Dissertations / Theses on the topic 'Daily rainfall'

For the design of hydraulic structures for flood conveyance and discharge, or protection of territory against flood is fundamental the knowledge of the ``extreme rainfall regime'' in the area where the hydraulic structures must be set up. Indeed the design flood is commonly evaluated as output of rainfall-runoff models that receive as input the quantitative description of a rainfall extreme event with a given exceedance probability. This dissertation assesses the performance of different statistical approaches in characterizing extreme rainfall in the island of Sardinia (Italy). After a detailed review of the theoretical bases of existing methodologies, we compare the results obtained from the use of: a) a Generalized Extreme value (GEV) distribution model, and a Two component Extreme Value (TCEV) distribution model, both applied to yearly maxima of daily rainfall, and b) a Generalized Pareto (GP) distribution model applied to rainfall excesses above a properly specified threshold. For the latter purpose, we use the Multiple Threshold Method (MTM) developed by Deidda(2010), which demonstrate good performance also in the case of quantized records. In order to describe the spatial variation of TCEV, GEV and GP model parameters a regional approach based on homogeneous regions, and two versions of Kriging (a commonly used geostatistical approach) i.e. ordinary Kriging (OK), and Kriging for uncertain Data (KUD), are compared. The obtained results are very promising, pointing towards the use of: a)a GEV distribution model for yearly rainfall maxima, and a KUD model to describe the spatial variation of model parameters, and b)a GP model for rainfall excesses and either an OK or a KUD model for the spatial variation of model parameters. The reason why the OK and KUD approaches lead to the same results in the GP case, is attributed to the robustness of the MTM method.

Rainfall erosivities as defined by the R factor from the universal soil loss equation were determined for all events during a two-year period at the station La Cuenca in western Amazonia. Three methods based on a power relationship between rainfall amount and erosivity were then applied to estimate event and daily rainfall erosivities from the respective rainfall amounts. A test of the resulting regression equations against an independent data set proved all three methods equally adequate in predicting rainfall erosivity from daily rainfall amount. We recommend the Richardson model for testing in the Amazon Basin, and its use with the coefficient from La Cuenca in western Amazonia.

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.

Rainfall data are usually gathered at daily timescales due to the availability of daily rain-gauges throughout the world. However, rainfall data at fine timescale are required for certain hydrologic modellings such as crop simulation modelling, erosion modelling etc. Limited availability of such data leads to the option of daily rainfall disaggregation. This research investigates the use of a stochastic rainfall disaggregation model on a regional basis to disaggregate daily rainfall into any desired fine timescale in the State of Queensland, Australia. With the incorporation of seasonality into the variance relationship and capping of the fine timescale maximum intensities, the model was found to be a useful tool for disaggregating daily rainfall in the regions of Queensland. The degree of model complexity in terms of binary chain parameter calibration was also reduced by using only three parameters for Queensland. The resulting rainfall Intensity-Frequency-Duration (IFD) curves better predicted the intensities at fine timescale durations compared with the existing Australian Rainfall and Runoff (ARR) approach. The model has also been linked to the SILO Data Drill synthetic data to disaggregate daily rainfall at sites where limited or no fine timescale observed data are available. This research has analysed the fine timescale rainfall properties at various sites in Queensland and established sufficient confidence in using the model for Queensland.

Rainfall occurrence and intensity are the most important drivers of the surface runoff process. The knowledge of the occurrence and intensity of rainfall events is a crucial concern for water resources planners and designers. Stochastic rainfall generators are considered a robust tool that can generate the rainfall intensity of any time length at the interested locations. The validity of the stochastic daily rainfall generators for the Middle East in general and Jordan in specific has not been well researched. The aim of the present research is to estimate daily rainfall time series in different climates with particular focus on semiarid and arid regions. As an important result of the present research, a hybrid single-site stochastic daily rainfall generator (the hybrid model) has been developed using both a two-state first-order Markov chain based model and enhancing the simulation of long dry series using a modified serial approach. Long-term daily rainfall time series from rainfall stations under two different precipitation-hydrological regimes; namely, a frontal dominated precipitation-hydrological regime (Northern Ireland) and a semiarid to arid regime driven predominantly by convective rainfall (Jordan) have been used in testing and evaluation of the hybrid model, in addition to the two original approaches (Markov chain based model and Serial approach represented by LARS-WG). Standard statistical analysis and tests have been used to evaluate the performance of the single-site stochastic daily rainfall generators in both regimes. These single-site stochastic daily rainfall generators then have been assessed at multiple sites using a network of daily rainfall stations within the Lough Neagh basin in Northern Ireland and the Mujib basin in Jordan in order to evaluate their ability to correlate the generated time series of the neighbouring stations. According to the present research results of the comparative performance of the single-site stochastic daily rainfall generators, the hybrid model performance in both regimes was superior.

From the Proceedings of the 1987 Meetings of the Arizona Section - American Water Resources Association, Hydrology Section - Arizona-Nevada Academy of Science and the Arizona Hydrological Society - April 18, 1987, Northern Arizona University, Flagstaff, Arizona

