Dissertations / Theses on the topic 'Rain and rainfall Mathematical models'

Distributed Rainfall-Runoff models are gaining widespread acceptance; yet, a fundamental issue that must be addressed by all users of these models is definition of an acceptable level of watershed discretization (geometric model complexity). The level of geometric model complexity is a function of basin and climatic scales as well as the availability of input and verification data. Equilibrium discharge storage is employed to develop a quantitative methodology to define a level of geometric model complexity commensurate with a specified level of model performance. Equilibrium storage ratios are used to define the transition from overland to channel -dominated flow response. The methodology is tested on four subcatchments in the USDA -ARS Walnut Gulch Experimental Watershed in Southeastern Arizona. The catchments cover a range of basins scales of over three orders of magnitude. This enabled a unique assessment of watershed response behavior as a function of basin scale. High quality, distributed, rainfall -runoff data was used to verify the model (KINEROSR). Excellent calibration and verification results provided confidence in subsequent model interpretations regarding watershed response behavior. An average elementary channel support area of roughly 15% of the total basin area is shown to provide a watershed discretization level that maintains model performance for basins ranging in size from 1.5 to 631 hectares. Detailed examination of infiltration, including the role and impacts of incorporating small scale infiltration variability in a distribution sense, into KINEROSR, over a range of soils and climatic scales was also addressed. The impacts of infiltration and channel losses on runoff response increase with increasing watershed scale as the relative influence of storms is diminished in a semiarid environment such as Walnut Gulch. In this semiarid environment, characterized by ephemeral streams, watershed runoff response does not become more linear with increasing watershed scale but appears to become more nonlinear.

In the past, derivative-based optimization algorithms have not frequently been used to calibrate conceptual rainfall -riff (CRR) models, partially due to difficulties associated with obtaining the required derivatives. This research applies a recently- developed technique of analytically computing derivatives of a CRR model to a complex, widely -used CRR model. The resulting least squares response surface was found to contain numerous discontinuities in the surface and derivatives. However, the surface and its derivatives were found to be everywhere finite, permitting the use of derivative -based optimization algorithms. Finite difference numeric derivatives were computed and found to be virtually identical to analytic derivatives. A comparison was made between gradient (Newton- Raphsoz) and direct (pattern search) optimization algorithms. The pattern search algorithm was found to be more robust. The lower robustness of the Newton-Raphsoi algorithm was thought to be due to discontinuities and a rough texture of the response surface.

The U.S. Geological Survey and the City of Tucson, Arizona, have been collecting rainfall and runoff data on several watersheds in the Tucson area for several years. Among the purposes of this project is to use the data to test rainfall-runoff models in an effort to find one to successfully simulate flood flows in Tucson. One such model, the Distributed Routing Rainfall-Runoff Model (DR3M), was tested using data collected on Rob Wash in Tucson. It was found DR3M performs about as well as it does in other parts of the United States, although it tends to underestimate flood flows for large storms and overestimate flows for smaller storms. Unique features with regard to the hydrology of urban Tucson require special attention when using DR3M; these features are associated with the nature of dry washes and summer rainfall in Tucson. Experience indicates DR3M is not truly a deterministic model.

This thesis presents an approach for generating long synthetic sequences of single-site daily rainfall which can incorporate low-frequency features such as drought, while still accurately representing the day-to-day variations in rainfall. The approach is implemented in a two-stage process. The first stage is to generate the entire sequence of rainfall occurrence (i.e. whether each day is dry or wet). The second stage is to generate the rainfall amount on all wet days in the sequence. The models used in both stages are nonparametric (they make minimal general assumptions rather than specific assumptions about the distributional and dependence characteristics of the variables involved), and ensure an appropriate representation of the seasonal variations in rainfall. A key aspect in formulation of the models is selection of the predictor variables used to represent the historical features of the rainfall record. Methods for selection of the predictors are presented here. The approach is applied to daily rainfall from Sydney and Melbourne. The models that are developed use daily-level, seasonal-level, annual-level, and multi-year predictors for rainfall occurrence, and daily-level and annual-level predictors for rainfall amount. The resulting generated sequences provide a better representation of the variability associated with droughts and sustained wet periods than was previously possible. These sequences will be useful in catchment water management studies as a tool for exploring the potential response of catchments to possible future rainfall.

In recent years, increased demands have been placed on hydrologists to find the most effective methods of making predictions of hydrologic variables in ungauged basins. A huge part of the southern African region is ungauged and, in gauged basins, the extent to which observed flows represent natural flows is unknown, given unquantified upstream activities. The need to exploit water resources for social and economic development, considered in the light of water scarcity forecasts for the region, makes the reliable quantification of water resources a priority. Contemporary approaches to the problem of hydrological prediction in ungauged basins in the region have relied heavily on calibration against a limited gauged streamflow database and somewhat subjective parameter regionalizations using areas of assumed hydrological similarity. The reliance of these approaches on limited historical records, often of dubious quality, introduces uncertainty in water resources decisions. Thus, it is necessary to develop methods of estimating model parameters that are less reliant on calibration. This thesis addresses the question of whether physical basin properties and the role they play in runoff generation processes can be used directly in the estimation of parameter values of the Pitman monthly rainfall-runoff model. A physically-based approach to estimating the soil moisture accounting and runoff parameters of a conceptual, monthly time-step rainfall-runoff model is proposed. The study investigates the physical meaning of the model parameters, establishes linkages between parameter values and basin physical properties and develops relationships and equations for estimating the parameters taking into account the spatial and temporal scales used in typical model applications. The estimationmethods are then tested in selected gauged basins in southern Africa and the results of model simulations evaluated against historical observed flows. The results of 71 basins chosen from the southern African region suggest that it is possible to directly estimate hydrologically relevant parameters for the Pitman model from physical basin attributes. For South Africa, the statistical and visual fit of the simulations using the revised parameters were at least as good as the current regional sets, albeit the parameter sets being different. In the other countries where no regionalized parameter sets currently exist, simulations were equally good. The availability, within the southern African region, of the appropriate physical basin data and the disparities in the spatial scales and the levels of detail of the data currently available were identified as potential sources of uncertainty. GIS and remote sensing technologies and a widespread use of this revised approach are expected to facilitate access to these data.

The sertao of northeast Brazil is a semiarid region characterized by recurring droughts. The vastness of the area (650,000 km$ sp2)$ poses a challenge to the effective monitoring of the impacts of drought at a scale that would be useful to the inhabitants of the sertao. Remote sensing data provide a viable way of assessing the extent and nature of drought across the landscape.
The work present a more effective algorithm to estimate rainfall from both the cold and warm cloud types present. Using a decision-tree methodology, the analysis yields rainfall estimates over the 0-21 mm range. Because seasonal variations in rainfall produce differences in vegetation, soils and hydrologic responses, Principal Components Analysis was used to examine these land surface responses. Individual components and component pairings were useful in identifying variations in vegetation density, geobotanical differences and drainage characteristics. The presence of cloud cover was found to dampen the land surface information that could be extracted. Landsat Thematic Mapper (TM) imagery was then used to produce a moisture index which characterizes surface wetness in relation to other features present in a scene. The multispectral combination of TM bands 1, 4 and 6 allowed for the separation of the surface types present, in locational space. This space was defined by an open-ended triange made up of a vertical "water line", a horizontal line of equal vegetation density; and a negatively-slopping iso-moisture line. The stability of the moisture index was influenced by varying scale and seasonal conditions.
In the drought conditions that prevailed in 1991-1992, these methods provide important additions to existing drought monitoring approaches in the Brazilian northeast. Further calibration is required in order to extend their applicability to other geographical regions and time frames.

This thesis presents a discussion on the study undertaken in the application of the monthly time step Pitman rainfall-runoff model to the Kafue River basin. The study constituted one of the initial steps in the capacity building and expansion of the application of hydrologic models in the southern African region for water resources assessment, one of the core areas of the Southern African FRIEND project (Flow Regimes from International Experimental Network Data). The research process was undertaken in four major stages, each stage working towards achieving the research objectives. The first stage was the preparation of spatial data which included the selection and delineation of sub-catchments and inclusion of spatial features required to run the Pitman model and transferring the spatial data into SPATSIM. The second stage was the preparation of input data, mainly rainfall, streamflow, evaporation, and water abstraction data. This information was then imported into SPATSIM, which was able to assist in the further preparation of data by assessment of the input data quality, linking of observed flows and spatial interpolation of point rainfall data to average catchment rainfall in readiness for running and calibration of the model. The third stage was the running and calibration of the Pitman model. Use was made of both the automatic calibration facility, as well as manual calibration by means of the time series graph display and analysis facility of SPATSIM. Model calibration was used to obtain the best fit and an acceptable correlation between the simulated and the observed flows and to obtain simulation parameter sets for sub-catchments and regions within the Kafue catchment. The fourth stage was the analysis and evaluation of the model results. This included verification of results over different time periods and validation and testing of parameter transfers to other catchments. This stage also included the evaluation of SPATSIM as a tool for applying the model and as a database for the processing and storage of water resources data. The study’s output includes: A comprehensive database of hydrometeorological, physical catchment characteristics, landuse and water abstraction information for the Kafue basin; calibrated Pitman model parameters for the sub-catchments within the Kafue basin; recommendations for future work and data collection programmes for the application of the model. The study has also built capacity by facilitating training and exposure to rainfall-runoff models (specifically the Pitman model) and associated software, SPATSIM. In addition, the dissemination of the results of this study will serve as an effective way of raising awareness on the application of the Pitman model and the use of the SPATSIM software within Zambia and the region. The overall Pitman model results were found to be satisfactory and the calibrated model is able to reproduce the observed spatial and temporal variations in streamflow characteristics in the Kafue River basin.

