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

No description available.

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.

Approved for public release; distribution is unlimited / Results of a highly vectorized and multitasked model of the world ocean circulation were analyzed. This model which uses realistic physics, geometry, and forcing on a high-resolution grid, was run on the NCAR Cray X-MP/48 using a robust-diagnostic strategy. Twenty years of model integration using one-half degree horizontal resolution and 20 levels of vertical resolution were accomplished after 200 wall-clock hours at a maximum FORTRAN performance speed of 450 megaflops. Seven key regions of the world ocean were analyzed using an ocean model processor. A representation of the global ocean circulation emerged that compared well with observations and that included strong advective features, fronts, and subtropical meanders. A diagnostic analysis program was developed to analyze meridional heat and volume transports. The results in all basins appear to be reasonable when compared to the results of other studies. For example, an anomalous northward heat transport of 3.8 x 10 to the 14th power W at 30 deg in the South Atlantic compares favorably with the estimate of 4.2 x 10 to the 14th power W at 32 deg S by Bennett (1978) using hydrographic data. The results of simulations conducted in this study can be compared and contrasted against the results of future eddy-resolving simulations. Keywords: Digital simulation, Advection, Heat transport, Meridional volume transport, Oceanographic fronts, Meanders, Thermoclines, Finite difference analysis. Theses. (EDC) / http://archive.org/details/analysisofresult00bart / Lieutenant Commander, United States Naval Reserve

Made available in DSpace on 2016-12-23T14:08:13Z (GMT). No. of bitstreams: 1 Dissertacao de Felipe Patricio das Neves.pdf: 512132 bytes, checksum: d42e56e29214989211674c822342bbea (MD5) Previous issue date: 2009-12-04 / In this work is implemented a numerical model to simulate computationally the distribution of pressures, velocities, temperatures and heat flows in two-dimensional stationary control volumes. The relation between temperatures and velocities is established by the advective-diffusive Equation, using the Dual Reciprocity Boundary Element Method formulation... / Neste trabalho é desenvolvido um modelo numérico para simular computacionalmente a distribuição de pressões, velocidades, temperaturas e fluxos de calor estacionários em volumes de controle bidimensionais. A relação do campo de temperaturas e velocidades é governada pela equação da Difusão-Advecção, resolvida através da formulação com Dupla Reciprocidade do Método dos Elementos de Contorno. Admite-se a lei de Darcy para associar pressão e velocidade, resultando num modelo matemático dado pela Equação de Laplace, no caso linear. Na análise não-linear insere-se a dependência entre do campo de velocidades e as temperaturas, resultando num campo matematicamente representado pela Equação de Poisson. Os resultados da solução desse problema são então implementados no modelo difusivo-advectivo, gerando temperaturas e fluxos de calor

