## Abrupt Latitudinal Movement of the ITCZ Monsoon Onset

The intertropical convergence zone (ITCZ) is the location where surface winds converge and rise into the upward branch of the Hadley/Walker circulation. The latent heat released in the ITCZ drives the Hadley/Walker circulation. In other words, the ITCZ is a part of the Hadley/Walker circulation. The latitudinal location and the intensity of the ITCZ impact the tropical surface wind distribution, which, in turn, impacts the air-sea interaction. The latter is known to play a crucial role in El Nino. The convection within the ITCZ in the Indian Ocean and western Pacific has an intraseasonal oscillation, which is called the Madden-Julian oscillation (MJO). The MJO is strongest when the ITCZ is over the equator. Thus the annual cycle of the ITCZ latitudinal movement determines the seasonal variation of the MJO intensity.

Because of its importance the latitudinal location of the ITCZ has attracted the attention of many prominent researchers, such as Charney (1971). Charney's theory of the latitudinal location of the ITCZ was built on his CISK theory (conditional instability of the second kind; Charney and Eliassen, 1964; and Ooyama 1964), which he used to explain tropical cyclo-genesis. Chaney's ITCZ theory is a zonal mean version of his CISK idea. According to CISK, synoptic-scale convection relies on frictionally induced boundary-layer convergence (i.e. the Ekman pumping), and thus favors higher latitudes, i.e. the poles. Charney also invoked the idea that the moisture supply is higher over the equatorial tropics than over the polar regions. The compromise of these two factors gives the ITCZ a latitudinal location close to, but not at, the equator.

The Charney ITCZ theory was quite influential. Many people adopted or embellished it (see the appendix of Chao and Chen, 2004). However, Charney's ITCZ theory and its offshoots turned out to be in conflict with the aqua-planet (AP) experiments of Sumi (1991), Kirtman and Schneider (1996), Chao (2000) and Chao and Chen (2001a, 2004). These researchers used AP models with uniform sea surface temperature (SST) and solar angle — which eliminated the second factor in Charney's theory — and obtained the ITCZ over or near the equator (at about 14° N or S) instead of over the polar region, as the first factor of Charney's ITCZ theory would predict.c What is relevant to our topic is that the region adjacent to the equator (e.g. from 4° to 8°) is not, or rarely, accessible by the AP ITCZ, which gives a clear indication of multiple equilibria.

cCharney realized the problem with the CISK theory in the last years of his life (Arakawa, personal communication).

The following is the author's explanation (from Chao and Chen, 2004) for the AP model results. An AP model with uniform SST and solar angle would have uniform time-averaged precipitation if the earth's rotation rate, Q, were set to zero, since in the absence of Q, one location on the globe is indistinguishable from another. When the earth's true rotation rate is used, convection finds preferred latitudes. To explain these preferred latitudes, one should look at the cause of convection, which is that vertical instability in the presence of the Coriolis parameter turns negative; in other words, the squared frequency of the inertial gravity wave, w2 = f2 + a2 N2 + |, turns negative, and convection occurs [Eq. (8.4.23) of Gill, 1982]. Here, N2 is the vertical stability, |f | is the stabilization due to friction, and a is the ratio of the vertical scale to the horizontal scale of the wave or convective cell. The fact that f2 is added to a term proportional to N2 in the definition of w2 indicates that f2 has an equivalent effect on convection to N2; see Chao and Chen (2001a) for an explanation of this equivalence. When a is large, as in the case of individual clouds with small horizontal scales, f2 can be ignored. However, when we consider synoptic-scale convective systems in the ITCZ, f2 is not negligible. The equivalence of f to N makes the equator an attractor for the ITCZ. Thus when N2 is globally uniform, w2 is a minimum at the equator. This implies that convection, or the ITCZ, should occur at the equator — this being a first effect of f on the ITCZ. In an AP model convection must occur somewhere, given the destabilizing effects of radiative cooling and the surface sensible and latent heat fluxes. Convection, or more generally the ITCZ, occurs at the latitude where the atmosphere is most unstable, i.e. dw2/d$ = 0, where $ is the latitude. This means that the ITCZ occurs at the latitude where —df2/d$ is balanced by d(a2 N2)/d$, if |f | is ignored. N2 is reduced by the boundary evaporation, which is enhanced by the tangential wind component in the boundary layer, which, in turn, is induced by the Coriolis parameter — which is a second effect of f. Thus the poles are additional attractors of the ITCZ.

d(a2N2)/d$ is the latitudinal gradient of the f-modified surface wind-evaporation feedback mechanism (the role of a2 is yet to be explored). Unfortunately, it remains a very difficult challenge, if not an impossibility, to obtain an analytical expression for d(a2N2)/d$. For the stability of the individual clouds, N2 is equal to gdln0/dz, where 0 is the potential temperature (or equivalent potential temperature for a saturated atmosphere); but for synoptic-scale cloud systems (or as in GCMs, where individual clouds are not simulated and cumulus parame-trization is used to represent an ensemble of clouds), N2 should be the vertical stability for cumulus ensembles rather than for individual clouds. Thus, N2 has no known simple tractable analytical expression. Therefore, one has to seek other means to push the investigation forward, as we will soon discuss.

