A Simple Model of Convectively Coupled Equatorial Rossby Waves

Abstract

Intraseasonal oscillations affect the weather not just in the tropics but all around the globe. The convectively coupled equatorial Rossby wave is observed as the westward-moving intraseasonal oscillation. The fundamental physics of its coupling is still unknown; thus, many questions remain unanswered. How is its phase speed altered by convection? What makes it unstable? Why is it an intraseasonal oscillation? Using the Fuchs and Raymond model with linearized governing equations on an equatorial beta plane, first baroclinic mode vertical structure, and moisture and wind-induced surface heat exchange (WISHE) convective parametrizations, this paper seeks a fundamental analytical theory that can explain the basic features of the convectively coupled equatorial Rossby wave. The WISHE-moisture theory leads to a large-scale, unstable westward propagating mode in the n = 1 case, which we call the westward propagating WISHE-moisture mode. We find that the westward propagating WISHE-moisture mode is indeed the free equatorial Rossby wave in the absence of moisture closure and WISHE. It is propagating westward due to the beta effect, and it slows down when it is convectively coupled. Its phase speed decreases mainly due to WISHE and cloud-radiation interactions. The x-y structure of the pressure and horizontal winds is similar to the free and observed Rossby wave, with convergent net flow. The strongest easterlies are to the west of the precipitation maximum increasing the moisture in that area. The mode is unstable due to the interplay of surface fluxes and moisture, which increases as a function of zonal wavelength.

References Chen, S., Majda, A. J., & Stechmann, S. (2015). Multiscale asymptotics for the skeleton of the Madden-Julian oscillation and tropical-extratropical interactions. Mathematics of Climate and Weather Forecasting, 1, 1. https://doi.org/10.1515/mcwf-2015-0003 Emanuel, K. A. (1987). An air-sea interaction model of intraseasonal oscillations in the tropics. Journal of the Atmospheric Sciences, 44(16), 2324–2340. https://doi.org/10.1175/1520-0469(1987)044<2324:AASIMO>2.0.CO;2 Emanuel, K. (1993). The effect of convective response time on WISHE modes. Journal of the Atmospheric Sciences, 50(12), 1763–1776. https://doi.org/10.1175/1520-0469(1993)050<1763:TEOCRT>2.0.CO;2 Fuchs, Ž, Gjorgjievska, S., & Raymond, D. J. (2012). Effects of varying the shape of the convective heating profile on convectively coupled gravity waves and moisture modes. Journal of the Atmospheric Sciences, 69(8), 2505–2519. https://doi.org/10.1175/JAS-D-11-0308.1 Fuchs, Z., & Raymond, D. J. (2005). Large-scale modes in a rotating atmosphere with radiative-convective instability and WISHE. Journal of the Atmospheric Sciences, 62(11), 4084–4094. https://doi.org/10.1175/JAS3582.1 Fuchs, Ž, & Raymond, D. J. (2017). A simple model of intraseasonal oscillations. Journal of Advances in Modeling Earth Systems, 9, 1195–1211. https://doi.org/10.1002/2017MS000963 Gray, W. M. (1998). The formation of tropical cyclones. Meteorology and Atmospheric Physics, 67(1), 37–69. https://doi.org/10.1007/BF01277501 Hoskins, B. J., & Yang, G. Y. (2000). The equatorial response to higher-latitude forcing. Journal of the Atmospheric Sciences, 57(9), 1197–1213. https://doi.org/10.1175/1520-0469(2000)057<1197:TERTHL>2.0.CO;2 Kiladis, G. N. (1998). Observations of