The subject of this study is rainfall-runoff forecasting and flood warning. Denote by (X(t),Y(t)) a sequence of equally spaced bivariate random variables representing rainfall and runoff, respectively. A flood is said to occur at time period (n + 1) if Y(n + 1) > T where T is a fixed number. The main task of flood warning is that of deciding whether or not to issue a flood alarm for the time period n + 1 on the basis of the past observations of rainfall and runoff up to and including time n. With each decision, warning or no warning, there is a certain probability of an error (false alarm or no alarm). Using notions from classical decision theory, the optimal solution is the decision that minimizes Bayes risk. In Chapter 1 a more precise definition of flood warning will be given. A critical review (Chapter 2) of classical methods for forecasting used in hydrology reveals that these methods are not adequate for flood warning and similar types of decision problems unless certain Gaussian assumptions are satisfied. The purpose of this study is to investigate the application of a nonparametric technique referred to as the k-nearest neighbor (k-NN) methods to flood warning and least squares forecasting. The motivation of this method stems from recent results in statistics which extends nonparametric methods for inferring regression functions in a time series setting. Assuming that the rainfall-runoff process can be cast in the framework of Markov processes then, with some additional assumptions, the k-NN technique will provide estimates that converge with an optimal rate to the correct decision function. With this in mind, and assuming that our assumptions are valid, then we can claim that this method will, as the historical record grows, provide the best possible estimate in the sense that no other method can do better. A detailed description of the k-NN estmator is provided along with a scheme for calibration. In the final chapters, the forecasts of this new method are compared with the forecasts of several other methods commonly used in hydrology, on both real and simulated data.

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 Caribbean is a complex region that heavily relies on its seasonal rainfall cycle for its economic and societal needs. This makes the Caribbean especially susceptible to hydro-meteorological disasters (e.g., droughts and floods), and other weather/climate risks. Therefore, effectively predicting the Caribbean rainfall cycle is valuable for the region. The efficacy of predicting the Caribbean rainfall cycle is largely dependent on effectively characterizing the climate dynamics of the region. However, the dynamical processes and climate drivers that shape the seasonal cycle are not fully understood, as previous observational studies show inconsistent findings as to what mechanisms influence the mean state and variability of the cycle. These inconsistencies can be attributed to the limitations previous studies have when investigating the Caribbean rainfall cycle, such as using monthly or longer resolutions in the data or analysis that often mask the seasonal transitions and regional differences of rainfall, and investigating the Caribbean under a basin-wide lens rather than a sub-regional lens. This inhibits the ability to accurately calculate and predict subseasonal-to-seasonal (S2S) rainfall characteristics in the region. To address these limitations and inconsistencies, the research in this thesis examines the seasonal climatology, variability, and characteristics of the Caribbean rainfall cycle under a sub-regional and temporally fine lens in order to investigate the prediction of the cycle. Regional variations and dynamical processes of the Caribbean annual rainfall cycle are assessed using (1) a principal component analysis across Caribbean stations using daily observed precipitation data; and, (2) a moisture budget analysis. The results show that the seasonal cycle of rainfall in the Caribbean hinges on three main facilitators of moisture convergence: the Atlantic Intertropical Convergence Zone (ITCZ), the Eastern Pacific ITCZ, and the North Atlantic Subtropical High (NASH). A warm body of sea-surface temperatures (SSTs) in the Caribbean basin known as the Atlantic Warm Pool (AWP) and a low-level jet centered at 925hPa over the Caribbean Sea known as the Caribbean Low-Level Jet (CLLJ) modify the extent of moisture provided by these main facilitators. The interactions of these dynamical processes are responsible for shaping the seasonal components of the annual rainfall cycle: The Winter Dry Season (WDS; mid-November to April); the Early-Rainy Season (ERS; mid-April to mid-June); an intermittent relatively dry period known as the mid-summer drought, (MSD; mid-June to late August), and the Late-Rainy Season (LRS; late August to late November). Five geographical sub-regions are identified in the