O presente trabalho propõe avaliar a habilidade do Modelo Regional Climático, versão 4, (RegCM4) em simular a variabilidade temporal e espacial do sinal associado à propagação da Oscilação de Madden-Julian (OMJ) nos trópicos. A avaliação foi feita através da comparação dos dados observados obtidos do conjunto da Reanálise do ERA-Interim e dos dados simulados pelo RegCM4, para o período de 2005 a 2009. Foram utilizados dados globais diários de precipitação, Radiação de Onda Longa Emergente e componentes zonal do vento em 850 e 200 hPa, provenientes da Reanálise do ERA-Interim, tanto na simulação, quanto nos dados observados. Como condição inicial do modelo, optou-se pela utilização da banda tropical, cujo principal aspecto é o de simular características tanto da circulação quanto dos padrões de precipitação tropicais. Para a validação do modelo, foi utilizada a precipitação diária do Global Precipitation Climatology Project (GPCP). Todos os dados foram filtrados na escala de 30-60 dias a fim de se observar o sinal referente à OMJ. A análise dos padrões globais de precipitação e Radiação de Onda Longa (ROL), após filtragem, permitiu a seleção de cinco áreas, com sinais associados à OMJ, sendo elas: África (AFR), Indonésia (IND), Norte da América do Sul (NAS), Nordeste brasileiro (NEB) e Sudeste brasileiro (SEB). A área NEB, apresentou valores de correlação linear de 0,63 e 0,32 para a anomalia e anomalia de ROL filtrada, respectivamente. Já a área SEB, apresentou valores de correlação linear de 0,30 e 0,54, para a anomalia e anomalia de ROL filtrada. O BIAS calculado entre o modelo e a precipitação do GPCP, para as estações secas (MAI-OUT) e chuvosas (NOV-ABR) mostrou que para a América do Sul, Sul do continente Africano e Índico, o modelo superestima os valores de precipitação do GPCP nas duas estações do ano. Quanto à análise multivariada entre a ROL, vento zonal em 850 e 200 hpa a comparação com o obtido para os dados do Era-Interim, a Empirical Orthogonal Function (EOF1) aplicada aos dados do RegCM4 apresenta convecção e inibição da convecção em áreas distintas da faixa longitudinal entre 15º N e 15º S. Enquanto os valores mínimos de EOF1 para ROL (intensificação da convecção) do Era-Interim são observados próximo a 90º L, os valores mínimos de ROL para os dados do RegCM4 são observados próximos à 120º O, com defasagem longitudinal de 30º. L, enquanto os valores máximos da EOF1 para ROL (inibição de convecção) do Era-Interim são observados próximo a 150º L, os valores máximos para os dados simulados pelo RegCM4 são observados próximos à 60º L, com uma defasagem longitudinal de 90°. / The present work proposes to evaluate the ability of the Regional Climatic Model (RegCM4) to simulate the temporal and spatial variability of the signal associated with the propagation of the Madden-Julian Oscillation in the tropics. The evaluation was done by comparing the observed data obtained from the Reanalysis of the ERA-Interim and the data simulated by RegCM4, for the period from 2005 to 2009. Daily global data were used for precipitation, Emergent Long Wave Radiation and zonal wind components at 850 and 200 hPa from the ERA-Interim Reanalysis, both in the simulation and in the observed data. As initial conditions of the model, we chose to use the tropical band, whose main characteristic is to simulate the circulation and the tropical precipitation patterns. The validation of the model was performed with the daily precipitation of the Global Precipitation Climatology Project (GPCP). All data were filtered in the 30-60 day scale in order to observe the signal concerning the MJO. The analysis of the global precipitation and Outgoing Longwave Radiation (OLR) patterns, after filtration, allowed the selection of five areas, with signs associated to the MJO, being: Africa (AFR), Indonesia (IND), North of South America (NAS), Northeast Brazil (NEB) e Southeast Brazil (SEB). The NEB area presented linear correlation values of 0,63 and 0,32 for the anomaly and filtered anomaly of OLR, respectively. The SEB area presented linear correlation values of 0.30 and 0.54 for the anomaly and anomaly of filtered OLR. The BIAS calculated between the model and GPCP precipitation for the dry (MAY-OCT) and rainy seasons (NOV-APR) showed that for South America, South Africa and Indian continent, the model overestimates precipitation values of GPCP in the two seasons. The multivariate analysis between OLR, zonal wind at 850 and 200 hp compared to that obtained for Era-Interim data, the EOF1 applied to RegCM4 data presents convection and convection inhibition in different areas between 15º N and 15º S. While the minimum Empirical Orthogonal Function (EOF1) values for OLR (convection enhancement) of the Era-Interim are observed close to 90º E, the minimum OLR values for the RegCM4 data are observed close to 120º O, with a longitudinal lag of 30º. And while maximum EOF1 values for OLR (convection inhibition) of the ERA-Interim are observed close to 150º E, the maximum values for the simulated data by RegCM4 are observed close to 60º E, with a longitudinal lag of 90º.