Climate change and a growing demand for freshwater resources due to population increases and socio-economic changes will make water a limiting factor (in terms of both quantity and quality) in development. The need for reliable quantitative estimates of water availability cannot be over-emphasised. However, there is frequently a paucity of the data required for this quantification as many basins, especially in the developing world, are inadequately equipped with monitoring networks. Existing networks are also shrinking due mainly to shortages in human and financial resources. Over the past few decades mathematical models have been used to bridge the data gap by generating datasets for use in management and policy making. In southern Africa, the Pitman monthly rainfall-runoff model has enjoyed relatively popular use as a water resources estimation tool. However, it is acknowledged that models are abstractions of reality and the data used to drive them is imperfect, making the model outputs uncertain. While there is acknowledgement of the limitations of modelled data in the southern African region among water practitioners, there has been little effort to explicitly quantify and account for this uncertainty in water resources estimation tools and explore how it affects the decision making process. Uncertainty manifests itself in three major areas of the modelling chain; the input data used to force the model, the parameter estimation process and the model structural errors. A previous study concluded that the parameter estimation process for the Pitman model contributed more to the global uncertainty of the model than other sources. While the literature abounds with uncertainty estimation techniques, many of these are dependent on observations and are therefore unlikely to be easily applicable to the southern African region where there is an acute shortage of such data. This study focuses on two aspects of making hydrologic predictions in ungauged basins. Firstly, the study advocates the development of an a priori parameter estimation process for the Pitman model and secondly, uses indices of hydrological functional behaviour to condition and reduce predictive uncertainty in both gauged and ungauged basins. In this approach all the basins are treated as ungauged, while the historical records in the gauged basins are used to develop regional indices of expected hydrological behaviour and assess the applicability of these methods. Incorporating uncertainty into the hydrologic estimation tools used in southern Africa entails rethinking the way the uncertain results can be used in further analysis and how they will be interpreted by stakeholders. An uncertainty framework is proposed. The framework is made up of a number of components related to the estimation of the prior distribution of the parameters, used to generate output ensembles which are then assessed and constrained using regionalised indices of basin behavioural responses. This is premised on such indices being based on the best available knowledge covering different regions. This framework is flexible enough to be used with any model structure to ensure consistent and comparable results. While the aim is to eventually apply the uncertainty framework in the southern African region, this study reports on the preliminary work on the development and testing of the framework components based on South African basins. This is necessitated by the variations in the availability and quality of the data across the region. Uncertainty in the parameter estimation process was incorporated by assuming uncertainty in the physical and hydro-meteorological data used to directly quantify the parameter. This uncertainty was represented by the range of variability of these basin characteristics and probability distribution functions were developed to account for this uncertainty and propagate it through the estimation process to generate posterior distributions for the parameters. The results show that the framework has a great deal of potential but can still be improved. In general, the estimated uncertain parameters managed to produce hydrologically realistic model outputs capturing the expected regimes across the different hydro-climatic and geo-physical gradients examined. The regional relationships for the three indices developed and tested in this study were in general agreement with existing knowledge and managed to successfully provide a multi-criteria conditioning of the model output ensembles. The feedback loop included in the framework enabled a systematic re-examination of the estimation procedures for both the parameters and the indices when inconsistencies in the results were identified. This improved results. However, there is need to carefully examine the issues and problems that may arise within other basins outside South Africa and develop guidelines for the use of the framework.
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Distributed rainfall-runoff models are gaining widespread acceptance; yet, a fundamental issue that must be addressed by all users of these models is definition of an acceptable level of watershed discretization (geometric model complexity). The level of geometric model complexity is a function of basin and climatic scales as well as the availability of input and verification data. Equilibrium discharge storage is employed to develop a quantitative methodology to define a level of geometric model complexity commensurate with a specified level of model performance. Equilibrium storage ratios are used to define the transition from overland to channel-dominated flow response. The methodology is tested on four subcatchments in the USDA-ARS Walnut Gulch Experimental Watershed in southeastern Arizona. The catchments cover a range of basins scales of over three orders of magnitude. This enabled a unique assessment of watershed response behavior as a function of basin scale. High quality, distributed, rainfall-runoff data were used to verify the model (KINEROSR). Excellent calibration and verification results provided confidence in subsequent model interpretations regarding watershed response behavior. An average elementary channel support area of roughly 15% of the total basin area is shown to provide a watershed discretization level that maintains model performance for basins ranging in size from 1.5 to 631 hectares. Detailed examination of infiltration, including the role and impacts of incorporating small-scale infiltration variability in a distribution sense, into KINEROSR, over a range of soils and climatic scales was also addressed. The impacts of infiltration and channel losses on runoff response increase with increasing watershed scale as the relative influence of storms is diminished in a semi-arid environment such as Walnut Gulch. In this semi-arid environment, characterized by ephemeral streams, watershed runoff response does not become more linear with increasing watershed scale but appears to become more nonlinear.