Caribbean Islands, each with its unique set of dynamical processes, and consequently, its unique pattern of rainfall distribution throughout the rainy season: Northwestern Caribbean, the Western Caribbean, the Central Caribbean, the Central and Southern Lesser Antilles, and Trinidad and Tobago and Guianas. Convergence by sub-monthly transients contributes little to Caribbean rainfall. The wettest and driest Caribbean ERS and LRS years’ are then explored by conducting the following: (1) a spatial composite of rainfall using the daily rainfall data; and, (2) spatial composites of SSTs, sea-level pressure (SLP), and mean flow moisture convergence and transports using monthly data. The ERS and LRS are impacted in distinctly different ways by two different, and largely independent, large-scale phenomena, external to the region: a SLP dipole mode of variability in the North Atlantic known as the North Atlantic Oscillation (NAO), and the El Nino Southern Oscillation (ENSO). Dry ERS years are associated with a persistent dipole of cold and warm SSTs over the Caribbean Sea and Gulf of Mexico, respectively, that are caused by a preceding positive NAO state. This setting involves a wind-evaporation-SST (WES) feedback expressed in enhanced trade winds and consequently, moisture transport divergence over all of the Caribbean, except in portions of the Northwestern Caribbean in May. A contribution from the preceding winter cold ENSO event is also discernible during dry ERS years. Dry LRS years are due to the summertime onset of an El Niño event, developing an inter-basin SLP pattern that moves moisture out of the Caribbean, except in portions of the Northwestern Caribbean in November. Both large-scale climate drivers would have the opposite effect during their opposite phases leading to wet years in both seasons. Existing methodologies that calculate S2S rainfall characteristics were not found to be suitable for a region like the Caribbean, given its complex rainfall pattern; therefore, a novel and comprehensive method is devised and utilized to calculate onset, demise, and MSD characteristics in the Caribbean. When applying the method to calculate S2S characteristics in the Caribbean, meteorological onsets and demises, which are calculated via each year’s ERS and LRS mean thresholds, effectively characterize the seasonal evolution of mean onsets and demises in the Caribbean. The year-to-year variability of MSD characteristics, and onsets and demises that are calculated by climatological ERS and LRS mean thresholds resemble the variability of seasonal rainfall totals in the Caribbean and are statistically significantly correlated with the identified dynamical processes that impact each seasonal component of the rainfall cycle. Finally, the seasonal prediction of the Caribbean rainfall cycle is assessed using the identified variables that could provide predictive skill of S2S rainfall characteristics in the region. Canonical correlation analysis is used to predict seasonal rainfall characteristics of station-averaged sub-regional frequency and intensity of the ERS and LRS wet days, and magnitude of the MSD. Predictor fields are based on observations from the ERA-Interim reanalysis and GCM output from the North America Multi-Model Ensemble (NMME). Spearman Correlation and Relative Operating Characteristics are applied to assess the forecast skill. The use of SLP, 850-hPa zonal winds (u850), vertically integrated zonal (UQ), and meridional (VQ) moisture fluxes show comparable, if not better, forecast skill than SSTs, which is the most common predictor field for regional statistical prediction. Generally, the highest ERS predictive skill is found for the frequency of wet days, and the highest LRS predictive skill is found for the intensity of wet days. Rainfall characteristics in the Central and Eastern Caribbean have statistically significant predictive skill. Forecast skill of rainfall characteristics in the Northwestern and Western Caribbean are lower and less consistent. The sub-regional differences and consistently significant skill across lead times up to at least two months can be attributed to persistent SST/SLP anomalies during the ERS that resemble the North Atlantic Oscillation pattern, and the summer-time onset of the El Niño-Southern Oscillation during the LRS. The spatial pattern of anomalies during the MSD bears resemblance to both the ERS and LRS spatial patterns. The findings from this thesis provide a more comprehensive and complete understanding of the climate dynamics, variability, and annual mean state of the Caribbean rainfall cycle. These results have important implications for prediction, decision-making, modeling capabilities, understanding the genesis of hydro-meteorological disasters, investigating rainfall under other modes of variability, and Caribbean impact studies regarding weather risks and future climate.

