Convectively coupled Kelvin and easterly waves in a regional climate simulation of the tropics
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- Tulich, S.N., Kiladis, G.N. & Suzuki-Parker, A. Clim Dyn (2011) 36: 185. doi:10.1007/s00382-009-0697-2
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This study evaluates the performance of a regional climate model in simulating two types of synoptic tropical weather disturbances: convectively-coupled Kelvin and easterly waves. Interest in these two wave modes stems from their potential predictability out to several weeks in advance, as well as a strong observed linkage between easterly waves and tropical cyclogenesis. The model is a recent version of the weather research and forecast (WRF) system with 36-km horizontal grid spacing and convection parameterized using a scheme that accounts for key convective triggering and inhibition processes. The domain spans the entire tropical belt between 45°S and 45°N with periodic boundary conditions in the east–west direction, and conditions at the meridional/lower boundaries specified based on observations. The simulation covers 6 years from 2000 to 2005, which is long enough to establish a statistical depiction of the waves through space-time spectral filtering of rainfall data, together with simple lagged-linear regression. Results show that both the horizontal phase speeds and three-dimensional structures of the waves are qualitatively well captured by the model in comparison to observations. However, significant biases in wave activity are seen, with generally overactive easterly waves and underactive Kelvin waves. Evidence is presented to suggest that these biases in wave activity (which are also correlated with biases in time–mean rainfall, as well as biases in the model’s tropical cyclone climatology) stem in part from convection in the model coupling too strongly to rotational circulation anomalies. Nevertheless, the model is seen to do a reasonable job at capturing the genesis of tropical cyclones from easterly waves, with evidence for both wave accumulation and critical layer processes being importantly involved.
KeywordsConvectively coupled equatorial wavesEasterly wavesKelvin wavesRegional climate modelingTropical climateTropical cyclonesTropical cyclogenesis
The tropical atmosphere is found to support a broad spectrum of zonally-propagating wave-like disturbances in both cloudiness and circulation. Relevant examples include convectively coupled Kelvin waves with periods of 3–10 days (Takayabu and Murakami 1991; Straub and Kiladis 2002), easterly waves or tropical depression-type disturbances with periods of 4–7 days (Chang 1970; Reed et al. 1977), and the planetary-scale Madden–Julian oscillation (MJO) with a period of 30–60 days (Madden and Julian 1994). Such waves can often be tracked for many days (sometimes even traveling around the globe) and constitute an important predictable component of medium- to extended-range weather in the tropics (Wheeler and Weickmann 2001; Miura et al. 2007; Mapes et al. 2008) and extratropics, via Rossby-wave teleconnections (Ferranti et al. 1990; Hendon et al. 2000). Yet current state-of-the-art global climate models are known to poorly simulate these waves (Slingo et al. 1996; Lin et al. 2006; Ringer et al. 2006; Yang et al. 2009; Straub et al. 2009).
While a variety of factors could be involved, there is growing evidence that deficiencies in model convective parameterization schemes are primarily responsible for this poor simulation of tropical waves. A telling example is the study by Khairoutdinov et al. (2008) who replaced the standard convection scheme of the National Center for Atmospheric Research (NCAR) Community Atmosphere Model (CAM) with a series of two-dimensional (2D) cloud-resolving models (CRMs), one for each grid box in the CAM. Results showed a dramatic improvement in the CAM’s simulation of convectively-coupled Kelvin waves and the MJO, the latter of which was virtually absent from the standard CAM formulation. However, these improvements came at a considerable computational expense; the cost of running the “super-parameterized” CAM was reported to be roughly 200 times greater than running the standard CAM (Khairoutdinov et al. 2005). Moreover, such coarse-resolution models cannot directly address one of the most pressing scientific questions facing society today, namely, whether the intensity and occurrence rate of tropical cyclones (TCs) will change in a warming world.
