Modelagem numérica da evolução da linha de costa das praias localizadas a oeste da cidade de Fortaleza, Ceará : trecho compreendido entre o rio Ceará e a praia do Cumbuco

Há aproximadamente meio século, as praias situadas a sotamar do Porto do Mucuripe, em Fortaleza, vem sofrendo intensos processos erosivos, creditados em grande parte à construção e ampliação deste porto. O fato é que o acentuado crescimento urbano da capital cearense ocasionou a fixação de dunas e a quebra do fluxo longitudinal de sedimentos em seu litoral, resultando no recuo da linha de costa e na necessidade de intervenção antrópica por meio de obras rígidas que viessem a garantir a preservação da infra-estrutura existente nos trechos mais afetados. Como conseqüência da fixação das praias, o suprimento de material sedimentar passou a ficar retido, enquanto que o potencial de transporte das ondas se preservou. A quebra deste equilíbrio dinâmico acarretou a transferência dos processos erosivos para as praias adjacentes, o que tornou-se um problema cada vez maior, pois as soluções adotadas nestas praias eram idênticas às anteriores. As conseqüências deste processo para uma cidade como Fortaleza, onde o turismo é uma das principais fontes de renda, são graves, dado que como resultado final, encontramos longos trechos de praias com a balneabilidade comprometida e perda de qualidade visual. O litoral situado a oeste da capital é limitado à direita pela foz do Rio Ceará e à esquerda por um promontório rochoso, onde situa-se a Ponta do Pecém. Este trecho compreende aproximadamente 30 km de praias arenosas, com granulometria média e fina, e com ondas incidindo sobre a costa de forma obliqua, o que as torna o principal mecanismo de transporte de sedimentos. A ocupação urbana concentra-se principalmente nas praias mais próximas a Fortaleza, onde observa-se ainda, o afloramento de rochas de praia e grande perda de material sedimentar, fornecendo indícios da transferência dos processos erosivos da orla marítima da capital para estas praias. Com a conclusão das obras do Porto do Pecém e de um pólo industrial que visa desfrutar da localização estratégica deste porto, é natural que ocorra uma intensificação nos processos de ocupação urbana das praias próximas à área. Tal constatação motivou um trabalho de modelagem da dinâmica desta zona com o objetivo de nortear um plano de uso e ocupação das áreas localizadas próximas à praia, de forma que se possa prever o comportamento da linha de costa e evitar que sejam repetidos certos equívocos como a construção em zonas de forte dinâmica e a fixação das fontes primárias de fornecimento de sedimentos, que são as dunas frontais. Dada a disponibilidade de dados, bons processadores e aos custos significativamente reduzidos da modelagem numérica, adotou-se o pacote GENESIS – RCPWAVE, que além de ser de domínio público, é a base do sistema de modelagem de linha de costa adotado pelo CERC (Coastal Engineering Research Center), U.S.A., para aplicações em costa aberta, em regiões sujeitas às intervenções humanas. A calibração do modelo se fez considerando as linhas de praia medidas em 1974 pela DHN e em 2001 com o uso de GPS. Os dados de onda utilizados foram obtidos por um ondógrafo direcional do tipo Waverider, instalado a uma profundidade de 18 metros nas proximidades da Ponta do Pecém. Os dados relativos ao modelo conceitual dos processos predominantes na região, como: contribuições externas, variação granulométrica e variações sazonais de perfis foram obtidos de levantamentos bibliográficos de trabalhos anteriores. Por último, informações relativas às estruturas existentes e seu comportamento, ao afloramento de formações rochosas e o último levantamento da linha de praia, foram obtidas através de trabalhos de campo. De uma forma geral, o comportamento previsto pelo modelo mostrou-se semelhante ao observado nos diferentes levantamentos. Considerando-se as limitações dos processos envolvidos no levantamento de dados, onde tanto a carta da DHN quanto o mapeamento por satélite estão sujeitos a imprecisões e ainda, que a série de dados confiáveis de ondas para a região possuía apenas dois anos, é importante notar que, em linhas gerais, a formulação matemática do modelo representou satisfatoriamente os processos envolvidos. Os resultados fornecidos possibilitam a extrapolação da evolução da linha de costa e indicam pontos de provável recuo ou avanço da praia, norteando a sua ocupação. A ferramenta gerada proporciona ainda a avaliação do impacto de intervenções por meio de estruturas rígidas ou engordamento de praia ao longo do tempo e gera uma estimativa dos valores de deriva litorânea para os diferentes trechos de praia, possibilitando avaliar os efeitos das intervenções nas praias adjacentes.