This study considered runoff of pesticides from cotton fields using a rainfall simulator. The Australian cotton industry is based on clay soils on low sloping land and uses a hill-furrow surface geometry. These conditions are unlike those in many studies of pesticide dissipation, sorption and runoff and there has been little previous research into hydrology, erosion and pesticide runoff in the industry. Of particular interest was to characterise runoff of different pesticides, clarity the underlying factors controlling pesticide runoff, and investigate management practices to reduce runoff of pesticides with contrasting chemical properties, for the conditions found in the cotton industry. Runoff behaviour of different pesticides has often been studied independently. Separating the inherent behaviour of the pesticide and the conditions of the study, and comparing pesticides, is difficult. Runoff concentrations depend on the hydrology and erosion of each site, and particularly on the timing of runoff events after spraying. These factors can be controlled and/or measured using a rainfall simulator. Furthermore, multi-residue pesticide analysis now allows study of a number of pesticides simultaneously, so that their behaviour can be compared directly for the same site conditions and management options. Review of the literature indicated that a large variation in pesticide runoff is related to application rate, formulation and placement, and dissipation, and that only a shallow soil surface layer contributes pesticides to runoff. In this study, the analysis was simplified by only considering placement on the soil surface (i.e. not on plant foliage) of liquid/emulsified formulations and soilincorporated sprays. A simple conceptual framework was used to compare and integrate data from simulated rainfall studies of pesticides used in the cotton industry and contrast them with data in the literature. By comparing pesticide runoff to the concentration in the soil surface at the start of rain, one set of factors, those that occur before the rainfall event - application and dissipation, were separated from those that occur during the rainfall event - leaching and runoff extraction. To complete the picture of how pesticides get from the spray nozzle to the edge of a field in runoff, four main areas were considered - dissipation, runoff extraction, sediment-water partitioning and management. Dissipation data were collected at four sites across the cotton growing areas and runoff data at three of these sites, on soils with medium to high clay content. Some 14 pesticides were studied, including the insecticide endosulfan (a- and (3-isomers and the breakdown product endosulfan sulfate) at all sites. Dissipation studies concentrated on the 3-6 weeks after application, when concentrations are highest, and on the soil surface layer that contributes pesticides to runoff. For practical reasons, soil concentrations were measured in the 0-25mm soil depth. While the major emphasis was on dissipation of endosulfan from soil and crop residues, several organophosphate (OP) insecticides (chlorpyrifos, dimethoate and profenofos) and a range of herbicides (fluometuron, metolachlor, prometryn, diuron, pendimethalin, pyrithiobac sodium) were also studied. Dissipation in the 0-25mm soil depth followed first-order exponential decay, with one phase, for most pesticides. However, large initial losses occurred for several of the insecticides studied: 35-55% for endosulfan, but only when applied at higher temperatures, most likely due to volatilisation. Initial losses of 50-75% occurred for the OP’s, dimethoate (inconsistently), chlorpyrifos and profenofos. Dissipation half-lives in the 0-25mm soil depth (after initial losses) were 6-20 days for endosulfan (total of a-, (3- and sulfate), 8-13 days for organophosphates, and 13-32 days for herbicides, a-endosulfan consistently dissipated more rapidly than p-endosulfan, but the two isomers were affected differently by site and/or climatic factors. Dissipation of endosulfan was similar for ULV and EC formulations, for bare and covered soil and for band and blanket sprays, but was somewhat slower after two applications. Only small amounts of endosulfan sulfate formed in dry soils, while more formed in temporarily wet soil, contributing about half the total endosulfan remaining after 30 days. Dissipation in surface 0-25mm soil was more rapid than in 0-50mm soil, but this varied from no effect for the rapidly dissipated OP’s to 1.6 times faster for endosulfan, and varied according to Koc for the herbicides. Herbicides with lower Koc dissipated faster in the surface layer than those with higher Koc, due to greater downward movement. Downward movement decreased the apparent halflife in the 0-25mm soil and increased the apparent half-life in 0-50mm soil. Half-lives in 0-25mm soil were considerably lower than published ‘selected’ values. Dissipation of endosulfan was consistent with studies in other warmer climates. The shallow depth of soil studied (which enhanced downward movement) and application on the surface contributed to this more rapid dissipation. The results are consistent with observations that “runoff available residues” dissipate more rapidly than generally expected for bulk soil. Endosulfan dissipated rapidly (e.g. 75-90%) from crop residue cover (wheat or cotton trash) within the first day after spraying, apparently a result of volatilisation. Half-lives for endosulfan on crop residues after the initial loss were similar to those in bare and covered soils. The data indicate that a benefit of retaining crop residues on the soil surface, in addition to reducing runoff and sediment losses, is that it intercepts and dissipates the endosulfan more rapidly than when sprayed onto soil. Runoff extraction was investigated, in a simple empirical analysis, by comparing concentration in soil (mg/kg) before rain and event average concentration in runoff (pg/L), using data from three rainfall simulator studies in cotton fields, for 14 pesticides, and from the literature. The ratio of runoff to soil concentrations, or the linear regression slope fitted through the origin, was termed the runoff extraction ratio (ER0). The pesticides varied widely in solubility (0.003-700,OOOmg/L) and ranged from strongly (DDE, KD~ 15,000) to weakly sorbed (fluometuron, dimethoate, pyrithiobac sodium, KD <30). Runoff extraction behaviour from bare soil was remarkably consistent for pesticides of widely different properties. Total concentrations in runoff of each pesticide were closely related to concentrations in the soil (0-25mm) before rain, generally with a similar relationship for all pesticides and sites, over four orders of magnitude range in concentrations. As a first approximation, concentration in runoff (pg/L) = 28 times concentration in soil (mg/kg), (or Ero = 28). Runoff extraction was also somewhat similar for dissolved N and P, and organic N. Ero values were not related to partition coefficients (KP) measure in runoff. However, runoff extraction did decrease with time after spraying and was lower for aged DDE and trifluralin at one site. This is considered to relate to lower concentrations in the surface few mm of soil (c.f. 0-25mm soil) over time. ERO values were similar for the slopes studied (0.2-4%), for long and short plots, and for banded and blanket spray plots. Runoff extraction was reduced where cover reduces sediment concentration. Runoff extraction was significantly lower for a weakly sorbed pesticide (dimethoate) in only one instance and not for a range of other weakly sorbed pesticides at the other sites. Concentrations in the water and sediment phases in runoff, and in sediment (mg/kg), were also linearly related to soil concentrations for pesticides of similar KP, but extraction in two phases varied according to normal partitioning (Eqn 5-5). The sediment concentration in runoff (10-60 g/L from bare plots) had a secondary effect on ER0, and only affected ERO when sediment concentration was low (i.e. with cover). This is because higher sediment concentrations were associated with lower concentrations in the sediment (mg/kg), due to greater desorption and decreasing physical enrichment. Less physical enrichment (due to size-selective sediment sorting) occurred than observed on coarser textured soil (e.g. enrichment ratio up to 8), with enrichment ratios mostly less than 1.0 (due to desorption) and no greater than 2.0. For all pesticides, the concentration in sediment (mg/kg) was within a factor of about two of the soil concentration adjusted for desorption using the normal partitioning equation. Organic carbon and clay were also only slightly enriched in sediment, despite considerable deposition in the furrows. This is because the soils eroded as aggregates (due to low sand and high clay content), and because coarser sediment had greater concentrations of sorbed pesticides than finer sediment, the opposite of what is normally expected (e.g. where coarser sediment is sand). The notable similarity of runoff extraction ratio for all pesticides in the rainfall simulator studies was probably because (a) the main factor that limit runoff of weakly sorbed chemicals, i.e. leaching from the runoff mixing zone, was ineffective because of low infiltration and ponding of infiltrated water in the shallow tilled layer in the bottom of furrows, (b) sediment concentrations were high enough to ensure transport of strongly sorbed pesticides, and (c) all pesticides had some transport in both the water and sediment phases, diluting the response to sediment load. The concentration of pesticide extracted from soil into runoff appears to be determined by the soil concentration, with, in the absence of significant leaching and with sufficient sediment transport, little differentiation between pesticides of different partition properties. This is partly because, on any plot, the same mass of soil and the same volume of water are involved in mixing, independent of the chemical being considered, and because factors that increase extraction of solutes also tend to increase detachment of sediment. Analysis of published runoff data for a range of pesticides in US croplands indicated similar average runoff extraction to the rainfall simulator studies in Australian cotton fields. However, runoff extraction was higher for much more erosive conditions (e.g. cultivated 10-15% slopes) and lower for low erosion conditions (furrow irrigation on low sloping fields in California). Runoff extraction was similar for this latter case (i.e. ERO~30) once adjusted to a higher sediment concentration. Analysis of the rainfall simulator and published data presents a conceptual framework where the major drivers of pesticide runoff were separated between (a) application rate and dissipation, described by soil concentration at the start of rain, which accounts for five orders of magnitude differences in runoff concentrations, and (b) runoff extraction during the rainfall event, which varied over a limited range. The first of these factors causes most of the difference in runoff between pesticides. Partition coefficients in runoff (KP) were not affected by cover and wheel traffic treatments even though these treatments had large effects on pesticide runoff concentrations. KP values increased with time after spraying, rapidly in the first few days and more slowly over the next few weeks, for all pesticides. KP values were greater than soil sorption KD values, increasingly so for pesticides of lower sorption. Thus pesticides normally considered weakly sorbed were much more sorbed in sediment than expected, particularly at longer times. Conversely, moderately/strongly sorbed pesticides, such as endosulfan, were less sorbed than expected in the first day or so. Partitioning appeared to be influenced by both time of contact with soil and time of mixing (during rain). The results are conceptually consistent with a two-compartment, bi-phasic (fast-slow) sorption model, with the soil in the runoff-mixing layer under rainfall being a continuous dilution system. The ‘slow’ phase, due to diffusion into less accessible soil domains, leads to increasing partition coefficients with greater time of contact. The short time of mixing means that the water phase is mainly interacting with the ‘fast’ or most accessible fraction, while the ‘slow’ fraction remains in the sediment phase. Percentages in the water phase in runoff, for 14 pesticides, roughly followed a published relationship with solubility, and an empirical relationship with soil sorption Koc values, but only for erosive conditions. These relationships do not reflect the full range in responses that occur due to the likely range of concentrations and organic carbon content of sediment, or the increase in KP with time. Because of lower KP values soon after spraying, less soluble pesticides had 20-45% in water. Conversely, a few days/weeks after spraying, more soluble pesticides had only 60-80% in water. Thus all pesticides tended to have a ‘foot in each camp’ and some potential for management using erosion control practices. It is an over simplification to expect ‘percent in water’ to be a characteristic of a pesticide. So long as sediment concentration and KP can be estimated, the percentage in the water phase can be calculated quite simply from first principles (Eqn 5-5) and behaviour for relevant field conditions can be assessed. This equation was used to show that reported values of percentage in the water phase for endosulfan that appeared to conflict (20-95%) and the values from the rainfall simulator plots (15- 45%) are explained by differences in sediment concentration and organic carbon in the studies. A wide range of percentages in water (10-95%) will occur for pesticides with KP of 5-500 (or solubilities -1-100), such as endosulfan, for the range of sediment concentrations and organic carbon that might occur in the environment. Improved practices are needed to minimise soil erosion, and related agrochemical transport, from cotton fields during rain. The most influential practice used in other agricultural industries, that is, retaining crop residues as surface cover, is rarely practiced in the Australian cotton industry. Therefore two options available to cotton growers, namely retention of surface cover and controlling wheel traffic, were evaluated using simulated rain on a well-aggregated black Vertosol. Increasing cover (0-60%) resulted in decreasing runoff, soil loss and sediment concentration. Runoff and soil loss were reduced by an order of magnitude with about 50% cover and by a small amount with notraffic. Cover and no traffic combined gave least runoff and soil loss. Pesticide transport in runoff was also reduced strongly by retaining on-ground cover and somewhat reduced by avoiding prior wheel traffic. With 45-60% cover, concentrations were reduced 5-fold for a-, |3- and total endosulfan; halved for endosulfan sulfate, trifluralin and DDE, and unchanged for prometryn. Cover had more effect on endosulfan because cover intercepted and dissipated the sprayed endosulfan, reducing concentrations in surface soil. Cover greatly reduced total pesticide losses (g/ha) because cover reduced runoff and soil loss considerably. With 45-60% cover, total losses were reduced by 90-98%. No-traffic gave 40% lower losses, and enhanced the effect of cover, but did not prevent large pesticide losses from bare plots. Cover provided more control of more soil-sorbed pesticides (endosulfan, trifluralin and DDE). Control of the less sorbed prometryn was largely due to cover reducing runoff. An examination of the practical requirements for maintaining effective cover in cotton farming systems indicated that most of the perceived conflicts with insect, weed and irrigation management could be overcome, although further study is needed. Many of these results have only been possible because of the use of the rainfall simulator, multiresidue pesticide analysis and the availability of sufficient resources. Such opportunities are rare in field research. By allowing an intensive regime of runoff sampling at controlled times after pesticide applications, the study has yielded data with more significance, enabling the conclusions made above regarding the relative behaviour of individual pesticides and their extraction from soil in runoff. The author acknowledges the contributions made by others to this study, but all of the experimental work and the data reported in this thesis were under his control.

