Monitoring the Madden–Julian oscillation with geopotential height

This paper examines the three-dimensional geopotential height structure of the Madden–Julian oscillation (MJO) and proposes that the MJO convection signals can be well reflected by upper-tropospheric zonal anomalous height gradient (ZAHG, ∇xz′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nabla_{x} z'$$\end{document}). A case study in 2011 and composite analyses have been done by applying a wavenumber-frequency filtering method on daily variable anomalies derived from different reanalysis datasets. Results show that the upper-level eastward-moving intraseasonal geopotential height anomaly does not exactly display a Rossby–Kelvin wave structure of the Gill model. Instead, it shows a height quadrupole pattern and is well associated with temperature and zonal wind anomalies. The notable tilted upper-tropospheric temperature structure can be derived from the height anomalies by the hydrostatic balance relationship. The first baroclinic mode vertical structure of zonal wind anomalies can be approximated from the height anomalies by the geostrophic equation. A highlight of the paper is the proposal of tracing the MJO convection center by the upper-tropospheric ZAHG (∇xz′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nabla_{x} z'$$\end{document}). Composite analyses of all MJO events during extended winter (NDJFM) from 1979 to 2013 suggest that positive upper-tropospheric ZAHG is exactly in phase with negative outgoing longwave radiation (OLR) anomalies in the eastern Indian Ocean and Maritime Continent during a MJO event. On the other hand, positive upper-tropospheric ZAHG leads (lags) negative OLR anomalies by 1 (2) days in the western Indian Ocean (western Pacific Ocean), where MJO events generally initiate (dissipate). ZAHG can also be applied to modeling data and observation data before the satellite era. This study provides a new diagnostic parameter option to monitor MJO events, and an alternative for studying MJOs before the satellite era and model evaluation.