Text in Afrikaans, abstract in Afrikaans and English / As deel van die weermodifikasie-eksperiment in Bethlehem, Suid-Afiika, is 'n reenmeternetwerk geinstalleer, en word die neerslagwaardes R; wat by 43 reenmeterstasies waargeneem is, vergelyk met die waargenome radar reflektiwiteit Z;. Alhoewel radar ruimtelike en tydskontinue metings van reflektiwiteit bied wat onmiddellik by een sentrale punt beskikbaar is, is die akkuraatheid van radar om reenval te meet onseker as gevolg van verskeie potensiele foute in die omskakeling van reflektiwiteit na reenval. Dit word aanvaar dat reenmeters akkurate puntwaarnemings van reenval gee en daar bestaan eenstemmigheid dat die kombinasie van die twee metodes beter is as enigeen van die metodes afsonderlik. In hierdie studie ondersoek ek die toepassing van die veralgemeende lineere model as 'n beramingstegniek. Vorige studies gebruik die log-log transformasie, d. w.s. logZ = logA + b(logR) van die Z = ARb verwantskap om die koeffisiente A en b met behulp van kleinste-kwadrate-regressie te bepaal. Die implisiete aanname hiermee is dat die foute ongekorreleerd is. Met die inverse verwantskap R = czd d.w.s. logR = logC + d(logZ) neem ek aan dat die waarnemings nie onafhanklik is nie sodat die regressiekoeffisiente bereken word met behulp van die metode van die veralgemeende lineere model. Om die ruimtelike afhanklikheid van die reenmeterwaarnemings te modelleer, word eksperimentele variogramme uit die data bereken en gepas met teoretiese variogramme wat gebruik word om die variansie-kovariansiematriks te vu!. "Gemiddeld" vaar hierdie metode beter as gewone regressie vir analises wat reenmeters wat verder as 45km vanaf die radarstel is, insluit. Residu-stipping wys dat die afstand van die meter vanaf die radarstel as 'n afsonderlike onafhanklike veranderlike in die regressievergelyking ingesluit behoort te word, d.w.s. die beraming verbeter met logR = 3-0 + a,(logZ) + a2(afstand). Hierdie meervoudige regressiemodel stem ooreen met die teoretiese model van Smith en Krajewski omdat e -- afstand as 'n praktiese manifestasie van die foutproses [e.,, (ij)] beskou kan word. Omdat E(ez) = eE<ZJ e'"a' as Z 'n lognormaalverdeling het, kan die sydigheid wat ontstaan wanneer antilogaritmes geneem word, reggestel word deur die beraamde reenval met e112 "' te vermenigvuldig. Die studie !ewer 'n bydrae met die afleiding van 'n beramingstegniek wat die beraming van neerslag uit radar betekenisvol verbeter. / In a study of a rain-gauge network that was installed for a weather modification experiment in Bethlehem, South Africa, precipitation values R; observed at 43 gauging stations are compared to the observed radar reflectivity Z;. Although radar provides spatial and temporal measurements of reflectivity that are immediately available at one location, the accuracy of radar estimation of rainfall is uncertain due to various potential errors in the conversion from reflectivity to rainfall. Rain-gauges are assumed to give accurate point measurements of rainfall and there is general agreement that the combination of systems is better than either system alone. In this study I explore the application of the general linear model as an estimation technique. Previous studies have used the log-log transform, i.e. logZ = logA + b(logR) of the Z = ARb relation, and applied least-squares regression analysis to determine the coefficients A and b. This implicitly assumes that the disturbances are uncorrelated. Working with the inverse relation R = czd i.e. logR = logC + d(logZ) and assuming that the observations are not independent we compute the regression coefficients using generalised least squares. To model the spatial dependence of the rain-gauge observations we compute experimental variograms from the data and fit them with theoretical variograms which are then used to fill the variance-covariance matrix. "On average" this method performs better than ordinary regression for the analyses that included rain-gauges further than 45km from the radar set. Residual plotting revealed that distance of the rain-gauge from the radar set should be included as a separate independent variable in the regression equation, i.e. logR = ao + a1(logZ) + a1(distance) improved the estimation of rainfall as it performs better than ordinary regression. This multiple regression model agrees with the theoretical model of Smith and Krajewski in the sense that e "'distance is a practical manifestation of the error process [ e,, (ij)]. Showing that E( ez) = el!.(!.) e 112 "' if Z has a lognormal distribution, the bias when taking antilogs can be removed by multiplying estimated rainfall by e1 ' 2a'. The contribution of this study is the derivation of an estimation technique which significantly improves the estimation of rainfall from radar / Mathematical Sciences / D. Phil. (Statistics)