In the stochastic hydrology literature, suitable time series modelling approaches have been developed for modelling daily streamflow. However, problems arise with this approach if changes are occurring to the precipitation regime generating the historic streamflow data, or if land-use changes are occurring within the catchment which may alter the water balance and the streamflow regime. Traditional time series modelling approaches employ historic streamflow data only and will generate synthetic data which are representative only of the historic conditions. It is not possible to predict how the model parameters should be changed to reflect changes in the climate (precipitation) and catchment response regimes. Developing a methodology to deal with the stochastic generation of daily streamflow that reflects changes to the catchment system and climatic inputs (rainfall and potential evapotranspiration) and then applying the corresponding methodology to a study catchment (upper Thames) in England is the focus of this study. To study the water resources impacts of land-use change on the daily streamflow regime of a catchment, a daily rainfall-runoff model is needed which can accommodate various land cover characteristics and provide separate estimates of potential and actual evapotranspiration in its evapotranspiration component for each land cover type. Given a model with this capability, the impacts of various land-use scenarios on daily streamflow can be investigated. In the case of climate change, since GCMs do not provide useable results on a short time scale such as a day and on a spatial scale such as a catchment of about 1000 km2, a methodology is required to predict the changes which may occur in the climate inputs of a catchment, and the resulting impacts on water resources. The approach developed here for water resources impact studies of land-use change and climate change has three main elements: (I) Two stochastic models, one for rainfall (Neyman-Scott Rectangular Pulses, NSRP, model) and the other for potential evapotranspiration (PET), are employed to generate daily rainfall and daily PET sequencesr,e spectively. Thesem odels have been validated using historic records for the study catchment. ABSTRACT ii (II) The ARNO model has been calibrated and validated using daily streamflow data for the study catchment. The evapotranspiration component of the model has been modified to obtain a satisfactory water balance. The model is then extended to include the explicit calculation of interception for different land cover types within the catchment. The runoff from these areas is then routed to the catchment outlet. The rainfall and PET models are used to generate synthetic daily input series to the modified ARNO model for present catchment land-use conditions, and overall procedure is validated using the historic streamflow record. This is then worked out using the extended model and referred to as the constructed` control' scenariow hich is used as a benchmarkf or assessingla nd-usec hange impacts on water resources for two different land-use scenarios. (III) The transient GCM climate scenarios are used as the starting point for assessing climate change impacts. Regression relationships are derived between atmospheric circulation variables and rainfall statistics used in fitting the NSRP model for present climate conditions and then used to predict the rainfall statistics for future conditions using GCM outputs. That is, the scenarios of a climate model are downscaled by a regression technique to a resolution sufficient to represent daily rainfall at the catchment scale. To generate potential evapotranspiration (PET) scenarios, an empirical equation is used to estimate PET daily values as a function of temperature, thus enabling future scenarios to be generated as a function of GCM temperature predictions. Generated rainfall and PET scenarios are used as inputs to the adapted ARNO catchment response model to generate daily streamflow data. Impact assessments using both land-use change and climate change scenarios are then carried out using a range of water resources assessment measures such as flow duration curves, cumulative run sums and storage/yield relationships, and the practical implications discussed.

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

Thesis (doctoral) - Delft University of Technology, Delft, 2002.<br>"Dissertation submitted in fulfillment of the requirements of the Board for Doctorates of Delft University of Technology and of the Academic Board of the International Institute for Infrastructural, Hydraulic and Environmental Engineering for the Degree of Doctor to be defended in public on Monday, 29 April 2002 at 13:30 hours in Delft, The Netherlands." Includes bibliographical references (p. [191]-199).

Published Article<br>Although deterministic models still dominate hydrological modelling, there is a notable paradigm shift in catchment response modelling. An approach to represent the daily rainfall-flow (R-F) relationship using Data-Based Mechanistic (DBM) modelling is presented. DBM modelling is an inductive empirical transfer function (TF) approach relating input to output. The study used secondary data from the Department of Water Affairs and Forestry for the Upper Vaal water management area at station C1H007. The R-F model identification and optimisation was implemented in the CAPTAIN Toolbox in MATLAB. The best estimated R-F model was a 2nd order TF with an input lag of one day and R 2T= 56%. In mechanistic interpretation, three parallel flow pathways were discerned; the fast flow, slow flow and the loss component each constituting 49.8%, 24% and 26.2% of the modelled flow respectively. The study demonstrates that the approach adopted herein produces reasonably satisfactory results with a minimum of the readily available catchment data.

The upper part of a probability distribution (or right tail) control the extent and the frequency of occurrence of extreme events. Studying the tail behaviour of extreme rainfall events has become an important task in the estimation of these events. The main goal of this research is to characterize the regime of severe rainfall events, and to identify the morphological and climatic variables that influence the most these events. The study is based on data coming from 1206 rain gauges across Germany that recorded daily rainfall depth for the amazing period of 110 years, which allowed a fair assessment of the upper tail behaviour. The upper tail behaviour is evaluated through six estimated parameters used as tail indicators. The information provided by these descriptors were analysed by two multivariate techniques, namely the principal component analysis and the cluster analysis that ultimately returned a grouping of stations based on their upper tail behaviour.

Global Circulation Models of climate predict not only a change of annual precipitation amounts but also a shift in the daily distribution. To improve the understanding of the importance of daily rain pattern for annual plant communities, which represent a large portion of semi-natural vegetation in the Middle East, I used a detailed, spatially explicit model. The model explicitly considers water storage in the soil and has been parameterized and validated with data collected in field experiments in Israel and data from the literature. I manipulated daily rainfall variability by increasing the mean daily rain intensity on rainy days (MDI, rain volume/day) and decreasing intervals between rainy days while keeping the mean annual amount constant. In factorial combination, I also increased mean annual precipitation (MAP). I considered five climatic regions characterized by 100, 300, 450, 600, and 800 mm MAP. Increasing MDI decreased establishment when MAP was >250 mm but increased establishment at more arid sites. The negative effect of increasing MDI was compensated by increasing mortality with increasing MDI in dry and typical Mediterranean regions (c. 360–720 mm MAP). These effects were strongly tied to water availability in upper and lower soil layers and modified by competition among seedlings and adults. Increasing MAP generally increased water availability, establishment, and density. The order of magnitudes of MDI and MAP effects overlapped partially so that their combined effect is important for projections of climate change effects on annual vegetation. The effect size of MAP and MDI followed a sigmoid curve along the MAP gradient indicating that the semi-arid region (≈300 mm MAP) is the most sensitive to precipitation change with regard to annual communitie

Thesis (Ph.D.)--Kent State University, 2007.<br>Title from PDF t.p. (viewed Mar. 19, 2009). Advisor: Scott C Sheridan. Keywords: climatology, irrigation, precipitation, Great Plains, atmospheric flow types, air mass types. Includes bibliographical references (p. 253-257).

