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Análise de materiais biológicos usando o coeficiente de atenuação linear / Biological Material Analisis using linear attenuation coefficientsSoares, Leonardo Diniz Hipolito 27 October 2015 (has links)
O conhecimento do coeficiente de atenuação linear (µ) é de extrema importância para estudos de contraste em imagens de radiodiagnóstico, dose e caracterização de materiais. Parâmetros como a densidade eletrônica (?e), o número atômico médio (Z¯), entre outros, podem ser determinados a partir do coeficiente de atenuação linear em diferentes energias. A proposta deste trabalho é determinar experimentalmente coeficientes de atenuação linear de 80 amostras de tecidos mamários (classificadas previamente como tecido adiposo, tecido glandular, fibroadenoma ou carcinomas) e, posteriormente, extrair parâmetros que possibilitem a caracterização e diferenciação desses tecidos. Os coeficientes de atenuação linear foram medidos usando geometria de feixe estreito, no intervalo de energia entre 10 e 50 keV, utilizando um tubo de raios X com anodo de tungstênio (W) e um detector dispersivo em energia de Si (SDD). Dois modelos de parametrizações foram utilizadas para extrair ?e e Z¯. As metodologias de determinação de µ e de parametrização foram validadas utilizando 8 materiais equivalentes a tecido (4 soluções e 4 sólidos). Os resultados obtidos para tecidos mamários foram comparados com predições teóricas, obtidas usando a regra das misturas, e com dados experimentais previamente publicados, apresentando diferenças máximas de até 7%. Foram também estudadas as variações de µ intra- e inter-amostras de um mesmo grupo, obtendo variações máximas de 5% e 12%, respectivamente. Foi mostrado que o coeficiente de atenuação linear consegue distinguir apenas o tecido adiposo dos demais grupos de tecidos para energia menores de 24 keV. Finalmente, foi elaborado um modelo de diagnóstico, baseados nos parâmetros ?e e Z¯. As análises estatísticas mostram que 71% das amostras foram classificadas corretamente. / The knowledge of the linear attenuation coefficient (µ) is of extreme importance for radiodiagnostic image contrast studies, dose and material characterization. Parameters as electronic density (?e), average atomic number (Z¯), among others, can be determined using the linear attenuation coefficient at different energies. The purpose of this work is to experimentally determine the linear attenuation coefficient of 80 mammary tissues samples (classified as adipose tissue, glandular tissue, fibroadenoma or carcinoma) and then extract parameters that allow the characterization and differentiation of those tissues. The linear attenuation coefficients were measured using narrow bean geometry, with an energy interval between 10 and 50 keV, using a x-ray tube with a tungsten (W) anode and a Silicon energy dispersive detector (SDD). Two parameterization models were used to extract ?e and Z¯. The methodologies of determination of µ and parameterizations were validated using 8 tissue equivalent materials (4 solutions and 4 solids). The results obtained for mammary tissues were compared with theoretical predictions, using the mixture rule, and with previously published experimental data, presenting maximum differences of 7%. Intra and between samples variations of the same group were also studied, obtaining maximum variations of 5% and 12%, respectively. The linear attenuation coefficient was able to differentiate only the adipose tissue from others tissues groups, for energies below 24 keV. At last, a diagnostic model was elaborated, based on ?e and Z¯ parameters. The statistical analysis showed that 71% of the samples were correctly classified.
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Quantitative Analysis of High Resolution Chirp Sub-Bottom Profiler Data in Shallow Marine SedimentsAbushaheen, Yahya Rhadi January 2016 (has links)
Thesis advisor: John E. Ebel / This research describes a method to carry out quantitative analyses of sub-seabed sediments using high-resolution chirp seismic profiles in order to estimate the properties of subsurface sediments. The method identifies significant sedimentary interfaces, extracts them from the seismic record, and measures the inelastic attenuation coefficients (k) of the sedimentary layers. The k values and their variations with increasing depth of sediments are indicative of the amount of compaction of the sediment. The k values are correlated with borehole lithology to provide a relationship between k measurements and local borehole lithology. Once determined for an area, the correlation can be applied to other seismic records from the area to analyze sedimentary properties even if no borehole lithology is locally available. / Thesis (MS) — Boston College, 2016. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Earth and Environmental Sciences.