O presente trabalho propõe avaliar a habilidade do Modelo Regional Climático, versão 4, (RegCM4) em simular a variabilidade temporal e espacial do sinal associado à propagação da Oscilação de Madden-Julian (OMJ) nos trópicos. A avaliação foi feita através da comparação dos dados observados obtidos do conjunto da Reanálise do ERA-Interim e dos dados simulados pelo RegCM4, para o período de 2005 a 2009. Foram utilizados dados globais diários de precipitação, Radiação de Onda Longa Emergente e componentes zonal do vento em 850 e 200 hPa, provenientes da Reanálise do ERA-Interim, tanto na simulação, quanto nos dados observados. Como condição inicial do modelo, optou-se pela utilização da banda tropical, cujo principal aspecto é o de simular características tanto da circulação quanto dos padrões de precipitação tropicais. Para a validação do modelo, foi utilizada a precipitação diária do Global Precipitation Climatology Project (GPCP). Todos os dados foram filtrados na escala de 30-60 dias a fim de se observar o sinal referente à OMJ. A análise dos padrões globais de precipitação e Radiação de Onda Longa (ROL), após filtragem, permitiu a seleção de cinco áreas, com sinais associados à OMJ, sendo elas: África (AFR), Indonésia (IND), Norte da América do Sul (NAS), Nordeste brasileiro (NEB) e Sudeste brasileiro (SEB). A área NEB, apresentou valores de correlação linear de 0,63 e 0,32 para a anomalia e anomalia de ROL filtrada, respectivamente. Já a área SEB, apresentou valores de correlação linear de 0,30 e 0,54, para a anomalia e anomalia de ROL filtrada. O BIAS calculado entre o modelo e a precipitação do GPCP, para as estações secas (MAI-OUT) e chuvosas (NOV-ABR) mostrou que para a América do Sul, Sul do continente Africano e Índico, o modelo superestima os valores de precipitação do GPCP nas duas estações do ano. Quanto à análise multivariada entre a ROL, vento zonal em 850 e 200 hpa a comparação com o obtido para os dados do Era-Interim, a Empirical Orthogonal Function (EOF1) aplicada aos dados do RegCM4 apresenta convecção e inibição da convecção em áreas distintas da faixa longitudinal entre 15º N e 15º S. Enquanto os valores mínimos de EOF1 para ROL (intensificação da convecção) do Era-Interim são observados próximo a 90º L, os valores mínimos de ROL para os dados do RegCM4 são observados próximos à 120º O, com defasagem longitudinal de 30º. L, enquanto os valores máximos da EOF1 para ROL (inibição de convecção) do Era-Interim são observados próximo a 150º L, os valores máximos para os dados simulados pelo RegCM4 são observados próximos à 60º L, com uma defasagem longitudinal de 90°. / The present work proposes to evaluate the ability of the Regional Climatic Model (RegCM4) to simulate the temporal and spatial variability of the signal associated with the propagation of the Madden-Julian Oscillation in the tropics. The evaluation was done by comparing the observed data obtained from the Reanalysis of the ERA-Interim and the data simulated by RegCM4, for the period from 2005 to 2009. Daily global data were used for precipitation, Emergent Long Wave Radiation and zonal wind components at 850 and 200 hPa from the ERA-Interim Reanalysis, both in the simulation and in the observed data. As initial conditions of the model, we chose to use the tropical band, whose main characteristic is to simulate the circulation and the tropical precipitation patterns. The validation of the model was performed with the daily precipitation of the Global Precipitation Climatology Project (GPCP). All data were filtered in the 30-60 day scale in order to observe the signal concerning the MJO. The analysis of the global precipitation and Outgoing Longwave Radiation (OLR) patterns, after filtration, allowed the selection of five areas, with signs associated to the MJO, being: Africa (AFR), Indonesia (IND), North of South America (NAS), Northeast Brazil (NEB) e Southeast Brazil (SEB). The NEB area presented linear correlation values of 0,63 and 0,32 for the anomaly and filtered anomaly of OLR, respectively. The SEB area presented linear correlation values of 0.30 and 0.54 for the anomaly and anomaly of filtered OLR. The BIAS calculated between the model and GPCP precipitation for the dry (MAY-OCT) and rainy seasons (NOV-APR) showed that for South America, South Africa and Indian continent, the model overestimates precipitation values of GPCP in the two seasons. The multivariate analysis between OLR, zonal wind at 850 and 200 hp compared to that obtained for Era-Interim data, the EOF1 applied to RegCM4 data presents convection and convection inhibition in different areas between 15º N and 15º S. While the minimum Empirical Orthogonal Function (EOF1) values for OLR (convection enhancement) of the Era-Interim are observed close to 90º E, the minimum OLR values for the RegCM4 data are observed close to 120º O, with a longitudinal lag of 30º. And while maximum EOF1 values for OLR (convection inhibition) of the ERA-Interim are observed close to 150º E, the maximum values for the simulated data by RegCM4 are observed close to 60º E, with a longitudinal lag of 90º.