Driven largely by this last point, scientists at NCAR recently used the weather research and forecast (WRF) model to perform a pair of multiyear simulations of the global tropics at 36-km horizontal grid spacing, with periodic boundary conditions in the zonal direction and meridional/lower boundary conditions specified based on observations. These novel “channel” simulations were made as first step towards a broader ongoing effort at NCAR of developing a global, coupled ocean–atmosphere model with local mesh refinement capabilities, so that studies of regional/global climate can be performed using a single framework. The WRF tropical channel model can thus be thought of as type of nested regional climate model (NRCM), whereby observational nudging at the boundaries serves as one-way driving of the NRCM by a “perfect” model of the rest of the atmosphere (and oceans).
Meanwhile other modeling centers have started to perform short-term [O(10-year)] global climate simulations with horizontal grid spacings comparable to the WRF channel model (e.g., Chauvin et al. 2006; Oouchi et al. 2006; Bengtsson et al. 2007; Lau and Ploshay 2009). A distinct advantage of all of these high-resolution models is their ability to at least partially resolve key mesoscale circulations and heating processes associated with organized convective cloud systems (cf. Mapes 2000; Tulich et al. 2007; Tulich and Mapes 2008). On the other hand, the horizontal grid spacing of these models is still too coarse to resolve convective-scale circulations and heating processes, so some type of parameterization is needed. The WRF tropical channel model is unique in this regard in that its convective parameterization, based on the schemes of Kain (2004) and Kain and Fritsch (1993), is specifically designed for models with mesoscale [O(10-km)] grid spacing, and thus accounts for key convective inhibition and triggering processes (cf. Tulich and Mapes 2009; Kuang 2009).
This study examines the ability of the WRF tropical channel model to simulate two types of convectively-coupled synoptic wave disturbances: Kelvin and easterly waves. Interest in these two wave modes stems from their central role in determining the day-to-day weather of the tropics, as well as a strong observed linkage between easterly waves and TC genesis (e.g., Landsea 1993; Chen et al. 2008). The ability of the model to capture the lower-frequency MJO, while also of interest, is considered only briefly here—more detailed assessments can be found in Caron (2009) and Ray et al. (2009).
The organization of this paper is as follows. The next section briefly describes the experiment setup and observational data used for model evaluation. Section 3 then gives an overview of the simulated versus observed space-time variability of rainfall, followed by detailed evaluations of the simulated Kelvin and easterly waves in Sects. 4 and 5, respectively. Section 5 also evaluates the statistical relationship between easterly waves and TC genesis. This study’s main findings are summarized and discussed in Sect. 6.
2 Experiment and observational data
2.1 Experiment description
The WRF channel model was used to perform a pair of multiyear simulations of the global tropics, each with lower oceanic boundary conditions specified using observed monthly sea-surface temperatures (SSTs; linearly interpolated to 6-h increments) and with meridional boundary conditions specified using six-hourly model reanalysis data (see Holland et al. 2009 for further details). The two runs together span the 10-year period, 1996–2005, but each has slightly different domain/grid configurations. In particular, the first run (covering the 5-year period, 1996–2000) has meridional boundaries at 30°S and 45°N, with 35 vertical levels, ranging from the surface to pressure p = 50 hPa. Meanwhile, the second run (covering the 6-year period, 2000–2005) has meridional boundaries at 45°S and 45°N, with 51 vertical levels, ranging from the surface to p = 10 hPa. Most of the results of this study were found to be independent of these changes in model configuration, however, we restrict our attention to the second run, for brevity.
Post-processing of the model output consisted of vertically interpolating six-hourly winds, temperature, etc. from the native sigma-coordinate system of the model to a set of 38 pressure levels, with finer resolution near the top and bottom boundaries. To further expedite the analysis (and reduce storage requirements), these interpolated data were coarse-grained from 36- to 108-km grid spacing in the horizontal (roughly 1° in the tropics).