Hydrological models are widely used tools in water resources estimation, but they are simple representations of reality and are frequently based on inadequate input data and uncertainties in parameter values. Data observation networks are expensive to establish and maintain and often beyond the resources of most developing countries. Consequently, measurements are difficult to obtain and observation networks in many countries are shrinking, hence obtaining representative observations in space and time remains a challenge. This study presents some guidelines on the identification, quantification and reduction of sources of uncertainty in water resources estimation in southern Africa, a data scarce region. The analyses are based on example sub-basins drawn from South Africa and the application of the Pitman hydrological model. While it has always been recognised that estimates of water resources availability for the region are subject to possible errors, the quantification of these uncertainties has never been explicitly incorporated into the methods used in the region. The motivation for this study was therefore to contribute to the future development of a revised framework for water resources estimation that does include uncertainty. The focus was on uncertainties associated with climate input data, parameter estimation (and recognizing the uncertainty due model structure deficiencies) methods and water use data. In addition to variance based measures of uncertainty, this study also used a reservoir yield based statistic to evaluate model output uncertainty, which represents an integrated measure of flow regime variations and one that can be more easily understood by water resources managers. Through a sensitivity analysis approach, the results of the individual contribution of each source of uncertainty suggest regional differences and that clear statements about which source of uncertainty is likely to dominate are not generally possible. Parameter sensitivity analysis was used in identifying parameters which are important withinspecific sub-basins and therefore those to focus on in uncertainty analysis. The study used a simple framework for evaluating the combined contribution of uncertainty sources to model outputs that is consistent with the model limitations and data available, and that allows direct quantitative comparison between model outputs obtained by using different sources of information and methods within Spatial and Time Series Information Modelling (SPATSIM) software. The results from combining the sources of uncertainties showed that parameter uncertainty dominates the contribution to model output uncertainty. However, in some parts of the country especially those with complex topography, which tend to experience high rainfall spatial variability, rainfall uncertainty is equally dominant, while the contributions of evaporation and water use data uncertainty are relatively small. While the results of this study are encouraging, the weaknesses of the methods used to quantify uncertainty (especially subjectivity involved in evaluating parameter uncertainty) should not be neglected and require further evaluations. An effort to reduce data and parameter uncertainty shows that this can only be achieved if data access at appropriate scale and quality improves. Perhaps the focus should be on maintaining existing networks and concentrating research efforts on making the most out of the emerging data products derived from remote sensing platforms. While this study presents some initial guidelines for evaluating uncertainty in South Africa, there is need to overcome several constraints which are related to data availability and accuracy, the models used and the capacity or willingness to adopt new methods that incorporate uncertainty. The study has provided a starting point for the development of new approaches to modelling water resources in the region that include uncertain estimates.

The world is undergoing rapid changes and the future is uncertain. The changes are related to modification of the landscape due to human activities, such as large and small scale irrigation, afforestation and changes to the climate system. Understanding and predicting hydrologic change is one of the challenges facing hydrologists today. Part of this understanding can be developed from observed data, however, there often too few observations and those that are available are frequently affected by uncertainties. Hydrological models have become essential tools for understanding historical variations of catchment hydrology and for predicting future possible trends. However, most developing countries are faced with poor spatial distributions of rainfall and evaporation stations that provide the data used to force models, as well as stream flow gauging stations to provide the data for establishing models and for evaluating their success. Hydrological models are faced with a number of challenges which include poor input data (data quality and poorly quantified human activities on observed stream flow data), uncertainties associated with model complexity and structure, the methods used to quantify model parameters, together with the difficulties of understanding hydrological processes at the catchment or subbasin. Within hydrological modelling, there is currently a trend of dealing with equifinality through the evaluation of parameter identifiability and the quantification of uncertainty bands associated with the predictions of the model. Hydrological models should not only focus on reproducing the past behaviour of a basin, but also on evaluating the representativeness of the surface and subsurface model components and their ability to simulate reality for the correct reasons. Part of this modelling process therefore involves quantifying and including all the possible sources of uncertainty. Uncertainty analysis has become the standard approach to most hydrological modelling studies, but has yet to be effectively used in practical water resources assessment. This study applied a hydrological modelling approach for understanding the hydrology of a large Tanzanian drainage basin, the Great Ruaha River that has many areas that are ungauged and where the available data (climate, stream flow and existing water use) are subject to varying degrees of uncertainty. The Great Ruaha River (GRR) is an upstream tributary of the Rufiji River Basin within Tanzania and covers an area of 86 000 km2. The basin is drained by four main tributaries; the Upper Great Ruaha, the Kisigo, the Little Ruaha and the Lukosi. The majority of the runoff is generated from the Chunya escarpment, the Kipengere ranges and the Poroto Mountains. The runoff generated feeds the alluvial and seasonally flooded Usangu plains (including the Ihefu perennial swamp). The majority of the irrigation water use in the basin is located where headwater sub‐basins drain towards the Usangu plains. The overall objective was to establish uncertain but behavioural hydrological models that could be useful for future water resources assessments that are likely to include issues of land use change, changes in patterns of abstraction and water use, as well the possibility of change in future climates.

A pesquisa trata da distribuiÃÃo infradiÃria de precipitaÃÃes intensas no MunicÃpio de Fortaleza, Estado do CearÃ. Foram utilizados 30 anos de observaÃÃes pluviogrÃficas, digitalizadas, da estaÃÃo climatolÃgica da Universidade Federal do Cearà no Campus do Pici. Os estudos foram realizados com uma Ãnica sÃrie, com todos os valores para determinar o regime anual. Posteriormente, foram utilizadas as 12 sÃries mensais, cobrindo o perÃodo de 30 anos, para estudar a sazonalidade. Os dados anuais foram ajustados a curvas senoidais e a polinÃmios do terceiro grau, forÃados para manter a continuidade, denominados polinÃmios cÃclicos. Observou-se que o horÃrio de mÃxima pluviosidade ocorre no inÃcio do dia e o mÃnimo ocorre no inÃcio da noite, Estudou-se tambÃm, nas sÃries mensais, o tamanho do intervalo de tempo entre o mÃximo e o mÃnimo de pluviosidade. Esse intervalo de tempo foi correlacionado com a duraÃÃo do dia de insolaÃÃo. Conclui-se que hà uma forte correlaÃÃo entre a duraÃÃo do dia de insolaÃÃo e o intervalo de tempo entre o pico de mÃxima e de mÃnima pluviosidade.
The research deals with the daily distribution of intense rainfall in the city of Fortaleza, CearÃ. Were used 30 years of pluvi ograph observations of the climatological station of the Federal University of CearÃ, in Campus do Pici. The studies were conducted with a single series, with all the values to determine an annual basis. Later, were used 12 monthly series, covering the p eriod from 30 years, to study the seasonality. Annual data were adjusted to sinusoidal curves and polynomials of the third degree, forced to maintain continuity, called cyclic polynomials. It was observed that the maximum rainfall occurs in the early hours of the day and the minimum rainfall occurs in the early evening. It was also studied in the monthly series the time interval size between the maximum and the minimum rainfall. This time interval was correlated with the duration of insolation. It concludes that there is a strong correlation between duration of insolation and the time interval between the maximum and the minimum rainfall