Calibração e aplicação do modelo numérico genesis nas praias de Tramandaí e Imbé-RS

O modelo numérico GENESIS (Generalized Model for Simulating Shoreline Change) é parte de um sistema de modelagem de linha de praia, o SMS (Shoreline Modeling System), desenvolvido pelo CERC (Coastal Engineering Research Center), U.S.A. É um modelo genérico, determinístico e bidimensional, com grande flexibilidade para ser adaptado a costas abertas, arenosas e sujeitas a intervenção humana. Utilizado na previsão da resposta da linha praia as diversas obras costeiras que podem ser implantadas na mesma. Características estas, que fazem dele uma ferramenta indicada para a o estudo costa do Rio Grande do Sul e para o objetivo deste estudo. A aplicação do modelo de evolução de linha praia – GENESIS neste trabalho, tem como objetivos: calibrar o modelo numérico GENESIS para a costa centro norte do Rio Grande do Sul e avaliar seu uso como ferramenta na previsão de impactos ambientais gerados por obras costeiras, Alem de reproduzir as condições do modelo físico reduzido de 1965 e comparar os resultados entre as simulações matemática e física. O modelo foi aplicado num trecho de linha de praia da região centro norte do Rio Grande do Sul, nas praias de Tramandaí e Imbé. As quais já foram alvo de estudos anteriores através de modelo físico reduzido, em função do desejo deste município em construir molhes na desembocadura do canal da Laguna de Tramandaí. Para implementação do modelo numérico GENESIS foram utilizados dados das posições da linha de praia em três diferentes anos, coletados pelo CECO/UFRGS, dados de onda coletados pelo ondógrafo do IPH/UFRGS, e diversos dados sobre as praias e sua história, retirados da extensa bibliografia publicada sobre a região de estudo. A calibração do modelo foi realizada através das linhas de praia medidas em 1997 e em 2000. O modelo foi considerado calibrado quando o mesmo consegui reproduzir a linha de praia do ano 2000 a partir da linha de 1997, obtendo um erro máximo de 15 m. Foram realizadas simulações que reproduziam as simulações feitas em modelo físico reduzido do IPH em 1965. Através da comparação dos dados de onda utilizados no modelo físico reduzido de 1965 e dos dados de onda coletados pelo ondógrafo em 1996, pudemos observar a importância do uso de um série de dados de onda neste tipo de estudo, bem como, a desenvoltura e limitações do modelo numérico GENESIS na situações geradas.

Potential output in Latin America: a standard approach for the 1950-2002 period

Includes bibliography

Estimating Patterns of CD4+ Lymphocyte Decline Using Data from a Prevalent Cohort of HIV Infected Individuals

In natural history studies of chronic disease, it is of interest to understand the evolution of key variables that measure aspects of disease progression. This is particularly true for immunological variables in persons infected with the Human Immunodeficiency Virus (HIV). The natural timescale for such studies is time since infection. However, most data available for analysis arise from prevalent cohorts, where the date of infection is unknown for most or all individuals. As a result, standard curve fitting algorithms are not immediately applicable. Here we propose two methods to circumvent this difficulty. The first uses repeated measurement data to provide information not only on the level of the variable of interest, but also on its rate of change, while the second uses an estimate of the expected time since infection. Both methods are based on the principal curves algorithm of Hastie and Stuetzle, and are applied to data from a prevalent cohort of HIV-infected homosexual men, giving estimates of the average pattern of CD4+ lymphocyte decline. These methods are applicable to natural history studies using data from prevalent cohorts where the time of disease origin is uncertain, provided certain ancillary information is available from external sources.