Flood estimation is often required in hydrologic design and has important economic significance. For example, in Australia, the annual spending on infrastructure requiring flood estimation is of the order of $650 million ARR (I.E. Aust., 1998). Rainfall-based flood estimation techniques are most commonly adopted in practice. These require several inputs to convert design rainfalls to design floods. Of all the inputs, loss is an important one and defined as the amount of precipitation that does not appear as direct runoff. The concept of loss includes moisture intercepted by vegetation, infiltration into the soil, retention on the surface, evaporation and loss through the streambed and banks. As these loss components are dependent on topography, soils, vegetation and climate, the loss exhibits a high degree of temporal and spatial variability during the rainfall event. In design flood estimation, the simplified lumped conceptual loss models were used because of their simplicity and ability to approximate catchment runoff behaviour. In Australia, the most commonly adopted conceptual loss model is the initial losscontinuing loss model. For a specific part of the catchment, the initial loss occurs prior to the commencement of surface runoff, and can be considered to be composed of the interception loss, depression storage and infiltration that occur before the soil surface saturates. ARR (I. E. Aust., 1998) mentioned that the continuing loss is the average rate of loss throughout the remainder of the storm. At present, there is inadequate information on design losses in most parts of Australia and this is one of the greatest weaknesses in Australian flood hydrology. Currently recommended design losses are not compatible with design rainfall information in Australian Rainfall and Runoff. Also design losses for observed storms show a wide variability and it is always difficult to select an appropriate value of loss from this wide range for a particular application. Despite the wide variability of loss values, in the widely used Design Event Approach, a single value of initial and continuing losses is adopted. Because of the non-linearity in the rainfall-runoff process, this is likely to introduce a high degree of uncertainty and possible bias in the resulting flood estimates. In contrast, the Joint Probability Approach can consider probability-distributed losses in flood estimation. In ARR (I. E. Aust., 1998) it is recommended to use a constant continuing loss value in rainfall events. In this research it was observed that the continuing loss values in the rainfall events were not constant, rather than it decays with the duration of the rainfall event. The derived loss values from the 969 rainfall and streamflow events of Queensland catchments would provide better flood estimation than the recommended design loss values in ARR (I. E. Aust., 1998). In this research, both the initial and continuing losses were computed using IL-CL loss model and a single median loss value was used to estimate flood using Design Event Approach. Again both the initial and continuing losses were considered to be random variables and their probability distribution functions were determined. Hence, the research showed that the probability distributed loss values can be used for Queensland catchments in near future for better flood estimate. The research hypothesis tested was whether the new loss value for Queensland catchments provides significant improvement in design flood estimation. A total of 48 catchments, 82 pluviograph stations and 24 daily rainfall stations were selected from all over Queensland to test the research hypothesis. The research improved the recommended design loss values that will result in more precise design flood estimates. This will ultimately save millions of dollars in the construction of hydraulic infrastructures.

Flood estimation is often required in hydrologic design and has important economic significance. For example, in Australia, the annual spending on infrastructure requiring flood estimation is of the order of $650 million ARR (I.E. Aust., 1998). Rainfall-based flood estimation techniques are most commonly adopted in practice. These require several inputs to convert design rainfalls to design floods. Of all the inputs, loss is an important one and defined as the amount of precipitation that does not appear as direct runoff. The concept of loss includes moisture intercepted by vegetation, infiltration into the soil, retention on the surface, evaporation and loss through the streambed and banks. As these loss components are dependent on topography, soils, vegetation and climate, the loss exhibits a high degree of temporal and spatial variability during the rainfall event. In design flood estimation, the simplified lumped conceptual loss models were used because of their simplicity and ability to approximate catchment runoff behaviour. In Australia, the most commonly adopted conceptual loss model is the initial losscontinuing loss model. For a specific part of the catchment, the initial loss occurs prior to the commencement of surface runoff, and can be considered to be composed of the interception loss, depression storage and infiltration that occur before the soil surface saturates. ARR (I. E. Aust., 1998) mentioned that the continuing loss is the average rate of loss throughout the remainder of the storm. At present, there is inadequate information on design losses in most parts of Australia and this is one of the greatest weaknesses in Australian flood hydrology. Currently recommended design losses are not compatible with design rainfall information in Australian Rainfall and Runoff. Also design losses for observed storms show a wide variability and it is always difficult to select an appropriate value of loss from this wide range for a particular application. Despite the wide variability of loss values, in the widely used Design Event Approach, a single value of initial and continuing losses is adopted. Because of the non-linearity in the rainfall-runoff process, this is likely to introduce a high degree of uncertainty and possible bias in the resulting flood estimates. In contrast, the Joint Probability Approach can consider probability-distributed losses in flood estimation. In ARR (I. E. Aust., 1998) it is recommended to use a constant continuing loss value in rainfall events. In this research it was observed that the continuing loss values in the rainfall events were not constant, rather than it decays with the duration of the rainfall event. The derived loss values from the 969 rainfall and streamflow events of Queensland catchments would provide better flood estimation than the recommended design loss values in ARR (I. E. Aust., 1998). In this research, both the initial and continuing losses were computed using IL-CL loss model and a single median loss value was used to estimate flood using Design Event Approach. Again both the initial and continuing losses were considered to be random variables and their probability distribution functions were determined. Hence, the research showed that the probability distributed loss values can be used for Queensland catchments in near future for better flood estimate. The research hypothesis tested was whether the new loss value for Queensland catchments provides significant improvement in design flood estimation. A total of 48 catchments, 82 pluviograph stations and 24 daily rainfall stations were selected from all over Queensland to test the research hypothesis. The research improved the recommended design loss values that will result in more precise design flood estimates. This will ultimately save millions of dollars in the construction of hydraulic infrastructures.

