Oscillations of the intertropical convergence zone and the genesis of easterly waves. Part I: diagnostics and theory

Abstract

We examine the mean and transient state of the intertropical convergence zone (ITCZ) by analyzing data and using simple theory. We concentrate on the tropical eastern Pacific Ocean noting that there exists in this region a well-developed mean ITCZ. Furthermore, it is a region where there has been considerable discussion in the literature of whether easterly waves develop in situ or propagate westwards from the Atlantic Ocean. The region is typical of tropical regions where there is a strong cross-equatorial pressure gradient (CEPG): mean convection well removed from the equator but located equatorward of the maximum sea-surface temperature (SST) and minimum sea level pressure (MSLP). Further to the west, near the dateline where the CEPG is much smaller, convection is weaker and collocated with SST and MSLP extrema. It is argued that in regions of significant CEPG that the near-equatorial tropical system is inertially unstable and that the rectification of the instability for a given CEPG determines the location and intensity of the climatological ITCZ. Using simple theoretical arguments, we develop an expression for the mean latitude of the ITCZ as a function of the CEPG. We note on a day-by-day basis that the ITCZ is highly transient state with variability occurring on 3–8 day time scales. Transients with amplitudes about half of the mean ITCZ, propagate northwards from the near-equatorial southern hemisphere as anomalous meridional oscillations, eventually amplifying convection in the vicinity of the mean ITCZ. It is argued that in these longitudes of strong CEPG the mean ITCZ is continually inertially unstable with advections of anticylonic vorticity across the equator resulting in the creation of an oscillating divergence–convergence doublet. The low-level convergence produces convection and the resultant vortex tube stretching generates cyclonic vorticity which counteracts the northward advection of anticylonic vorticity. During a cycle, the mid-troposphere heating near 10ºN oscillates between 6 and 12 K/day at the inertial frequency of the latitude of the mean convection. As a result, there exists an anomalous and shallower, oscillating meridional circulation with a magnitude about 50% of the mean ITCZ associated with the stable state following the generation of anticylonic vorticity. Further, it is argued that the instabilities of the ITCZ are directly associated with in situ development of easterly waves which occur with the inertial period of the latitude of the mean ITCZ. The dynamical sequences and the genesis of easterly waves are absent in the regions further to the east where the CEPG is much weaker or absent altogether. In a companion study (Part II), numerical experiments are conducted to test the hypothesis raised in the present study.

Appendix

We examine the assumptions made by THW in concluding that the linear stability criterion is not met in near equatorial regions of substantial CEPG. In regions where the atmosphere is inertially unstable, the meridional wind accelerates poleward resulting in a divergence–convergence pattern, with divergence equatorward of the zero absolute vorticity line and convergence on the poleward side of η = 0 line. However, the effect of the low level horizontal convergence on vertical motion depends on the static stability of the atmosphere. THW assumed a well-mixed boundary layer model topped by a temperature inversion (δθ = 3°K) at an altitude of 1–2 km and concluded that the observed zonal wind shear was several time smaller than the shear required to meet the linear instability criterion. To reexamine this issue, we start with the THW model (described in detail in TWH, Sect. 3) that is linearized about a basic zonal wind state:

$$ \frac{\partial u}{dt} + v\left( {\frac{dU}{dy} - \beta y} \right) + \alpha u = 0 $$

(8)

$$ \frac{\partial v}{\partial t} + \beta yu + \frac{{\partial \phi^{{}} }}{\partial y} + \alpha v = 0 $$

(9)

$$ \frac{\partial \phi }{\partial t} + C_{B}^{2} \frac{\partial v}{\partial y} = - \varepsilon \phi $$

(10)

where u and v represent zonal and meridional wind perturbations, α is a linear damping coefficient, Φ represent the perturbation geopotential, and ɛ ⁻¹ the boundary layer relaxation time. The parameter C _B is given by: $C_{B} = \left( {{{gH_{B} \delta \theta } \mathord{\left/ {\vphantom {{gH_{B} \delta \theta } {\theta_{0} }}} \right. \kern-\nulldelimiterspace} {\theta_{0} }}} \right)^{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$2$}}}},$ where g the gravitational acceleration, H _B the mean boundary layer depth, δθ a potential temperature jump at the top of the boundary layer. θ ₀ the reference state potential temperature.

