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M.Sc. (Geography) / Hailstorms are well-known phenomena in the summer rainfall region of southern Africa where they cause extensive damage - especially in the agricultural sector. This thesis examines the geography and climatology of hail in the Transvaal. It deals with three main issues, namely a) the spatial and temporal characteristics of hail days (HDs); b) rainfall and atmospheric conditions prevailing during hail events; and c) the geography of hail damage as it pertains to maize. In the Transvaal, hail day frequency (HDF) increases with altitude and latitude in a non-linear (exponential) manner. Variations in altitude, as reflected in the diverse physiography of the area, account for most of the spatial and temporal variations in hail occurrence. Seven hail regions can be distinguished which differ from one another in terms of the onset times of hail, its seasonal occurrence and annual HDF patterns. In general, most hailstorms occur during November with the peak onset time varying between 16:00 and 20:00. The most notable finding concerning rain - hail interrelationships, is that rainfall and HDF appear to be inversely related, years/months with high hail incidence being dry and vice versa. Daily and seasonal precipitation characteristics also differ between 'high hail years' (HHYs; dry) and 'low hail years' (LHYs; wet). For instance, during HHYs, the peak hail season is delayed while the rain season peaks earlier. Moreover, while the frequency of convective systems remains nearly the same during HHYs as in 'normal' years, the average precipitation area and the volumetric production decreases significantly. These anomalies appear to be the result of changes in the large-scale circulation patterns (as reflected by the transition from baroclinic to quasi-barotropic conditions) which influence the precipitation from mesoscale convective systems. It is likely that the Southern Oscillation plays a role in these changes, particularly during November and December. However, although these Southern Oscillation Index (SOl) - HDF associations are weak, they are appreciably stronger than those between the SOl and rainfall. Rainfall characteristics on HDs differ from those of non-hail rain days in that, on HDs, more rain falls and the rain-bearing systems are more extensive. In general, atmospheric conditions are less stable, and the humidity level is higher, on HDs than on other days. Furthermore, HDs are characterized by warm north easterly winds near the surface but cold, dry south westerlies at the 600 hPa level. Above this the south westerlies become progressively stronger

