We study diffusion-reaction-advection models describing population dynamics of aquatic organisms subject to a constant drift, with reflecting upstream and outflow downstream boundary conditions. We consider three different models: single logistically growing species, two and three competing species. In the case of a single population, we determine conditions for existence, uniqueness and stability of non-trivial steady-state solutions. We analyze the dependence of such solutions on advection speed, growth rate and length of the habitat. Such analysis offers a possible explanation of the "drift paradox" in our context. We also introduce a spatially implicit ODE (nonspatial approximation) model which captures the essential behavior of the original PDE model. In the case of two competing species, we use a diffusion-advection version of the Lotka-Volterra competition model. Combining numerical and analytical techniques, in both the spatial and nonspatial approximation settings, we describe the effect of advection on competitive outcomes. Finally, in the case of three species, we use the nonspatial approximation approach to analyze and classify the possible scenarios as we change the flow speed in the habitat.

We study diffusion-reaction-advection models describing population dynamics of aquatic organisms subject to a constant drift, with reflecting upstream and outflow downstream boundary conditions. We consider three different models: single logistically growing species, two and three competing species. In the case of a single population, we determine conditions for existence, uniqueness and stability of non-trivial steady-state solutions. We analyze the dependence of such solutions on advection speed, growth rate and length of the habitat. Such analysis offers a possible explanation of the "drift paradox" in our context. We also introduce a spatially implicit ODE (nonspatial approximation) model which captures the essential behavior of the original PDE model. In the case of two competing species, we use a diffusion-advection version of the Lotka-Volterra competition model. Combining numerical and analytical techniques, in both the spatial and nonspatial approximation settings, we describe the effect of advection on competitive outcomes. Finally, in the case of three species, we use the nonspatial approximation approach to analyze and classify the possible scenarios as we change the flow speed in the habitat.

We study diffusion-reaction-advection models describing population dynamics of aquatic organisms subject to a constant drift, with reflecting upstream and outflow downstream boundary conditions. We consider three different models: single logistically growing species, two and three competing species. In the case of a single population, we determine conditions for existence, uniqueness and stability of non-trivial steady-state solutions. We analyze the dependence of such solutions on advection speed, growth rate and length of the habitat. Such analysis offers a possible explanation of the "drift paradox" in our context. We also introduce a spatially implicit ODE (nonspatial approximation) model which captures the essential behavior of the original PDE model. In the case of two competing species, we use a diffusion-advection version of the Lotka-Volterra competition model. Combining numerical and analytical techniques, in both the spatial and nonspatial approximation settings, we describe the effect of advection on competitive outcomes. Finally, in the case of three species, we use the nonspatial approximation approach to analyze and classify the possible scenarios as we change the flow speed in the habitat.