2.2 Observational datasets
TRMM 3B42 The TRMM 3B42 product consists of three-hourly satellite-based estimates of rainfall on a uniform 0.25° × 0.25° latitude–longitude grid. The data are obtained by merging passive microwave estimates of rainfall together with geostationary infrared radiance (IR) data, as well as surface rain gauge observations (see Huffman et al. 2007 for further details). The data are currently available from the present back to 1 January 1998, but here the focus is mainly on the 2000–2005 period of the second WRF channel run. To ensure “apples-to-apples” comparisons between the WRF output and observations, the TRMM data were coarse-grained from three- to six-hourly in time and from 0.25° to 1° in space.
JRA-25 The JRA consists of six-hourly global atmospheric fields obtained using the Japanese Meteorological Association (JMA) numerical assimilation and forecast system. All fields are defined on a 1.25° × 1.25° latitude-longitude grid, which is comparable to the coarse-grained WRF output examined here. Onogi et al. (2007) provide evidence that the JRA is superior to other reanalyses in terms of capturing observed tropical rainfall variability, which is one of the reasons it was chosen for this study.
UWYO sounding archive Routine soundings for numerous stations around the globe are available from the UWYO sounding archive, including two tropical island stations examined here: Majuro (171°E, 7°N) and Yap (138°E, 9.5°N). Twice-daily soundings for these two stations were analysed for the period 1999–2007. Prior to analysis, each sounding was interpolated to a set of 24 pressure levels between the surface and p = 25 hPa.
3 Space-time variability of rainfall
Observations show a strong linkage between the time–mean distribution of convective heating (using rainfall here as a proxy) and the overall level (and type) of transient convective wave activity. For example, easterly waves are typically most active during boreal summer when convection is generally located well north of the equator (Serra et al. 2008; Magnusdottir and Wang 2008). Meanwhile, Kelvin waves are typically most active during boreal spring when convection is generally closest to the equator (Roundy and Frank 2004). This section begins with an assessment of the time–mean distribution of rainfall simulated by the WRF channel model, followed by an evaluation of the simulated space-time spectral characteristics of rainfall. These evaluations set the stage for a detailed assessment of the simulated climatology and structures of tropical waves in Sects. 4 and 5.
3.1 Time–mean spatial pattern
Interestingly, a very similar type of bias pattern has been found in the superparameterized CAM (SP-CAM) mentioned previously (Khairoutdinov et al. 2008), as well as the superparameterized version of the NASA Goddard finite-volume general circulation model (fvGCM; Tao et al. 2009). Meanwhile, a positive off-equatorial rain bias has been seen in a number of recent high-resolution (but still not convection-resolving) simulations of the Asian summer monsoon (Cherchi and Navarra 2007; Lau and Ploshay 2009; Nguyen and McGregor 2009; Ratnam et al. 2009). Given that this type of bias does not appear as prominently in the conventional versions of the CAM and NASA fvGCM (Khairoutdinov et al. 2008; Tao et al. 2009), it would seem that the coupling between parameterized convection and the resolved circulation is somehow involved. Along these lines, Khairoutdinov et al. (2005) showed that the SP-CAM’s excessive rainfall in the northwest Pacific could be mitigated by altering the domain configuration of the model’s cloud-resolving convective parameterization. Alternatively, Ratnam et al. (2009) showed that the positive rainfall bias in their simulations of the Asian summer monsoon could be mitigated by allowing two-way coupling between the ocean and atmosphere. However, this improvement came at the expense of producing a compensating negative bias in the underlying SST (with amplitude of ∼1°C). Thus the bias in precipitation was simply shifted to a different component of the coupled model system. Similar findings were obtained in the recent coupled-model studies of Cherchi and Navarra (2007) and Lau Ploshay (2009).