The study presents the results of applying two isolated event, constant runoff proportion, conceptual models to a range of catchments drawn from various climatic and physiographic regions of South Africa and the USA. The models can be operated in either lumped or semi-distributed modes. The research progressed through the following stages. The initial stage involved the calibration of both models on two sets of catchments so that an initial evaluation of the performance of the models could be carried out and any deficiencies in the model structure identified, and where practical, corrected. The models were then calibrated on a further 8 catchments. An important result of the calibration is that for both models to produce reasonably acceptable simulations, at least one parameter has to vary between storms on the same catchment to account for variations in storm or antecedent moisture characteristics. The next stage consisted of compiling quantitative descriptions of the physical characteristics of the catchments and rainfall events and an attempt to relate the calibrated parameter values to relevant physical characteristics for the purpose of estimating parameter values when calibration is not possible. Despite the difficulties encountered in quantifying some of the hydrological characteristics the general trends exhibited by many of the relationships are encouraging and the format of the combinations of physical variables used, do make sense with respect to the original parameter conceptualisations. The relationships between storm characteristics and parameters of both models are less satisfactory. There is a high degree of scatter and the between-catchment variation in the form of the relationships, indicates that the derived relationships are likely to be of little use for parameter estimation purposes. The final stage involved a validation exercise in which new parameters were estimated from the physical variable-parameter relationships for all the catchments previously used, as well as a further four. The new parameters were used to re-simulate all the storms and comparison of these results were made with the original calibration results. Both models produced poor results and are unlikely to give reliable results where calibration is not possible. The parameter relationships for the parameters related to storm characteristics are so catchment specific that transfer to other areas will produce unpredictable results. Foot note:- For compatability with computer printouts decimal full stops are used in the format of real numbers in tables etc

This thesis addresses the problem of predicting satellite path rain fade duration statistics for an arbitrary location, frequency, elevation angle and polarization. It summarizes the development of a dynamic stochastic model. From this model a technique is derived for predicting fade duration statistics for one site using measured attenuation data at another site. This technique is evaluated by comparing predicted and experimental results for several locations, frequencies, elevation angles and polarizations.
M.S.

Simulated annealing (Kirkpatrick et al, 1983) is used to estimate the parameters of a mathematical model that predicts the water yield from a catchment. The calibration problem involves finding the global minimum of a multivariate function that has many extraneous local minima, a situation in which conventional optimisation methods are ineffective. The objective function which quantifies discrepancies between the computed and observed streamflows must be carefully selected to satisfy the least square assumptions. Several published simulated annealing algorithms have been implemented, tested and evaluated using standard test functions. Appropriate cooling schedules are found for each algorithm and test function investigated. The number of function evaluations required to find the minimum is compared to published results for the test functions using either simulated annealing and other global optimisation methods. A new simulated annealing algorithm based on the Hooke and Jeeves (1961) pattern search method is developed and compared with existing algorithms from the literature.

Intraregional variability in tropospheric environments during freezing rain events is investigated for the South Central United States. National Weather Service (NWS) Automated Surface Observing Stations (ASOS) are used to detect the occurrence of freezing rain, and rawinsonde observations (RAOB) employed to analyze lower tropospheric vertical profiles of temperature, dew point temperature, wind, and layer thicknesses during these periods. The study area consists of seven 100 mile radius RAOB proximity sub-regions centered around Peachtree City Georgia, Nashville Tennessee, Birmingham Alabama, Jackson Mississippi, Shreveport Louisiana, Little Rock Arkansas, and Springfield Missouri. A series of difference of means tests are performed to determine if statistically significant differences exist in mean values of selected tropospheric variables during periods of freezing rain between adjacent RAOB sites to determine the character of intraregional variability within the South Central United States. Results of these tests suggest 5 sub-regions exist in which freezing rain events can be forecast based upon thresholds and ranges of lower tropospheric environmental variables. As a final step, flow charts are developed for each of the 5 subregions to aid meteorologists in forecasting freezing rain within the Southeast United States.
Department of Geography

Thesis (Ph.D.)--University of Adelaide, Dept. of Civil and Environmental Engineering, 2002.
"May 2002" Includes list of papers published during this study. Errata slip inserted inside back cover of v. 1. Includes bibliographical references (leaves 331-357).

The atmospheres of exoplanets are being characterised in increasing detail by observational facilities and will be examined with even greater clarity with upcoming space based missions such as the James Webb Space Telescope (JWST) and the Wide Field InfraRed Survey Telescope (WFIRST). A major component of exoplanet atmospheres is the presence of cloud particles which produce characteristic observational signatures in transit spectra and influence the geometric albedo of exoplanets. Despite a decade of observational evidence, the formation, dynamics and radiative-transport of exoplanet atmospheric cloud particles remains an open question in the exoplanet community. In this thesis, we investigate the kinetic chemistry of cloud formation in hot Jupiter exoplanets, their effect on the atmospheric dynamics and observable properties. We use a static 1D cloud formation code to investigate the cloud formation properties of the hot Jupiter HD 189733b. We couple a time-dependent kinetic cloud formation to a 3D radiative-hydrodynamic simulation of the atmosphere of HD 189733b and investigate the dynamical properties of cloud particles in the atmosphere. We develop a 3D multiple-scattering Monte Carlo radiative-transfer code to post-process the results of the cloudy HD 189733b RHD simulation and compare the results to observational results. We find that the cloud structures of the hot Jupiter HD 189733b are likely to be highly inhomogeneous, with differences in cloud particle sizes, number density and composition with longitude, latitude and depth. Cloud structures are most divergent between the dayside and nightside faces of the planet due to the instability of silicate materials on the hotter dayside. We find that the HD 189733b simulation in post-processing is consistent with geometric albedo observations of the planet. Due to the scattering properties of the cloud particles we predict that HD 189733b will be brighter in the upcoming space missions CHaracterising ExOPlanet Satellite (CHEOPS) bandpass compared to the Transiting Exoplanet Space Survey (TESS) bandpass.

[Truncated abstract] Generally hydrologic and ecologic models operate on arbitrary time and space scales, selected by the model developer or user based on the availability of field data. In reality rainfall is highly variable not only annually, seasonally and monthly but also the intensities within a rainfall event and infiltration properties on semi-arid hillslopes can also be highly variable as a result of discontinuous vegetation cover that form mosaics of areas with vegetation and areas of bare soil. This thesis is directed at improving our understanding of the impacts of the temporal representation of rainfall and spatial heterogeneity on model predictions of hydrologic thresholds and surface runoff coefficients on semi-arid landscapes at the point and hillslope scales. We firstly quantified within storm rainfall variability across a climate gradient in Western Australia by parameterizing the bounded random cascade rainfall model with one minute rainfall from 15 locations across Western Australia. This study revealed that rainfall activity generated in the tropics had more within storm variability and a larger proportion of the storm events received the majority of rain in the first half of the event. Rainfall generated from fontal activity in the south was less variable and more evenly distributed throughout the event. Parameters from the rainfall analysis were then used as inputs into a conceptual point scale surface runoff model to investigate the sensitivity of point scale surface runoff thresholds to the resolution of rainfall inputs. This study related maximum infiltration capacities to average storm intensities (k*) and showed where model predictions of infiltration excess were most sensitive to rainfall resolution (ln k* = 0.4) and where using time averaged rainfall data can lead to an under prediction of infiltration excess and an over prediction of the amount of water entering the soil (ln k* > 2). For soils susceptible to both infiltration excess and saturation excess, total runoff sensitivity was scaled by relating drainage coefficients to average storm intensities (g*) and parameter ranges where predicted runoff was dominated by infiltration excess or saturation excess depending on the resolution of rainfall data were determined (ln g* <2). The sensitivity of surface runoff predictions and the influence of specific within storm properties were then analysed on the hillslope scale. '...' It was found that using the flow model we still get threshold behaviour in surface runoff. Where conditions produce slow surface runoff velocities, spatial heterogeneity and temporal heterogeneity influences hillslope surface runoff amounts. Where conditions create higher surface runoff velocities, the temporal structure of within storm intensities has a larger influence on runoff amounts than spatial heterogeneity. Our results show that a general understanding of the prevailing rainfall conditions and the soil's infiltration capacity can help in deciding whether high rainfall resolutions (below 1 h) are required for accurate surface runoff predictions. The results of this study can be considered a contribution to understanding the way within storm properties effect the processes on the hillslope under a range of overall storm, slope and infiltration conditions as well as an improved understanding of how different vegetation patterns function to trap runoff at different total vegetation covers and rainfall intensities.