Text in Afrikaans, abstract in Afrikaans and English / As deel van die weermodifikasie-eksperiment in Bethlehem, Suid-Afiika, is 'n reenmeternetwerk geinstalleer, en word die neerslagwaardes R; wat by 43 reenmeterstasies waargeneem is, vergelyk met die waargenome radar reflektiwiteit Z;. Alhoewel radar ruimtelike en tydskontinue metings van reflektiwiteit bied wat onmiddellik by een sentrale punt beskikbaar is, is die akkuraatheid van radar om reenval te meet onseker as gevolg van verskeie potensiele foute in die omskakeling van reflektiwiteit na reenval. Dit word aanvaar dat reenmeters akkurate puntwaarnemings van reenval gee en daar bestaan eenstemmigheid dat die kombinasie van die twee metodes beter is as enigeen van die metodes afsonderlik. In hierdie studie ondersoek ek die toepassing van die veralgemeende lineere model as 'n beramingstegniek. Vorige studies gebruik die log-log transformasie, d. w.s. logZ = logA + b(logR) van die Z = ARb verwantskap om die koeffisiente A en b met behulp van kleinste-kwadrate-regressie te bepaal. Die implisiete aanname hiermee is dat die foute ongekorreleerd is. Met die inverse verwantskap R = czd d.w.s. logR = logC + d(logZ) neem ek aan dat die waarnemings nie onafhanklik is nie sodat die regressiekoeffisiente bereken word met behulp van die metode van die veralgemeende lineere model. Om die ruimtelike afhanklikheid van die reenmeterwaarnemings te modelleer, word eksperimentele variogramme uit die data bereken en gepas met teoretiese variogramme wat gebruik word om die variansie-kovariansiematriks te vu!. "Gemiddeld" vaar hierdie metode beter as gewone regressie vir analises wat reenmeters wat verder as 45km vanaf die radarstel is, insluit. Residu-stipping wys dat die afstand van die meter vanaf die radarstel as 'n afsonderlike onafhanklike veranderlike in die regressievergelyking ingesluit behoort te word, d.w.s. die beraming verbeter met logR = 3-0 + a,(logZ) + a2(afstand). Hierdie meervoudige regressiemodel stem ooreen met die teoretiese model van Smith en Krajewski omdat e -- afstand as 'n praktiese manifestasie van die foutproses [e.,, (ij)] beskou kan word. Omdat E(ez) = eE<ZJ e'"a' as Z 'n lognormaalverdeling het, kan die sydigheid wat ontstaan wanneer antilogaritmes geneem word, reggestel word deur die beraamde reenval met e112 "' te vermenigvuldig. Die studie !ewer 'n bydrae met die afleiding van 'n beramingstegniek wat die beraming van neerslag uit radar betekenisvol verbeter. / In a study of a rain-gauge network that was installed for a weather modification experiment in Bethlehem, South Africa, precipitation values R; observed at 43 gauging stations are compared to the observed radar reflectivity Z;. Although radar provides spatial and temporal measurements of reflectivity that are immediately available at one location, the accuracy of radar estimation of rainfall is uncertain due to various potential errors in the conversion from reflectivity to rainfall. Rain-gauges are assumed to give accurate point measurements of rainfall and there is general agreement that the combination of systems is better than either system alone. In this study I explore the application of the general linear model as an estimation technique. Previous studies have used the log-log transform, i.e. logZ = logA + b(logR) of the Z = ARb relation, and applied least-squares regression analysis to determine the coefficients A and b. This implicitly assumes that the disturbances are uncorrelated. Working with the inverse relation R = czd i.e. logR = logC + d(logZ) and assuming that the observations are not independent we compute the regression coefficients using generalised least squares. To model the spatial dependence of the rain-gauge observations we compute experimental variograms from the data and fit them with theoretical variograms which are then used to fill the variance-covariance matrix. "On average" this method performs better than ordinary regression for the analyses that included rain-gauges further than 45km from the radar set. Residual plotting revealed that distance of the rain-gauge from the radar set should be included as a separate independent variable in the regression equation, i.e. logR = ao + a1(logZ) + a1(distance) improved the estimation of rainfall as it performs better than ordinary regression. This multiple regression model agrees with the theoretical model of Smith and Krajewski in the sense that e "'distance is a practical manifestation of the error process [ e,, (ij)]. Showing that E( ez) = el!.(!.) e 112 "' if Z has a lognormal distribution, the bias when taking antilogs can be removed by multiplying estimated rainfall by e1 ' 2a'. The contribution of this study is the derivation of an estimation technique which significantly improves the estimation of rainfall from radar / Mathematical Sciences / D. Phil. (Statistics)

From the Proceedings of the 1972 Meetings of the Arizona Section - American Water Resources Assn. and the Hydrology Section - Arizona Academy of Science - May 5-6, 1972, Prescott, Arizona / There have been many efforts in recent years to modify thunderstorms through cloud seeding. Collective cloud seeding efforts in Arizona before 1971 are reviewed and an operational convective cloud seeding program carried out in Arizona in the summer of 1971 is analyzed. The comprehensive Santa Catalina cloud seeding experiment (1957 to 1964) was a randomized seeding using silver iodide. Results of this experiment are uncertain as numerous interpretations are possible. Numerous individual experiments from 1966 to 1970 at flagstaff were conducted, with uncertain results. An intensive program of seeding individual cumulus clouds with silver iodide was carried out in the summer of 1971 in central and eastern Arizona. No statistically significant changes were noted. Results of the Catalina experiment imply that seeding decreased rainfall on and downwind from the target. Two other experiments were inconclusive. Nine figures show precipitation patterns.

