21 results on '"trapezoid method"'
Search Results
2. Multispectral Optical Remote Sensing for Water-Leak Detection
- Author
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Jean-Claude Krapez, Javier Sanchis Muñoz, Christophe Mazel, Christian Chatelard, Philippe Déliot, Yves-Michel Frédéric, Philippe Barillot, Franck Hélias, Juan Barba Polo, Vincent Olichon, Guillaume Serra, Céline Brignolles, Alexandra Carvalho, Duarte Carreira, Anabela Oliveira, Elsa Alves, André B. Fortunato, Alberto Azevedo, Paolo Benetazzo, Alessandro Bertoni, and Isabelle Le Goff
- Subjects
remote sensing ,water leak ,infrared ,Triangle Method ,Trapezoid Method ,soil moisture ,Chemical technology ,TP1-1185 - Abstract
Water losses from water distribution means have a high environmental impact in terms of natural resource depletion (water, energy, ecosystems). This work aims to develop an optical airborne surveillance service for the detection of water leaks (WADI—Water-tightness Airborne Detection Implementation) to provide water utilities with adequate and timely information on leaks in water transportation mains outside urban areas. Firstly, a series of measurement campaigns were performed with two hyperspectral cameras and a thermal infrared camera in order to select the most appropriate wavelengths and combinations thereof for best revealing high moisture areas, which are taken as a proxy for water leakage. The Temperature-Vegetation-Index method (T-VI, also known as Triangle/Trapezoid method) was found to provide the highest contrast-to-noise ratio. This preliminary work helped select the most appropriate onboard instrumentation for two types of aerial platforms, manned (MAV) and unmanned (UAV). Afterwards, a series of measurement campaigns were performed from 2017 to 2019 in an operational environment over two water distribution networks in France and Portugal. Artificial leaks were introduced and both remote sensing platforms successfully detected them when excluding the unfavorable situations of a recent rain event or high vegetation presence. With the most recent equipment configuration, known and unknown real leaks in the overflown part of a water transportation network in Portugal have been detected. A significant number of false alarms were also observed which were due either to natural water flows (groundwater exfiltration, irrigation runoff and ponds) or to vegetation-cover variability nearby water-distribution nodes. Close interaction with the water utilities, and ancillary information like topographic factors (e.g., slope orientation), are expected to reduce the false alarm rates and improve WADI’s methodology performance.
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- 2022
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3. Integration
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Dadkhah, Kamran and Dadkhah, Kamran
- Published
- 2011
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4. Estimation of Surface Soil Moisture from Thermal Infrared Remote Sensing Using an Improved Trapezoid Method
- Author
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Yuting Yang, Huade Guan, Di Long, Bing Liu, Guanghua Qin, Jun Qin, and Okke Batelaan
- Subjects
surface soil moisture ,trapezoid method ,thermal infrared remote sensing ,MODIS ,Tibet Plateau ,Science - Abstract
Surface soil moisture (SM) plays a fundamental role in energy and water partitioning in the soil–plant–atmosphere continuum. A reliable and operational algorithm is much needed to retrieve regional surface SM at high spatial and temporal resolutions. Here, we provide an operational framework of estimating surface SM at fine spatial resolutions (using visible/thermal infrared images and concurrent meteorological data) based on a trapezoidal space defined by remotely sensed vegetation cover (Fc) and land surface temperature (LST). Theoretical solutions of the wet and dry edges were derived to achieve a more accurate and effective determination of the Fc/LST space. Subjectivity and uncertainty arising from visual examination of extreme boundaries can consequently be largely reduced. In addition, theoretical derivation of the extreme boundaries allows a per-pixel determination of the VI/LST space such that the assumption of uniform atmospheric forcing over the entire domain is no longer required. The developed approach was tested at the Tibetan Plateau Soil Moisture/Temperature Monitoring Network (SMTMN) site in central Tibet, China, from August 2010 to August 2011 using Moderate Resolution Imaging Spectroradiometer (MODIS) Terra images. Results indicate that the developed trapezoid model reproduced the spatial and temporal patterns of observed surface SM reasonably well, with showing a root-mean-square error of 0.06 m3·m−3 at the site level and 0.03 m3·m−3 at the regional scale. In addition, a case study on 2 September 2010 highlighted the importance of the theoretically calculated wet and dry edges, as they can effectively obviate subjectivity and uncertainties in determining the Fc/LST space arising from visual interpretation of satellite images. Compared with Land Surface Models (LSMs) in Global Land Data Assimilation System-1, the remote sensing-based trapezoid approach gave generally better surface SM estimates, whereas the LSMs showed systematic underestimation. Sensitivity analyses suggested that the trapezoid method is most sensitive to field capacity and temperature but less sensitive to other meteorological observations and parameters.
