Abstract

A methodology for diagnosing convectively coupled equatorial waves is applied to output from two high-resolution versions of atmospheric models, the Hadley Centre Atmospheric Model, version 3 (HadAM3), and the new Hadley Centre Global Atmospheric Model, version 1 (HadGAM1), which have fundamental differences in dynamical formulation. Variability, horizontal and vertical structures, and propagation characteristics of tropical convection and equatorial waves, along with their coupled behavior in the models, are examined and evaluated against a previous comprehensive study of observed convectively coupled equatorial waves using the 15-yr ECMWF Re-Analysis (ERA-15) and satellite observed data. The extent to which the models are able to represent the coupled waves found in real atmospheric observations is investigated. It is shown that, in general, the models perform well for equatorial waves coupled with off-equatorial convection. However, they perform poorly for waves coupled with equatorial convection. Convection in both models contains much-reduced variance in equatorial regions, but reasonable off-equatorial variance.

The models fail to simulate coupling of the waves with equatorial convection and the tendency for equatorial convection to appear in the region of wave-enhanced near-surface westerlies. In addition, the simulated Kelvin wave and its associated convection generally tend to have lower frequency and slower phase speed than that observed. The models are also not able to capture the observed vertical tilt structure and signatures of energy conversion in the Kelvin wave, particularly in HadAM3. On the other hand, models perform better in simulating westward-moving waves coupled with off-equatorial convection, in terms of horizontal and vertical structures, zonal propagation, and energy conversion signals. In most cases both models fail to simulate well a key picture emerging from the observations, that some wave modes in the lower troposphere can act as a forcing agent for equatorial convection, and that the upper-tropospheric waves generally appear to be forced by the convection both on and off the equator.

1. Introduction

Convectively coupled equatorial waves (CCEWs) are fundamental components of the complete picture of the tropical atmosphere, which involve the interactions of convection and other physical processes with each other and with the dynamics. A number of observational studies have shown that much of the convection in the tropics can be associated with theoretical equatorially trapped modes (e.g., Hendon and Liebmann 1991; Takayabu 1994a,b; Magaña and Yanai 1995; Pires et al. 1997; Wheeler and Kiladis 1999; Wheeler et al. 2000; Straub and Kiladis 2002, 2003; Yang et al. 2003; Yang et al. 2007ac). Yang et al. 2003 and Yang et al. 2007ac have described in detail the horizontal and vertical structures and propagation of these modes, how they depend on the background state, and how coupling with convection modifies their structures.

A faithful representation of these interactions and wave modes is needed for predictions on all time scales. However, at present there is little understanding of how well they are treated in state-of-the-art models and our overall knowledge of these waves is very limited. Current large-scale models fail to simulate well-organized tropical phenomena in which convection interacts with dynamics and physics. Lin et al. (2006) showed that 14 atmospheric global circulation models (AGCMs) that participated in the Intergovernmental Panel on Climate Change (IPCC) have significant problems in simulating tropical subseasonal variability and the organization of convection by equatorial wave modes. Only about half of the 14 IPCC climate models have signals of CCEWs, and the variances are generally too weak for all wave modes except the eastward inertiogravity wave. Ringer et al. (2006) showed that the Met Office Unified Model suffers from similar problems in both climate and weather forecast (NWP) configurations, with limited convective variance coincident with equatorial wave modes, especially near and on the equator.

The possibility that formulation of the convection scheme may have a significant role has been discussed by Suzuki et al. (2006). They showed that an AGCM run with a convective suppression scheme, in which cumulus convection is suppressed until the cloud layer–averaged relative humidity exceeds the threshold of 80%, can reproduce convectively coupled equatorial Kelvin, n = 1 Rossby (R1), mixed Rossby–gravity (MRG), and n = 1 eastward inertiogravity waves, whereas without convective suppression only Rossby waves are coupled with convection. In this case, cumulus convection is controlled by convective available potential energy (CAPE), and only the larger frictional convergence of the Rossby wave mode can produce enough CAPE to generate favorable conditions for organized cumulus convection. On the other hand, in the case with convective suppression, cumulus convection is largely controlled by the humidity in the free atmosphere under the condition that abundant CAPE exists everywhere in the tropics. Only the large-scale convergence associated with the dynamical wave can produce the moisture anomaly necessary to overcome the relative humidity threshold and maintain the favorable conditions for cumulus convection once it starts. This is suggestive that inclusion of some kind of mechanism connecting free tropospheric moisture with convection under the condition of abundant CAPE could be a key factor for coupling between equatorial waves and convection.

Recently, Lin et al. (2008) showed that both the moisture convective trigger and the actual convective parameterization have significant impacts on AGCM-simulated precipitation associated with CCEWs. However, in all cases, the simulated spectral peaks corresponding to the Kelvin, R1, and eastward-moving MRG waves are much weaker than observed.

The poor performance of GCMs in representing CCEWs has therefore remained a major research issue. However, compared with observational studies of CCEWs, there are relatively few detailed studies of CCEWs in models, especially in terms of their horizontal and vertical structures, as well as their propagation. Lin et al. (2006), Ringer et al. (2006), and Lin et al. (2008) only focused on the variance of convection associated with equatorial waves and, although Suzuki et al. (2006) showed horizontal and vertical structures of CCEWs, they did not give any comparison with observations or discussion of the propagation characteristics of CCEWs. Therefore, a comparison study of observed and modeled CCEWs in terms of their variances, 3D structures, and propagation features would be beneficial for increasing the understanding of the large-scale interaction of physics and dynamics in the tropical atmosphere in the context of CCEWs, and for understanding in what ways models are deficient. This is the stimulus for this study.

Most studies on CCEWs, either observational or modeling, identify equatorial waves using filters in specific zonal wavenumber-frequency domains related to the theoretical dispersion relationships for specified equivalent depths. While it is the case that tropical convection can be organized on preferred space and time scales that coincide approximately with those of theoretical equatorial waves, as seen in Wheeler and Kiladis (1999), in the real atmosphere the complicated space–time dependence of the ambient state can be expected to lead to Doppler shifting and distortion of theoretical dispersion curves for equatorial waves and to variations in the vertical heating profile and, hence, the equivalent depth h. Also, convectively coupled modes might be expected to exhibit rather different behavior from dry waves. Hence, different equatorial modes may not in reality be well separated in their frequency–zonal wavenumber domain.

Yang et al. (2003, hereafter YHS) developed a different but complementary methodology for analyzing convectively coupled equatorial waves. This exploits the usual theory for adiabatic normal modes on a resting atmosphere but does not demand that all aspects of this theory are valid. The only imposition from theory is the use of the horizontal normal mode structures as a basis for projecting the data. The method was applied to the 15-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-15) data and satellite-observed window brightness temperature provided by the Cloud Archive User Service (CLAUS) project (Hodges et al. 2000). In the case study of July 1992 described in YHS, various CCEWs at upper and lower tropospheric levels were revealed. Kelvin, eastward and westward propagating mixed Rossby–gravity (EMRG and WMRG), and R1 waves were all identified with a robust consistency between the two independent data sources.

In an extension of YHS, Yang et al. (2007ac, hereafter YHS07ac) investigated the seasonal characteristics of CCEWs, their horizontal and vertical structures, and zonal propagation. Coherent eastward- and westward-moving CCEWs with wavenumbers 6–8 were found and their association with convection analyzed. It was shown that over the warm waters of the Eastern Hemisphere, the Kelvin and R1 waves tend to have equatorial convection in the region of enhanced lower-level westerlies, suggesting that enhanced surface energy fluxes associated with these waves may play an important organizing role for equatorial convection. While wave structures in the lower troposphere can act as a forcing agent for convection, the convection itself can modify the structures of the theoretical modes. Coexistence of different wave structures was also found for westward-moving waves and eastward-moving upper-tropospheric waves. It was also shown that the midtropospheric Kelvin wave and the Western Hemisphere barotropic R1 wave were closely associated with extratropical wave activity in the winter hemisphere.

This analysis of the behavior of CCEWs provides a basis for evaluating weather and climate model performance and provides a test bed for experimentation aimed at improving the coupling of physics and dynamics in models. The aim of this study is to use results from observations to evaluate the ability of high-resolution climate models from the Hadley Centre to capture CCEWs. The performance of models in representing equatorial waves and their coupled behavior will be examined and compared with the observed variance, composite horizontal and vertical structures, and propagation characteristics of various CCEWs.

The outline of this paper is as follows. Section 2 describes the models, data, and method. Section 3 presents the overall activity of the tropical convection and various dynamical wave modes. The horizontal and vertical structures and propagation of CCEWs will be shown in section 4. Some conclusions and a discussion will be given in section 5.

2. Model description, data, and method

The atmospheric components of two general circulation climate models developed at the Met Office’s Hadley Centre, Hadley Centre Atmospheric Model (HadAM3, 30 levels) and the Hadley Centre Global Atmospheric Model (HadGAM1, 38 levels), are used. HadGAM1 differs markedly from the predecessor model HadAM3. The most significant structural difference is that HadGAM1 has a new dynamical core (Davies et al. 2005). Description of the two models can be found in Pope et al. (2000), Johns et al. (2006), Martin et al. (2006), and Ringer et al. (2006). A brief description is provided here. Both are gridpoint models. HadAM3 uses Eulerian dynamics and is a hydrostatic primitive equation model with a split-explicit advection scheme. The vertical coordinate is hybrid pressure with no staggering of winds and temperature in the vertical and using the Arakawa B grid in the horizontal. HadGAM1 is nonhydrostatic, fully compressible, and uses the full primitive equations. The advection scheme is semi-Lagrangian with an off-centered two-time level semi-implicit time discretization. The dynamics uses an Eulerian treatment of the continuity equation and conserves the dry mass of the model. The model uses the Arakawa C grid in the horizontal and the Charney–Phillips grid in the vertical. The vertical coordinate is a hybrid height with levels near the bottom boundary following the surface terrain and those at the top of the model being flat.