Recent droughts in South Africa have highlighted the vulnerability of the economy to water restrictions. However, the degree of surface aridity in southern Africa is not only a function of precipitation, but also one of evaporation. The quantitative assessment of evaporative loss is important since it is a major component of the water budget. For example, in southern Africa, evaporation accounts for 79.5% of the hydrological water budget. As the cost of water resource development increases, so there has been an increasing demand for hydrological modelling to optimise project planning. Reliable estimates of evaporation are essential to significant improvements in the practice of hydrology and particularly in a country like South Africa which is prone to the adverse effects of drought. It is difficult to adequately measure potential evaporation over an area as large and as sparsely populated as southern Africa. Despite the research that has been undertaken to estimate evaporation from related meteorological and physical variables, generally, the estimation of evaporation in southern Africa has been unsatisfactory. There are a number of methods for estimating potential evaporation. However, a major problem tends to be the incompatibility between the data requirements of some of the more physically-based models, and the actual data that is available and collected on a routine basis at a sufficient number of stations. In existing water resources estimation models, evaporation is often incorporated as a time series input of pan evaporation, using daily or monthly values. The lack of a nearby record of pan evaporation often necessitates the use of published regionalised mean monthly pan values. This technique of using the mean monthly evaporation values in water resources estimation models tends to overestimate or underestimate the actual evaporation that is occurring, depending on the actual amount of rain occurring in a specific month. This is because no attempt has been made to correct these mean evaporation values for the amount of rainfall that occurs in a specific month, in a specific region. The regional rainfall/evaporation relationships (that vary spatially and temporally) are not taken into account. A need was identified for an assessment of the value of grouping data by rainfall as a better tool for estimating evaporation. Here, the monthly evaporation and the mean monthly evaporation for a specific rainfall group category will be estimated using daily data. Due to data availability, the most appropriate time scale to use is one day. Therefore, in this study an attempt has been made to relate rainfall amounts to evaporation values and to develop rainfall/evaporation relationships, identifying variations by season and region. It is important to identify and quantify these relationships and assess the possibility of incorporating these variations into existing Water Resource Estimation Models. The ability to derive and develop meaningful relationships between daily rainfall and daily evaporation for each season, and for a number of sites considered representative of the climatological zones for southern Africa was assessed. The first approach was to compare daily evaporation plotted against daily rainfall, and in the process develop a quantitative rainfall/evaporation relationship. Unfortunately, no direct linear relationships were identified. The second approach was to test the performance of the water resource estimation model using the following possible choices, (i) a real daily input (COREVAP1) - here the estimated monthly evaporation is the sum of the product number of days within each month * mean daily evaporation for each specified raingroup category, (ii) a distributed mean monthly input (COREVAP2) - here evaporation is estimated using a random sampling procedure to draw samples from a restricted part of the daily evaporation distribution for each raingroup and is defined by the mean and standard deviation, and (iii) a distributed mean monthly input and correction (COREVAP3) - here samples are drawn from the full distribution of daily evaporation for each raingroup category. The performance of the COREVAP programs was analyzed in terms of the improvement effected by estimating evaporation using the mean monthly evaporation regardless of rain. COREVAP1 produced the best simulations of monthly evaporation. This was expected as the program uses the straight-forward mean evaporation value multiplied by the number of days to simulate the monthly evaporation values. However, the COREVAP programs did not perform well when using the monthly evaporation data based on daily infilled values using the transformed parameters. Any regionalisation of parameter files would mean that a range of parameters in a region would now be represented by a single value. The need to assess the effect of this change from a regional range of values to a single representative value was identified. This was done by conducting a sensitivity analysis, in terms of what effect a percentage increase or decrease in the lambda, mean evaporation and mean rainfall values would have on the resultant simulated monthly evaporation and coefficient of efficiency values. A sensitivity analysis was conducted on COREVAP1 to determine which parameters of the model had the greatest influence on the simulations. This was done with reference to the percentage error of monthly evaporation and the monthly and accumulative coefficient of efficiency values. Generally, the percentage increase/decrease in mean evaporation values that are acceptable for the representative stations are low. In contrast, fairly high percentage changes in mean rainfall values are tolerated. The objective of the regionalisation of parameters was to determine whether general characteristics can be applied to some stations that are significantly different compared to other stations, so that the stations may be combined to represent a separate region. The demarcation of regions was conducted on the basis of the regional relative mean evaporation values (per raingroup, per season), the daily mean evaporation values per month and the average number of days within each raingroup, per season. Intra-station and inter-region variability was analysed using the Kruskal-Wallis H test and the Friedman Fr test. The regional parameters were then used as input into the COREVAP programs and the simulation results were analysed in terms of whether the simulations still produce positive accumulative coefficient of efficiency values. The results obtained when substituting the regional parameters were not good. Based on these results, it has been concluded that the hypothesis that grouping data by rainfall may be a better tool for estimating evaporation compared to simply using the mean monthly evaporation, may be rejected.

The objective of the study was to update and improve the reliability and accuracy of short duration (s 24 h) design rainfall values for South Africa. These were to be based on digitised rainfall data whereas previous studies conducted on a national scale in South Africa were based on data that were manually extracted from autographic charts. With the longer rainfall records currently available compared to the studies conducted in the early 1980s, it was expected that by utilising the longer, digitised rainfall data in conjunction with regional approaches, which have not previously been applied in South Africa, that more reliable short duration design rainfall values could Ix: estimated. A short duration rainfall database was established for South Africa with the majority of the data contributed by the South African Weather Bureau (SAWB). Numerous errors such as negative and zero time steps were identified in the SAWB digitised rainfall data. Automated procedures were developed to identify the probable cause of the errors and appropriate adjustments to the data were made. In cases where the cause of the error could be established, the data were adjusted to introduce randomly either the minimum, average or maximum intensity into the data as a result of the adjustment. The effect of the adjustments was found to have no significant effect on the extracted Annual Maximum Series (AMS). However, the effect of excluding erroneous points or events with erroneous points resulted in significantly different AMS. The low reliability of much of the digitised SAW B rainfall data was evident by numerous and large differences between daily rainfall totals recorded by standard, non-recording raingauges, measured at 08:00 every day, and the total rainfall depth for the equivalent period extracted from the digitised data. Hence alternative techniques of estimating short duration rainfall values were developed, with the focus on regional approaches and techniques that could be derived from daily rainfall totals measured by standard raingauges. Three approaches to estimating design storms from the unreliable short duration rainfall database were developed and evaluated. The first approach used a regional frequency analysis, the second investigated scaling relationships of the moments of the extreme events and the third approach used a stochastic intra-daily model to generate synthetic rainfall series. In the regional frequency analyses, 15 relatively homogeneous rainfall clusters were identified in South Africa and a regional index storm based approach using L-moments was applied. Homogeneous clusters were identified using site characteristics and tested using at-site data. The mean of the AMS was used as the index value and in 13 of the 15 relatively homogeneous clusters the index value for 24 h durations were well estimated as a function of site characteristics only, thus enabling the estimation of 24 h duration design rainfall values at any location in South Africa. In 13 of the 15 clusters the scaling properties of the moments of the AMS were used to successfully estimate design rainfall values for duration < 24h, using the moments of the AMS extracted from the data recorded by standard raingauges and regional relationships based on site characteristics. It was found that L-moments scaled better and over a wider range of durations than ordinary product moments. A methodology was developed for the derivation of the parameters for two Bartlett-Lewis rectangular pulse models using only standard raingauge data, thus enabling the estimation of design values for durations as short as 1 h at sites where only daily rainfall data are available. In view of the low reliability of the majority of short duration rainfall data in South Africa, it is recommended that the regional index value approach be adopted for South Africa, but scaled using values derived from the daily rainfall data. The use of the intra-daily stochastic rainfall models to estimate design rainfall values is recommended as further independent confirmation of the reliability of the design values. / Thesis (M.Sc.)-University of Natal, Pietermaritzburg, 1998.