<p>Nedbrytning av organiskt material är en nyckelfaktor som påverkar omvandlingar av de många grundämnen som utgör eller är associerade till just organiskt material. En stor del av nedbrytningen av akvatiskt organiskt material (OM) sker i gränsskiktet mellan sediment och vatten. Eftersom så många biogeokemiska cykler styrs av nedbrytningen av OM är det viktigt att ha kunskap om processer och påverkansfaktorer både på mikro- och makronivå. Mineraliseringshastigheten av OM är en vanligt förekommande mätparameter, men vanligtvis inkluderar mätningarna inte de naturliga processer som kan påverka nedbrytnings-hastigheterna, t.ex. fysiska krafter.</p><p>Syftet med den här studien är att studera mineraliseringshastigheten av det OM som finns naturligt i ytsediment i söt- och brackvatten när det utsätts för fysiska krafter som orsakar förändringar i redox-förhållanden, resuspension eller advektivt porvattenflöde. Fem</p><p>laborativa experiment har utförts för att belysa syftet:</p><p>Åldrat ytsediment från en sötvattens å utsattes för olika redox förhållanden där oxisk respiration, sulfatreduktion respektive metanogenes gynnades. Resultaten visade ingen skillnad i mineraliseringshastighet beroende på behandling. Detta motsäger studier utförda i marina miljöer, där anoxiska förhållanden ger en lägre mineraliseringshastighet än oxiska.</p><p>Vidare gjordes två studier på brackvattensediment där effekten av resuspension var i centrum. Den ena studien fokuserade på frekvens och varaktighet av resuspensionstiderna, den andra på olika typer av sediment. Studierna visade att väldigt korta resuspensionstider med upp till 48 timmars stillhet mellan varje resuspension ökade mineraliseringstakten med fem gånger jämfört med diffusivt utbyte, och mer än dubblerades i jämförelse med kontinuerlig resuspension eller resuspension i långa perioder. Resuspensionen under kort tid var troligen gynnande då resuspension fysiskt stör bildningen av stabila bakteriesamhällen. Mineraliseringshastigheterna i sediment som domineras av väldigt fin, fin eller medium sand visade lika hastigheter, medan grov sand visade en signifikant lägre mineraliseringshastighet. Likheterna mellan de tre första sedimenttyperna kan dock ha påverkats av tillgång på lättnedbrytbart OM då sediment och vatten hämtades in under en algblomning.</p><p>Till sist studerades effekten på mineraliseringshastigheten av advektivt porvattenflöde. Detta gjordes på åldrat sediment dels från en sötvattensbäck dels från en brackvattenstrand. Inget av de två sedimenttyperna visade någon skillnad i mineraliseringshastighet i jämförelse med diffusivt styrda system. Det är i motsats till tidigare marina studier, men är i linje med den första studien, där mineraliseringshastigheten var oberoende av redox-förhållande.</p><p>Den generella slutsatsen från den här studien är nödvändigheten att studera samma aspekter i olika typer av akvatiska system, eftersom responsen verkar vara annorlunda beroende på system, t.ex. söt- brack- och saltvatten. Faktorer som kan förklara de här skillnaderna finns ännu inte, vilket gör att småskaliga studier och modeller blir viktiga verktyg för att utreda detta.</p> / <p>Organic matter mineralisation is a key parameter that affects most other element transformations associated with organic matter. A substantial part of aquatic organic matter (OM) mineralisation takes place at the interface between sediment and water. Understanding OM mineralisation is important at both the micro and macro scales, since it drives many biogeochemical cycles. OM mineralisation rates are widely measured, but generally not all the natural factors possibly affecting the rates, such as physical forcing, are considered.</p><p>This thesis examines the mineralisation rates of indigenous OM in fresh and brackish surface sediments, subjected to different physical forces inducing changed redox conditions, resuspension, and advective pore water flow. Five experiments were performed to this end.</p><p>Aged surface sediment from a freshwater river was subjected to different redox conditions favouring oxic respiration, sulphate reduction, and methanogenesis, respectively. Results indicated no difference in mineralisation rate irrespective of treatment. This contradicts what has been found in marine environments, where anoxic mineralisation rates are lower than oxic ones.</p><p>Further, two studies of resuspension of brackish sediments were performed, one addressing the impact of the frequency and duration of the resuspension events, and the other addressing the impact of resuspension on different types of sediments. The studies found that very brief resuspension events followed by calm periods of up to 48 h increased mineralisation rates by five times compared to diffusion, and more than doubled the rate compared to continuous or long-term resuspension. The short-term events were possibly favoured because resuspension physically disturbs the arrangement of a stable bacteria community. Mineralisation rates on sediments dominated by very fine, fine, or medium-grained sand were the same, while coarse sand displayed a significantly lower rate. The similar rates of the three first sediment types could stem from access to labile OM, due to an ongoing algae bloom when the sediment and water samples were collected.</p><p>Finally, the effect of advective pore water flow on aged sediment from one fresh and one brackish sediment was studied. Neither of the sediments displayed a mineralisation rate different from those occurring in incubations in which only diffusive exchange occurred. This contradicts the findings of previous marine studies, but is in line with the first study, which did not detect different mineralisation rates irrespective of redox conditions.</p><p>The general conclusion is that it is necessary to study the same physical forces in different aquatic environments, since responses appear to differ, for example, between freshwater, brackish, and marine environments. Factors explaining these differences have not yet been expressed, making small-scale studies and modelling a challenge for future research.</p>