Both models are run at higher resolution (N144: 0.83° latitude × 1.25° longitude) than normal. The high-resolution version of HadGAM1, HiGAM, has been developed within the U.K.-HiGEM project and its performance coupled to a high-resolution ocean (1/3° latitude–longitude) is described in Shaffrey et al. (2009). Both models are forced with observed Atmospheric Model Intercomparison Project (AMIP II) SSTs in May–October 1992 using initial atmospheric conditions from a previous integration. Observational data used are multilevel ERA-15 and satellite-observed brightness temperature provided by the CLAUS project for the same period.

The dynamical fields used to analyze equatorial waves are daily (1200 UTC) horizontal winds (u, υ) and geopotential height (Z) from ERA-15 and from the simulations with the HadAM3 and HiGAM. The proxies used for tropical convection are observed brightness temperature (Tb) and model outgoing longwave radiation (OLR). For a quantitative comparison, model OLR is converted to Tb using the formula OLR = σTf4, where Tf = Tb(a + bTb) is the flux equivalent brightness temperature, and a = 1.228 and b = 1.106 × 10−3 K−1 (see Ohring and Gruber 1984). The ERA data have a grid resolution of ∼1.125° and the observed Tb data a grid resolution of 0.5°. Model data have been regridded to a coarser grid (1.25° × 1.25°) to be comparable to the ERA data before analysis.

Since the intensity of mean convection strongly affects the amplitude of CCEWs, and tropical background winds can affect the structures and zonal propagation of equatorial waves through Doppler shifting (YHS07a,b), Fig. 1 shows the horizontal distribution of the seasonal mean Tb (Fig. 1a) and vertical distribution of the seasonal mean equatorial zonal winds (Fig. 1b) during May–October 1992 for the observations and the two simulations. The spatial patterns of the mean convection fields (Fig. 1a) suggest that both models simulate the mean geographical distribution of tropical convection reasonably well. However, modeled Tb are generally higher than observed over the equatorial Indian Ocean and eastern Pacific clear-sky regions, indicative of weaker convection over the former region and stronger clear skies over the latter region. Over the ITCZ and South Pacific convergence zone (SPCZ) Tb in the models is comparable to that observed, suggesting that a double-ITCZ pattern in precipitation (characterized by excessive precipitation over the ITCZ and SPCZ, together with a precipitation region over the SPCZ extending too far to the east) as shown in Lin (2007) for the IPCC Fourth Assessment Report (AR4) version of the N96 AMIP run with HadGAM (Fig. 11e) seems not to occur for the two high-resolution models. However, as will be shown in section 3, there is a sign of a double ITCZ in convective activity. In the troposphere both models give zonal wind distributions similar to those observed: upper-tropospheric strong easterlies in the Eastern Hemisphere (EH) associated with the Asian summer monsoon and westerlies in the Western Hemisphere (WH) associated with the two well-known equatorial westerly ducts, and weaker lower-tropospheric winds with reversed sign from those in the upper troposphere. However, these winds in HadAM3 and the Atlantic westerly duct in HiGAM are stronger than in observations. Major differences between the observations and models are seen in the stratosphere. The observed winds are in the easterly phase of the quasi-biennial oscillation (QBO) in the lower stratosphere with the strongest easterly wind around 50 hPa. In HadAM3 easterly winds are weaker with the maximum appearing at a higher level, above 30 hPa, whereas in HiGAM the easterly winds are generally stronger and monotonically increasing with height, with the strongest wind occurring at the top level, 10 hPa.

Fig. 1.

Seasonal mean of (a) the horizontal distribution of tropical brightness temperature Tb (K) and (b) the longitude–pressure distribution of equatorial (5°N–5°S) averaged zonal winds (u) in (top) ERA-15, (middle) HadAM3, and (bottom) HiGAM in May–October 1992. The contour interval in (b) is 2 m s−1 for winds smaller than 10 m s−1, and 5 m s−1 for winds larger than 10 m s−1, with easterly contours dotted and the zero contour dashed. Regions with easterly winds larger than 10 m s−1 are shaded.

Fig. 1.

Seasonal mean of (a) the horizontal distribution of tropical brightness temperature Tb (K) and (b) the longitude–pressure distribution of equatorial (5°N–5°S) averaged zonal winds (u) in (top) ERA-15, (middle) HadAM3, and (bottom) HiGAM in May–October 1992. The contour interval in (b) is 2 m s−1 for winds smaller than 10 m s−1, and 5 m s−1 for winds larger than 10 m s−1, with easterly contours dotted and the zero contour dashed. Regions with easterly winds larger than 10 m s−1 are shaded.

Fig. 11.

As in Fig. 6 but for (a),(b) horizontal structures of the westward-moving n = 1 wave and the associated convection regressed on the extrema in the off-equatorial convective index over the region 6°–18°N for the observations and 7.5°–17.5°N for the models. (c) Correlation between the convective index extrema and R1 wave υ at 8°N.

Fig. 11.

As in Fig. 6 but for (a),(b) horizontal structures of the westward-moving n = 1 wave and the associated convection regressed on the extrema in the off-equatorial convective index over the region 6°–18°N for the observations and 7.5°–17.5°N for the models. (c) Correlation between the convective index extrema and R1 wave υ at 8°N.

To extract the wave structures, the dynamical and convective fields are first separated into eastward- and westward-moving components using a space–time spectral analysis (Hayashi 1982). The data are filtered in a domain of zonal wavenumber k = ±2 to ±10 and period 3–30 days, which contains most of the lower-frequency equatorial waves. At each level, υ and two variables, q = αZ + u and r = αZu (where α is related to the trapping scale predetermined by the data, see YHS), are projected onto different wave modes given by equatorial wave theory. Details of the methodology have been described in YHS and YHS07a.

As in YHS07a, linear regression techniques are used to obtain composite horizontal structures of the convective and 3D dynamical fields, and the spatial relationships between them. First, convective fields likely to be associated with different modes are obtained by linear regression of the Tb field onto a key aspect of the lower-level relevant dynamical fields. Having determined latitude–longitude convective structures likely to be associated with the waves, these are used to provide convective indices for each “wave” as a function of longitude and time, where the convective indices involve Tb values averaged latitudinally over their preferred latitude bands. The complete horizontal structures of convectively coupled modes are then obtained by regression of the u and υ fields for a specified wave, as well as the total eastward or westward Tb, against the extrema (Tb > 0.5 K) of the convective index associated with the particular wave. The vertical structures of the CCEWs are described by the correlations between convective index extrema and wave meridional structures as a function of longitude and pressure levels.

To investigate wave evolution and zonal propagation, convective and appropriate dynamical fields are regressed onto extrema in the specified convective index as a function of time and longitude using lagged regression. The Radon transform method, first described by Radon (1917), and applied in a number of studies on oceanic and atmospheric planetary waves (e.g., Challenor et al. 2001; YHS07b) is used to calculate phase speed in a specified longitude–time domain. Details of the method have been described in YHS07b.

CCEWs investigated in this study include the eastward-moving Kelvin wave coupled with equatorial convection, westward-moving MRG waves coupled with off-equatorial convection, and R1 waves coupled with off-equatorial and equatorial convection. Detailed analysis is only performed for the Eastern Hemisphere (0° eastward to 180°), that is, the more convective hemisphere. The observational analysis parallels that in YHS07ac with some minor differences: in section 4 the coupled Kelvin wave is for the region 0°–180° instead of 50 eastward to 230° as in YHS07ac; the westward-moving n = 0 and 1 waves are for the whole season (May–October 1992) instead of being separated into midsummer and transition seasons. Comparison with YHS07ac shows that the results are not sensitive to these choices.

3. Mean convective and dynamical variability

a. Convective variability

To examine the fraction of large-scale variability associated with transient, propagating tropical convection, the standard deviation of Tb is separated into westward- and eastward-moving components in zonal wavenumbers from 2 to 10 and periods from 3 to 30 days (Fig. 2). The observed westward-moving convection (Fig. 2a) is predominantly off the equator with strongest amplitudes over the Indian summer monsoon, south Indian Ocean, Pacific ITCZ, and SPCZ. Eastward-moving convective activity (Fig. 2b), on the other hand, is mainly centered near the equator over the warmer waters, whereas to the west of the date line it is weaker and mainly along the ITCZ.

Fig. 2.

Westward- and eastward-moving standard deviation of Tb (K) for the (a),(b) observations, (c),(d) HadAM3, and (e),(f) HiGAM for May–Oct 1992.

Fig. 2.

Westward- and eastward-moving standard deviation of Tb (K) for the (a),(b) observations, (c),(d) HadAM3, and (e),(f) HiGAM for May–Oct 1992.