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- 2015
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5. Estimating Evapotranspiration From Satellite Using Easily Obtainable Variables: A Case Study Over the Southern Great Plains, USA.
- Author
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Yagci, Ali L. and Santanello, Joseph A.
- Abstract
Evapotranspiration (ET) is a critical component of the earth's water budget, a critical modulator of land–atmosphere interactions, and also plays a crucial role in managing the earth's energy balance. In this study, the feasibility of generating spatially continuous daily evaporative fraction (EF) and ET from minimal remotely sensed and meteorological inputs in a trapezoidal framework is demonstrated. A total of four variables, normalized difference vegetation index, land surface temperature (T_s ), gridded daily average temperature (T_a ), and elevation (z) are required to estimate EF. Then, ET can be estimated with the available soil heat flux (G) and net radiation (Rn) data. First, the crucial model variable T_s - T_a is examined how well it characterizes the variation in EF using in-situ data recorded at two eddy correlation flux towers in Southern Great Plains, USA in 2011. Next, the accuracy of satellite-based T_s\ is compared to ground-based T_s. Finally, EF and ET estimates are validated. The results reveal that the model performed satisfactorily in modeling EF and ET variation at winter wheat and deciduous forest during the high evaporative months. Even though the model works best with the observed Moderate Resolution Imaging Spectroradiometer-T_s as opposed to temporally interpolated T_s, results obtained from interpolated T_s are able to close the gaps with reasonable accuracy. Due to the fact that T_s - T_a is not a good indicator of EF outside the growing season when deciduous forest is dormant, potential improvements to the model are proposed to improve accuracy in EF and ET estimates at the expense of adding more variables. [ABSTRACT FROM PUBLISHER]
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- 2018
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6. Bifurcation equations for periodic orbits of implicit discrete dynamical systems.
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Oliveira, Henrique M.
- Abstract
Bifurcation equations, non-degeneracy and transversality conditions are obtained for the fold, transcritical, pitchfork and flip bifurcations for periodic points of one-dimensional implicitly defined discrete dynamical systems. The backward Euler method and the trapezoid method for numeric solutions of ordinary differential equations fall in the category of implicit dynamical systems. Examples of bifurcations are given for some implicit dynamical systems including bifurcations for the backward Euler method when the step size is changed. [ABSTRACT FROM AUTHOR]
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- 2018
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7. Definite integrals
- Author
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Ben-Israel, Adi, Gilbert, Robert, Buchberger, B., editor, Collins, G. E., editor, Ben-Israel, Adi, and Gilbert, Robert
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- 2002
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8. ОПТИМІЗОВАНИЙ РОЗРАХУНОК АДСОРБЦІЙНОГО ПРОЦЕСУ ЧЕРЕЗ НАСАДКОВИЙ АДСОРБЕР МЕТОДОМ КОМІРКОВОЇ МОДЕЛІ
- Subjects
теплові процеси ,trapezoid method ,математична модель ,adsorption ,cell model ,thermal processes ,адсорбція ,метод трапеції ,коміркова модель ,mathematical model ,MathCAD - Abstract
This paper considers the main theoretical calculations of adsorption kinetics, time of the flow in the nozzle adsorber, time of protective action of the adsorbent layer, average speed of adsorption process and the differential equation of the adsorption process according to initial and boundary conditions. Graphically, C-curve has been obtained, which is presented in dimensionless coordinates and demonstrates a mathematical model of adsorption process. The optimal number of cells is calculated by comparing the experimentally obtained response curve with the curves calculated according to the equation of the cell model at different values. In addition, the amount of heat according to the Langmuir's law for adsorption on activated carbon and the dependence of the amount of heat adsorbed on temperature using the Truton's equation have been determined. A mathematical model of the adsorp-tion process, which has been studied using the cell model method and software, is presented. Using the MathCAD application package and the Langmuir's equation, this model has been solved by com-paring the required number of cells n, which is defined as its main parameter. Based on the experimental curve, an assumption is made about the possible form of the cell model of adsorption process and mathematical processing of this curve is performed. The obtained values of model parameters have been calculated, the experimental data have been normalized by the trapezoidal method and the model has been tested for adequacy. The process of exchange of ions with the same charge, which takes place between the adsorbent and the adsorbate in exactly equivalent proportions in order to soften the water intended for the production of soft and alcoholic beverages, wine materials, is studied, as the taste of these products improves with the reduction of magnesium, copper and iron ions. Problems of mathematical modeling of adsorption processes in inhomogeneous media and methods of constructing mathematical problems of such models require further study and have the prospect of further research., В статті показано оптимізовану модель адсорбції через насадковий адсорбер в ізотермічних умовах. Розглянуто теоретичні розрахунки кінетики адсорбції, часу перебування потоку в насадковому адсорбері, часу захисної