Rossby waves linked to convection over the Eastern Tropical Pacific. Journal of the Atmospheric Sciences, 55(3), 321–339. https://doi.org/10.1175/1520-0469(1998)055<0321:OORWLT>2.0.CO;2 Kiladis, G. N., & Wheeler, M. C. (1995). Horizontal and vertical structure of observed tropospheric equatorial Rossby waves. Journal of Geophysical Research, 100(D11), 22,981–22,997. https://doi.org/10.1029/95JD02415 Kiladis, G. N., Wheeler, M. C., Haertel, P. T., Straub, K. H., & Roundy, P. E. (2009). Convectively coupled equatorial waves. Reviews of Geophysics, 47, RG2003. https://doi.org/10.1029/2008RG000266 Kuang, Z. (2008). A moisture-stratiform instability for convectively coupled waves. Journal of the Atmospheric Sciences, 65(3), 834–854. https://doi.org/10.1175/2007JAS2444.1 Majda, A. J., & Biello, J. A. (2003). The nonlinear interaction of barotropic and equatorial baroclinic Rossby waves. Journal of the Atmospheric Sciences, 60(15), 1809–1821. https://doi.org/10.1175/1520-0469(2003)060<1809:TNIOBA>2.0.CO;2 Majda, A. J., Khouider, B., Kiladis, G. N., Straub, K. H., & Shefter, M. G. (2004). A model for convectively coupled tropical waves: Nonlinearity, rotation, and comparison with observations. Journal of the Atmospheric Sciences, 61(17), 2188–2205. https://doi.org/10.1175/1520-0469(2004)061<2188:AMFCCT>2.0.CO;2 Majda, A. J., & Shefter, M. G. (2001a). Models for stratiform instability and convectively coupled waves. Journal of the Atmospheric Sciences, 58(12), 1567–1584. https://doi.org/10.1175/1520-0469(2001)058<1567:MFSIAC>2.0.CO;2 Majda, A. J., & Shefter, M. G. (2001b). Waves and instabilities for model tropical convective parameterizations. Journal of the Atmospheric Sciences, 58, 896–914. Mapes, B. E. (2000). Convective inhibition, subgrid-scale triggering energy, and stratiform instability in a toy tropical wave model. Journal of the Atmospheric Sciences, 57(10), 1515–1535. https://doi.org/10.1175/1520-0469(2000)057<1515:CISSTE>2.0.CO;2 Matsuno, T. (1966). Quasi-geostrophic motions in the equatorial area. Journal of the Meteorological Society of Japan. Ser. II, 44(1), 25–43. https://doi.org/10.2151/jmsj1965.44.1.25 Neelin, J. D., Held, I. M., & Cook, K. H. (1987). Evaporation-wind feedback and low-frequency variability in the tropical atmosphere. Journal of the Atmospheric Sciences, 44(16), 2341–2348. https://doi.org/10.1175/1520-0469(1987)044<2341:EWFALF>2.0.CO;2 Randall, D. A., Harshvardhan, Dazlich, D. A., & Corsetti, T. G. (1989). Interactions among radiation, convection, and large-scale dynamics in a general circulation model. Journal of the Atmospheric Sciences, 46(13), 1943–1970. https://doi.org/10.1175/1520-0469(1989)046<1943:IARCAL>2.0.CO;2 Raupp, C. F. M., & Silva Dias, P. L. (2009). Resonant wave interactions in the presence of a diurnally varying heat source. Journal of the Atmospheric Sciences, 66(10), 3165–3183. https://doi.org/10.1175/2009JAS2899.1 Raymond, D. J. (2000a). The Hadley Circulation as a radiative-convective instability. Journal of the Atmospheric Sciences, 57(9), 1286–1297. https://doi.org/10.1175/1520-0469(2000)057<1286:THCAAR>2.0.CO;2 Raymond, D. J. (2000b). Thermodynamic control of tropical rainfall. Quarterly Journal of the Royal Meteorological Society, 126(564), 889–898. https://doi.org/10.1002/qj.49712656406 Raymond, D. J. (2001). A new model of the Madden-Julian oscillation. Journal of the Atmospheric Sciences, 58(18), 