Nedbrytning av organiskt material är en nyckelfaktor som påverkar omvandlingar av de många grundämnen som utgör eller är associerade till just organiskt material. En stor del av nedbrytningen av akvatiskt organiskt material (OM) sker i gränsskiktet mellan sediment och vatten. Eftersom så många biogeokemiska cykler styrs av nedbrytningen av OM är det viktigt att ha kunskap om processer och påverkansfaktorer både på mikro- och makronivå. Mineraliseringshastigheten av OM är en vanligt förekommande mätparameter, men vanligtvis inkluderar mätningarna inte de naturliga processer som kan påverka nedbrytnings-hastigheterna, t.ex. fysiska krafter. Syftet med den här studien är att studera mineraliseringshastigheten av det OM som finns naturligt i ytsediment i söt- och brackvatten när det utsätts för fysiska krafter som orsakar förändringar i redox-förhållanden, resuspension eller advektivt porvattenflöde. Fem laborativa experiment har utförts för att belysa syftet: Åldrat ytsediment från en sötvattens å utsattes för olika redox förhållanden där oxisk respiration, sulfatreduktion respektive metanogenes gynnades. Resultaten visade ingen skillnad i mineraliseringshastighet beroende på behandling. Detta motsäger studier utförda i marina miljöer, där anoxiska förhållanden ger en lägre mineraliseringshastighet än oxiska. Vidare gjordes två studier på brackvattensediment där effekten av resuspension var i centrum. Den ena studien fokuserade på frekvens och varaktighet av resuspensionstiderna, den andra på olika typer av sediment. Studierna visade att väldigt korta resuspensionstider med upp till 48 timmars stillhet mellan varje resuspension ökade mineraliseringstakten med fem gånger jämfört med diffusivt utbyte, och mer än dubblerades i jämförelse med kontinuerlig resuspension eller resuspension i långa perioder. Resuspensionen under kort tid var troligen gynnande då resuspension fysiskt stör bildningen av stabila bakteriesamhällen. Mineraliseringshastigheterna i sediment som domineras av väldigt fin, fin eller medium sand visade lika hastigheter, medan grov sand visade en signifikant lägre mineraliseringshastighet. Likheterna mellan de tre första sedimenttyperna kan dock ha påverkats av tillgång på lättnedbrytbart OM då sediment och vatten hämtades in under en algblomning. Till sist studerades effekten på mineraliseringshastigheten av advektivt porvattenflöde. Detta gjordes på åldrat sediment dels från en sötvattensbäck dels från en brackvattenstrand. Inget av de två sedimenttyperna visade någon skillnad i mineraliseringshastighet i jämförelse med diffusivt styrda system. Det är i motsats till tidigare marina studier, men är i linje med den första studien, där mineraliseringshastigheten var oberoende av redox-förhållande. Den generella slutsatsen från den här studien är nödvändigheten att studera samma aspekter i olika typer av akvatiska system, eftersom responsen verkar vara annorlunda beroende på system, t.ex. söt- brack- och saltvatten. Faktorer som kan förklara de här skillnaderna finns ännu inte, vilket gör att småskaliga studier och modeller blir viktiga verktyg för att utreda detta. / Organic matter mineralisation is a key parameter that affects most other element transformations associated with organic matter. A substantial part of aquatic organic matter (OM) mineralisation takes place at the interface between sediment and water. Understanding OM mineralisation is important at both the micro and macro scales, since it drives many biogeochemical cycles. OM mineralisation rates are widely measured, but generally not all the natural factors possibly affecting the rates, such as physical forcing, are considered. This thesis examines the mineralisation rates of indigenous OM in fresh and brackish surface sediments, subjected to different physical forces inducing changed redox conditions, resuspension, and advective pore water flow. Five experiments were performed to this end. Aged surface sediment from a freshwater river was subjected to different redox conditions favouring oxic respiration, sulphate reduction, and methanogenesis, respectively. Results indicated no difference in mineralisation rate irrespective of treatment. This contradicts what has been found in marine environments, where anoxic mineralisation rates are lower than oxic ones. Further, two studies of resuspension of brackish sediments were performed, one addressing the impact of the frequency and duration of the resuspension events, and the other addressing the impact of resuspension on different types of sediments. The studies found that very brief resuspension events followed by calm periods of up to 48 h increased mineralisation rates by five times compared to diffusion, and more than doubled the rate compared to continuous or long-term resuspension. The short-term events were possibly favoured because resuspension physically disturbs the arrangement of a stable bacteria community. Mineralisation rates on sediments dominated by very fine, fine, or medium-grained sand were the same, while coarse sand displayed a significantly lower rate. The similar rates of the three first sediment types could stem from access to labile OM, due to an ongoing algae bloom when the sediment and water samples were collected. Finally, the effect of advective pore water flow on aged sediment from one fresh and one brackish sediment was studied. Neither of the sediments displayed a mineralisation rate different from those occurring in incubations in which only diffusive exchange occurred. This contradicts the findings of previous marine studies, but is in line with the first study, which did not detect different mineralisation rates irrespective of redox conditions. The general conclusion is that it is necessary to study the same physical forces in different aquatic environments, since responses appear to differ, for example, between freshwater, brackish, and marine environments. Factors explaining these differences have not yet been expressed, making small-scale studies and modelling a challenge for future research.