The effects of a non-zero background state on atmospheric dynamics is explored through simple models and observations. Firstly, we examine the effects of moisture gradients on the stability and propagation of Rossby waves in a mid-latitude -plane. We begin by a consistent derivation of the forced quasi-geostrophic equations on a -plane to understand the constraints placed by geostrophy on the time scale of condensation. We see that the presence of meridional gradients of moisture results in a slowdown of the waves. On the introduction of zonal gradients of moisture, the waves become unstable, and for certain parameters which are representative of the real atmosphere, they propagate eastward and mature on an intra-seasonal timescale. The mechanism of the in hence of moisture on waves is understood by thinking of condensation as providing an \equivalent" potential vorticity (PV) gradient which opposes the dynamical PV gradient. Secondly, we look at the effects of a mean background ow on the Matsuno-Gill response in the spherical shallow water system. The mean ow is prescribed to resemble the climatological upper tropospheric zonal wind structure in the atmosphere. As the strength of the ow increases, the equatorially trapped Matsuno-Gill response rst transforms into a poleward propagating Rossby wavetrain. As the strength of the mean ow reaches values similar to that observed in the atmosphere, the stationary wave response becomes a zonally oriented quadrupole structure. This structure bears a striking resemblance to the observed upper level structure of the Madden-Julian oscillation (MJO). The time evolution of this quadrupole structure is quick enough to be relevant on MJO timescales, and the structure is quite robust across a range of values for the drag coefficient. Finally, we look at the role played by low frequency variability in the Pacific in the recent expansion of the Hadley cell. We find that the dominant effect of the low frequency variability is a stationary dispersive Rossby wavetrain extending from the tropical Paci. We further find that most of the observed expansion of the Hadley cell can be accounted for by this low frequency variability. We nd that large scale changes such as the changes in the equator-pole temperature gradient or midlatitude static stability need not be invoked to understand the observed expansion.

