Rainfall is a natural process, which has a high degree of variability in both space and time. Information on the spatial and temporal variability of rainfall plays an important role in the process of surface runoff generation. Hence it is important for a variety of applications in hydrology and water resources management. The spatial variability of rainfall can be substantial even for very small catchments and an important factor in the reliability of rainfall-runoff simulations. Catchments in urban areas usually are small, and the management problems often require the numerical simulation of catchment processes and hence the need to consider the spatial and temporal variability of rainfall. A need exists, therefore, to analyse the sensitivity of rainfall-runoff behaviour of catchment modelling systems (CMS) to imperfect knowledge of rainfall input, in order to judge whether or not they are reliable and robust, especially if they are to be used for operational purposes. Development of a methodology for identification of storm events according to the degree of heterogeneity in space and time and thence development of a detailed spatial and temporal rainfall model within a hydroinformatic environment utilising real-time data has been the focus of this project. The improvement in runoff prediction accuracy and hence the importance of the rainfall input model in runoff prediction is then demonstrated through the application of a CMS for differing variability of real storm events to catchments with differing orders of scale. The study identified both spatial and temporal semi-variograms, which were produced by plotting the semi-variance of gauge records in space and time against distance and time respectively. These semi-variograms were utilised in introducing estimators to measure the degree of heterogeneity of each individual storm events in their space and time scale. Also, the proposed estimators use ground based gauge records of the real storm events and do not rely on delicate meteorological interpretations. As the results of the investigation on the developed semi-variogram approach, real storm events were categorised as being High Spatial-High Temporal (HS-HT); High Spatial-Low Temporal; (HS-LT); Low Spatial-High Temporal (LS-HT); and Low Spatial-Low Temporal variability.A comparatively detailed rainfall distribution model in space and time was developed within the Geographical Information Systems (GIS). The enhanced rainfall representation in both space and time scale is made feasible in the study by the aid of the powerful spatial analytic capability of GIS. The basis of this rainfall model is an extension of the rainfall model developed by Luk and Ball (1998) through a temporal discretisation of the storm event. From this model, improved estimates of the spatially distributed with smaller time steps hyetographs suited for especially the urban catchments could be obtained. The importance of the detailed space-time rainfall model in improving the robustness of runoff prediction of CMS was investigated by comparing error parameters for predictions from CMS using alternate rainfall models, for various degrees of spatiotemporal heterogeneity events. Also it is appropriate to investigate whether the degree of this improvement to be dependent on the variability of the storm event which is assessed by the adopted semi-variogram approach. From the investigations made, it was found that the spline surface rainfall model, which considered the spatial and temporal variability of the rainfall in greater detail than the Thiessen rainfall model resulted in predicted hydrographs that more closely duplicated the recorded hydrograph for the same parameter set. The degree of this improvement in the predicted hydrograph was found to be dependent on the spatial and temporal variability of the storm event as measured by the proposed semi-variogram approach for assessing this feature of a storm event. The analysis is based on forty real events recorded from the Centennial Park Catchment (1.3km2) and the Upper Parramatta River Catchment (110km2) in Sydney, Australia. These two case study catchments were selected to ensure that catchment scale effects were incorporated in the conclusions developed during the study.

Rainfall is a natural process, which has a high degree of variability in both space and time. Information on the spatial and temporal variability of rainfall plays an important role in the process of surface runoff generation. Hence it is important for a variety of applications in hydrology and water resources management. The spatial variability of rainfall can be substantial even for very small catchments and an important factor in the reliability of rainfall-runoff simulations. Catchments in urban areas usually are small, and the management problems often require the numerical simulation of catchment processes and hence the need to consider the spatial and temporal variability of rainfall. A need exists, therefore, to analyse the sensitivity of rainfall-runoff behaviour of catchment modelling systems (CMS) to imperfect knowledge of rainfall input, in order to judge whether or not they are reliable and robust, especially if they are to be used for operational purposes. Development of a methodology for identification of storm events according to the degree of heterogeneity in space and time and thence development of a detailed spatial and temporal rainfall model within a hydroinformatic environment utilising real-time data has been the focus of this project. The improvement in runoff prediction accuracy and hence the importance of the rainfall input model in runoff prediction is then demonstrated through the application of a CMS for differing variability of real storm events to catchments with differing orders of scale. The study identified both spatial and temporal semi-variograms, which were produced by plotting the semi-variance of gauge records in space and time against distance and time respectively. These semi-variograms were utilised in introducing estimators to measure the degree of heterogeneity of each individual storm events in their space and time scale. Also, the proposed estimators use ground based gauge records of the real storm events and do not rely on delicate meteorological interpretations. As the results of the investigation on the developed semi-variogram approach, real storm events were categorised as being High Spatial-High Temporal (HS-HT); High Spatial-Low Temporal; (HS-LT); Low Spatial-High Temporal (LS-HT); and Low Spatial-Low Temporal variability.A comparatively detailed rainfall distribution model in space and time was developed within the Geographical Information Systems (GIS). The enhanced rainfall representation in both space and time scale is made feasible in the study by the aid of the powerful spatial analytic capability of GIS. The basis of this rainfall model is an extension of the rainfall model developed by Luk and Ball (1998) through a temporal discretisation of the storm event. From this model, improved estimates of the spatially distributed with smaller time steps hyetographs suited for especially the urban catchments could be obtained. The importance of the detailed space-time rainfall model in improving the robustness of runoff prediction of CMS was investigated by comparing error parameters for predictions from CMS using alternate rainfall models, for various degrees of spatiotemporal heterogeneity events. Also it is appropriate to investigate whether the degree of this improvement to be dependent on the variability of the storm event which is assessed by the adopted semi-variogram approach. From the investigations made, it was found that the spline surface rainfall model, which considered the spatial and temporal variability of the rainfall in greater detail than the Thiessen rainfall model resulted in predicted hydrographs that more closely duplicated the recorded hydrograph for the same parameter set. The degree of this improvement in the predicted hydrograph was found to be dependent on the spatial and temporal variability of the storm event as measured by the proposed semi-variogram approach for assessing this feature of a storm event. The analysis is based on forty real events recorded from the Centennial Park Catchment (1.3km2) and the Upper Parramatta River Catchment (110km2) in Sydney, Australia. These two case study catchments were selected to ensure that catchment scale effects were incorporated in the conclusions developed during the study.

