Pedro L. Silva Dias ^{(1),}

Carlos F. M. Raupp ^{(1)}

Enver Ramirez Gutierrez ^{(2)}

Breno Raphaldini ^{(1)}

(1) Institute of Astronomy, Geophysics and Atmospheric Sciences , University of São Paulo – BRAZIL

(2) Center for Weather Forecasting and Climate Research /INPE – BRAZIL

Tropical convection is characterized by strong spectral peaks in some well defined frequency bands and numerical models do not always realistically reproduce the observed power. Our goal is to explore the role of nonlinear resonance as a plausible mechanism to promote energy transfer from higher frequencies (e.g. the diurnal scale) to synoptic, intraseasonal, interannual and longer time scales. The presentation will explore highlights of the papers published by the authors, discuss some recent advances both from the point of view of the role of non-hydrostatic processes and the interaction between the periodic solar forcing and the resonating triads in the decadal and longer timescales.

This work was initially motivated by the numerical evidence in the late 90’s that models with stronger diurnal variation had a stronger signal in the intraseasonal band. Non-linear resonance was invoked as a potential mechanism to explain the connection between the diurnal and intraseasonal variability in tropical convection. Numerical integrations of the resonant three-wave problem show that the energy of the waves in a resonant triad evolves periodically in time, with the period and amplitude of the energy oscillations dependent on the magnitude of the initial amplitudes of the waves and the way in which the initial energy is distributed among the triad components. The high-frequency modes are found to be energetically more active than the low-frequency modes. The latter tend to act as catalytic components in a resonant triad. Integrations of the problem of two resonant triads coupled by a single mode point out the importance of gravity waves in the intertriad energy exchanges, suggesting the significance of these modes in the redistribution of energy throughout the atmospheric motion spectrum. The results also show that the inter-triad energy exchanges provided by the highest frequency mode of two triads occur in a longer time-scale than the intra-triad interactions. Therefore, these results also suggest the importance of the high-frequency modes in the generation of the low-frequency variability (intraseasonal and even longer term) of the atmospheric flow.

Later, the full primitive equation model was decomposed in vertical modes and the nonlinear interaction between internal modes and the external mode were explored. In this case, it was shown that a Rossby wave associated with the baroclinic basic state, resonant with the stationary component of the daytime heat source, and two dispersive modes, given by Mixed Rossby-gravity wave and a slow barotropic mode (Rossby) may interact and provoke vacillation in the time scale of many days (between intraseasonal and interannual time scales).

The importance of the fast modes in the resonant triplets raises the following question: what is the role of diurnal variation in the generation of these fast modes? We have also shown, for example, that a Rossby wave associated with the baroclinic (i.e., associated with an internal mode) basic state, resonant with the stationary component of the daytime heat source, and two dispersive modes, given by Mixed Rossby-gravity wave and a slow barotropic mode (Rossby) may interact and provoke vacillation in the time scale of several days (between intraseasonal and interannual). Another class of resonant modes is identified with the interaction between two internal modes of gravity generated by the diurnal forcing with clear manifestation in the intraseasonal scale.

A generalization of the previous results on the role of the diurnal forcing was also developed in the context of a heat source parameterized by the simplest form according to the hypothesis that the heat source intensity is proportional to the low level moisture convergence. The study was developed in the context of a two-layer model that allows interaction between the external (barotropic) mode and the internal (baroclinic) mode. It introduces a forcing that has meridional dependence and, therefore, it becomes feasible to explore the non-linear resonance involving the interaction of only two waves. The reduced dynamics of the two-layer model shows that a Rossby mode is significantly modulated in longer time scales when interacting with an internal gravity mode (interannual to the decadal scale).

More recently we have explored a simplified multi-scale atmosphere-ocean coupled model for studying the interactions between synoptic-intraseasonal-interannual scales. Two coupled nonlinear equatorial beta-plane shallow water equations are considered: one for the ocean and the other for the atmosphere. The nonlinear terms are the intrinsic advective nonlinearity and the atmosphere/ocean coupling. Simplified parameterizations for the air-sea coupling are developed. To mimic the main differences between the fast- atmosphere and the slow-ocean, suitable multi-space and multi-time scaling are applied, yielding a balanced synoptic/intraseasonal/interannual-El Niño regime. In this limit, the synoptic scale is the fastest atmospheric scale, the intraseasonal is the intermediate air-sea coupling scale and El Niño refers to the slowest interannual ocean scale. The model equations reveal that the slow wave amplitude evolution depends on both types of nonlinearities. The wind stress parameterization allows synoptic scale atmospheric waves to force intraseasonal variability in the ocean. The intraseasonal ocean temperature anomaly coupled with the atmosphere through evaporation is able to force higher order atmospheric variability, whereas wave-convection coupling provides another source for higher order atmospheric variability. Nonlinear interactions of intraseasonal ocean perturbations can also force interannual oceanic variability. Analytical solutions of the reduced model equations for a discrete resonant triad interacting through the atmosphere-ocean fluxes illustrate the model potential to connect synoptic, intraseasonal, interannual and decadal/multi-decadal time-scales in the coupled system.

We have also analyzed the role of periodic forcing induced by the sun energy output variability in the decadal and longer timescales. The presence of periodic forcing leads to larger amplitude effects at the longer time-scales. In the fast portion of the time scales, we are exploring possible resonating triads in non-hydrostatic models with potential applications in the organization of mesoscale systems.