No presente trabalho utiliza-se um m´etodo multi-escala para estudar de forma te´orica as intera¸coes nao lineares entre o oceano e a atmosfera atrav´es de ressonancia onda-onda. Desenvolve-se uma hierarquia de modelos acoplados oceano-atmosfera nao lineares que foram escalonados convenientemente para representar as principais escalas de variabilidade clim´atica (i.e., intrasazonal, interanual, e decenal). A enfase dos modelos desenvolvidos foi dado para a regiao tropical. As fontes de nao linearidade inclu´das no modelo sao de dois tipos: I) nao linearidade intr´nsica (advectiva) e II) nao linearidade relacionada com os termos da f´sica e ambas sao abordadas neste trabalho. Para obter as equa¸coes que regem a dinamica de intera¸coes ressonantes a partir da hierarquia de modelos acoplados, aplicou-se um m´etodo perturbativo multi-escala. As solu¸coes sao escritas em termos de solu¸coes de ordem dominante e solu¸coes seculares. Para as solu¸coes de ordem dominante e seculares utilizam-se as fun¸coes base do problema linear, em uma aproxima¸cao do tipo Galerkin. As propriedades das fun¸coes base permitem calcular de forma anal´tica os coeficientes de intera¸cao associados com os termos nao lineares, assim como tamb´em permitem projetar estes termos nos modos de oscila¸cao natural do sistema (ressonancia). Com este m´etodo obt´em-se modelos reduzidos que permitem determinar as contribui¸coes de diversos processos para a evolu¸cao em escala lenta de um determinado modo de variabilidade natural. Para aplicar estes conceitos ao problema de acoplamento oceano-atmosfera utiliza-se como Ansatz (hip´otese inicial para a solu¸cao do problema) um tripleto composto por duas ondas atmosf´ericas e uma onda oceanica, sendo uma onda de Kelvin e de Rossby na atmosfera e uma onda Kelvin no oceano. O tripleto escolhido representa uma aproxima¸cao de v´arios fenomenos encontrados na regiao tropical, e.g. o desenvolvimento do El Nino, a intera¸cao da oscila¸cao de Madden-Julian com o oceano, a intera¸cao entre el Nino e variabilidade intrasazonal. No presente trabalho ´e mostrado que existe a ressonancia envolvendo ondas atmosf´ericas e oceanicas e que a modula¸cao em baixa frequencia produto desta ressonancia pode afetar desde escalas r´apidas sin´oticas equatoriais, intrasazonais, interanuais e at´e variabilidade da ordem de dezenas de anos. Palavras chave: Dinamica Equatorial nao linear, Intera¸coes Ressonantes, Modelos Acoplados Oceano-Atmosfera, El Nino, Oscila¸cao de Madden Julian, Oscila¸coes Decenais (Decadal) / In the present work a multiscale method is used to study resonant nonlinear wave-wave interactions between the ocean and the atmosphere. A hierarchy of coupled atmosphere-ocean models is developed using typical scalings found in the tropical region with the aim to represent some of the dominant modes of climate variability (intraseasonal, interannual and decadal). The sources of nonlinearity included into model are of two types: I) intrinsic nonlinearity (advective form) and II) nonlinearity related to physical terms. A multi-scale perturbation method is applied to obtain equations governing dynamics of ressonant interactions. The solutions are described in terms of dominant and secular solutions. For the dominant modes basis functions of the linear problem are used in a approximation of the Galerkin type. The properties of the basis functions allows the analytical computation of the interaction coefficients associated with non-linear terms and the projection into the natural oscillation modes of the system (resonance). Using this method it is possible to obtain reduced models to determine the contributions of several processes to the slow time evolution of a specific mode of natural variability. To apply these concepts to the problem of atmosphere-ocean coupling an Ansatz composed of a three waves (two atmospheric Rossby and Kelvin waves and an ocean Kelvin wave) is used. The triad chosen represents a aproximation of several phenomena found in the tropical region, e.g. desenvolving of El Nino, interaction of the Madden-Julian oscillation with the ocean, interaction between El Nino and intra-seasonal variability, etc. It is shown that system allows a resonance involving atmospheric and oceanic waves and that the low-frequency modulation resulting from these ressonance can affect the system from fast equatorial synoptic scales to decadal timescales, including the intermediate scales i.e., intraseasonal and interannual.

L'oscillation de Madden-Julian (MJO) est la composante dominante de la variabilité intrasaisonnière dans l'atmosphère tropicale, se propageant vers l'est dans la bande équatoriale. Elle se compose d'un centre convectif (phase active) accompagné de la convergence des anomalies du vent zonal de bas niveau et de la divergence de niveau supérieur, et de zones de convection faible (phases supprimées). Trois périodes de l'activité MJO sur l'océan Indien et le continent maritime ont été choisies : 6-14 avril 2009, 23-30 novembre 2011 et 9-28 février 2013. Les simulations avec et sans paramétrisation de la convection ont été réalisées pour un grand domaine avec le modèle atmosphérique Méso-NH. Il a été obtenu que les simulations avec convection paramétrée n'étaient pas capables de reproduire un signal MJO. Pour 2009 et 2011, lorsque le couplage entre la convection et la circulation de grande échelle était fort, les simulations avec convection explicite ont montré une propagation visible de la MJO, ce qui n'a pas été le cas pour 2013. Pour 2011, les processus contribuant à la suppression de la convection ont été étudiés avec une analyse isentropique pour séparer les masses d'air