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)

The purpose of this study was to develop a rainfall model, continuous in space-time, which captures both the spatial and temporal structure of rainfall over a range of scales varying from lkm to 128km pixels at temporal resolutions ranging from 5 minute up to 1 year. Such a model could find application in a variety of hydrological fields including the management of flash flood scenarios where it could be used in combination with runoff models as a training tool in the operation of flood control structures, the assessment of flood risk, the management of water resources in an area through the simulation of long rainfall sequences and as a short term rainfall forecasting tool, to name a few. The String of Beads Model (SBM) is a high-resolution space-time model of radar rainfall images. It is a stochastic model that takes advantage of the detailed spatial and temporal information captured by weather radar and combines it with the long term seasonal variation captured by a network of daily raingauges. The alternating wet-dry process, or event arrival and duration, is modelled as a one dimensional process, while the detailed wet process is modelled as a three-dimensional (two space and one time) process at 1km, 5 minute spatial and temporal resolutions respectively, over an area of 16000km2, consistent with the observed radar data. The three-dimensional rainfall events distributed on a one-dimensional time line, is analogous to a "String of Beads". The SBM makes use of a combination of power law numerical filtering techniques and well-known time series models to achieve an efficient algorithm that can be run on an ordinary personal computer. Model output is in the form of image files which, when viewed as an animated sequence, are difficult to distinguish from observed radar rainfall images. Apart from the realistic appearance of these images, when calibrated to daily raingauge data for the region, analysis of the simulated sequences over periods of up to ten years, reveal convincing rainfall statistics for a wide range of spatial and temporal scales. It can be used both as a simulation tool and as a short term forecasting tool. In simulation mode, it can quickly produce long sequences (tens of years) of 128 x 128 km rainfall images at five minute, one kilometre resolution. Such simulations can be used as input to distributed and semi-distributed hydrological models to produce "what if" scenarios for applications in water resources management and flood risk assessment amongst others. In forecasting mode, the SBM has proved effective in producing real time forecasts of up to two hours making it a useful tool for flood warning and management, particularly in steep or urban catchments which react quickly and often give rise to flash floods. It can also be used in a combined simulation-forecasting mode to quickly produce many short term "what if" scenarios which can be used to assess the risk of possible growth or decay scenarios in real time. / Thesis (Ph.D.)-University of Natal, Durban, 2003.

Radio frequencies at millimeter wavelengths suffer greatly from rain attenuation. It is therefore essential to study rainfall characteristics for efficient and reliable design of radio networks at frequencies above 10GHz. These characteristics of rain are geographically based, which need to be studied for estimation of rain induced attenuation. The ITU-R, through recommendations P.837 and P.838, have presented global approaches to rain-rate variation and rain-induced attenuation in line-of-sight radio links. Therefore, in this dissertation characteristics of rainfall rate and its applications for South Africa are evaluated. The cumulative distributions of rain intensity for 12 locations in seven regions in South Africa are presented in this dissertation based on five-year rainfall data. The rain rate with an integration time of 60 minutes is converted into an integration time of 1 minute in accordance with ITU-R recommendations. The resulting cumulative rain intensities and relations between them are compared with the global figures presented in ITU-R Recommendation P.837, as well as with the work in other African countries, notably by Moupfuma and Martin. Based on this work, additional rain-climatic zones are proposed alongside the five identified by ITU-R for South Africa. Finally, the study compares the semi-empirical raindrop-size distribution models such as Laws and Parsons, Marshall and Palmer, Joss, Thams and Waldvogel, and Gamma distribution with the estimated South Africa models. / Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, 2006.

