Methods
To isolate signals corresponding to distinct equatorial wave modes, we applied a wavenumber-frequency spectral analysis following Wheeler & Kiladis (1999), across the 15°N—15°S meridional band. This analysis was performed using NCAR's command language (NCL) script, filter_waves, available from Dr. C. Schreck on GitLab. The process involved performing a two-dimensional Fast Fourier Transform (FFT) on daily anomalies (with the annual cycle removed) to transform the data into wavenumber-frequency space. The data was filtered to isolate the variability for each mode and subsequently transformed back to longitude-time space.
Convectively Coupled Kelvin Waves (CCKWs) were defined as eastward propagating signals with phase speeds between 8.9 and 29.7 m/s, and a filtering period between 17 and 2.5 days. Zonal wavenumber cutoffs were set between 1 and 14 (Straub & Kiladis, 2002).
Convectively Coupled Equatorial Rossby Waves (CCERWs) were defined as westward propagating signals with phase speeds between -7.0 and -9.4 m/s. Periods between 48 and 9.7 days, with zonal wavenumbers of 1 to 10, were used to filter these modes (Wheeler & Kiladis, 1999).
To detect CCKWs and CCERWs over Indonesia, we conducted an empirical orthogonal function (EOF) analysis of wavenumber-frequency-filtered data for the boreal winter (DJF) from January 1998 to June 2019. As suggested by Roundy (2015), multiple EOFs were necessary to describe each phenomenon due to the range of spatial scales. For each mode, the two leading EOFs were extracted, representing the most dominant modes of variability.
The resulting principal component (PC) time series was used as an index of equatorial wave activity. A wave was considered active when the amplitude, defined as √(PC1² + PC2²), exceeded 1.5 standard deviations over the 1998-2019 period. This technique was applied similarly to both CCKWs and CCERWs.
The index was developed primarily to identify active equatorial modes near Sulawesi, part of the Maritime Continent. Active days were determined using EOFs of filtered precipitation anomalies (for CCKWs) and zonal wind anomalies (for CCERWs). CCKWs were linked to precipitation in convergence zones, while CCERWs were associated with wind fields and moisture advection.
The leading two EOFs of:
(a) CCKWs-filtered precipitation anomalies
(b) CCERWs-filtered zonal wind anomalies.
How to Use the Index
In the enclosed .mat file (below):
CCER_index: A binary vector (1 or 0) indicating whether CCER activity is present based on the criteria outlined above.
CCKW_index: A binary vector (1 or 0) indicating whether CCKW activity is present.
Days: A vector containing DJF days starting from January 1, 1999, to February 28, 2019 (Note: leap years are not accounted for).
Example
Imagine a vector of rainfall rates corresponding to 1859 DJF days between January 1999 and February 2019.
To find the mean rainfall during CCER activity:
python code
nanmean(RAINFALL(CCER_index_days == 1))
You can then compare this to the mean rainfall on a random day.
References
Roundy, P. E. (2015): On the interpretation of EOF analysis of ENSO, atmospheric Kelvin waves, and the MJO. Journal of Climate.
Straub, K. H., & Kiladis, G. N. (2002): Observations of a convectively coupled Kelvin wave in the eastern Pacific ITCZ. Journal of the Atmospheric Sciences.
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.