Extreme rainfall events are responsible for social disorder and economic problems, especially in large urban centers. Densely populated areas suffer from flooding , landslide and building destruction that cause deaths and wide-spread diseases, such as malaria, dengue and leptospirosis. They are recurrent phenomena that wear down the life of the urban population, particularly the least privileged ones. The focal area of this work was the Metropolitan Region of São Paulo (MRSP), Brazil, one of the largest cities in the world. Rainfall daily totals of 21 rain gage network in the MRSP were analyzed to i) estimate the annual maximum daily rainfall (PMDA), by means of the Gumbel distribution; II) group different rainfall rates into classes (from drizzle to extreme rates) and verify the similarity between seasons (clustering), that is annual and seasonal rain rates, for the period 1947 to 1998, making use of the technique known as Cluster Analysis, and III) identify possible trends of three rain rate classes (drizzle, moderate and above 30.0 mm / day) for the annual and seasonal periods, for the whole dataset length of each gage, using the Mann-Kendall trend test. The results showed that the maximum daily rainfall observed data fit the Gumbel distribution in the annual period, with the estimated annual daily maximum rain rate equal to 239.3 mm / day with a return period of 500 years in Barrocada gage, located in MRSP north-central region. Cluster analysis showed little similarity amongst gages, with respect to some rain rate classes, both in the number of events and the classes rain totals, in the annual and seasonal periods. The Mann-Kendall test showed significant increasing trend of the cumulative totals for a larger number of gages for both annual and seasonal periods. The trend of the number of drizzle events class was significantly upward for most gages, again both in the annual and seasonal periods, but not all gages presented increasing trend for the moderate events class. Also, significant increasing trend of the rain rate classes above 30.0 mm / day was found at some gages in the year period. In general, there was significant upward trend of rain rate classes in the MRSP.<br>Fundação de Amparo a Pesquisa do Estado de Alagoas<br>Eventos extremos de chuva são responsáveis por distúrbios sociais e problemas econômicos, principalmente nos grandes centros urbanos. Áreas densamente povoadas sofrem deslizamentos, inundações e destruição de construções, que causam mortes e doenças em larga escala, tais como malária, dengue e leptospirose. Eles são fenômenos recorrentes que desgastam a vida da população urbana, principalmente aos menos privilegiados. A área de foco deste trabalho foi a Região Metropolitana de São Paulo (RMSP), Brasil, uma das maiores cidades do mundo. Foi analisada uma rede de 21 estações, na RMSP, com totais diários de precipitação para: i) estimar a precipitação máxima diária anual (PMDA), por meio da distribuição de Gumbel, ii) grupos com diferentes taxas de precipitação dentro das classes (de chuvisco a precipitação extrema), e, verificar a similaridade entre as estações (clustering), para taxas de precipitação anual e sazonal, para o período de 1947 a 1998, fazendo uso da técnica conhecida como análise de cluster, e III) identificar possíveis tendências nas três classes de taxa de precipitação (chuvisco, moderado e acima de 30mm/dia) para os períodos anuais e sazonais, para o comprimento total de cada estação, utilizando o teste de tendência de Mann-Kendall. Os resultados mostraram que os dados observados de precipitação máxima diária se ajustam à distribuição de Gumbel no período anual, com taxa anual estimada de precipitação máxima diária igual a 239,3 mm/dia com período de retorno de 500 anos na estação Barrocada, localizada na região centro-norte da RMSP. A análise de agrupamento mostrou pouca similaridade entre as estações, com relação a algumas taxas de classes de precipitação, tanto em número de eventos das classes de precipitação total, nos períodos anuais como sazonais. O teste de Mann-Kendall apresentou tendência de aumento significativo dos totais acumulados em um maior número de estações para ambos os períodos, anuais e sazonais. A tendência do número de eventos de classe chuvisco, foi significativamente alta para a maioria das estações, novamente tanto em períodos anuais como sazonais, mas nem todas as estações apresentaram tendência de aumento para a classe de eventos moderados. Além disso, a tendência de aumento significativo das classes de taxa de precipitação acima de 30 mm/dia foi encontrada em algumas estações no período anual. Em geral, houve tendência de aumento significativo das taxas de classes de precipitação na RMSP.

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.<br>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

Clear characterisation of daily rainfall over the southern African continent is necessary for the purpose of achieving sustainable human and agricultural-environmental development. In this research, daily rainfall variability over southern Africa is investigated to determine the relations between rainfall, rainfall frequency, and amount of rain per rain day. Firstly, the characterisation of daily rainfall over the region from 1950 to 1997 is given. This is followed by the analysis of daily rainfall variability during the 10 wettest and driest years. Thirdly, the influence of Sep-Nov and Dec-Feb seasons on the 10 wettest and driest years is then highlighted. Lastly, to determine whether the relation between the three rainfall parameters determined over the whole southern African region holds true for local areas, daily rainfall variability over Swaziland during the period of meteorological records is discussed. Analyses of daily rainfall over southern Africa indicate that on scales of days to years, rainfall departures from mean result from changes in both daily rainfall frequency and intensity. Positive rainfall changes are due to an increase in the number of rainy days and amount of rainfall falling on those rain days. Negative rainfall changes results from a decrease in rainfall frequency and rain falling on those rain days. Southern Africa does not show uniform changes in these rainfall variables, but patterns. of spatial and temporal variability. This variability increases from the Western regions of the subcontinent (i.e. rainfall variability increases from the eastern humid to the western arid regions of the subcontinent). The conclusion is that over the whole of southern African region changes in mean rainfall are dependent on the number of rain days and rain per rain day. This result also holds true over smaller areas of the subcontinent, such as Swaziland.

This thesis describes the development of a new technique which significantly extends the applicability of stochastic point rainfall models that require historical data for calibration. The technique is demonstrated using a high-resolution point rainfall model based on wet-dry alternating storm events. A model has been produced that is well defined and can be vigorously compared against numerous observed statistics in a quantative manner. The rainfall model presented in this thesis can be used to provide accurate synthetic rainfall data at sites with minimal historical rainfall data providing a powerful tool for application in hydrological risk analysis across Australia.<br>Thesis (Ph.D.) -- University of Adelaide, Dept. of Civil and Environmental Engineering, 2007

Title page, abstract and table of contents only. The complete thesis in print form is available from the University of Adelaide Library.<br>This thesis describes the development of a new technique which significantly extends the applicability of stochastic point rainfall models that require historical data for calibration. The technique is demonstrated using a high-resolution point rainfall model based on wet-dry alternating storm events. A model has been produced that is well defined and can be vigorously compared against numerous observed statistics in a quantative manner. The rainfall model presented in this thesis can be used to provide accurate synthetic rainfall data at sites with minimal historical rainfall data providing a powerful tool for application in hydrological risk analysis across Australia.<br>http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1282259<br>Thesis (Ph.D.) -- University of Adelaide, Dept. of Civil and Environmental Engineering, 2007

Investigates "the use of a stochastic rainfall disaggregation model on a regional basis to disaggregate daily rainfall into any desired fine timescale in the State of Queensland ... required for certain hydrologic modellings such as crop simulation modelling, erosion modelling etc."--Abstract.