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Medidas experimentais dos coeficientes de atenuação de tecidos mamários e sua influência no contraste e dose mamográfica / Experimental Measurements of the Attenuation Coefficients of Breast Tissues and their Influence on Contrast and Mammographic DoseTomal, Alessandra 09 March 2007 (has links)
O estudo e a determinação das propriedades de atenuação de tecidos mamários são fundamentais para o entendimento e para a quantificação do contraste e da dose absorvida em um exame mamográfico. A proposta deste trabalho é determinar experimentalmente os coeficientes de atenuação de tecidos mamários e, posteriormente, incorporar esses resultados a um modelo teórico-analítico que possibilite o estudo da influência de diversos parâmetros no contraste de objetos e na dose em mamografia. Dentre os fatores de estudo, destacam-se as características da mama (geometria e composição), a técnica radiográfica, a combinação ânodo-filtro e o receptor de imagem. Os coeficientes de atenuação foram medidos usando geometria de feixe estreito, no intervalo de energia entre 8 e 30 keV, utilizando um difratômetro de raios-X 4-círculos P3 Nicolet-Siemens e um monocromador de Si (111). Para essas medidas foram utilizadas 63 amostras de tecidos mamários (classificadas previamente como tecidos normais, fibroadenomas e/ou diferentes tipos de carcinomas). Os coeficientes de atenuação medidos foram comparados com predições teóricas, obtidas usando a regra das misturas, e com dados experimentais previamente publicados. O modelo desenvolvido para o contraste objeto leva em conta as contribuições primária e secundária na radiação transmitida. A dose média absorvida foi estimada através de duas aproximações, que permitem predizer os limites superior e inferior, e de uma aproximação mais completa, que inclui as componentes espalhadas simples e duplas. O modelo desenvolvido neste trabalho permite a obtenção de resultados de forma simples e rápida, com valores similares aos obtidos por simulação Monte Carlo, bem como definir limites de detecção de massas tumorais. / The study and determination of attenuation properties of breast tissues are fundamental to understand and quantify contrast and absorbed dose in the mammographic examination. The purpose of this work is to experimentally determine the attenuation coefficient of breast tissues, and then to include these results into a theoretical analytical model, in order to study the influence of several parameters on subject contrast and dose in mammography. Among the parameters studied, one can emphasize the breast characteristics (geometry and composition), the radiographic technique, the target-filter combination and the image receptor. The attenuation coefficients were measured using narrow beam geometry, within the energy range of 8-30 keV, using an x-ray diffractometer 4-circle P3 Nicolet-Siemens and a monocromator of Si (111). For these measurements were analyzed 63 breast tissue samples (previously classified as normal tissues, fibroadenomas and several types of carcinomas). The linear attenuation coefficients measured were compared with theoretical predictions obtained from the mixture rule, and with experimental data previously published. The developed model to the subject contrast takes into account the primary and scattered contribution of the transmitted radiation. The average absorbed dose was estimated considering two simplified approaches, which allowed to predict upper and lower limit values, and a more complete approach, which included the contribution of single and double scattered radiation. The analytical model developed in this work provided results in a fast and simple way, with a good agreement with those reported by others authors who had used Monte Carlo simulation, as well it allowed to define limit values for detection of tumor masses.
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Desenvolvimento e aplicação de um sistema de raios X dispersivo em energia para determinação do coeficiente de atenuação linear e do perfil de espalhamento de neoplasias mamárias / Development and Application of an Energy Dispersive X-ray System for Determining the Linear Attenuation Coefficient and Scattering Profile of Breast DiseasesGeraldelli, Wender 13 March 2013 (has links)
As propriedades de espalhamento de raios X e atenuação de tecidos mamários normais (adiposo e fibroglandular), neoplásicos (benigno e maligno) e vários materiais tecido-equivalente (nylon, poliacetato, polimetilmetacrilato (PMMA), água, músculo-equivalente, osso-equivalente e adiposo-equivalente) foram determinados usando um sistema de raios X dispersivo em energia (SRXDE). O SRXDE consistiu de um tubo de raios X com anodo de tungstênio operando a 60kVp, um goniômetro e dois detectores: um detector de telureto de cádmio (CdTe), posicionado a 7 graus com relação ao feixe incidente usado para detectar a distribuição em energia dos fótons espalhados (numa faixa de momento transferido de 0,5nm-1 - 3,5nm-1) e um detector de silício (Silicon Drift Detector, SDD), posicionado a zero graus e usado para detectar a distribuição em energia do feixe transmitido (com amostra) ou do feixe incidente (sem amostra). A distribuição espectral foi processada para se obter o perfil de espalhamento e o coeficiente de atenuação linear de 100 amostras de tecidos mamários (59 normal, 30 maligno e 11 benigno). Este sistema foi, também, aplicado ao estudo de regiões de transição entre tecidos com diferentes composições. Os resultados encontrados neste trabalho mostram que os tecidos mamários podem ser caracterizados através de suas propriedades de atenuação e espalhamento. Perfis de espalhamento neoplásico apresentam formato do pico