дії шару адсорбенту, середньої швидкості процесу адсорбції. Проедставлено в граничних умовах диференціальне рівняння адсорбційного процесу в ізотермічних умовах. Крім того, визначено кількість теплоти згідно з законом Ленгмюра при адсорбції на активованому вугіллі, та, використовуючи рівняння Трутона, визначено залежність кількості тепла, що поглинається, від температури. Наведено математичну модель адсорбційного процесу, що досліджувалась із застосуванням методу коміркової моделі та програмного забезпечення. Використовуючи пакет прикладних програм MathCAD та рівняння Ленгмюра, ця модель розв’язана шляхом порівняння необхідної кількості комірок n, яка була визначена як її основний параметр. На основі експериментальної кривої зроблено припущення про можливий вигляд коміркової моделі адсорбційного процесу і проведено математичну обробку цієї кривої. Розраховано отримані значення параметрів моделі, проведено нормування експериментальних даних методом трапецій та перевірку моделі на адекватність. Вивчено процес обміну іонів з одинаковим зарядом, який проходить між адсорбентом і адсорбатом в точно еквівалентних співвідношеннях, для того щоб пом’якшити воду, яка призначена для виготовлення безалкогольних і алкогольних напоїв, виноматеріалів, оскільки смакові якості цих продуктів поліпшуються в разі зменшення в них іонів магнію, міді, заліза.
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- 2022
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9. Practical Point-in-Polygon Tests Using CSG Representations of Polygons
- Author
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Walker, Robert J., Snoeyink, Jack, Goos, Gerhard, editor, Hartmanis, Juris, editor, van Leeuwen, Jan, editor, Goodrich, Michael T., editor, and McGeoch, Catherine C., editor
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- 1999
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10. Optimized calculation of adsorption process through the nozzle adsorber by the cell model method
- Author
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Oksana Onyshchuk
- Subjects
теплові процеси ,математична модель ,trapezoid method ,adsorption ,cell model ,адсорбція ,метод трапеції ,thermal processes ,коміркова модель ,mathematical model ,MathCAD - Abstract
В статті показано оптимізовану модель адсорбції через насадковий адсорбер в ізотермічних умовах. Розглянуто теоретичні розрахунки кінетики адсорбції, часу перебування потоку в насадковому адсорбері, часу захисної дії шару адсорбенту, середньої швидкості процесу адсорбції. Проедставлено в граничних умовах диференціальне рівняння адсорбційного процесу в ізотермічних умовах. Крім того, визначено кількість теплоти згідно з законом Ленгмюра при адсорбції на активованому вугіллі, та, використовуючи рівняння Трутона, визначено залежність кількості тепла, що поглинається, від температури. Наведено математичну модель адсорбційного процесу, що досліджувалась із застосуванням методу коміркової моделі та програмного забезпечення. Використовуючи пакет прикладних програм MathCAD та рівняння Ленгмюра, ця модель розв’язана шляхом порівняння необхідної кількості комірок n, яка була визначена як її основний параметр. На основі експериментальної кривої зроблено припущення про можливий вигляд коміркової моделі адсорбційного процесу і проведено математичну обробку цієї кривої. Розраховано отримані значення параметрів моделі, проведено нормування експериментальних даних методом трапецій та перевірку моделі на адекватність. Вивчено процес обміну іонів з одинаковим зарядом, який проходить між адсорбентом і адсорбатом в точно еквівалентних співвідношеннях, для того щоб пом’якшити воду, яка призначена для виготовлення безалкогольних і алкогольних напоїв, виноматеріалів, оскільки смакові якості цих продуктів поліпшуються в разі зменшення в них іонів магнію, міді, заліза. This paper considers the main theoretical calculations of adsorption kinetics, time of the flow in the nozzle adsorber, time of protective action of the adsorbent layer, average speed of adsorption process and the differential equation of the adsorption process according to initial and boundary conditions. Graphically, C-curve has been obtained, which is presented in dimensionless coordinates and demonstrates a mathematical model of adsorption process. The optimal number of cells is calculated by comparing the experimentally obtained response curve with the curves calculated according to the equation of the cell model at different values. In addition, the amount of heat according to the Langmuir's law for adsorption on activated carbon and the dependence of the amount of heat adsorbed on temperature using the Truton's equation have been determined. A mathematical model of the adsorption process, which has been studied using the cell model method and software, is presented. Using the MathCAD application package and the Langmuir's equation, this model has been solved by comparing the required number of cells n, which is defined as its main parameter. Based on the experimental curve, an assumption is made about the possible form of the cell model of adsorption process and mathematical processing of this curve is performed. The obtained values of model parameters have been calculated, the experimental data have been normalized by the trapezoidal method and the model has been tested for adequacy. The process of exchange of ions with the same charge, which takes place between the adsorbent and the adsorbate in exactly equivalent proportions in order to soften the water intended for the production of soft and alcoholic beverages, wine materials, is studied, as the taste of these products improves with the reduction of magnesium, copper and iron ions. Problems of mathematical modeling of adsorption processes in inhomogeneous media and methods of constructing mathematical problems of such models require further study and have the prospect of further research.