Characterizing the uncertainty in rainfall using stochastic models has been a challenging area of research in the field of operational hydrology for about half a century. Simulated sequences drawn from such models find use in a variety of hydrological applications. Traditionally, parametric models are used for simulating rainfall. But the parametric models are not parsimonious and have uncertainties associated with identification of model form, normalizing transformation, and parameter estimation. None of the models in vogue have gained universal acceptability among practising engineers. This may either be due to lack of confidence in the existing models, or the inability to adopt models proposed in literature because of their complexity or both. In the present study, a new nonparametric Matched Block Bootstrap (MABB) model is proposed for stochastic simulation of rainfall at daily time scale. It is based on conditional matching of blocks formed from the historical rainfall data using a set of predictors (conditioning variables) proposed for matching the blocks. The efficiency of the developed model is demonstrated through application to rainfall data from India, Australia, and USA. The performance of MABB is compared with two non-parametric rainfall simulation models, k-NN and ROG-RAG, for a site in Melbourne, Australia. The results showed that MABB model is a feasible alternative to ROG-RAG and k-NN models for simulating daily rainfall sequences for hydrologic applications. Further it is found that MABB and ROG-RAG models outperform k-NN model. The proposed MABB model preserved the summary statistics of rainfall and fraction of wet days at daily, monthly, seasonal and annual scales. It could also provide reasonable performance in simulating spell statistics. The MABB is parsimonious and requires less computational effort than ROG-RAG model. It reproduces probability density function (marginal distribution) fairly well due to its data driven nature. Results obtained for sites in India and U.S.A. show that the model is robust and promising.

Characterizing the uncertainty in rainfall using stochastic models has been a challenging area of research in the field of operational hydrology for about half a century. Simulated sequences drawn from such models find use in a variety of hydrological applications. Traditionally, parametric models are used for simulating rainfall. But the parametric models are not parsimonious and have uncertainties associated with identification of model form, normalizing transformation, and parameter estimation. None of the models in vogue have gained universal acceptability among practising engineers. This may either be due to lack of confidence in the existing models, or the inability to adopt models proposed in literature because of their complexity or both. In the present study, a new nonparametric Matched Block Bootstrap (MABB) model is proposed for stochastic simulation of rainfall at daily time scale. It is based on conditional matching of blocks formed from the historical rainfall data using a set of predictors (conditioning variables) proposed for matching the blocks. The efficiency of the developed model is demonstrated through application to rainfall data from India, Australia, and USA. The performance of MABB is compared with two non-parametric rainfall simulation models, k-NN and ROG-RAG, for a site in Melbourne, Australia. The results showed that MABB model is a feasible alternative to ROG-RAG and k-NN models for simulating daily rainfall sequences for hydrologic applications. Further it is found that MABB and ROG-RAG models outperform k-NN model. The proposed MABB model preserved the summary statistics of rainfall and fraction of wet days at daily, monthly, seasonal and annual scales. It could also provide reasonable performance in simulating spell statistics. The MABB is parsimonious and requires less computational effort than ROG-RAG model. It reproduces probability density function (marginal distribution) fairly well due to its data driven nature. Results obtained for sites in India and U.S.A. show that the model is robust and promising.

Thesis (M.S.)--Florida State University, 2006.<br>Advisor: Sharon E. Nicholson, Florida State University, College of Arts and Sciences, Dept. of Meteorology. Title and description from dissertation home page (viewed June 16, 2006). Document formatted into pages; contains xvi, 152 pages. Includes bibliographical references.

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 .<br>Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2005.

碩士<br>國立成功大學<br>水利及海洋工程學系<br>87<br>The daily probability rainfall of South Taiwan can be analyzed by using statistical methods. Hydrologic applications of statistical methods followed the growth of statistical theory. This study collected observed rainfall of fourteen stations,and applied traditional methods and two modified methods proposed by the author to compare the probability daily rainfall of above stations. Based on the independence and stationaries of the data, statistical theory can be applied to estimate probability rainfall. There are some probability distributions we often used such as extreme value distribution, normal distribution, log-normal distribution, Pearson type Ⅲ distribution and log-Pearson type Ⅲ distribution. But which is the best one is not confirmed. Therefore, we often compare estimated value with observed record. From frequency analysis, we know that when estimated probability rainfall is closer to the observed record the confidence is larger.

The current generation of climate models in the Coupled Model Intercomparison Project Phase 5 (CMIP5) is used to assess the future changes in daily precipitation and its extremes. The simple average of all the models, i.e. the multi-model ensemble mean (MMEM), has been widely used due to its simplicity and better performance than most individual models. Weighting techniques are also proposed to deal with the systematic biases within the models. However, both methods are designed to reduce the uncertainties for the study of climate mean state. They will induce problems when the climate extremes are of interest. We utilize a Bayesian weighting method to investigate the rainfall mean state and perform a probability density function based assessment of daily rainfall extremes. Satellite measurement is used to evaluate the short historical period. The weighting method can be only applied to regions rather than hemispheric scale, and thus three tropical regions including the Amazon, Congo, and Southeast Asia are studied. The method based on the Gamma distribution for daily precipitation is demonstrated to perform much better than the MMEM with respect to the extreme events. A use of the Kolmogorov-Smirnov statistic for the distribution assessment indicates the method is more applicable in three tropical wet regions over land mentioned above. This is consistent with previous studies showing the Gamma distribution is more suitable for daily rainfall in wet regions. Both methods provide consistent results. The three regions display significant changes at the end of the 21st century. The Amazon will be drier, while the Congo will not have large changes in mean rainfall. However, both of the Amazon and Congo will have large rainfall variability, implying more droughts and floods. The Amazon will have 7.5% more little-rain days (defined as > 0.5 mm/d) and 4.5 mm/d larger 95th percentile for 2092-2099, and the Congo will have 2.5% more little-rain days and 1 mm/d larger 95th percentile. Southeast Asia will be dryer in the western part and wetter in the eastern part, which is consistent with the different changes in the 5th percentile. It will also experience heavier rainfall events with much larger increases in the 95th percentile. The future changes, especially the increase in rainfall extremes, are very likely associated with the strengthening of hydrological cycle.<br>text