[pt] Estudamos sincronização completa em aneis de mapas logísticos, usando um esquema de acoplamento advectivo-difusivo. O alcance das interações diminui algebricamente com a distância entre mapas, varrendo do caso totalmente conectado ao de primeiros vizinhos, com atualização sincronizada ou com retardo. Estudamos os efeitos do retardo e da advecção separada-mente e combinados. Embora os estudos numéricos tenham sido realizados utilizando o mapa logístico como dinâmica local, alguns resultados analíticos são mais gerais. Na dinâmica síncrona, os estados sincronizados são caóticos, enquanto a presença de atrasos permite a sincronização em órbitas regulares. No entanto, uma forte contribuição de retardos na atualização também pode produzir sincronização caótica. Em todos os casos, as interações de longo alcance favorecem a sincronização, a advecção dificulta a sincronização, e os atrasos podem compensar os efeitos destrutivos da ad-vecção. / [en] We study complete synchronization in rings of logistic maps, using an advection-diffusion coupling scheme. The range of the interactions decays algebraically with distance between maps, sweeping from the totally connected to nearest-neighbor model, with synchronous or delayed lattice update. We studied the effects of delays and advection separately and combined. Although numerical studies were performed using the logistic map as local dynamics, some analytical results are more general. In the synchronous dynamics, synchronized states are chaotic, while the presence of delays allows synchronization in regular orbits. However, a strong contribution of delays in the updating can also produce chaotic synchronization. In all cases, longer interaction range favors synchronization, advection hinders synchronization and delays compensate the destructive effects of advection.

Time splitting is a numerical procedure used in solution of partial differential equations whose solutions allow multiple time scales. Numerical schemes are split for handling the stiffness in equations, i.e. when there are multiple time scales with a few time scales being smaller than the others. When there are such terms with smaller time scales, due to the Courant number restriction, the computational cost becomes high if these terms are treated explicitly. In the present work a nonlinear advective equation is solved numerically using different techniques based on a generalised framework for splitting methods. The nonlinear advective equation was chosen because it has an analytical solution making comparisons with numerical schemes amenable and also because its nonlinearity mimics the equations encountered in atmospheric modelling. Using the nonlinear advective equation as a test bed, an analysis of the splitting methods and their influence on the split solutions has been made. An understanding of influence of splitting schemes requires knowledge of behaviour of unsplit schemes beforehand. Hence a study on unsplit methods has also been made. In the present work, using the nonlinear advective equation, it shown that the three time level schemes have high phase errors and underestimate energy (even though they have a higher order of accuracy in time). It is also found that the leap-frog method, which is used widely in atmospheric modelling, is the worst among examined unsplit methods. The semi implicit method, again a popular splitting method with atmospheric modellers is the worst among examined split methods. Three time-level schemes also need explicit filtering to remove the computational mode. This filtering can have a significant impact on the obtained numerical solutions, and hence three-time level schemes appear to be unattractive in the context of the nonlinear convective equation. Based on this experience, splitting methods for the two-time level schemes is proposed. These schemes realistically capture the phase and energy of the nonlinear advective equation.