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.

Orientador: Glauco de Souza Rolim / Resumo: Precipitação, em pequenas escalas de tempo, é um fenômeno associado a altos níveis de incerteza e variabilidade. Dada a sua natureza, técnicas tradicionais de previsão são dispendiosas e exigentes em termos computacionais. Este trabalho apresenta um modelo para prever a ocorrência de chuvas em curtos intervalos de tempo por Redes Neurais Artificiais (RNAs) em períodos acumulados de 3 a 7 dias para cada estação climática, mitigando a necessidade de predizer o seu volume. Com essa premissa pretende-se reduzir a variância, aumentar a tendência dos dados diminuindo a responsabilidade do algoritmo que atua como um filtro para modelos quantitativos, removendo ocorrências subsequentes de valores de zero(ausência) de precipitação, o que influencia e reduz seu desempenho. O modelo foi desenvolvido com séries temporais de 10 regiões agricolamente relevantes no Brasil, esses locais são os que apresentam as séries temporais mais longas disponíveis e são mais deficientes em previsões climáticas precisas, com 60 anos de temperatura média diária do ar e precipitação acumulada. foram utilizados para estimar a evapotranspiração potencial e o balanço hídrico; estas foram as variáveis ​​utilizadas como entrada para as RNAs. A precisão média para todos os períodos acumulados foi de 78% no verão, 71% no inverno 62% na primavera e 56% no outono, foi identificado que o efeito da continentalidade, o efeito da altitude e o volume da precipitação normal , tem um impacto direto na precisão das RNAs. Os... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Precipitation, in short periods of time, is a phenomenon associated with high levels of uncertainty and variability. Given its nature, traditional forecasting techniques are expensive and computationally demanding. This paper presents a model to forecast the occurrence of rainfall in short ranges of time by Artificial Neural Networks(ANNs) in accumulated periods from 3 to 7 days for each climatic season, mitigating the necessity of predicting its amount. With this premise it is intended to reduce the variance, rise the bias of data and lower the responsibility of the model acting as a filter for quantitative models by removing subsequent occurrences of zeros values of rainfall which leads to bias the and reduces its performance. The model were developed with time series from 10 agriculturally relevant regions in Brazil, these places are the ones with the longest available weather time series and and more deficient in accurate climate predictions, it was available 60 years of daily mean air temperature and accumulated precipitation which were used to estimate the potential evapotranspiration and water balance; these were the variables used as inputs for the ANNs models. The mean accuracy of the model for all the accumulated periods were 78% on summer, 71% on winter 62% on spring and 56% on autumn, it was identified that the effect of continentality, the effect of altitude and the volume of normal precipitation, have a direct impact on the accuracy of the ANNs. The models have ... (Complete abstract click electronic access below) / Mestre

Approved for public release; distribution is unlimited / This thesis presents a statistical analysis of the monthly rainfall for the Monterey Peninsula and the Carmel Valley in Central California. The analysis begins with the simple first-order autoregressive Markov model, which is found to be weak. Next, 2X2 contingency tables are used to identify predictors, one of which is found to be January rainfall. Finally, logistic analysis is used to quantify the predictive ability of January. This paper attempts to analyze rainfall time series in the statistical sense. No attempt is made to provide a physical explanation of the findings from the point of view of a meteorologist. / http://archive.org/details/statisticalanaly00davi / Captain, United States Army

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.

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.