Estimation with Interval Censored Data in Longitudinal Studies

In biostatistical applications interest often focuses on the estimation of the distribution of a time-until-event variable T. If one observes whether or not T exceeds an observed monitoring time at a random number of monitoring times, then the data structure is called interval censored data. We extend this data structure by allowing the presence of a possibly time-dependent covariate process that is observed until end of follow up. If one only assumes that the censoring mechanism satisfies coarsening at random, then, by the curve of dimensionality, typically no regular estimators will exist. To fight the curse of dimensionality we follow the approach of Robins and Rotnitzky (1992) by modeling parameters of the censoring mechanism. We model the right-censoring mechanism by modeling the hazard of the follow up time, conditional on T and the covariate process. For the monitoring mechanism we avoid modeling the joint distribution of the monitoring times by only modeling a univariate hazard of the pooled monitoring times, conditional on the follow up time, T, and the covariates process, which can be estimated by treating the pooled sample of monitoring times as i.i.d. In particular, it is assumed that the monitoring times and the right-censoring times only depend on T through the observed covariate process. We introduce inverse probability of censoring weighted (IPCW) estimator of the distribution of T and of smooth functionals thereof which are guaranteed to be consistent and asymptotically normal if we have available correctly specified semiparametric models for the two hazards of the censoring process. Furthermore, given such correctly specified models for these hazards of the censoring process, we propose a one-step estimator which will improve on the IPCW estimator if we correctly specify a lower-dimensional working model for the conditional distribution of T, given the covariate process, that remains consistent and asymptotically normal if this latter working model is misspecified. It is shown that the one-step estimator is efficient if each subject is at most monitored once and the working model contains the truth. In general, it is shown that the one-step estimator optimally uses the surrogate information if the working model contains the truth. It is not optimal in using the interval information provided by the current status indicators at the monitoring times, but simulations in Peterson, van der Laan (1997) show that the efficiency loss is small.

The Design and Analysis of Partner Studies of HIV Transmission

Common goals in epidemiologic studies of infectious diseases include identification of the infectious agent, description of the modes of transmission and characterization of factors that influence the probability of transmission from infected to uninfected individuals. In the case of AIDS, the agent has been identified as the Human Immunodeficiency Virus (HIV), and transmission is known to occur through a variety of contact mechanisms including unprotected sexual intercourse, transfusion of infected blood products and sharing of needles in intravenous drug use. Relatively little is known about the probability of IV transmission associated with the various modes of contact, or the role that other cofactors play in promoting or suppressing transmission. Here, transmission probability refers to the probability that the virus is transmitted to a susceptible individual following exposure consisting of a series of potentially infectious contacts. The infectivity of HIV for a given route of transmission is defined to be the per contact probability of infection. Knowledge of infectivity and its relationship to other factors is important in understanding the dynamics of the AIDS epidemic and in suggesting appropriate measures to control its spread. The primary source of empirical data about infectivity comes from sexual partners of infected individuals. Partner studies consist of a series of such partnerships, usually heterosexual and monogamous, each composed of an initially infected "index case" and a partner who may or may not be infected by the time of data collection. However, because the infection times of both partners may be unknown and the history of contacts uncertain, any quantitative characterization of infectivity is extremely difficult. Thus, most statistical analyses of partner study data involve the simplifying assumption that infectivity is a constant common to all partnerships. The major objectives of this work are to describe and discuss the design and analysis of partner studies, providing a general statistical framework for investigations of infectivity and risk factors for HIV transmission. The development is largely based on three papers: Jewell and Shiboski (1990), Kim and Lagakos (1990), and Shiboski and Jewell (1992).

Efficient and Ad Hoc Estimation in the Bivariate Censoring Model

A large number of proposals for estimating the bivariate survival function under random censoring has been made. In this paper we discuss nonparametric maximum likelihood estimation and the bivariate Kaplan-Meier estimator of Dabrowska. We show how these estimators are computed, present their intuitive background and compare their practical performance under different levels of dependence and censoring, based on extensive simulation results, which leads to a practical advise.