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O semiárido brasileiro é caracterizado por chuvas irregulares, alta evapotranspiração, elevadas temperaturas e baixa pluviometria, fenômenos que assolam grande parte do território brasileiro, sendo visualizado com maior intensidade na região Nordeste. Dentro deste espaço, localiza-se o estado da Paraíba, que periodicamente vivencia o fenômeno da seca, a qual é causadora das irregularidades de safras agrícolas e prejuízos nas lavouras. Buscou-se, neste estudo, demonstrar a influência da variação de temperatura e da sazonalidade pluviométrica, nos polos receptores do fruto, Rio de Janeiro e São Paulo, na formação do preço unitário deste, independentemente das variações de temperatura e das chuvas na região de São Gonçalo, o que faz oscilar o seu valor unitário, deixando o produtor sem possibilidades de negociação ou mesmo de um maior lucro em relação à demanda e à oferta. Nesta dissertação tem-se por objetivo verificar as possibilidades de aproveitamento dos derivados do coco, em substituição à venda do fruto verde in natura, desenvolvendo em um primeiro momento, a análise de um questionário sobre as características socioeconômicas deste produtor, de sua propriedade e da relação com os atravessadores na produção e venda do fruto in natura. Utilizando-se os dados coletados, realizou-se o confronto entre os índices pluviométricos e de temperatura média mensal, tanto do polo produtor, como do polo receptor, com o preço unitário do coco verde em São Gonçalo no período de 2012 a 2014. Na sequência, foram utilizadas ferramentas matemáticas de modelagem e de custo, para observar quais as possibilidades de agroindustrialização dos derivados do coco, analisando os seus custos e as suas devidas restrições, buscando uma situação máxima de receita que possibilite ao produtor armazenar, beneficiar, agregar valor e até mesmo agroindustrializar os derivados do coco a exemplo de: água, leite, óleo, fibra, ralados, etc. Verificou-se que existem alternativas mais lucrativas, para o produtor, ao realizar a agroindustrialização dos derivados do fruto, principalmente na produção do óleo de coco.
The Brazilian semiarid region is characterized by irregular rainfall, high evapotranspiration, high temperatures and low rainfall, phenomena that plague much of the Brazilian territory, being viewed with greater intensity in the Northeast. Within this space is located the state of Paraiba, which periodically experiences the phenomenon of drought, which is the cause of the irregularities of agricultural crops and damage to crops. We sought in this study demonstrate the influence of changes in temperature and rainfall seasonality in recipient poles of fruit, Rio de Janeiro and São Paulo, in the pricing of this unit, regardless of temperature variations and rainfall in the region of São Gonçalo, which makes oscillate the unit value, leaving the producer without tradability or even a higher profit in relation to demand and supply. In this dissertation has for objective to verify the possibilities of use of derivatives coconut, replacing the sale of the green fruit fresh, developing in the first place, the analysis of a questionnaire on the socioeconomic characteristics of this producer, its property and relationship with the middlemen in the production and sale of fresh fruit. Using the data collected, there was the confrontation between the rainfall and average temperatures of both the production hub, and the recipient pole, with the unit price of coconut in São Gonçalo in the 2012 period to 2014. In sequence, mathematical modeling tools and cost were used to observe which industrialization possibilities of coconut derivatives, analyzing their costs and their due restrictions, seeking a maximum state revenue that enables the producer storing, processing, adding value and even agroindustrializar derived from coconut example: water, milk, oil, fiber, grating, etc. It was found that more profitable alternative for the producer to perform the industrialization of the derivatives of fruit, especially in the production of coconut oil.

Un evenement hydrologique est souvent defini d'apres plusieurs variables aleatoires presentant un certain degre de liaison. L'etude probabiliste de cet evenement necessite alors la composition de lois de probabilite. Nous avons considere deux cas d'applications : 1) l'extrapolation de la distribution du debit de pointe et du debit seuil ; 2) l'estimation du quantile du debit de crue a l'aval d'une confluence. Nous avons teste plusieurs fonctions de deux variables : les modeles de farlie-gumbel-morgenstern, de farlie et hashino, en utilisant des echantillons sup-seuil. Pour ce dernier modele, nous utilisons le coefficient de correlation obtenu avec la totalite de l'information (evenements concomitants et non concomitants). Les performances des modeles de composition ont ete testees sur des donnees reelles, puis sur des donnees simulees a l'aide du modele de generation de pluies journalieres shypre, du modele pluie-debit gr4j et d'un modele de liaison spatiale des pluies. Nous avons enfin etudie les hydrogrammes d'apport a injecter dans un modele hydraulique, de facon a rester homogene en frequence sur tout le lineaire de la riviere.

La modélisation des combinaisons de phénomènes d’inondation est une problématique d’actualité pour la communauté scientifique qui s’intéresse en priorité aux sites urbains et nucléaires. En effet, il est fort probable que l’approche déterministe explorant un certain nombre de scénarios possède certaines limites car ces scénarios déterministes assurent un conservatisme souvent excessif. Les approches probabilistes apportent une précision supplémentaire en s’appuyant sur les statistiques et les probabilités pour compléter les approches déterministes. Ces approches probabilistes visent à identifier et à combiner plusieurs scénarios d’aléa possibles pour couvrir plusieurs sources possibles du risque. L’approche probabiliste d’évaluation de l’aléa inondation (Probabilistic Flood Hazard Assessment ou PFHA) proposée dans cette thèse permet de caractériser une (des) quantité(s) d’intérêt (niveau d’eau, volume, durée d’immersion, etc.) à différents points d’un site en se basant sur les distributions des différents phénomènes de l’aléa inondation ainsi que les caractéristiques du site. Les principales étapes du PFHA sont : i) identification des phénomènes possibles (pluies, niveau marin, vagues, etc.), ii) identification et probabilisation des paramètres associés aux phénomènes d’inondation sélectionnés, iii) propagation de ces phénomènes depuis les sources jusqu’aux point d’intérêt sur le site, iv) construction de courbes d’aléa en agrégeant les contributions des phénomènes d’inondation. Les incertitudes sont un point important de la thèse dans la mesure où elles seront prises en compte dans toutes les étapes de l’approche probabiliste. Les travaux de cette thèse reposent sur l’étude de la conjonction de la pluie et du niveau marin et apportent une nouvelle méthode de prise en compte du déphasage temporel entre les phénomènes (coïncidence). Un modèle d’agrégation a été développé afin de combiner les contributions des différents phénomènes d’inondation. La question des incertitudes a été étudiée et une méthode reposant sur la théorie des fonctions de croyance a été utilisée car elle présente des avantages divers par rapport aux autres concepts (modélisation fidèle dans les cas d’ignorance totale et de manque d’informations, possibilité de combiner des informations d’origines et de natures différentes, etc.). La méthodologie proposée est appliquée au site du Havre, en France
The modeling of the combinations of flood hazard phenomena is a current issue for the scientific community which is primarily interested in urban and nuclear sites. Indeed, it is very likely that the deterministic approach exploring several scenarios has certain limits because these deterministic scenarios ensure an often excessive conservatism. Probabilistic approaches provide additional precision by relying on statistics and probabilities to complement deterministic approaches. These probabilistic approaches aim to identify and combine many possible hazard scenarios to cover many possible sources of risk. The Probabilistic Flood Hazard Assessment (PFHA) proposed in this thesis allows to characterize a quantity(ies) of interest (water level, volume, duration of immersion, ect.) at different points of interest of a site based on the distributions of the different phenomena of the flood hazard as well as the characteristics of the site. The main steps of the PFHA are: i) screening of the possible phenomena (rainfall, sea level, waves, ect.), ii) identification and probabilization of the parameters representative of the selected flood phenomena, iii) propagation of these phenomena from their sources to the point of interest on the site, iv) construction of hazard curves by aggregating the contributions of the flood phenomena. Uncertainties are an important topic of the thesis insofar as they will be taken into account in all the steps of the probabilistic approach. The work of this thesis is based on the study of the conjunction of rain and sea level and provide a new method for taking into account the temporal phase shift between the phenomena (coincidence). An aggregation model has been developed to combine the contributions of different flood phenomena. The question of uncertainties has been studied and a method based on the theory of belief functions has been used because it has various advantages (faithful modeling in cases of total ignorance and lack of information, possibility to combine information of different origins and natures, ect.). The proposed methodology is applied on the site of Le Havre in France

L'objectif de ce travail est de contribuer a la comprehension du fonctionnement hydrologique d'un bassin versant mediterraneen, notamment a l'occasion de ses crues. Il est compose d'un premier volet experimental destine a l'observation du comportement des eaux souterraines. Ce volet inclut des mesures de pression de l'eau dans le sol et de niveaux des nappes (fugitives ou perennes) sous un versant (ligne de plus grande pente perpendiculaire a la riviere), et une analyse approfondie des sols du versant: granulometries, conductivites hydrauliques in situ mesurees a l'aide de differents appareillages, mesures de la retention en eau des sols etc. Les proprietes hydrodynamiques des sols en place sont egalement decrites. Utilisant cette description hydrodynamique, on tente ensuite de modeliser le comportement du versant lorsqu'il est soumis a la pluie. La modelisation cherche a reproduire les infiltrations et les mouvements de nappes observes. Pour ce faire on developpe un modele d'infiltration et de montee de nappe dans une zone inclinee d'un sol multicouche. Pour resoudre l'equation de richards differentes methodes ont ete developpees. La meilleure, dans notre travail, s'avere etre celle qui utilise les differences finies avec un procede iteratif des directions alternees. Les resultats de la modelisation confirment qu'en cas de pluies importantes, une nappe peut s'elever relativement rapidement a proximite de la riviere et l'alimenter. Toutefois, les forts debits ne peuvent s'expliquer que par la saturation de l'ensemble du profil du sol qui engendre la montee de ces nappes et par les ecoulements de surface que ces aires saturees entrainent

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.