Compared with observations, the HadAM3 (Figs. 2c and 2d) simulation of off-equatorial convective variability is generally quite accurate, although its westward variance is too weak over the Indian summer monsoon and Pacific ITCZ, and its eastward variance is too strong over the central South Pacific. However, the model gives a poor simulation near the equator, with the variability being much lower than observed, especially for the eastward-moving, equatorially centered convection over the Indian Ocean–western Pacific region, where the observed maxima are centered close to the equator and are associated with the Kelvin wave. The eastward-moving variance averaged over the whole equatorial band between 5°N and 5°S in the HadAM3 is about 58% of that observed. On the other hand, HiGAM generally shows larger variance than observed for westward-moving convection, except over the Indian summer monsoon region (Fig. 2e). The spatial distribution of the Northern Hemisphere (NH) westward variance in HiGAM is somewhat different from that in observations with strong variance over the ITCZ instead of over the Indian summer monsoon region as observed, related to poor overall simulation of rainfall over India during summer (see Martin et al. 2006; Shaffrey et al. 2009). For eastward-moving convection, the HiGAM (Fig. 2f) simulation of the variance associated with the equatorially centered convection over the Indian Ocean–west Pacific region is more realistic than with HadAM3. However, the modeled variance is less confined to the equatorial region than in observations. It is interesting to note that there is stronger convective activity than observed over the SPCZ and ITCZ in HiGAM and the activity over the SPCZ extends too far southeast in both models, perhaps a sign of a double ITCZ, although it is not clear in the mean Tb field (Fig. 1a).

To assess the organization of convection by equatorial waves in the models, space–time spectra of observed and modeled Tb, averaged between 15°N and 15°S, have been calculated and are shown in Fig. 3, both the raw spectra (Fig. 3a) and with the background red spectrum removed (Fig. 3b), as described by Wheeler and Kiladis (1999). Compared to observations, the modeled raw spectra are confined at lower frequency, with no significant power above a frequency of 0.4 day−1 or period 2.5 days. In HiGAM, the power at lower frequency is much stronger than observed, especially for the westward component, consistent with the stronger westward variance seen in Fig. 2e. In contrast to observations in which the Kelvin wave signal is evident, even in the raw spectrum, both models show a flat distribution of eastward symmetric power concentrated around periods of about 30 days, with some similarity to the signature of the Madden–Julian oscillation (MJO), but rather shorter period.

Fig. 3.

Zonal wavenumber–frequency power spectra of the (a) raw spectra and (b) spectra divided by background power for the (top) symmetric (the odd meridional mode number n) and (bottom) antisymmetric (even n) components of Tb for the (left) observations, (middle) HadAM3, and (right) HiGAM. The power has been averaged over 15°N–15°S. Superimposed lines in (b) are the dispersion curves for the odd and even n equatorial waves at the equivalent depths of h = 8, 24, and 48 m, including a Doppler shift by a 3 m s−1 easterly flow (the observed average tropical low-level zonal wind).

Fig. 3.

Zonal wavenumber–frequency power spectra of the (a) raw spectra and (b) spectra divided by background power for the (top) symmetric (the odd meridional mode number n) and (bottom) antisymmetric (even n) components of Tb for the (left) observations, (middle) HadAM3, and (right) HiGAM. The power has been averaged over 15°N–15°S. Superimposed lines in (b) are the dispersion curves for the odd and even n equatorial waves at the equivalent depths of h = 8, 24, and 48 m, including a Doppler shift by a 3 m s−1 easterly flow (the observed average tropical low-level zonal wind).

With the background red spectrum removed (Fig. 3b), the organization of observed tropical convection on preferred space and time scales is evident, which coincide with those for various theoretical equatorial waves with equivalent depths 8–48 m. However, it is clear that both HadAM3 and HiGAM contain very limited variability associated with the equatorial Kelvin, EMRG, and gravity wave time and space scales, although there is variance associated with Rossby and WMRG wave values. It is seen that the observed MJO signal is more evident in the asymmetric component associated with its NH summer location, but the two models show stronger 30-day signals in the symmetric component. This feature is also seen in the raw spectrum.

b. Dynamical wave activity

To summarize the overall dynamical wave activity, Fig. 4 shows vertical cross sections of the standard deviation for various dynamical wave structures in observations and models. In the troposphere, observed Kelvin wave activity (Fig. 4a), characterized by large variations in equatorial zonal wind u, are greatest around 150–100 hPa, over the warm waters of the EH. There is also a secondary maximum in the lower stratosphere associated with upward propagating waves, although the vertical resolution of ERA-15 is probably not sufficient to represent this adequately. The model results (Figs. 4b and 4c) show that the Kelvin wave activity is poorly simulated. In general, the dynamical signature of the EH upper-tropospheric Kelvin wave is overestimated in the models, although it appears to have little interaction with, or influence on, the convection, as will be shown below. HadAM3 fails to capture the feature of upward propagation of the wave, with no peak in the 30–70-hPa region. On the other hand, HiGAM gives too much variance in the stratosphere above 30 hPa, with the increase with height being consistent with the corresponding easterly wind distribution (bottom panel in Fig. 1b). However, both models have very limited resolution above the tropopause.

Fig. 4.

Longitude–pressure cross section of the standard deviation of various equatorial waves for the (left) observations, (middle) HadAM3, and (right) HiGAM: (a)–(c) equatorial zonal wind u of the Kelvin wave, (d)–(f) equatorial meridional wind υ of the westward-moving n = 0 MRG wave, and (g)–(i) υ at 8°N/S of the westward-moving R1 wave. The units are m s−1.

Fig. 4.

Longitude–pressure cross section of the standard deviation of various equatorial waves for the (left) observations, (middle) HadAM3, and (right) HiGAM: (a)–(c) equatorial zonal wind u of the Kelvin wave, (d)–(f) equatorial meridional wind υ of the westward-moving n = 0 MRG wave, and (g)–(i) υ at 8°N/S of the westward-moving R1 wave. The units are m s−1.

On the other hand, it is seen from Figs. 4d–f that the MRG wave activity, measured by the equatorial meridional wind υ, is generally well simulated by both models in terms of geographic and vertical location, although the amplitude in the upper troposphere is too strong over most regions for HadAM3 and over the Atlantic westerly duct and its downstream region for HiGAM, consistent with the stronger basic winds there. Strong westerlies in the westerly duct of the Atlantic are favorable for middle-latitude wave activity propagating to the equator and triggering MRG waves. Similarly, the R1 wave activity (Figs. 4g–i), measured by the off-equatorial υ, is also quite well simulated by the models. However, the activity is too strong over the warm pool in both models. HiGAM also underestimates the westward-moving wave activity in the lower stratosphere, in contrast to the case for the Kelvin wave, which again can be partly explained by its stronger easterly wind in the stratosphere since easterly winds are favorable for the vertical propagation of the Kelvin wave but unfavorable for the westward-moving waves.

4. Structures and propagation of CCEWs

Since convective activity is strongest in the EH, the subsequent analysis will focus on it.

a. Convective fields associated with equatorial waves

To investigate the convective patterns associated with each wave mode, the Tb field is regressed at each latitude onto a lower-tropospheric (850 hPa) wind characteristic of the different equatorial waves and the result is shown in Fig. 5. The 0° relative longitude corresponds to the center of the specified characteristic wind component of the wave (schematic arrow). Observed convection associated with the Kelvin wave equatorial u (Fig. 5a) is centered close to the equator, toward the region of maximum westerly wind, and away from the convergence maximum, consistent with Wheeler et al. (2000) and Straub and Kiladis (2003). In contrast, convective fields associated with westward-moving MRG equatorial υ and R1 wave 8°N/S υ (Figs. 5d and 5g) are off-equator and strongly biased toward the NH (i.e., summer hemisphere). It is also apparent that convection associated with the R1 wave has an equatorial component that is closely connected to the equatorial u of the wave (Fig. 5j). This is discussed in detail in YHS and YHS07a.

Fig. 5.

Brightness temperature Tb regressed on various equatorial waves at 850 hPa for the (left) observations, (middle) HadAM3, and (right) HiGAM: (a)–(c) eastward-moving Tb regressed on Kelvin wave equatorial u, (d)–(f) westward-moving Tb regressed on westward-moving n = 0 MRG wave equatorial υ, (g)–(i) westward-moving Tb regressed on westward-moving n = 1 wave υ at 8°N/S, and (j)–(l) westward-moving Tb regressed on n = 1 wave (R1) equatorial u. Arrows schematically show the winds of the various waves to be regressed. The 0° relative longitude corresponds to the center of the relevant characteristic wind component. Dashed (solid) contours denote negative (positive) Tb with a contour interval of 0.4 K and the zero contours suppressed. Shaded areas denote Tb exceeding the 95% significance level. The regression value is taken to be 1.5 times the standard deviation peak of the waves.

Fig. 5.

Brightness temperature Tb regressed on various equatorial waves at 850 hPa for the (left) observations, (middle) HadAM3, and (right) HiGAM: (a)–(c) eastward-moving Tb regressed on Kelvin wave equatorial u, (d)–(f) westward-moving Tb regressed on westward-moving n = 0 MRG wave equatorial υ, (g)–(i) westward-moving Tb regressed on westward-moving n = 1 wave υ at 8°N/S, and (j)–(l) westward-moving Tb regressed on n = 1 wave (R1) equatorial u. Arrows schematically show the winds of the various waves to be regressed. The 0° relative longitude corresponds to the center of the relevant characteristic wind component. Dashed (solid) contours denote negative (positive) Tb with a contour interval of 0.4 K and the zero contours suppressed. Shaded areas denote Tb exceeding the 95% significance level. The regression value is taken to be 1.5 times the standard deviation peak of the waves.