A Note on the Asymptotic Variance of Survival Function in the Semi-Markov Model

In Malani and Neilsen (1992) we have proposed alternative estimates of survival function (for time to disease) using a simple marker that describes time to some intermediate stage in a disease process. In this paper we derive the asymptotic variance of one such proposed estimator using two different methods and compare terms of order 1/n when there is no censoring. In the absence of censoring the asymptotic variance obtained using the Greenwood type approach converges to exact variance up to terms involving 1/n. But the asymptotic variance obtained using the theory of the counting process and results from Voelkel and Crowley (1984) on semi-Markov processes has a different term of order 1/n. It is not clear to us at this point why the variance formulae using the latter approach give different results.

Markers Models in Survival Analysis and Applications to Issues Associated with AIDS

Jewell and Kalbfleisch (1992) consider the use of marker processes for applications related to estimation of the survival distribution of time to failure. Marker processes were assumed to be stochastic processes that, at a given point in time, provide information about the current hazard and consequently on the remaining time to failure. Particular attention was paid to calculations based on a simple additive model for the relationship between the hazard function at time t and the history of the marker process up until time t. Specific applications to the analysis of AIDS data included the use of markers as surrogate responses for onset of AIDS with censored data and as predictors of the time elapsed since infection in prevalent individuals. Here we review recent work on the use of marker data to tackle these kinds of problems with AIDS data. The Poisson marker process with an additive model, introduced in Jewell and Kalbfleisch (1992) may be a useful "test" example for comparison of various procedures.

Locally Efficient Estimation with Current Status Data and High Dimensional Covariates

In biostatistical applications, interest often focuses on the estimation of the distribution of time T between two consecutive events. If the initial event time is observed and the subsequent event time is only known to be larger or smaller than an observed monitoring time, then the data is described by the well known singly-censored current status model, also known as interval censored data, case I. We extend this current status model by allowing the presence of a time-dependent process, which is partly observed and allowing C to depend on T through the observed part of this time-dependent process. Because of the high dimension of the covariate process, no globally efficient estimators exist with a good practical performance at moderate sample sizes. We follow the approach of Robins and Rotnitzky (1992) by modeling the censoring variable, given the time-variable and the covariate-process, i.e., the missingness process, under the restriction that it satisfied coarsening at random. We propose a generalization of the simple current status estimator of the distribution of T and of smooth functionals of the distribution of T, which is based on an estimate of the missingness. In this estimator the covariates enter only through the estimate of the missingness process. Due to the coarsening at random assumption, the estimator has the interesting property that if we estimate the missingness process more nonparametrically, then we improve its efficiency. We show that by local estimation of an optimal model or optimal function of the covariates for the missingness process, the generalized current status estimator for smooth functionals become locally efficient; meaning it is efficient if the right model or covariate is consistently estimated and it is consistent and asymptotically normal in general. Estimation of the optimal model requires estimation of the conditional distribution of T, given the covariates. Any (prior) knowledge of this conditional distribution can be used at this stage without any risk of losing root-n consistency. We also propose locally efficient one step estimators. Finally, we show some simulation results.

Smooth Estimation of a Monotone Density

We investigate the interplay of smoothness and monotonicity assumptions when estimating a density from a sample of observations. The nonparametric maximum likelihood estimator of a decreasing density on the positive half line attains a rate of convergence at a fixed point if the density has a negative derivative. The same rate is obtained by a kernel estimator, but the limit distributions are different. If the density is both differentiable and known to be monotone, then a third estimator is obtained by isotonization of a kernel estimator. We show that this again attains the rate of convergence and compare the limit distributors of the three types of estimators. It is shown that both isotonization and smoothing lead to a more concentrated limit distribution and we study the dependence on the proportionality constant in the bandwidth. We also show that isotonization does not change the limit behavior of a kernel estimator with a larger bandwidth, in the case that the density is known to have more than one derivative.