Made available in DSpace on 2014-06-11T19:33:39Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-04-16Bitstream added on 2014-06-13T19:04:52Z : No. of bitstreams: 1 ferreira_jop_dr_jabo.pdf: 1268842 bytes, checksum: 715de8aae3de8bec81a7a441b78ef9c9 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Este experimento foi conduzido em Alvorada do Gurguéia, situada no vale do rio Gurguéia, estado do Piauí, localizado na latitude de 8º 26’ S, longitude 43º 47’ W e altitude de 251 m. Os objetivos deste estudo foram determinar a evapotranspiração (ETc) e os coeficientes de cultura (Kc) da melancieira irrigada por gotejamento. A evapotranspiração de referência (ETo) foi determinada diariamente por dez modelos de estimativa, com parte dos elementos climáticos obtidos em uma estação agrometeorológica automática localizada no centro da área experimental. Os modelos foram: Penman-Monteith-FAO56 (PMFAO56), Penman-Monteith-ASCE (PMASCE), Hargreaves-Samani (HS), Priestley-Taylor (PT), Camargo (CAM), Thornthwaite original (THW), Thornthwaite com correção para a temperatura efetiva calculada como uma função da temperatura média e da amplitude diária e valores de K=0,69 (THW2(0,69)) e K=0,72 (THW3(0,72)) e Thornthwaite com a mesma temperatura efetiva corrigida para o fotoperíodo e valores de K=0,69 (THW2(0,69)) e K=0,72 (THW2(0,72)). A ETc foi medida a partir de três lisímetros de pesagem localizados no centro da área experimental. O desempenho dos métodos foi avaliado utilizando regressão linear simples e diferentes índices: raiz quadrada do erro médio quadrático (RMES), erro percentual absoluto médio (MAPE), índice de concordância (d) e o teste de Scott-Knott, usando como padrão EToPMFAO56. O modelo PMASCE foi semelhante ao PMFAO56, com RMES = 0,05 mm dia-1, MAPE = 0,74%, d = 1,0 e R2 = 0,99. Apenas os modelos, THW2(0,69) e THW3(0,72), não apresentaram médias gerais significativamente diferentes de PMFAO56. Os valores médios de Kc obtidos com o PMFAO56 foram 0,44; 1,58 e 1,28 para os estádios inicial, intermediário e final, respectivamente. Valores estes, assim como os de todos os demais métodos de estimativa de ET0 testados, foram superiores aos obtidos... / This experiment was carried out at the Gurguéia river valley, state of Piauí, Brazil, located at 8º 26’ S latitude, 43º 47’ W longitude an altitude of 251 m. The objectives of this study were to determine the evapotranspiration (ETc) and crop coefficients (Kc) of watermelon by drip irrigated. Reference evapotranspiration (ETo) was daily determined by ten models of the estimation, with part climatics variable obtained an automatic agrometeorological station located in the center of the experimental area. The models were: Penman-Monteith-FAO56 (PMFAO56), Penman- Monteith-ASCE (PMASCE), Hargreaves-Samani (HS), Priestley-Taylor (PT), Camargo (CAM), original Thornthwaite (THW), Thornthwaite with correction for effective temperature computed as a function of the average temperature and of the daily amplitude and values of K=0,69 (THW2(0,69)) and K=0,72 (THW3(0,72)) and Thornthwaite with the same effective temperature corrected for the photoperiod and value of K=0,69 (THW2(0,69)) and K=0,72 (THW3(0,72)). ETc was measured from three weighing lysimeters located in the center of the experimental area. Methods performance was evaluated by using single linear regression and different indices, root mean square error (RMES), mean absolute percentage error (MAPE), index of agreement (d) and Scott-Knott test, using how standard PMFAO56. The model PMASCE was resembling to PMFAO56, with RMES = 0,05 mm dia-1, MAPE = 0,74%, d = 1,0 and R² = 0,99. Only the models, THW2(0,69) e THW3(0,72), not presents generals average significant difference of the PMFAO56. The Kc values obtained were 0,44, 1,58 and 1,28 for the initial, intermediate and final stages, respectively. This values, thus as of the every methods of estimation of the ETo tested, was upper to obtained for watermelon in the Bulletin 56 of irrigation and drainage of the FAO, principally for the intermediate and final stages... (Complete abstract click electronic access below)