Compared with observations, the convection associated with the Kelvin wave in the models (Figs. 5b and 5c) is weaker and the phase relationship between the lower-tropospheric wind and convection is not correct, the convection being collocated with the convergence instead of with the maximum westerly wind. Also, the spatial structure of the convective field is not well simulated by the models. On the other hand, the off-equatorial convection associated with the MRG (Figs. 5e and 5f) and R1 (Figs. 5h and 5i) waves is more consistent with observations, and with the low-level convergence given by basic equatorial wave theory, tending to be antisymmetric (symmetric) about the equator for the MRG (R1) wave. The observed eastward tilt with latitude in the convection is well captured by both models, and the observed wavelength and longitudinal development is reasonably simulated by the models, particularly for the R1 wave. However, the models tend to have an unrealistically strong convective signal in the austral winter (southern) hemisphere. More importantly, the observed feature of equatorial convection, associated with the equatorial u of the R1 wave (Fig. 5j), is only weakly evident in HiGAM (Fig. 5l) and totally missing in HadAM3 (Fig. 5k).

The preferred latitude bands for the convection associated with the different waves seen in Fig. 5 are used to create convective indices for subsequent regression and correlation analyses. The index of convection involves the Tb value averaged over a latitude band usually spanning 10°–12° in width. The band is either at a constant longitude (no tilt) or oriented southwest–northeast with a slope of 1° latitude × 1° longitude. For the Kelvin wave and westward-moving R1 wave coupled with equatorial convection, nontilted north–south-oriented bands are used for the index, with an equatorial latitude band of 6°N–6°S for the observation and 5°N–5°S for the models. For the westward-moving MRG and R1 modes coupled with off-equatorial convection, the index is calculated along a tilted line since the convective fields associated with them are strongly tilted, as seen in Figs. 5d–i. For the observations, the latitude bands for off-equatorial convection related to MRG and R1 waves are 4°–16° N and 6°–18°N, respectively. For the models, they are 5°–15°N and 7.5°–17.5°N, respectively. The latitude bands for the two waves are slightly different, as convection associated with the R1 wave is poleward compared with that for the MRG wave, as seen in Fig. 5 and suggested by theory. Investigation shows that the dynamical structures of waves are not, in fact, sensitive to the choice of a tilted or nontilted line for the index.

The complete horizontal structures of convectively coupled modes have been obtained by linearly regressing the u and υ fields for a specified wave, as well as the total eastward or westward Tb, against extrema (Tb > 0.5 K) in the convective index associated with the particular wave. The pictures thus obtained describe the basic structures of convectively coupled waves. In the following sections the structures and propagation of eastward- and westward-moving waves are presented.

b. The Kelvin wave coupled with equatorial convection

Figures 6a and 6b show the horizontal structures of the coupled Kelvin wave in the upper and lower troposphere, obtained by regressing the eastward-moving Tb and u of the Kelvin wave on the extrema in the convective index over the equatorial regions. The thick (thin) contours indicate areas of regressed negative (positive) Tb, indicating intensified (suppressed) convection exceeding the 95% significance level. The vectors are the regressed winds of the Kelvin wave. The significance of these winds is not shown in Figs. 6a and 6b but can be seen in the correlation between the extrema in the convective index and u of the Kelvin wave shown in Fig. 6c. For comparison, the theoretical horizontal lower-tropospheric structure of the dry Kelvin wave and its convergence/divergence is also shown in the top right of Fig. 6.

Fig. 6.

(a),(b) Horizontal structures of the Kelvin wave at the upper and lower levels and the associated eastward-moving Tb field, regressed on the extrema in the convective index over the equatorial regions 6°N–6°S for the (left) observations, and 5°N–5°S for (middle) HadAM3 and (right) HiGAM. The convective maximum (minimum in Tb) is taken to be located at 0° relative longitude, and a value of 1.5 times the peak standard deviation of Tb in the corresponding latitude band is used. The thick (thin) contour shows the region of regressed negative (positive) Tb that exceeds the 95% significance level, indicating the area of intensified (suppressed) convection. (c) Correlation coefficients between the convective index extrema and Kelvin wave u as a function of longitude and height. Solid (dashed) contours denote negative (positive) correlation corresponding to positive (negative) winds, with a contour interval of 0.1 but the zero contours not shown. The shaded area denotes correlations exceeding the 95% significance level. It should be noted that in the correlation diagrams the longitude range is from −60° to 60°, larger than the domain used in (a),(b). The top-right panel is the theoretical horizontal structure of the dry Kelvin wave, with thick (thin) contour showing the region of convergence (divergence).

Fig. 6.

(a),(b) Horizontal structures of the Kelvin wave at the upper and lower levels and the associated eastward-moving Tb field, regressed on the extrema in the convective index over the equatorial regions 6°N–6°S for the (left) observations, and 5°N–5°S for (middle) HadAM3 and (right) HiGAM. The convective maximum (minimum in Tb) is taken to be located at 0° relative longitude, and a value of 1.5 times the peak standard deviation of Tb in the corresponding latitude band is used. The thick (thin) contour shows the region of regressed negative (positive) Tb that exceeds the 95% significance level, indicating the area of intensified (suppressed) convection. (c) Correlation coefficients between the convective index extrema and Kelvin wave u as a function of longitude and height. Solid (dashed) contours denote negative (positive) correlation corresponding to positive (negative) winds, with a contour interval of 0.1 but the zero contours not shown. The shaded area denotes correlations exceeding the 95% significance level. It should be noted that in the correlation diagrams the longitude range is from −60° to 60°, larger than the domain used in (a),(b). The top-right panel is the theoretical horizontal structure of the dry Kelvin wave, with thick (thin) contour showing the region of convergence (divergence).

The observed Kelvin wave has its upper-level zonal wind divergence collocated with intensified convection. However, in the lower troposphere there is a displacement of the convective maximum away from the region of maximum convergence toward the region of maximum wind, as already noted. Since the strongest activity of the eastward-moving equatorially centered convection and Kelvin wave activity is over the Indian Ocean (Fig. 2b and Fig. 4a), where there are lower-level westerlies (top panel in Fig. 1b) and warm SSTs, it is suggestive that surface energy fluxes may play an important role in organizing equatorial convection. The possible importance of convective organization by wind-dependent surface energy fluxes has previously been discussed in a number of studies (e.g., Emanuel 1987; Neelin et al. 1987; Hendon and Salby 1994; Zhang 1996; Zhang and McPhaden 2000; YHS07a).

It is clear that this lower-level structure of convectively coupled Kelvin waves is poorly simulated by models, especially HadAM3 in which convection tends to be located directly over the lower-level convergence region instead of the westerly region as observed. In addition, the lower-level wave amplitude is weaker than observed. This is consistent with the results shown in Figs. 2 and 3. This is suggestive that the surface energy flux mechanism may be poorly simulated in the models.

The vertical structure of the observed and simulated coupled Kelvin wave, indicated by the correlation between the extrema in the convective indices and the equatorial u of the Kelvin wave, is shown Fig. 6c. The observed Kelvin wave has a tilted vertical structure with the upper-level wave shifted to the west of the lower-level wave compared with a first vertical mode structure. It also has a third peak at 500 hPa that, as proposed in YHS07c, may be associated with extratropical forcing from the Southern Hemisphere. This can be interpreted as the observed Kelvin wave having a second mode or modified first mode structure in the vertical. Above 300 hPa, the wave tilts eastward with height and significant amplitudes are seen at 70 hPa and beyond, a clear indication of upward wave propagation into the lower stratosphere, consistent with Fig. 4a. This observed upward propagation is in agreement with theoretical wave propagation behavior (e.g., Andrews et al. 1987), particularly since the 1992 summer is in the easterly phase of QBO in the lower stratosphere (top panel in Fig. 1b). In the models the simulated vertical structure is very different from that observed. It is basically a first internal vertical mode with no peak in the middle troposphere. In addition, although there is a sign of eastward-tilted structures between 150 and 100 hPa, the signal vanishes below 70 hPa, indicating a lack of the observed propagation into the stratosphere. This suggests that the strong Kelvin wave variance in the lower stratosphere in HiGAM (Fig. 4c) may not be simply connected to convectively coupled Kelvin waves in the troposphere. In support of this view, spectral analysis indicates that the waves in the lower stratosphere have higher frequency and smaller wavenumber than the convectively coupled waves in the troposphere.

To examine the zonal propagation of the convectively coupled Kelvin wave, longitude–time diagrams of the regressed Kelvin wave equatorial u (black contours) and associated eastward equatorial Tb index (colors), have been constructed (Fig. 7). Some propagation parameters, such as the typical wavelength (λ) estimated from successive peaks of a field at day 0, the phase speed (s) calculated using the RT method, and the period (p) deduced from λ/s, can be obtained. To avoid excessive numerical detail in the text and to help consolidate the results, these parameters are summarized in Table 1.

Fig. 7.

Longitude–time diagram of the eastward-moving equatorial convective (Tb) index (K; color) and Kelvin wave equatorial u (black thin contours) at (a) 200 hPa and (b) 850 hPa regressed on the extrema in the convective index in the equatorial region with a negative value of 1.5 times its peaked standard deviation, for the (left) observations, (middle) HadAM3, and (right) HiGAM. The Tb index is the same in the bottom and top panels. Positive (negative) day on the time axis indicates convective and wind fields lag (lead) the index extrema, which are at days 0 and 0° longitude. The contour interval is 0.2 m s−1 in (a) and 0.1 m s−1 in (b), with negative winds dashed and zero contours not drawn. Thick solid (dashed) contours indicate the boundaries of regions with positive (negative) winds exceeding the 95% significant level. The red contours indicate regions of regressed Tb index exceeding the 95% significance level.

Fig. 7.