Rain affects the design of any communication system that relies on the propagation of electromagnetic waves. Above a certain threshold of frequency, the attenuation due to rain becomes one of the most important limits to the performance of terrestrial line-of-sight (LOS) microwave links. Rain attenuation which is the dominant fading mechanism at these frequencies is based on nature which can vary from location-to-Iocation and from year-to year. In this dissertation, the ITU-R global prediction techniques for predicting the cumulative distribution of rain attenuation on terrestrial links are studied using a five-year rain rate data for twelve different geographical locations in the Republic of South Africa. The specific attenuation rR (dB/km) for both horizontal and vertical polarization is determined. The path attenuation (dB) exceeded for 0.01% of the time is estimated using the available existing models for the twelve different geographical locations on a I-minute integration time rain rate at 0.01% exceedance of the time averaged over a period of 5 years. A comparison study is done on these available rain attenuation mode'ls; The ITU-R model, Crane Global model, and the Moupfouma models at different frequencies and propagation path lengths based on the actual I-minute integration time rain rate exceeded at 0.01% of the time averaged over a period of 5 years for each geographical locations. Finally, from the actual signal attenuation measurements recorded in Durban over a period of 1 year at 19.5 GHz and a propagation path length of 6.73 km, a logarithmic attenuation model and power attenuation model is proposed for Durban, South Africa. Recommendation for future work is given in the concluding chapter for future improvement on this study. Radio communication designers will find the results obtain in the report useful. / Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2006.

There is need to improve prediction results in rain attenuation in order to achieve reliable wireless communication systems. Existing models require improvements or we need fresh approaches. This dissertation presents a model of rain attenuation prediction for terrestrial and satellite radio links based on a novel approach. This approach postulates that the difference in rain attenuation for various locations is attributed to the dissimilar rain drop sizes and rain cell diameter sizes and that cell sizes derived from local measurements would depict the true nature of rain cells better than the cells derived from long term rain data gathered from different climates. Therefore all other link parameters used in the attenuation equation are presented by the use of mathematical analysis; but the rain cell size is derived from local rain rate measurements. The physical link aspects considered in the mathematical attenuation model are: the Fresnel ellipsoid of the link path, the effect of elevation angle, the rain cell diameter size and the shape of growth of rain rates in the cell. The effect of the elevation angle of the link on the scale of attenuation is accounted for through the proposed coefficient of elevation equation. The coefficient of elevation is considered to modify the size of the rain cell diameter in proportion to the elevation angle of the link and the rain rate growth is taken to be of the truncated-Gaussian form. On the other hand, the rain cell diameter is derived from rain rate measurements as a power law model and substituted in the attenuation expression. The rain cell size model evaluated in this dissertation is based on point rain rate measurement data from the disdrometer located at the University of KwaZulu-Natal, South Africa. The “Synthetic Storm” technique is applied to develop the rain cell diameter distributions and the rain cell diameter model. In addition, the impact of the rain cell diameter size model in site diversity and cellular network-area planning for the region is discussed. To validate the model for terrestrial links, attenuation data collected from Durban, South Africa is used while that for satellite links, attenuation data from 15 links which are located in tropical climatic zones are used. In each case, the new model is tested against some well-known global rain attenuation prediction models including the standard ITU-R models. The performance of the proposed models for the sampled radio links based on error estimations shows that improvements have been achieved and may be regarded as a universal tropical model especially for satellite links. / Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2011.

Simulations based on a month of radar data from Florida, and a summer of radar data from Nelspruit, South Africa, were used to quantify the errors in the measurement of mean areal rainfall which arise simply as a result of the extreme variability of convective rainfall, even with perfect remote sensing instruments. The raingauge network measurement errors were established for random and regular network configurations using daily and monthly radar-rainfall accumulations over large areas. A relationship to predict the measurement error for mean areal rainfall using sparse networks as a function of raining area, number of gauges, and the variability of the rainfield was developed and tested. The manner in which the rainfield probability distribution is transformed under increasing spatial and temporal averaging was investigated from two perspectives. Firstly, an empirical relationship was developed to transform the probability distribution based on some measurement scale, into a distribution based on a standard measurement length. Secondly, a conceptual model based on multiplicative cascades was used to derive a scale independent probability distribution.