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)
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:unisa/oai:umkn-dsp01.int.unisa.ac.za:10500/18737 |
| Date | 06 1900 |
| Creators | Nieuwoudt, Reina |
| Contributors | Steffens, F. E. (Francois Eliza) |
| Source Sets | South African National ETD Portal |
| Language | Afrikaans |
| Detected Language | English |
| Type | Thesis |
| Format | 1 online resource (xv, 209 leaves) |
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