Madden–Julian Oscillation analog and intraseasonal variability in a multicloud model above the equator

Majda et al. 10.1073/pnas.0703572104.

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SI Text
SI Figure 5
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SI Table 3

SI Figure 5

Fig. 5. Numerical simulation of the multicloud model using the parameter values in Table 1. (Part of this figure is shown in Fig. 2.) (a) Contour plot of the deep convective heating P(x, t). Heating values of >2 K/day are shaded in gray, and values of >10 K/day are shaded in black. (b) Contour plot of the velocity at the bottom of the troposphere, u₁(x, t) + u₂(x, t).

SI Figure 6

Fig. 6. Moving average of model variables for the simulation in Fig. 5. (Part of this figure is shown in Fig. 3.) The moving average was taken in a reference frame moving with the planetary-scale envelope of deep convection in Fig. 5, at 6 m/s. RCE values have been removed from all variables except P for these plots.

SI Figure 7

Fig. 7. Moving average (as in Fig. 6) of model variables with their vertical structures. (Part of this figure is shown in Fig. 4.) Dashed contours are for negative values, and solid contours are for positive values, with the zero contour removed. (a) Velocity field (U, W) with contours of potential temperature. The domain-means of q₁ and q₂ were removed for this plot (see Fig. 6b). Contour interval is 0.075 K. (b) Velocity field (U, W) with contours of total convective heating (congestus, stratiform, and deep convective heating combined). RCE values of P, H_s, H_c were removed for this plot. The contour interval is 1 K/day. (c) Contours of horizontal velocity with contour interval of 1 m/s.

SI Figure 8

Fig. 8. Scaled plots of moving averages of vertical velocity and convective heating from Fig. 6. The scaled vertical velocity and convective heating are balanced as in the weak temperature gradient (WTG) approximation.

SI Figure 9

Fig. 9. Fluctuation of deep convection P(x, t) about its moving average. The fluctuations are shown here in the moving reference frame to emphasize the westward-propagating deep convection disturbances in the convectively active phase of the envelope. The moving average of P(x, t) is shown in Fig. 6.

SI Figure 10

Fig. 10. Standard deviations of the fluctuations about the moving averages from Fig. 6. Although there are significant fluctuations in q_eb and q in the inactive preconditioning phase, the strongest fluctuations are mainly confined to the convectively active phase of the wave, which is ≈0 < x <10,000 km and 20,000 km < x <30,000 km in the moving reference frame as shown here.

SI Figure 11

Fig. 11. Numerical simulation of multicloud model using the parameter values from Table 1 except q_eb - q_em = 15 K. (a) Contour plot of the deep convective heating P(x, t). (b) Contour plot of the velocity at the bottom of the troposphere.

SI Figure 12

Fig. 12. Moving averages of model variables for the simulation in Fig. 11. Plots a-d and f show moving averages, and plot e shows the standard deviation of P about the moving average in the moving reference frame. The moving average was taken in a reference frame moving with the large-scale envelope of deep convection in Fig. 11, at 7 m/s.

SI Figure 13

Fig. 13. Moving average of deep convective heating <P> (Left) and its two components: mean, P_<> (Left), and fluctuation, <P> - P_<> (Right). Results are shown for four values of q_eb - q_em: 11 K (a and b), 12 K (c and d), 14 K (e and f), and 15 K (g and h). All other parameters take the values shown in Table 1. Note that plot h uses a different axis limit than plots b, d, and f. As q_eb - q_em increases, the fluctuation <P> - P_<> decreases.

SI Figure 14

Fig. 14. Numerical simulation of multicloud model using the parameter values from Table 1 except l = 0.8, a₀ = 10, t_s = t_c = 6 days, and q_eb - q_em = 11 K. A warm pool SST profile is used with a warm pool in the range 15,000 km < x < 25,000 km. (a) Domain-averaged root mean square (RMS) of model variables. A statistical steady state appears to have been reached (but see the continuation in Fig. 15). (b) Contour plot of the deep convective heating P(x, t).

SI Figure 15

Fig. 15. Continuation of Fig. 14, using the data from there at t = 2,000 days as the initial condition. (a) Contour plot of the deep convective heating P(x, t). (b) Contour plot of the velocity at the bottom of the troposphere, u₁ + u₂. The repeating pattern seen from time t = 100-250 days persisted for as long as the simulation was run (for 1,750 days beyond the data shown).

SI Figure 16

Fig. 16. Numerical simulation of the multicloud model using the parameter values from Table 1; an easterly barotropic wind of -5 m/s was added to the shallow water systems in Eqs. 5a and 5b, and a nonuniform SST profile with a warm pool in the range 15,000 km < x < 25,000 km. Shown here are contours of deep convective heating P(x, t). Notice the slow modulation of P on a time scale of ≈1,000 days.

SI Figure 17

Fig. 17. As in Fig. 16, but contours of u₁ + u₂, the velocity at the bottom of the troposphere, with the time-averaged Walker circulation removed.