Uncertainty has become a primary issue for modellers and decision makers concerned about understanding the behaviour of natural systems. Characterising uncertainty is an important modelling step for assessing the options for managing it. Without an understanding of a model's strength and weakness and of model uncertainty we cannot judge if management interventions will cause significant change. Methods for characterising uncertainty range from empirical, through naive Monte Carlo to formal Bayesian methods. Most uncertainty methods are complex and difficult to implement. But uncertainty analysis can be so much simpler than this and lead to powerful insights and model improvements. This is illustrated in this thesis where it demonstrates that simple methods can provide useful insight into model uncertainty. This thesis uses four hydrological models of varying complexity applied to five catchments of differing characteristics. It shows that uncertainty analysis can be simple and provide crucial insights into the behaviour of environmental models. This thesis begins by showing how a simple global sensitivity analysis can identify parameters in a model that are unimportant in explaining model outputs, and that might improve identifiability either by checking which ones can be fixed or by changing the objective function. The results confirm that for the catchment examined a minimum of five years is required to characterise the sensitivities assuredly and that only the simpler models have well-identified parameters, but parameter sensitivities vary between catchments. The simple global sensitivity analysis is then complemented with an identifiability analysis of the four models. More complex models have more uncertain and poorly-identified parameters. Model structure is shown to be the major problem in obtaining a global solution, far outweighing data informativeness and the objective function selected. Moreover, the more complex models do not dominate the performance of the less complex, the best model depending on the catchment of interest and even the calibration period. This thesis then considers the issue of minimum acceptable model performance. It is argued that a typical hydrological model identification process of optimising the objective function and reporting the performance in a validation period is no longer sufficient practice. If models with lower objective function values are to be accepted, we need to know how bad a model will be considered as good enough. It proposes a generic approach that uses elimination of Pareto-dominated models and cross-validation to identify minimal criteria for which models should be accepted. Finally, this thesis investigated uncertainties introduced by variable time delays between rainfall events and hydrograph response, a response complexity not handled well by rainfall-runoff models. Smaller events tend to have larger time delays and variability compared to larger events. It proposes a simple solution for model calibration by shifting rainfall and/or modelled times series in events by the amount of observed time lag, as calculated by a cross-correlation function. A variable integer time delay method leads to general improvements in simulation on independent periods, when invoking performance metrics of a Shifted Nash-Sutcliffe Efficiency and absolute relative bias. Overall the variable integer time delay method also improved parameter identifiability.

In order to address rain attenuation scattering of millimetric waves and microwave sin Botswana, we have employed a comparison technique to determine the Ro.o1 at fourteen diverse locations in Botswana. In addition we have identified two rain climatic zones for Botswana. We note that Matzler employs Mie Scattering technique to determine the specific attenuation due to rain in Central Europe. Both Matzler and Olsen use the exponential distribution of N(D) to calculate y. In this dissertation we use the Mie scattering approach, but assume several distributions, including the log-normal distribution of N(D) as expounded by Ajayi et aI., to determine y for tropical and subtropical regions of Africa. The results show that the extinction coefficients depend more strongly on temperature at lower frequencies than at higher frequencies for lognormal distribution: at selected frequencies, we record high attenuation values at rising SHF bands: at 300 GHz, tropical showers take on values of 12, 12.5, 11.9 and 14 dB/km for Gaborone, Francistown, Kasane and Selebi-Phikwe, respectively. The absorption coefficient is significant but decreases exponentially with rain temperature at lower microwave frequencies. The application of the proposed model (Continental Thunderstorm is shown using practical results from Durban) is corroborated using practical results from Durban. Further, based on attenuation measurements, it is found that the lognormal distribution is suitable for Durban at rain rates greater than or equal to 21 mm/h. At rain rates below this, the loss-Thunderstorm is the better fit. Finally in this dissertation the results show that for rainfall intensity below about 10 mm/h for Marshall-Palmer (MP), Joss-Drizzle (JD), Joss-Thunderstorm (JT) and Law-Parson (LP) distributions, and below about 4 mm/h for Continental-Showers (CS), Tropical Showers (TS), Continental Thunderstorms (CT) and Tropical Thunderstorm (TT) distributions, the specific rain backscattering follows Rayleigh scattering law where the rain drops are small with respect to the wavelength when the frequency is 19.5 GHz. At rain rates above 10 mm/h for exponential distribution, and above 4 mm/h for lognormal distribution, the specific backscattering follows Mie scattering law. When the received echo power from rain becomes significant, it contributes to the rise in the noise floor and the radar receiver can lose its target. In addition, the result shows that Mie backscattering efficiency is highest at a raindrop diameter of 4.7mm.
Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2008.

Mawson Lakes is a new suburban housing development, situated 12 kms from the city of Adelaide in South Australia. The developers, the Mawson Lakes Joint Venture (MLJV), and the local council, the City of Salisbury, intend to capture all stormwater entering the site and recondition all wastewater. The water will then be supplied to residents and businesses for non-potable usage. Modelling the behaviour of the Mawson Lakes catchment under extreme conditions such as drought and prolonged periods of high rainfall will allow the project team to determine optimal water management strategies for the catchment. One of the problems facing the team is the prediction of future rainfall patterns and the typical form of extreme events. In this thesis I have used historical records to construct synthetic rainfall data that will allow the project team to investigate a wide range of typical behaviour. The Gamma distribution has been widely used to approximate the probability density function (PDF) of monthly rainfall totals. However, there is no natural way to extend this method directly to obtain a joint PDF for rainfall densities associated with two or more months, unless the monthly totals are independent. I propose a modified method to construct a suitable PDF using parameters from the maximum likelihood estimate for a marginal Gamma distribution and a series of associated Laguerre polynomials. This series of special functions allows us to match the correlation between monthly totals and to match the observed moments with any level of precision needed. The joint PDF for two months is constructed using a sum of products of associated Laguerre polynomials. In order to get an analytic expression for the marginal distributions and the associated cumulative probabilities, it is convenient to use a weighted total and a weighted proportion contributed from the first month. The method makes extensive use of well-known formulae from the theory of special functions. The cumulative marginal probability density for the weighted total and the cumulative conditional probability density for the weighted proportion are used to generate simulated rainfall totals for each month in a two month period. In theory the simulated data is statistically identical to the observed data. In practice we apply standard statistical methods to check that the simulated data is consistent with the observed data. This method can be extended to the general case of any number of months, but computationally is restricted to only three. For this reason an alternative method is proposed to generate synthetic data for more than three months, which uses groups and subgroups of months, but still retains the characteristics of the original PDF. Although the series method could also be used to model a sequence of days, I propose an alternative method using Markov processes. This method will match a sequence of daily totals, generated from a probability transition matrix, to the monthly total generated by the series method. This methodology allows the research team to simulate certain special cases such as droughts and prolonged periods of high rainfall. These unusual events are of great interest in catchment planning and management.
thesis (PhDMathematics)--University of South Australia, 2004.