Resumo: Este experimento foi conduzido em Alvorada do Gurguéia, situada no vale do rio Gurguéia, estado do Piauí, localizado na latitude de 8º 26' S, longitude 43º 47' W e altitude de 251 m. Os objetivos deste estudo foram determinar a evapotranspiração (ETc) e os coeficientes de cultura (Kc) da melancieira irrigada por gotejamento. A evapotranspiração de referência (ETo) foi determinada diariamente por dez modelos de estimativa, com parte dos elementos climáticos obtidos em uma estação agrometeorológica automática localizada no centro da área experimental. Os modelos foram: Penman-Monteith-FAO56 (PMFAO56), Penman-Monteith-ASCE (PMASCE), Hargreaves-Samani (HS), Priestley-Taylor (PT), Camargo (CAM), Thornthwaite original (THW), Thornthwaite com correção para a temperatura efetiva calculada como uma função da temperatura média e da amplitude diária e valores de K=0,69 (THW2(0,69)) e K=0,72 (THW3(0,72)) e Thornthwaite com a mesma temperatura efetiva corrigida para o fotoperíodo e valores de K=0,69 (THW2(0,69)) e K=0,72 (THW2(0,72)). A ETc foi medida a partir de três lisímetros de pesagem localizados no centro da área experimental. O desempenho dos métodos foi avaliado utilizando regressão linear simples e diferentes índices: raiz quadrada do erro médio quadrático (RMES), erro percentual absoluto médio (MAPE), índice de concordância (d) e o teste de Scott-Knott, usando como padrão EToPMFAO56. O modelo PMASCE foi semelhante ao PMFAO56, com RMES = 0,05 mm dia-1, MAPE = 0,74%, d = 1,0 e R2 = 0,99. Apenas os modelos, THW2(0,69) e THW3(0,72), não apresentaram médias gerais significativamente diferentes de PMFAO56. Os valores médios de Kc obtidos com o PMFAO56 foram 0,44; 1,58 e 1,28 para os estádios inicial, intermediário e final, respectivamente. Valores estes, assim como os de todos os demais métodos de estimativa de ET0 testados, foram superiores aos obtidos... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This experiment was carried out at the Gurguéia river valley, state of Piauí, Brazil, located at 8º 26' S latitude, 43º 47' W longitude an altitude of 251 m. The objectives of this study were to determine the evapotranspiration (ETc) and crop coefficients (Kc) of watermelon by drip irrigated. Reference evapotranspiration (ETo) was daily determined by ten models of the estimation, with part climatics variable obtained an automatic agrometeorological station located in the center of the experimental area. The models were: Penman-Monteith-FAO56 (PMFAO56), Penman- Monteith-ASCE (PMASCE), Hargreaves-Samani (HS), Priestley-Taylor (PT), Camargo (CAM), original Thornthwaite (THW), Thornthwaite with correction for effective temperature computed as a function of the average temperature and of the daily amplitude and values of K=0,69 (THW2(0,69)) and K=0,72 (THW3(0,72)) and Thornthwaite with the same effective temperature corrected for the photoperiod and value of K=0,69 (THW2(0,69)) and K=0,72 (THW3(0,72)). ETc was measured from three weighing lysimeters located in the center of the experimental area. Methods performance was evaluated by using single linear regression and different indices, root mean square error (RMES), mean absolute percentage error (MAPE), index of agreement (d) and Scott-Knott test, using how standard PMFAO56. The model PMASCE was resembling to PMFAO56, with RMES = 0,05 mm dia-1, MAPE = 0,74%, d = 1,0 and R² = 0,99. Only the models, THW2(0,69) e THW3(0,72), not presents generals average significant difference of the PMFAO56. The Kc values obtained were 0,44, 1,58 and 1,28 for the initial, intermediate and final stages, respectively. This values, thus as of the every methods of estimation of the ETo tested, was upper to obtained for watermelon in the Bulletin 56 of irrigation and drainage of the FAO, principally for the intermediate and final stages... (Complete abstract click electronic access below) / Orientador: Luiz Carlos Pavani / Coorientador: Edson Alves Bastos / Banca: Aderson Soares de Andrade Junior / Banca: Regina Célia de Matos Pires / Banca: Jose Renato Zanini / Banca: Mario Benincasa / Doutor

We study diffusion-reaction-advection models describing population dynamics of aquatic organisms subject to a constant drift, with reflecting upstream and outflow downstream boundary conditions. We consider three different models: single logistically growing species, two and three competing species. In the case of a single population, we determine conditions for existence, uniqueness and stability of non-trivial steady-state solutions. We analyze the dependence of such solutions on advection speed, growth rate and length of the habitat. Such analysis offers a possible explanation of the "drift paradox" in our context. We also introduce a spatially implicit ODE (nonspatial approximation) model which captures the essential behavior of the original PDE model. In the case of two competing species, we use a diffusion-advection version of the Lotka-Volterra competition model. Combining numerical and analytical techniques, in both the spatial and nonspatial approximation settings, we describe the effect of advection on competitive outcomes. Finally, in the case of three species, we use the nonspatial approximation approach to analyze and classify the possible scenarios as we change the flow speed in the habitat.