2807–2819. https://doi.org/10.1175/1520-0469(2001)058<2807:ANMOTM>2.0.CO;2 Raymond, D. J., & Fuchs, v. (2007). Convectively coupled gravity and moisture modes in a simple atmospheric model. Tellus A, 59(5), 627–640. https://doi.org/10.1111/j.1600-0870.2007.00268.x Raymond, D. J., & Fuchs, v. (2018). The Madden-Julian oscillation and the Indo-Pacific warm pool. Journal of Advances in Modeling Earth Systems, 10(4), 951–960. https://doi.org/10.1002/2017MS001258 Reznik, G., & Zeitlin, V. (2007). Resonant excitation and nonlinear evolution of waves in the equatorial waveguide in the presence of the mean current. Physical Review Letters, 99, 064501. https://doi.org/10.1103/PhysRevLett.99.064501 Roundy, P. E., & Frank, W. M. (2004). A Climatology of waves in the equatorial region. Journal of the Atmospheric Sciences, 61(17), 2105–2132. https://doi.org/10.1175/1520-0469(2004)061<2105:ACOWIT>2.0.CO;2 Sherwood, S. C., Ramanathan, V., Barnett, T. P., Tyree, M. K., & Roeckner, E. (1994). Response of an atmospheric general circulation model to radiative forcing of tropical clouds. Journal of Geophysical Research, 99(D10), 20,829–20,845. https://doi.org/10.1029/94JD01632 Slingo, A., & Slingo, J. M. (1988). The response of a general circulation model to cloud longwave radiative forcing. I: Introduction and initial experiments. Quarterly Journal of the Royal Meteorological Society, 114(482), 1027–1062. https://doi.org/10.1002/qj.49711448209 Slingo, J. M., & Slingo, A. (1991). The response of a general circulation model to cloud longwave radiative forcing. II: Further studies. Quarterly Journal of the Royal Meteorological Society, 117(498), 333–364. https://doi.org/10.1002/qj.49711749805 Wang, B., & Xie, X. (1996). Low-frequency equatorial waves in vertically sheared zonal flow. Part I: Stable waves. Journal of the Atmospheric Sciences, 53(3), 449–467. https://doi.org/10.1175/1520-0469(1996)053<0449:LFEWIV>2.0.CO;2 Wheeler, M., & Kiladis, G. N. (1999). Convectively coupled equatorial waves: Analysis of clouds and temperature in the wavenumber-frequency domain. Journal of the Atmospheric Sciences, 56(3), 374–399. https://doi.org/10.1175/1520-0469(1999)056<0374:CCEWAO>2.0.CO;2 Wheeler, M., Kiladis, G. N., & Webster, P. J. (2000). Large-scale dynamical fields associated with convectively coupled equatorial waves. Journal of the Atmospheric Sciences, 57(5), 613–640. https://doi.org/10.1175/1520-0469(2000)057<0613:LSDFAW>2.0.CO;2 Xie, X., & Wang, B. (1996). Low-frequency equatorial waves in vertically sheared zonal flow. Part II: Unstable waves. Journal of the Atmospheric Sciences, 53(23), 3589–3605. https://doi.org/10.1175/1520-0469(1996)053<3589:LFEWIV>2.0.CO;2 Yang, G. Y., Hoskins, B., & Slingo, J. (2007a). Convectively coupled equatorial waves. Part I: Horizontal and vertical structures. Journal of the Atmospheric Sciences, 64(10), 3406–3423. https://doi.org/10.1175/JAS4017.1 Yang, G. Y., Hoskins, B., & Slingo, J. (2007b). Convectively coupled equatorial waves. Part II: Propagation characteristics. Journal of the Atmospheric Sciences, 64(10), 3424–3437. https://doi.org/10.1175/JAS4018.1 Yano, J. I., & Emanuel, K. A. (1991). An improved model of the equatorial troposphere and its coupling with the stratosphere. Journal of the Atmospheric Sciences, 48(3), 377–389. https://doi.org/10.1175/1520-0469(1991)048<0377:AIMOTE>2.0.CO;2 Zhang, C. (2005). Madden-Julian oscillation. Reviews of Geophysics, 43, RG2003. https://doi.org/10.1029/2004RG000158