The objective of the present study is to forecast annual rainfall taking into account the periodicities and structure of the stochastic component. This study has six Chapters. Chapter 1 presents introduction to the problem and objectives of the study. Chapter 2 consists of review of literature. Chapter 3 deals with the model formulation and development. Chapter 4 gives an account of the application of the model. Chapter 5 presents results and discussions. Chapter 6 gives the conclusions drawn from the study. In this thesis the following model formulations are presented in order to achieve the objective. Fourier analysis model is used to identify periodicities that are present in the rainfall series.1 These periodic components are used to obtain discrotized ranges which is an essential input for the Fourier series model. Auto power regression model is developed for estimation of rainfall and hence to compute the first order residuals errlt The parameters of the model are estimated using genetic algorithm. The auto power regression model is of the form, ( Refer the PDF File for Formula) where αi and βi are parameters and M indicates modular value. Fourier series model is formulated and solved through genetic algorithm to estimate the parameters amplitude R, phase Φ and periodic frequency wj for the residual series errlt. The ranges for the parameters R, Φ and wj were obtained from Fourier analysis model. errl't= /µerrlt+ Σj Rcos(wjt+ Φ) Further, an integrated auto power regression and Fourier series model developed (with parameters of the model being known from the above analysis) to estimate new rainfall series Zesťt=Zµ Σ t αi(ZMi-t ) βi+µerrl+ Σj Rcos(wjt+ Φ) and the second order residuals, err2t is computed using, err2t = (zt –Zesťt) Thus, the periodicities are removed in the errlt series and the second order residuals err'2f obtained represents the stochastic component of the actual rainfall series. Auto regressive model is formulated to study the structure of the stochastic component err2t. The auto regressive model of order two AR(2) is found to fit well. The parameters of the AR(2) model were estimated using method of least squares. An exponential weighting function is developed to compute the weight considering weight as a function of AR{2) parameters. The product of weight and Gaussian white noise N(0, óerr2) is termed as weighted stochastic component. Also, drought analysis is performed considering annual (January to December) and summer monsoon (June to September) rainfall totals, to determine average drought interval (idrt) which is used in assigning signs to the random component of the forecasting model. In the final form of the forecasting model. Zest”t = Z µ Σ t αi(ZMi-t ) βi+µerrl+ Σj Rcos(wjt+ Φ) ± WT(Φ1, Φ2)N(0, óerr2) The weighted stochastic component is added or subtracted considering two criteria. Criterion I is used for all rainfall series except all-India series for which criterion II is used. The criteria also consider average drought interval Further, it can be seen that a ± sign is introduced to add or subtract the weighted stochastic component, albeit the stochastic component itself can either be positive or negative. The introduction of ± sign on the already signed value (instead of absolute value) is found to improve the forecast in the sense of obtaining more number of point rainfall estimates within 20 percent error. Incorporating significant periodicities, and weighted stochastic component along with average drought interval into the forecasting formulation is the main feature of the model. Thus, in the process of rainfall prediction, the genetic algorithm is used as an efficient tool in estimating optimal parameters of the auto power regression and the Fourier series models, without the use of an expensive nonlinear least square algorithm. The model application is demonstrated considering different annual rainfall series relating to IMD-Regions (RI...R5), all-india (AI), IMD-Subdivisions (S1...S29), Zones (Z1...Z10) and all-Karnataka (AK). The results of the proposed model are encouraging in providing improved forecasts. The model considers periodicity, average critical drought frequency and weighted stochastic component in forecasting the rainfall series. The model performed well in achieving success-rate of 70 percent with percentage error less than 20 percent in 4 out of 5 IMD Regions (R2 to R5), all-India, 17 out of 29 IMD Subdivisions (S1 to S5, S7 to S9, S18, S19, S21, S24 to S29) and all-Karnataka rainfall series. The model performance for Zones was not that-satisfactory as only 2 out of 10 Zones [Z1 and Z2) met the criterion. In a separate study, an effort was made to forecast annual rainfall using IMSL subroutine SPWF -which estimates Wiener forecast parameters. Monthly data is considered for the study. The Wiener parameters obtained were used to estimate monthly rainfall. The annual estimates obtained by simple aggregation of the monthly estimates compared extremely well with the actual annual rainfall values. A success rate of more than 80 percent with percentage error less than 10 percent is achieved in 4 out of 5 IMD Regions (R2 to R5), all-India, 18 out of 29 IMD Subdivisions (S1 to S8, S14, S18, S19, S22 to S24, S26 to S29) and all-Karnataka rainfall series. Whereas a success rate of 80 percent within 20 percent error is achieved in 4 out of 5 IMD Regions (except R1), all-India, 25 outof 29 IMD Subdivisions (except S10, S11, S12 and S17), all- Karnataka and 8 out of 10 Zones (except Z6 and Z8)(Please refer PDF File for Formulas)