In this study, geographical Madden–Julian oscillation (MJO) propagation in association with precipitation rate was obtained using lag correlation applied to empirical orthogonal function (EOF) analysis modes 1 and 2 of filtered MJO data. The precipitation rate over Indonesia was provided at day -10 through day +10 in five-day steps during the December, January, and February (DJF) Western North Pacific (WNP) and July, August and September (JAS) Australian (AU) monsoon phases. Connection with local atmospheric factors was then sought through comparison of local precipitation, represented by 3-hourly precipitation, and dynamical processes, represented by multilevel wind, at seven locations across Indonesia. The results show a global MJO contribution toward local-scale phenomena in Tangerang, Surabaya, and Makassar during the DJF-WNP monsoon phase and in Padang, Medan, Surabaya, Makassar, and Kupang during the JAS-AU monsoon phase. Meanwhile, a lack of MJO contribution toward local factors is presumably due to other local through wider atmospheric-scale phenomena which are suspected to have more influence, particularly in Medan, Padang, Manado, and Kupang during the DJF-WNP monsoon phase, and in Manado and Tangerang during the JAS-AU monsoon phase. This research uses a dataset of 15-year series of daily and three-hourly Tropical Rainfall Measuring Mission (TRMM) (3B42 V7 derived) measurements, 850 hPa zonal wind measurements from 30-year reanalysis data from the ERA-Interim reanalysis dataset, and a 15-year series of 12-hourly observational soundings data from seven stations of the Indonesian Meteorological Climatological and Geophysical Agency (BMKG).

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Tropical Rainfall Measuring Mission (TRMM) and ERA-Interim forecast data analyzed using second-order autoregressive AR(2) and space-time-spectra analysis methods (respectively) revealed contrasting results for predicting Madden Julian Oscillation (MJO) and Convectively Coupled Equatorial Waves (CCEW) phenomena over Indonesia. This research used the same 13-year series of daily TRMM 3B42 V7 derived datasets and ERA-Interim reanalysis model datasets from the European Center for Medium-Range Weather Forecasts (ECMWF) for precipitation forecasts. Three years (2016 to 2018) of the filtered 3B42 and ERA-Interim forecast data was then used to evaluate forecast accuracy by looking at correlation coefficients for forecast leads from day +1 through day +7. The results revealed that rainfall estimation data from 3B42 provides better results for the shorter forecast leads, particularly for MJO, equatorial Rossby (ER), mixed Rossby-gravity (MRG), and inertia-gravity phenomena in zonal wavenumber 1 (IG1), but gives poor correlation for Kelvin waves for all forecast leads. A consistent correlation for all waves was achieved from the filtered ERA-Interim precipitation forecast model, and although this was quite weak for the first forecast leads it did not reach a negative correlation in the later forecast leads except for IG1. Furthermore, Root Mean Square Error (RMSE) was also calculated to complement forecasting skills for both data sources, with the result that residual RMSE for the filtered ERA-Interim precipitation forecast was quite small during all forecast leads and for all wave types. These findings prove that the ERA-Interim precipitation forecast model remains an adequate precipitation model in the tropics for MJO and CCEW forecasting, specifically for Indonesia.