3.2 Fourier spectral analysis
The methodology of Wheeler et al. (2000) is used to isolate Kelvin and easterly waves in the model and observations (see also Straub and Kiladis 2002; Kiladis et al. 2006). Briefly, spectral filters are constructed based on space-time spectra of some form of proxy data for convective activity; the filters are tailored to capture the wavenumbers and frequencies of the wave modes of interest. Upon applying the filter and then transforming back to physical space, one obtains a filtered time series at each grid point. This method is appealing both for its simplicity and ease of implementation, but suffers from at least one drawback. Namely, the filtered time series includes a background “noise” component, as well as a component due to the waves. This noise component makes it difficult to quantitatively assess the spatial patterns of wave activity in the model (using the filtered variance as a proxy), since the simulated levels of background noise may be different than observed. However, qualitative evaluations are still possible.
While the simulated and observed spectra in Fig. 3 appear broadly similar, there are at least two notable differences. First, the Kelvin wave signals in Fig. 3a are not as prominent as in Fig. 3b, suggesting that the simulated Kelvin waves are generally less active than observed. Secondly, the most prominent spectral speak in Fig. 3b, appearing at wavenumbers k = 1–4 and periods in the range 40–50 days, is absent from Fig. 3a, suggesting that the model is not producing an MJO, at least in terms of rainfall. Given that the model spectrum in Fig. 3a looks otherwise realistic, this failure of the model indicates that the dynamics of the MJO involves more than just coupling between convection and planetary-scale Kelvin waves (see also Lin et al. 2006).
3.3 Definition of spectral filters
4 Kelvin wave assessment
Results in the previous section showed that Kelvin and easterly waves are both present in the WRF channel model, although their overall levels of activity are different than observed. In this section, we examine more closely the simulated Kelvin waves, including their spatial climatology, structures, and evolution. A similar evaluation of the simulated easterly waves is given thereafter in Sect. 5.
4.1 Spatial climatology
In addition to north–south biases in variance, east–west biases can also be seen. Figure 7a indicates that Kelvin waves in the model are confined mainly to the Indo-Pacific region, whereas Fig. 7b suggests Kelvin waves in nature can be found throughout the tropics, including over South America and Africa (see also the observations by Liebmann et al. 2009 and Mekonnen et al. 2008). Presumably, the dearth of Kelvin wave activity over South America and Africa stems from the same mechanistic process responsible for corresponding deficits in time–mean rainfall and convection (e.g., compensating subsidence and convective stabilization due to enhanced time–mean rainfall elsewhere; cf. Fig. 1c).
4.2 Composite evolution of rainfall
The method of lagged-linear regression is used to characterize the typical structures and evolution of Kelvin waves in the model and observations (e.g., Straub and Kiladis 2003). Briefly, time series of raw data are regressed onto a time series of filtered data (in this case, Kelvin-wave-filtered rainfall) at a selected base point. For convenience, the filtered time series is normalized to have a standard deviation of unity, so that regression coefficients have the same units as the raw data and convey the typical amplitude of wave anomalies. The base point for the model analysis is chosen as the location where the simulated Kelvin wave activity is largest (165°E, 4.5°N; see Fig. 7a). Meanwhile, the base point for the observational analysis is chosen as the tropical island of Majuro (171°E, 7.5°N), where twice-daily soundings are recorded and observed Kelvin waves are relatively active (see Fig. 7b).
4.3 Vertical dynamical structures
Another deficiency of the model is the generally larger amplitude of low-level temperature versus moisture anomalies. For example, the ratio of 850-hPa moisture to temperature anomalies at lag 0 is roughly three times larger in the model than observed. While this deficiency could stem from parameterized convection in the model being overly sensitive to temperature as compared to moisture, it could also simply reflect errors in the parameterized convective heating and drying rates, so interpretation is not clear. Either way, the qualitative similarities between the simulated and observed vertical wave structures suggests that the model is capturing the basic dynamics of the phenomenon.
4.4 Horizontal dynamical structures
The overall success of the model in capturing the observed structures and phase speeds of convectively coupled Kelvin waves stands in contrast to many contemporary low-resolution global climate models. For example, Straub et al. (2009) recently found that only 5 out of 20 IPCC-AR4 models produce moist Kelvin waves resembling observations.