If a constant mean shear is assumed (e.g., Dunkerton 1981) then $U = \gamma y,$ where γ is a constant of proportionality. Elimination of u and ϕ from Eq. (8–10) gives:

$$ \left( {\frac{\partial }{\partial t} + \alpha } \right)^{2} v + \left( {\beta y\left( {\beta y - \gamma } \right)} \right) v - C_{B}^{2} \frac{{\partial^{2} v}}{\partial y} = 0 $$

(11)

Assuming an exponential form for v:

$$ v\left( {y,t} \right) = V\left( y \right)e^{i\omega t} , $$

(12)

a solution with the form $V\left( y \right) = V_{0} \exp \left( {{{ - \nu^{*2} } \mathord{\left/ {\vphantom {{ - \nu^{*2} } 2}} \right. \kern-\nulldelimiterspace} 2}} \right)$ has been found, where $\nu^{*} = \left( {{\beta \mathord{\left/ {\vphantom {\beta {C_{B} }}} \right. \kern-\nulldelimiterspace} {C_{B} }}} \right)^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}} y$ which possess eigenvalues:

$$ \left( {\omega - i\alpha } \right)^{2} + \frac{{\gamma^{2} }}{4} = \beta C_{B} $$

(13)

Equation 13 shows that instability (i.e., ω imaginary) occurs only if the linear shear of the zonal wind (γ) is greater than a critical value: $\gamma^{2} > 4 \beta C_{B}.$ THW calculated that for inertial instability to occur with H _B  ~ 1 km and a potential temperature jump (δθ) of 3°K, the flow speed must increase by more than 30 ms⁻¹ over 10° latitude. However, for much smaller values of potential temperature jump (i.e., a reduced cap at the top of the boundary layer) instability can occur for much smaller value of shear of the zonal wind. This turns out to be the case for the eastern Pacific Ocean.

Figure 13 shows the vertical profile of potential temperature and equivalent potential temperature obtained from atmospheric soundings launched from the NOAA Research Ship Ron Brown cruise (thick line) during the East Pacific Investigation of Climate (EPIC) 2001 field campaign (Raymond et al. 2004). Analyses close to 1800 UTC are presented for 1°S, 2°N, 5°N, and 8°N, and 95°W. The character of the atmospheric boundary layer changes from equator to the north, with very distinct profiles of potential temperature. While at 1°S and 2°N there is an apparent cap at the top of the atmospheric boundary layer (δθ = 3° − 6°K), at 5°N and 8°N the atmosphere seems to be at least neutrally stratified with no stable cap at the top of the boundary layer. The data used in Fig. 13 is similar to the EPIC 2001 NCAR C-130 research aircraft dropwindsondes (deSzoeke et al. 2005). When moisture is considered, it is apparent from both Fig. 13c and d that the more northward profiles (5°N and 8°N) are conditionally unstable. For comparisons, long-term mean (1981–2000) potential temperature and equivalent potential temperature profiles for July, were calculated using the ERA 40 reanalysis dataset. A similar vertical structure of both potential temperature and equivalent potential temperature was found. Thus, the conclusions made by THW do not hold for the northern regions (5°N and 8°N) and, for values of δθ ≈ 0, the linear criterion for inertial instability is met for any shear of the zonal wind γ > 0.

Fig. 13

Vertical profiles of potential temperature (black) and equivalent potential temperature (red) for the eastern Pacific ITCZ during 1–10 October, 2001 period using atmospheric soundings from the NOAA ship Ron Brown cruise in support of the Eastern Pacific Investigations of Climate (EPIC) field campaign (thick line). For comparison, long term mean (1981–2000) profiles for July (dotted lines) were calculated using the ERA 40 dataset