysis (NVA) has been used to develop statistical–synoptic tropical cyclone forecast schemes for the Southern Hemisphere. Results, from a limited sample, showed that the best objective techniques were at least as good as the official Joint Typhoon Warning Center (JTWC) forecasts. Development and testing of the aids also indicated that approaches used in the Northern Hemisphere did not necessarily lead to better forecasts. Geographically orientated, rather than track-orientated coordinate systems, were found to have lower errors, especially with operational data. Stratification of the datasets by geographical location did not result in any significant improvements in the forecasting accuracy. Similarly, use of prediction equations based on storm position relative to the subtropical ridge did not result in the improvement found for the Northern Hemisphere. A comparison of techniques using height versus wind field data for the synoptic forcing component of the equations showed lowest errors with the mass field predictors. However, the differences were not statistically significant and this finding may have been a result of data quality rather than the field type.

Numerical analysis of variation among Nigerian Dioscorea rotundata accessions

In order to identify the major characters which account for variation among Dioscorea rotundata, 14 high yielding accessions were studied using Single Linkage Cluster Analysis (SLCA) and Principal Component Analysis (PCA). The accessions were planted under the same environmental conditions for 3 years. Altogether, 40 characters were selected and coded for analyses. Results of SLCA agreed with that of PCA ordination on axes I, II and III. Three Groups of accessions were revealed. The PCA showed that the main distinguishing characters between the yam accessions were Leaf size, tuber size, colour of tuber, number of flower spikes per node and length of spike. Some accessions failed to flower and they were easily differentiated. The discrimination between groups and description of differences between groups were more strongly marked from the PCA than in the SLCA.

Impact of Different Objective Analyses on the Tropical Cyclone Forecast Model

We have investigted the performance of a numerical tropical cyclone forecast model over the eastern North Pacific Ocean using two different analysis schemes. These are the spectral global model analysis of the U. S. A. National Meteorological Center and the tropical numerical variational analysis of U. S. Navy Fleet Numerical Oceanography Center. We found that the storm track forecasts using the two analyses were very different and a comparison of the prediction errors is given.

Numerical Variational Methods for Data Filtering and Interpolation

Abstract An objective representation of an observed meteorological field is obtained by minimizing a quadratic functional that measures both the smoothness (and regularity) of the objective field and the closeness to the observed data. This is a particular form of the general model for numerical variational analysis suggested by Wahba and Wendelberger to generalize the idea introduced by Sasaki. The solution of this minimization problem can be obtained by using homogeneous splines and cross validation or by using the finite element method to determine an approximate solution. Finite elements can provide data compression for large N. Testud and Chong proposed such a method, based on bilinear finite elements for 3-dimensional wind field analysis. We go further with the same principle and study a more regular approximation, which can be analytically differentiated, obtained by bicubic splines. The numerical simulations proposed by Chong and Testud are used to compare the capability of all these methods (spli...

Three-Dimensional Wind Field Analysis from Dual-Doppler Radar Data. Part I: Filtering, Interpolating and Differentiating the Raw Data

This paper is the first of three dealing with the three-dimensional wind field analysis from dual-Doppler radar data. Here we deal with the first step of the analysis which consists in interpolating and filtering the raw radial velocity fields within each coplane (or common plane simultaneously scanned by the two radars). To carry out such interpolation and filtering, a new method is proposed based on the principles of numerical variational analysis described by Sasaki (1970): the “filtered” representation of the observed field should be both “close” to the data points (in a least-squares sense) and verify some imperative of mathematical regularity. Any method for interpolating and smoothing data is inherently a filtering process. The proposed variational method enables this filtering to be controlled. The presented method is developed for any function of two variables but could be extended to the case of three or more variables. Numerical simulations substantiate the theoretically predicted filtering characteristics and show an improvement on other filtering schemes. It is found, compared to the classical filtering using the Cressman weighting function, that the variational method brings a substantial improvement of the gain curve (in the sense of a steeper cut-off), when the “regularity” of the second-order derivatives is imposed. It is worth noting that this improvement is achieved without increasing the computing time. It is also emphasized that an elaborate numerical differentiation scheme should be used to estimate the divergence, otherwise the gain curve for this parameter may be different from that for the Cartesian coplane velocities (which may induce distortion in the final three-dimensional wind field).