Longitude–time diagram of the eastward-moving equatorial convective (Tb) index (K; color) and Kelvin wave equatorial u (black thin contours) at (a) 200 hPa and (b) 850 hPa regressed on the extrema in the convective index in the equatorial region with a negative value of 1.5 times its peaked standard deviation, for the (left) observations, (middle) HadAM3, and (right) HiGAM. The Tb index is the same in the bottom and top panels. Positive (negative) day on the time axis indicates convective and wind fields lag (lead) the index extrema, which are at days 0 and 0° longitude. The contour interval is 0.2 m s−1 in (a) and 0.1 m s−1 in (b), with negative winds dashed and zero contours not drawn. Thick solid (dashed) contours indicate the boundaries of regions with positive (negative) winds exceeding the 95% significant level. The red contours indicate regions of regressed Tb index exceeding the 95% significance level.

Table 1.

Wavelength (λ), phase speed (s), and period (p) for various waves and the associated equatorial (eq) or off-equatorial (Off-eq) centered convection. The R1 wave u is for 850 hPa only, and other waves are for 200 and 850 hPa. If values for the upper and lower levels are different, they are indicated by a pair of numbers separated by a shill with the first (second) number corresponding to that at 200 (850) hPa. Negative values of s indicate westward phase speed.

Wavelength (λ), phase speed (s), and period (p) for various waves and the associated equatorial (eq) or off-equatorial (Off-eq) centered convection. The R1 wave u is for 850 hPa only, and other waves are for 200 and 850 hPa. If values for the upper and lower levels are different, they are indicated by a pair of numbers separated by a shill with the first (second) number corresponding to that at 200 (850) hPa. Negative values of s indicate westward phase speed.
Wavelength (λ), phase speed (s), and period (p) for various waves and the associated equatorial (eq) or off-equatorial (Off-eq) centered convection. The R1 wave u is for 850 hPa only, and other waves are for 200 and 850 hPa. If values for the upper and lower levels are different, they are indicated by a pair of numbers separated by a shill with the first (second) number corresponding to that at 200 (850) hPa. Negative values of s indicate westward phase speed.

The propagation features of the Kelvin wave in the models differ significantly from observations. First, the modeled Kelvin wave exhibits westward group velocity (indicated by the region of largest wave activity moving westward with time). This is not consistent with the nondispersive nature of the classical theoretical dry Kelvin wave. Second, the spatial patterns and evolution of the convective and dynamical fields in the models are much less coherent than those observed, especially at the lower level, with large differences in speeds both between the dynamical wave and convection and between the upper- and lower-level waves. The convection and the upper-level dynamical wave in the models both have a much longer period, 10–12 days, than that observed, 6 days (see Table 1). This is consistent with the spectral analysis of convection, shown in Fig. 3, where there are no spectral peaks associated with the Kelvin wave with a period shorter than 10 days in the models. The lower-level wave in the models also has a longer period than observed. Consequently, for a similar wavelength the phase speeds, about 5–10 m s−1 in the models, are slower than the observed, 10–13 m s−1 (see Table 1). This is in contrast with the 14 IPCC climate models analyzed by Lin et al. (2006), which generally gave a faster phase speed than observed.

It is interesting to note that, both in observations and models, the lower-level wave has a longer wavelength and faster phase speed than both the upper-level wave and the convection. However, this difference is too large in models, with the phase speed of the lower-level wave being about twice that of convection. As a result, the lower-level convective coupling time (convective and dynamical fields connected in a coherent way) in the models is shorter than observed. In observations (Fig. 7b), the westerly (easterly) wind is almost in phase with intensified (suppressed) convection and this structure can last for several days. However, in the early stages, days −4 to −2, the intensified convection is close to being in phase with the convergence. The notion that the dynamical wave appears to move through the convection in the lower troposphere, with its structure changing from the Indian Ocean to the western Pacific, has also been suggested for the MJO (e.g., Rui and Wang 1990; Zhang 1996). This evolution is not simulated by either model, especially HadAM3. Although the simulated upper-level wave has propagation parameters closer to those for convection, the models fail to simulate the interesting observed aspect that the upper-level wave possesses identical wavelength, phase speed, and period with those for the convection and appears later than the convection, an indication of a possible convective forcing of the upper-level wave.

Given the structure of the Kelvin wave, it is of interest to examine further the total eastward dynamical fields associated with equatorial convection. Figure 8 gives the longitude–pressure cross sections of total eastward-moving equatorial (u, ω) vectors, Z (color), and temperature (red contours) regressed on the extrema in the equatorial convective indices. The associated regressed equatorial Tb is also indicated at the bottom of each panel. Several interesting features stand out in the observations (Fig. 8a).

Fig. 8.

Longitude–pressure cross sections of the total eastward-moving (u, ω) vectors, Z (color) and temperature T (red contours) at 0° latitude for the (a) observations, (b) HadAM3, and (c) HiGAM, regressed on the extrema in the eastward-moving equatorial convective index. It should be noted the observed T is derived from Z using the hydrostatic relation, which should be valid on these scales. The plot at the bottom of each panel shows the corresponding regressed Tb at 0° latitude. The vertical coordinate is pressure so that (u, ω) vectors are in proportion to the zonal and vertical coordinates. Units are m s−1 for u, 0.02 Pa s−1 for ω, gpm for Z, and K for T. Solid (dashed) red contours denote positive (negative) values of T with a contour interval of 0.05 K but the zero contours are not shown. The boxes in the observation panel indicate particular regions of ascent with T ′w′ > 0 (red) and T ′w′ < 0 (blue).

Fig. 8.

Longitude–pressure cross sections of the total eastward-moving (u, ω) vectors, Z (color) and temperature T (red contours) at 0° latitude for the (a) observations, (b) HadAM3, and (c) HiGAM, regressed on the extrema in the eastward-moving equatorial convective index. It should be noted the observed T is derived from Z using the hydrostatic relation, which should be valid on these scales. The plot at the bottom of each panel shows the corresponding regressed Tb at 0° latitude. The vertical coordinate is pressure so that (u, ω) vectors are in proportion to the zonal and vertical coordinates. Units are m s−1 for u, 0.02 Pa s−1 for ω, gpm for Z, and K for T. Solid (dashed) red contours denote positive (negative) values of T with a contour interval of 0.05 K but the zero contours are not shown. The boxes in the observation panel indicate particular regions of ascent with T ′w′ > 0 (red) and T ′w′ < 0 (blue).

First, there is a well-organized circulation with the basic structure of a simple Kelvin wave in the upper and lower troposphere, Z and u being in phase, and the upper-level divergence accompanied by strong ascent in the mid to upper troposphere. As before, a third peak in the u and Z fields near 500 hPa is seen with the Z field being shifted to the west of the u field by about a quarter of a wavelength, a pattern that is consistent with being a forced response associated with SH midlatitude forcing (see Figs. 3c and 4 in YHS07c).

Second, over the region of intensified convection there are anomalous westerly winds in the lower troposphere (775–1000 hPa). Therefore, the lower-tropospheric u convergence is to the east of the convection. There are also anomalous lower-tropospheric easterly winds in phase with suppressed convection to the east.

Third, different contributions to energy conversion can be deduced in the upper and lower troposphere. The region of ascent in the mid to upper troposphere and convective heating (Q, indicated by the cold Tb peak) are in phase with a region of warmer temperatures (T ′ > 0). This indicates convective creation of potential energy through Q′T ′ > 0, and its conversion into kinetic energy through T ′w′ > 0 in the mid- to upper troposphere, suggesting a convective forcing/feeding of the upper-tropospheric Kelvin wave. In contrast, between 500 and 775 hPa, the ascent between 0° and 12° longitude tends to be in a region of cooler temperatures, indicating an energy conversion contribution in the sense of kinetic to potential energy through T ′w′ < 0. The ascent near the tropopause is also in phase with cooler temperatures. The analysis that deep convection associated with the Kelvin wave occurs in regions of anomalously cold temperatures in the lower troposphere, warm temperatures in the upper troposphere, and cold temperatures at the level of the tropopause is in agreement with that found in Wheeler et al. (2000).

Comparing Fig. 8a with Figs. 8b and 8c, it is seen that the models simulate reasonably well the upper-tropospheric circulation. Although the signature of energy conversion in the upper troposphere is represented by the models, the T ′w′ correlation is weak. In the mid- lower troposphere, the simulated temperature is weak and the wave is basically neutral (T ′w′= 0), indicating that the observed energy conversion contribution there is not captured by the models. Also, the simulated intensified convection is weaker than observed and tends to be in phase with lower-tropospheric zonal wind convergence and ascent; the lower-tropospheric westerly is weaker and to the west of the convection. To the east of the convection, the lower-level circulation is incoherent.

Analysis of the horizontal structures of the total winds and Z at 850 hPa regressed on the extrema in eastward equatorial convective indices (not shown) indicates that the observed total fields in the tropics are, indeed, dominated by a Kelvin-wave-like structure, with the Z and u fields in phase and having a maximum centered on the equator. The relationship between the dynamical fields and convection is typical of the coupled Kelvin wave shown in Fig. 6b. However, in the simulations, the Kelvin-wave-like structure is only evident to the west of the convection, especially in HadAM3, and the convective coupling is poorly simulated by both models, with the intensified convection being in phase with the lower-tropospheric convergence.

