An examination of the use of the logratio transformation for the testing of endmember hypotheses

Given a compositional dataset in the absence of any prior information on any mixing process which may have formed it, a complete analysis of mixtures determines three distinct types of estimates in order. These are: (i) the estimate of the number of endmembers or fixed source compositions, of which all the sample compositions of the dataset must be approximate mixtures; (ii) the estimated compositions for each of these chosen number of endmembers; and (iii) the estimated contributions of each of these endmember estimates to each sample. Traditionally, the estimate for the number of endmembers has been assessed either by mapping or by inspection of the coefficients of determination between the observed and estimated variables. Mapping entails the plotting on a map of the region from which the samples were taken, either the contours of the contributions of each endmember to each sample, or some other portrayal of the distribution of endmember abundances. Because it requires the complete analysis, assessment by this method is too elaborate except for final confirmation and display. Alternatively, choosing a number of endmembers, which result in suitability high coefficients of determination for all or most variables, may account for elements which are not part of the conjectured mixing process or, worse, may result in the identification of endmembers which may never in fact have existed. Such an error is similar to overspecifying a multiple regression model. So, the obvious starting point from which to assess the validity, or otherwise choice of endmember numbers, is to examine the matrix of residuals. The differences between the logratio-transformed observed and estimated data form an array of residual logratios. A linear combination of these may be formed for each sample, which, under a random perturbation assumption, should follow a univariate normal distribution. Whether or not this scalar is normal can be readily tested. It can also be examined graphically for such desirable qualities as symmetry when the test for normality may be too severe. This procedure is employed to assess the decompositions of the U.S.G.S. Mid-Pacific data and the Nazca Plate Surface sediments.This paper was presented at the 18th Geochautauqua, Newark, Delaware, 13–14 October 1989.     

A solution of the elastodynamic equation in an anelastic earth model

A formal solution to the elastodynamic equation in an anelastic earth model is presented. The derivation also incorporates the effects of aspherical structure, rotation, self-gravitation, and pre-stress. It is found that the solution can be expressed as a sum of the normal modes of the earth model along with additional terms accounting for anelastic relaxation processes. However, the derivation does not assume that such an eigenfunction expansion is possible, and so avoids difficulties previously encountered due to the non self-adjointness of the problem.     

Sensitivity of Mesoscale Model Forecast During a Satellite Launch to Different Cumulus Parameterization Schemes in MM5

The identification of the model discrepancy and skill is crucial when a forecast is issued. The characterization of the model errors for different cumulus parameterization schemes (CPSs) provides more confidence on the model outputs and qualifies which CPSs are to be used for better forecasts. Cases of good/bad skill scores can be isolated and clustered into weather systems to identify the atmospheric structures that cause difficulties to the forecasts. The objective of this work is to study the sensitivity of weather forecast, produced using the PSU-NCAR Mesoscale Model version 5 (MM5) during the launch of an Indian satellite on 5th May, 2005, to the way in which convective processes are parameterized in the model. The real-time MM5 simulations were made for providing the weather conditions near the launch station Sriharikota (SHAR). A total of 10 simulations (each of 48 h) for the period 25th April to 04th May, 2005 over the Indian region and surrounding oceans were made using different CPSs. The 24 h and 48 h model predicted wind, temperature and moisture fields for different CPSs, namely the Kuo, Grell, Kain-Fritsch and Betts-Miller, are statistically evaluated by calculating parameters such as mean bias, root-mean-squares error (RMSE), and correlation coefficients by comparison with radiosonde observation. The performance of the different CPSs, in simulating the area of rainfall is evaluated by calculating bias scores (BSs) and equitable threat scores (ETSs). In order to compute BSs and ETSs the model predicted rainfall is compared with Tropical Rainfall Measuring Mission (TRMM) observed rainfall. It was observed that model simulated wind and temperature fields by all the CPSs are in reasonable agreement with that of radiosonde observation. The RMSE of wind speed, temperature and relative humidity do not show significant differences among the four CPSs. Temperature and relative humidity were overestimated by all the CPSs, while wind speed is underestimated, except in the upper levels. The model predicted moisture fields by all CPSs show substantial disagreement when compared with observation. Grell scheme outperforms the other CPSs in simulating wind speed, temperature and relative humidity, particularly in the upper levels, which implies that representing entrainment/detrainment in the cloud column may not necessarily be a beneficial assumption in tropical atmospheres. It is observed that MM5 overestimates the area of light precipitation, while the area of heavy precipitation is underestimated. The least predictive skill shown by Kuo for light and moderate precipitation asserts that this scheme is more suitable for larger grid scale (>30 km). In the predictive skill for the area of light precipitation the Betts-Miller scheme has a clear edge over the other CPSs. The evaluation of the MM5 model for different CPSs conducted during this study is only for a particular synoptic situation. More detailed studies however, are required to assess the forecast skill of the CPSs for different synoptic situations.     