The land–atmosphere interactions and the coupling between climate and land surface hydrological processes are gaining interest in the recent past. The increased knowledge in hydro climatology and the global hydrological cycle, with terrestrial and atmospheric feedbacks, led to the utilization of the climate variables and atmospheric tele-connections in modeling the hydrological processes like rainfall and runoff. Numerous statistical and dynamical models employing different combinations of predictor variables and mathematical equations have been developed on this aspect. The relevance of predictor variables is usually measured through the observed linear correlation between the predictor and the predictand. However, many predictor climatic variables are found to have been switching the relationships over time, which demands a replacement of these variables. The unsatisfactory performance of both the statistical and dynamical models demands a more authentic method for assessing the dependency between the climatic variables and hydrologic processes by taking into account the nonlinear causal relationships and the instability due to these nonlinear interactions. The most obvious cause for limited predictability in even a perfect model with high resolution observations is the nonlinearity of the hydrological systems [Bloschl and Zehe, 2005]. This is mainly due to the chaotic nature of the weather and its sensitiveness to initial conditions [Lorenz, 1963], which restricts the predictability of day-to-day weather to only a few days or weeks. The present thesis deals with developing association rules to extract the causal relationships between the climatic variables and rainfall and to unearth the frequent predictor patterns that precede the extreme episodes of rainfall using a time series data mining algorithm. The inherent nonlinearity and uncertainty due to the chaotic nature of hydrologic processes (rainfall and runoff) is modeled through a nonlinear prediction method. Methodologies are developed to increase the predictability and reduce the predictive uncertainty of chaotic hydrologic series. A data mining algorithm making use of the concepts of minimal occurrences with constraints and time lags is used to discover association rules between extreme rainfall events and climatic indices. The algorithm considers only the extreme events as the target episodes (consequents) by separating these from the normal episodes, which are quite frequent and finds the time-lagged relationships with the climatic indices, which are treated as the antecedents. Association rules are generated for all the five homogenous regions of India (as defined by Indian Institute of Tropical Meteorology) and also for All India by making use of the data from 1960-1982. The analysis of the rules shows that strong relationships exist between the extreme rainfall events and the climatic indices chosen, i.e., Darwin Sea Level Pressure (DSLP), North Atlantic Oscillation (NAO), Nino 3.4 and Sea Surface Temperature (SST) values. Validation of the rules using data for the period 1983-2005, clearly shows that most of the rules are repeating and for some rules, even if they are not exactly the same, the combinations of the indices mentioned in these rules are the same during validation period with slight variations in the representative classes taken by the indices. The significance of treating rainfall as a chaotic system instead of a stochastic system for a better understanding of the underlying dynamics has been taken up by various studies recently. However, an important limitation of all these approaches is the dependence on a single method for identifying the chaotic nature and the parameters involved. In the present study, an attempt is made to identify chaos using various techniques and the behaviour of daily rainfall series in different regions. Daily rainfall data of three regions with contrasting characteristics (mainly in the spatial area covered), Malaprabha river basin, Mahanadi river basin and All India for the period 1955 to 2000 are used for the study. Auto-correlation and mutual information methods are used to determine the delay time for the phase space reconstruction. Optimum embedding dimension is determined using correlation dimension, false nearest neighbour algorithm and also nonlinear prediction methods. The low embedding dimensions obtained from these methods indicate the existence of low dimensional chaos in the three rainfall series considered. Correlation dimension method is repeated on the phase randomized and first derivative of the data series to check the existence of any pseudo low-dimensional chaos [Osborne and Provenzale, 1989]. Positive Lyapunov exponents obtained prove the exponential divergence of the trajectories and hence the unpredictability. Surrogate data test is also done to further confirm the nonlinear structure of the rainfall series. A limit in predictability in chaotic system arises mainly due to its sensitivity to the infinitesimal changes in its initial conditions and also due to the ineffectiveness of the model to reveal the underlying dynamics of the system. In the present study, an attempt is made to quantify these uncertainties involved and thereby improve the predictability by adopting a nonlinear ensemble prediction. A range of plausible parameters is used for generating an ensemble of predictions of rainfall for each year separately for the period 1996 to 2000 using the data till the preceding year. For analyzing the sensitiveness to initial conditions, predictions are made from two different months in a year viz., from the beginning of January and June. The reasonably good predictions obtained indicate the efficiency of the nonlinear prediction method for predicting the rainfall series. Also, the rank probability skill score and the rank histograms show that the ensembles generated are reliable with a good spread and skill. A comparison of results of the three regions indicates that although they are chaotic in nature, the spatial averaging over a large area can increase the dimension and improve the predictability, thus destroying the chaotic nature. The predictability of the chaotic daily rainfall series is improved by utilizing information from various climatic indices and adopting a multivariate nonlinear ensemble prediction. Daily rainfall data of Malaprabha river basin, India for the period 1955 to 2000 is used for the study. A multivariate phase space is generated, considering a climate data set of 16 variables. The redundancy, if any, of this atmospheric data set is further removed by employing principal component analysis (PCA) method and thereby reducing it to 8 principal components (PCs). This multivariate series (rainfall along with 8 PCs) are found to exhibit a low dimensional chaotic nature with dimension 10. Nonlinear prediction is done using univariate series (rainfall alone) and multivariate series for different combinations of embedding dimensions and delay times. The uncertainty in initial conditions is thus addressed by reconstructing the phase space using different combinations of parameters. The ensembles generated from multivariate predictions are found to be better than those from univariate predictions. The uncertainty in predictions is reduced or in other words, the predictability is improved by adopting multivariate nonlinear ensemble prediction. The restriction on predictability of a chaotic series can thus be reduced by quantifying the uncertainty in the initial conditions and also by including other possible variables, which may influence the system. Even though, the sensitivity to initial conditions limit the predictability in chaotic systems, a prediction algorithm capable of resolving the fine structure of the chaotic attractor can reduce the prediction uncertainty to some extent. All the traditional chaotic prediction methods are based on local models since these methods model the sudden divergence of the trajectories with different local functions. Conceptually, global models are ineffective in modeling the highly unstable structure of the chaotic attractor [Sivakumar et al., 2002a]. This study focuses on combining a local learning wavelet analysis (decomposition) model with a global feedforward neural network model and its implementation on phase space prediction of chaotic streamflow series. The daily streamflow series at Basantpur station in Mahanadi basin, India is found to exhibit a chaotic nature with dimension varying from 5-7. Quantification of uncertainties in future predictions are done by creating an ensemble of predictions with wavelet network using a range of plausible embedding dimension and delay time. Compared with traditional local approximation approach, the total predictive uncertainty in the streamflow is reduced when modeled with wavelet networks for different lead times. Localization property of wavelets, utilizing different dilation and translation parameters, helps in capturing most of the statistical properties of the observed data. The need for bringing together the characteristics of both local and global approaches to model the unstable yet ordered chaotic attractor is clearly demonstrated.