The striking similarities in the horizontal and vertical structures between the Kelvin wave deduced from theory and the total eastward-moving u and Z fields in the observations support the robustness of the analysis methodology. That the models show less coherent Kelvin wave activity in their total fields reinforces the suggestion that some aspect of the physical–dynamical coupling, necessary for producing coherent structures, is lacking. This point will be returned to in the discussion.

c. Westward-moving n = 0 MRG wave coupled with off-equatorial convection

Figures 9a and 9b shows the horizontal structures of the n = 0 MRG wave at the upper and lower levels and the westward-moving Tb field, all regressed on the extrema in the indices of westward convection in the NH off-equatorial region. This indicates that the horizontal structure of the MRG wave and its convective coupling are quite well simulated by the models, with lower-level southerly (northerly) winds in the NH collocated with intensified (suppressed) convection, and an opposite connection in the upper troposphere, as suggested by the convergence field of the simple dry equatorial wave. However, as was also shown in Fig. 5, the models show significant convective signals in the SH that are not consistent with observations. This may be related to a tendency in the models to simulate double-ITCZ structures.

Fig. 9.

As in Fig. 6 but for (a),(b) horizontal winds of the westward-moving n = 0 MRG wave and the associated convection regressed on the extrema in the off-equatorial convective index over the region 4°–16°N for the observations and 5°–15°N for the models. (c) Correlation between the convective index extrema and MRG wave equatorial υ.

Fig. 9.

As in Fig. 6 but for (a),(b) horizontal winds of the westward-moving n = 0 MRG wave and the associated convection regressed on the extrema in the off-equatorial convective index over the region 4°–16°N for the observations and 5°–15°N for the models. (c) Correlation between the convective index extrema and MRG wave equatorial υ.

Despite the zonal and meridional winds being analyzed separately, the regressed winds show coherent structures quite similar to those of the theoretical WMRG wave, especially in the lower troposphere. However, in the upper troposphere for both the observations and HadAM3 the horizontal structure near intensified convection appears to be modified, with the zonal wind being reversed in direction compared with the simple WMRG wave, so that the structure there is more similar to that of an EMRG wave. Further analysis indicates that the observed modified upper-tropospheric wave structure is nearly always accompanied by strong convection. It is suggestive of a forced response to deep convection leading to a much stronger divergent component. This may also occur in HadAM3, which similarly has strong convection associated with the MRG wave (Fig. 5e).

Correlations between the extrema in the off-equatorial convective index and equatorial υ of the MRG wave are shown in Fig. 9c. The first internal mode structure of the MRG wave seen in the observations is successfully captured by the two models, although HadAM3 gives a less coherent structure and weaker coupling intensity (correlation). In the observations, the stronger wave train to the east of convection, especially in the upper troposphere when examined in a larger longitude range (see Fig. 7e of YSH07a), which for an eastward group velocity is indicative of stronger (weaker) convective coupling occurring in the more mature (new) waves, suggests that the upper-level wave may be excited by the organized convection. This behavior is also shown in the models.

The MRG wave propagation in both dynamical and convective fields is summarized in Fig. 10. Compared with the Kelvin wave, the modeled MRG wave shows more coherent propagation between convective and dynamical fields, and both models give a phase speed more comparable with the observations, although HiGAM is slightly slower (see Table 1). The eastward group velocity signature is also captured by the two models. However, the convective coupling time in HadAM3 is clearly shorter than in the observations, where it is about two weeks at the upper level and one week at the lower level. This is consistent with the weaker correlation in HadAM3 seen in Fig. 9.

Fig. 10.

As in Fig. 7 but for the westward-moving off-equatorial Tb index over the region 4°–16°N for the observations and 5°–15°N for the models, and the n = 0 MRG equatorial υ. The contour interval is 0.5 m s−1 for the upper level and 0.15 m s−1 for the lower level.

Fig. 10.

As in Fig. 7 but for the westward-moving off-equatorial Tb index over the region 4°–16°N for the observations and 5°–15°N for the models, and the n = 0 MRG equatorial υ. The contour interval is 0.5 m s−1 for the upper level and 0.15 m s−1 for the lower level.

In the observations the MRG wave has similar propagation characteristics in the upper and lower levels, indicating a strong vertical coupling. This feature is captured by HiGAM, but not by HadAM3, where the MRG wave shows a shorter wavelength and period in the lower level than in the upper level (Fig. 10 and Table 1). It is also clear that the observed MRG wave appears later than convection (biased to positive time lag), especially at the lower level, indicating that the wave may be forced by the convection. This feature is less clear in the models, especially in HiGAM, suggesting that the physical–dynamical coupling may be operating in a different way in the models.

d. Westward-moving R1 wave coupled with off-equatorial and equatorial convection

As shown in Fig. 4, the EH R1 wave is not only associated with off-equatorial convection (as expected from theory), but also has related equatorial convection; consequently we examine separately the R1 wave coupled with off-equatorial and equatorial convection.

1) Coupled with off-equatorial convection

Figures 11a and 11b show the horizontal structures of the R1 wave at the upper and lower levels and westward-moving Tb field, regressed on the extrema in the convective indices over the NH off-equatorial region. Compared with observations, the horizontal structure of the R1 wave is quite accurately simulated by the models, and the separate analysis of u and υ fields has again given coherent R1 wave structures, as for the MRG wave. In observations, the lower-level NH southerly winds are shifted to the east of the convective center, by several degrees compared with that suggested by the basic theoretical wave convergence, such that convection tends to be in phase with the cyclonic center. This feature is also seen in the two simulations. This shift reflects a feature of the NH midsummer Asian monsoon circulation, in which convection is closely connected to cyclonic circulation in the lower troposphere, as shown in Fig. 5c in YHS07c. This suggests that low-level frictional wave convergence may be important for off-equatorial convection. This convective coupling pattern is similar to that of the simulation with convective suppression in Suzuki et al. (2006, their Fig. 11).

It is also demonstrated in YHS07c that the observed total westward-moving fields connected to off-equatorial convection contain a mixture of MRG and R1 horizontal structures, with the former dominating to the east and the latter to the west of the convection, consistent with the modeling results of Hoskins and Yang (2000, Fig. 16). The lower-level R1 wave appears first, which may play an important role in organizing the convection that then forces the MRG wave (Figs. 5 and 7 in YHS07c). However, analysis indicates that the observed relationship between the MRG and R1 waves is not significant in the two simulations, although there is a tendency for the lower-level R1 wave to appear earlier than the MRG wave (not shown).

The corresponding vertical structure diagram (Fig. 11c) shows that the observed R1 wave has a basic first internal mode structure, but with the upper-level waves shifted several degrees to the east of the lower-level waves. The eastward tilt in the vertical is better simulated by HiGAM. It is possible that the eastward tilt is related to the upper-level waves appearing later than the low-level waves, as will be seen below in the zonal propagation diagram (Fig. 12). Both in the observations and HiGAM, stronger convective coupling occurs in the lower troposphere where the maximum correlation descends and decreases from west to east, with the strongest convective coupling appearing at 600–700 hPa near and to the west of convection and weaker correlations at lower levels to the east of convection. However, HiGAM gives a stronger eastward bias of the wave train in the lower troposphere than in observations, where this bias only exists near the surface and is not clear at the strongest coupling level around 600–700 hPa. For the observed convectively coupled R1 waves it is suggestive that they may be initiated around 600–700 hPa and then excite the wave below this with an eastward group velocity.

Fig. 12.

As in Fig. 7 but for the westward-moving off-equatorial Tb index over the region 6°–18°N for the observations and 7.5°–17.5°N for the models, and the n = 1 υ at 8°N. The contour interval is 0.3 m s−1 for the upper level and 0.1 m s−1 for the lower level.

Fig. 12.

As in Fig. 7 but for the westward-moving off-equatorial Tb index over the region 6°–18°N for the observations and 7.5°–17.5°N for the models, and the n = 1 υ at 8°N. The contour interval is 0.3 m s−1 for the upper level and 0.1 m s−1 for the lower level.

The zonal propagation results for the R1 wave given in Fig. 12 indicate that the observed eastward group velocity is generally reproduced in the simulations, and the two models show quite similar propagation parameters with those observed (see Table 1). Low-level southerly winds and upper-level northerly winds shifted to the east of convection are clearly seen for both the observations and the models. In observations the upper-tropospheric R1 wave occurs later than the lower-tropospheric wave and convection, which suggests a possible lower-level dynamical forcing for the convection and convective forcing of the upper-level wave, in contrast to the case for the MRG wave. This signature of the different nature of the coupling in the upper and lower troposphere is simulated by HiGAM but is not apparent in HadAM3.

Further information on the vertical structure is given in Fig. 13, which presents longitude–pressure cross sections of the total westward-moving structures at 10°N for υ (contours), ω (arrows), Z (color), and temperature (red contours), regressed on the extrema in the NH off-equatorial convective indices. It is seen that the structures simulated in the two models are quite similar to those observed. Both υ and Z exhibit what can be described as a modified first internal vertical mode structure, with maximum amplitudes near the outflow level around 150–200 hPa and maxima of reversed sign in the middle to lower troposphere. The heights of these centers decrease from west to east. Lower and middle tropospheric southerly winds and upper-tropospheric northerly winds are to the east of the convection, similar to that for the R1 wave, shown in Fig. 11, so that convection and the associated ascent occur almost in phase with the trough of the wave. There are differing contributions to the energy conversion in the upper and lower troposphere. Above 600 hPa, heating, ascent, and warm temperatures are in phase, indicating convective creation of potential energy through QT ′ > 0 and its conversion into kinetic energy (wT ′> 0), suggestive of convective forcing of the dynamical fields. This upper-level energy conversion is similar to that shown in the simulation with convective suppression in Suzuki et al. (2006). In contrast, at levels below 600 hPa heating and ascent are in phase with cold temperatures, indicating that kinetic energy is converted into potential energy (wT ′ < 0), which is destroyed by the heating (QT ′ < 0), which suggests dynamical forcing of the convection.