谱模式T63L9正规模初值化方案及试验

推导了全球谱模式T63L9的正规模,对求得的垂直和水平正规模做了分析,与其他文献进行了比较.在此基础上,为其资料四维同化系统研制了一套合适的绝热非线性正规模初值化方案,并进行了一系列试验.分析表明:方案的研制是成功的,它有效地消除了模式早期积分中虚假的高频振荡,明显改进了短期预报的效果;初值化不仅对随后的一次预报有明显的改进,而且通过同化循环,提高了整个资料同化和预报的质量.     

Arnol'd Nonlinear Stability Theorems and their Application to the Atmosphere and Oceans

Within the context of atmospheric and oceanic fluid dynamicsthe problems of nonlinear stability and instability, particularlythe Arnol'd second type nonlinear stability, are surveyed.The stability criteria obtained by means of the energy-Casimirand energy-Lagrange methods are presented for a varietyof models, the estimates for various generalized perturbationenergy and enstrophy are given. Potential applications of thesecriteria are shown in the estimation of bounds on the perturbationenergy and enstrophy, in the diagnostic study of the persistence orbreakdown of jet flows in the middle and high latitudes, and in theverification of the validity of the tangent linear model in bothatmospheric dynamics and oceanography.Some further research results are also highlighted.     

水库洪水标准的风险分析

将标准风险评估方法应用到水库洪水标准的风险分析中，并以柴河水库为例，说明水库洪水标准的风险分析方法是可行的，具有推广价值。     

Earth’s density flattening and hypothesis of latitudinal normal density

In this paper, the definition of latitudinal density and density flattening of the level ellipsoid is given, and integral formulas of latitudinal density for pole gravity and equator gravity are derived. According to the pole gravity condition and equator gravity condition for the level ellipsoid, latitudinal density distribution function of the level ellipsoid is obtained. It is proved mathematically that latitudinal density of the earth’s equator is larger than that of the pole, the earth’s density flattening calculated preliminarily is 1/322, and hypothesis of the earth’s latitudinal normal density is further proposed, so that theoretical preparation for studying the forming cause of the earth gravity in problems such as continent drift, mantle convection, and submarine extension is made well.     

B-polarization induction in two thin half-sheets coupled to the mantle by a conducting crust—II. Solution by the mode-matching method, the fields above the conductors, and example results

The mode-matching method is used to obtain an exact analytical solution to the problem of B -polarization induction in two adjacent thin half-sheets, lying on a conducting layer that is terminated by a perfect conductor at finite depth. These components of the model represent, respectively, the Earth's conducting surface layers, crust, and mantle. In dimensionless variables, the model has three independent parameters, these being the two thin-sheet conductances and the layer thickness. The mode-matching solution obtained in this paper is shown to be identical lo that derived via the Wiener-Hopf method in a companion paper (Dawson 1996), and so provides additional verification of that solution. As was shown in the companion paper, the solution for the present model contains, as special limiting cases, those for three models considered earlier by various authors. The second part of the present paper addresses the solutions for the electric fields in the non-conducting half-space above the conductors, which represents the atmosphere. In the final part, sample numerical calculations are presented to illustrate the solution.     

泥沙起动条件与卵石浅滩航道整治线宽度的确定

在简述泥沙起动条件表达式的基础上,本文分析卵石浅滩整治与泥沙起动条件的关系。根据起动拖曳力和起动流速的概念,分别导出了卵石浅滩航道整治宽度计算公式,并用北江整治河段的实测资料对诸公式作了比较。结果表明,式(16)的计算值与实际采用值有较好的一致性。