The Adjustment of Surface Wind and Pressure by Sasaki's Variational Matching Technique

Abstract The sea level pressure and surface wind fields operationally produced at Fleet Numerical Weather Central are adjusted by using numerical variational analysis. The analysis region is a global band extending from 40S to 6ON and the successive corrections method is used to generate the initial or input fields. These fields are then adjusted within the framework of the variational method by requiring that they satisfy certain governing dynamical equations. A detailed study of this method is made in the Atlantic Ocean region on 4 January 1971. There is convincing evidence that small-scale wind information is incorporated into the pressure field and that the adjusted wind field has been modified to account for ageostrophic motion.

A THEORETICAL INTERPRETATION OF ANISOTROPICALLY WEIGHTED SMOOTHING ON THE BASIS OF NUMERICAL VARIATIONAL ANALYSIS

Abstract The weighting factors used in conventional objective analysis methods are reviewed on the basis of numerical variational analysis. Special emphasis is placed on anisotropy (ellipticity) of the factors. The weighting factors of the objective analysis methods were empirically determined and are two dimensional in a horizontal plane (x, y). Most of these weighting factors are isotropic. However, anisotropic weighting factors have recently been used to give greater weight to the upstream and downstream observations as compared to those of the crosswind direction. A simple advection equation is used as a dynamical constraint in the numerical variational analysis in order to take into account quantitatively the effect of wind direction and speed on the anisotropy. A simple low-pass filter is also included in the variational formalism. A Green's function, derived for the Eular equation, is used to discuss the theoretical basis of the isotropic and anisotropic weighting factors. The results obtained from...

SOME BASIC FORMALISMS IN NUMERICAL VARIATIONAL ANALYSIS

Abstract This study aims at the theoretical development of a method of “four-dimensional analysis,” namely the numerical variational analysis. The three basic types of variational formalism in the numerical variational analysis method are discussed. The basic formalisms are categorized into three areas: (1) “timewise localized” formalism, (2) formalism with strong constraint, and (3) formalism with weak constraint. Exact satisfaction of selected prognostic equations were formulated as constraints in the functionals for the first two formalisms. However, only the second formalism contains explicitly the time variation terms in the Euler equations. The third formalism is characterized by the subsidiary condition which requires that the prognostic or diagnostic equations must be approximately satisfied. The variational formalisms and the associated Euler-Lagrange equations are obtained in the form of finite-difference analogs. In this article, the filtering of cach formalism and the uniqueness of solutions o...

NUMERICAL VARIATIONAL ANALYSIS WITH WEAK CONSTRAINT AND APPLICATION TO SURFACE ANALYSIS OF SEVERE STORM GUST

An investigation of the numerical variational analysis method is made for a case of “weak constraint” where the subsidiary condition is given in the form of an approximation. The simple example of a system moving with an optimized velocity is used to illustrate the theoretical development. The method is applied to analysis of the National Severe Storms Laboratory mesonetwork data of the severe storm gust that passed over the network on May 31, 1969.

NUMERICAL VARIATIONAL ANALYSIS FORMULATED UNDER THE CONSTRAINTS AS DETERMINED BY LONGWAVE EQUATIONS AND A LOW-PASS FILTER

Abstract The “timewise localized” variational formalism of the numerical variational analysis method is used (1) to filter and suppress unnecessary high-frequency noises contained in initial and forecast fields and (2) to obtain dynamically sound initial values in the areas lacking data. A set of nonlinear longwave equations and a low-pass filter minimizing local changes are used in this paper as dynamical constraints. Also proposed in this study is a technique to assure the convergence of a numerical solution of the nonlinear Euler equations by an iterative process. Three applications of the method are presented. The first two examples demonstrate that the initial guess in the iterative process influences significantly the speed of convergence. The last example is an application to the 500-mb analysis of hurricane Dora, 1964, and demonstrates a reasonable analysis in the data-sparse area where the hurricane was located at 1200 GMT on Sept. 8, 1964.