- Published
- 2022
11. Two Improvements of an Operational Two-Layer Model for Terrestrial Surface Heat Flux Retrieval
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Jun Xia, Shaohui Chen, Xiaomin Sun, Hongbo Su, Jing Tian, and Renhua Zhang
- Subjects
Two-layer model ,surface evapotranspiration ,surface energy balance ,Bowen Radio ,trapezoid method ,Chemical technology ,TP1-1185 - Abstract
In order to make the prediction of land surface heat fluxes more robust, two improvements were made to an operational two-layer model proposed previously by Zhang. These improvements are: 1) a surface energy balance method is used to determine the theoretical boundary lines (namely ‘true wet/cool edge’ and ‘true dry/warm edge’ in the trapezoid) in the scatter plot for the surface temperature versus the fractional vegetation cover in mixed pixels; 2) a new assumption that the slope of the Tm – f curves is mainly controlled by soil water content is introduced. The variables required by the improved method include near surface vapor pressure, air temperature, surface resistance, aerodynamic resistance, fractional vegetation cover, surface temperature and net radiation. The model predictions from the improved model were assessed in this study by in situ measurements, which show that the total latent heat flux from the soil and vegetation are in close agreement with the in situ measurement with an RMSE (Root Mean Square Error) ranging from 30 w/m2~50 w/m2,which is consistent with the site scale measurement of latent heat flux. Because soil evaporation and vegetation transpiration are not measured separately from the field site, in situ measured CO2 flux is used to examine the modeled λEveg. Similar trends of seasonal variations of vegetation were found for the canopy transpiration retrievals and in situ CO2 flux measurements. The above differences are mainly caused by 1) the scale disparity between the field measurement and the MODIS observation; 2) the non-closure problem of the surface energy balance from the surface fluxes observations themselves. The improved method was successfully used to predict the component surface heat fluxes from the soil and vegetation and it provides a promising approach to study the canopy transpiration and the soil evaporation quantitatively during the rapid growing season of winter wheat in northern China.
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- 2008
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12. ГРАФОАНАЛІТИЧНИЙ МЕТОД ВИЗНАЧЕННЯ КОМПЛЕКСНОГО ПОКАЗНИКА ЯКОСТІ ОБ’ЄКТІВ КВАЛІМЕТРІЇ
- Author
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Cherniak, Olena, Sorocolat, Nataliia, and Kanytska, Iryna
- Subjects
об’єкт кваліметрії ,показник якості ,математичні залежності ,метод прямокутників ,метод трапецій ,объект квалиметрии ,показатель качества ,математические зависимости ,метод прямоугольников ,метод трапеций ,qualimetry object ,quality indicator ,mathematical dependencies ,rectangle method ,trapezoid method - Abstract
The subject of research in the article is a method for determining a complex quality indicator of qualimetry objects that have quality indicators with different units of measurement. The purpose of the work is proposing a method for determining a complex quality indicator of multicriteria objects of qualimetry, using integration methods. The article solves the following task: to investigate the possibility of assessing the quality of qualimetry objects by graph analytical method, ie to apply the principle of determining the area and volume under curved surfaces both on the plane and in space, created by combining estimates of unit quality indicators on dimensionless scale. The following methods are used: mathematical statistics; qualimetry. The following results were obtained: the analysis of scientific literature on quality assessment of qualimetry objects in terms of existing mathematical relationships between the measured quality indicators and their assessment on a dimensionless scale was carried out. It was shown that, as a rule, mathematical dependences are nonlinear and their research is reduced to the development of universal methods that could be applied to objects of qualimetry, regardless of their nature, complexity, importance, etc. Research that involves nonlinear relationships between measured quality scores and their estimates on a dimensionless scale should be based on quality ideology and have a physical explanation. Having single quality indicators in a single (dimensionless) rating scale, it is proposed to determine a single comprehensive quality indicator of the object of qualimetry using integration methods. It is proposed to find the area under the broken curve, which is built as a result of combining estimates of quality indicators on a dimensionless scale over a period of observations. Since the calculation of definite integrals by the Newton-Leibniz formula is not always possible, to solve practical problems, it is enough to know the approximate value of a certain integral with a given degree of accuracy, so it is proposed to use methods of numerical integration, methods: rectangles and trapezoids. A method for determining a generalized indicator of the quality of the object of qualimetry, which can be considered universal, as it can be used for multi-criteria assessment of the quality of objects of qualimetry of different nature. Conclusions: To determine the complex quality indicator of multicriteria qualimetry objects, it is proposed to apply integration by the method