Thesis (M.S.)----University of North Carolina Wilmington, 2008. / Title from PDF title page (viewed May 26, 2009) Includes bibliographical references (p. 61)

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

On most tropical volcanic islands the risk for soil erosion is enhanced due to a complex topography, high intensity rainfall and the exploitation of land for agriculture. Mauritius is a typical maritime tropical volcanic island with a distinct elevated interior. Rainfall is dominated by tropical weather systems and trade winds and the island is under intensive cultivation. Rainfall depth, duration, intensity, kinetic energy and erosivity were analysed for 385 erosive rainfall events at five locations over a five year period (2004 to 2008) on the island of Mauritius. Two stations located on the west coast and three stations sited on the Central Plateau above 550 m a.s.l. are used to provide detailed rainfall data at six minute intervals. Erosive storm events, defined here as a total rainfall exceeding 12.5 mm and a maximum 6-minute intensity exceeding 25 mm/hour, are found to differ markedly between the coastal lowlands and the elevated interior with regards to the frequency, the total rainfall generated, the duration, total kinetic energy and total erosivity of individual events. However, mean kinetic energy, mean and maximum rainfall erosivity (EI30) and maximum intensities (I30) from individual erosive events do not show this distinct differentiation. Erosivity measured during summer exceeds that recorded in winter, but the data indicate that large percentages of winter rainfall on Mauritius are defined as erosive and non-tropical cyclone rainfall can pose a substantial erosion risk. In this maritime tropical environment with its elevated interior, soil erosion risk occurs from storm scale to synoptic scale rainfall events and extreme events generate the bulk of the erosivity. Findings show that using rainfall records at an event scale within soil erosion risk assessments on tropical islands with a complex topography will increase the effectiveness of erosivity estimates

Thesis (M. Sc. (Statistics)) -- University of Limpopo, 2020 / The main purpose of modelling rare events such as heavy rainfall, heat waves, wind speed, interest rate and many other rare events is to try and mitigate the risk that might arise from these events. Heavy rainfall and floods are still troubling many countries. Almost every incident of heavy rainfall or floods might result in loss of lives, damages to infrastructure and roads, and also financial losses. In this dissertation, the interest was in modelling average monthly rainfall for South Africa using extreme value theory (EVT). EVT is made up mainly of two approaches: the block maxima and peaks-over thresh old (POT). This leads to the generalised extreme value and the generalised Pareto distributions, respectively. The unknown parameters of these distri butions were estimated using the method of maximum likelihood estimators in this dissertation. According to goodness-of-fit test, the distribution in the Weibull domain of attraction, Gumbel domain and generalised Pareto distri butions were appropriate distributions to model the average monthly rainfall for South Africa. When modelling using the POT approach, the point process model suggested that some areas within South Africa might experience high rainfall in the coming years, whereas the GPD model suggested otherwise. The block maxima approach using the GEVD and GEVD for r-largest order statistics also revealed similar findings to that of the GPD. The study recommend that for future research on average monthly rainfall for South Africa the findings might be improved if we can invite the Bayesian approach and multivariate extremes. Furthermore, on the POT approach, time-varying covariates and thresholds are also recommended. / National Research Foundation (NRF) and South African Weather Service (SAWS)

Thesis. 1976. M.S. cn--Massachusetts Institute of Technology. Dept. of Meteorology. / Microfiche copy available in Archives and Science. / Bibliography: leaves 113-116. / M.S.cn

付記する学位プログラム名: グローバル生存学大学院連携プログラム / 京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第19975号 / 工博第4219号 / 新制||工||1653(附属図書館) / 33071 / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 立川 康人, 教授 寶 馨, 教授 堀 智晴 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

No description available.