The land–atmosphere interactions and the coupling between climate and land surface hydrological processes are gaining interest in the recent past. The increased knowledge in hydro climatology and the global hydrological cycle, with terrestrial and atmospheric feedbacks, led to the utilization of the climate variables and atmospheric tele-connections in modeling the hydrological processes like rainfall and runoff. Numerous statistical and dynamical models employing different combinations of predictor variables and mathematical equations have been developed on this aspect. The relevance of predictor variables is usually measured through the observed linear correlation between the predictor and the predictand. However, many predictor climatic variables are found to have been switching the relationships over time, which demands a replacement of these variables. The unsatisfactory performance of both the statistical and dynamical models demands a more authentic method for assessing the dependency between the climatic variables and hydrologic processes by taking into account the nonlinear causal relationships and the instability due to these nonlinear interactions. The most obvious cause for limited predictability in even a perfect model with high resolution observations is the nonlinearity of the hydrological systems [Bloschl and Zehe, 2005]. This is mainly due to the chaotic nature of the weather and its sensitiveness to initial conditions [Lorenz, 1963], which restricts the predictability of day-to-day weather to only a few days or weeks. The present thesis deals with developing association rules to extract the causal relationships between the climatic variables and rainfall and to unearth the frequent predictor patterns that precede the extreme episodes of rainfall using a time series data mining algorithm. The inherent nonlinearity and uncertainty due to the chaotic nature of hydrologic processes (rainfall and runoff) is modeled through a nonlinear prediction method. Methodologies are developed to increase the predictability and reduce the predictive uncertainty of chaotic hydrologic series. A data mining algorithm making use of the concepts of minimal occurrences with constraints and time lags is used to discover association rules between extreme rainfall events and climatic indices. The algorithm considers only the extreme events as the target episodes (consequents) by separating these from the normal episodes, which are quite frequent and finds the time-lagged relationships with the climatic indices, which are treated as the antecedents. Association rules are generated for all the five homogenous regions of India (as defined by Indian Institute of Tropical Meteorology) and also for All India by making use of the data from 1960-1982. The analysis of the rules shows that strong relationships exist between the extreme rainfall events and the climatic indices chosen, i.e., Darwin Sea Level Pressure (DSLP), North Atlantic Oscillation (NAO), Nino 3.4 and Sea Surface Temperature (SST) values. Validation of the rules using data for the period 1983-2005, clearly shows that most of the rules are repeating and for some rules, even if they are not exactly the same, the combinations of the indices mentioned in these rules are the same during validation period with slight variations in the representative classes taken by the indices. The significance of treating rainfall as a chaotic system instead of a stochastic system for a better understanding of the underlying dynamics has been taken up by various studies recently. However, an important limitation of all these approaches is the dependence on a single method for identifying the chaotic nature and the parameters involved. In the present study, an attempt is made to identify chaos using various techniques and the behaviour of daily rainfall series in different regions. Daily rainfall data of three regions with contrasting characteristics (mainly in the spatial area covered), Malaprabha river basin, Mahanadi river basin and All India for the period 1955 to 2000 are used for the study. Auto-correlation and mutual information methods are used to determine the delay time for the phase space reconstruction. Optimum embedding dimension is determined using correlation dimension, false nearest neighbour algorithm and also nonlinear prediction methods. The low embedding dimensions obtained from these methods indicate the existence of low dimensional chaos in the three rainfall series considered. Correlation dimension method is repeated on the phase randomized and first derivative of the data series to check the existence of any pseudo low-dimensional chaos [Osborne and Provenzale, 1989]. Positive Lyapunov exponents obtained prove the exponential divergence of the trajectories and hence the unpredictability. Surrogate data test is also done to further confirm the nonlinear structure of the rainfall series. A limit in predictability in chaotic system arises mainly due to its sensitivity to the infinitesimal changes in its initial conditions and also due to the ineffectiveness of the model to reveal the underlying dynamics of the system. In the present study, an attempt is made to quantify these uncertainties involved and thereby improve the predictability by adopting a nonlinear ensemble prediction. A range of plausible parameters is used for generating an ensemble of predictions of rainfall for each year separately for the period 1996 to 2000 using the data till the preceding year. For analyzing the sensitiveness to initial conditions, predictions are made from two different months in a year viz., from the beginning of January and June. The reasonably good predictions obtained indicate the efficiency of the nonlinear prediction method for predicting the rainfall series. Also, the rank probability skill score and the rank histograms show that the ensembles generated are reliable with a good spread and skill. A comparison of results of the three regions indicates that although they are chaotic in nature, the spatial averaging over a large area can increase the dimension and improve the predictability, thus destroying the chaotic nature. The predictability of the chaotic daily rainfall series is improved by utilizing information from various climatic indices and adopting a multivariate nonlinear ensemble prediction. Daily rainfall data of Malaprabha river basin, India for the period 1955 to 2000 is used for the study. A multivariate phase space is generated, considering a climate data set of 16 variables. The redundancy, if any, of this atmospheric data set is further removed by employing principal component analysis (PCA) method and thereby reducing it to 8 principal components (PCs). This multivariate series (rainfall along with 8 PCs) are found to exhibit a low dimensional chaotic nature with dimension 10. Nonlinear prediction is done using univariate series (rainfall alone) and multivariate series for different combinations of embedding dimensions and delay times. The uncertainty in initial conditions is thus addressed by reconstructing the phase space using different combinations of parameters. The ensembles generated from multivariate predictions are found to be better than those from univariate predictions. The uncertainty in predictions is reduced or in other words, the predictability is improved by adopting multivariate nonlinear ensemble prediction. The restriction on predictability of a chaotic series can thus be reduced by quantifying the uncertainty in the initial conditions and also by including other possible variables, which may influence the system. Even though, the sensitivity to initial conditions limit the predictability in chaotic systems, a prediction algorithm capable of resolving the fine structure of the chaotic attractor can reduce the prediction uncertainty to some extent. All the traditional chaotic prediction methods are based on local models since these methods model the sudden divergence of the trajectories with different local functions. Conceptually, global models are ineffective in modeling the highly unstable structure of the chaotic attractor [Sivakumar et al., 2002a]. This study focuses on combining a local learning wavelet analysis (decomposition) model with a global feedforward neural network model and its implementation on phase space prediction of chaotic streamflow series. The daily streamflow series at Basantpur station in Mahanadi basin, India is found to exhibit a chaotic nature with dimension varying from 5-7. Quantification of uncertainties in future predictions are done by creating an ensemble of predictions with wavelet network using a range of plausible embedding dimension and delay time. Compared with traditional local approximation approach, the total predictive uncertainty in the streamflow is reduced when modeled with wavelet networks for different lead times. Localization property of wavelets, utilizing different dilation and translation parameters, helps in capturing most of the statistical properties of the observed data. The need for bringing together the characteristics of both local and global approaches to model the unstable yet ordered chaotic attractor is clearly demonstrated.