ascendantes ayant une température potentielle équivalente élevée des masses d'air subsidentes ayant une température potentielle équivalente faible. Trois circulations de grande échelle ont été trouvées : une circulation troposphérique, une circulation de percées nuageuses dans la couche de tropopause tropicale, et une circulation de masses d'air à faible température potentielle équivalente dans la basse troposphère. Cette dernière correspond aux intrusions d'air sec de grande échelle des zones subtropicales dans la bande équatoriale, trouvées principalement pendant la phase supprimée de la MJO sur l'océan Indien. / The Madden-Julian Oscillation (MJO) is the dominant component of the intraseasonal variability in the tropical atmosphere, propagating eastward in the equatorial band. It consists of a convective center (active phase) accompanied by the low-level zonal wind anomaly convergence and the upper-level zonal wind anomaly divergence, and zones of weak convection (suppressed phases). Three time periods of the MJO activity over the Indian Ocean and the Maritime Continent were chosen: 6-14 April 2009, 23-30 November 2011, and 9-28 February 2013. The simulations with and without convective parameterizations were performed for a large domain with the atmospheric model Méso-NH. It was obtained that the simulations with parameterized convection were not able to reproduce an MJO signal. For 2009 and 2011 when the coupling between convection and large-scale circulation was strong, the convection-permitting simulations showed a visible MJO propagation, which was not the case for 2013. For the 2011 episode, the processes contributing to the suppression of the convection were studied using an isentropic analysis to separate the ascending air masses with high equivalent potential temperature from the subsiding air masses with low equivalent potential temperature. Three large-scale circulations were found: a tropospheric circulation, an overshoot circulation within the tropical tropopause layer, and a circulation of air masses with low equivalent potential temperature in the lower troposphere. The latter corresponds to the large-scale dry air intrusions from the subtropical zones into the equatorial band, mostly found during the suppressed MJO phase over the Indian Ocean.

Large-scale atmospheric disturbances play important roles in determining the general circulation of the atmosphere during the North Pacific boreal winter. A number of scientific questions have been raised due to these disturbances’ spatial and temporal complexity as well as the hydrological implication associated with them. In this dissertation, the principal goal is to further improve our understanding of the atmospheric high frequency (HF) and intermediate frequency (IF) disturbances active over the North Pacific. The study focuses on their energetics, intraseasonal and interannual variability, and the resulting hydrological impact over the eastern North Pacific and Western U.S. including extreme events. To delineate the characteristics of HF and IF disturbances in the troposphere, we first derive a new set of equations governing the local eddy kinetic energy (EKE), and assess the critical processes maintaining local budgets of the HF and IF EKE. The diagnosis assesses the 3-D patterns of energy flux convergence (EFC), barotropic conversion (BT), baroclinic conversion (BC), and cross-frequency eddy-eddy interaction (CFEI). The local EKE budget analysis is followed by an investigation of the modulation of HF and IF eddy activity by different modes of low frequency climate variability. On interannual timescales, the response of various local energetic processes to El Niño-Southern Oscillation (ENSO) determines the HF and IF EKE anomalies and the role of CFEI process is important in producing these anomalies. Also on interannual timescales, winter precipitation deficits associated with suppressed cyclonic activity, i.e., negative HF EKE anomalies, are linked to severe droughts over the U.S. Southern Great Plain (SGP) region. The suppressed cyclonic activity is, in turn, tied to phase changes in the West Pacific (WP) teleconnection pattern. On intraseasonal timescales, variations in HF disturbances (a.k.a. storm tracks) over the North Pacific are closely coupled with tropical convection anomalies induced by the Madden-Julian Oscillation (MJO), and partly drive larger scale intraseasonal flow anomalies in this region through eddy-eddy interactions. Anomalous HF eddy activity induces subseasonal transitions between “wet” and “dry” regimes over the west coast of North America. Also on intraseasonal timescales, the East Asian cold surge (EACS) is found to provide a remote forcing of the winter precipitation anomalies in the western U.S. This modulation is achieved through “atmospheric rivers” (ARs), which are narrow channels of concentrated moisture transport in the atmosphere and are responsible for over 70% of the extreme precipitation events in the western U.S.. EACS effectively modulates the IF disturbance activity over the North Pacific, and the anomalous IF disturbances lead to the formation of an AR over the eastern North Pacific that ultimately induces precipitation anomalies in the western U.S. Analyses of the simulations from the NCAR Community Climate System Model version 4 (CCSM4) demonstrate that the connections among the EACS, AR and western U.S. precipitation are better captured by a model with higher spatial resolutions. The improved simulation of these connections is achieved mainly through a better representation of the IF disturbances, and the associated scale-interaction processes in the higher resolution model.