Societies in much of the Horn of Africa are affected by variability in two distinct rainy seasons: the March-May (MAM) “long” rains and the October-December (OND) “short” rains. The region is the driest area of the tropics, while its societies are heavily dependent on the rainfall cycle. Especially worrying are anomalously dry conditions, which, together with other factors, contribute to food insecurity in the region. The recent 2020-2023 5-season drought, associated with the concurrent “triple-dip” La Niña and resulting in tens of millions of people facing “high levels of food insecurity” (cf: IGAD), renewed fears of long-term and possibly anthropogenically-forced drying trends, especially during the MAM long rains. A long-term decline in the long rains beginning in the early 1980s and lasting until the 2010s had indeed been noted in studies examining historical station-based observations, satellite observations, and farmer recollections in the region, though seasonal average rainfall has since partially recovered. Consequently, global climate models (GCMs) are increasingly used to project changes in rainfall characteristics under global warming scenarios and associated impacts on societies, such as agricultural production, groundwater resources, and urban infrastructure, in addition to providing seasonal forecasts used for near-term decision-making. However, GCMs uniformly predict long-term wetting in both seasons despite observed drying trends in the long rains, an “East African Paradox” that complicates the ability of decisionmakers to plan for future rainfall conditions. Previous generations of GCMs have known biases in key dynamics of the regional hydroclimate. Decisionmakers relying on projections of future rainfall in the GHA therefore need to know whether current GCM projections are trustworthy. In other words, can we be confident in future modeled wetting trends in both the long and short rains? This thesis pursues this question in three parts. Chapter 2 seeks to understand the fundamental dynamics affecting the East African seasonal rainfall climatology, which is unique for its latitude in both its aridity and for the dynamical differences between its two rainy seasons. I explain these characteristics through the climatology of moist static stability, estimated as the difference between surface moist static energy h? and midtropospheric saturation moist static energy h*. In areas and at times when this difference, h? − h*, is higher, rainfall is more frequent and more intense. However, even during the rainy seasons, h? − h* < 0 on average and the atmosphere remains largely stable, in line with the region’s aridity. The seasonal cycle of h? − h*, to which the unique seasonal cycles of surface humidity, surface temperature, and midtropospheric temperature all contribute, helps explain the double-peaked nature of the regional hydroclimate. Despite tropospheric temperature being relatively uniform in the tropics, even small changes in h* can have substantial impacts on instability; for example, during the short rains, the annual minimum in regional h* lowers the threshold for convection and allows for instability despite surface humidity anomalies being relatively weak. This h? − h* framework can help identify the drivers of interannual variability in East African rainfall or diagnose the origin of biases in climate model simulations of the regional climate. Chapter 3 applies these results to conduct a process-based model evaluation of the ability of GCMs from the 6th phase of the Coupled Model Intercomparison Project (CMIP6, the latest GCM generation) to simulate the historical climatology and variability in the East African long and short rains. I find that key biases from the 5th phase of the Coupled Model Intercomparison Project (CMIP5) remain or are worsened, including long rains that are too short and weak and short rains that are too long and strong. Model biases are driven by a complex set of related oceanic and atmospheric factors, including simulations of the Walker Circulation. h? − h* is too high in models, requiring more instability for the same amount of rainfall than in observations. Biased wet short rains in models are connected with Indian Ocean zonal sea surface temperature (SST) gradients that are too warm in the west and convection that is too deep. Models connect equatorial African winds with the strength of the short rains, though in observations a robust connection is primarily found in the long rains. Model mean state biases in the timing of the western Indian Ocean SST seasonal cycle are associated with certain rainfall timing biases, though both biases may be due to a common source. Simulations driven by historical SSTs (so-called ‘AMIP’ runs) often have larger biases than fully coupled runs. However, models generally respond to teleconnections with the Indian Ocean Dipole and the El Niño Southern Oscillation in particular as expected, maintaining the possibility that trends in the long and short rains may also respond correctly to simulated trends in large-scale dynamics. Finally, Chapter 4 applies these results to directly tackle the East African Paradox by analyzing model trends across the entire observational record to identify under what conditions they fail to reproduce observed trends. Since even with perfect models and observational records model output may differ from observations due to internal variability, I analyze the full spread of CMIP6 output, including Large Ensembles and totalling 598 runs from 47 models. I find that while observed trends are always within the model spread if all runs from all Large Ensembles are considered, the Paradox remains in CMIP6 models, since GCMs substantially underproduce strong drying trends compared to observations. Within the observational record, the Paradox is limited to the time period with the most anomalous drying trends (especially in the years 1980-2010); the recent recovery in rainfall falls comfortably within the range of GCM simulations. The Paradox is not visible in AMIP runs forced with observed historical SSTs, suggesting that biases in simulations of SSTs may be part of the explanation, though clear causality remains elusive. The transition towards more biased trends from SST-forced to coupled runs can also be seen in output from hindcasts from seasonal forecast models, where trends calculated from short-lead-time projections (when the ocean state resembles observations) do not feature the Paradox, while lead times starting with 1.5 months do. More broadly, I show that climate model simulations of observed trends alone cannot be used to reject model predictions of increased (or decreased) precipitation under future forcings. Decision-makers relying on future projections of rainfall trends in East Africa will likely need to consider the possibility of further drying in addition to wetting trends from GCMs.