Fig. 13.

As in Fig. 8 but for longitude–pressure cross sections of the total westward-moving υ (contour), ω (vector), Z (color), and temperature T (red contours) at 10°N, regressed on the extrema in the westward-moving off-equatorial convective index in the (a) observations, (b) HadAM3, and (c) HiGAM. The curves underneath show the corresponding regressed Tb at 10°N. Solid (dashed) contours denote positive (negative) values of υ with a contour interval of 0.3 m s−1 but the zero contours are not shown.

Fig. 13.

As in Fig. 8 but for longitude–pressure cross sections of the total westward-moving υ (contour), ω (vector), Z (color), and temperature T (red contours) at 10°N, regressed on the extrema in the westward-moving off-equatorial convective index in the (a) observations, (b) HadAM3, and (c) HiGAM. The curves underneath show the corresponding regressed Tb at 10°N. Solid (dashed) contours denote positive (negative) values of υ with a contour interval of 0.3 m s−1 but the zero contours are not shown.

2) Coupled with equatorial convection

It is found in YHS and YHS07a that in the EH with the ambient westerlies equatorial convection can be associated with westerly wind maxima in R1 waves in the lower troposphere, as also seen here in Fig. 5j. The R1 wave convection in low-level westerlies was also found in Wheeler et al. (2000). This suggests a possible organizational role being played by surface energy fluxes. Figure 14 shows the horizontal and vertical structures of the R1 wave regressed on the extrema of the westward equatorial convective index. A coherent R1 wave structure emerges in the observations with equatorial convection collocated with the equatorial westerlies of the R1 wave, as was the case for the Kelvin wave (Fig. 6). As indicated by the correlation between the equatorial convective index and the equatorial zonal winds of the R1 wave (Fig. 14b), the relationship between equatorial convection and u is very significant and can exist in a rather deep layer from 1000 to 400 hPa. It can also be seen that the westerly winds connected with intensified convection are much stronger than the easterly winds, consistent with a positive feedback between the convection and the wind field in an ambient westerly flow.

Fig. 14.

As in Fig. 6 but for (a) the horizontal structure of the westward-moving n = 1 wave at 850 hPa and the associated westward-moving convection, regressed on the extrema in the equatorial convective index over the region 6°N–6°S for the observations and 5°N–5°S for the models. (b) Correlation between the convective index extrema and the R1 wave equatorial u.

Fig. 14.

As in Fig. 6 but for (a) the horizontal structure of the westward-moving n = 1 wave at 850 hPa and the associated westward-moving convection, regressed on the extrema in the equatorial convective index over the region 6°N–6°S for the observations and 5°N–5°S for the models. (b) Correlation between the convective index extrema and the R1 wave equatorial u.

This important connection between the R1 wave and equatorial convection is not well simulated by the models. In the simulations, weak correlations between the wind and convection only exist above 850 hPa, indicating that there are unlikely to be any wind-induced enhanced surface energy fluxes that may contribute to the equatorial convection. Moreover, the westerly winds associated with the intensified convection are not significantly stronger than their easterly counterparts as seen in the observations, suggesting that a positive feedback between the convection and the dynamics is missing. These missing links could partly explain the weak variance in convection over most of the near-equatorial region in the Hadley Centre climate models.

The propagation of the low-level R1 wave, with equatorial convection, shown in Fig. 15, further demonstrates that the observed coincidence of the westerly (easterly) wind of the R1 wave with intensified (suppressed) convection generally lasts for about two weeks. The dynamical and convective fields move westward with propagation characteristics similar to each other and to those found for the off-equatorial υ and convection. HadAM3 shows a less coherent evolution, with the wind field appearing later than the convection, indicating that the winds are forced by convection rather than acting as a forcing agent for convection. Although in HiGAM the winds seem to occur earlier, the coupled winds, as indicated by the thick contours, are very local and weak, and the convective coupling time is very short compared with observations. In contrast with the observed fields, in the models, the dynamical fields have a longer wavelength and period than the convection. (Fig. 15 and Table 1).

Fig. 15.

As in Fig. 7 but for the westward-moving equatorial Tb index and the westward n = 1 equatorial u. The contour interval is 0.2 m s−1.

Fig. 15.

As in Fig. 7 but for the westward-moving equatorial Tb index and the westward n = 1 equatorial u. The contour interval is 0.2 m s−1.

5. Conclusions and discussion

In this paper, equatorial wave activity, composite horizontal and vertical structures of various convectively coupled equatorial waves, and their propagation characteristics in observational data have been used to assess the performance of two versions of the Hadley Centre models with very different formulation.

The general conclusion is that the models perform well for equatorial waves coupled with off-equatorial convection. However, they perform poorly for waves coupled with equatorial convection.

It is shown that convection in both models contains very limited equatorial variance, but quite realistic off-equatorial variance. Although these models can simulate the dynamical aspects of equatorial waves, the coupling of these waves with convection in equatorial regions is deficient. Both models fail to simulate a key feature of the convectively coupled Kelvin and R1 waves in observations, namely near-surface anomalous equatorial zonal winds together with intensified equatorial convection and westerly winds in phase with the convection. Furthermore, the models fail to simulate a positive feedback between the equatorial convection and zonal winds of the R1 wave suggested by observations. If in the real world wind-dependent energy fluxes play a role in triggering equatorial convection, which can then modify and possibly amplify the waves, then this appears to be absent in the models.

In the observed Kelvin wave, intensified equatorial convection occurring with low-level westerlies in the wave is also consistent with deep convection following preconditioning by shallow convection in the convergence region, as discussed in previous observational studies of, for example, the Kelvin wave and the MJO (e.g., Straub and Kiladis 2002; Kiladis et al. 2005). This is not the case for the R1 wave since this westward-moving wave has its low-level equatorial convergence behind (to the east of) the convection.

Both models poorly simulate the vertical structure of the Kelvin wave. They fail to capture the vertical propagation of the Kelvin wave into the lower stratosphere as well as the secondary peak in the midtroposphere. Observed convective forcing of the upper-tropospheric Kelvin wave, associated with the convective creation of potential energy and its conversion into kinetic energy is only weakly evident in HiGAM and not clearly present in HadAM3. The lower-tropospheric conversion of kinetic energy into potential energy is similarly not captured in either model. Therefore, the observed energy cycle, which may act to amplify the wave, is missing in the models. In addition, the zonal propagation of the Kelvin wave and R1 wave with coupled equatorial convection is poorly simulated by the models. The Kelvin wave shows unrealistic westward group velocity and has a longer period and slower eastward phase speed than observed. The simulated equatorial u of the R1 wave coupled with equatorial convection does not show the observed coherent propagation with convection. The differing speeds for dynamical and convective fields would result in the period of any coupling between them being very limited.

On the other hand, the models perform better for westward-moving MRG and R1 waves coupled with off-equatorial convection. An eastward tilt with latitude of the convection and its antisymmetric/symmetric features associated with the two waves are successfully simulated by both models, although the convection in SH tends to be too strong, indicative of a tendency to produce a double ITCZ. Both models successfully simulate a coherent first internal WMRG wave structure with lower-level convergence coincident with intensified convection, as well as a coherent R1 wave structure with a lower-level cyclonic center in phase with convection but with a less clear first vertical mode structure. The two models also give a better simulation of the zonal propagation of the two waves with off-equatorial convection. For the R1 wave, the observed contribution to the energy cycle in the sense of potential energy converted into kinetic energy in the upper troposphere and a reverse conversion in the lower troposphere is also quite well simulated in the models.

However, it seems that in several cases, both models do not simulate well the key aspect emerging from observations that some wave modes in the lower troposphere can act as a forcing agent for equatorial convection. In addition, the two models do not represent the observed feature that upper-tropospheric waves generally appear to be forced by convection both on and off the equator.

It is interesting to note that in Suzuki et al. (2006), although both simulations without and with convective suppression produce convectively coupled R1 waves, the convective coupling is different in the two cases, and the R1 wave in the latter case is much stronger. Without convective suppression, off-equatorial convection associated with the R1 wave is located ahead of the low-level cyclone, the implied convergence expected by basic theory. With convective suppression the off-equatorial convection is in phase with the lower-level cyclonic center, which is coincident with a strong convergence (Suzuki et al. 2006, their Fig. 13), a feature also seen in our study. This suggests that for the lower-level R1 wave frictional convergence may play an important role in intensifying the wave and organizing the off-equatorial convection. However, in the Suzuki et al. (2006) study the convection in the equatorial region associated with the R1 wave is very weak, compared to observations. This suggests that the mechanism that connects equatorial convection with the R1 wave may not be well represented in their model either.

There are a number of difficulties in trying to analyze errors in coupled waves in climate models. In particular, the waves could be wrong because the ambient state in which they are embedded is in error due to climate drift in the model. YHS07a,b show that there is significant Doppler shifting of the wave structures by the background zonal flow, and this study also indicates the influence of ambient flow on the vertical propagation of equatorial waves. Also, there is no possibility of comparing particular events in the model with those in other models or in the real atmosphere. However, observational studies in this paper and in YHS07b have shown that convectively coupled waves often have structures that are coherent for one to two weeks and, therefore, could provide predictive power in weather forecasting on those time scales. An alternative approach is therefore to use the methodology described here to analyze the behavior in a weather forecast context. A projection method similar to that in YHS has, indeed, been used to diagnose tropical background errors in ECMWF forecasts in a study of predictability and initialization (Žagar et al. 2005). Further development of this approach may enable the error growth in the simulations to be studied in order to disentangle the errors in the dynamical–physical coupling outlined in this paper.