No presente trabalho utiliza-se um m´etodo multi-escala para estudar de forma te´orica as intera¸coes nao lineares entre o oceano e a atmosfera atrav´es de ressonancia onda-onda. Desenvolve-se uma hierarquia de modelos acoplados oceano-atmosfera nao lineares que foram escalonados convenientemente para representar as principais escalas de variabilidade clim´atica (i.e., intrasazonal, interanual, e decenal). A enfase dos modelos desenvolvidos foi dado para a regiao tropical. As fontes de nao linearidade inclu´das no modelo sao de dois tipos: I) nao linearidade intr´nsica (advectiva) e II) nao linearidade relacionada com os termos da f´sica e ambas sao abordadas neste trabalho. Para obter as equa¸coes que regem a dinamica de intera¸coes ressonantes a partir da hierarquia de modelos acoplados, aplicou-se um m´etodo perturbativo multi-escala. As solu¸coes sao escritas em termos de solu¸coes de ordem dominante e solu¸coes seculares. Para as solu¸coes de ordem dominante e seculares utilizam-se as fun¸coes base do problema linear, em uma aproxima¸cao do tipo Galerkin. As propriedades das fun¸coes base permitem calcular de forma anal´tica os coeficientes de intera¸cao associados com os termos nao lineares, assim como tamb´em permitem projetar estes termos nos modos de oscila¸cao natural do sistema (ressonancia). Com este m´etodo obt´em-se modelos reduzidos que permitem determinar as contribui¸coes de diversos processos para a evolu¸cao em escala lenta de um determinado modo de variabilidade natural. Para aplicar estes conceitos ao problema de acoplamento oceano-atmosfera utiliza-se como Ansatz (hip´otese inicial para a solu¸cao do problema) um tripleto composto por duas ondas atmosf´ericas e uma onda oceanica, sendo uma onda de Kelvin e de Rossby na atmosfera e uma onda Kelvin no oceano. O tripleto escolhido representa uma aproxima¸cao de v´arios fenomenos encontrados na regiao tropical, e.g. o desenvolvimento do El Nino, a intera¸cao da oscila¸cao de Madden-Julian com o oceano, a intera¸cao entre el Nino e variabilidade intrasazonal. No presente trabalho ´e mostrado que existe a ressonancia envolvendo ondas atmosf´ericas e oceanicas e que a modula¸cao em baixa frequencia produto desta ressonancia pode afetar desde escalas r´apidas sin´oticas equatoriais, intrasazonais, interanuais e at´e variabilidade da ordem de dezenas de anos. Palavras chave: Dinamica Equatorial nao linear, Intera¸coes Ressonantes, Modelos Acoplados Oceano-Atmosfera, El Nino, Oscila¸cao de Madden Julian, Oscila¸coes Decenais (Decadal) / In the present work a multiscale method is used to study resonant nonlinear wave-wave interactions between the ocean and the atmosphere. A hierarchy of coupled atmosphere-ocean models is developed using typical scalings found in the tropical region with the aim to represent some of the dominant modes of climate variability (intraseasonal, interannual and decadal). The sources of nonlinearity included into model are of two types: I) intrinsic nonlinearity (advective form) and II) nonlinearity related to physical terms. A multi-scale perturbation method is applied to obtain equations governing dynamics of ressonant interactions. The solutions are described in terms of dominant and secular solutions. For the dominant modes basis functions of the linear problem are used in a approximation of the Galerkin type. The properties of the basis functions allows the analytical computation of the interaction coefficients associated with non-linear terms and the projection into the natural oscillation modes of the system (resonance). Using this method it is possible to obtain reduced models to determine the contributions of several processes to the slow time evolution of a specific mode of natural variability. To apply these concepts to the problem of atmosphere-ocean coupling an Ansatz composed of a three waves (two atmospheric Rossby and Kelvin waves and an ocean Kelvin wave) is used. The triad chosen represents a aproximation of several phenomena found in the tropical region, e.g. desenvolving of El Nino, interaction of the Madden-Julian oscillation with the ocean, interaction between El Nino and intra-seasonal variability, etc. It is shown that system allows a resonance involving atmospheric and oceanic waves and that the low-frequency modulation resulting from these ressonance can affect the system from fast equatorial synoptic scales to decadal timescales, including the intermediate scales i.e., intraseasonal and interannual.