principal significativamente diferente na faixa de momento transferido de 0,8nm-1 - 2,0nm-1, aos tecidos normais. Especificamente, o tecido adiposo apresentou um perfil de espalhamento muito diferente (pico principal em 1,12nm-1 e LMA de 0,33nm-1) quando comparado com tecidos neoplásico maligno e benigno e normal fibroglandular (pico principal em torno de 1,54nm-1 e LMA em torno de 0,73nm-1). O coeficiente de atenuação linear observado para os tecidos maligno, benigno e fibroglandular são muito similares e mostraram diferenças menores que 8% para energias entre 10 e 35keV. Entretanto, o tecido adiposo apresentou diferenças significativas com relação aos outros tecidos em toda faixa de energia (diferenças de até 40% foram observadas). Os resultados obtidos da varredura espacial das amostras heterogêneas mostram que o sistema desenvolvido permite o estudo de regiões de transição entre tecidos com diferentes composições. Finalmente, nossos resultados foram comparados com dados experimentais previamente publicados na literatura, mostrando boa concordância dentro das incertezas estatísticas. / The X-ray scattering and attenuation properties for normal (adipose and glandular) and neoplastic (benign and malignant) breast tissues and several tissue-equivalent materials (nylon, polyacetate, polymethylmethacrylate (PMMA), water, muscle-equivalent, bone-equivalent and adipose-equivalent) were determined using an energy dispersive X-ray system (EDXS). The EDXS consisted of a tungsten anode X-ray tube operating at 60kVp, a goniometer, and two detectors: a Cadmium Telluride (CdTe) detector, positioned at 7 degrees with relation to the incident beam used for detecting the energy distribution of scattered photons (over the momentum transfer range of 0,5nm-1- 3,5nm-1) and a Silicon Drift Detector (SSD), positioned at zero degree used for detecting the energy distribution of the transmitted beam (with the sample) or the incident beam (without the sample). The spectra distributions were processed to obtaine the scattering profile and the linear attenuation coefficient of 100 samples of breast tissues (59 normal, 30 malignant and 11 benign). This system was also applied to the study of the transition regions between tissues with different composition. The results found in this work show that breast tissues may be characterized through their attenuation and scattering properties. Neoplastic scattering profiles presented format and the main peak position significantly different in the range of momentum transfer from 0,8nm-1- 2,0nm-1, to normal tissues. Specifically, adipose tissue presented a very different scattering profile (main peak at 1,12nm-1and FWHM of 0,33nm-1) when compared with malignant, benign and also normal glandular tissues (main peak around 1,54nm-1and FWHM about of 0,73nm-1). The linear attenuation coefficient observed for malignant, benign and normal glandular tissues were quite similar and showed differences smaller than 8% for energies between 10 and 35keV. However, adipose tissue presented significant differences from the others tissues type in all energy range (differences up to 40% were observed). The results of the spatial scan of heterogeneous samples show that the developed system allows the study of transition regions between tissues with different composition. Finally, our results were compared with previous experimental data showing a good agreement within the experimental uncertainties
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Coral reef habitat change and water clarity assessment (1984-2002) for the Florida Keys national marine sanctuary using landsat satellite dataPalandro, David A 01 June 2006 (has links)
The decline of coral reef habitats has been witnessed on a global scale, with some of the most dramatic decline occurring in the florida keys. as remote sensing can provide a synoptic view of coral reef ecosystems, 28 landsat images (1984-2002) were utilized to study water clarity and habitat change. first, the data were used to derive the diffuse attenuation coefficient (kd, m-1), a measure of water clarity, for 29 sites throughout the florida keys national marine sanctuary (fknms). landsat-derived kd values from bands 1 (blue) and 2 (green) provided useful information for 26 of 29 sites, whereas band 3 (red) provided no consistent data due to the high absorption of red light by water. it was not possible to assess long-term temporal trends as data were acquired, at most, twice a year. spatial variability was high between sites and between regions (upper, middle and lower keys) for bands 1 (0.019 m-1 - 0.060 m-1) and 2 (0.036 m-1 - 0.076 m-1). the highest kd values were f
ound in the upper keys, followed by the middle and lower keys, respectively. this trend was corroborated by in situ monitoring of kd(par). second, the data were used to assess benthic habitat changes in eight coral reef sites located in the fknms. a mahalanobis distance classification was trained for four classes using in situ ground-truth data. overall coral habitat decline was 61% (3.4%/y), from 19% (1984) to 7.7% (2002). in situ monitoring data acquired by the coral reef evaluation and monitoring project (cremp) for the eight reef sites (1996-2002) showed a loss in coral cover of 52%, whereas the landsat-derived coral-habitat cover declined 37% for the same time period. a trend comparison between the full cremp percent coral cover data (1996-2004) and the full landsat-derived coral habitat class (1984-2002) showed no significant difference between the rates of change (ancova f-test, p = 0.303). The derivation of Kd and benthic habitat maps produced from Landsat data could provide c
oastal marine managers another tool to help in the decision-making process.