In this thesis the two disciplines of Statistics and Artificial Neural Networks are combined into an integrated study of a data set of a weather modification Experiment. An extensive literature study on artificial neural network methodology has revealed the strongly interdisciplinary nature of the research and the applications in this field. An artificial neural networks are becoming increasingly popular with data analysts, statisticians are becoming more involved in the field. A recursive algoritlun is developed to optimize the number of hidden nodes in a feedforward artificial neural network to demonstrate how existing statistical techniques such as nonlinear regression and the likelihood-ratio test can be applied in innovative ways to develop and refine neural network methodology. This pruning algorithm is an original contribution to the field of artificial neural network methodology that simplifies the process of architecture selection, thereby reducing the number of training sessions that is needed to find a model that fits the data adequately. [n addition, a statistical model to classify weather modification data is developed using both a feedforward multilayer perceptron artificial neural network and a discriminant analysis. The two models are compared and the effectiveness of applying an artificial neural network model to a relatively small data set assessed. The formulation of the problem, the approach that has been followed to solve it and the novel modelling application all combine to make an original contribution to the interdisciplinary fields of Statistics and Artificial Neural Networks as well as to the discipline of meteorology. / Mathematical Sciences / D. Phil. (Statistics)

The unique problems encountered when analyzing weather data sets - that is, measurements taken while conducting a meteorological experiment- have forced statisticians to reconsider the conventional analysis methods and investigate permutation test procedures. The problems encountered when analyzing weather data sets are simulated for a Monte Carlo study, and the results of the parametric and permutation t-tests are compared with regard to significance level, power, and the average coilfidence interval length. Seven population distributions are considered - three are variations of the normal distribution, and the others the gamma, the lognormal, the rectangular and empirical distributions. The normal distribution contaminated with zero measurements is also simulated. In those simulated situations in which the variances are unequal, the permutation test procedure was performed using other test statistics, namely the Scheffe, Welch and Behrens-Fisher test statistics. / Mathematical Sciences / M. Sc. (Statistics)

From the Proceedings of the 1975 Meetings of the Arizona Section - American Water Resources Assn. and the Hydrology Section - Arizona Academy of Science - April 11-12, 1975, Tempe, Arizona / From the establishment of the Arizona resources board in 1928 until the Arizona Water Commission was formed in 1971, no state water plan was developed. Since 1971, the longest and most intensive planning studies have been concerned with allocation of Colorado River water through the central Arizona project. Future plans involve desalting sea water, weather modification, importation of water, etc. The Arizona state water plan ultimately will be a plan of management of Arizona's limited water resources. Water plans and economic and environmental impact evaluations are scheduled for completion by july, 1977.

In this thesis the two disciplines of Statistics and Artificial Neural Networks are combined into an integrated study of a data set of a weather modification Experiment. An extensive literature study on artificial neural network methodology has revealed the strongly interdisciplinary nature of the research and the applications in this field. An artificial neural networks are becoming increasingly popular with data analysts, statisticians are becoming more involved in the field. A recursive algoritlun is developed to optimize the number of hidden nodes in a feedforward artificial neural network to demonstrate how existing statistical techniques such as nonlinear regression and the likelihood-ratio test can be applied in innovative ways to develop and refine neural network methodology. This pruning algorithm is an original contribution to the field of artificial neural network methodology that simplifies the process of architecture selection, thereby reducing the number of training sessions that is needed to find a model that fits the data adequately. [n addition, a statistical model to classify weather modification data is developed using both a feedforward multilayer perceptron artificial neural network and a discriminant analysis. The two models are compared and the effectiveness of applying an artificial neural network model to a relatively small data set assessed. The formulation of the problem, the approach that has been followed to solve it and the novel modelling application all combine to make an original contribution to the interdisciplinary fields of Statistics and Artificial Neural Networks as well as to the discipline of meteorology. / Mathematical Sciences / D. Phil. (Statistics)

The unique problems encountered when analyzing weather data sets - that is, measurements taken while conducting a meteorological experiment- have forced statisticians to reconsider the conventional analysis methods and investigate permutation test procedures. The problems encountered when analyzing weather data sets are simulated for a Monte Carlo study, and the results of the parametric and permutation t-tests are compared with regard to significance level, power, and the average coilfidence interval length. Seven population distributions are considered - three are variations of the normal distribution, and the others the gamma, the lognormal, the rectangular and empirical distributions. The normal distribution contaminated with zero measurements is also simulated. In those simulated situations in which the variances are unequal, the permutation test procedure was performed using other test statistics, namely the Scheffe, Welch and Behrens-Fisher test statistics. / Mathematical Sciences / M. Sc. (Statistics)