of average rectangles. The method of definition of a complex indicator of quality of object of qualimetry with application of integration which considers receipt of estimations of unit indicators of quality is proposed., Предметом исследования в статье является метод определения комплексного показателя качества объектов квалиметрии, которые имеют показатели качества с различными единицами измерения. Цель работы – предложить метод определения комплексного показателя качества многокритериальных объектов квалиметрии, применяя методы интегрирования. В статье решается следующая задача: исследовать возможность оценивания качества объектов квалиметрии графоаналитическим методом, то есть применить принцип определения площади и объема под криволинейными поверхностями, как на плоскости, так и в пространстве, созданных путем объединения оценок единичных показателей качества на безразмерной шкале. Используются методы: математической статистики; квалиметрии. Получены следующие результаты: проведен анализ научной литературы по вопросам оценки качества объектов квалиметрии в части существующих математических зависимостей между измеренным показателям качества и их оценке на безразмерной шкале. Показано, что, как правило, математические зависимости имеют не линейный характер и их исследования сводятся к разработке универсальных методик, которые можно было бы применять к объектам квалиметрии независимо от их природы, сложности, важности и прочее. Исследования, связанные с нелинейными зависимостями между измеренным показателям качества и их оценками на безразмерной шкале должны базироваться на идеологии качества и иметь физическое объяснение. Имея единичные показатели качества в единой (безразмерной) шкале оценивания, предложено определять единый комплексный показатель качества объекта квалиметрии с применением методов интегрирования. Предложено найти площадь под ломаной кривой, которая строится в результате объединения оценок показателей качества на безразмерной шкале в течение определенного времени наблюдений. Так как вычисление определенных интегралов по формуле Ньютона-Лейбница не всегда возможно, и часто, для решения практических задач, достаточно знать приближенное значение определенного интеграла с заданной степенью точности, поэтому предлагается применять методы численного интегрирования, методы: прямоугольников и трапеций. Предложена методика определения обобщенного показателя качества объекта квалиметрии, которую можно считать универсальной, так как ее можно применять для многокритериального оценивания качества объектов квалиметрии различной природы. Выводы: Для определения комплексного показателя качества многокритериальных объектов квалиметрии предлагается применить интегрирование методом средних прямоугольников. Предложена методика определения комплексного показателя качества объекта квалиметрии с применением интегрирования, которая учитывает получения оценок единичных показателей качества., Предметом дослідження в статті є метод визначення комплексного показника якості об’єктів кваліметрії, які мають показники якості з різними одиницями вимірювання. Мета роботи – запропонування методу визначення комплексного показника якості багатокритеріальних об’єктів кваліметрії, застосовуючи методи інтегрування. В статті вирішується наступне завдання: дослідити можливість оцінювання якості об’єктів кваліметрії графоаналітичним методом, тобто застосувати принцип визначення площі та об’єму під криволінійними поверхнями як на площині, так і в просторі, які створені шляхом об’єднання оцінок одиничних показників якості на безрозмірній шкалі. Використовуються методи: математичної статистики; кваліметрії. Отримано наступні результати: проведено аналіз наукової літератури з питань оцінювання якості об’єктів кваліметрії в частині існуючих математичних залежностей між виміряними показниками якості та їх оцінкою на безрозмірній шкалі. Показано, що, як правило, математичні залежності мають нелінійний характер і їх дослідження зводяться до розроблення універсальних методик, які можна було би застосовувати до об’єктів кваліметрії незалежно від їх природи, складності, важливості та інше. Дослідження, які пов’язані з нелінійними залежностями між виміряними показниками якості та їх оцінками на безрозмірній шкалі повинні базуватися на ідеології якості та мати фізичне пояснення. Маючи одиничні показники якості у єдиній (безрозмірній) шкалі оцінювання, запропоновано визначати єдиний комплексний показник якості об’єкту кваліметрії із застосуванням методів інтегрування. Запропоновано знайти площу під ламаною кривою, яка будується внаслідок об’єднання оцінок показників якості на безрозмірній шкалі протягом певного часу спостережень. Так як обчислення визначених інтегралів за формулою Ньютона-Лейбніца не завжди можливо, то для вирішення практичних завдань, досить знати наближене значення певного інтегралу з заданим ступенем точності, тому пропонується застосовувати методи чисельного інтегрування, методи: прямокутників та трапецій. Запропоновано методику визначення узагальненого показника якості об’єкту кваліметрії, яку можна вважати універсальною, так як її можна застосовувати для багатокритеріального оцінювання якості об’єктів кваліметрії різної природи. Висновки: Для визначення комплексного показника якості багатокритеріальних об’єктів кваліметрії пропонується застосувати інтегрування методом середніх прямокутників. Запропоновано методику визначення комплексного показника якості об’єкту кваліметрії з застосуванням інтегрування, яка враховує отримання оцінок одиничних показників якості.