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Attenuation Coefficient of High Temperature Molten Salts: An Experimental ApproachGonzález, Rafael Yari Cabanillas January 2014 (has links)
In order to make thermal solar power compete with the traditional sources of energy, the efficiency must increase and one way of doing it is by changing the operating fluid. Among the alternate fluids is the use of molten salts as a part of the process; either for thermal storage and later utilization for electrical production during the hours without sun or as a substitute of the operating fluid to provide higher temperatures resulting in better efficiency. The difficulty of using molten salts is the lack of physical properties in literature; such as viscosity, boiling point, vapor pressure and volumetric absorption of solar radiation, thus making the selection of a suitable salt a very difficult endeavor. As a part of the Multidisciplinary Research Initiative (MURI) of the Department of Energy in the project of High Operating Fluids, this work will focus on the optical properties of the molten salts (volumetric absorption). The objective of this Thesis is to design, build and test a device capable of measuring the light attenuation coefficient; which is directly related to volumetric absorption of solar radiation, as well as determine the attenuation coefficient of various eutectic systems for the ternary salt mixture of ZnCl2, NaCl and KCl. Based on the little existent literature, a device capable of measuring the attenuation coefficient was designed, built, validated and tested. This was done by projecting a stable beam of light simulating sun radiation through the molten salt sample and to a spectrometer with a wavelength range going from 400 nm to 1000 nm with operating temperatures going from 350oC to 600oC. This device is capable of controlling the thickness, from 1 to 60 mm, of the molten salt sample by a computer controlled linear stage with an accuracy of 0.1mm. Quartz was used as a container for the molten salts because of its high melting point and transparency. A ceramic heater was used as a heat source, which can heat up the sample to temperatures up to 1200 oC if necessary. Two validation tests for the device were done by measuring the light attenuation coefficient of clear water and extra virgin olive oil and then they were compared to the ones in literature. The eutectic systems were tested next; the results characterized the attenuation coefficient as a function of wavelength and temperature, something that no other experimental work has done before for this specific fluid. These values will help to determine an optimal operating fluid for high temperature thermal applications.
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Application of frequency-dependent nudging in biogeochemical modeling and assessment of marine animal tag data for ocean observationsLagman, Karl Bryan 28 June 2013 (has links)
Numerical models are powerful and widely used tools for environmental prediction; however, any model prediction contains errors due to imperfect model parameterizations, insufficient model resolution, numerical errors, imperfect initial and boundary conditions etc. A variety of approaches is applied to quantify, correct and minimize these errors including skill assessments, bias correction and formal data assimilation. All of these require observations and benefit from comprehensive data sets. In this thesis, two aspects related to the quantification and correction of errors in biological ocean models are addressed: (i) A new bias correction method for a biological ocean model is evaluated, and (ii) a novel approach for expanding the set of typically available phytoplankton observations is
assessed.
The bias correction method, referred to as frequency-dependent nudging, was proposed
by Thompson et al. (Ocean Modelling, 2006, 13:109-125) and is used to nudge a model
only in prescribed frequencies. A desirable feature of this method is that it can preserve
high frequency variability that would be dampened with conventional nudging. The method
is first applied to an idealized signal consisting of a seasonal cycle and high frequency
variability. In this example, frequency-dependent nudging corrected for the imposed
seasonal bias without affecting the high-frequency variability. The method is then applied
to a non-linear, 1 dimensional (1D) biogeochemical ocean model. Results showed that
application of frequency-dependent nudging leads to better biogeochemical estimates than
conventional nudging.