Wong Chun Kit.
Thesis (M.Phil.)--Chinese University of Hong Kong, 1999.
Includes bibliographical references (leaves [132-143]).
Abstracts in English and Chinese.
List of Tables --- p.i
List of Figures --- p.iv
List of Symbols --- p.v
Chapter CHAPTER ONE: --- INTRODUCTION --- p.1
Chapter 1.1 --- Objectives and Significance of the Study --- p.4
Chapter 1.2 --- Physical Setting of Hong Kong --- p.5
Chapter 1.3 --- Climate of Hong Kong --- p.9
Chapter 1.4 --- Data Acquisition --- p.11
Chapter 1.4.1 --- Raingauges in Hong Kong --- p.11
Chapter 1.4.2. --- Database for the Spatial Variation Analyses --- p.14
Chapter 1.4.2.1. --- Data Selection for the Analyses for Factors Affecting Rainfall ´ؤ Elevation and Aspect --- p.15
Chapter 1.4.2.2. --- Data Selection for the Classification of Stations and Inter-station Correlation Analysis --- p.17
Chapter 1.4.3 --- Database for the Temporal Variation Analyses --- p.20
Chapter CHAPTER TWO : --- LITERATURE REVIEW --- p.22
Chapter 2.1 --- Spatial Variation of Rainfall --- p.22
Chapter 2.2 --- Detection of Temporal Changes in Rainfall --- p.28
Chapter 2.3 --- Urban Influence on Rainfall --- p.29
Chapter 2.4 --- Studies in Hong Kong --- p.33
Chapter CHAPTER THREE : --- METHODOLOGY --- p.33
Chapter 3.1 --- Preliminary Processing of the Data --- p.38
Chapter 3.2 --- Data Analysis --- p.40
Chapter 3.2.1 --- General Pattern of Rainfall Distribution --- p.40
Chapter 3.2.2 --- Data Analyses of Spatial Variation --- p.41
Chapter 3.2.2.1 --- Correlation between Rainfall and Elevation --- p.41
Chapter 3.2.2.2 --- Correlation between Rainfall and Aspect --- p.42
Chapter 3.2.2.3 --- Classification of Stations --- p.43
Chapter 3.2.2.4 --- Inter-Station Correlation Analysis --- p.46
Chapter 3.2.3 --- Data Analysis of Temporal Variation --- p.46
Chapter 3.2.3.1 --- The Running Mean Method --- p.47
Chapter 3.2.3.2 --- The 'Standard Error of the Difference' Test --- p.49
Chapter CHAPTER FOUR: --- RESULTS AND DISCUSSION --- p.50
Chapter 4.1 --- Graphical Representation of Spatial Rainfall Pattern --- p.50
Chapter 4.1.1 --- Annual Rainfall Pattern --- p.50
Chapter 4.1.2 --- Monthly Rainfall Pattern --- p.56
Chapter 4.1.3 --- Frequency Distribution of Raindays --- p.59
Chapter 4.1.4 --- Pentade Rainfall Pattern --- p.64
Chapter 4.1.5 --- Diurnal Rainfall Pattern --- p.67
Chapter 4.1.6 --- Implications of the Spatial Rainfall Pattern --- p.70
Chapter 4.2 --- Analyses of Spatial Variation in Rainfall --- p.78
Chapter 4.2.1 --- Relationship between Rainfall and Elevation --- p.78
Chapter 4.2.2 --- Relationship between Rainfall and Aspect --- p.82
Chapter 4.2.3 --- Classification of Stations --- p.85
Chapter 4.2.3.1 --- Principal Components Interpretation --- p.87
Chapter 4.2.3.2 --- Result of Classification --- p.90
Chapter 4.2.4 --- Inter-Station Correlation Analysis --- p.98
Chapter 4.2.5 --- Discussion of the Rainfall Spatial Variation --- p.103
Chapter 4.3 --- Analyses of Temporal Variation in Rainfall --- p.107
Chapter 4.3.1 --- Annual Rainfall --- p.107
Chapter 4.3.2 --- Monthly Rainfall --- p.110
Chapter 4.3.3 --- Pentade Rainfall --- p.112
Chapter 4.3.4 --- Diurnal Rainfall --- p.117
Chapter 4.3.5 --- Discussion of the Rainfall Temporal Variation --- p.118
Chapter CHAPTER FIVE: --- CONCLUSIONS AND RECOMMENDATIONS --- p.126
Chapter 5.1 --- Summary of Findings --- p.126
Chapter 5.2 --- Limitation of this Research --- p.129
Chapter 5.3 --- Prospects of this Research --- p.130
Bibliography

Long sequences of rainfall at fme spatial and temporal details are increasingly required, not only for hydrological studies, but also to provide inputs for models of crop growth, land fills, tailing dams, disposal of liquid waste on land and other environmentally-sensitive projects. However, rainfall records from raingauges frequently fail to meet the requirements of the above studies. Therefore, it is important to improve the estimation of the depth and spatial distribution of rainfall falling over a catchment. A number of techniques have been developed to improve the estimation of the spatial distribution of rainfall from sparsely distributed raingauges. These techniques range from simple interpolation techniques developed to estimate areal rainfall from point rainfall measurements, to statistical and deterministic models, which generate rainfall values and downscale the rainfall values based on the physical properties of the clouds or rain cells. Furthermore, these techniques include different statistical methods, which combine the rainfall information gathered from radar, raingauges and satellites. Although merging the radar and raingauge rainfall fields gives a best estimate of the "true rainfall field", the length of the radar record and spatial coverage of the radar in a country such as South Africa is relatively short and hence is of limited use in hydrological studies. Therefore, the relationship between the average merged rainfall value for a catchment and a "driver" station, which is selected to represent rainfall in the catchment, is developed and assessed in this study. Rainfall data from the Liebenbergsvlei Catchment near Bethlehem in the Free State Province and a six-month record of radar data are used to develop relationships between the average merged subcatchment rainfall for each of the Liebenbergsvlei subcatchments and a representative raingauge selected to represent the rainfall in each of the subcatchments. The relationships between daily raingauges and the average rainfall depth of the subcatchments are generally good and in most of the subcatchments the correlation coefficient is greater than 0.5. It was also noted that, in most of the subcatchments, the daily raingauges overestimate the average areal rainfall depth of the subcatchments. In addition, the String of Beads Model (SBM) developed by Clothier and Pegram (2002) was used to generate synthetic rainfall series for the Liebenbergsvlei catchments. The SBM is able to produce rainfall values at a spatial resolution of IxI km with a 5 minute temporal resolution. The SBM is a high-resolution space-time model of radar rainfall images, which 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. Statistics from a 50 year period of generated rainfall values were compared with the statistics computed from a 50 year raingauge data series, and it was found that the generated rainfall values mimic the rainfall data from the raingauges reasonably well. The relationship developed between the merged catchment rainfall values and driver rainfall station values, which are selected to represent the mean areal rainfall of the subcatchment, was used to adjust the Conventional Driver rainfall Station (CDS) into Modified Driver Station (MDS) values. Streamflow was simulated using both the CDS and MDS rainfall compared against the observed streamflow from the Liebenbergsvlei catchment. In general, the streamflow simulated by the ACRU model do not correlate well with the observed streamflow, which is attributed to unrealistic observed flow and inter-catchments transfers of water. However, it is noted that the volume of streamflow simulated with the MDS rainfall is only 71 % of that simulated with the CDS rainfall, thus highlighting the limitation of using the CDS rainfall approach for modelling and the need to apply the methodology to improve the estimation of catchment rainfall developed in this study to other catchments in South Africa.
Thesis (M.Sc.)-University of KwaZulu-Natal, 2005.

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.

"May 2002" Includes list of papers published during this study Errata slip inserted inside back cover of v. 1 Includes bibliographical references (leaves 331-357) V. 1. [Text} -- v. 2. Appendices Develops an alternative design flood estimation methodology. Establishing a relationship between catchment characteristics and the rainfall excess frequency duration proportions enables the definition of these proportions for generic catchment types, increasing the potential for translation to catchments with limited data but similar hydrographic properties, thereby improving design process.

The temporal distribution of rainfall , viz. the distribution of rainfall intensity during a storm, is an important factor affecting the timing and magnitude of peak flow from a catchment and hence the flood-generating potential of rainfall events. It is also one of the primary inputs into hydrological models used for hydraulic design purposes. The use of short duration rainfall data inherently accounts for the temporal distribution of rainfall, however, there is a relative paucity of short duration data when compared to the more abundantly available daily data. One method of overcoming this is to disaggregate courser-scale data to a finer resolution, e.g. daily to hourly. A daily to hourly rainfall disaggregation model developed by Boughton (2000b) in Australia has been modified and applied in South Africa. The primary part of the model is the . distribution of R, which is the fraction of the daily total that occurs in the hour of maximum rainfall. A random number is used to sample from the distribution of R at the site of interest. The sample value of R determines the other 23 values, which then undergo a clustering procedure. This clustered sequence is then arranged into 1 of 24 possible temporal arrangements, depending when the hour the maximum rainfall occurs. The structure of the model allows for the production of 480 different temporal distributions with variation between uniform and non-uniform rainfall. The model was then regionalised to allow for application at sites where daily rainfall data, but no short duration data, were available. The model was evaluated at 15 different locations in differing climatic regions in South Africa. At each location, observed hourly rainfall data were aggregated to yield 24-hour values and these were then disaggregated using the methodology. Results show that the model is able to retain the daily total and most of the characteristics of the hourly rainfall at the site, for when both at-site and regional information are used. The model, however, is less capable of simulating statistics related to the sequencing of hourly rainfalls, e.g. autocorrelations. The model also tends to over-estimate design rainfalls, particularly for the shorter durations .
Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2005.