- Published
- 2020
13. A simple technique for calculation of numerical integration errors for physically meaningful functions.
- Author
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Sujecki, Slawomir
- Abstract
A simple technique for calculation of numerical integration errors for physically meaningful functions is presented. In this paper, first the function classes are introduced that relate a function studied directly to a particular physical problem. The matrix elements defining a particular class of functions are then directly incorporated into the error formula. The proposed technique relies on the extension of the concept of the Taylor series. Since the standard Taylor series can be used for calculating the errors for smooth functions, in this paper the behaviour of the error in the immediate vicinity of discontinuity is considered only. The extended Taylor series is obtained by performing the Taylor series expansion on both sides of the discontinuity, using a matrix to describe the behaviour of the function at the discontinuity position and finally summing up all terms proportional to the function value and of all its derivatives. For illustration, several basic classes of physically meaningful functions are introduced and the extended Taylor series is derived. The series is then used to calculate the local error of the numerical integration. The numerical results obtained confirm the accuracy of the derived formulae. [ABSTRACT FROM AUTHOR]
- Published
- 2014
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14. Multispectral Optical Remote Sensing for Water-Leak Detection.
- Author
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Krapez, Jean-Claude, Sanchis Muñoz, Javier, Mazel, Christophe, Chatelard, Christian, Déliot, Philippe, Frédéric, Yves-Michel, Barillot, Philippe, Hélias, Franck, Barba Polo, Juan, Olichon, Vincent, Serra, Guillaume, Brignolles, Céline, Carvalho, Alexandra, Carreira, Duarte, Oliveira, Anabela, Alves, Elsa, Fortunato, André B., Azevedo, Alberto, Benetazzo, Paolo, and Bertoni, Alessandro
- Subjects
- *
OPTICAL remote sensing , *WATER leakage , *WATER distribution , *PONDS , *MARITIME shipping , *NATURAL resources - Abstract
Water losses from water distribution means have a high environmental impact in terms of natural resource depletion (water, energy, ecosystems). This work aims to develop an optical airborne surveillance service for the detection of water leaks (WADI—Water-tightness Airborne Detection Implementation) to provide water utilities with adequate and timely information on leaks in water transportation mains outside urban areas. Firstly, a series of measurement campaigns were performed with two hyperspectral cameras and a thermal infrared camera in order to select the most appropriate wavelengths and combinations thereof for best revealing high moisture areas, which are taken as a proxy for water leakage. The Temperature-Vegetation-Index method (T-VI, also known as Triangle/Trapezoid method) was found to provide the highest contrast-to-noise ratio. This preliminary work helped select the most appropriate onboard instrumentation for two types of aerial platforms, manned (MAV) and unmanned (UAV). Afterwards, a series of measurement campaigns were performed from 2017 to 2019 in an operational environment over two water distribution networks in France and Portugal. Artificial leaks were introduced and both remote sensing platforms successfully detected them when excluding the unfavorable situations of a recent rain event or high vegetation presence. With the most recent equipment configuration, known and unknown real leaks in the overflown part of a water transportation network in Portugal have been detected. A significant number of false alarms were also observed which were due either to natural water flows (groundwater exfiltration, irrigation runoff and ponds) or to vegetation-cover variability nearby water-distribution nodes. Close interaction with the water utilities, and ancillary information like topographic factors (e.g., slope orientation), are expected to reduce the false alarm rates and improve WADI's methodology performance. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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15. Bifurcation equations for periodic orbits of implicit discrete dynamical systems
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Oliveira, Henrique M.
- Published
- 2017
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16. Fast algorithm for multiple time-scale simulation of power system using parallel processing.