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.

South Africa experiences some of the lowest water resource system yields in the world as a result of the high regional variability of rainfall and runoff. Population growth and economic development are placing increasing demands on the nation's scarce water resources. These factors, combined with some of the objectives of the new National Water Act (1998), are highlighting the need for efficient management of South Africa's water resources. In South Africa's National Water Act (1998) it is stated that its purpose is to ensure that the nation's water resources are protected, used, conserved, managed and controlled in a way, which takes into account, inter alia, i. promoting the efficient, sustainable and beneficial use of water in the public interest, and ii. managing floods and droughts. Efficient and sustainable water resource and risk management can be aided by the application of runoff forecasting. Forecasting thus fits into the ambit of the National Water Act and, therefore, there is a need for its operational application to be investigated. In this document an attempt is made to test the following hypotheses: Hypothesis 1: Reliable and skilful hydrological forecasts have the ability to prevent loss of life, spare considerable hardship and save affected industries and commerce millions of Rands annually if applied operationally within the context of water resources and risk management. Hypothesis 2: Long to medium term rainfall forecasts can be made with a degree of confidence, and these rainfall forecasts can be converted into runoff forecasts which, when applied within the framework of water resources and risk management, are more useful to water resource managers and users than rainfall forecasts by themselves. The validity of Hypothesis 1 is investigated by means of a literature review. South Africa's high climate variability and associated high levels of uncertainty as well as its current and future water resources situation are reviewed in order to highlight the importance of runoff forecasting in South Africa. Hypothesis 1 is further examined by reviewing the concepts of hazards and risk with a focus on the role of effective risk management in preventing human, financial and infrastructural losses. A runoff forecasting technique using an indirect methodology, whereby rainfall forecasts are translated into runoff forecasts, was developed in order to test Hypothesis 2. The techniques developed are applied using probabilistic regional rainfall forecasts supplied by the South African Weather Service for 30 day periods and categorical regional forecasts for one, three and four month periods for I regions making up the study area of South Africa, Lesotho and Swaziland. These forecasts where downscaled spatially for application to the 1946 Quaternary Catchments making up the study area and temporally to give daily rainfall forecast values. Different runoff forecasting time spans produced varying levels of forecast accuracy and skill, with the three month forecasts producing the worst results, followed by the four month forecasts. The 30 day and one month forecasts for the most part produced better results than the more extended forecast periods. In the study it was found that hydrological forecast accuracy results seem to be inversely correlated to the amount of rainfall received in a region, i.e. the wetter the region the less accurate the runoff forecasts. This trend is reflected in both temporal and spatial patterns where it would seem that variations in the antecedent moisture conditions in wetter areas and wetter periods contribute to the overall variability, rendering forecasts less accurate. In general, the runoff forecasts improve with corresponding improvements in the rainfall forecast accuracy. There are, however, runoff forecast periods and certain regions that produce poor runoff forecast results even with improved rainfall forecasts. This would suggest that even perfect rainfall forecasts still cannot capture all the local scale variability of persistence of wet and dry days as well as magnitudes of rainfall on individual days and the effect of catchment antecedent moisture conditions. More local scale rainfall forecasts are thus still needed in the South African region. In this particular study the methods used did not produce convincing results in terms of runoff forecast accuracy and skill scores. The poor performance can probably be attributed to the relatively unsophisticated nature of the downscaling and interpolative techniques used to produce daily rainfall forecasts at a Quaternary Catchment scale. It is the author's opinion that in the near future, with newly focussed research efforts, and building on what has been learned in this study, more reliable agrohydrological forecasts can be used within the framework of water resources and risk management, preventing loss of life, saving considerable hardship and saving affected industry and commerce millions of rands annually. / Thesis (M.Sc.)-University of Natal, Pietermaritzburg, 2002.