The gradient df2/d$ can be identified as the forcing due to the ITCZ attractor at the equator, and d(a2N2)/d$ as the forcing due to the other attractors at the poles. The former gradient is equal to 8Q2 sin$ cos$, and is represented by curve A in Fig. 5(a); the latter gradient is represented by curve B in Fig. 5(a). In this figure the abscissa S, is the latitude of the ITCZ. Since curve A has a known analytic form and does not depend on the model design, it is easily understood. Curve B, however, has no known analytic form; it has been constructed through numerical experimental results and theoretical arguments. Curve B depends on the way N2 is affected by the model design and, in particular, by the design of the model physics. Since curve B represents the attraction on convective systems due to the attractor at the poles through the second effect of f, it is zero at the poles — the center of the attractor. Also, curve B depends on the gradient of f — remember that it is the gradient of a2 N2, and a2 N2 is affected by f. In other words, curve B depends on [. This gives Curve B a maximum at the equator. However, since the convective system is fairly sizeable,

Figure 5(a). Schematic diagram showing the strength of the two types of attraction acting on the ITCZ. The difference between the solid and dashed curve Bras lies in their slopes at the equator.

when its center is close to the equator a part of the system is in the other hemisphere; therefore, it also experiences the attraction by the other pole. Thus, curve B has to be zero at the equator, where the attractions due to both poles cancel. This is shown in Fig. 5(b), with the dashed curve being the attraction due to the second effect of f if the size of the convective system is not accounted for. The solid curve, curve B — being the running average of the dashed curve with an averaging window the size of a tropical synoptic system — represents the net attraction experienced by the convective system.

The dependence of curve B on the cumulus scheme is illustrated in Fig. 5(a). Bras and Bmca, represent curve B when the relaxed Arakawa and Schubert scheme (RAS, Moorthi and Suarez, 1992) and Manabe's moist con-vective adjustment (MCA) scheme are used, respectively. As for the relative height of BRAS and Bmca , let us first recall that curve B represents the latitudinal gradient of f-modified surface heat fluxes. When f is larger, the surface winds that converge toward the center of a synoptic-scale convective system (which is a constituent of the ITCZ) develop a greater tangential wind component, which adds to the wind speed and thus enhances the surface heat fluxes. Convective cells simulated with MCA are usually smaller than those simulated with RAS and have faster surface wind speed toward the center of a convective system which does not allow enough time for the surface wind to be fully modified by the Coriolis parameter to allow the tangential wind component to fully develop. Therefore, curve B under MCA is smaller than

that under RAS. See Chao and Chen (2004) for a more detailed discussion. If a condition is imposed on the RAS cumulus parametrization scheme such that the boundary layer relative humidity must exceed a critical value in order for the scheme to operate, then this critical value is increased from 90% to 95%, and curve B will change from Bras to Bmca. At 90%, the criterion does not impose much restriction on RAS, but at 95% the restriction is strong enough to make RAS behave more like MCA. MCA requires both neighboring levels of the model to be saturated for it to operate, and thus is quite restrictive. In Fig. 5(a), as curve B rises from Bmca to Bras, the location of the intercept between curve A and curve B — i.e. the location of the ITCZ — remains at the equator until the slope of curve B at the equator exceeds that of curve A at the equator. Then the equator is no longer a stable equilibrium location, and the ITCZ jumps to the latitude of the other intercept, P. This jump is very fast, because the ITCZ is pulled in a "free fall" by the large difference between the two curves. On the other hand, when curve B decreases from Bras to Bmca, point P — or the ITCZ — moves gradually toward the equator until the peak of Curve B gets below curve A. At this moment P disappears, and the state jumps toward the equator. But, in this case, the difference between the two curves is much smaller than in the case of the ITCZ jumping away from the equator, which involves a rising curve B. Thus, the move of the ITCZ back to the equator is not as abrupt.

The above deductions are borne out in experiments shown in Fig. 6(a), where the boundary layer relative humidity criterion is held at 90% for the first 200 days and is changed linearly in time to 95% over the next 100 days and then kept unchanged for the reminder of the experiment. As expected, at the beginning of the experiment shown in Fig. 6(a) the ITCZ is away from the equator and then moves to the equator gradually as the RH criterion is increased. The fact that the simulated ITCZ is asymmetric with respect to the equator in the first phase of the experiment remains to be explained. Figure 6(b) shows the results of an identical experiment except that the values of 90% and 95% are switched. In this experiment the move away from the equator is abrupt, characteristic of a catastrophe. Also, in another experiment, the

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