5 Easterly wave assessment
The previous section showed that the structures and phase speeds of convectively coupled Kelvin waves are reasonably well captured by the WRF channel model, although their spatial climatology is not. In this section, we describe a similar evaluation of the model’s easterly waves, and also assess the statistical relationship between the simulated waves and TC genesis.
5.1 Spatial climatology
5.2 Composite evolution of rainfall
5.3 Vertical dynamical structures
5.4 Horizontal dynamical structures
5.5 Easterly waves and TC genesis
This behavior is consistent with the “marsupial” paradigm of TC genesis from easterly waves, recently proposed by Dunkerton et al. (2009). As its name suggests, the marsupial paradigm envisions the closed gyre circulation of an easterly wave critical layer as being especially favorable for TC genesis, by protecting the incipient storm from the detrimental effects of horizontal mixing and straining, analogous to a joey inside a mother kangaroo’s pouch. This protection is thought to provide a window for the buildup of vorticity on the TC-scale (mainly through diabatic processes), until the storm has reached sufficient amplitude to survive on its own. However, the marsupial paradigm is basically silent as to the precise timing of TC genesis.
6 Summary and discussion
This study examined the performance of the WRF tropical channel model in simulating two types of synoptic tropical weather disturbances: convectively-coupled Kelvin and easterly waves. Generally good agreement was found between the simulated and observed wave structures and their evolution, suggesting that the model is able to capture the basic dynamics of the phenomena. However, the climatologies of both wave types were found to be deficient, with easterly waves being much too active over the Pacific (but relatively inactive elsewhere) and Kelvin waves being relatively inactive throughout the tropics, especially over South America, Africa, and the Atlantic. Errors in the model’s easterly wave climatology were seen to directly impact the simulated frequency of TC genesis, with too many storms developing from easterly waves over the north Pacific, and too few over the north Atlantic. Still the kinematics of the wave-to-TC-genesis process appear to be well simulated, with evidence for both wave accumulation and critical layer processes being importantly involved.
Many of this study’s findings are similar to those of Yang et al. (2009), who examined convective variability in two Hadley Centre climate models (HadAM3 and HiGAM) with very different dynamical cores, but similar horizontal grid spacings (∼100 km). In particular, their analysis showed that tropical convection in both models tends to preferentially couple to westward-propagating Rossby-type wave disturbances, as opposed to eastward-propagating Kelvin modes, which apparently results in synoptic-scale convection variability being heavily biased towards off-equatorial latitudes, especially over the tropical warm pool region.
In conclusion, a similar pattern of tropical biases (in both a time–mean and/or time-varying sense) can be found across a broad range of contemporary high-resolution climate models, as well as the superparameterized versions of the low-resolution CAM and the NASA fvGCM. This similarity is reminiscent of the double-ITCZ problem found in many low-resolution, coupled-ocean-atmosphere models (e.g., Kim et al. 2008). However, while the double-ITCZ problem appears mainly over the central and eastern Pacific, where meridional gradients in SST are relatively large, here the biases are most prominent over the western Pacific and Indian Ocean basins, where meridional gradients in SST are relatively weak. We anticipate that further diagnosis of these tropical biases will shed light on the model modifications needed to improve the representation of convection variability in next-generation climate models.
Dr. Tulich was supported by a visiting post-doctoral appointment at the National Center for Atmospheric Research. Mrs. Suzuki-Parker acknowledges the support of the World Bank, Chevron, and the Research Partnership to Secure Energy for America (RPSEA). The reanalysis data were provided from the cooperative research project of the JRA-25 long-term reanalysis by the Japan Meteorological Agency (JMA) and the Central Research Institute of Electric Power Industry (CRIEPI). Archived output from the SP-CAM was provided graciously by Prof. Marat Khairoutdinov. This manuscript was improved through comments by Prof. Brian Mapes and one anonymous viewer.