- Author
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Harada, Yuji and Oyama, Tsutomu
- Subjects
- *
ELECTRIC power systems , *SIMULATION methods & models , *PARALLEL processing , *ALGORITHMS , *ELECTRONIC data processing , *ELECTRICAL engineering - Abstract
Power system analysis is the basis of operation and planning. Since power systems are very large and complex, however, long computation time is required for the analysis. Development of a fast calculation method for stability analysis is desirable. Recently, the method using multiple time-scale numerical integration algorithm was developed for analyzing long-term dynamics. This method has the problem of calculation time since the coefficient matrix is very large. It is expected that calculation time can be shortened using parallel processing. In order to increase the efficiency of parallel processing, the coefficient matrix must be divided since solution of a set of linear equations is the main part of stability analysis. In this paper, coefficient matrix is converted into BBDF matrix for effective calculation of parallel processing. Each subnetwork block can be divided again since it is sparse. The algorithm discussed in this paper was implemented on the nCUBE2S parallel processing computer system. The computing time is measured so that it can be compared to the computer time of a single-processor system. © 1997 Scripta Technica, Inc. Electr Eng Jpn, 120(4): 14–22, 1997 [ABSTRACT FROM AUTHOR]
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- 1997
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17. Estimation of Surface Soil Moisture from Thermal Infrared Remote Sensing Using an Improved Trapezoid Method
- Author
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Jun Qin, Di Long, Guanghua Qin, Yuting Yang, Bing Liu, Okke Batelaan, and Huade Guan
- Subjects
trapezoid method ,Land surface temperature ,Visual interpretation ,thermal infrared remote sensing ,surface soil moisture ,Tibet Plateau ,Vegetation cover ,Field capacity ,Data assimilation ,MODIS ,Thermal infrared remote sensing ,General Earth and Planetary Sciences ,Environmental science ,lcsh:Q ,Moderate-resolution imaging spectroradiometer ,lcsh:Science ,Water content ,Remote sensing - Abstract
Surface soil moisture (SM) plays a fundamental role in energy and water partitioning in the soil–plant–atmosphere continuum. A reliable and operational algorithm is much needed to retrieve regional surface SM at high spatial and temporal resolutions. Here, we provide an operational framework of estimating surface SM at fine spatial resolutions (using visible/thermal infrared images and concurrent meteorological data) based on a trapezoidal space defined by remotely sensed vegetation cover (Fc) and land surface temperature (LST). Theoretical solutions of the wet and dry edges were derived to achieve a more accurate and effective determination of the Fc/LST space. Subjectivity and uncertainty arising from visual examination of extreme boundaries can consequently be largely reduced. In addition, theoretical derivation of the extreme boundaries allows a per-pixel determination of the VI/LST space such that the assumption of uniform atmospheric forcing over the entire domain is no longer required. The developed approach was tested at the Tibetan Plateau Soil Moisture/Temperature Monitoring Network (SMTMN) site in central Tibet, China, from August 2010 to August 2011 using Moderate Resolution Imaging Spectroradiometer (MODIS) Terra images. Results indicate that the developed trapezoid model reproduced the spatial and temporal patterns of observed surface SM reasonably well, with showing a root-mean-square error of 0.06 m3·m−3 at the site level and 0.03 m3·m−3 at the regional scale. In addition, a case study on 2 September 2010 highlighted the importance of the theoretically calculated wet and dry edges, as they can effectively obviate subjectivity and uncertainties in determining the Fc/LST space arising from visual interpretation of satellite images. Compared with Land Surface Models (LSMs) in Global Land Data Assimilation System-1, the remote sensing-based trapezoid approach gave generally better surface SM estimates, whereas the LSMs showed systematic underestimation. Sensitivity analyses suggested that the trapezoid method is most sensitive to field capacity and temperature but less sensitive to other meteorological observations and parameters.
- Published
- 2015
18. Accelerating convergence for backward Euler and trapezoid time discretization schemes
- Author
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Osman Raşit Işık and Tarkan Öner
- Subjects
Time relaxation ,lcsh:T57-57.97 ,lcsh:Mathematics ,Trapezoid method ,lcsh:Applied mathematics. Quantitative methods ,Accelerating convergence ,lcsh:QA1-939 ,Backward-Euler method - Abstract
In this study, we introduce two algorithms to numerically solve any initial value problem (IVP). These algorithms depend on time relaxation model (TRM) which is obtained adding a time relaxation term into IVP. Discretizing TRM by using backward Euler (BE) method gives the first algorithm. Similarly, the second algorithm is followed by using trapezoid (TR) time stepping scheme . Under some conditions, the first algorithm increases the order of convergence from one to two and the second one increases the order from two to three. Thus, more accurate results can be obtained. To verify the accuracy of the methods, they are applied to some numerical examples. Numerical results overlap with the theoretical results.