Em ambientes costeiros, a variabilidade da biomassa de fitoplâncton é dirigida por forçantes físicas locais que apresentam distintas escalas temporais em ocorrência, intensidade e durabilidade. No canal de São Sebastião, ambiente advectivo, parte-se do pressuposto de que qualquer adição da biomassa de fitoplâncton não se deve ao crescimento local, mas ao transporte de células fitoplanctônicas movidas pelas correntes guiadas a ventos e marés. Dessa maneira, o objetivo central deste trabalho é analisar a variabilidade em alta frequência das variações da biomassa fitoplanctônica e investigar suas relações temporais com a intensidade e direção dos ventos e a amplitude das marés. Em média, o acúmulo de clorofila é estável no tempo, com curtos episódios de lento aumento e diminuições bruscas da biomassa fitoplanctônica, sendo os valores encontrados relativamente baixos, característicos de ambientes oligomesotróficos. Análises espectrais da série temporal da concentração de clorofila-a e da altura da maré revelaram alta correlação entre as duas séries durante as marés de sizígia, com periodicidades de aproximadamente 12 e 24 horas. Em relação à direção e intensidade do vento, o espectro cruzado de ondaletas apresentou áreas de forte correlação com a clorofila-a e periodicidades dominantes de três dias. Além disso, observou-se que ventos vindos do quadrante norte/nordeste carregam águas com maiores concentrações de materiais particulados ou detritos. / In coastal environments, the dynamics of phytoplankton biomass is driven by local physical forcings that have different time scales in occurrence, intensity and durability. For being an advective environment, it is normally assumed that any positive change in phytoplankton biomass in the São Sebastião Channel is not due to local growth, but to the transport of phytoplankton cells moved by currents associated with winds and tides. Thus, the main objective of this project is to analyze the variability in high-frequency variations of the phytoplankton biomass and investigate their temporal relationships with intensity and direction of winds and high tides. On average, the chlorophyll accumulation is stable over time, with short episodes of slow rise and sudden decreases of phytoplankton biomass and relatively low values, characteristic of oligo-mesotrophic environments. Spectral analysis of the time series of chlorophyll a concentration and tide height showed a high correlation between the two series during the spring tides, and dominant periodicities of about 12 to 24 hours. Regarding direction and intensity of the wind, the cross wavelet spectrum presented strong correlation areas with chlorophyll a and dominant periodicities of 3 days. In addition, it was observed that winds from the north/northeast quadrant carry water with higher concentrations of particulate matter or debris.

Em ambientes costeiros, a variabilidade da biomassa de fitoplâncton é dirigida por forçantes físicas locais que apresentam distintas escalas temporais em ocorrência, intensidade e durabilidade. No canal de São Sebastião, ambiente advectivo, parte-se do pressuposto de que qualquer adição da biomassa de fitoplâncton não se deve ao crescimento local, mas ao transporte de células fitoplanctônicas movidas pelas correntes guiadas a ventos e marés. Dessa maneira, o objetivo central deste trabalho é analisar a variabilidade em alta frequência das variações da biomassa fitoplanctônica e investigar suas relações temporais com a intensidade e direção dos ventos e a amplitude das marés. Em média, o acúmulo de clorofila é estável no tempo, com curtos episódios de lento aumento e diminuições bruscas da biomassa fitoplanctônica, sendo os valores encontrados relativamente baixos, característicos de ambientes oligomesotróficos. Análises espectrais da série temporal da concentração de clorofila-a e da altura da maré revelaram alta correlação entre as duas séries durante as marés de sizígia, com periodicidades de aproximadamente 12 e 24 horas. Em relação à direção e intensidade do vento, o espectro cruzado de ondaletas apresentou áreas de forte correlação com a clorofila-a e periodicidades dominantes de três dias. Além disso, observou-se que ventos vindos do quadrante norte/nordeste carregam águas com maiores concentrações de materiais particulados ou detritos. / In coastal environments, the dynamics of phytoplankton biomass is driven by local physical forcings that have different time scales in occurrence, intensity and durability. For being an advective environment, it is normally assumed that any positive change in phytoplankton biomass in the São Sebastião Channel is not due to local growth, but to the transport of phytoplankton cells moved by currents associated with winds and tides. Thus, the main objective of this project is to analyze the variability in high-frequency variations of the phytoplankton biomass and investigate their temporal relationships with intensity and direction of winds and high tides. On average, the chlorophyll accumulation is stable over time, with short episodes of slow rise and sudden decreases of phytoplankton biomass and relatively low values, characteristic of oligo-mesotrophic environments. Spectral analysis of the time series of chlorophyll a concentration and tide height showed a high correlation between the two series during the spring tides, and dominant periodicities of about 12 to 24 hours. Regarding direction and intensity of the wind, the cross wavelet spectrum presented strong correlation areas with chlorophyll a and dominant periodicities of 3 days. In addition, it was observed that winds from the north/northeast quadrant carry water with higher concentrations of particulate matter or debris.