In order to expand the set of available phytoplankton observations, light measurements
from sensors attached on grey seals where assessed to determine if they provide a useful
proxy of phytoplankton biomass. A controlled experiment at Bedford Basin showed
that attenuation coefficient estimates from light attenuation measurements from seal tags
were found to correlate significantly with chlorophyll. On the Scotian Shelf, results of
the assessment indicate that seal tags can uncover spatio-temporal patterns related to
phytoplankton biomass; however, more research is needed to derive absolute biomass
estimates in the region.
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Imaging And Radiation Interactions Of Polymer Gel DosimetersTrapp, Jamie Vincent January 2003 (has links)
Aim: The past two decades have seen a large body of work dedicated to the development of a three dimensional gel dosimetry system for the recording of radiation dose distributions in radiation therapy. The purpose of much of the work to date has been to improve methods by which the absorbed dose information is extracted. Current techniques include magnetic resonance imaging (MRI), optical tomography, Raman spectroscopy, x-ray computed tomography (CT) and ultrasound. This work examines CT imaging as a method of evaluating polymer gel dosimeters. Apart from publications resulting from this work, there has been only two other journal articles to date reporting results of CT gel dosimetry. This indicates that there is still much work required to develop the technique. Therefore, the aim of this document is to develop CT gel dosimetry to the extent that it is of use to clinical and research physicists. Scope: Each chapter in this document describes an aspect of CT gel dosimetry which was examined; with Chapters 2 to 7 containing brief technical backgrounds for each aspect. Chapter 1 contains a brief review of gel dosimetry. The first step in the development of any method for reading a signal is to determine whether the signal can actually be obtained. However, before polymer gel dosimeters can be imaged using a CT scanner, imaging techniques are required which are employable to obtain reliable readings. Chapter 2 examines the various artifacts inherent in CT which interfere with the quantitative analysis of gel dosimeters and a method for their removal is developed. The method for artifact reduction is based on a subtraction technique employed previously in a feasibility study and a system is designed to greatly simplify the process. The simplification of the technique removes the requirement for accurate realignment of the phantom within the scanner and the imaging of calibration vials is enabled. Having established a method by which readings of polymer gel dosimeters can be obtained with CT, Chapter 3 examines the CT dose response. A number of formulations of polymer gel dosimeter are studied by varying the constituent chemicals and their concentrations. The results from this chapter can be employed to determine the concentration of chemicals when manufacturing a polymer gel dosimeter with a desired CT dose response. With the CT dose response characterised in Chapter 3, the macroscopic cause of the CT signal is examined in Chapter 4. To this end direct measurement of the linear attenuation coefficient is obtained with a collimated radiation source and detector. Density is measured by Archimedes' principle. Comparison of the two results shows that the cause of the CT signal is a density change and the implications for polymer gel dosimetry are discussed. The CT scanner is revisited in Chapter 5 to examine the CT imaging techniques required for optimal performance. The main limitation of the use of CT in gel dosimetry to date has been image noise. In Chapter 5 stochastic noise is investigated and reduced. The main source of non-stochastic noise in CT is found and imaging techniques are examined which can greatly reduce this residual noise. Predictions of computer simulations are verified experimentally. Although techniques for the reduction of noise are developed in Chapter 5, there may be situations where the noise must be further reduced. An image processing algorithm is designed in Chapter 6 which employs a combination of commonly available image filters. The algorithm and the filters are tested for their suitability in gel dosimetry through the use of a simulated dose distribution and by performing a pilot study on an irradiated polymer gel phantom. Having developed CT gel dosimetry to the point where a suitable image can be obtained, the final step is to investigate the uncertainty in the dose calibration. Methods used for calibration uncertainty in MRI gel dosimetry to date have either assumed a linear response up to a certain dose, or have removed the requirement for linearity but incorrectly ignored the reliability of the data and fit of the calibration function. In Chapter 7 a method for treatment of calibration data in CT gel dosimetry is proposed which allows for non-linearity of the calibration function, as well as the goodness of its fit to the data. Alternatively, it allows for the reversion to MRI techniques if linearity is assumed in a limited dose range. Conclusion: The combination of the techniques developed in this project and the newly formulated normoxic gels (not extensively studied here) means that gel dosimetry is close to becoming viable for use in the clinic. The only capital purchase required for a typical clinic is a suitable water tank, which is easily and inexpensively producible if the clinic has access to a workshop.