- Published
- 2014
19. Two Improvements of an Operational Two-Layer Model for Terrestrial Surface Heat Flux Retrieval
- Author
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Jing Tian, Renhua Zhang, Shaohui Chen, Hongbo Su, Xiaomin Sun, and Jun Xia
- Subjects
Canopy ,Bowen Radio ,trapezoid method ,Meteorology ,Two-layer model ,surface evapotranspiration ,surface energy balance ,Vegetation ,lcsh:Chemical technology ,Atmospheric sciences ,Biochemistry ,Article ,Atomic and Molecular Physics, and Optics ,Analytical Chemistry ,Flux (metallurgy) ,Latent heat ,Evapotranspiration ,Soil water ,Environmental science ,lcsh:TP1-1185 ,Electrical and Electronic Engineering ,Water-use efficiency ,Instrumentation ,Transpiration - Abstract
In order to make the prediction of land surface heat fluxes more robust, two improvements were made to an operational two-layer model proposed previously by Zhang. These improvements are: 1) a surface energy balance method is used to determine the theoretical boundary lines (namely ‘true wet/cool edge’ and ‘true dry/warm edge’ in the trapezoid) in the scatter plot for the surface temperature versus the fractional vegetation cover in mixed pixels; 2) a new assumption that the slope of the Tm – f curves is mainly controlled by soil water content is introduced. The variables required by the improved method include near surface vapor pressure, air temperature, surface resistance, aerodynamic resistance, fractional vegetation cover, surface temperature and net radiation. The model predictions from the improved model were assessed in this study by in situ measurements, which show that the total latent heat flux from the soil and vegetation are in close agreement with the in situ measurement with an RMSE (Root Mean Square Error) ranging from 30 w/m2~50 w/m2,which is consistent with the site scale measurement of latent heat flux. Because soil evaporation and vegetation transpiration are not measured separately from the field site, in situ measured CO2 flux is used to examine the modeled λEveg. Similar trends of seasonal variations of vegetation were found for the canopy transpiration retrievals and in situ CO2 flux measurements. The above differences are mainly caused by 1) the scale disparity between the field measurement and the MODIS observation; 2) the non-closure problem of the surface energy balance from the surface fluxes observations themselves. The improved method was successfully used to predict the component surface heat fluxes from the soil and vegetation and it provides a promising approach to study the canopy transpiration and the soil evaporation quantitatively during the rapid growing season of winter wheat in northern China.
- Published
- 2008
20. Adjoint estimation using direct transcription multipliers: compressed trapezoidal method
- Author
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Engelsone, Anna and Campbell, Stephen L.
- Published
- 2008
- Full Text
- View/download PDF
21. Two Improvements of an Operational Two-Layer Model for Terrestrial Surface Heat Flux Retrieval.
- Author
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Zhang R, Tian J, Su H, Sun X, Chen S, and Xia J
- Abstract
In order to make the prediction of land surface heat fluxes more robust, two improvements were made to an operational two-layer model proposed previously by Zhang. These improvements are: 1) a surface energy balance method is used to determine the theoretical boundary lines (namely 'true wet/cool edge' and 'true dry/warm edge' in the trapezoid) in the scatter plot for the surface temperature versus the fractional vegetation cover in mixed pixels; 2) a new assumption that the slope of the T
m - f curves is mainly controlled by soil water content is introduced. The variables required by the improved method include near surface vapor pressure, air temperature, surface resistance, aerodynamic resistance, fractional vegetation cover, surface temperature and net radiation. The model predictions from the improved model were assessed in this study by in situ measurements, which show that the total latent heat flux from the soil and vegetation are in close agreement with the in situ measurement with an RMSE (Root Mean Square Error) ranging from 30 w/m²~50 w/m²,which is consistent with the site scale measurement of latent heat flux. Because soil evaporation and vegetation transpiration are not measured separately from the field site, in situ measured CO₂ flux is used to examine the modeled λEveg . Similar trends of seasonal variations of vegetation were found for the canopy transpiration retrievals and in situ CO₂ flux measurements. The above differences are mainly caused by 1) the scale disparity between the field measurement and the MODIS observation; 2) the non-closure problem of the surface energy balance from the surface fluxes observations themselves. The improved method was successfully used to predict the component surface heat fluxes from the soil and vegetation and it provides a promising approach to study the canopy transpiration and the soil evaporation quantitatively during the rapid growing season of winter wheat in northern China.- Published
- 2008
- Full Text
- View/download PDF
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