APPENDIX A Sensitivity of quantities derived for “rainy” and “dry” periods to precipitation threshold

The selection of a rainfall threshold to separate “rainy” and “dry” periods during an active CELCE is a somewhat subjective process. If the threshold is too low (i.e. 0 mm), then an insufficient amount of the time series will be classified as a dry period to make any meaningful statistical comparison of echo-top PDFs during rainy and dry periods. If the threshold is too high, then dry periods are biased by times when a significant amount of rainfall is falling over some portion of the radar domain. An hourly domain-averaged precipitation estimate of 0.25 mm (or 6 mm day^-1) typically occurs during the beginning or end of a short-term (1- to 2-day long) precipitation event (Fig. 2), and the precipitation echo during such times is classified either by many isolated convective echo clusters or stratiform in some part of the radar domain. Thus, any threshold above 0.25 mm is likely too high. Figure A1 shows two panels: They are duplicates of Figs. 6c and 9, except using a rainfall threshold of 0.25 mm. The peak of the PDF for rainy periods in Fig. A1a is at the same location as that in Fig. 6c, though the probability is about 0.01 higher. The PDF for dry periods in Fig A1a is shifted upward by 0.5 km or less, which is less than the resolution of the interpolated radar dataset. Fig A1b reveals RH profiles for rainy and dry periods using a threshold of 0.25 mm. Both profiles are shifted toward moister conditions than in Fig. 9, but the difference in RH between 850 hPa and 500 hPa remains about 10-15%. Additionally, the dry period RH profile maintains its shape and remains between the profiles for phases 8-3 and phases 4-7. The RH profiles below 800 hPa for dry periods and phases 4-7 remain nearly identical. Thus, we determine that our main conclusions are not unduly influenced by the choice of rainfall threshold given in separating times during an active CELCE into rainy and dry periods.

Statistical significance among differences in echo-top PDFs described in Sec. 5 and RH profiles shown in Section 6 is determined using a two-tailed Student t-testMann-Whitney U-test with a 95% confidence level. For echo-top PDFs, each separate contiguous cloud echo observed by S-Polka theoretically represents a separate degree of freedom (DOF). Determining the exact DOF would thus require a complicated radar echo tracking algorithm or determining spatial and temporal autocorrelation of radar data at each data point for three and a half months. Instead we make an unrealistically conservative assumption: that on any given day, only four separate convective cells or echo clusters are observed that very few individual echo objects exist. For a rainfall threshold of 0.1mm, the number of convective echoes detected during wet periods is greater than that observed during dry periods by a factor of about 12. Suppose we assume that only one new contiguous convective echo is observed each hour, and we assume that 12 times that amount is observed during wet conditions. Thus, the DOF in each category shown for dry periods in Fig. 6c are four times the number of days contained within each category.is equal to the number of hours classified as falling within a dry period, or 133; and the DOF for wet periods is 12*(number of hours classified as wet period), or 12*190 = 2280.

The mean and standard deviation of echo-top height is computed using its unnormalized histogram for each category.

For RH profiles on MCS days and non-MCS days, one DOF is assumed per day. Three suppressed periods, or intervals during which the WH MJO phase was between 4 and 7, are included in the Fig. 9 composite--one before CE1, one between CE1 and CE2, and one between CE2 and CE3. Each suppressed period is an independent continuous time series. The DOF during each is determined by first calculating the autocorrelation function at all possible lag times given the length of each time series. The DOF for each time series is computed following Bretherton et al., [1999] for a first-order process as

N* = N(1 - r₁)/(1 + r₁)

where N* is the number of DOF, N is the number of elements in each time series, and r₁ is the value of the autocorrelation function at one lag period, which for sounding data, is three hours. The sum of the DOF for each time series is the total DOF for suppressed periods.

Andersen, J. A., and Z. Kuang (2012), Moist static energy budget of MJO-like disturbance in the atmosphere of a zonally symmetric aquaplanet, J. Clim., 25, 2782-2804.

Bretherton, C. S., M. Widmann, V. P. Dymnikov, J. M. Wallace, and I. Bladé (1999), The effective number of spatial degrees of freedom of a time-varying field, J. Climate, 12, 1990-2009.

Matthews, A. J. (2000), Propagation mechanisms for the Madden-Julian oscillation, Q. J. R. Meteorol. Soc., 126, 2637-2651.

Virts, K. S., and J. M. Wallace (2010), Annual, Interannual, and Intraseasonal Variability of Tropical Tropopause Transition Layer Cirrus, J. Atmos. Sci., 67, 3113-3129.

, S. M. Ellis, R. Oye, A. V. Ryzhkov, and J. Straka (1999), Cloud microphysics retrieval using S-band dual-polarization radar measurements, Bull. Am. Meteorol. Soc., 80, 381-388.

Table 1: Dates of occurrence of each WH MJO phase during DYNAMO-AMIE.

Table 2: Maximum lag correlation coefficients and the lag (in days) at which they occur (in parentheses) for filtered specific humidity anomaly time series at 850 hPa, 700 hPa, 500 hPa, and 300 hPa, as well as for the filtered time series of stratiform and convective areal coverage and the negative Eulerian derivative of the 150 hPa zonal wind anomaly. Positive lags indicate that the quantity listed in that column occurs first. Because of the small sample size, none of the correlations are statistically significant.