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High-accuracy measurements of the x-ray mass attenuation coefficients of molybdenum and tin: testing theories of photoabsorptionde Jonge, Martin D. Unknown Date (has links) (PDF)
The x-ray atomic form-factor determines the x-ray optical properties of materials and is a fundamental parameter for critical x-ray investigations. However, despite uncertainty estimates of order 1%, differences of 2-10% between x-ray mass attenuation measurements render comparison with the various theoretical tabulations meaningless. Moreover, such uncertainties impose limits on the accuracy of various quantitative investigations. We determine the imaginary component of the atomic form-factor from measurements of the x-ray mass attenuation coefficient. With the exception of the measurements of Tran et.al. [Phys. Rev. A 64, (062506); 67, (042716); J. Phys. B 38, (89)] with a 0.3% accuracy, previous work has been unable to achieve accuracies below 1%, and differences between results claiming this accuracy often exceed 6%.We have developed a full-foil mapping technique which has improved the measurement accuracy by an order of magnitude. This technique overcomes limitations arising from absorber thickness variations, using the average integrated column density and attenuation measurements across the entire surface of the absorber. We have examined measurements obtained over a wide range of parameter space for systematic deviations indicative of experimental error. Among others, this has led to the identification and correction of a 1% discrepancy arising from the x-ray bandwidth. Resulting measurement accuracies for molybdenum are 0.02-0.15%. Preliminary results for tin suggest a final accuracy of 0.1-1%. We compare these measurements with several commonly-used tabulations and identify a number of systematic discrepancies whose causes are discussed.
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Estimativa da radiação solar direta na incidência nas partições instantânea, horária e diária a partir da radiação solar global /Oliveira, Leuda da Silva. January 2001 (has links)
Orientador: João Francisco Escobedo / Banca: Dinival Martins / Banca: Roberto Naves Domingues / Resumo : A partir de uma base de dados das radiações solar global e direta na incidência, desenvolveu-se no presente trabalho modelos de estimativas da radiação solar direta da incidência a partir da radiação solar global para as partições de tempo instantânea, horária e diária. Foi também equacionado o coeficiente de atenuação da radiação solar direta ela atmosfera (K) em função do índice de claridade (K). Os modelos foram gerados a partir da função logística modificada de Boltzmann, no período de março/96 a fevereiro/98, e a mensal e anual no período de março/98 a fevereiro/99, para as três partições de , obtendo-se as equações: o j 0, -0,85 2 para a partição mstantanea -* Kb = 1+eKt_O5SO95/OO7455 + 0,85, com R =0,804, II 0,00002-0,89999 2 para a partição horária -* Kb = 1 +eKt_O59228/OIO364 + 0,89999, com R =0,816 e para a partição diária -* K = 1 + et°,0"°°8185 + 0,97, com R20,987.Na validação mensal dos modelos, obteve-se uma correlação de Kb em função de K de 95,1% a 98,8% para a partição instantânea; 85,5% a 96,7% para a partição horária, de 74,2% a 96,9% para a partição diária. Na validação anual do modelo obteve-se uma correlação de 97,4% para a partição instantânea, de 98,7% para a partição horária e de 96,9% para a partição diária, sendo que quando se defiuiiu o intervalo de O<IÇ<O,70, observou- se uma melhoria nos coeficientes de determinação na validação dos modelos. A equação de correlação média de K em função de K encontrada foi: K =1 1,35.e49t com coeficiente de determinação de 95%. / Abstract: In this work it was aimed at to establish the estimation models for direct normal solar irradiance (Kb) in funetion of instantaneous, hourly and daily global radiation (IÇ), as well as to set out the atmospheric attenuation coefficient (K) in function of the clearness index (K) for Botucatu-São Paulo-Brazil. The observed data of I( instantaneous, hourly and daily, were adjusted to a function growth logistic modified of Boltzmann in the period from march /96 to february/98, and the monthly and annual validation was made in the period from march/98 to february/99, with the foilowing results: - for the instantaneous, -* K, = + etO 095)10,07455 + 0,85, with R2=0,804, - for the hourly, -* K = + 0,89999, with R2=0,8 16 and - for the daily, -* = 1 + e ,08185 + 0,97, with R20,987. The atmospheric attenuation coefficient (K) had an exponential behavior in the form: K = 1 1,35.e49t with determination coefficient of 95%. / Mestre
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