Streamflow data are critical for water resource investigations, and their development projects. However, the scarcity of such data, particularly measured streamflow through streamflow gauges, constitutes a serious impediment to the successful implementation of development projects. In the absence of such measured streamflow data, streamflow estimation using measured meteorological data represents a viable alternative. Nevertheless, this alternative is not always possible due to the unavailability of required meteorological data. In the face of such data limitations, many have advocated the use of remote sensing (RS) data to estimate streamflow. The aim of this study was to generate daily streamflow time series data using remote sensing data through catchment process modelling and statistical modelling.

碩士<br>國立成功大學<br>水利及海洋工程學系<br>88<br>The phenomena of natrure are all nonlinear. These physical processes are all random. Tranditionally, we analysed the properties of them by using statistical methods such like ARMA or ARIMA model. Statistical methods were applied in suitable application areas. Since 1970 Mandelbrot proposed fractal theory, it was widely applied in many domains. The scholars were absorbed in the study of fractal theory after 1970. There is a lot of resar-ch effort in the field of Hydrology. The rainfall is a substaintial set of the study of fractal theory in Hydrology. Fractal theory can be viewed as powerful tool of analysing the tempo-ral-spatial peculiarities. In the last decade, multifractals have been given considerable attention. Schertzer and Lovejoy(1987, 1989) modeled the variability of rainfall by a (multiplicative) cascade. The methods, probability distribution / multiple scaling technique (PDMS) and trace moment (TM), usually used to determine whether a measure to be or not to be multifractals. To dis-cribe multifractal measure, it can be employed codimesion function with PDMS method and empirical moment scaling exponent function with TM method. The relationship between codimension function and empirical moment scaling exponent function can be constructed by Legendre transform. The foreign scholars have applied multifractal theory to many appli-cation areas especially in the study of the temporal-spatial properties of rainfall that to be or not to be multifractals. The main objective of this paper is to study the behavior of the rainfall data, collected at 24 rainfall stations in Taiwan area, over periods up to 30 years. The results show that all rainfall data exist codimension function and empirical moment scaling exponent function. This implies that the rainfall in Taiwan is multifractals. The deviation of using Legendre transform and power spectrum are not significant.

O presente trabalho académico focou-se em dois grandes objetivos. Por um lado focou-se na investigação do funcionamento dos udógrafos como equipamentos de monitorização de precipitação bem como o contributo indispensável que os mesmos proporcionam, em conjunto com outros equipamentos e outras ferramentas, como dispositivo de alerta para uma eventual ocorrência de aluvião. Por outro lado, focou-se no tratamento e análise dos dados monitorizados pelos mesmos equipamentos. A investigação dos equipamentos baseou-se no estudo de diferentes soluções de equipamentos, analisando as suas vantagens e desvantagens. Foi descrito a forma de funcionamento de alguns modelos de udógrafos e sucintamente o funcionamento dos satélites e dos radares meteorológicos, revelando-se estes últimos, como os mais eficientes para a prevenção de aluviões. O estudo dos equipamentos deu maior destaque ao funcionamento dos udógrafos de recetáculo basculante. O tratamento dos dados udográficos efetuado neste trabalho baseou-se na criação de folhas de cálculo em Excel para a organização, tratamento e análise das séries de dados. Inicialmente estava previsto o tratamento de dados de nove postos udográficos pertencentes à rede udográfica do Laboratório Regional de Engenharia Civil (LREC), contudo posteriormente um dos postos foi excluído devido à elevada percentagem de lacunas que continha. Após a organização dos dados, procedeu-se à colmatação das lacunas existentes nas séries e posteriormente à análise da qualidade das mesmas séries de dados. Finalmente foram analisadas as séries de dados recorrendo a gráficos e ao Software ArcGIS for Desktop versão 10.4 da Environmental Systems Research Institute (ESRI).<br>This academic work has focused on two main objectives. On the one hand, focused on the investigation of the operation of udógrafos as precipitation monitoring equipment and the essential contribution that they provide in conjunction with other equipment and other tools, as a warning device for a possible occurrence of flash floods. On the other hand, focused on the treatment and analysis of data monitored by the same equipment. The research of the equipment was based on the study of different equipment solutions, discuss their advantages and disadvantages. It has been described the operating mode of some diferentes rain gauges models. It was also described briefly the operation of weather satellites and radar, revealing the latter as the most efficient for the prevention of flash floods. The equipment of the study gave greater prominence to the functioning was tipping bucket rain gauge. Treatment of rain gauge data carried out in this work was based on the creation of Excel spreadsheets for organizing, processing and analysis of the data series. Initially was planned to analyse nine data series of nine rain gauges stations belonging to the rain gauge network of Regional Civil Engineering Laboratory (LREC), but then one of the stations was excluded due to high percentage of gaps contained. After the organization of the data, it proceeded to filling gaps in the series and after the analysis of the quality of the same data series. Finally we analyzed the data series using graphics, and ArcGIS for Desktop software version 10.4 of the Environmental Systems Research Institute (ESRI).