Acknowledgments

GYY acknowledges the support of the National Centre for Atmospheric Science (NCAS) and an earlier U.K. Met Office Grant (C79660). Both JS and and GYY are members of NCAS. The third author is supported by a Royal Society Research Professorship.

REFERENCES

REFERENCES
Andrews
,
D. G.
,
J. R.
Holton
, and
C. B.
Leovy
,
1987
:
Middle Atmosphere Dynamics.
Academic Press, 489 pp
.
Challenor
,
P. G.
,
P.
Cipollini
, and
D.
Cromwell
,
2001
:
Use of the radon transform to examine properties of oceanic Rossby waves.
J. Atmos. Oceanic Technol.
,
18
,
1558
1566
.
Davies
,
T.
,
M. J. P.
Cullen
,
A. J.
Malcolm
,
M. H.
Mawson
,
A.
Staniforth
,
A. A.
White
, and
N.
Wood
,
2005
:
A new dynamical core for the Met Office’s global and regional modelling of the atmosphere.
Quart. J. Roy. Meteor. Soc.
,
131
,
1759
1782
.
Emanuel
,
K. A.
,
1987
:
An air–sea interaction model of intraseasonal oscillation in the tropics.
J. Atmos. Sci.
,
44
,
2324
2340
.
Hayashi
,
Y.
,
1982
:
Space–time spectral analysis and its applications to atmospheric waves.
J. Meteor. Soc. Japan
,
60
,
156
171
.
Hendon
,
H. H.
, and
B.
Liebmann
,
1991
:
The structure and annual variation of antisymmetric fluctuations of tropical convection and their association with Rossby–gravity waves.
J. Atmos. Sci.
,
48
,
2127
2140
.
Hendon
,
H. H.
, and
M. L.
Salby
,
1994
:
The life circle of the Madden–Julian oscillation.
J. Atmos. Sci.
,
51
,
2225
2237
.
Hodges
,
K. I.
,
D. W.
Chappell
,
G. J.
Robison
, and
G-Y.
Yang
,
2000
:
An improved algorithm for generating global window brightness temperatures from multiple satellite infrared imagery.
J. Atmos. Oceanic Technol.
,
17
,
1296
1313
.
Hoskins
,
B. J.
, and
G-Y.
Yang
,
2000
:
The equatorial response to higher-latitude forcing.
J. Atmos. Sci.
,
57
,
1197
1213
.
Johns
,
T. C.
, and
Coauthors
,
2006
:
The new Hadley Centre Climate Model (HadGEM1): Evaluation of coupled simulations.
J. Climate
,
19
,
1327
1353
.
Kiladis
,
G. N.
,
K. H.
Straub
, and
P. T.
Haertel
,
2005
:
Zonal and vertical structure of the Madden–Julian oscillation.
J. Atmos. Sci.
,
62
,
2790
2809
.
Lin
,
J-L.
,
2007
:
The double-ITCZ problem in IPCC AR4 coupled GCMs: Ocean– atmosphere feedback analysis.
J. Climate
,
20
,
4497
4525
.
Lin
,
J-L.
, and
Coauthors
,
2006
:
Tropical variability in 14 IPCC AR4 climate models. Part I: Convective signals.
J. Climate
,
19
,
2665
2690
.
Lin
,
J-L.
,
M-I.
Lee
,
D.
Kim
,
I-S.
Kang
, and
D. M. W.
Frierson
,
2008
:
The impacts of convective parameterization and moisture triggering on AGCM-simulated convectively coupled equatorial waves.
J. Climate
,
21
,
883
909
.
Magaña
,
V.
, and
M.
Yanai
,
1995
:
Mixed Rossby–gravity waves triggered by lateral forcing.
J. Atmos. Sci.
,
52
,
1473
1486
.
Martin
,
G. M.
,
M. A.
Ringer
,
V. D.
Pope
,
A.
Jones
,
C.
Dearden
, and
T. J.
Hinton
,
2006
:
The physical properties of the atmosphere in the new Hadley Centre Global Environmental Model (HadGEM1). Part I: Model description and global climatology.
J. Climate
,
19
,
1274
1301
.
Neelin
,
J. D.
,
I. M.
Held
, and
K. H.
Cook
,
1987
:
Evaporation–wind feedback and low-frequency variability in the tropical atmosphere.
J. Atmos. Sci.
,
44
,
2341
2348
.
Ohring
,
G.
, and
A.
Gruber
,
1984
:
Satellite determination of the relationship between total longwave radiation flux and infrared window radiance.
J. Climate Appl. Meteor.
,
23
,
416
425
.
Pires
,
P.
,
J-L.
Redelsperger
, and
J-P.
Lafore
,
1997
:
Equatorial atmospheric waves and their association to convection.
Mon. Wea. Rev.
,
125
,
1167
1184
.
Pope
,
V. D.
,
M. L.
Gallani
,
P. R.
Rowntree
, and
R. A.
Stratton
,
2000
:
The impact of new physical parametrizations in the Hadley Centre climate model: HadAM3.
Climate Dyn.
,
16
,
123
146
.
Radon
,
J.
,
1917
:
Über die Bestimmung von Funktionen durch ihre Integralwerte längs Gewisser Mannigfaltigkeiten.
Math.-Phys. Kl.
,
69
,
262
267
.
Ringer
,
M. A.
, and
Coauthors
,
2006
:
The physical properties of the atmosphere in the new Hadley Centre Global Environmental Model (HadGEM1). Part II: Aspects of variability and regional climate.
J. Climate
,
19
,
1302
1326
.
Rui
,
H.
, and
B.
Wang
,
1990
:
Development characteristics and dynamic structure of tropical intraseasonal convection anomalies.
J. Atmos. Sci.
,
47
,
357
379
.
Shaffrey
,
L.
, and
Coauthors
,
2009
:
U.K. HiGEM: The new U.K. High-Resolution Global Environment Model—Model description and basic evaluation.
J. Climate
,
22
,
1861
1896
.
Straub
,
K. H.
, and
G. N.
Kiladis
,
2002
:
Observations of a convectively coupled Kelvin wave in the eastern Pacific ITCZ.
J. Atmos. Sci.
,
59
,
30
53
.
Straub
,
K. H.
, and
G. N.
Kiladis
,
2003
:
The observed structure of convectively coupled Kelvin waves: Comparison with simple models of coupled wave instability.
J. Atmos. Sci.
,
60
,
1655
1668
.
Suzuki
,
T.
,
Y. N.
Takayabu
, and
S.
Emori
,
2006
:
Coupling mechanisms between equatorial waves and cumulus convection in an AGCM.
Dyn. Atmos. Oceans
,
42
,
81
106
.
Takayabu
,
Y. N.
,
1994a
:
Large scale cloud disturbances associated with equatorial waves. Part I: Spectral features of the cloud disturbances.
J. Meteor. Soc. Japan
,
72
,
433
449
.
Takayabu
,
Y. N.
,
1994b
:
Large scale cloud disturbances associated with equatorial waves. Part II: Westward propagation of inertio–gravity waves spectral features of the cloud disturbances.
J. Meteor. Soc. Japan
,
72
,
451
465
.
Wheeler
,
M.
, and
G. N.
Kiladis
,
1999
:
Convectively coupled equatorial waves: Analysis of clouds and temperature in the wavenumber–frequency domain.
J. Atmos. Sci.
,
56
,
374
399
.
Wheeler
,
M.
,
G. N.
Kiladis
, and
P.
Webster
,
2000
:
Large-scale dynamical fields associated with convectively coupled equatorial waves.
J. Atmos. Sci.
,
57
,
613
640
.
Yang
,
G. Y.
,
B.
Hoskins
, and
J.
Slingo
,
2003
:
Convectively coupled equatorial waves: A new methodology for identifying wave structures in observational data.
J. Atmos. Sci.
,
60
,
1637
1654
.
Yang
,
G. Y.
,
B.
Hoskins
, and
J.
Slingo
,
2007a
:
Convectively coupled equatorial waves: Part I: Horizontal structure.
J. Atmos. Sci.
,
64
,
3406
3423
.
Yang
,
G. Y.
,
B.
Hoskins
, and
J.
Slingo
,
2007b
:
Convectively coupled equatorial waves: Part II: Zonal propagation.
J. Atmos. Sci.
,
64
,
3424
3437
.
Yang
,
G. Y.
,
B.
Hoskins
, and
J.
Slingo
,
2007c
:
Convectively coupled equatorial waves: Part III: Synthesis structures and extratropical forcing.
J. Atmos. Sci.
,
64
,
3438
3451
.
Žagar
,
N.
,
E.
Andersson
, and
M.
Fisher
,
2005
:
Balanced tropical data assimilation based on a study of equatorial waves in ECMWF short-range forecast errors.
Quart. J. Roy. Meteor. Soc.
,
131
,
987
1011
.
Zhang
,
C.
,
1996
:
Atmospheric intraseasonal variability at the surface in the western Pacific Ocean.
J. Atmos. Sci.
,
53
,
739
758
.
Zhang
,
C.
, and
M. J.
McPhaden
,
2000
:
Intraseasonal surface cooling in the equatorial western Pacific.
J. Climate
,
13
,
2261
2276
.

Footnotes

Corresponding author address: Gui-Ying Yang, Dept. of Meteorology, University of Reading, Earley Gate, Reading RG6 6BB, United Kingdom. Email: g.y.yang@reading.ac.uk